1. science
2. mathematics
3. geometry

Q UEENSLAND U NIVERSITY OF
T ECHNOLOGY
Promoted Ignition Testing: An
Investigation of Sample Geometry and
Data Analysis Techniques
By
Miss Terese Suvorovs
B.E. Hons. I
A THESIS SUBMITTED FOR THE DEGREE OF
D OCTOR OF P HILOSOPHY
School of Engineering Systems
Queensland University of Technology
2007
© Copyright 2007
by
Miss Terese Suvorovs
i
Keywords
Promoted ignition, sample geometry, metallic material, oxygen, iron, burning, combustion, flammability, statistics, logistic regression, confidence interval, microanalysis.
ii
Abstract
Metallic materials and oxygen can be a volatile combination when accompanied by
ignition mechanisms. Once ignited, metallic materials can readily burn in high pressure oxygen atmospheres, releasing an enormous amount of energy and potentially
destroying equipment, space missions and resulting in the loss of life. The potential
losses associated with these fires led to research into the conditions under which metal
fires propagate. Several organisations, including the American Society for Testing
and Materials (ASTM) and the International Organisation for Standardisation (ISO),
have published recommended standard test practices with which to assess the relative
flammability of metallic materials. These promoted ignition tests, so called because
samples are ignited with an overwhelming source of energy, are typically used to examine two important parameters as an indication of a metallic material’s flammability:
Threshold Pressure (TP) and the Regression Rate of the Melting Interface (RRMI). A
material’s TP is the minimum pressure at which it burns, therefore, TPs of different
materials can be compared to assess which materials are most suited for a range of
high pressure applications. The RRMI is a useful measure for ranking materials, particularly if they have the same TP, but can be used as a ranking method irrespective of
TP. In addition, it is a crucial parameter to aid in understanding the complex burning
process and is one of the few experimental parameters that can be measured.
Promoted ignition test standards specify a standard sample geometry to use when
performing the test, typically a 3.2 mm diameter cylindrical rod. The recent addition of a 3.2 × 3.2 mm square rod as an optional standard sample geometry raises
the issue of how the geometry of a sample affects its flammability. Promoted ignition test results for standard geometries are often applied to assess the flammability
risk for the complex geometries of real components within oxygen systems, including
regulators, valves, piping etc. Literature shows that sample geometry has a significant
effect on material rankings when rankings are based on testing of standard geometries,
for example, cylindrical rods, compared to non-standard geometries, for example, sintered filters and meshes. In addition, the RRMI has been shown to be dependent on a
iii
sample’s cross-sectional area (XA). However, it remains unclear, from a simple heat
transfer analysis, why the RRMI is dependent on XA or how the shape of a sample
affects its melting rate. These questions are particularly relevant since understanding
how sample geometry affects burning contributes to two important research goals: to
be able to accurately model and predict the flammability risk of a metallic component
without the need for physical testing, and to understand the effects of different sample
geometries on their relative flammabilities within the standard tests used.
Promoted ignition tests were conducted on iron rods with cylindrical, rectangular
and triangular cross sections for a range of XAs. Their RRMIs were measured and
analysed using a statistical approach which allowed differences in RRMI to be quantitatively assessed. Statistically significant differences in RRMI were measured for rods
with the same XA but of different shape. Furthermore, the magnitude of the difference
was dependent on XA. Triangular rods had the fastest RRMIs, followed by rectangular
rods and then cylindrical rods. Differences in RRMI based on rod shape are due to heat
transfer effects and the dynamic motion of the attached molten mass during the drop
cycle. The corners of the rectangular and triangular rods melt faster due to their locally
higher Surface Area to Volume ratio (SA/V). This dynamic effect increases the area of
contact between the molten mass and the solid rod (solid liquid interface (SLI)) which
facilitates increased heat transfer to the rod resulting in a faster RRMI. This finding
highlights the importance of the SLI in the heat transfer process. Although the SLI is
largely dependent on the XA, the shape of the rod causes subtle changes to the size of
the SLI and thus affects heat transfer, burning and observed RRMI.
The relationship between rod diameter, test pressure and Extent of Reaction (ER),
the proportion of metal that reacts (oxidises) whilst attached to the burning rod, was
investigated. During promoted ignition testing of iron rods of varying diameter the
detached drops were rapidly quenched by immersion in a water bath. Microanalysis techniques were used to qualitatively assess the ER as a function of pressure and
rod diameter. It was found that the pressure dramatically affects ER. High pressure
tests resulted in a slag mass consisting of oxide, with no unreacted iron, whereas low
pressure tests resulted in a significant fraction of unreacted iron within the slag. This
indicates that the ER contributes directly to the observed increase in RRMI with increasing test pressure. At high pressures the ER is not affected by rod diameter, since
all available liquid metal reacted, but at low pressures ER is a function of rod diameter,
ER decreases as XA increases.
This thesis also investigates the analysis of promoted ignition test data through
iv
suitable statistical methods. Logistic regression is identified as an appropriate method
for modelling binary burn/no-burn test data. The relationship between the reaction
probability, defined as the probability that a sample will undergo sustained burning,
and pressure, is evaluated for two different data sets. The fits of the logistic regression
models are assessed and found to model the available data well. The logistic regression method is contrasted with the confidence levels associated with binary data based
on the Bernoulli distribution. It is concluded that a modelling approach is beneficial
in providing an overall understanding of the transition between pressures where no
burning occurs and pressures where burning is expected.
v
List of Publications
The following is a list of publications to which I contributed throughout my PhD.
Suvorovs, T., Ward, N., Wilson, R., Steinberg, T., “Effect of Sample Geometry on
Regression Rate of the Melting Interface for Carbon Steel Burned in Oxygen,” Journal
of ASTM International, 3(4), April 2006.
Ward, N., Suvorovs, T., Steinberg, T., “An Investigation of Regression Rate of the
Melting Interface for Iron Burning in Normal-Gravity and Reduced-Gravity”, Journal
of ASTM International, 3(4), April 2006.
Suvorovs, T. DeWit, J., Osborne, B., Steinberg, T., “Investigations of Burning Aluminum in Oxygen-Enriched Atmospheres through Microanalysis Techniques,” Journal
of ASTM International, 1(8), August 2004.
Suvorovs, T., DeWit, J., Osborne, B., Steinberg, T., “Investigations of Burning
Iron in Oxygen-Enriched Atmospheres through Microanalysis Techniques,” Journal
of ASTM International, 1(5), May 2004.
B.P. Osborne, T. Suvorovs, J. De Wit and T. A. Steinberg, “Microanalysis of
Quenched and Self-extinguished Aluminium Rods Burned in Oxygen,” Flammability and Sensitivity of Materials in Oxygen-Enriched Atmospheres: Tenth Volume, STP
1454, ASTM International, 2003.
Osborne, B. P., Pienaar, C. L., Nash, C. E., Suvorovs T., Edwards, A. and Steinberg T. A., “Reduced gravity testing and research at The University of Queensland”,
Australian International Aerospace Congress, Brisbane 2003.
vi
Acknowledgements
First and foremost I would like to thank my supervisor, Dr. Ted Steinberg for his
guidance and friendship throughout this process. Thanks also go to Dr. Richard Wilson
for his invaluable statistical contributions and to Dr. Thor Bostrom for assisting, often
at the drop of a hat, with the microanalysis work.
This work would not have been possible without funding from the Australian Government and the Queensland University of Technology. I am also grateful for the
support from staff at The University of Queensland Mechanical and Electrical Engineering Workshops. Thanks also to Mr Loc Duong in The Queensland University of
Technology Analytical Electron Microscopy Facility, and to Mr David Allen in The
Queensland University of Technology Engineering Materials Laboratory, for their assistance and advice.
Many thanks to Nick Ward and Barnaby Osborne for making the day-to-day life of
a PhD student that much more exciting, for all the laughs, lunches and encouragement.
Final thanks go to my family and friends. To Mum, Dad and my brother for
their love and support and to ‘The Boys’ for providing a welcome distraction. And
to Michael, for his love, support and advice, and for keeping me grounded.
vii
The work contained in this thesis has not been previously submitted to meet requirements for an award at this or any other higher
education instutution. To the best of my knowledge and belief,
the thesis contains no materials previoulsy published or written
by another person except where due reference is made.
Signature
Date
Miss Terese Suvorovs
viii
Contents
1
2
Introduction
1
1.1
Metals Flammability . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.2
Promoted Ignition Testing . . . . . . . . . . . . . . . . . . . . . . .
4
1.2.1
Promoted Ignition Test Method . . . . . . . . . . . . . . . .
5
1.2.2
Promoted Ignition Test Standards . . . . . . . . . . . . . . .
6
1.2.3
Issues Arising from the Standard Promoted Ignition Test . . .
8
1.3
Objectives and Approach . . . . . . . . . . . . . . . . . . . . . . . .
9
1.4
Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
Literature Review
12
2.1
Physics and Chemistry of Burning Metals . . . . . . . . . . . . . . .
12
2.1.1
A General Burning Model . . . . . . . . . . . . . . . . . . .
13
2.1.2
Rate-Limiting Mechanisms . . . . . . . . . . . . . . . . . . .
18
2.1.3
Excess Oxygen . . . . . . . . . . . . . . . . . . . . . . . . .
20
2.1.4
Formation and Detachment Dynamics for Pendant Drops . . .
22
Geometry and Flammability . . . . . . . . . . . . . . . . . . . . . .
25
2.2.1
Geometry and Threshold Pressure . . . . . . . . . . . . . . .
26
2.2.2
Geometry and Regression Rate of the Melting Interface . . . .
33
2.2.3
Geometry and Material Rankings . . . . . . . . . . . . . . .
38
Microanalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
42
2.3.1
General Techniques . . . . . . . . . . . . . . . . . . . . . . .
42
2.3.2
Microanalysis of Iron/Mild Steel . . . . . . . . . . . . . . . .
43
2.4
Statistical Methods in Materials Testing . . . . . . . . . . . . . . . .
46
2.5
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
51
2.2
2.3
ix
3
Statistical Theory
52
3.1
A Statistical Approach to Calculating RRMI . . . . . . . . . . . . . .
52
3.1.1
One-Sample Approach . . . . . . . . . . . . . . . . . . . . .
53
3.1.2
Multi-Sample Approach . . . . . . . . . . . . . . . . . . . .
54
3.1.3
Confidence Intervals . . . . . . . . . . . . . . . . . . . . . .
55
Statistical Modelling . . . . . . . . . . . . . . . . . . . . . . . . . .
58
3.2.1
Linear Regression . . . . . . . . . . . . . . . . . . . . . . .
58
3.2.2
Logistic Regression . . . . . . . . . . . . . . . . . . . . . . .
60
Binomial Distribution Confidence Intervals . . . . . . . . . . . . . .
63
3.2
3.3
4
5
Materials and Methods
65
4.1
Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
65
4.2
Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
67
4.3
Test Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
67
4.4
Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
68
4.4.1
Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
68
4.4.2
Analysis
70
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
Experimental Results and Analysis
73
5.1
General Observations . . . . . . . . . . . . . . . . . . . . . . . . . .
73
5.1.1
Burning Rod . . . . . . . . . . . . . . . . . . . . . . . . . .
73
5.1.2
Solid Liquid Interface . . . . . . . . . . . . . . . . . . . . .
74
5.1.3
Slag . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
79
5.1.4
Chamber Pressure and Temperature . . . . . . . . . . . . . .
79
RRMI Results and Analysis . . . . . . . . . . . . . . . . . . . . . . .
81
5.2.1
RRMI Data Tables . . . . . . . . . . . . . . . . . . . . . . .
81
5.2.2
Drop Cycle RRMI Analysis . . . . . . . . . . . . . . . . . .
87
5.2.3
Instantaneous RRMI . . . . . . . . . . . . . . . . . . . . . .
92
5.2.4
RRMI, VFR and Cross-Sectional Area . . . . . . . . . . . . .
97
5.2.5
RRMI and Rod Shape . . . . . . . . . . . . . . . . . . . . . 102
5.2.6
Drop Cycle Times . . . . . . . . . . . . . . . . . . . . . . . 104
5.2
5.3
Extent of Reaction: Microanalysis . . . . . . . . . . . . . . . . . . . 106
5.3.1
General Observations . . . . . . . . . . . . . . . . . . . . . . 106
5.3.2
Photographic Record and Microanalysis Results . . . . . . . 106
x
6
Discussion
6.1
7
RRMI and Sample Geometry . . . . . . . . . . . . . . . . . . . . . . 117
6.1.1
Visual Observations . . . . . . . . . . . . . . . . . . . . . . 117
6.1.2
Drop Cycle RRMI Analysis . . . . . . . . . . . . . . . . . . 119
6.1.3
Instantaneous RRMI . . . . . . . . . . . . . . . . . . . . . . 121
6.1.4
RRMI, VFR and Cross-Sectional Area . . . . . . . . . . . . . 122
6.1.5
RRMI and Rod Shape . . . . . . . . . . . . . . . . . . . . . 124
6.1.6
Drop Cycle Times . . . . . . . . . . . . . . . . . . . . . . . 126
6.2
Extent of Reaction: Microanalysis . . . . . . . . . . . . . . . . . . . 127
6.3
The Burning Rod System . . . . . . . . . . . . . . . . . . . . . . . . 129
Statistical Considerations in the Analysis of Promoted Ignition Test Data 132
7.1
7.2
8
117
Statistical Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
7.1.1
Standard Test Methodology . . . . . . . . . . . . . . . . . . 133
7.1.2
Confidence Intervals and the Standard Test . . . . . . . . . . 135
Logistic Regression Modelling . . . . . . . . . . . . . . . . . . . . . 138
7.2.1
Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
7.2.2
Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
7.3
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
7.4
Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . 150
Summary
153
8.1
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
8.2
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
8.3
Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
References
177
A Electrical Systems
179
A.1 Test Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
A.2 Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
A.3 Electrical Schematic Diagram . . . . . . . . . . . . . . . . . . . . . 182
B Pressure Gauge Calibration
183
C Pneumatic Systems
184
C.1 Test Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
xi
C.2 Pneumatic Schematic Diagram . . . . . . . . . . . . . . . . . . . . . 185
D Promoted Ignition Test Data used for Logistic Regression Analysis
xii
186
List of Tables
2.1
2.2
2.3
2.4
Threshold pressures for cylindrical ion/steel rods. . . . . . . . .
Threshold pressure and RRMI of wire mesh. . . . . . . . . . . .
Test data for cylindrical iron and steel samples burned in oxygen.
Oxygen compatibility ranking for various engineering alloys. . .
.
.
.
.
27
32
34
39
4.1
4.2
Test Matrix - Sample Geometry vs RRMI. . . . . . . . . . . . . . . .
Test Matrix - Rod Diameter vs Extent of Reaction. . . . . . . . . . .
69
70
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
RRMI results for cylindrical rods. . . . . . . . . . .
RRMI results for rectangular rods. . . . . . . . . . .
RRMI results for triangular rods. . . . . . . . . . . .
RRMI summary table. . . . . . . . . . . . . . . . .
S-PLUS ANOVA results - RRMI rod comparison. . .
RRMI confidence interval analysis results. . . . . . .
S-PLUS ANOVA results - RRMI shape comparison.
Drop time summary table. . . . . . . . . . . . . . .
Microanalysis summary table. . . . . . . . . . . . .
7.1
7.2
7.3
Confidence levels for promoted ignition tests. . . . . . . . . . . . . . 137
R-Program logistic model data for Hastelloy® C-276. . . . . . . . . . 140
R-Program logistic model data for Hastelloy® G-3. . . . . . . . . . . 141
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82
83
84
85
94
103
104
105
116
B.1 Calibration Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
D.1 Hastelloy® G-3 Data. . . . . . . . . . . . . . . . . . . . . . . . . . . 187
D.2 Hastelloy® C-276 Data. . . . . . . . . . . . . . . . . . . . . . . . . 188
xiii
List of Figures
1.1
1.2
1.3
Extended fire triangle. . . . . . . . . . . . . . . . . . . . . . . . . . .
Sketch of a typical drop-growth-and-detachment cycle. . . . . . . . .
Typical drop-growth-and-detachment cycle for an iron rod. . . . . . .
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
2.11
2.12
2.13
Physical model of a burning mild steel cylindrical rod. . . . . . . . .
Molten mass temperature profile for a burning iron rod. . . . . . . . .
RRMI along opposite sides of a burning 2 mm diameter mild steel rod.
Promoted ignition data for 316/316L SS for various geometries. . . .
Threshold pressure for Aluminium alloy 6061 rods and strips. . . . .
Comparative RRMIs for mild steel and iron. . . . . . . . . . . . . . .
RRMIs for 3.2 mm and 6.4 mm ∅ cylindrical rods. . . . . . . . . . .
Quenched detached drops for 3.2 mm iron rods burned at 0.69 MPa. .
Post-test nub of quenched and sectioned iron rod burned at 0.69 MPa.
Quenched aluminium rod viewed with an optical microscope (0.69 MPa).
Schematic of Promoted Ignition Combustion Transition Curve. . . . .
Promoted Ignition Combustion Transition Curve for Hastelloy® . . .
Cumulative distribution and sample frequency curves. . . . . . . . . .
14
16
24
28
31
37
41
44
45
46
48
48
49
3.1
3.2
Confidence limits from the T-distribution with N degrees of freedom. .
Typical S-shaped curve of the logistic response function. . . . . . . .
57
62
4.1
4.2
Promoted ignition testing apparatus. . . . . . . . . . . . . . . . . . .
Sample ID code - example. . . . . . . . . . . . . . . . . . . . . . . .
66
68
5.1
Video images of a typical drop cycle for a 2 mm diameter cylindrical
rod. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Video images of a typical drop cycle for a 4 mm diameter cylindrical
rod. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Video images of a typical drop cycle for a 6 mm diameter cylindrical
rod. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2
5.3
xiv
2
5
6
75
76
77
5.4
Images of burning cylindrical rods (C6) showing a planar SLI. . . . .
78
5.5
Images of burning triangular rods (T6) showing the convex SLI. . . .
78
5.6
Images of burning rectangular rods (R6) showing the convex SLI. . .
78
5.7
Sample C62 slag. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
79
5.8
Images of a burning cylindrical rod showing ejecta from the slag pool.
80
5.9
Images of a burning rectangular rod showing ejecta from the slag pool.
80
5.10 Images of a burning triangular rod showing ejecta from the slag pool.
80
5.11 Typical test pressure trace. . . . . . . . . . . . . . . . . . . . . . . .
81
5.12 RRMI vs XA for the geometries tested. . . . . . . . . . . . . . . . .
86
5.13 Time series plot for X2, X4 and X6 rods. . . . . . . . . . . . . . . . .
88
5.13 Time series plot for X2, X4 and X6 rods. . . . . . . . . . . . . . . . .
89
5.14 Current vs previous drop cycle RRMI data. . . . . . . . . . . . . . .
89
5.15 Current vs previous drop cycle RRMI data for rod ID’s R4, C6 and T6.
90
5.16 Rod series scatterplots. . . . . . . . . . . . . . . . . . . . . . . . . .
93
5.17 SLI position versus time for C2 rods. . . . . . . . . . . . . . . . . . .
95
5.18 SLI position versus time for individual drop cycles of C2 rods. . . . .
95
5.19 SLI position versus time for C6 rods. . . . . . . . . . . . . . . . . . .
96
5.20 SLI position versus time for individual drop cycles of C6 rods. . . . .
96
5.21 RRMI drop cycle data versus XA. . . . . . . . . . . . . . . . . . . .
99
5.22 VFR drop cycle data versus XA. . . . . . . . . . . . . . . . . . . . . 100
5.23 Drop cycle data versus XA for X2 to X7 geometries. . . . . . . . . . 101
5.24 Relative differences in RRMI and VFR with respect to the cylindrical
rods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.25 Tukey method 95% confidence intervals for RRMI. . . . . . . . . . . 105
5.26 Post-test quenched slag masses. . . . . . . . . . . . . . . . . . . . . 107
5.27 Polished cross sections of the high pressure slag mounted in resin. . . 108
5.28 Optical and SEM images for Q0.25H . . . . . . . . . . . . . . . . . . 110
5.29 Optical and SEM images for Q0.5H . . . . . . . . . . . . . . . . . . . 111
5.30 Optical images for sample Q1H . . . . . . . . . . . . . . . . . . . . . 111
5.31 Optical images for sample Q4H . . . . . . . . . . . . . . . . . . . . . 112
5.32 Optical images for sample Q6H . . . . . . . . . . . . . . . . . . . . . 113
5.33 Polished cross sections of the low pressure slag mounted in resin. . . . 114
5.34 Optical and SEM images for sample Q6-AL . . . . . . . . . . . . . . . 114
5.35 Optical and SEM images for sample Q0.5L . . . . . . . . . . . . . . . 115
xv
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
Reaction probability versus number of trials for varying confidence
levels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
Reaction probability versus confidence level for varying numbers of
trials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
Logistic regression model and data for Hastelloy® C-276. . . . . . . 140
Logistic regression model and data for Hastelloy® G-3. . . . . . . . . 141
Logistic regression schematic diagram. . . . . . . . . . . . . . . . . . 142
Hastelloy® C-276 logistic regression models for three burn criteria. . 145
Hastelloy® G-3 logistic regression models for three burn criteria. . . . 145
Hastelloy® C-276 logistic regression model and confidence interval plot.146
Hastelloy®G3 logistic regression model and confidence interval plot. 147
A.1 Electrical Schematic Diagram. . . . . . . . . . . . . . . . . . . . . . 182
B.1 Pressure Transducer Calibration Curve. . . . . . . . . . . . . . . . . 183
C.1 Pneumatic Schematic Diagram. . . . . . . . . . . . . . . . . . . . . . 185
xvi
Abbreviations and Nomenclature
α
β0
β1
δ
γ
λ
µ
ρ
σ
ASLI
cp
df
Fγ
g
k
m
p
pupper
pw
rw
s
t
tα/2,df
ts
T0
TM
Significance level
Regression coefficients - intercept
Regression coefficients - slope
Measurement error
Random error
Surface tension
Latent heat of fusion, J kg−1
Population mean
Density kg m−3
Population standard deviation
Area of the Solid Liquid Interface
Specific heat capacity, J kg−1 K−1
Degrees of freedom
Surface tension line force, N
Acceleration due to gravity, 9.81 mm s−2
Conduction heat transfer coefficient, W m−1 K−1
Mass
Probability of success/burn, reaction probability
Upper limit of reaction probability
Wetted perimeter
Wetted radius
Vertical scale
Time, s
Value from the t-distribution for the 100(1-α) quantile and df
Test statistic
Ambient Temperature, K
Melting Temperature, K
xvii
TR
x
y
¯
X
zi
ˆ
ANOVA
AVI
BSE
C
EDS
EPMA
ER
fps
GLM
N
ND
OI
PICT
RRMI
S
SA/V
SEM
Sp
SS
SS
SE
SLI
TP
VFR
WDS
XA
XRD
Z
Reaction Temperature, K
Distance
Length
Sample mean
Value from the standard normal distribution
Estimate of parameter
Analysis of Variance
Audio Video Interleaved
Back-Scattered Electron
Confidence Level
Energy Dispersive Spectrometry
Electron Probe Microanalysis
Extent of Reaction
Frames per second
General Linear Model
Number of samples/tests/observations
Neutral Density
Oxygen Index
Promoted Ignition Combustion Transition
Regression Rate of the Melting Interface
Sample standard deviation
Surface Area to Volume ratio
Scanning Electron Microscope
Pooled sample standard deviation
Stainless Steel (Materials context)
Regression Sum of Squares (Statistical context)
Standard Error
Solid Liquid Interface
Threshold Pressure
Volume Flow Rate
Wavelength Dispersive Spectrometry
Cross-sectional area
X-ray Diffraction
Atomic Number
xviii
C HAPTER 1
I NTRODUCTION
This thesis investigates the effect of a sample’s geometry on how it burns under the
framework of a standard promoted ignition test for metallic materials. The extent
to which the cross-sectional area (XA) and the shape of a sample affect its melting
and subsequent burning is evaluated. These effects are assessed in terms of both the
Regression Rate of the Melting Interface (RRMI) and the Extent of Reaction (ER).
Promoted ignition tests were performed on iron/mild steel rods in oxygen for a range
of XAs for three different shapes. The relationship between sample geometry and ER
is assessed at two different pressures. A second component of the work investigates
the methodology of the standard promoted ignition test in relation to test numbers and
confidence levels. Logistic regression modelling was applied to two typical data sets
in order to evaluate the model as a tool for interpreting test data.
This chapter discusses the motivation behind studying the behaviour of metallic
materials in environments that support combustion. The terms ‘metal’, ‘material’ and
‘metallic material’ are used interchangeably throughout this thesis and refer collectively to both pure metals and alloys, unless otherwise stated. The concept of a standard promoted ignition test is introduced in Section 1.2 along with published standard
test methods. Section 1.3 outlines the objectives and approach of the thesis followed
by an overview of the format of this dissertation, Section 1.4.
1.1
Metals Flammability
Metals and alloys are some of the most commonly used engineering materials. Their
versatility as a construction material has led to their use in applications ranging from
ships, aircraft and buildings, to nails, pipes and light fittings. Material properties and
1
1.1 M ETALS F LAMMABILITY
mechanical, thermal and electrical characteristics are used to assess their suitability
for a given application. Material properties are determined using approved standard
test methods, for example, the tensile test is used to obtain a characteristic stress-strain
curve of a material from which important material parameters can be derived. As well
as assessing a metallic material’s mechanical, thermal and electrical properties, another important consideration is its flammability. That is, under what conditions will
the material support burning (flammable) and under what conditions will the material
not support burning (non-flammable). A good general definition of flammability is
provided by Wilson and Stoltzfus [1], “the sustained, steady state burning, after ignition, of a specific sample in a defined configuration under specified environmental
conditions”. Flammability, in the sense of flammable vs non-flammable, must be associated with a specific burn criteria, e.g., sustained burning for more than 50% of a
sample’s length. In this thesis the word flammability is often used, and, unless otherwise specified, refers generally to conditions which support burning.
Although metals are often considered non-flammable this is not the case when they
are subject to certain oxidising environments including elevated oxygen concentrations
and pressures. Under these conditions their flammability becomes a major concern.
Three basic elements must co-exist to achieve a fire: fuel, oxidiser and an ignition
source. These elements form the basic fire triangle. Zawierucha et al. [2] present a
modified fire triangle based on that of Slusser and Miller [3] and list additional factors
affecting the legs of the basic fire triangle, Figure 1.1.
This figure is not available online.
Please consult the hardcopy thesis
available from the QUT Library
Figure 1.1: Extended fire triangle indicating factors related to ignition and burning [2].
Thus, in the presence of fuel, oxidiser and an ignition source, and given the right
ambient conditions, metals are flammable. Factors including temperature, pressure,
2
1
I NTRODUCTION
oxygen concentration, geometry and configuration, collectively distinguish between
circumstances under which metals are considered flammable and under which they
are considered non-flammable. It is important to note that subtle changes in these
factors may affect a material’s classification as flammable or non-flammable and alter
the oxygen compatibility rankings of various materials relative to each other.
Though the study of burning metal powders dates back several centuries the propensity of bulk metals to burn has been of interest for only the past half century. Glassman [4] and Kirschfeld [5–9] performed early theoretical and experimental work investigating the conditions under which bulk metals burn. Study in the field of bulk
metals combustion is, to some degree, driven by the desire to eliminate the oftentimes catastrophic incidents which result from a metal fire. Many cases have been
reported where a metal component within an oxygen system has been at the heart of
a fire. Dicker and Wharton [10] tallied incidents occurring in the compressed gas industry in Great Britain in the early 1980’s, many involved pressure regulators, cylinder
filling operations and cylinder valves. A significant incident in Australia’s recent history was the destruction of a Royal Australian Air Force P3B Orion Aircraft in 1984.
Fire initiated in an aluminium oxygen manifold check valve with contamination and
incorrect maintenance procedures considered to be contributory factors [11]. Such accidents highlight not only the need for appropriate materials and designs but also the
need to enforce correct cleaning, inspection and operating procedures, as specified in
standards such as ASTM G93 Standard Practice for Cleaning Methods and Cleanliness Levels for Material and Equipment Used in Oxygen-Enriched Environments [12].
The issue of flammability is particularly relevant on aircraft or in buildings, houses
and systems where the safety of passengers, inhabitants or users is paramount. A
few Australian Standards outline methods for assessing material flammability: AS
1530.2-1993 [13] addresses building materials, components and structures, AS/NZS
60695.2.12:2001 [14] addresses electrical insulating materials and AS4267-1995 [15]
targets pressure regulators.
A number of organisations are committed to the study of fires, metal or otherwise,
in oxygen systems. They include the National Aeronautics and Space Administration
(NASA), the Compressed Gas Association (CGA), the National Fire and Protection
Association (NFPA) and the American Society for Testing and Materials (ASTM).
ASTM Committee G04 deals with the compatibility and sensitivity of materials in oxygen enriched atmospheres. The International Organization for Standardization (ISO),
in particular Technical Committee (TC) 20 Aircraft and Space Vehicles, and TC 92
3
1.2 P ROMOTED I GNITION T ESTING
Fire Safety, and Standards Australia’s Committee FP-018 Fire Safety, working in conjunction with ISO TC 92, also specialise in this field.
1.2
Promoted Ignition Testing
In order to identify conditions in which a metallic material is considered flammable,
researchers investigate the effect of pressure, oxygen concentration, diluents, temperature, configuration and geometry on measurable burning parameters. Promoted ignition test standards outline methodologies for assessing bulk metallic material flammability and define appropriate sample geometries, oxygen concentrations, test procedures and reporting practices. Standard promoted ignition tests are conducted in
order to assess flammability under a set of standard test conditions thereby allowing a
qualitative comparison of the results for different metallic materials. For metals, flammability is typically assessed by two parameters: Threshold Pressure (TP) and RRMI.
In ASTM G124-95 (2003) Standard Test Method for Determining the Combustion Behavior of Metallic Materials in Oxygen-Enriched Atmospheres [16], TP is defined as
the “minimum gas pressure (at a specified oxygen concentration and ambient temperature) that supports self-sustained combustion” and the RRMI is defined as the
“average rate at which the burning/solid-metal interface advances along the test specimen length”. TP therefore indicates the boundary between pressures which will and
will not support self-sustained burning of a sample. Materials can then be qualitatively
ranked according to TP for the specific geometry tested. The standard test method is
also often used as a basis for testing other sample geometries or test conditions.
TP and RRMI are dependent on a number of factors including sample geometry [17, 18], oxygen concentration [19], static pressure [20, 21], material purity, alloying elements [22] and initial temperature [23–25]. Therefore, when comparing results
for different materials it is important that values obtained from similar test conditions
be compared, which is why standardised tests are developed and used. However, the
results from standard tests are applied to assess flammability in non-standard environments for non-standard configurations and geometries. The standard test geometry is
typically a 3.2 mm diameter cylindrical rod and difficulties arise when using standard
test results to pass judgement on the flammability of components of various shapes and
sizes. A better understanding of the effect of sample geometry on a metallic material’s
flammability will allow a safer assessment of the flammability of a complex system
4
1
I NTRODUCTION
based on the standard test data that is available.
In cases where materials have the same TP, the RRMI can be and is often used to
further differentiate these materials by identifying faster burning metals (less desirable)
from those that burn more slowly (more desirable). The RRMI may also be used to
elucidate the complex metal burning process. Understanding the process by which
metallic materials burn, in particular rate-limiting mechanisms, provides information
which can then be used to more comprehensively assess flammability in real systems
with less reliance on standard tests and their necessary assumptions. Understanding
the effect of sample geometry on the burning process is critical to developing a widely
applicable burning model for these materials.
1.2.1
Promoted Ignition Test Method
The promoted ignition test involves forcibly igniting a vertically held test sample
by providing it with an overwhelming source of energy so that it will undergo selfsustained burning if the environment to which the sample is exposed is conducive to
burning. The burning of a metal test sample involves a repeatable drop-growth-anddetachment cycle. The material at the base of the sample that melts and/or reacts forms
a drop that grows as the solid metal above it continues to melt, burn and become incorporated into the drop, increasing its volume. This occurs until the weight of the
suspended molten material exceeds the upward restoring forces of surface tension and
adhesion supporting the mass, at which point the drop detaches. This process is shown
in Figures 1.2 and 1.3 and is typical for all liquid burning metals.
This figure is not available online.
Please consult the hardcopy thesis
available from the QUT Library
Figure 1.2: Sketch of a typical drop-growth-and-detachment cycle [26].
5
1.2 P ROMOTED I GNITION T ESTING
This figure is not available online.
Please consult the hardcopy thesis
available from the QUT Library
Figure 1.3: Typical drop-growth-and-detachment cycle for a 3.2 mm diameter iron rod
burned in oxygen at 6.9 MPa [27].
Since the promoted ignition test involves providing the sample with an overwhelming ignition source, test results are not a measure of the propensity of a material to
ignite under specific conditions, but rather, they are a measure of the propensity of the
material to sustain burning under those conditions. The ignition source is typically an
aluminium-palladium wire that, when a current is passed through it, heats and melts,
releasing the energy needed to melt the end of the test sample which, if the material is
flammable, results in sustained burning.
1.2.2
Promoted Ignition Test Standards
Three major organisations have published promoted ignition test standards to assess
the flammability of metallic materials in gaseous oxygen. ASTM has published G12495 (2003) Standard Test Method for Determining the Combustion Behavior of Metallic
Materials in Oxygen-Enriched Atmospheres [16], NASA has published NASA-STD6001 Flammability, Odor, Offgassing and Compatibility Requirements and Test Procedures for Materials in Environments that Support Combustion1 [28] and the ISO has
published ISO 14624-4 Determination of upward flammability of materials in pressurized gaseous oxygen or oxygen-enriched environments [29]. Although some differences exist in the specifics of these three standards they essentially present the same
approach. The main objective of the NASA and ISO standards is to assess a material’s flammability at its maximum use pressure. In contrast, the scope of the ASTM
standard is to provide information about the relationship between pressure and flammability without necessarily having an intended use for the material which is being
evaluated. Details of these three standards are now presented.
1
Formerly NHB 6080.1C
6
1
I NTRODUCTION
American Society for Testing and Materials
One of the most referenced and adopted standards for evaluating metallic material
flammability is ASTM G124-95 (2003) [16]. The standard specifies that a 3.2 mm
diameter cylindrical rod or a 3.2 mm × 3.2 mm side square rod be tested. The optional
square geometry reflects a recent change to the standard which formerly stipulated
a cylindrical rod be tested. In light of this recent change the results from this work
are of interest to ascertain the degree to which geometry affects burning and hence,
assess whether the comparison of cylindrical and square results is valid. The first test
is performed and if sustained burning occurs the test pressure is reduced and the test
is repeated at a lower pressure. Self-sustained burning occurs when the test sample
is consumed “past the point at which the promoter influences the combustion of the
material”, typically more than 50 mm (for a 100, 150 or 300 mm initial sample length).
The definition for self-sustained burning is referred to as the ‘burn criteria’. Problems
arise when researchers adopt their own definition of burn criteria, as will be shown
later, which may invalidate the direct comparison of test results for different materials.
The standard specifies that at a test pressure where the sample did not burn the test
must be repeated several times before the next highest test pressure can be recorded as
the TP. The statement that ‘several’ samples must be tested for a given condition, rather
than the previously specified five samples, reflects a recent change to the standard. The
difference between the TP and the pressure at which sustained burning did not occur
is the margin of error.
National Aeronautics and Space Administration
The standard sample geometry in NASA-STD-6001 Test 17 is a 3.2 mm diameter
cylindrical rod with a length of 300 mm. Samples are tested at the maximum use
pressure but may be tested at a range of pressures. Materials are classified as flammable
if more than 150 mm (50%) of the sample’s initial length is consumed during the test.
The standard stipulates that at least five samples must be tested and if one test results
in a burn the material is deemed flammable at pressures greater than, or equal to, the
test pressure at which the burn occurred.
International Organization for Standardization
The recently introduced ISO 14624-4 outlines a test procedure similar to NASA-STD6001 Test 17. The standard sample geometry is a 3.2 mm diameter cylindrical rod
7
1.2 P ROMOTED I GNITION T ESTING
with a length of 305 mm but the standard states that a 3.2 × 3.2 mm square rod is a
typically tested non-standard sample geometry. The ISO standard is more conservative
than both the ASTM and NASA standards in that it specifies a minimum of ten samples
be tested at a single test pressure with all ten tests resulting in no-burns for the material
to pass the test at that pressure.
1.2.3
Issues Arising from the Standard Promoted Ignition Test
At this point it is interesting to address the interpretation of TP in relation to material
flammability. According to the current definition, it is clear that using a material at
pressures above the TP would be inherently risky as the material is considered flammable. However, unless the next lowest pressure tested (for which no burns occurred)
is also provided it is not known at what pressures the material is classified as nonflammable, since the next lowest pressure tested could have been much less than the
TP or only slightly less. In a draft revision of G94-92 (2005) Standard Guide for Evaluating Metals for Oxygen Service [30] issued by ASTM, the inconsistent references
to threshold pressure in the literature are acknowledged. Two common definitions are
presented; 1) “the maximum pressure at which no burns, per the test criteria, were observed and above which burns were experienced or tests were not conducted” and 2)
“the minimum gas pressure (at a specified oxygen concentration and ambient temperature) that supports self-sustained combustion of the entire standard sample”. The first
definition is more conservative and clearly indicates the pressure range where a material is considered non-flammable, which is more important information, in an applied
sense, than knowing flammable pressures. It has also been suggested that reporting
raw burn length data for all pressures tested is a preferred approach as it would allow
the end-user to make a more informed judgement based on the test data (E. Forsyth,
Personal Communication, April 18, 2006). It is clear that the concept of TP is a confusing issue and reported results must be interpreted with care. The availability of raw
data from which to assess oxygen compatibility would certainly benefit the community. Of greater benefit would be a model to characterise flammability as a function of
test pressure.
Another contentious issue is the fact that the standards do not justify their specific
burn criteria. Also, it is advisable that the reference to the minimum of ‘several’ tests
in the ASTM G124-95 (2003) be changed to a specific number of tests so that results
can be easily compared and repeatable.
8
1
I NTRODUCTION
The statistical relevance of standard test results requires formal evaluation due to
the small data sets normally used. Typically only a handful of tests are conducted at
a set test pressure from which the material is judged as flammable or non-flammable
at the test condition evaluated. The practise of testing only a limited number of samples is driven by economic considerations. The results from the standard test are then
applied to qualitatively assess the flammability risk of other components. A common
assessment practise is as follows; if a component is thicker than the standard sample
and is to be used at the minimum pressure where the standard sample underwent selfsustained burning, then it would be deemed suitable. If however, the component was
thinner than the standard sample, then the component is likely to burn at pressures below that at which the standard sample exhibited self-sustained burning in which case
it is unsuitable. Given that the standard test results are applied to pass judgement on
whether a material is non-flammable and hence acceptable to use at a particular pressure it is desired that one is fairly confident in the results or is at least aware of the
specific confidence level for the results, based on the number of tests performed. A
Promoted Ignition Combustion Transition (PICT) curve, a plot of the length of sample
remaining versus test pressure, was introduced by Zawierucha et al. [21] to assist in
identifying flammable and non-flammable pressure regions. Extending this approach,
logistic regression is evaluated as an appropriate method for using binary burn/no-burn
test data, generated over a range of pressures, to provide an assessment of the probability that a material will undergo self-sustained burning as a function of pressure.
The approach provides end-users with a broader picture of the flammability characteristics of the metal and enables them to choose an acceptable level of risk with which
to interpret data.
1.3
Objectives and Approach
Research investigating the effect of sample geometry for burning metals is limited.
Most studies target real components, regulators, sintered filters, meshes and tubes and
although the results are valuable in an applied sense, they provide limited information
on how sample geometry effects the general burning process. The above geometries
vary greatly from the standard test geometry, a solid cylindrical or square rod, making
it difficult to isolate the effect of sample geometry from other effects, for instance, flow
induced due to ‘chimney’ effects or the effects of heat conduction into the test sample.
Therefore, by considering solid rods with the same XA and comparing rods of different
9
1.3 O BJECTIVES AND A PPROACH
shape the effect of sample geometry can be isolated and studied.
The objectives of this thesis are:
• To investigate the relationship between sample geometry and RRMI for a constant test pressure.
1. RRMI as affected by XA.
2. RRMI as affected by rod shape.
• To investigate the effect of XA and pressure on the ER.
• To interpret the effect of sample geometry in terms of the burning process for
liquid-burning metal systems.
• To quantify the confidence associated with current standard promoted ignition
test data.
• To develop and evaluate a logistic regression method for interpreting promoted
ignition test data.
The approach that was used to meet these objectives was to conduct a series of promoted ignition tests on samples of various geometry. In this context the term geometry
encompasses both the size of the sample, or its XA, since all the samples were of the
same length, as well as its shape, the shape of the cross section: circle, rectangle or
triangle. To assess the effect of XA on RRMI promoted ignition tests were conducted
on cylindrical, rectangular and triangular rods for a range of XAs. To assess the effect of shape on RRMI the results for the circular, rectangular and triangular rods of
the same XA were compared. The effect of sample geometry and pressure on the ER
was assessed by testing cylindrical rods of varying diameter at both a high and low
pressure. The drops which detached during the promoted ignition test were quenched
and examined using microanalysis techniques. In addition, logistic regression methods
were explored and applied to two typical promoted ignition data sets.
This research focuses on sample geometry in relation to the RRMI, that is, the
effect of geometry on a sample once it is successfully burning. It does not seek to
address the relationship, if any, between sample geometry and TP.
10
1
1.4
I NTRODUCTION
Chapter Summary
The chapters of this thesis are arranged as follows:
Chapter 2 presents a detailed review of current literature in the field. The review
outlines the current understanding of liquid-burning metal systems and highlights limitations in this previous work. The review describes the effect of sample geometry on
metal flammability, as measured by TP and RRMI. In addition, a statistical approach
to the interpretation of materials test data is discussed.
Chapter 3 introduces relevant statistical theory upon which experimental results
and discussion are based and the chapter also outlines basic theory underlying logistic
regression.
Chapter 4 presents a description of the materials and equipment that were used to
conduct experiments and briefly describes the experimental procedures. In addition,
this chapter introduces the sample identification scheme that is used throughout the
remainder of the thesis.
Chapter 5 presents experimental results and analysis. The chapter discusses the
promoted ignition testing of rods of varying geometry as well as the microanalysis of
quenched slag from cylindrical rods of varying diameter for different test pressures.
Chapter 6 provides a discussion of the experimental results and analysis and highlights the relevance and implications of the work to the field of metals combustion.
Chapter 7 presents statistical considerations in the interpretation and analysis of
promoted ignition test data. The chapter includes results and discussion for logistic
regression models of promoted ignition data sets. Recommendations are made to apply
this modelling methodology to promoted ignition test data.
Chapter 8 summarises the thesis, the contributions of the work and major conclusions and finishes with suggestions of future work in the field.
11
C HAPTER 2
L ITERATURE R EVIEW
This chapter presents a critical review of literature relevant to the research undertaken
for this thesis. Section 2.1 presents a detailed review of the physics and chemistry
of a liquid-burning (heterogeneous) metal system. Iron and iron alloys were selected
for the experimental component of this research and they are consistently reported to
burn heterogeneously. Included in this review is a brief analysis of the physics of drop
formation and detachment since this process dominates the burning of a standard test
sample. The effect of a change in sample geometry on drop formation and detachment
are discussed with reference to analogous cases in other fields. Section 2.2 presents a
detailed review of promoted ignition testing of various materials, geometries and components. The section is divided into three parts, Section 2.2.1 focuses on the effect of
geometry on TP, Section 2.2.2 concentrates on the effect of geometry on the RRMI and
Section 2.2.3 addresses the development of material rankings based on TP and RRMI
for different environmental conditions (pressure, oxygen concentration, temperature
etc.) and comments on the effect that changing a sample’s geometry has on material
rankings. Microanalysis methods and their application in metals combustion research
are discussed in Section 2.3. Finally, material test methods are reviewed from a statistical perspective in Section 2.4. The chapter ends with a brief summary highlighting
the contribution of this thesis and how it relates to and furthers current knowledge in
the field.
2.1
Physics and Chemistry of Burning Metals
The underlying physics and chemistry of burning metallic materials is nontrivial. Given
the nature of the system under review, the high temperatures and oxidizing atmosphere
12
2
L ITERATURE R EVIEW
place limitations on equipment which is capable of real-time measurements. Therefore, post-test sample analysis and video recordings of promoted ignition tests are invaluable to provide insight into the processes occurring during burning. Visual recordings also enable the RRMI to be calculated based on the movement of the leading edge
of the molten mass along the test sample. In addition, they provide insight into the motion of the molten mass, surface luminosity, and hence surface temperatures and any
evidence indicating whether reactions occur in a gaseous phase, which may manifest
in the form of ejecta and/or smoke. This section presents a review of the literature dedicated to understanding the mechanism/s of bulk metals burning in oxygen enriched
atmospheres with a focus on the heterogeneous burning system.
2.1.1
A General Burning Model
The burning of metals is typically classified into two types; liquid-phase burning and
vapour-phase burning. Iron, aluminium and their respective alloys have been the focus of extensive research as these metals are reported to burn via contrasting mechanisms [24, 26, 31–35]. In the case of liquid-phase (heterogeneous) burning, reactions
between oxygen, incorporated at the surface of the molten mass, and liquid metal fuel
occur within the molten mass between two distinct phases at an interface. In vapourphase (homogeneous) burning, reactions between vapourised metal and oxygen occur
above the surface of the molten mass. There also exists the possibility of dual or
mixed vapour-liquid-phase burning which is suspected in the case of aluminium due
to its unique oxide formed [34]. Real-time measurement of the mass of a burning aluminium rod and attached drop indicated that the mass both increased and decreased
during a drop cycle [36] which supports the argument for dual-phase combustion. This
discussion is limited to the modelling of burning iron/mild steel, although the model is
representative of most liquid burning metals.
Most metals are suspected to at least partially undergo liquid-phase burning and
this has been the subject of numerous investigations. Wilson and Stoltzfus provide a
comprehensive definition for burning in the context of metals combustion as distinguished from ‘cold burning’ or rusting:
“The continuous reaction, after ignition, of a fuel and oxidizer until the
limiting reactant is consumed. Fuels and oxidizers may be multicomponent or single species. There may be multiple products distributed in mul13
2.1 P HYSICS AND C HEMISTRY
OF
B URNING M ETALS
tiple phases. The reactions are exothermic and temperatures in excess of
2500K are expected.” [26]
The early 1980’s saw an influx of papers from Japanese researchers who presented
models for the combustion of metals, predominantly iron/mild steel and aluminium, in
high pressure oxygen. K., T., Y., and J. Sato and T. Hirano et al. published a number
of papers on the subject [22–24,37–43]. The authors presented a physical model of the
iron system, Figure 2.1, and outlined the steps associated with their model which are
summarised below;
1. At surface A oxidation occurs releasing energy.
2. At surface B oxygen atoms are physically absorbed, dissociate and are chemically absorbed.
3. The solid rod melts, due to heat transfer, and is incorporated into the drop at
surface C. Surface C is commonly referred to as the Solid Liquid Interface (SLI).
4. The chemically absorbed oxygen diffuses through the oxide and reacts with the
liquid metal.
This figure is not available online.
Please consult the hardcopy thesis
available from the QUT Library
Figure 2.1: Physical model of a burning iron cylindrical rod [41].
Sato and Hirano dismiss heat transfer to the solid rod due to oxidation reactions
at the solid surface above the molten mass as negligible. Thermodynamically, heat
14
2
L ITERATURE R EVIEW
transferred from the molten mass to the solid rod is expected to far exceed that generated due to solid oxidation on the rod surface. This assumption is supported by other
researchers as oxidation at the solid rod’s surface is excluded from their models. This
general model is presented by Sato and Hirano in a number of their publications from
1983 to 1993 [24, 39, 43].
In 1997 both Steinberg et al. [44] and Wilson and Stoltzfus [26] published works
outlining a suitable model for the macroscopic kinetic analysis of burning iron. Steinberg et al. outline the heterogeneous reaction of metals in five steps which are in
general agreement with Sato and Hirano’s model.
1) “Adsorption of oxygen or Absorption of oxygen.
2) Transport of oxygen.
3) Chemical reaction.
4) Transport of thermal energy to solid.
5) Transfer of thermal energy to surroundings.” [44]
By correlating theoretical RRMI expressions (where RRMI is assumed proportional to
the reaction rate of the metal) with empirical results, for aluminium, magnesium, iron
and copper the authors concluded that heat transfer between the reaction interface and
the solid rod was the rate-limiting process. Wilson and Stoltzfus took an alternative
approach and identified the Langniuir-Hinshelwood-Hougen-Watson (LHHW) model
as appropriate for modelling burning iron at pressures where the RRMI appears linear
(0.3 - 10 MPa for 1 mm and 2 mm diameter rods and 0.3 - 5 MPa for 3.2 mm diameter rods). This RRMI trend supports a likely change in rate-limiting mechanism with
pressure and rod diameter. The LHHW model is commonly used to model reactions involving adsorption and chemical kinetics. The authors advocate the work of Steinberg
et al. [44, 45] stating that reactions occur at a phase boundary between the liquid iron
and liquid iron oxide. This reaction surface increases in area over the course of a drop
cycle, accompanied by an increase in temperature due to increased reactions. Thus, it
is implied that the rate limiting mechanism is the availability of oxygen at the reaction
interface. Since the RRMI of 3.2 mm diameter rods did not increase with increasing
pressure above 5 MPa the authors conclude that the reaction surface became saturated
with oxygen and another rate-limiting mechanism came into effect. In this work the
authors observed that after the slag detached there were no further exothermic reactions. However, Suvorovs et al. [32] reported that the fraction of unreacted metal in
15
2.1 P HYSICS AND C HEMISTRY
OF
B URNING M ETALS
the slag of both iron and aluminium decreased during cooling by visually comparing
slowly cooled and rapidly quenched samples, therefore reaction must continue, to a
finite extent, after a drop detaches.
The argument for increasing drop temperature over the course of a drop cycle is
addressed in detail by Kurtz et al. [46]. The emission spectra of burning iron rods
was measured and the temperature calculated. Although the measured temperatures
were affected by the location of the drop relative to the spectrometer’s field of view
the experiments indicated that the drop temperature and the size of the molten mass
are related, as shown in Figure 2.2. At the start of a drop cycle the temperature of the
molten mass was 2500-2800K and this increased to between 3500-3900K just prior to
drop detachment.
This figure is not available online.
Please consult the hardcopy thesis
available from the QUT Library
Figure 2.2: Molten mass temperature profile versus frame rate (30 fps) for an iron rod
burned oxygen at 1.63 MPa [46].
A qualitative physical description of burning iron rods was presented by Suvorovs
et al. [32] based on the microanalysis work of DeWit [47]. The combustion chemistry, although brief, was in agreement with the literature and the physical description
accurately incorporated the micrographic evidence. DeWit, in contradiction to Sato
and Hirano et al., concluded that the of the molten mass was not an influential factor
with regard to the rate limiting mechanism since excess oxygen was present within
the attached nubs of quenched iron rod and detached drops. However, the author acknowledged that the molten mass surface area and oxygen incorporation may be more
critical at lower pressure [47]. Heat transfer was identified as the rate-limiting mechanism with the RRMI dependent on the size and attachment conditions of the molten
16
2
L ITERATURE R EVIEW
mass.
Edwards [48] developed a mathematical lumped parameter model to describe burning iron rods for the purpose of evaluating the two major rate limiting mechanisms discussed in the literature, oxygen incorporation and heat transfer. The model comprised
of eight sub-systems described by 45 independent equations which incorporated a host
of adjustable parameters. The concept of an ‘oxygen shuttle’ in the form of FeO3 ,
a liquid oxygen-rich iron oxide, was used to transport oxygen from the gaseous surroundings to the reaction interface. This concept was in agreement with the existence
of ferrite ions previously proposed [26, 44]. In formulating a mathematical model to
describe such a complex process, about which there is limited knowledge and few measurable material properties, a number of simplifying assumptions were made. Model
results agreed fairly well with experimental results, although, experimental input was
used to initially estimate the adjustable parameters so relative agreement is expected.
The author concluded that the rate limiting mechanism was dependent on oxygen pressure and purity. At lower pressures and purities it was found that oxygen incorporation
at the surface of the molten mass was rate limiting, but for higher pressures and purities it was expected that heat transfer to the solid rod was rate limiting. It was also
postulated that a transition between rate limiting mechanisms is related to the size of
the molten mass and may change during a single test.
Most recently, taking a simple one dimensional conduction heat transfer approach
and ignoring chemical considerations or reaction mechanisms, Ward et al. [49] related
RRMI to the surface area of the SLI by considering the increased RRMIs observed
in reduced gravity promoted ignition testing of 3.2 mm diameter iron rods. The work
attributed the increased reduced gravity RRMI to an increased SLI area, assumed to
result from the molten mass ‘engulfing’ the rod in reduced gravity but not in normal
gravity, and supports heat transfer as the rate-limiting mechanism. In their heat transfer
analysis the authors equated the heat required to produce the observed RRMI with the
heat transferred to the solid rod from the molten mass. The RRMI being given by:
RRM I =
kASLI (TR − TM )
∆xρXA[cp (TM − T0 ) + λ]
(2.1)
where, k, cp , λ and ρ are material properties, conduction heat transfer coefficient, the
specific heat capacity, the latent heat of fusion and the density of iron respectively,
ASLI and XA are the area of the SLI and XA of the rod respectively, with TR , TM
and T0 the reaction, melting and ambient temperatures respectively. If ASLI = XA,
as is commonly assumed, changes in temperature aside, then RRMI is independent of
17
2.1 P HYSICS AND C HEMISTRY
OF
B URNING M ETALS
rod diameter and yet experimental results indicate a definite relationship between rod
diameter and RRMI.
Energy generated in the molten mass originates from the reaction of iron and oxygen and it is this energy that is transferred to the solid rod to cause the observed RRMI.
It would follow that the RRMI is dependant on the ER within the molten mass. That
is, the higher the ER while the molten mass is attached to the rod, the more energy
that is generated resulting in a higher heat flux into the solid rod thus producing a
higher RRMI. Since RRMI is also dependant on the rod diameter, as will be shown in
Section 2.2.2, it is likely that the ER is also related to rod diameter. This theory was
investigated by Benz et al. [50] and their theoretical approach to determining the ER
showed promising results for an inverse relationship between rod diameter and ER.
This relationship is yet to be verified experimentally.
The models of Sato/Hirano and Wilson/Steinberg are in general agreement. The
three major stages; 1) the incorporation of oxygen at the oxide surface, 2) the transport
of oxygen through the molten mass and 3) reaction at the metal-oxide interface, are
consistent although, the actual mechanism of oxygen incorporation differs.
2.1.2
Rate-Limiting Mechanisms
The rate-limiting mechanism has long been disputed but is generally agreed to be one
of two factors; oxygen availability or heat transfer to the solid rod. Sato and Hirano investigated possible rate-limiting mechanisms for burning mild steel rods and presented
theoretical analyses of heat transfer, oxygen consumption and RRMI. The authors evaluated the dominant mode of heat transfer from the molten mass to the solid rod by
examining the motion of the molten mass captured on high speed camera. The authors
concluded that convective heat transfer was dominant based on the observed surface
velocity of the molten mass purportedly causing a boundary layer to develop along
the interface between the molten mass and the solid rod. The authors attributed variation in RRMI to inconsistent convective heat transfer [24, 37, 42, 43]. Benz et al. [50]
whose work is discussed in more detail in the following paragraph, in contradiction
to Sato and Hirano et al., concluded that for 3.2 mm diameter rods, conduction was
the dominant mode of heat transfer. Sato and Hirano advocated oxygen incorporation
at the molten mass surface as the rate-limiting mechanism [39, 41]. This conclusion
was based on both experimental and theoretical work. They assumed that the oxygen
consumption rate was proportional to the iron consumption rate and hence RRMI. X18
2
L ITERATURE R EVIEW
ray microanalysis and a theoretical surface tension force balance prompted the authors
to conclude the attached drops consisted of oxide (predominantly Fe3 O4 with some
Fe2 O3 ). However, this is contradictory to an oxygen limited scheme. Should oxygen
be rate limiting one would expect excess melted but unreacted metal in the attached
drop. Evidence of unreacted iron in the molten mass was demonstrated by [32, 50]
through the analysis of quenched samples proving that the rate at which the iron rod
melts does not necessarily equate to the rate at which the iron burns.
Benz et al. [50] set about evaluating the rate-limiting mechanism by modelling the
combustion of 316 Stainless Steel (SS) as a semi-batch reactor. A semi-batch reactor is
a system which typically begins with a fixed quantity of reactants to which further reactants are added progressively until a final uniform composition is achieved [51]. This
does not appear entirely appropriate given that the burning drop is shown to contain
separate phases of oxide and molten metal. However, this lumped-parameter approach
is commonly used to simplify the analysis of complex systems. The authors assumed
conservation of mass and energy in the molten mass and developed an enthalpy balance
for the system using experimentally determined RRMIs to solve a system of equations
for the ER. The authors concluded that the rate-limiting mechanism for small rods
(0.51 mm diameter) differed to that for large (≥3.2 mm diameter) rods. The theory
of a rate-limiting mechanism that is dependent on the size of the molten mass, hence,
rod diameter, is also supported by Edwards [48]. In the case of small rods, a theoretical ER of one was predicted. In addition, the presence of excess oxygen led the
authors to conclude that the rate-limiting mechanism for small rods was the rate of
convective heat transfer to the solid rod. Heat transfer in the large rods was reported
to be dominated by conduction and the presence of unreacted metal in slowly cooled
nubs of burned 3.2 mm diameter rods led the authors to report that incorporation and
mixing of oxide/oxygen and melted but unreacted metal was rate-limiting for this case.
Research examining the relative amount of oxygen present during burning, which revealed excess oxygen was present within the molten mass, led Steinberg et al. [45] to
conclude that the rate-limiting mechanism is reaction at the iron/iron oxide interface
and consequently heat transfer to the solid rod. This finding does not contradict Benz
et al.’s findings as although excess oxygen may be present within the molten mass it
may not be available at the reaction surface.
Dreizin contrasted the rate-limiting mechanisms proposed by Sato and Hirano and
Steinberg et al., incorporation of oxygen at the molten mass surface, and heat transfer
to the solid rod, respectively. The author recognised that the conclusions reached by
19
2.1 P HYSICS AND C HEMISTRY
OF
B URNING M ETALS
both parties were consistent with their available experimental data and that differences
in experimental methods most likely resulted in their contradictory conclusions. However, it seems clear that the rate-limiting mechanism appears to depend on pressure and
rod diameter.
2.1.3
Excess Oxygen
The arguments surrounding the presence, availability and form of excess oxygen during burning are extensive. Steinberg et al. [45] disproved Benz et al’s early work [50]
by demonstrating the presence of excess oxygen in the molten mass during the burning of 3.2 mm diameter iron rods. The Ideal Gas Law and the measured pressure and
temperature profiles were used to calculate the mass of oxygen in the chamber. The
discrepancy between the mass of oxygen in the chamber and the stoichiometric requirement of oxygen to form magnetite (Fe3 O4 ), hematite (Fe2 O3 ) and wustite (FeO)
was attributed to excess oxygen incorporated into the molten mass. Lending weight
to this argument was the measured increase in oxygen mass within the chamber after
the rod finished burning as excess oxygen was released from the slag during cooling.
Quenched samples revealed melted but unreacted metal within a nub attached to the
rod and the authors postulated that at detachment only the oxide portion of the drop
separated, the melted unreacted metal remaining attached to the rod. This conclusion
was clearly refuted by Suvorovs et al.’s [32] report on the microanalysis of iron rods.
Water quenched drops detached from burning iron rods were examined and found to
contain a significant proportion of unreacted metal. Steinberg et al. postulated that an
increased reaction rate (it is unlikely that the authors experimentally measured an instantaneous reaction rate) and RRMI immediately after drop detachment was attributed
to rapid reaction of the freshly exposed liquid metal. The authors supported this conclusion by citing the observed spike in oxygen chamber temperature coinciding with
drop detachment and corresponding to the increased reaction rate/RRMI. DeWit [47]
suggested that the RRMI slows prior to drop detachment due to the increasing weight
of the drop, hence decreasing the extent to which the drop is observed to envelop the
rod. The surface area of the SLI may decrease during this time so the apparent increase
in RRMI after drop detachment reported by Steinberg et al. may not have resulted from
increased reactions, but rather from the surface tension force, now acting on a smaller
attached mass, which visibly ‘pulled’ the mass upwards.
Wilson and Stoltzfus [26] used surface tension values for liquid iron and liquid
20
2
L ITERATURE R EVIEW
iron oxide to argue that there is an inwardly directed flow within the drop mixing the
oxide and transporting oxygen to the reaction surface. Steinberg et al. [31] provided a
host of arguments supporting the presence of excess oxygen, defined as an oxygen to
iron molar ratio above that required to form Fe2 O3 , the highest stoichiometric oxide.
The research was based on both real-time measurements (oxygen gas density) and the
analysis of post-test samples. They elaborated on their model [44] by describing the
burning mechanism of iron as the exothermic dissolution of oxygen in the molten iron
oxide or the higher oxidation of the iron (above that of Fe2 O3 ) to form ferrite species,
−4
−3
−8
for example FeO−1
2 , Fe2 O5 , FeO3 and Fe2 O7 . Excess oxygen is transported to the
reaction surface via an oxygen concentration gradient and circulation, where heterogeneous reaction occurs between the liquid iron and oxygen, the number of reactions
themselves being the rate-limiting step. Based on the approximate drop mass and volume the authors claim excess oxygen is in the form of higher oxides, rather than a gas.
But, on cooling, this excess oxygen is released as a gas into the oxide forming voids in
the cooled slag. This supports the earlier report of Wilson and Stoltzfus who concluded
that at the high temperatures expected during burning there would be limited molecular
oxygen in solution, hence excess oxygen must be in the form of reacted oxygen or ionic
oxygen (ferrite ions) [26]. Steinberg et al. [44] also stated that, in pure high pressure
oxygen, volatilisation of oxide products would be minimal. Wilson et al. [52] discussed excess oxygen in burning iron, cobalt and nickel and reasserted that “chemical
adsorption is the process by which oxygen is incorporated into burning metal systems,
though this process (nature of the bonds formed) may be different for the different systems”. The authors reinforced the concept of ferritic species present during the burning
of iron and the release of excess oxygen from the slag during cooling. The work of
Dreizin [53, 54] reported evidence of oxygen dissolution in quenched aluminium and
zirconium particles (drops with diameters <500µm) and oxide inclusions in quenched
copper drops that were examined using an SEM. Suvorovs et al. [32, 33] also reported
oxide inclusions within the melted but unreacted portions of iron and aluminium within
quenched nubs and detached drops from rods burned in oxygen, also examined using
an SEM.
In summary, the heterogeneous burning of metals involves the following processes;
oxygen is chemically sorbed at the oxide surface and an oxygen concentration gradient
together with surface tension induced circulation facilitates oxygen transport (for iron
the oxygen is in the form of ferritic ions), to the reaction surface, the interface between
the unreacted liquid metal and metal oxide. The rate-limiting mechanism is the reac21
2.1 P HYSICS AND C HEMISTRY
OF
B URNING M ETALS
tion between oxygen and metal at this interface and consequently heat transfer to the
solid rod.
2.1.4
Formation and Detachment Dynamics for Pendant Drops
Promoted ignition and burning of a vertically mounted rod involves the melting and
burning of the solid material and subsequent growth of the molten mass. Detachment
occurs when the weight of the molten mass overcomes the supporting forces of surface
tension and adhesion. This process continues until either the sample burns completely
or is extinguished. RRMI, along with pressure and temperature, is one of the few
parameters that is typically recorded during a test. It has been shown that analysing
the movement of the molten mass and the resulting RRMI will provide insight into the
overall burning process [26, 37, 38, 44, 55].
The physics of pendant drop formation and detachment, and its application to the
measurement of a liquid’s surface tension, has been studied since the 19th century. Of
particular interest are the drop-weight and pendant drop methods for surface tension
measurement as the process is analogous to that occurring during the burning of a
metal rod.
The drop-weight method involves slowly injecting liquid into a hollow vertical tube
so that a drop forms at the base and as liquid is added the drop increases in size. The
weight of a detached drop is measured and used to calculate the surface tension, γ, of
the liquid via the Tate’s Law equilibrium condition [56];
mg = 2πrw γ
(2.2)
with, m the weight of the drop, g acceleration due to gravity and rw the wetted radius,
either the outer or inner tube diameter depending on the fluid.
However, at the point of drop detachment not all of the supported liquid detaches
resulting in the measured weight of the drop being less than was actually supported by
the surface tension force. Harkins and Brown [57] reasoned that the shape of the drop
affects the proportion that detaches, the shape being dependent on the radius of the
capillary tip and the drop volume. They recommended an empirical correction factor,
a function of tip radius and drop volume, to account for the mass of the drop that does
not detach in the drop-weight method. Based on their correction factors the authors
reported improved accuracy in the calculation of surface tension values for water and
benzene drops detaching from glass, brass and Monel capillary tubes.
22
2
L ITERATURE R EVIEW
The pendant drop method is an alternative to the drop-weight method whereby the
drop is in equilibrium and does not detach and the drop’s profile is used to measure
surface tension. The drop profile is dependant on the competition between surface
tension, which attempts to form the drop into a sphere, and gravity, which attempts to
elongate and stretch the drop. The ratio of these two body forces is represented by the
Bond number which appears in the Bashforth and Adams Equation [58] developed to
relate drop profile to surface tension, an approach adopted successfully in a number of
studies measuring the surface tension of water, glycerol and various polymers [59–61].
Knowing the surface tension of liquid metals is important in industrial processes
including welding, casting, crystal growth, smelting, brazing and sintering [62–67].
Conventional pendant drop and drop-weight methods have been successfully used to
measure the surface tension of metals [68–70] whereby the lower end of a metal rod is
melted via electron bombardment to form a drop. In this way the liquid metal is unaffected by interaction with capillary tubes/tips and is only in contact with neighbouring
liquid and solid metal, as is the case during the melting and burning of metal rods. The
surface tension of metals is highly dependent on surface active elements hence measurements are only valid for a specific material composition [71]. These surface active
elements also change the relationship between surface tension and temperature [72].
The influence of impurities on the measurement of the surface tension of pure metals has led to the use of a containerless oscillating drop technique based on observing
the frequency of oscillations of a levitated drop of liquid metal about its equilibrium
shape [73–75].
Studies measuring the surface tension of metals via drop-weight or pendant drop
methods, and most welding applications, involve cylindrical rods. Limited literature
exists investigating the effect of the shape of a rod on drop dynamics or detachment
conditions. The surface tension line force, Fγ = σpw , is dependant on the wetted
perimeter, pw , therefore, the surface tension line force will vary based on the shape
(perimeter) of the cross section (e.g., circle, square, oval). Hirano et al. [41] showed
that for burning rods the drop volume is proportional to the rod diameter and independent of test pressure. It is clear that the shape of the rod will dictate the maximum
drop volume that can be supported. Research by Chen and Brenner [76] on small
droplet production demonstrated theoretically that, for the same applied pressure, a
circular nozzle produces a droplet with the biggest volume. They found that the drop
volume could be decreased by up to 20% by using a triangular nozzle with “stretched”
corners. Nozzle and capillary systems, although similar in terms of drop-growth-and23
2.1 P HYSICS AND C HEMISTRY
OF
B URNING M ETALS
detachment, are simpler to study than burning rods. Experimental conditions are easier
to control in a non-reacting system and the geometry of the nozzle or capillary tube
does not change throughout the drop cycle as is likely the case for a burning rod. Systems inside the molten mass (SLI, liquid metal and oxide) will change as a result of a
change in the wetted perimeter and drop volume. Therefore the shape of the rod should
affect burning and this effect will be explored in this thesis.
Analysis of the size, shape and motion of the attached molten mass in the context
of promoted ignition testing is limited. RRMIs of iron, mild steel and aluminium rods
have been reported to vary cyclicly depending on the motion of the molten mass and
the point in the drop-growth-and-detachment cycle [17, 32, 37, 38, 41, 48, 49, 55, 77].
Sato et al. [37] attributed molten mass oscillations to surface tension, and stated that
variation in RRMI was due to an inconsistent rate of convective heat transfer to the
solid rod resulting from the motion of the molten mass. Experiments showed that the
SLI was not always planar and perpendicular, rather the orientation of its leading edge
alternated as illustrated in Figure 2.3. This behaviour is accentuated in reduced gravity
whereby the molten mass climbs up the rod and has been observed to precess around
the rod [55, 78, 79].
This figure is not available online.
Please consult the hardcopy thesis
available from the QUT Library
Figure 2.3: RRMI measured along opposite sides of a burning 2 mm diameter mild
steel rod during a single drop cycle at 10 MPa [37].
In later work Sato and Hirano [38,41] verified that the overall RRMI fluctuated during a drop cycle. Immediately after a drop detached the RRMI increased slightly, thereafter decreasing during the remainder of the drop cycle until the molten mass detached.
This pattern was confirmed in a recent independent study on iron rods [32]. The
24
2
L ITERATURE R EVIEW
increasing-decreasing RRMI pattern contradicts the trend reported by Chiffoleau [77]
for iron rods. Chiffoleau reported that the RRMI decelerated immediately after drop
detachment and increased during the remainder of the drop cycle. Chiffoleau applied a
novel ultrasonic method to measure the RRMI. The ultrasonic method involves measuring the time of flight between the transmission of an excitation pulse from a transducer
at the top of the sample and when it is received back at the transducer after traveling
the length of the rod and reflecting off the SLI. The length of the rod is calculated
based on the speed of sound of the material. This method was considered more accurate to measure the RRMI than the typical visual method. However, advances in digital
technology have improved the accuracy and ease with which the SLI can be tracked
via the visual method but for fast melting materials such as aluminium the ultrasonic
method would be a better option. In either case, it is consistently reported that the
RRMI fluctuates during a drop cycle.
In summary, the burning of iron rods in gaseous oxygen is complex and produces an
extreme reacting system which is difficult to study leading to a limited understanding
of the burning phenomena. Attempts have been made to model the burning process
based on experimental results and various models incorporating kinetics, thermodynamics and oxygen incorporation have been presented. However, modelling is made
difficult due to the unknown species and high temperature material and thermodynamic
properties for the species present in the subsystems within the molten mass. Compounding the problem, is a limited understanding of the effect of sample geometry on
these systems.
2.2
Geometry and Flammability
The purpose of promoted ignition testing is to assess the flammability of metallic materials under a variety of conditions in order to assess whether the material is suitable
to use in a pressurised oxygen environment. Standards describe an accepted method
for measuring TP and RRMI to justify the direct comparison of results for different
materials. However, researchers often deviate from the standard test conditions in order to investigate other conditions such as the critical oxygen concentration required
to support combustion at a given pressure, the effect of temperature (both ambient and
of the sample) on flammability or the flammability of different geometries or whole
components. Although cylindrical rods are the most commonly tested sample geome25
2.2 G EOMETRY
AND
F LAMMABILITY
try, square rods, sheets, meshes and tubes have also been tested [17, 80–82]. It is also
not uncommon for researchers to test components such as regulators, sintered filters
or structured metallic packing [18, 83–86]. These tests are necessary due to a limited
understanding of how the geometry of a component affects its flammability.
Test results allow the oxygen compatibility of a material to be assessed. Highly
compatible materials typically have high TPs and small RRMIs making them favourable
for use in oxygen atmospheres from a flammability standpoint, for instance, nickel and
copper alloys. Among many factors which have been found to significantly influence
a materials flammability, including alloying constituents, temperature, pressure and
oxygen purity, is its geometry. Geometry plays a role in ignition and affects whether a
sample will sustain burning and also how it burns. Although the scope of this thesis is
confined to examining the effect of sample geometry on RRMI, for completeness, this
section incorporates literature addressing the relationship between sample geometry
and TP. Literature addressing the effects of sample geometry on oxygen compatibility
material rankings is also presented.
2.2.1
Geometry and Threshold Pressure
Standard Geometries
Research investigating relationships between sample geometry and TP have been ongoing since the middle of the last century. As the XA of a sample increases its TP
also increases. This trend has been observed for cylindrical rods in the upward burning configuration for both flowing [87,88] and non-flowing [17,81,87] test conditions.
Table 2.1 presents reported TP results for iron based alloys.
Werley et al. [87] did not apply a consistent definition of TP in their analysis of
308 SS data. The data in Table 2.1 assumes complete combustion occurred if ≥130
mm of the initial 150 mm long sample was consumed. The authors reported test results for various pressures, materials and geometries but the number of tests that were
performed under each set of conditions varied. Samant et al. [88] applied two different
burn criteria in their experimental work. The burn criteria were based on the sample
diameter. For their 100 mm long samples the criteria were 30 mm (30%) for sample
diameters ≥2.39 mm and 50 mm (50%) for sample diameters <2.39 mm. The stated
percentages are therefore only valid for a 100 mm sample length. The use of a 50%
burn criteria was attributed to increased scatter in thin sample data. Although a burn
26
2
L ITERATURE R EVIEW
Table 2.1: Threshold pressures for cylindrical iron/steel rods.
Material
Diameter
(mm)
Threshold
Pressure
(MPa)1
Next Lowest
Pressure Tested
(MPa)1
Oxygen
Conc.
(%)
Ref.
Non-Flowing Conditions
308 SS4
308 SS
308 SS
1.1
2.4
3.2
3.89 (1/2)
4.24 (1/2)
4.58 (1/2)
3.55 (0/2)
3.89 (0/4)
4.41 (0/1)
99.9+
99.9+
99.9+
[87]2
316 SS
316 SS
316 SS
3.2
4.8
6.4
3.45 (3/3)
6.90 (3/3)
20.69 (5/5)
LPT
3.45 (0/6)
6.90 (0/3)
99.9+
99.9+
99.9+
[17]2
Iron
3.0
0.5 (-)
LPT
99.5+
[89]
Carbon Steel
3.2
0.69 (3/3)
LPT
99.7+
[90]
Carbon Steel 1018
6.4
0.17 (-)
- (-)
99.99
[81]2
LPT
LPT
LPT
1.14 (0/5)
2.69 (0/3)
5.62 (0/5)
5.62 (0/5)
99.7+
99.7+
99.7+
99.7+
99.7+
99.7+
99.7+
[88]3
Flowing Conditions
316/316L SS
316/316L SS
316/316L SS
316/316L SS
316/316L SS
316/316L SS
316/316L SS
0.89
1.59
1.98
2.79
3.17
6.35
9.52
0.2 (3/3)
0.2 (3/3)
0.45 (2/5)
1.82 (1/3)
2.86 (2/3)
10.44 (3/4)
10.44 (1/1)
1
Brackets indicate (Burns/No. Tests) at that pressure.
Burn criteria: complete burning/melting of the sample.
3
Burn criteria: 30%, flow conditions not reported.
4
Stainless Steel (SS)
2
under a 50% criterion is also a burn under a 30% criterion, a no-burn under a 50% criterion is not necessarily a no-burn under a 30% criterion. Hence, a 30% criterion was
adopted for the data in Table 2.1. Tests were also performed under both flowing (direction not explicitly specified but interpreted to be opposite to the direction of burning)
and non-flowing conditions. Some samples were subjected to flowing conditions, and
others to both static and flowing conditions, but not always at the same pressures. The
complete set of results for the testing of 316/316L SS that were published are shown
27
2.2 G EOMETRY
AND
F LAMMABILITY
in Figure 2.4. Two non-intuitive results are:
• 0.89 mm and 1.59 mm diameter rods burned in three tests at 0.2 MPa and yet
no-burns were observed at test pressures up to 3.55 MPa (flowing conditions).
• Under a 30% burn criteria a burn was observed at 1.82 MPa for the 2.79 mm
diameter rod but three tests of the smaller 2.54 mm or 2.39 mm diameter rods
resulted in no-burns at this pressure (flowing conditions).
This figure is not available online.
Please consult the hardcopy thesis
available from the QUT Library
Figure 2.4: Promoted ignition data for 316/316L stainless steel for various geometries [88].
Samant et al.’s results highlight the consequences of testing only a small number of
samples and this is demonstrated by considering the results for the 1.59 mm diameter
rod. Under the standard test method testing would have commenced at 3.55 MPa. A
burn was obtained at this pressure so testing commenced at the next lowest scheduled
pressure. At 1.82 MPa no-burn results were obtained for the three tests that were
conducted so 3.5 MPa would be declared the TP. However, Figure 2.4 clearly shows
that 1.59 mm diameter rods burned at as low as 0.2 MPa. If a greater number of tests
had been performed, burn results may have been observed at either 1.82 MPa or 0.9
MPa.
28
2
L ITERATURE R EVIEW
The recent inclusion of 3.2 mm × 3.2 mm square rods as an acceptable standard
geometry for promoted ignition testing was a motivation for the investigation on the
effect of rod shape on RRMI and burning behaviour. TP data for square rods is presented here to supplement the later discussion of RRMIs. Steinberg et al. [17] and Key
et al. [91] published results for 3.2 mm × 3.2 mm square rods and 3.2 mm diameter
cylindrical rods under static test conditions. Of the five materials tested by Key et al.
only the TPs of 321 SS and Inconel 600 were affected by rod shape. Under a 100%
burn criteria, the TPs of cylindrical and square rods of 321 SS were 5.1 MPa and 3.5
MPa respectively. However, when the burn criteria was reduced to 54% the TP was
1.7 MPa for both shapes. In contrast, under a 54% burn criteria, the TPs for cylindrical
and square Inconel 600 rods were 20.7 MPa and 41.3 MPa, respectively. However,
under a 100% burn criteria both shapes had TPs of 55.1 MPa. This result indicates
that for 321 SS, the pressure to sustain burning over approximately 50% of the rod was
the same for both shapes, but the cylindrical rod required a higher pressure to sustain
burning over its entire length. Conversely, for Inconel 600, the square rod required a
higher pressure to sustain burning for at least 50% of its length but required a smaller
pressure increase to induce burning of the entire rod. The TPs of Inconel 625, 718
and Rene 41 were identical for both the cylindrical and square rods under both burn
criteria. Steinberg et al. reported that 316 SS and Aluminium 2219 square rods were
flammable at the same pressures as 3.2 mm cylindrical rods. The result was based on
a burn criteria of 10%.
Changes in TP between cylindrical 3.2 mm diameter rods and square 3.2 mm × 3.2
mm rods may be caused by the differences in their XAs, XASquare > XACylinder . If
the trend for cylindrical rods, that TP ∝ XA, is applicable to other shapes, this would
imply that the square rods would have a higher TP. From Key et al.’s experiments this
was true for Inconel 600 but not for 321 SS, but the difference in both XA and rod
shape had no effect for 316 SS and Aluminium 2219 based on Steinberg et al.’s tests.
These discrepancies could be a result of the materials that were tested.
Non-Standard Geometries
Experiments on similarly sized rectangular samples of 316 SS were reported by Steinberg et al. [17] and Janoff and Pedley [82], 12.7 mm × 0.8 mm and 12.7 mm × 3.2
mm, and, 13 mm × 0.8 mm and 13 mm × 3 mm, respectively. Interestingly, both sets
of results reported that the 3.2 mm and 3 mm thick samples were less flammable than
29
2.2 G EOMETRY
AND
F LAMMABILITY
the 0.8 mm thick samples. Both geometries were classified as flammable under a 20
mm (10%) burn criteria, but the thick sheets burned completely at 34.48 MPa whereas
the thin sheets self-extinguished with 54% remaining [17]. This result suggests that
the TP for the thin sheet may be higher than the TP for the thick sheet. This finding
is not intuitive as one would expect specimens with a smaller XA to burn better under
the same conditions, however, a limited number of these tests were conducted. Nevertheless, Steinberg et al.’s finding is supported by Janoff and Pedley in comments on
an investigation by the NASA Johnson Space Center White Sands Test Facility [92]
which reported that 13 mm × 0.8 mm strips of 316 SS had a TP of 34.5 MPa which
exceeded the TP of the 13 × 3 mm strips, 6.9 MPa. The next lowest pressure tested
was not specified. Janoff and Pedley alleged this interesting TP result related to the
interaction of the end of the rod and the attached molten mass. They postulated that an
“instability in molten drop adherence” was caused when the attached mass attempted
to adhere to the thin rod. Such an instability would result in small drop times and/or
chaotic dripping behaviour but experimental evidence supporting their theory was not
presented. Steinberg et al. also tested rectangular rods of Monel® 400 and Aluminium
2219. Monel® 400 did not burn in tests up to 68.95 MPa, the maximum pressure
tested, for both thick and thin samples whilst Aluminium 2219 burned completely at
3.45 MPa, the lowest pressure tested, for both geometries.
Tests under flowing conditions, with flow in the opposite direction to burning, were
conducted by Benning et al. [93]. The TPs of Aluminium 6061 rectangular rods, 12.7
mm × 6.4 mm, and 6.4 mm diameter cylindrical rods were obtained. For two different
oxygen concentrations they found that the rectangular rods had higher TPs than the
cylindrical rods. The data in Table 2.1 shows that as the XA of a cylindrical rod increases its TP also increases. It is therefore likely that the difference in XA of the cylindrical and rectangular rods, 32.1 mm2 and 81.28 mm2 respectively, was a major factor
which contributed to the measured difference in TP. Effects due to the shape of the rod
were likely outweighed by effects due to the difference in XAs. The difference in TP
between the cylindrical and rectangular rods decreased as the rod diameter/thickness
increased, as shown in Figure 2.5. This trend correlates with the converging XAs of the
two shapes. The ratio of the XA of the cylinder to the XA of the rectangle for the 4.8
mm, 6.4 mm and 9.5 mm diameter/thick samples is 30%, 39% and 59%, respectively.
The TP results were based on a 100% burn criteria and the next lowest pressure tested
was 34 kPa lower than the reported TPs.
A variety of metals have been tested in the form of wire mesh under both flowing
30
2
L ITERATURE R EVIEW
This figure is not available online.
Please consult the hardcopy thesis
available from the QUT Library
Figure 2.5: Threshold pressure for Aluminium alloy 6061 rods and strips [93].
and static test conditions. TP results published by Samant et al. [88] and Stoltzfus et
al. [80] are in agreement based on the pressure ranges that were tested in each case.
Table 2.2 presents the TP data along with RRMIs measured by Stoltzfus et al. The
researchers used different burn criteria; Samant et al. applied a burn criteria of >50%,
whereas Stoltzfus et al. adopt Benning et al.’s burn criteria, 100%. The mesh size of the
samples was 60x60 and the wire diameter ranged from 0.17 - 0.19 mm. Oxygen purities of 99.7% and 99.5% were used by Samant et al. and Stoltzfus et al., respectively.
In both cases, the mesh was rolled to form cylinders with a 6 mm outer diameter and
a 3.2 mm inner diameter. Table 2.2 includes TP data for 3.2 mm diameter rods of the
same materials, for comparison. These independent studies clearly demonstrate that
TP decreases when materials are in the form of wire mesh. Monel® 400 mesh burned
readily at atmospheric pressure and Copper 100 burned at relatively low pressures. In
comparison, the TPs of 3.2 mm diameter rods for the same materials were reported
to be >33.5 MPa [94] and >55.1 MPa [20] respectively. Samant et al. tested Copper
31
2.2 G EOMETRY
AND
F LAMMABILITY
Table 2.2: Threshold pressure and RRMI of wire mesh and 3.2 mm diameter
rods for various engineering alloys.
Material
Threshold Pressure
(MPa)
Mesh [88] Mesh [80]
3.2 mm ∅ rods
RRMI
(mm/s)
[80]
Nickel 200
>34.582
>0.772
> 68.9 [91]5
-
Copper 100
12.17
0.33 (0.26)4
> 55.1 [20]
3.6
> 33.5 [94]
3.1
Monel® 400
0.14
1,3
≤0.085
1
316 SS
0.141,3
≤0.0851
3.45 (2.76)4 [95]
8.1
Carbon Steel
-
≤0.0851
1.7 [91]5
9.5
304 SS
-
≤0.085
1
-
9.9
Hastelloy®C276
0.141,3
-
20.7 [91]5
-
1
Lowest pressure tested.
Highest pressure tested.
3
Flowing conditions.
4
Brackets designate next lowest pressure tested for which no burns were obtained.
5
Maximum pressure at which sustained burning did not occur based on a 50% burn
criteria.
2
100 mesh under flowing conditions at 34.58 MPa and observed no burns even though
under static conditions burns were achieved at 12.17 and 20.79 MPa. Flow conditions
have been reported to produce more severe burning conditions, particulary when flow
is in the same direction as the burning, resulting in burns at lower pressures than would
normally occur under static test conditions [90].
Sintered filter materials in the form of cylindrical rods were tested by Schadler
and Stoltzfus [18]. Tests were performed on 316 SS, tin-bronze and Monel® 400 and
sample dimensions varied for the three materials. 316 SS samples were cylindrical
rods with a 4.7 mm diameter and were 58 mm in length, tin bronze samples were
elliptical rods with major axis 4.0 mm, minor axis 3.6 mm and length 76 mm and
Monel® 400 samples were cylindrical rods of 6.3 mm diameter and 76 mm in length.
The burn criteria was defined as sustained burning of the entire sample. Experiments
demonstrated that in the form of a sintered rod Monel® 400 burned at 0.69 MPa and
had an RRMI of 1.9 mm/s. 316 SS burned at 0.082 MPa and at 0.69 MPa its RRMI
was 4.6 mm/s. Tin bronze samples for a range of filter powder grades were tested.
Results demonstrated that TP was affected by the powder’s particle size, as the particle
32
2
L ITERATURE R EVIEW
size decreased so did TP. The authors did not hypothesise reasons for this but it is
likely due to the increased Surface Area to Volume ratio (SA/V) of the particles [85].
The authors proposed that the particle size had a greater effect on the RRMI of the tin
bronze samples than pressure. Grade 103A samples (coarser) had slower RRMIs than
grade 153A samples (finer), 8.3 mm/s compared to 9.5 mm/s respectively, even though
the test pressure of the grade 103A sample was 68.9 MPa, almost double that of the
grade 153A sample, 37.9 MPa.
In summary, it is clear that sample geometry affects TP. As the sample, or its constituent parts (i.e., wire diameters or particles sizes) decrease in size, TP also decreases.
2.2.2
Geometry and Regression Rate of the Melting Interface
Standard Geometries
Early work by Kirschfeld [5–9] identified general relationships between RRMI, test
pressure and diameter for cylindrical rods. It was reported that as the test pressure
increased the RRMI also increased, and inversely, as the diameter increased the RRMI
decreased. This trend is widely reported in the literature and is reflected in Table 2.3
which contains RRMI data for iron and iron alloy rods of varying diameter and tested
at varying pressures.
Standard 3.2 mm diameter cylindrical rods and 3.2 × 3.2 mm square rods were
tested by Steinberg et al. [17] for Aluminium 2219 and 316 SS. The results demonstrated that the extent to which sample geometry affects RRMI varies for different
materials. RRMIs for the aluminium alloy cylindrical and square rods, 35.6 mm/s and
42 mm/s, respectively, differed more than those of the SS cylindrical and square rods,
11.7 mm/s and 10.7 mm/s, respectively. The XAs of these two geometries are not
equal. The square rod has a XA of 10.2 mm2 which is 27% greater than the XA of
the 3.2 mm diameter rod. Based on the inverse relationship between RRMI and XA
from the data in Table 2.3 it is expected that the RRMIs for the cylindrical rods should
exceed those for the square rods, however this was not the case for Aluminium 2219.
The authors do not provide error bounds on any of their data and used visual methods
to determine the RRMI, which are known to be error prone for rapidly burning aluminium [96, 97]. Regardless, this work emphasises that sample geometry is a critical
factor which influences RRMI.
33
2.2 G EOMETRY
AND
F LAMMABILITY
Table 2.3: Test data for cylindrical iron and steel samples burned in oxygen.
Material
Diameter
(mm)
Test Pressure
(MPa)
RRMI
(mm/s)
Oxygen
(%)
Reference
Mild Steel (Fe 99.5%)
1
5
24
-
[22]
Iron (99.998%)
1
5
23
-
[22]
Iron (99.999%)
1
5.2
23
99.99
[31]
Iron (99.995%)
1.5
1.0
8.73
99.5
[48]
Mild Steel (Fe 99.5%)
2
5
13
-
[22]
Iron (99.998%)
2
5
13
-
[22]
Iron (99.999%)
2
5.04
14
99.99
[31]
Iron (99.9995%)
2
6
15
99.5
[55]
316 SS (Fe ≥61.85%)
2
7
17
-
[22]
Mild Steel (Fe 99.5%)
3
5
11
-
[22]
Iron (99.998%)
3
5
11
-
[22]
Iron (99.9995%)
3
6
11
99.5
[55]
316 SS (Fe ≥61.85%)
3
7
13.2
-
[22]
316 SS (Fe 65.5%)
3.175
6.9
9
100
[94]
Iron
3.2
0.5
3.5
-
[1]
Iron
3.2
0.69
4.2
99.7
[96]
Iron
3.2
0.73
4.78
-
[44]
Iron (99.995%)
3.2
1.0
4.35
99.5
[48]
Iron (99.999%)
3.2
5
11
99.99
[31]
316 SS
3.2
6.3
11
-
[50]
316 SS
3.2
6.89
11.2
≥99.75
[20]
Iron (99.954%)
3.2
6.9
11.4
100
[45]
Iron (99.995%)
4.0
0.7
3.5
99.5
[48]
Iron (99.995%)
4.0
1.0
3.83
99.5
[48]
Iron (99.995%)
4.0
1.4
4.0
99.5
[48]
- Not specified.
34
2
L ITERATURE R EVIEW
Non-Standard Geometries
Stoltzfus et al. [80] performed promoted ignition tests on rolled wire mesh. The RRMI
of 304 SS was slightly higher than that for carbon steel, 9.9 mm/s and 9.5 mm/s respectively, Table 2.2. The authors attributed the higher RRMI of 304 SS to the slightly
smaller wire diameter of the samples, 0.17 mm compared to 0.19 mm for carbon steel.
However the differences could be a result of measurement error which was not reported
and/or differences in alloying constituents.
Yeh et al. reported on the burning of aluminium sheets, 0.15 mm, 0.2 mm and 0.4
mm thick and 25.4 mm wide which were mounted horizontally [98, 99]. The RRMI
decreased with increasing sheet thickness which is similar to the trend of decreasing
RRMI with increasing rod diameter.
Steinberg et al. reported that oscillatory and irregular movement of the molten mass
made the measurement of RRMI using the visual method difficult for non-standard
geometries [17]. The authors described oscillatory motion of the molten mass when attached to thin sheets. The motion prevented an accurate determination of the RRMI by
the same method used for the cylindrical rods. Initial burning concentrated the molten
material along the bottom of one side of the sheet until the small amount of metal remaining on the far side formed a point. Propagation then transferred to this side, most
likely due to the small surface area and hence faster melting rate, until enough metal
had been consumed to cause propagation to transfer again to the opposite side and so
on. A drop-growth-and-detachment cycle, similar to that for the cylindrical rods, was
established and melting and burning on alternating sides of the sheet continued until
the sample was either consumed or self-extinguished. This process was observed for
both Aluminium 2219 and 316 SS.
Factors Affecting the Regression Rate of the Melting Interface
RRMI is affected by several factors including material composition, sample geometry,
temperature, pressure, oxygen purity and diluents. These factors are independent and,
to some extent, controllable. On the other hand, the structure and composition of the
subsystems within the molten mass also influence the RRMI, and these are dependent
on the controllable factors. The effect of these dependent factors on RRMI has not
been widely investigated.
35
2.2 G EOMETRY
AND
F LAMMABILITY
RRMI is consistently reported to increase with increasing oxygen pressure, although the rate of increase varies. Kirchfeld experimented with 1 mm and 2 mm
diameter iron wires and reported that the RRMI was linearly related to the square
root of pressure (P) for pressures up to 1.5 MPa [8]:
RRM I ∝ P 0.5
≤ 1.5 MPa.
(2.3)
Benz et al. [20] tested 3.2 mm diameter rods of 316 SS and reported that the dependence of RRMI on pressure varied depending on the pressure range:
RRM I ∝ P 0.075 ; 6.89 − 27.57 MPa
(2.4)
RRM I ∝ P 0.26 ;
(2.5)
27.57 − 68.91 MPa
The above two relationships indicate that RRMI increases rapidly at pressures exceeding 27.5 MPa but below this pressure the RRMI increases more gradually. Sato and
Hirano [23, 38, 39, 41] reported an RRMI versus pressure relationship for iron given
by [41]:
RRM I ∝ P 0.4±0.05
≤ 10 MPa.
(2.6)
An increase in RRMI with increasing pressure has been observed for many materials [22, 48, 80, 98, 100–102]. The gradient of the RRMI versus pressure curve is steepest at lower pressures and declines as the pressure increases, up to 10 MPa. This trend
has been theoretically attributed to a change in rate-limiting mechanism brought about
by a reaction surface saturated with oxygen [26, 44, 45]. Equation 2.5 indicates that
above 10 MPa the RRMI increases more rapidly with pressure and this could also be
due to changes in rate-limiting mechanism or changes in temperature.
RRMI is also proportional to rod diameter, or XA. Kirschfeld concluded RRMI
was inversely proportional to the XA [7]:
RRM I ∝
K
≤ 1.5 MPa
XA
(2.7)
where, K is a constant. This relationship has been verified for mild steel by other
researchers in tests at various pressures, Equation 2.8 - 2.11:
RRM I ∝ D−0.81 ≤ 20.7, 34.5 MPa
[50]
(2.8)
RRM I ∝ D−0.87
2 MPa
[38]
(2.9)
RRM I ∝ D−0.81
5 MPa
[38]
(2.10)
RRM I ∝ D−0.76
10 MPa
[38]
(2.11)
36
2
L ITERATURE R EVIEW
where, D is the rod diameter. The RRMIs for mild steel and iron rods, 1 - 3 mm
diameter, are similar, as shown in Figure 2.6 [22, 38]. The graph validates the comparison of RRMI results for mild steel in this thesis with modeling and experimental
data for iron. Figure 2.6 also shows that the RRMI increases with pressure, but the
effect of pressure on RRMI reduces as the pressure approaches 10 MPa. As the XA
increases/decreases, the RRMI does not continue to decrease/increase indefinitely. If
the pressure is held constant and the XA increases there reaches a point where the
sample will not sustain burning and the RRMI will effectively become zero. In the
case of progressively smaller rods the RRMI will reach some finite value based on the
manufacturing limitations for rods and wires.
This figure is not available online.
Please consult the hardcopy thesis
available from the QUT Library
Figure 2.6: Comparative RRMIs for mild steel [22] and iron [38].
Dunbobbin et al. [85] used the SA/V to explain the significant increase in the
RRMIs of thin wires and sheets over the RRMI of their thicker counterparts. SA refers
to the sample geometry and not the surface area of the molten mass. It is clear that
SA/V for powders would directly affect their rate of melting and burning since the
reaction surface is equal to the SA. However, for solid rods, this relationship is not
as straightforward, particularly when burning established at one end, rather than uniformly over the surface. For rods, SA/V per unit length is effectively the perimeter
divided by XA. As rod diameter increases, SA/V decreases, so too does the RRMI.
37
2.2 G EOMETRY
AND
F LAMMABILITY
Although this SA/V trend fits the observed experimental trend for RRMI it is unclear
from a heat transfer perspective why this is the case since XA is considered more important in terms of heat transfer than the perimeter [38, 39, 44, 50]. An investigation
into the relationship between perimeter, XA and RRMI form part of this thesis.
Internal subsystems and processes within the molten mass have also been suggested
to affect the RRMI. Benz et al. [50] reported that RRMI is a function of the reaction
rate and rod diameter. The authors attributed the inverse relationship between RRMI
and diameter to either a smaller ER for larger diameter rods, resulting in less heat
being generated within the molten mass, or to a decrease in heat transfer from the
molten mass to the solid rod in the case of larger rods. These claims were not verified
experimentally and are addressed in this thesis. Sato and Hirano [23] attributed the
change in RRMI with rod diameter to variable heat transfer from the molten mass to the
solid rod caused by changing SLI geometry. Steel rods, with and without gold plated
coatings, were burned in oxygen and the RRMIs of the coated rods were reportedly
20% higher than the same rods without the coating. The authors proposed that the gold
plating ‘wet’ the surface directly above the molten mass causing the mass to ‘climb’
up the rod increasing the SLI and consequently increasing heat transfer to the solid rod
and hence, RRMI. Although this is a valid argument, introducing gold into the system
would have changed the dynamics of the melting and burning of the rod and could
have acted as a catalyst. Palladium, a component of commonly used igniter wire has
been identified as a catalyst, however, catalysis is not a concern in normal gravity since
the igniter material is removed within the first one or two drops [102]. The effect of
the SLI on the RRMI will be investigated as part of this thesis by considering rods of
different shape.
In summary, there are many factors which affect the RRMI. It has been suggested
that the geometry of the SLI is one factor, this being the interface across which heat is
transferred to the solid rod. The ER, and hence the amount of energy generated within
the molten mass, is also critical, as is the location of the oxidation reactions within the
molten mass which will affect heat transfer paths. Therefore, continued research into
the complexities governing the RRMI in metals combustion is warranted.
2.2.3
Geometry and Material Rankings
One motivation for promoted ignition testing is to elucidate how, why and under what
conditions metals burn. Also important is the development of rankings for metals used
38
2
L ITERATURE R EVIEW
in or near oxygen systems, based on their oxygen compatibility. Rankings are used as
guidelines for material selection. A number of ranking schemes have been previously
employed, these include: TP, RRMI and oxygen index. Oxygen Index (OI) is defined
as the minimum concentration of oxygen that will support combustion of a sample
at room temperature, and typically ambient pressure, and is given as a volume percent [103]. Oxygen index is more commonly used in relation to non-metallic materials
since metals often require 100% oxygen to sustain burning. For metals which have
been shown to burn at far lower oxygen concentrations, e.g., titanium, it is a useful
measure [104]. OI is also used throughout the industrial gas industry, for instance, in
applications involving the cryogenic distillation of air, as the thin structural packing
used in the distillation columns has been shown to burn at oxygen levels considerably
lower than 99.5%. TP is primarily used to discern between the oxygen compatibility of
different metals. A high TP indicates high oxygen compatibility and conversely a low
TP indicates low oxygen compatibility. When materials have the same TP, the RRMI
can be used as a means to further discriminate materials on the basis of their oxygen
compatibility. Rankings are then used to select materials for oxygen service, however,
rankings based on a standard test geometry may not always hold for other geometries and may not be the most appropriate geometry to test in order to distinguish the
flammability of different metallic materials.
Table 2.4: Oxygen compatibility ranking for various engineering alloys based on testing 3.2 mm diameter rods [94].
This figure is not available online.
Please consult the hardcopy thesis
available from the QUT Library
McIlroy et al. [94] tested 3.2 mm diameter cylindrical rods of fifty different engineering alloys and ranked them according to their promoted ignition resistance as
measured by TP. The term promoted ignition resistance is perhaps misleading since a
39
2.2 G EOMETRY
AND
F LAMMABILITY
promoted ignition test is designed to provide an overwhelming ignition source so that a
material will sustain burning if the test pressure exceeds the materials’ TP [81]. Thus,
the test does not proffer an indication of ignitability or resistance to ignition. Rather,
what McIlroy et al. refers to as promoted ignition resistance, should be regarded as a
measure of oxygen compatibility. Table 2.4 is an extract of the summarised results.
Materials were classified as having high oxygen compatibility if they did not sustain
burning at pressures above 33.5 MPa, a low oxygen compatibility was designated if
materials indicated a propensity that they would sustain burning at pressures below 6.9
MPa (6.9 MPa was the lowest pressure tested) and materials were classified as having
an intermediate oxygen compatibility if they exhibited sustained burning at 33.5 MPa
but did not sustain burning at lower test pressures (often up to 24.1 MPa). Materials
were tested in three pressure ranges: 6.9 - 11 MPa, 20.7 - 24.1 MPa and 30.3 - 38.6
MPa. It should be noted that these pressures are not specified as TPs. Testing commenced at the highest pressure and was thereafter reduced if sustained burning was
observed. No mention is made to the number of tests conducted for each material or
test condition. Overall, the results indicate that nickel and copper based alloys have a
high oxygen compatibility whereas SS and aluminium alloys have a low oxygen compatibility. The researchers credited a higher nickel content, and hence lower heat of
combustion, as the reason Nickel 200, Monel® 400 and Inconel 600 exhibited a higher
oxygen compatibility than Hastelloy C-276, Incoloy 825 and Inconel 625. The high
oxygen compatibility of Nickel 200 and Monel® 400 is supported by Samant et al.’s
result that wires of 0.89 mm and 1.59 mm diameter did not burn more than 50% of
their initial length at pressures up to 34.58 MPa [88]. Copper was also tested for these
geometries with similar results.
Promoted ignition testing of Monel® 400 and Copper 100 meshes was reported
earlier, Section 2.2.1. The results from the promoted ignition testing of meshes appear
to better differentiate these less flammable materials than results based on 3.2 mm
diameter rods. Monel® 400 was found to burn at 20.79 MPa, Copper 100 at 12.17
MPa (the lowest static pressure tested in each case) and Nickel 200 mesh did not burn
at 34.58 MPa (highest pressure tested). The heat of combustion of Nickel 200, based on
nominal alloy composition, is 4.1 KJ/g, greater than that of Monel® 400, 3.6kJ/g [94].
The higher heat of combustion of Nickel 200 over that of Monel® 400 and the fact that
Monel® 400 burned at a lower pressure contradicts the argument proposed by McIlroy
et al., that higher oxygen compatibility is associated with a lower heat of combustion,
for the these two materials.
40
2
L ITERATURE R EVIEW
Zabrenski et al. [81] tested a wide range of engineering materials in the form of
6.4 mm diameter rods in oxygen under flowing conditions1 . The lowest pressure,
in 99.99% oxygen, at which the entire sample was consumed regardless of igniter
method, was deemed the TP. The results are in agreement with the relative rankings
published by McIlroy et al. which were developed based on test results for 3.2 mm
diameter rods [94]. These two works indicate that increasing the size (diameter) of
a sample above that of the standard geometry does not alter material rankings. The
works were based on TP but RRMIs have also been compared for increases in rod diameter. Steinberg et al. [17] tested several metals and found that for 4.8 mm diameter
rods the RRMIs lay within a 3.8 mm/s band but this decreased to a 2.3 mm/s band for
6.4 mm diameter rods. This result indicates that RRMIs converge as rod diameter increases, as shown in Figure 2.7 in which the RRMIs for 3.2 mm and 6.4 mm diameter
rods are plotted. The authors concluded that the composition of the rod may have a
greater effect on RRMI for small diameter samples.
This figure is not available online.
Please consult the hardcopy thesis
available from the QUT Library
(a) 3.2 mm ∅ Rods.
(b) 6.4 mm ∅ Rods.
Figure 2.7: RRMIs for 3.2 mm and 6.4 mm ∅ cylindrical rods of various engineering
alloys [17].
Decreasing, rather than increasing, sample geometry causes changes in the relative
rankings of metals based on TP [80]. This trend is reflected through Dunbobbin et
al.’s [85] experiments on structured metallic packing, which has a high SA/V made
from Aluminium 3003, 304 SS, brass and Copper 110. The oxygen concentration
necessary to support burning was used to rank the metals under this scheme and aluminium ranked superior to brass. This result contrasts with results for 6.4 mm rods
1
Flow rate was not specified, flow direction opposed direction of burning.
41
2.3 M ICROANALYSIS
tested under flowing conditions. Brass exhibited a TP of >10.34 MPa in 99.99% oxygen [81] whilst Aluminium alloy 6061 burned at a much lower 0.21 MPa under the
same conditions [93]. In the form of 3.2 mm diameter rods brass also exhibits a higher
oxygen compatibility than aluminium [94].
In summary, it is apparent that regardless of the ranking method, changes in sample
geometry can significantly alter the relative ranking of metallic materials. In addition,
although a material may exhibit a high oxygen compatibility for one particular geometry, it cannot be assumed that this will be the case for other geometries. This behaviour
emphasises the need for care when applying rankings based on promoted ignition testing of standard samples to non-standard geometries.
2.3
2.3.1
Microanalysis
General Techniques
Real-time analysis of the burning system is restricted due to the high temperature and
oxidising atmosphere which prohibits the use of intrusive instrumentation. Post-test
analysis of the remaining sample and detached mass (slag) is a useful way to gain
insight into the composition and structure of the burning system. Post-test samples fall
into one of three categories which are outlined below:
Self-extinguished: The sample extinguishes part way through the burning after some
period of self-sustained burning. Typically this occurs immediately after a drop has
detached [47] and the remaining attached mass and sample cool slowly.
Complete burn: The sample burns up to the sample holder and extinguishes due to
interaction (heat loss) with the sample holder which acts as a heat sink.
Quenched: The burning sample is forcibly extinguished by rapid cooling [32, 33] or
any other method that stops the reaction, such as changing the composition of the
atmosphere, e.g., replacing oxygen with argon [23].
The major difference between self-extinguished and quenched samples is their rate of
cooling. A sample is estimated to self-extinguish in less than ten seconds whilst a
sample extinguishes much more rapidly via quenching, under one second in the case
of water quenched samples, as indicated by a visible reduction in luminosity. Studies
42
2
L ITERATURE R EVIEW
at test pressures ranging from 0.3 MPa to 10 MPa that employed slow extinguishment
of the samples reported that the slag was typically composed of oxide, with very little, if any, unreacted material [37, 39, 41, 44]. It has since been shown, for iron and
aluminium rods tested at 0.69 MPa, that the fraction of unreacted material in the slag
is significantly higher in water quenched samples which are rapidly extinguished and
cooled [32, 33]. Under standard test conditions, after a drop detaches, continued reaction occurs between the melted but unreacted iron present in the drop and oxygen in the
atmosphere, as well as any excess oxygen which has been incorporated into the drop.
Rapid quenching significantly reduces the period of time during which these reactions
continue to occur, thus, the composition of the quenched slag gives a better representation of the actual physical and chemical state present during burning and immediately
prior to drop detachment.
Extensive microanalysis of both self-extinguished and quenched rods and detached
drops was reported by DeWit [47]. Microanalysis tools were used to obtain detailed
image and species distributions of the sectioned melted and resolidified rod and slag
samples. Scanning Electron Microscopy (SEM) was used to obtain high-resolution
images of the metallic surfaces. When operated in Back-Scattered Electron (BSE)
mode the brightness of the image is proportional to the atomic number (Z) of the
element or the average atomic number of the molecule present. Pure iron (Z = 26)
appears the brightest and the oxides, ranked in order of decreasing brightness, are
wustite (FeO: Z = 17), magnetite (Fe3 O4 : Z = 15.7) and hematite (Fe2 O3 : Z = 15.2),
respectively. Electron Probe Microanalysis (EPMA) was used to accurately analyse the
composition of the samples. Two techniques are typically used to gather compositional
data, Energy Dispersive Spectrometry (EDS) which utilises the characteristic energies
of emitted x-rays to identify elements and Wavelength Dispersive Spectrometry (WDS)
which identifies elements by making use of the characteristic wavelength of emitted
x-rays. An alternative microanalysis technique that was used to gather compositional
information was X-Ray Diffraction (XRD). XRD can be used to identify the crystalline
compounds present in the sample but this technique requires that the sample be ground
to a fine homogeneous powder.
2.3.2
Microanalysis of Iron/Mild Steel
This section addresses the limited literature relating to the microanalysis of iron and
mild steel as iron and mild steel were tested in the experimental component of this
43
2.3 M ICROANALYSIS
thesis. It was initially reported that slag from tests at 0.3 - 10 MPa consisted predominantly of Fe3 O4 with a smaller amount of Fe2 O3 present [31, 41, 45, 105]. The reports
were from quenched drops but did not make the method of quenching clear in all cases.
There was no mention of unreacted metal in the slag from burned rods in these reports.
In contrast, a significant proportion of melted and resolidified unreacted metal was
clearly visible in the water quenched slag examined by DeWit [47] as shown in Figure 2.8, for testing at 0.69 MPa. The resolidified iron within these samples, although
unreacted, was found to be oxygen rich and encased in a thin oxide shell.
This figure is not available online.
Please consult the hardcopy thesis
available from the QUT Library
(a) Optical image.
(b) SEM BSE image indicating oxygen
rich but unreacted iron within the detached drop.
Figure 2.8: Quenched detached drops for 3.2 mm iron rods burned at 0.69 MPa [47].
Nubs of extinguished rods have also been examined in order to identify both the
phases present and their location within the molten mass during burning. Benz et
al. [50] reported visible regions of unoxidised metal in a cross-sectioned self-extinguished
nub of 316 SS and concluded that there was limited mixing or a lack of oxygen within
the molten mass. Steinberg et al. [45] confirmed the presence of a melted and resolidified iron core located between the solid metal and product oxide in quenched iron
nubs. Based on the relative surface tension of the liquid iron and liquid iron oxide the
authors concluded that only the oxide component of the molten mass detached during
burning. This contradicts the recent results reported by Suvorovs et al. [32] which
confirmed the presence of unreacted metal in quenched slag and have also shown isolated detached drops of melted and resolidified iron within the attached molten mass,
as shown in Figure 2.9.
The quantities of reacted and unreacted material in the quenched nubs and detached
drops of burning rods are important as this information allows ER to be assessed. The
ER in this context is the fraction of material that reacts whilst a drop is attached to
the burning rod. The ER can therefore be assessed by examining quenched detached
44
2
L ITERATURE R EVIEW
This figure is not available online.
Please consult the hardcopy thesis
available from the QUT Library
Figure 2.9: Post-test nub of quenched and sectioned iron rod burned at 0.69 MPa [47].
drops, assuming that reactions occurring between the time of drop detachment and
quenching are limited. Knowledge of the extent to which the melted iron reacts whilst
attached to the rod can be used to verify rate-limiting mechanisms and assess relative
heat transfer to the solid rod. For instance, if the solid rod melts but this material does
not react, the material acts as a heat sink, but, if the material reacts it generates energy
which is then transferred back to the solid rod. For these reasons, microanalysis is a
useful tool to improve the understanding of the burning system.
The SLI is also important in terms of heat transfer to the solid rod. Sato and Hirano [23] commented on a relative increase in the size of the SLI of argon quenched
rods of mild steel that were coated in gold plating, as compared to un-coated rods.
After removing the attached oxide layer from both the coated and un-coated samples
the authors made inferences about the shape of the SLI. It is not clear in their paper
whether the surface they examined was actually the SLI as stated or rather the interface
between reacted oxide and unreacted molten metal. The SLI is difficult to distinguish
by eye or even using SEM BSE analysis since unmelted solid iron appears similar to
melted and resolidified but unreacted iron, as shown in Figure 2.10a. A more appropriate method with which to visualise the SLI is by acid etching the sectioned samples
and viewing them under polarised light. Images of iron treated in this way were unavailable, however, the aluminium sample pictured in Figure 2.10b clearly indicates
the contrast in grain structure between the heat affected zone (HAZ, heat affected but
unmelted metal) and the melted and resolidified but unreacted material. A combination
of both normal white light and polarised light are therefore useful to identify zones and
interfaces within the rod and attached nub.
In summary, microanalysis provides a useful tool with which to gain detailed information about the composition of the phases present in post-test nub and slag samples
45
2.4 S TATISTICAL M ETHODS IN M ATERIALS T ESTING
This figure is not available online.
Please consult the hardcopy thesis
available from the QUT Library
(a) Normal white light.
(b) Etched, viewed with polarising light.
Figure 2.10: Quenched aluminium rod viewed with an optical microscope (0.69
MPa) [47].
as well as their location and distribution. Analysing quenched samples has been shown
to be more informative than analysing self-extinguished samples since rapid cooling
essentially ‘freezes’ the burning rod thereby retaining much of the compositional and
physical information. Microanalysis also allows key surfaces within the burning system to be clearly identified, in particular the SLI.
2.4
Statistical Methods in Materials Testing
Promoted ignition testing is a series of Bernoulli trials. Tests are conducted independently under identical conditions a specific number of times with one-of-two possible
outcomes, burn or no-burn. The number of tests that should be conducted is disputed
and, importantly determines the confidence of the results. Theory associated with
confidence levels and the binomial distribution is presented in Chapter 3 along with
statistic methods relevant to the modelling of promoted ignition test data.
Of the three major standards for promoted ignition testing, ASTM G124-95 (2003) [16],
NASA-STD-6001(1998) [28] and ISO 14624-4(2003) [29], none address the statistical
aspects associated with the test method and results. The scope of all three standards is
46
2
L ITERATURE R EVIEW
similar, to provide a means of assessing the flammability of materials in gaseous oxygen thus providing a basis from which to compare the behaviour of different materials
in an economic fashion, that is, with the minimum number of data points. The similar
NASA and ISO standards include a statement regarding the minimum permitted tolerances for the measurement of pressure, sample dimensions and burn length, but no
information is provided on the confidence of test results based on the minimum number of tests specified by the method. Further, the ASTM standard states, “The precision
and bias of this test method have not been determined.” [16].
NASA-STD-6001 states that at a pressure where a no-burn is first observed, four
additional tests must be conducted. Thus, five no-burn results at a given pressure is
sufficient to certify that sustained burning does not occur at that pressure, hence the
material is permitted to be used under those conditions. ISO 14624-4 stipulates that
ten tests be conducted and ASTM G124-95 (2003) states that several tests should be
conducted.2 The scope of the ASTM standard, specifically for the testing of metallic
materials, reads:
“This test method covers a test apparatus and technique to determine the minimum test gas pressure that supports self-sustained combustion (the threshold
pressure) and the average regression rate (apparent burn rate) of a standard
specimen of a metallic material that has been ignited using a suitable promoter.” [16]
This statement implies that there exists a pressure at which self-sustained burning occurs and for all pressures below this threshold self-sustained burning will not occur.
However, the standard also discusses the need to conduct several tests at pressures
where a no-burn is first observed. This contradicts the idea of a TP, above which the
material always exhibits self-sustained burning and below which the material never
exhibits self-sustained burning. The test method also discusses “discernible transitional behaviour” for some materials and supports the concept of a Promoted Ignition
Combustion Transition (PICT) curve [21].
The PICT curve, introduced by Zawierucha et al. [21], is formed by plotting posttest sample length against test pressure. This results in a curve with three distinct
regions: upper shelf, transition and lower shelf, as shown in Figure 2.11. The upper
shelf region covers lower test pressures, pressures below the TP. Encompassing the
2
The former 1995 version of Standard G124 stipulated five tests be conducted.
47
2.4 S TATISTICAL M ETHODS IN M ATERIALS T ESTING
TP is a transition zone where there is a greater spread in burn length data, and finally,
pressures exceeding the TP fall in the lower shelf region since test samples usually burn
to completion. The shape of the curve varies depending on the material, geometry,
environmental factors and of course the number of tests conducted. The change in
shape due to differences in material composition is exemplified in the PICT curves for
Hastelloy® G-3 and Hastelloy® C-276 shown in Figure 2.12.
This figure is not available online.
Please consult the hardcopy thesis
available from the QUT Library
Figure 2.11: Schematic of Promoted Ignition Combustion Transition Curve [21].
This figure is not available online.
Please consult the hardcopy thesis
available from the QUT Library
(a) PICT curve Hastelloy® G-3.
(b) PICT curve Hastelloy® C-276.
Figure 2.12: Promoted Ignition-Combustion Transition Curve for Hastelloy® [21].
48
2
L ITERATURE R EVIEW
Engel et al. [106] presented a similar approach in their analysis of promoted ignition data for a variety of non-metallic materials. The work focussed on OI test data
rather than TP, but their conclusion “The concept that there is a single oxygen level
that defines whether a sample will burn less or more than 15.24 cm is seen to be quite
inadequate” is also appropriate for the concept of TP. The authors presented cumulative burn length distribution curves which plot the percentage of samples which exhibit
a specific burn length or less, against burn length, as shown in Figure 2.13 for silicone
rubber and Kydex® 100. These plots are useful as they illustrate the underlying trend
in the data which is more beneficial than a single number, above which or below which
a material is/is not considered flammable. An engineer or designer can then assess
the fraction of samples that burned only a small amount, and the fraction of samples
that burned considerably for various oxygen concentrations. However, this approach
is not as useful as applying the available data to generate a model which can be used to
predict the behaviour of future tests based on past results. A modelling approach will
be addressed in relation to promoted ignition testing as part of this work.
This figure is not available online.
Please consult the hardcopy thesis
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(a) Silicone rubber.
(b) Kydex® 100.
Figure 2.13: Cumulative distribution and sample frequency curves for silicone rubber
and Kydex® 100 [106].
A modelling approach was used to interpret binary test data from an alterative
test method which is also used to evaluate material flammability. ASTM D2512-95
Standard Test Method for Compatibility of Materials with Liquid Oxygen (Impact Sensitivity Threshold and Pass-Fail Techniques) [107] or the similar NASA STD 6001
Test 13A Flammability, Odor, Offgassing, and Compatibility Requirements and Test
Procedures for Materials in Environments that Support Combustion [28] describe a
test method which involves impacting a sample covered in liquid oxygen with a striker
pin, released from various heights, in order to evaluate the threshold energy level of
the material. The threshold energy level is defined as a level for which no reactions in
twenty tests are observed. It is interesting that within the same organisation, ASTM,
49
2.4 S TATISTICAL M ETHODS IN M ATERIALS T ESTING
for impact testing the threshold point is associated with no-reaction test results (conservative), yet for promoted ignition testing the threshold point is associated with burn
results (non-conservative). Discussion surrounding statistical inferences that can be
made from impact test data is covered in greater depth in the literature than is the case
for promoted ignition testing.
In a study on contaminant ignition using the pneumatic impact test, where a sample is impinged with high pressure gaseous oxygen, Pedley et al. [108] applied logistic
regression to model the reaction/no-reaction results. The logistic regression model
takes all available data into account to model the reaction probability. The model is
based on transforming the reaction probability such that the transformed value can be
expressed linearly. Logistic regression modelling is covered in more detail in the following chapter. The authors presented a model with statistically significant fitted parameters although their reported significance levels were likely actually confidence levels
since the values exceeded 90% and significance is normally associated with small values (0.01-0.05, 1% - 5%). The model parameters are expected to be significant since
pressure was the single independent explanatory variable used to model the reaction
probability. The model failed to identify the ignition point (transition from zero to a
positive reaction probability) at low contaminant levels since the logistic regression
model is asymptotic at the tails.
In papers on mechanical impact testing in liquid oxygen and pneumatic impact
testing with gaseous oxygen on non-metallic materials, Moffett et al. [109, 110] commented on the statistical analysis of binary data. The authors quantified the lack of
confidence associated with test data claiming that there is a 36% chance of observing
no-reactions in twenty tests when the material has reaction probability of 5%. These
number are derived from the binomial probability distribution. They concluded that
logistic regression modelling was useful to distinguish the ignition sensitivities of different materials and was superior to the standard technique of identifying a single
reaction in a set of twenty tests. In a later paper [111] the authors retracted their previous finding that the logistic regression model was appropriate at discerning differences
in reactivity between materials, claiming that, when a larger data set was considered,
the variation in data was too great for the model to be useful. The two contradictory
findings were based on different sets of materials, the former compared two batches of
Nylon, and the later compared different batches of Teflon®and Viton®. Although logistic regression modeling may not have been useful in this instance it is likely that the
usefulness of the approach depends on the materials, test conditions and the number
50
2
L ITERATURE R EVIEW
of test performed. For materials with very similar reaction sensitivities a larger number of tests would be needed to confidently distinguish the materials. It was unclear
whether the authors’ attempt to distinguish different materials using logistic regression
was based on assessing differences in the logistic models that were developed or rather
by comparing the relative overlap of 95% confidence intervals for the data at various
energy levels. Comparing overlap in the 95% confidence intervals for the means is not
a valid approach, rather a confidence interval should be developed for the difference
between the means, an approach discussed in more detail in Chapter 3. Recent papers by Forsyth and Stoltzfus [112] and Hirsch et al. [113] offer logistic modelling as
promising for evaluating data on ignition resistance/sensitivity in the cases of particle
impact and autoignition temperature, respectively.
A logistic regression approach to interpret promoted ignition test data will be explored in this thesis.
2.5
Summary
Research investigating the combustion of metallic materials is yet to provide a complete and detailed picture of the burning system. One particular aspect that clearly
requires further study is the effect of the sample geometry on the burning process. Exploring the effect of sample geometry on the subsystems and the physical and chemical
processes occurring within the molten mass will contribute to an understanding of the
interdependence of geometry, test pressure, RRMI, ER and heat transfer. It has been
shown that the sample geometry significantly affects the RRMI and TP of a material.
Consequently, the relative ranking of materials based on their oxygen compatibility are
affected. Thus, a more complete understanding of how sample geometry influences the
burning process will be of great help in the application of the results from standardised
tests to industrially relevant systems and configurations. Furthermore, an exploration
of the statistical nature of the promoted ignition test and a simple modelling approach
with which to interpret promoted ignition test data would be beneficial.
51
C HAPTER 3
S TATISTICAL T HEORY
This chapter presents basic statistical theory that will be applied or referred to in Chapters 5, 6 and 7. Experiments were performed in order to assess the effect of sample
geometry on flammability, by way of the RRMI. It was therefore important to develop
and implement suitable statistical methods for evaluating and comparing RRMI data.
A novel method for calculating the RRMI from the promoted ignition test video is
described as it forms the basis for much of the statistical work.
Section 3.1 focusses on the statistical analysis of RRMI data in the case of one or
more samples, including measures for checking normality, analysis of variance and for
calculating confidence intervals. Section 3.2 presents an approach to statistical modelling by way of regression. Basic linear regression is briefly discussed and leading on
from this is a discussion of logistic regression. Logistic regression was identified as
having suitable qualities for the modelling of binary promoted ignition test data. Following the logistic regression analysis is an examination of the binomial distribution,
its applicability to promoted ignition testing and a simple method for calculating exact
confidence intervals based on burn/no-burn promoted ignition test data.
3.1
A Statistical Approach to Calculating RRMI
Multiple methods with which to calculate the RRMI have been reported. Predominantly, visual interrogation of the test video to examine the upward movement of the
molten mass and hence track the SLI, is performed. An alternative method involves
the use of thermopiles placed at intervals along the walls of the combustion chamber [17, 114]. The thermopiles register the passing molten mass and the RRMI can
52
3
S TATISTICAL T HEORY
be calculated based on the time between thermopile readings. Another method involves the use of a gravimetric transducer to record the mass of the rod and attached
molten region as a function of time [36]. In addition, ultrasonic transducers have been
used [44, 77, 96]. In these examples the location of the SLI is plotted versus time and a
straight line is fitted to the data over the duration of the test, with the slope giving the
overall RRMI for the test.
3.1.1
One-Sample Approach
Rather than calculate an RRMI based on the overall height difference of the SLI over
the duration of the test, as is commonly done, the RRMI was calculated on a drop cycle
basis. The point immediately after a drop detaches marks the end of one drop cycle
and the start of the next drop cycle. Given that the video record of a promoted ignition
test is divided into discrete frames, the start/end of a drop cycle was defined as a frame
in which a drop was observed to be attached to the rod, with the drop detaching at
some point between the frame in question and the following frame. The drop cycle
RRMI was calculated from the change in height of the SLI over a single drop cycle
and the total time of the particular cycle. The driving force behind the decision to
calculate the RRMI on a drop cycle basis was of a statistical nature. In order to obtain
sensible errors and confidence intervals for the RRMI, it is necessary to have a number
¯
of independent observations from which the sample mean, X:
N
X
¯= 1
Xi
X
N i=1
(3.1)
and sample standard deviation, S, the positive square root of the sample variance:
S=
N
X
1
¯ 2
(Xi − X)
N − 1 i=1
! 21
(3.2)
where, X1 , X2 , ..., XN represent the individual observations with N the total number of
observations [115], can be calculated. The mean is simply the sum of the data divided
by the number of data points and gives an average value. The standard deviation is
the positive square root of the sample variance and is a measure of the variability of
the data points around their mean. The sample variance is equal to the sum of the
differences between each individual data point and the sample mean, divided by the
number of data points less one [116, 117].
53
3.1 A S TATISTICAL A PPROACH
TO
C ALCULATING RRMI
Each drop cycle represents a single observation from which an RRMI can be calculated, hence, multiple drop cycle RRMI values are available for each test. As mentioned above, the sample mean and standard deviation given by Equations 3.1 and 3.2
rely on the availability of independent observations. For the observations to be considered independent they must be uncorrelated. Correlation between data can be explored
in a number of ways and is done so in this thesis via time series plots and drop series plots. The time series plots involve plotting each drop cycle RRMI in the order
in which it occurred (i.e., with increasing time). The axes of a drop series plot represent the value of the current drop cycle RRMI (x) and the value of the next drop cycle
RRMI (y). Both graphs can be used to visualise trends in the data that may suggest
correlation between drop cycles.
Assuming independent drop cycles, although the independence of the drop cycle
data is examined and verified in Chapter 5, the average of the drop cycle RRMIs for a
single test gives a mean RRMI for that test.
3.1.2
Multi-Sample Approach
The sample mean and standard deviation are used to estimate the population mean,
µ and standard deviation, σ, which in this case are unknown. Hence, the larger the
number of samples and observations available, the better the estimate of the population mean and standard deviation. In cases where a number of samples are available
it is important to assess the independence of the data, and whether the data appears
to be derived from the same population before pooling all observations together. In
the promoted ignition context, before combing the drop cycle RRMIs for each of the
five tests conducted for the same sample geometry it is important to verify that there
are in fact no test-to-test variations that caused significant differences in the RRMIs.
Significant differences between the RRMIs of particular rods implies that the tests are
not representative of the same population and this result invalidates the approach of
combining all the drop cycle data together to acquire a representative RRMI for the
geometry in question.
Rod series plots were used to assess similarities/differences between the individual
rods of the same geometry. The plots involve plotting the drop cycle RRMI data for
each rod of the same geometry in series. These plots allow a qualitative assessment of
differences between tests but a quantitative assessment is desirable and can be achieved
through ANalysis Of VAriance (ANOVA) testing. ANOVA is a means of assessing the
54
3
S TATISTICAL T HEORY
source of variability in the data. The method assesses whether variability is attributed
to variability in the RRMI data for individual rods or due to variability in the RRMI
data between different rods of the same geometry [117]. A judgement can then be
made as to whether the mean RRMI for each rod is significantly different. If the means
are found to be the same, the drop cycle RRMIs for each rod of a single geometry can
be pooled to calculated the sample mean and standard deviation for that geometry in
the same manner as for the one-sample case.
3.1.3
Confidence Intervals
Means
“A confidence interval for a parameter is a data-based interval of numbers thought
likely to contain the parameter possessing a stated probability-based confidence or
reliability” [115]. A confidence interval is determined based on collected data and
it is generally accepted that increasing the number of samples reduces the width of a
confidence interval [118].
In this setting we are assuming the data is from a normal distribution with mean, µ
and standard deviation, σ:
X1 , X2 , ......., XN ∼ N (µ, σ).
(3.3)
In many situations the parameter for which the confidence interval is desired is the
population mean. For cases where the population variance is unknown the sample
mean and sample standard deviation are used to generate a test statistic on which to
base the confidence interval. The test statistic, ts is given by:
¯ −µ
X
(3.4)
ts =
SE
¯ is the sample mean, µ is the population mean and SE is the standard error.
where X
The standard error is the estimate of the standard deviation of the sample mean and is
a measure of how well the population mean was estimated. The standard deviation is
given by:
σ
√
(3.5)
N
where, N is the number of observations. However, in the case of an unknown population variance, standard deviation is estimated by the SE:
S
SE = √ .
N
55
(3.6)
3.1 A S TATISTICAL A PPROACH
TO
C ALCULATING RRMI
A confidence interval has an associated confidence level, C:
C = 100(1 − α)
(3.7)
with 0 ≤ α ≤ 1 where α is the chosen significance level. The confidence interval is
formed using the appropriate test statistic:
!
¯ −µ
X
P r z1 <
< z2 = C
(3.8)
σ
√
N
rearranged to give:
¯ + z2 √σ
¯ − z1 √σ < µ < X
Pr X
N
N
=C
(3.9)
where z1 and z2 are from the standard normal distribution, N(0,1), such that the probability that the interval contains the mean equates to the desired level of confidence [119,
120].
In the case of small sample sizes the test statistic cannot be considered to have
an approximately standard normal probability distribution. Rather, the t-distribution
is appropriate for both one or two-sided confidence intervals [115, 121]. Hence the
interval in Equation 3.9 can now be rewritten as:
S
S
¯ + tα/2,N −1 √
¯ − tα/2,N −1 √ < µ < X
=C
(3.10)
P X
N
N
where tα/2,N −1 is the value taken from the t-distribution for the 100(1 − α/2) quantile
with (N − 1) degrees of freedom such that the area between tα/2,N −1 and −tα/2,N −1
represents the probability associated with the confidence level, represented graphically
in Figure 3.1. The upper and lower limits of the interval are thus given by:
S
S
¯ + tN −1,α/2 √
¯ − tN −1,α/2 √ , X
X
.
(3.11)
N
N
Confidence intervals for the mean RRMI for each test were calculated as were
confidence intervals for the mean RRMI for each geometry.
Differences Between Means
The above confidence interval analysis can be extended to develop confidence intervals
for the difference between two means, called a t-test. This approach is particularly
56
3
S TATISTICAL T HEORY
This figure is not available online.
Please consult the hardcopy thesis
available from the QUT Library
Figure 3.1: 100(1-α)% confidence limits from the T-distribution with N degrees of
freedom [119].
relevant to investigate the effect of sample shape on the RRMI. RRMIs obtained from
the promoted ignition testing of cylindrical, rectangular and triangular samples were
compared using the following method.
In cases where the number of samples is small and it can be assumed that the
underlying distribution of each sample is normal a further assumption, that σ1 = σ2 =
σ, where σ is the common population standard deviation, enables a suitable test statistic
with a t-distribution to be calculated. The individual sample standard deviations, S1
and S2 , can be used to create an estimate of σ in the form of the pooled sample standard
deviation, SP [115]:
(N1 − 1)S12 + (N2 − 1)S22
.
(3.12)
SP2 =
N1 + N2 − 2
Then, based on the test statistic, the probability that the interval contains the true difference between means (µ1 − µ2 ) is given by:


¯
¯
(X1 − X2 ) − (µ1 − µ2 )
q
P r −tα/2,df <
< tα/2,df  = C
(3.13)
1
1
SP N1 + N 2
where tα/2,df is from the t-distribution for the 100(1 − α/2) quantile with df = N1 +
N2 − 2. The bounds for the interval are then given by:
r
r
1
1
1
1
¯1 − X
¯ 2 ) − tα/2,df SP
¯1 − X
¯ 2 ) + tα/2,df SP
(X
+
, (X
+
(3.14)
N1 N2
N1 N2
57
3.2 S TATISTICAL M ODELLING
The assumption of equal population variance can be tested. The ratio of the two sample
variances has an F-distribution, provided that the samples are random and independent
and σ1 = σ2 = σ can be assumed [117]. With the ratio of sample variances as the test
statistic, an F-test can be performed based on a critical F value obtained for the chosen
significance level.
3.2
Statistical Modelling
Statistical methods are widely used to analyse data, and regression analysis is a commonly used statistical technique. Regression models are relevant to many scientific and
engineering applications [122]. Unfortunately, statistical approaches have seen limited
application in the field of promoted ignition testing. This section outlines the theory of
simple linear regression and describes logistic regression and its relevance to the field.
3.2.1
Linear Regression
Regression can be used to predict the value of a dependent variable (response variable)
from one or more independent variables (predictors or regressors). The basic simple
linear regression model is:
Y = β0 + β1 X + (3.15)
where Y and X are the dependent and independent variables respectively, β0 and β1
are the intercept and slope parameters to be estimated, and is the random error term.
If a regression model fits data well then it is assumed that future Y values will be
well predicted by the model if their corresponding X values are within the range from
which the model was initially built.
The regression model is based on the following implicit assumptions [122–125]:
I.
II.
III.
IV.
E() = 0 ⇔ E(Y) = β0 + β1 X
The errors have mean zero.
Variance(Y) = Variance() = σ 2
The errors have constant variance.
The errors are uncorrelated.
The errors are normally distributed, thus, from III., are independent.
58
3
S TATISTICAL T HEORY
In many situations simple linear regression may be insufficient to model the data
and extra variables must be included in the model (X1 , X2 , X3 ). These models are
referred to as multiple linear regression models and are a form of linear regression
as the relationship between the independent and dependent variables, X’s and Y, is
described by a linear function of the β parameters [126, 127]. The multiple linear
regression model can be written as:
Yi = X0 i β + i
(3.16)
where X0 i = [1, Xi1 , Xi2 ,...,Xik ] and β 0 = [β0 , β1 ,β2 ,...,βk ].
Each regressor in the model has an associated coefficient, β, which is estimated
using the available data. Coefficients are commonly estimated using the Method of
Least Squares. The method is based on minimising the sum of the squares of the errors
with respect to β0 and β1 . The residual (ˆi ) is the deviation of the observed value, Yi ,
to the predicted value, Yˆi :
ˆi = Yi − Yˆi = Yi − (βˆ0 + βˆ1 Xi ),
i = 1, 2, ..., n
(3.17)
where the predicted value is represented by βˆ0 + βˆ1 Xi , and β0 and β1 are assumed to
be fixed known values. This gives the least squares criterion:
S(β0 , β1 ) =
n
X
(Yi − β0 − β1 Xi )2 .
(3.18)
i=1
The method produces unbiased estimates for the coefficients regardless of the form of
the distribution of the errors [122, 128], provided assumption I. holds.
The Method of Maximum Likelihood is an alternative means by which the coefficients in the regression model can be estimated. The method is based on maximising
the likelihood of the unknown model coefficients based on the observed data. The
likelihood function:
L(β, σ) =
N
Y
i=1
1
2
1
√ e[− 2σ2 (Yi −β0 −β1 Xi ) ]
σ 2π
(3.19)
is the joint distribution of the observed data (so, from independence, the product of the
probability density function of the observed data), for each observation, as a function of
the unknown parameters. For simple linear regression, under the normal assumptions,
the least square estimators and the maximum likelihood estimators are the same [126].
59
3.2 S TATISTICAL M ODELLING
In many instances there may be an underlying non-linear relationship between the
response variable and the regressor, in which case it may be necessary to use a transformation. A transformation is implemented to allow a linear regression of the transformed data to be performed. The following section describes logistic regression which
is based on the logistic transformation.
3.2.2
Logistic Regression
Logistic regression is a particular form of the Generalised Linear Model (GLM). In
the case of GLM’s the response variable belongs to the exponential family of distributions including the normal, Poisson, binomial, exponential and gamma distributions [122, 127, 128]. GLM’s are often used when the normality and constant variance
assumptions are not satisfied.
In the case of a standard promoted ignition test only two possible outcomes exist;
burn (success) or no-burn (failure). The tests are independent and are conducted a number of times at various pressures and the number of burns and no-burns are counted.
In this situation the appropriate distribution for the response variable is the binomial
distribution. The response variable is considered a Bernoulli random variable that can
have only two possible values, 1 or 0 (success or failure).
Consider the binomial distribution:
Y ∼ Bin(N, p)
(3.20)
where, p is the probability of success, N is the number of independent trials and Y is
the number of successes.
A binary response variable violates the regression assumptions II. and IV. which
assumed constant variance and normally distributed errors, respectively. Since the
response variable can take only two possible values, the errors also take on only two
possible values, hence, they are not normally distributed. The assumption of constant
variance also does not apply since the probability distribution of Y is given by:
Pr(Y = x) =
N!
px (1 − p)N −x
x!(N − x)!
(3.21)
where x = 0,1,...N. The mean (expected value) and variance are given by:
E(Y ) =
N
X
x=0
x
N!
px (1 − p)N −x = N p
x!(N − x)!
60
(3.22)
3
S TATISTICAL T HEORY
and:
Var(Y ) =
N
X
x=0
(x − N p)2
N!
px (1 − p)N −x = N p(1 − p)
x!(N − x)!
(3.23)
respectively [129]. It is clear that the variance is a function of the mean and is dependent on p. Since p is dependent on the regressors the variance is not constant.
In light of the violation of the standard assumptions an alternative approach is
needed. Focussing on assumption I. a model for E(Y ) = N p is required, that is, a
model for p(X), the probability of a success. As this probability must lie between zero
and one, using the relationship:
p(X) = β0 + β1 X
(3.24)
requires considerable restriction on X for the different possible values of β0 and β1 .
One method of proceeding is to use the logit transformation or logistic transformation.
A logit transformation of the probability of a success is given by:
p
0
(3.25)
gˆ = X β = ln
1−p
with gˆ referred to as the linear predictor. The logistic transformation of the response
function is given by:
0
e(X β)
(3.26)
E(Y ) = p =
1 + e(X0 β)
[122, 129]. The typical s-shape of the logistic response function, bounded by 0 and 1,
is shown in Figure 3.2.
Two methods can be used to solve for β. The Method of Least Squares can be
applied to the transformed logistic model, Equation 3.25, in cases where repeated observations of the response have been recorded at each level of the independent variable.
An alternative and more generally applicable method, particularly if repeated observations are not available, is the Method of Maximum Likelihood [126].
A number of software programs can be used to fit a logistic regression model to binomial data and most use the Method of Maximum Likelihood to obtain the estimates
for β. R-Project is a freely available package for statistical computing and is based
on the S-PLUS® programming environment. The software is built around a programming language with various add-on packages available to extend the range of optional
functions [130]. Chapter 7 presents an approach to the modeling of promoted ignition
test data via logistic regression using the R-Project package.
61
3.2 S TATISTICAL M ODELLING
Figure 3.2: Typical S-shaped curve of the logistic response function.
Complications may arise in settings where sample sizes are small. Small sample
sizes negate the common assumptions, valid for large sample sizes, that estimated
model parameters are asymptotically normally distributed and that the likelihood ratio
has an asymptotic chi-square distribution [131]. Most software packages compute the
maximum likelihood estimates and corresponding confidence intervals based on the
assumption of large sample sizes [131].
ˆ are given by:
Confidence intervals for the coefficients, β’s,
ˆ βˆi ), βˆi + z1−α/2 SE(
ˆ βˆi ) .
βˆi − z1−α/2 SE(
(3.27)
In the context of promoted ignition testing, the confidence interval for the reaction
probability (probability of a success) can be evaluated by first evaluating the confidence
interval for the logit, Equation 3.25, at specific values of pressure (x). The confidence
interval for the estimated logit is given by:
ˆ g (x)]
gˆ(x) ± z1−α/2 SE[ˆ
(3.28)
ˆ equal to the square root of the estimated variwith the estimated standard error (SE)
ˆ
ance (Var):
q
q
ˆ βˆ0 , βˆ1 )
ˆ
ˆ βˆ1 ) + 2xCov(
ˆ
ˆ βˆ0 ) + x2 Var(
SE[ˆ
g (x)] = Var[ˆ
g (x)] = Var(
(3.29)
where the specific variance and covariances are obtained from the covariance matrix
provided by software packages. The bounds of the confidence intervals for the reaction
62
3
S TATISTICAL T HEORY
probability evaluated for the chosen value of pressure is then given by [131–133]:
!
ˆ g (x)]
ˆ g (x)]
gˆ(x)−z1−α/2 SE[ˆ
gˆ(x)+z1−α/2 SE[ˆ
e
e
.
(3.30)
,
ˆ g (x)]
ˆ
gˆ(x)−z1−α/2 SE[ˆ
1+e
1 + egˆ(x)+z1−α/2 SE[ˆg(x)]
Small sample sizes may negate the assumption that estimated model parameters
are asymptotically normally distributed and that the likelihood ratio has an asymptotic
chi-square distribution [131]. Exact methods have been proposed [134], along with
algorithms to evaluate the complex and computationally intensive exact method solutions [135–140]. Derivations for the theory behind the approach can be found in
Hosmer and Lemshow [131] and Mehta and Patel [141]. The approach is based on developing a solvable exact probability distribution from which a conditional maximum
likelihood estimate for the slope parameter can be calculated. Conditional maximum
likelihood estimators found in this way are typically smaller than the corresponding
maximum likelihood estimates, as are their standard errors [131]. The confidence
interval for the coefficients is slightly larger, as expected due to the smaller sample
size [132, 134]. For the data sets selected in this work the large sample assumptions
are reasonable.
3.3
Binomial Distribution Confidence Intervals
A further aspect of statistical analysis relevant to this thesis is in relation to confidence
intervals for the binomial distribution. As mentioned previously, promoted ignition
testing is a series of independent Bernoulli trials (assuming the test conditions are kept
the same with a constant probability of a burn) resulting in a binomial distribution
for the count of the number of burns. In the context of promoted ignition testing the
probability of a particular number of burns, (x), occurring is given by the binomial
probability distribution, Equation 3.21, with p equal to the probability of a burn, referred to as the reaction probability.
For the case where no burns occur it can be assumed that the lower limit for the
reaction probability is zero. Hence, a one-sided confidence interval for p is obtained
such that:
Pr(p ≤ pupper ) = C
(3.31)
where C is the desired confidence level and pupper is the upper limit of the reaction
probability (with a lower limit of zero). In the case where there are no burns recorded
63
3.3 B INOMIAL D ISTRIBUTION C ONFIDENCE I NTERVALS
in a series of tests, pupper represents the reaction probability derived from the binomial
probability distribution with x = 0:
Pr(Y = 0) =
N!
p0 (1 − pupper )N −0 = 1 − C
0!(N − x)! upper
(3.32)
which reduces to:
Pr(Y = 0) = (1 − pupper )N = 1 − C.
(3.33)
Rearranging gives:
1
pupper = 1 − (1 − C) N
(3.34)
Hence the confidence interval, with confidence level C, for the reaction probability,
p, assuming no burns are observed is expressed by Equation 3.35.
1
0, 1 − (1 − C) N
(3.35)
Chapter 7 presents the application of confidence interval theory to the analysis and
interpretation of promoted ignition test data.
64
C HAPTER 4
M ATERIALS AND M ETHODS
With the statistical framework in place it was necessary to perform a series of tests with
which to evaluate the effect of sample geometry on RRMI. Three simple cross sections:
circle, rectangle and triangle were tested and their dimensions were calculated such that
their XAs were equal. A range of XAs were chosen in order to assess the effect of rod
shape for rods of varying size.
This chapter describes the apparatus, materials and methods associated with the experimental component of this thesis. The majority of the experimentation centered on
the promoted ignition testing of rods of varying geometry. As a secondary focus, the
relationship between rod diameter, test pressure and ER was investigated by analysing
quenched slag from samples with various diameters. A test matrix is presented which
lists all samples tested and an identification scheme is introduced which is used hereafter to refer to specific samples discussed.
4.1
Apparatus
Promoted ignition testing was performed in a recommissioned NASA White Sands
Test Facility combustion chamber, Figure 4.1a. The chamber has a circular 50 mm
diameter view port fitted with a combined quartz and lexan window. The chamber has
a volume of 0.7 litres, a maximum allowable working pressure of 10.3 MPa and can
support testing of samples up to 120 mm in length. The chamber’s internal components include a base platform, sample support and holder, sheath and slag cup. These
components are made of copper to resist ignition and combustion in the high pressure
oxygen atmosphere. Igniter feed-throughs deliver the ignition current through the base
65
4.1 A PPARATUS
(a) Combustion chamber.
(b) Internal components with mounted sample.
Figure 4.1: Promoted ignition testing apparatus.
of the chamber to the sample which is isolated from the chamber by ceramic disks,
Figure 4.1b.
Appendix A lists the system’s major electrical components and contains an electrical schematic diagram and operating procedure. The ignition circuit is fitted with
lead acid batteries connected to two high power capacitors which combine to rapidly
deliver the high current required to ignite the Pyrofuze™ igniter wire and sample
(≤0.05seconds). The circuit includes both an arming and ignition switch to avoid
premature ignition. When activated, the ignition current passes through a length of
Pyrofuze™ wire wrapped around the lower end of the vertically mounted sample. The
Pyrofuze™ wire resistively heats and alloys and transfers sufficient energy to the sample to melt its end and ignite the sample which sustains burning if the metal is flammable at the test conditions. Test pressure was measured using a Sensotec Model TJE
pressure transducer (0 - 20.7 MPa range) and recorded using an AED Rocket Data Acquisition System (RDAS). The pressure transducer was calibrated using a dead weight
pressure gauge tester coupled with the signal conditioner and RDAS. Appendix B contains the calibration data. A digital pressure display was added to the system since the
precision of the available analog pressure gauge reading was inadequate to accurately
establish the pressure real-time. The digital display was not available for all of the
testing. The data acquisition circuitry operates from an independent power supply to
avoid error (noise) that can be introduced at the time of ignition (power spikes etc.).
66
4
M ATERIALS AND M ETHODS
All tests were recorded using a Canon MVX150i digital video camera recording at
25 frames per second (fps). The camera was set to its maximum shutter speed, 1/8000,
and lowest exposure compensation. Various Neutral Density (ND) filters were also
used to reduce the light level to which the camera was exposed. The level of filtration
differed depending on the luminosity of the burning sample.
4.2
Materials
Iron and mild steel were tested. These materials were chosen due to their previous
well documented history of testing and “well behaved”, steady and quiescent burning
behaviour. In addition, iron burns heterogeneously eliminating the complexity that
vapour-phase burning would introduce into the interpretation and analysis of results.
Further, given that the RRMI was measured via a visual interrogation of video data,
slower burning iron, which presented a clearly defined SLI in the video, was better
suited than relatively fast burning aluminium.
Test samples were either mild steel or pure iron. Mild steel was used to machine
(via wire cutting) cylindrical, rectangular and triangular samples in order to investigate the effect of sample geometry on RRMI. The nominal composition for the mild
steel was (weight %): Carbon: 0.2, Silicon: 0.25, Manganese: 0.45, Phosphorus:
0.040, Sulfur: 0.040 and Iron: balance ≥ 0.99. Cylindrical iron samples, purity 3N5
(99.95%), were burned to collect and quench the detached drops in order to investigate the relationship between ER and rod diameter, with the exception of the 6.00 mm
rod which was made of mild steel. Sample ID’s and dimensions are presented in the
following section.
The test atmosphere was oxygen with minimum 3N purity (99.9%). As previously
mentioned the rods were ignited via the resistive heating of Pyrofuze™. Pyrofuze™
wire is composed of an inner core of aluminium alloy wrapped in an outer layer consisting predominantly of palladium alloy with a small amount of ruthenium. The heat
provided by the electric current in the ignition circuit initiates an alloying of these
elements releasing sufficient energy and to melt the end of the sample.
4.3
Test Matrix
Tables 4.1 and 4.2 present a summary of all the tests performed. The I.D. column
67
4.4 M ETHODS
provides an identification code for the sample being referenced. For the geometry testing the code starts with a letter designating the shape of the cross-sectional face, circle
(C), rectangle (R) or triangle (T). This letter is followed by a number representing the
rod’s XA. The number, coded as 2,3,4,5,6 or 7, refers to the diameter (in mm) of a
cylindrical rod. For example, 3 indicates that the XA is equal to π(3/2)2 . The subscript, code 1-6, indicates the specific rod tested in a group of tests for that geometry.
The I.D. is clarified in Figure 4.2. The rods were manufactured from mild steel. The
Figure 4.2: Sample ID code - example.
shape and dimension columns in Table 4.1 indicate the shape of the rod, cylindrical,
rectangular or triangular, and the rod dimensions. All samples were 110 mm in length.
The target test pressure column indicates the desired initial test pressure, the actual initial test pressures achieved are listed in Tables 5.1, 5.2 and 5.3 in Chapter 5. Samples
with the same XA are referred to collectively with a prefix of ‘X’, followed by the rod
size, ie. X6 refers collectively to all cylindrical, rectangular and triangular samples
with a XA equal to that of a 6 mm diameter cylindrical rod.
The I.D.’s for the ER tests listed in Table 4.2 begin with ‘Q’ to indicate that the
sample was quenched. This letter is followed by a number which designates the diameter the rod tested. An additional subscript, code H or L, is included to indicate either
a high pressure test, 6.9 MPa, or a low pressure test, 1.1 MPa. Not all geometries were
tested at both pressures. The rod material is listed in the material column, and all samples were in the shape of cylindrical rods. The diameter of the rod is listed along with
the measured initial test pressure.
4.4
4.4.1
Methods
Testing
Test procedures were in accordance with the standard promoted ignition test method [16].
Samples were cleaned, weighed and prepared by cutting a shallow groove around their
68
4
M ATERIALS AND M ETHODS
base. A length of Pyrofuze™ wire was wrapped six times around the groove. The
sample was mounted vertically in the sample holder. Electrical continuity through the
igniter circuit and electrical isolation between the sample holder and chamber was verified. The chamber was then sealed and pressurised. To pressurise the test chamber it
was connected to an oxygen cylinder via a wall mounted gas panel. Appendix C contains the pneumatic diagram and procedures for the system. The chamber was flushed
three times with oxygen prior to pressurising to the desired test pressure. Recording
devices were activated and a test initiated. After a test was complete, the sample was
removed, weighed, bagged and labeled for further reference as required. Associated
pressure and video data for a test was then downloaded and archived. Quench tests
were performed in a similar manner to the standard promoted ignition test but in these
tests the detached drops were allowed to fall into a cold water bath.
Table 4.1: Test Matrix - Sample Geometry vs RRMI.
I.D.
Material
Shape
Dimensions 1
Length
(mm)
Oxygen
(mm)
Target Test
Pressure
(MPa)
(%)
C21−5
Mild Steel
Cylindrical
2.00
110
6.9
99.9
C31−6
Mild Steel
Cylindrical
3.00
110
6.9
99.9
C41−5
Mild Steel
Cylindrical
4.00
110
6.9
99.9
C51−5
Mild Steel
Cylindrical
5.00
110
6.9
99.9
C61−5
Mild Steel
Cylindrical
7.00
110
6.9
99.9
C71−3
Mild Steel
Cylindrical
2.00
110
6.9
99.9
R21−5
Mild Steel
Rectangular
1.02 × 3.07
110
6.9
99.9
R31−5
Mild Steel
Rectangular
1.53 × 4.60
110
6.9
99.9
R41−5
Mild Steel
Rectangular
2.05 × 6.14
110
6.9
99.9
R51−5
Mild Steel
Rectangular
2.56 × 7.67
110
6.9
99.9
R61−5
Mild Steel
Rectangular
3.07 × 9.21
110
6.9
99.9
T21−5
Mild Steel
Triangular
2.69
110
6.9
99.9
T41−5
Mild Steel
Triangular
5.39
110
6.9
99.9
T61−5
Mild Steel
Triangular
8.08
110
6.9
99.9
1
Dimensions refer to the diameter of the cylinder and the side lengths of the rectangle and equilateral
triangle.
69
4.4 M ETHODS
Table 4.2: Test Matrix - Rod Diameter vs Extent of Reaction.
I.D.
Material
Shape
Diameter
(mm)
Length
(mm)
Initial Test
Pressure (MPa)
Oxygen
(%)
Q0.25H
Iron
Cylindrical
0.25
150
6.9
99.9
Q0.5H
Iron
Cylindrical
0.51
100
6.9
99.9
Q1H
Iron
Cylindrical
1.02
100
6.9
99.9
Q4H
Iron
Cylindrical
4.06
55
6.9
99.9
Q6H
Mild Steel
Cylindrical
6.00
55
6.9
99.9
Q0.5L
Iron
Cylindrical
0.51
100
1.1
99.9
Q4L
Iron
Cylindrical
4.06
55
1.1
99.9
Q6L
Mild Steel
Cylindrical
6.00
55
1.1
99.9
4.4.2
Analysis
Calculation of the RRMI
The RRMIs of the burning samples were calculated from the test footage. The video
record was first downloaded from the digital camera as an Audio Video Interleaved
(AVI) file and then filtered through VirtualDub software to de-interlace the constituent
images providing an effective frame rate of 50 fps. The images were then passed
through an interactive MATLAB® program where the user selects two points representative of the SLI location in each image. The pixel co-ordinates for the positions
are stored and averaged to provide a single height reference for the SLI in the image.
The frames in which a drop detached were identified to allow the stream of SLI heights
to be broken into segments representing the transition of the SLI over the duration of a
single drop cycle. The difference between the initial height just prior to a drop detachment and the final height just prior to the next drop detachment is found and averaged
over the time difference in order to calculate an RRMI for each individual drop cycle.
The reasoning behind calculating RRMIs on a drop cycle basis is discussed in Section 3.1 along with the method for calculating representative RRMIs for each test from
the drop cycle RRMI data.
Error Analysis
Sources of error in the calculation of RRMI by visual observation are derived from
70
4
M ATERIALS AND M ETHODS
uncertainty in the vertical scale (s) and in the resolution of the time (t) and length (y)
over which the RRMI is calculated. The quadrature rule can be applied to obtain the
resulting error in RRMI which is given by:
∆RRM I
=
RRM I
s
∆s
s
2
+
∆t
t
2
+
∆y
y
2
.
(4.1)
Uncertainty in the pressure measurement was insignificant. In absolute terms the
error was ±0.01 MPa.
The drop cycle RRMIs are given by:
RRM I = µ + + δ
(4.2)
where the mean is represented by µ, and and δ represent the contributions due to
random error and measurement error (includes both visual and pressure sources) respectively. Measurement error is significantly smaller than the random error, hence,
the RRMI analysis is simplified as the RRMI can be expressed in terms of the mean
and random components only.
Microscopy
Microprobe analysis is a technique which was used to analyse for the elements present
in post-test slag samples. The technique enables a quantitative measurement of the
oxygen to iron ratios. The first phase in post-test microanalysis was sample preparation. Post-test slag samples were set in clear 31.5 mm diameter resin blocks. The
resin blocks were produced from lucite powder using a Metaserv® automatic mounting
press and moulding unit. When necessary, larger samples were divided between two
resin blocks. The resin blocks were ground to expose a cross section of each sample
and their surfaces were polished to a minimum finish of 1µm .
Digital images of the exposed cross section of a sample were taken using a Leica
CD200 camera attached to a Leica MZ8 stereo microscope. In these images, oxidised
and unoxidised material can be distinguished based on the colour of the material. The
oxide is dark grey/black and the unreacted metal is a lighter silver/white colour. Images
were also taken with a 3CCD camera attached to a Nikon reflected light microscope
which had higher magnification capabilities. The resin blocks were then carbon coated
and viewed using either an FEI Quanta 200 or a JEOL JXA-840A SEM. The JOEL
71
4.4 M ETHODS
JXA-840A microscope was fitted with a JEOL-2300 x-ray microanalysis system and
thin-window x-ray detector. Imaging and analysis was carried out using EPMA, specifically EDS, with an accelerating voltage of 15kV in both machines. Oxygen to iron
ratios obtained through the electron microprobe analysis were referenced to certified
Astimex® haematite (Fe2 O3 ) and magnetite (Fe3 O4 ) standards. Backscattered electron
intensity is dependent of the average atomic number of the specific area of the sample
being examined. Therefore, in the BSE images the colour/brightness of the materials
in the image is proportional to the atomic number of the element or the average atomic
number of the molecule present. Hence, the oxide appears dark relative to the unoxidised metal. The field of view in the SEM is small, therefore, larger samples could
not be viewed in their entirety, rather, specific regions of interest were identified and
examined.
72
C HAPTER 5
E XPERIMENTAL R ESULTS AND A NALYSIS
Experimentation was completed as per the methods and guidelines set out in the preceding chapter. Promoted ignition tests were performed on rods with circular, rectangular and triangular cross sections and having XAs ranging from 3 - 28 mm2 . Promoted ignition tests were also performed to quench and collect the slag from rods of
varying diameter for the purpose of assessing their ER as a function of rod diameter
and test pressure. This chapter is divided into three sections. Section 5.1 presents
general observations and features of the promoted ignition testing of samples of varying geometry that were performed to assess the effect of sample geometry on RRMI.
Section 5.2 presents the RRMI data for cylindrical, rectangular and triangular rods.
Section 5.3 describes the results of the microanalysis of quenched slag. The results
presented in this chapter are discussed in Chapter 6.
5.1
5.1.1
General Observations
Burning Rod
The visual burning of all test samples was qualitatively very similar. After ignition,
a molten drop formed at the base of the rod initiating a drop-growth-and-detachment
cycle. Burning continued either to the point where the entire sample was consumed
(most common) or, heat loss to the sample holder extinguished the test sample leaving
a small oxide nub attached to the rod (rarely). A single drop-growth-and-detachment
cycle is defined as the transition between a point just prior to a drop detaching to the
point just prior to the next drop detaching. Therefore, the end of one cycle coincides
with the beginning of the next cycle. In the digital images this point occurs between
73
5.1 G ENERAL O BSERVATIONS
consecutive frames. In the first frame a drop is attached, normally having undergone
significant necking and in the following frame the neck is broken, or the drop can be
seen falling to the slag pool. A typical drop-growth-and-detachment cycle for a 2 mm
diameter cylindrical rod is shown in Figure 5.1. Generally, burning was relatively quiescent and there was little or no smoke haze surrounding the molten mass, consistent
with a liquid-burning metal. The molten mass varied in colour, orange/yellow/white,
and luminosity, dim/bright, throughout the drop cycle and the SLI’s orientation varied
depending on the shape of the rod, images reflecting the changing SLI will be presented in the following section. Typical drop cycles for a 4 mm diameter cylindrical
rod, Figure 5.2, and a 6 mm diameter cylindrical rod, Figure 5.3, show more dynamic
burning behaviour including greater levels of ejecta and a “rougher” drop surface profile. The images also reflect a more elongated drop attached to the 4 mm and 6 mm
diameter rods than is attached to the 2 mm diameter rod. This behaviour is exemplified by comparing frames for times 0.26s, 0.3s and 0.32s in Figures 5.1. 5.2 and 5.3,
respectively. A colour transition is apparent as the XA decreases. ND filter levels for
the C2, C4 and C6 tests shown were (ND8, ND8, ND4), (ND8, ND8, ND2) and (ND8,
ND2) respectively. The same filter levels were used for rectangular and triangular rods
of the same XA.
5.1.2
Solid Liquid Interface
Although the SLIs did not appear perfectly horizontal over the duration of a test for
any of the geometries tested, the SLI of the cylindrical rod remained relatively planar,
as shown in Figure 5.4. However, the SLIs appeared to ‘climb’ at the corners of the
rectangular and triangular rods. This effect was more pronounced in the case of the
larger rods, and was even more pronounced for the triangular rods, Figure 5.5, than
the rectangular rods, Figure 5.6. Figures 5.4 - 5.6 include a schematic view of the
cross section of the burning rod to accentuate the shape of the SLI. In addition, a top
view of the rod is located beneath the triangular and rectangular images to indicate the
orientation of the sample with respect to the camera.
74
Figure 5.1: Video images showing a typical drop cycle for a 2 mm diameter cylindrical rod (C21 , 6.96 MPa) (time relative to first
image).
5
E XPERIMENTAL R ESULTS AND A NALYSIS
75
Figure 5.2: Video images showing a typical drop cycle for a 4 mm diameter cylindrical rod (C42 , 6.96 MPa) (time relative to first
image).
5.1 G ENERAL O BSERVATIONS
76
Figure 5.3: Video images showing a typical drop cycle for a 6 mm diameter cylindrical rod (C64 , 6.94 MPa) (time relative to first
image).
5
E XPERIMENTAL R ESULTS AND A NALYSIS
77
5.1 G ENERAL O BSERVATIONS
(a) C61
(b) C63
(c) C64
(d) C65
(e) SLI
Figure 5.4: Images of burning cylindrical rods (C6) showing the planar SLI.
(a) T62
(b) T62
(c) T64
(d) T65
(e) SLI
Figure 5.5: Images of burning triangular rods (T6) showing the convex SLI and the
orientation of the sample relative to the camera.
(a) R61
(b) R61
(c) R65
(d) R65
(e) SLI
Figure 5.6: Images of burning rectangular rods (R6) showing the slightly convex SLI
and the orientation of the sample relative to the camera.
78
5
5.1.3
E XPERIMENTAL R ESULTS AND A NALYSIS
Slag
The detached slag produced during the drop-growth-and-detachment cycle was caught
in a copper cup where it cooled forming a solidified mass. In the case of the X6
rods a spherical thin-walled shell of slag often formed, as shown in Figure 5.7. This
hollow shell sat atop a compacted slag deposit, although this too encapsulated a large
horizontal void connected to the dome via a small tunnel through the slag, Figure 5.7c.
(a) Slag inside quench
cup.
(b) Domed slag shell.
(c) Compacted slag base.
Figure 5.7: Sample C62 slag showing a solidified thin walled slag dome.
Large globules of molten ejecta were occasionally observed in the viewport during
the X6 tests. The trajectory of the masses indicated they originated within the slag
pool at the base of the chamber. Figures 5.8 - 5.10 provide examples of this ejecta for
cylindrical, rectangular and triangular samples, respectively.
5.1.4
Chamber Pressure and Temperature
The oxygen pressure within the test chamber increased during a test, as shown in Figure 5.11. Ignition is marked by an increase in pressure and after the sample has extinguished the pressure gradually decreases. The increase in chamber pressure during a
test was dependent on XA, the increase in pressure for all X2 rods was similar but was
less than the increase in pressure for the X6 rods, 3-5% compared to 10-15%.
The increase in chamber pressure during a test is consistent with an increase in
chamber temperature. Although no instrumentation was used to measure chamber
temperature it was evident that higher temperatures were reached during the X6 tests
than during the X2 tests. Equipment could be safely handled immediately following
testing of the X2 rods, however, following tests of the X6 rods the temperature of the
79
5.1 G ENERAL O BSERVATIONS
(a) 0.00s
(b) 0.02s
(c) 0.04s
(d) 0.06s
(e) 0.08s
(f) 0.10s
(g) 0.12s
Figure 5.8: Images of a burning cylindrical rod (C65 , 6.94 MPa) showing ejecta from
the slag pool, time is relative to the first image.
(a) 0.00s
(b) 0.02s
(c) 0.04s
(d) 0.06s
(e) 0.08s
Figure 5.9: Images of a burning rectangular rod (R63 , 6.94 MPa) showing ejecta from
the slag pool, time is relative to the first image.
(a) 0.00s
(b) 0.02s
(c) 0.04s
(d) 0.06s
(e) 0.08s
(f) 0.10s
(g) 0.12s
Figure 5.10: Images of a burning triangular rod (T61 , 6.94 MPa) showing ejecta from
the slag pool, time is relative to the first image. The molten mass has reached the
sample holder at this point in the test.
internal copper components was measured to exceed 100◦ C. Again, this is consistent
with a greater pressure increase during a test for rods of larger XA.
80
5
E XPERIMENTAL R ESULTS AND A NALYSIS
Figure 5.11: Typical test pressure trace (R21 ) indicating sample ignition and the pressure rise during the test together with the decrease in pressure after burning ceased.
5.2
5.2.1
RRMI Results and Analysis
RRMI Data Tables
Tables 5.1, 5.2 and 5.3 present RRMI data for the cylindrical, rectangular and triangular
rods, respectively, calculated on a drop cycle basis as described in Section 3.1. The
tables include the measured test pressure, the mean RRMI, the standard error of the
mean, the standard deviation, the number of drop cycles from which the mean RRMI
was calculated and the bounds of the 95% confidence interval for the mean RRMI.
The method for calculating the 95% confidence interval is discussed in Section 3.1.3.
It should be noted that there is a greater variation in initial test pressure for the C3, R3,
C5, R5 and C7 tests since the digital pressure gauge was not available at the time.
Table 5.4 presents a summary of the RRMI data for each geometry. The summary
data was calculated by combining the individual drop cycle RRMIs from each of the
tests for a single geometry, rather than averaging the mean RRMIs of the tests. The
validity of this approach is discussed briefly in this chapter and in more detail in Chapter 6.
The RRMI summary data reflects a trend of decreasing RRMI with increasing XA
and the triangular and rectangular rods had faster mean RRMIs than the cylindrical
rods. These trends are shown in Figure 5.12 in which the summarised data in Table 5.4
is plotted.
81
5.2 RRMI R ESULTS AND A NALYSIS
Table 5.1: RRMI results for cylindrical rods.
I.D.
Pressure
Absolute
(MPa)
Mean
RRMI
(mm/s)
Std. Error
Mean
(mm/s)
Std.
Dev.
(mm/s)
No.
Drops
(N)
95% CI
Lower
(mm/s)
95% CI
Upper
(mm/s)
C21
6.96
14.29
0.25
0.50
4
13.50
15.09
C22
6.96
13.96
0.23
0.40
4
12.96
14.96
C23
6.96
14.27
0.24
0.48
4
13.51
15.03
C24
6.96
14.51
0.55
1.10
4
12.77
16.26
C25
6.96
14.69
0.23
0.46
4
13.97
15.42
C31
6.72
9.61
0.31
0.75
6
8.82
10.39
C32
6.24
8.45
0.63
1.54
6
6.83
10.07
C33
6.98
11.11
0.32
0.78
6
10.29
11.94
C34
6.92
10.51
0.60
1.60
7
9.04
11.99
C35
6.76
10.11
0.28
0.80
8
9.44
10.78
C36
6.82
10.91
0.60
1.58
7
9.45
12.37
C41
6.96
7.87
0.26
0.86
11
7.30
8.45
C42
6.96
8.04
0.21
0.70
11
7.57
8.51
C43
6.96
8.13
0.21
0.69
11
7.67
8.60
C44
6.94
7.76
0.21
0.72
12
7.30
8.22
C45
6.90
7.77
0.24
0.79
11
7.24
8.30
C51
6.90
6.98
0.21
0.75
13
6.52
7.43
C52
6.74
6.82
0.23
0.82
13
6.33
7.32
C53
6.90
7.02
0.30
1.08
13
6.36
7.67
C54
6.82
7.07
0.25
0.91
13
6.52
7.62
C55
6.81
6.89
0.20
0.71
13
6.47
7.32
C61
6.96
5.03
0.24
0.98
17
4.52
5.53
C62
6.96
5.08
0.19
0.76
16
4.68
5.49
C63
6.96
5.19
0.32
1.29
16
4.50
5.87
C64
6.94
4.99
0.21
0.85
16
4.54
5.45
C65
6.94
5.20
0.19
0.75
16
4.81
5.61
C71
6.64
5.25
0.27
1.14
18
4.69
5.82
C72
7.23
5.29
0.29
1.24
18
4.68
5.91
C75
6.60
4.91
0.22
0.92
18
4.45
5.36
82
5
E XPERIMENTAL R ESULTS AND A NALYSIS
Table 5.2: RRMI results for rectangular rods.
I.D.
Pressure
Absolute
(MPa)
Mean
RRMI
(mm/s)
Std. Error
Mean
(mm/s)
Std.
Dev.
(mm/s)
No.
Drops
(N)
95% CI
Lower
(mm/s)
95% CI
Upper
(mm/s)
R21
6.94
16.00
0.31
0.61
4
15.05
16.97
R22
6.94
15.77
0.38
0.77
4
14.55
16.99
R23
6.94
15.05
0.19
0.37
4
14.46
15.64
R24
6.94
14.64
0.40
0.80
4
13.37
15.90
R25
6.94
15.50
0.38
0.76
4
14.29
16.70
R31
6.94
11.81
0.36
0.89
6
10.87
12.74
R32
6.82
11.40
0.41
1.08
7
10.39
12.40
R33
6.82
11.63
0.35
0.93
7
10.77
12.49
R34
6.78
10.70
0.39
1.11
8
9.78
11.63
R35
6.54
11.36
0.41
1.15
8
10.40
12.32
R41
6.94
8.72
0.28
0.89
10
8.09
9.36
R42
6.94
8.47
0.17
0.55
10
8.07
8.86
R43
6.94
8.36
0.29
0.91
10
7.72
9.01
R44
6.94
8.44
0.37
1.12
9
7.58
9.29
R45
6.94
8.83
0.14
0.43
9
8.50
9.16
R51
6.80
7.32
0.24
0.86
13
6.80
7.84
R52
6.82
7.32
0.35
1.24
13
6.57
8.07
R53
6.90
7.34
0.19
0.70
13
6.92
7.77
R54
6.90
7.49
0.29
1.03
13
6.87
8.12
R55
6.88
7.70
0.24
0.88
13
7.17
8.23
R61
6.94
5.45
0.23
0.88
15
4.97
5.94
R62
6.94
5.41
0.24
0.91
15
4.91
5.92
R63
6.94
5.79
0.20
0.79
16
5.37
6.21
R64
6.94
5.89
0.30
1.22
17
5.26
6.52
R65
6.96
6.03
0.14
0.49
12
5.72
6.35
83
5.2 RRMI R ESULTS AND A NALYSIS
Table 5.3: RRMI results for triangular rods.
I.D.
Pressure
Absolute
(MPa)
Mean
RRMI
(mm/s)
Std. Error
Mean
(mm/s)
Std.
Dev.
(mm/s)
No.
Drops
(N)
95% CI
Lower
(mm/s)
95% CI
Upper
(mm/s)
T21
6.94
15.47
0.36
0.73
4
14.31
16.63
T22
6.94
15.46
0.23
0.46
4
14.73
16.19
T23
6.94
15.87
0.71
1.41
4
13.62
18.12
T24
6.94
15.58
0.22
0.44
4
14.88
16.29
T25
6.94
15.91
0.53
1.07
4
14.22
17.61
T41
6.94
8.87
0.28
0.94
11
8.23
9.50
T42
6.94
9.25
0.27
0.85
10
8.64
9.85
T43
6.94
8.92
0.22
0.74
11
8.43
9.42
T44
6.94
9.25
0.31
0.97
10
8.55
9.95
T45
6.94
9.09
0.25
0.78
10
8.53
9.61
T61
6.94
6.28
0.26
1.05
16
5.72
6.84
T62
6.96
6.20
0.34
1.31
15
5.48
6.92
T63
6.94
6.17
0.25
1.02
16
5.63
6.71
T64
6.94
6.20
0.26
1.04
16
5.64
6.75
T65
6.96
5.82
0.21
0.83
16
5.38
6.26
84
5
E XPERIMENTAL R ESULTS AND A NALYSIS
Table 5.4: RRMI summary table.
I.D.
Pressure
Absolute
(MPa)
Mean
RRMI
(mm/s)
Std. Error
Mean
(mm/s)
Std.
Dev.
(mm/s)
No.
Drops
(N)
95% CI
Lower
(mm/s)
95% CI
Upper
(mm/s)
C2
6.96
14.27
0.17
0.75
20
13.92
14.62
1
6.84
10.45
0.21
1.23
40
10.02
10.88
C4
6.94
7.91
0.10
0.74
56
7.71
8.11
C5
6.83
6.96
0.10
0.84
65
6.75
7.16
C6
6.95
5.10
0.10
0.93
81
4.89
5.31
C7
6.82
5.15
0.15
1.10
54
4.85
5.45
R2
6.94
15.39
0.18
0.79
20
15.02
15.76
R3
6.78
11.35
0.18
1.06
36
10.99
11.71
R4
6.94
8.56
0.12
0.80
48
8.33
8.79
R5
6.86
7.43
0.12
0.94
65
7.20
7.67
R6
6.94
5.71
0.11
0.92
75
5.50
5.92
T2
6.94
15.66
0.18
0.83
20
15.07
16.05
T4
6.94
9.07
0.12
0.84
52
8.83
9.30
T6
6.95
6.13
0.12
1.04
79
5.90
6.37
C3
1
Excludes C32 data.
85
Figure 5.12: Mean RRMI and 95% confidence intervals plotted against XA for each geometry.
5.2 RRMI R ESULTS AND A NALYSIS
86
5
5.2.2
E XPERIMENTAL R ESULTS AND A NALYSIS
Drop Cycle RRMI Analysis
RRMIs were calculated on a drop cycle basis in order to obtain standard errors, deviations and confidence intervals. This approach is only valid if the drop cycles can be
considered independent events for which a mean RRMI and standard deviation can be
estimated. Therefore, the assumption of drop cycle independence must be investigated.
For the individual drop cycles to be considered independent one would expect no
obvious trends or patterns in the data. For example, drop cycle RRMIs consistently
alternating between fast and slow during a test suggests a correlation between the previous drop and the following drop, hence the cycles are not independent. Similarly, in
order to validate the approach of combining all available drop cycle data for five tests
of a single geometry, in order to gain a single mean RRMI for that geometry, it must
be shown that there are no significant differences in RRMI between each test.
Time Series Plots
Time series plots for the drop cycle RRMI data involve plotting each drop cycle RRMI
in the order in which it occurred (i.e., with increasing time). These plots are useful to
visualise trends, if any, in the data of an individual test [117]. Time series plots for
geometries X2, X4 and X6 are presented in Figure 5.13. Consecutive RRMIs, plotted
from left to right, are connected by lines. The first five tests (left) are for the cylindrical
rods, the next five tests (centre) are for the rectangular rods and the remaining five tests
(right) are for the triangular rods. There is no apparent trend in the individual test data
for any of the geometries.
Drop Series Plots
An alternative means with which to assess drop cycle independence is to plot the value
of the current drop cycle RRMI versus the next drop cycle RRMI, for each geometry.
An increasing linear trend would indicate that drop cycles are followed by drop cycles
of comparable speed. That is, a slow drop, on average, is followed by a slow drop and
a fast drop is followed by a fast drop. If a fast drop is followed by a slow drop and vice
versa this behaviour would manifest in a decreasing linear trend. The complete data set
is plotted in Figure 5.14. Within each of the geometry groupings there are no obvious
trends and the data appears to be randomly scattered. Data for selected geometries is
87
5.2 RRMI R ESULTS AND A NALYSIS
(a) X2 rods.
(b) X4 rods.
Figure 5.13: Time series plot for X2, X4 and X6 rods.
plotted independently, Figure 5.15, to clarify the lack of correlation between consecutive drop cycles. The lack of correlation is more easily demonstrated by examining the
data for rods with a larger XA since a greater amount of data was generated for these
geometries. Examples of a fast drop followed by a slow drop and vice versa are high88
5
E XPERIMENTAL R ESULTS AND A NALYSIS
(c) X6 rods.
Figure 5.13: Time series plot for X2, X4 and X6 rods (cont.).
Figure 5.14: Current vs previous drop cycle RRMI data.
lighted (circled in Figure 5.15) but overall the assumption of drop cycle independence
is clearly valid.
89
5.2 RRMI R ESULTS AND A NALYSIS
(a) R4.
(b) C6.
(c) T6.
Figure 5.15: Current vs previous drop cycle RRMI data for rod ID’s R4, C6 and T6.
90
5
E XPERIMENTAL R ESULTS AND A NALYSIS
Rod Series Plots
To legitimately combine the drop cycle RRMI data for all tests of a single geometry for
the purpose of calculating a single mean RRMI representative of that geometry requires
that the drop cycle RRMI data for the rods is independent. Rod series scatterplots were
valuable to detect difference between the drop cycle RRMI data for different rods of a
single geometry. The drop cycle RRMIs for individual rods are plotted, slightly offset
from one another for clarity, in a column above the rod I.D., Figure 5.16. Since the
RRMIs for different rods of a single geometry fall within a similar range it is clear that
their drop cycle RRMIs are relatively similar. Examples of outliers are circled and the
effect of these outliers is assessed through an ANOVA test. The grouping of C3 rods,
Figure 5.16b, displays a greater variation in RRMI between the individual rods than
the other geometries. Test C32 in particular appears to lie lower than the data for the
remaining C3 tests. This variation is attributed to the greater variation in test pressure
for the C3 tests.
ANOVA
A quantitative assessment of differences between the drop cycle RRMI data for each
rod of a single geometry was obtained by performing a one-way ANOVA. The null
hypothesis is that there is no difference in the mean RRMIs of the five rods tested for a
single geometry, the alternative hypothesis is that at least one of the means is different.
The ANOVA results are summarised in Table 5.5. The source column indicates the
source of the variation given by the Sum of Squares (SS) column. The SS column
lists the variation between the different rods of a particular geometry (SSrods ) and
the variation in the residuals, that is, the variation within the rod samples (SSR). The
Mean Sum of Squares (MSS) is simply the sum of squares divided by the degrees
of freedom (df). The ratio of SSrods /SSR forms a test statistic, F. The test statistic is
compared with a critical F-value (Fα ) calculated from the F-distribution such that the
probability to the right of Fα is equal to the chosen significance level. The significance
level represents the probability that the null hypothesis will be rejected even though
it is true. Hence, as the significance level decreases so does the probability that the
null hypothesis will be falsely rejected. A common value of α is 0.05. The p-value
measures the probability in the tail of the F-distribution to the right of the calculated
F-value and can be interpreted as the probability of obtaining the observed differences
between the mean rod RRMIs for that geometry by chance. Hence, the smaller the
91
5.2 RRMI R ESULTS AND A NALYSIS
p-value the less likely the observation was by chance and the more likely the mean rod
RRMIs for the particular geometry are statistically different [117]. The significance
level with which to interpret the p-values was set at 0.05. Therefore, p-values below
0.05 represent cases where the mean rod RRMIs for the five rods of that geometry
can not be considered equal and p-values exceeding 0.05 indicate that the mean rod
RRMIs can be considered equal. A single p-value below 0.05 was obtained for the C3
geometry, the significance of this result will be discussed in the following chapter.
5.2.3
Instantaneous RRMI
The position of the SLI, plotted against time, is a measure of the instantaneous RRMI
and can be used to show if cyclic changes in the RRMI are associated with the dropgrowth-and-detachment cycle. Many drop cycles demonstrate an initial increasing
gradient followed by a decreasing gradient just prior to drop detachment, as shown
in Figure 5.17. Figure 5.17 is a plot of SLI position versus time for the C2 rods. The
time axis provides a relative measure of the change in time during a test, each test was
offset to prevent the data from overlapping, the actual time value is inconsequential,
only the difference is relevant. In Figure 5.17 the points at which a drop detached are
marked with a square. Selected cycles (circled) were plotted individually to clarify the
change in instantaneous RRMI over a drop cycle, Figure 5.18. The SLI heights and
times were adjusted for the purposes of plotting and do not correspond to the actual
SLI height or test time for the drop cycles. Relative changes in height and time were
maintained.
The repetitive cyclic SLI motion is less pronounced in the X6 rods, as shown in
Figure 5.19, compared to the X2 rods. Although some drop cycles demonstrate an
increasing-decreasing instantaneous RRMI other cycles vary considerably, as shown
in the individual cycles plotted in Figure 5.20.
92
(d) Rod series plot for X5 rods.
(a) Rod series plot for X2 rods.
93
Figure 5.16: Rod series scatterplots.
(e) Rod series plot for X6 rods.
(b) Rod series plot for X3 rods.
(f) Rod series plot for C7 rods.
(c) Rod series plot for X4 rods.
5
E XPERIMENTAL R ESULTS AND A NALYSIS
5.2 RRMI R ESULTS AND A NALYSIS
Table 5.5: S-PLUS ANOVA results - RRMI rod comparison.
Source
Deg. of
Freedom
(df)
Sum of
Squares
(SS)
Mean
Square
(MS)
F
p-value
Significant
Difference
C2
Residuals
4
15
2.87
7.73
0.72
0.52
1.39
0.28
No
R2
Residuals
4
15
4.84
6.94
1.21
0.46
2.62
0.077
No
T2
Residuals
4
15
0.77
12.23
0.19
0.82
0.24
0.91
No
C3
Residuals
5
34
29.65
52.45
5.93
1.54
3.84
0.007
Yes
R3
Residuals
4
31
5.18
33.98
1.29
1.10
1.18
0.34
No
C4
Residuals
4
51
1.23
29.08
0.31
0.57
0.54
0.71
No
R4
Residuals
4
42
1.59
28.49
0.40
0.68
0.58
0.67
No
T4
Residuals
4
47
1.35
34.65
0.34
0.74
0.46
0.77
No
C5
Residuals
4
60
0.50
44.89
0.12
0.75
0.17
0.95
No
R5
Residuals
4
60
1.39
55.45
0.35
0.92
0.38
0.82
No
C6
Residuals
4
76
0.56
68.50
0.14
0.90
0.155
0.96
No
R6
Residuals
4
70
4.24
58.15
1.06
0.83
1.28
0.29
No
T6
Residuals
4
74
2.08
82.58
0.52
1.12
0.47
0.76
No
C7
Residuals
2
51
1.64
62.48
0.82
1.23
0.67
0.52
No
94
5
E XPERIMENTAL R ESULTS AND A NALYSIS
Figure 5.17: SLI position (relative to base of window) versus time (relative to start of
test) for C2 rods with drop detachment marked by a square.
Figure 5.18: SLI position versus time for individual drop cycles for C2 rods indicating
an increasing-decreasing trend in the instantaneous RRMI.
95
5.2 RRMI R ESULTS AND A NALYSIS
Figure 5.19: SLI position (relative to base of window) versus time (relative to start of
test) for C6 rods with drop detachment marked by a square.
Figure 5.20: SLI position versus time for individual drop cycles of C6 rods indicating
the variation in instantaneous RRMI than was measured.
96
5
5.2.4
E XPERIMENTAL R ESULTS AND A NALYSIS
RRMI, VFR and Cross-Sectional Area
RRMI varies according to the XA of the rod. RRMI as a function of XA is best
described by a power relationship. Regression models of the form:
ln(RRM I) = β0 + β1 ln(XA) + (5.1)
were developed based on the individual drop cycle data. Equation 5.1 can be written
in the power form:
RRM I = α0 (XA)α1 e
(5.2)
where, β0 = ln(α0 ) and β1 = α1 . This relationship is reflected in Figure 5.21 in which
individual drop cycle RRMIs for the cylindrical, rectangular and triangular rods are
plotted against XA. Figure 5.21 also displays the fitted regression model, mean RRMI
values for each geometry and the 95% confidence intervals based on the regression fit.
The fitted equations for the RRMIs of the cylindrical, rectangular and triangular rods
are given by:
RRM IC = 24.6(XA)−0.45
R2 = 78.2%
(5.3)
RRM IR = 27.3(XA)−0.46
R2 = 83.6%
(5.4)
RRM IT = 26.7(XA)−0.44
R2 = 84.0%
(5.5)
respectively, where the R2 values are the ratio of the variation accounted for by the
regression model to the total variation. Hence, they are a measure of the fraction of
variance in the data that is accounted for by the model [117]. Higher R2 values indicate
a better fit. Although every effort was made to maintain identical test conditions there
were uncontrollable factors, for example, variation in sample microstructure. Hence,
given the level of control in the promoted ignition tests conducted and the fact that the
RRMI is dependent on a number of factors, the R2 values for the models are reasonable.
The graphs indicate that the mean RRMI values lie close to the regression line and the
95% confidence intervals decrease with increasing XA due to the greater amount of
data for the larger XAs.
Although RRMI decreases as XA increases, the Volume Flow Rate (VFR) (volume
of material that melts and/or burns and is removed during a drop cycle) increases with
increasing XA. This trend is shown in Figure 5.22 in which VFR data for each drop
cycle is plotted against XA for the cylindrical, rectangular and triangular rods. The
figure includes the mean VFR’s for each geometry, the regression line and the 95%
97
5.2 RRMI R ESULTS AND A NALYSIS
confidence intervals based on the regression fit. The same regression approach was
taken and the power law equations for the VFR of the cylindrical, rectangular and
triangular rods as a function of XA are given by:
V F RC = 24.6(XA)0.55
R2 = 84.2%
(5.6)
V F RR = 27.3(XA)0.54
R2 = 87.7%
(5.7)
V F RT = 26.7(XA)0.56
R2 = 89.5%
(5.8)
respectively. The graphs indicate that the range in VFR data is greater for the larger
XAs and the 95% confidence intervals appear marginally wider. This is an artifact of
multiplying the RRMI data by a larger XA.
For comparison, the regression fits for the cylindrical, rectangular and triangular
rods are plotted on the same axes in Figures 5.23a and 5.23b for the RRMI and VFR
data, respectively. The graphs reflect the differences in RRMI based on shape and the
deviation in the regression fits as the XA increases.
Mean RRMI data was used to ascertain the relative difference between the RRMIs
of the rectangular and triangular rods compared to the RRMIs of cylindrical rods;
RRM IT /R − RRM IC
.
RRM IC
(5.9)
The results reflect an increasing deviation in RRMI as XA increases, as shown in
Figure 5.24. Since VFR is related to RRMI through the XA the relative increase in
VFR for the rectangular and triangular rods over that of the cylindrical rods is also
given by the data plotted in Figure 5.24.
98
5
E XPERIMENTAL R ESULTS AND A NALYSIS
(a) Cylindrical rods.
(b) Rectangular rods.
(c) Triangular rods.
Figure 5.21: RRMI drop cycle data versus XA with the fitted regression model, mean
and 95% confidence intervals shown.
99
5.2 RRMI R ESULTS AND A NALYSIS
(a) Cylindrical rods.
(b) Rectangular rods.
(c) Triangular rods.
Figure 5.22: VFR drop cycle data versus XA with the fitted regression model, mean
and 95% confidence intervals shown.
100
5
E XPERIMENTAL R ESULTS AND A NALYSIS
(a) RRMI vs XA.
(b) VFR vs XA.
Figure 5.23: Drop cycle data versus XA for X2 to X7 geometries with associated power
law fits.
101
5.2 RRMI R ESULTS AND A NALYSIS
Figure 5.24: Relative differences in RRMI with respect to the cylindrical rods versus
XA.
5.2.5
RRMI and Rod Shape
Confidence intervals were calculated using a t-test to compare the mean RRMI values
for the cylindrical, rectangular and triangular rods of the same XA. Associated theory
is presented in Section 3.1.3. Ninety-five percent confidence intervals for the difference
in mean RRMI were calculated using the summary data from Table 5.4 since ANOVA
testing indicated that individual tests of the same geometry were not statistically significantly different. Table 5.6 gives the 95% confidence intervals and an assessment
as to the significance of the difference in RRMI for the pairwise combinations evaluated based on a 5% significance level. The first column indicates which geometries
the confidence interval was calculated for, for example, the first row indicates that the
95% confidence interval for the difference between the mean RRMI of the C2 rods,
µ1 , and the R2 rods, µ2 is (-1.61, -0.63). The negative signs are consistent with the R2
rods having a faster RRMI than the C2 rods.
Differences in mean RRMI due to rod shape were also evaluated by conducting an
ANOVA test. The null hypothesis was that there is no difference in the mean RRMI
resulting from a change in rod shape. Results are presented in Table 5.7, note that
the X3 and X5 comparisons are for the cylindrical and rectangular rods only as no
102
5
E XPERIMENTAL R ESULTS AND A NALYSIS
Table 5.6: RRMI confidence interval analysis results.
µ1 − µ2
95% CI Lower
(mm/s)
95% CI Upper
(mm/s)
p-value
Significant
Difference
C2 - R2
-1.61
-0.63
0.0000
Yes
C2 - T2
-1.89
-0.88
0.0000
Yes
R2 - T2
-0.79
0.25
0.297
No
C3 - R3
-1.79
-0.61
0.0001
Yes
C4 - R4
-0.95
-0.35
0.0000
Yes
C4 - T4
-1.46
-0.85
0.0000
Yes
R4 - T4
-0.83
-0.18
0.0027
Yes
C5 - R5
-0.79
-0.17
0.0027
Yes
C6 - R6
-0.90
-0.32
0.0001
Yes
C6 - T6
-1.34
-0.72
0.0000
Yes
R6 - T6
-0.74
-0.11
0.0084
Yes
triangular samples were tested for those XAs. The ANOVA test results indicate if
there are any significant differences in RRMI due to shape but they do not indicate
which of the cylindrical/rectangular/triangular combinations caused the significant result. Following an ANOVA test in which differences were found to be significant, an
assessment as to which pairs of data contributed to the significant result was made via
post hoc testing. A common test is Tukey’s Honestly Significant Difference (HSD)
test by which groups can be compared on a pairwise basis to assess differences between means [117]. The method is an alternative to the t-test and ensures the stated
significance level is true. When performing multiple t-tests the chances of finding a
significant difference, when there are in fact no significant differences, increases as
the number of comparisons that are made increases, Tukey’s method compensates for
this fact. Tukey method confidence intervals were expected to be similar to those formulated via t-tests, Table 5.6 since at most three pairwise comparisons were made for
each XA. Confidence interval diagrams were developed based on the Tukey method
confidence intervals obtained through S-PLUS®. These diagrams graphically reflect
the differences in RRMI between geometries, Figure 5.25. The intervals are grouped
according to the shapes compared, cylinder and rectangle, cylinder and triangle, and,
rectangle and triangle. Within each group the confidence intervals for the X2, X4 and
103
5.2 RRMI R ESULTS AND A NALYSIS
X6 XAs are plotted, coded by colour. The critical information to be interpreted from
the graph is whether the confidence interval crosses the zero line. If zero lies within
the confidence interval there is no significant difference between the mean RRMIs of
the shapes being compared at the chosen significance level, 5%.
Table 5.7: S-PLUS ANOVA results - RRMI shape comparison.
Source
Deg. of
Freedom
(df)
Sum of
Squares
(SS)
Mean
Square
(MS)
F Value
p-value
Significant
Difference
X2
Residuals
2
57
21.70
35.37
10.85
0.62
17.48
1.2e-6
Yes
X31
Residuals
1
74
27.29
121.26
27.29
1.64
16.66
1.12e-4
Yes
X4
Residuals
2
153
36.25
96.51
18.13
0.63
28.74
2.54e-11
Yes
X51
Residuals
1
128
7.46
102.23
7.46
0.80
9.34
2.74e-3
Yes
X6
Residuals
2
232
43.14
216.11
21.57
0.93
23.16
6.77e-10
Yes
1
Comparison of cylindrical and rectangular rods only.
5.2.6
Drop Cycle Times
The drop cycle time is the duration of a single drop cycle and is equivalent to the time
during which a drop is attached to the rod. Table 5.8 contains summarised drop time
data for the geometries tested.
104
5
E XPERIMENTAL R ESULTS AND A NALYSIS
Figure 5.25: Tukey method 95% confidence intervals for RRMI.
Table 5.8: Drop time summary table.
I.D.
Pressure
Absolute
(MPa)
Mean
Time
(s)
Std. Error
Mean
(s)
Std.
Dev.
(s)
No.
Drops
(N)
95% CI
Lower
(mm/s)
95% CI
Upper
(mm/s)
C2
6.96
0.574
0.006
0.028
20
0.561
0.587
C31
6.84
0.508
0.004
0.023
40
0.500
0.516
C4
6.94
0.487
0.005
0.035
56
0.478
0.497
C5
6.83
0.512
0.005
0.043
65
0.501
0.523
C6
6.95
0.502
0.005
0.047
81
0.491
0.512
C7
6.82
0.483
0.006
0.044
54
0.471
0.495
R2
6.94
0.562
0.008
0.035
20
0.545
0.579
R3
6.78
0.503
0.006
0.035
36
0.491
0.515
R4
6.94
0.494
0.005
0.036
48
0.484
0.505
R5
6.86
0.495
0.005
0.036
65
0.486
0.504
R6
6.94
0.471
0.004
0.038
75
0.462
0.479
T2
6.94
0.554
0.004
0.020
20
0.545
0.563
T4
6.94
0.459
0.004
0.031
52
0.450
0.467
T6
6.95
0.458
0.005
0.045
79
0.448
0.468
1
Excludes C32 data.
105
5.3 E XTENT OF R EACTION : M ICROANALYSIS
5.3
Extent of Reaction: Microanalysis
This section presents results from the analysis of quenched samples that were examined
to assess the ER of detached drops as a function of sample geometry and pressure. This
work was performed to gain insight into the burning process. Most of the tests were
conducted at a pressure of 6.9 MPa, however, selected samples were also tested at
low pressure, 1.1 MPa, to compliment the high pressure work and to verify earlier
published work.
5.3.1
General Observations
During promoted ignition tests in which the detached drops were quenched the rod
appeared to burn in the same manner as was observed during the standard promoted
ignition tests. However, during quench tests of the larger diameter rods, a significant
amount of water vapour was generated which gradually obscured the burning rod. The
volume of a detached drop was significantly larger in the case of the Q4H and Q6H
rods, hence, to cool the drops a greater amount of heat is dissipated by the water bath
producing more vapour. The video record showed that the slag for Q0.25H originated
from a single drop formed from the entire rod. The slag for Q0.5H , Q1H , Q4H and
Q6H was formed from approximately three, six, twelve and twenty drops respectively.
The RRMIs in the low pressure quench tests were slower than in the high pressure
tests, otherwise, the burning appeared similar.
5.3.2
Photographic Record and Microanalysis Results
This section presents images of the quenched slag; pre-resin, post-resin and those captured using both light microscopy and scanning electron microscopy. The aim of this
work is to qualitatively ascertain the fraction of metal that undergoes oxidation whilst
attached to the rod prior to drop detachment. By quenching the slag in cold water
the detached drops were rapidly cooled, providing a far better representation of the
species present during burning than samples which cool slowly. It is assumed that the
effects of the short period of burning between drop detachment and immersion in the
water bath are not significant. Typical post-test quenched slag masses are shown in
Figure 5.26. The slag of Q0.5H comprised of small pieces even though it was formed
from a single detached drop. This is perhaps due to the high proportion of oxide within
106
5
E XPERIMENTAL R ESULTS AND A NALYSIS
the slag mass, which would have become extremely brittle once cooled or due to excess oxygen which was released during cooling contributing to the break up of the slag
mass. Satellite drops, sometimes visible in the test videos for larger rods, may also
partially account for some of the particulate matter present within the slag in general.
The slag from Q4H and Q6H was contained within a larger conglomerated mass, the
remainder of the slag was in smaller pieces. Since individual drops could not be easily
identified within the post-test slag masses the ER of the entire slag mass was assumed
to approximate the ER of a single drop.
(a) Q0.5H
(b) Q4H
(c) Q6H
Figure 5.26: Typical post-test quenched slag masses from high pressures tests (6.9
MPa).
When viewed in natural light, the unreacted metal visible in the polished cross
sections appears shiny and silver/white whilst oxide appeared a darker grey/black as
shown in Figure 5.27. The slag from Q4H and Q6H was divided into two resin blocks.
One containing a large conglomerated slag mass, the other containing smaller particles.
Figure 5.28 shows images of the quenched slag from Q0.25H . Initial photographs
of the polished resin blocks, Figures 5.28a and 5.28b, revealed a few larger regions
of unreacted metal and the remaining material appeared to be oxide. Figure 5.28c
is a BSE from the SEM of the region indicated in Figure 5.28b. The BSE image
is an excellent example of the various materials that were identified in each of the
slag masses that were examined using the SEM. The white semi-circular particle is
palladium. The darker mass is aluminium oxide containing specs of palladium. The
lighter grey masses are iron oxide. The igniter wire was an aluminium-palladium alloy
so it was not surprising that these elements were identified within the slag mass. Two
distinct phases were evident in the bright semi-circular particle in Figure 5.28a and
they are shown in Figure 5.28d. The spectra for the lighter and darker phases are
overlaid in Figure 5.28e. The two spectra were scaled to the Fe Kα peak so that the
relative difference in oxygen between the light and dark phases was clear. The darker
107
5.3 E XTENT OF R EACTION : M ICROANALYSIS
(a) Q0.25H
(d) Q4-AH
(b) Q0.5H
(e) Q4-BH
(c) Q1H
(f) Q6-AH
(g) Q6-BH
Figure 5.27: Polished cross sections of the high pressure(6.9 MPa) slag mounted in
resin which indicate the relative amount of reacted and unreacted material present.
phase, smaller atomic number, has a higher oxygen content. The oxygen to iron ratios,
standardised against certified hematite and magnetite samples, for the light and dark
regions were 1.04 and 1.22, respectively. This indicates that the lighter material is FeO
but the darker material is probably a combination of FeO and Fe3 O4 . Figure 5.28c
clearly shows that the oxide of both iron and aluminium was infused with voids which
gave it a porous appearance.
Images of Q0.5H showed that the slag mass was comprised predominantly of oxide,
Figure 5.29. The strip of unburned metal in the center of Figure 5.29a was identified
as palladium, as was the bright half of the semi-circular drop at the top of the image. The circular droplet in the top right corner of Figure 5.29a was magnified and
photographed using the reflected light microscope, Figure 5.29b and further examined
using the SEM, Figure 5.29c. The mass contained a multitude of voids and the oxide
appeared to consist of two different phases. The spectra for these phases indicate the
lighter phase is FeO, based on an oxygen to iron ratio of 1.00, and the darker phase
is a combination of FeO and Fe3 O4 as its oxygen to iron ratio is a higher 1.19. Similar patterns were observed in a handful of other oxide particles. An SEM image of
the particle to the right of the palladium strip (indicated in Figure 5.29a) is shown in
Figure 5.29d. The oxygen to iron ratios of the dark grey and light grey phases that
108
5
E XPERIMENTAL R ESULTS AND A NALYSIS
are visible are 1.37 and 1.21, respectively. Therefore, the darker material is Fe3 O4 and
the lighter material is a non-stoichiometric oxide or a combination of FeO and Fe3 O4 .
Again the darker phase has a higher oxygen content.
The slag masses of samples Q1H , Q4H and Q6H were not examined using the SEM.
These samples consisted of little unreacted material as shown in Figures 5.30, 5.31
and 5.32, respectively. Based on the SEM results from samples Q0.25H and Q0.5H
the composition of these remaining high pressure samples was assumed to consist
predominantly of FeO and Fe3 O4 . A small portion of the aluminium oxide alloy that
was detected in both Q0.25H and Q0.5H , generated during the ignition event, is also
likely present. The small regions of unreacted metal that are visible were assumed to
be palladium (igniter wire). The amount of unreacted palladium present in each of
the samples is consistent with the number of wraps of igniter wire that were used in
each test. The optical images indicate the slag masses were extremely porous. High
quantities of particulate matter indicate that the slag was also quite brittle which is
consistent with the slag being composed predominantly of oxide.
After it was determined that there was little or no unreacted iron present in the high
pressure quenched samples for the range of diameters that were tested, low pressure
tests were conducted. Previous quenching and microanalysis studies of iron showed
a significant fraction of the slag consisted of unreacted iron [32]. These tests were
conducted at a low pressure, 0.69 MPa, compared to 6.9 MPa used in this study. These
differing results suggest that the test pressure significantly affects the ER. Post-test
low pressure slag samples were set in resin and their cross-sectioned surfaces revealed
they contained a greater amount of unreacted metal, as shown in Figure 5.33, than the
high pressure samples. Sample Q6L was divided between two resin blocks, Q6AL and
Q6BL .
Q6-AL was examined under the SEM in order to identify the composition of the
unreacted metal. All but one of the silver regions was identified as pure iron (1-6). The
remaining region (7) was identified as a combination of unreacted iron and palladium.
A magnified view of (5) is shown in Figure 5.34b. Darker regions within the unreacted
iron, Figure 5.34c were examined and found to be a mix of iron, oxygen and manganese. Manganese was a minor alloying element of the 6 mm diameter mild steel rod.
Oxygen to iron ratios at points 9 and 10 indicate that they are composed of FeO and
Fe2 O3 , respectively. Oxygen to iron ratios were standardised against haematite and
magnetite samples to ensure these specific oxides were accurately identified. These
standards also formed a basis from which to identify non-stoichiometric oxides and
109
5.3 E XTENT OF R EACTION : M ICROANALYSIS
(a)
(b)
(c)
(d)
(e) Spectra of light and dark phases in Figure 5.28d
Figure 5.28: Optical (a,b) and SEM (c,d) images for Q0.25H including spectra for two
different oxides. The spectra are scaled to the Fe Kα peak.
110
5
E XPERIMENTAL R ESULTS AND A NALYSIS
(a)
(b)
(c)
(d)
Figure 5.29: Optical (a,b) and SEM (c,d) images for Q0.5H including spectra for two
different oxides.
(a)
(b)
Figure 5.30: Optical images for sample Q1H indicating extensive oxidation and no
unreacted iron.
111
5.3 E XTENT OF R EACTION : M ICROANALYSIS
(a)
(b)
(d)
(f)
(c)
(e)
(g)
(h)
Figure 5.31: Optical images for sample Q4H (a)-(e) conglomerated slag mass and (f)(h) remaining slag indicating extensive oxidation and no unreacted iron.
112
5
(a)
E XPERIMENTAL R ESULTS AND A NALYSIS
(b)
(d)
(f)
(c)
(e)
(g)
(h)
Figure 5.32: Optical images for sample Q6H (a)-(e) conglomerated slag mass and (f)(h) remaining slag indicating extensive oxidation and no unreacted iron.
113
5.3 E XTENT OF R EACTION : M ICROANALYSIS
(a) Q0.5L
(b) Q4L
(c) Q6-AL
(d) Q6-BL
Figure 5.33: Polished cross sections of the low pressure (1.1 MPa) slag mounted in
resin indicating relative amount of reacted and unreacted material present.
(a)
(b)
(c)
(d)
Figure 5.34: Optical (a) and SEM (b-d) images for sample Q6-AL indicating regions
of unreacted iron.
114
5
E XPERIMENTAL R ESULTS AND A NALYSIS
wustite. The surrounding oxide matrix was also examined, Figure 5.34d. Region 11
had an oxygen to iron ratio of 2.48 which is unusually high and exceeds that of the
common oxides, FeO, Fe2 O3 and Fe3 O4 . It is therefore possible that at this point there
was significant dissolved oxygen or that higher oxides, which transport oxygen from
the gaseous surroundings to the reaction surface have been captured due to the rapid
cooling process. Region 12 had an oxygen to iron ratio close to one so is likely FeO.
Q0.5L was also examined under the SEM in order to compare the results to those
for Q6-AL . Ten regions of unreacted metal are visible on the sectioned surface, as
shown in Figure 5.35a. Nine of these regions (2-10) are pure palladium and the remaining region (1), Figure 5.35b is a combination of palladium and iron in a ratio
of 2.5:1. Within the unreacted palladium/iron alloy, local regions of iron oxide are
present, similar to those identified in Figure 5.34c for Q6-AL . The oxygen to iron ratio
of these inclusions slightly exceeded that for wustite but was smaller than that of magnetite, hence, the material may be a non-stoichiometric oxide, FeOx , where,
1 < x < 1.33. Alternatively, the non-stoichiometric O:Fe ratios may be due to a mixture of stoichiometric oxides (FeO, Fe3 O4 and Fe2 O3 ). Generally the O:Fe ratios were
not high enough to indicate the presence of isolated Fe2 O3 .
(a)
(b)
Figure 5.35: Optical and SEM images for sample Q0.5L indicating extensive oxidation.
Table 5.9 presents a qualitative summary of the microanalysis results with regard
to the relative amount of unreacted iron detected, if any, and the amount of iron oxide
detected. A qualitative assessment of the ER is also provided.
115
5.3 E XTENT OF R EACTION : M ICROANALYSIS
Table 5.9: Microanalysis summary table.
I.D.
Diameter
(mm)
Pressure
(MPa)
Analysis
Results
ER
Q0.25H
Q0.5H
Q1H
Q4H
Q6H
0.25
0.5
1
4
6
6.9
Iron oxides
High
Q0.5L
0.5
1.1
Iron oxides and small amount
of unreacted iron
High
Q4L
4
1.1
Iron oxides and moderate
amount of unreacted iron
Medium-high
Q6L
6
1.1
Iron oxides and a large
amount of unreacted iron
Medium
116
C HAPTER 6
D ISCUSSION
This chapter presents a detailed analysis of the experimental results. The chapter is
divided into three main sections. Section 6.1 discusses the results of the RRMI data
collected from the promoted ignition testing of rods of varying geometry. Visual observations and data analysis are discussed and the relationship between RRMI and
sample geometry is further explored. Section 6.2 presents a brief discussion of the
microanalysis results and the implication of these results to the burning of iron rods.
The final section, Section 6.3, draws together the experimental results in a discussion
of the effects of sample geometry on a burning metal rod system.
6.1
6.1.1
RRMI and Sample Geometry
Visual Observations
The visual burning of all the test samples was similar to previous reports on the promoted ignition testing of iron and mild steel [26, 31, 37, 41, 50]. The luminosity of
the attached molten mass increased during a drop cycle, suggesting that the surface
temperature of the burning mass increased, which is consistent with the temperature
profile reported by Kurtz et al. [46] for iron rods. The luminosity of the molten mass
decreased with increasing XA since the smaller rods requiring a greater number of ND
filters to achieve a similar exposure. Correlating the increase in luminosity during a
drop cycle to the published increase in surface temperature during a drop cycle, this
trend suggests that the molten mass of the larger rods is cooler than that of the smaller
rods. The temperature difference could be due to the volume of liquid metal that is
incorporated into the molten mass during a drop cycle which acts as a heat sink.
117
6.1 RRMI
AND
S AMPLE G EOMETRY
There was evidence to suggest that gas was released from within the molten slag
during cooling, as has been previously reported [31, 32, 44, 52, 142]. The domes that
were produced during the cooling of slag from many of the X6 rods demonstrated the
large volume of gas released from the molten material, Figure 5.7. The released gas is
assumed to have been oxygen since volatilisation of the oxide or iron is unlikely [1,44].
In the slag mass, oxygen was present either dissolved in solution or chemically bound
to the iron (as ferrite ions), and on cooling, the oxygen came out of solution and/or the
ferrite ions reduced to more stable oxide species, releasing excess oxygen and forming
the observed domes. Further clear evidence of a dynamic slag pool is provided by the
molten drops that entered the field of view during X6 tests, Figures 5.8 - 5.10. The
drops were projected upward from the slag pool at the base of the chamber having
been propelled upwards by escaping oxygen as the slag mass cooled.
Although the chamber pressure increased during a test, Figure 5.11, the increase
did not result in markedly higher drop cycle RRMIs as the test progressed. The possibility of higher drop cycle RRMIs was considered based on the proportional relationship between RRMI and pressure. Since all tests were conducted at 6.9 MPa it is
reasoned that, although the pressure marginally increased, it did not adversely affect
oxygen incorporation, reaction rate or temperature. Hence, the RRMI did not increase
during the test. The ER work supports this conclusion as it was shown that at 6.9 MPa
all available iron within the molten mass had reacted, hence, a small increase in pressure had no effect on the observed drop cycle RRMI. This result demonstrates the value
of calculating the RRMI on a drop cycle basis in order to gain insight into variations
in the processes occurring throughout a test.
In order to melt the rod, sufficient heat must be transferred across the SLI. Thus,
the surface area of the SLI directly affects the RRMI. Increasing the area of the SLI,
other variables equal, increases the total energy transferred to the solid rod causing
the rod to melt more rapidly. Modelling a moving phase change boundary in three
dimensions is non-trivial [143–148], particularly when the geometry in question is not
axis-symmetric, or even well characterised, as is the case for rectangular and triangular
cross sections. Figures 5.5 and 5.6 show that the SLI of the rectangular and triangular
rods is slightly convex. Measured RRMIs for the three shapes, combined with the
video footage, shows that the rate of heat transfer is affected by the presence of corners
in the cross sections of the rectangular and triangular rods. For these two shapes the
melting rate at the corners exceeds that along the flat edges. This occurs because heat
transfer into material at a corner is greater due to the locally higher SA/V ratio. Heat
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is transferred into the material at the corner along two edges over a combined surface
area greater than along the flat edges for the shapes considered. Therefore, within
the corner, the rate of heat transfer is increased, and heat loss to cooler neighbouring
material is also reduced. Rapid melting in the corner establishes an SLI with a convex
shape, thereby increasing its surface area. Assuming a constant heat flux, an increase
in SLI surface area results in greater heat transfer to the solid rod causing the RRMIs
of the rectangular and triangular rods to be faster than the RRMIs of the cylindrical
rods.
6.1.2
Drop Cycle RRMI Analysis
The RRMI data presented in Section 5.2.1 was calculated, for a single test, using all
drop cycles observed during the test. This approach is only valid if the drop cycle data
is independent. In addition, the mean RRMI for each geometry was calculated based
on all the drop cycle RRMIs for tests of that geometry and this approach is valid only
if the data for tests of the same geometry represent the same population.
Factors that may lead to dependence between drop cycle RRMIs include chamber
pressure, chamber temperature and the temperature of the rod. The increase in chamber
pressure during a test, Figure 5.11, as well as chamber temperature would intuitively
contribute to an increase in drop cycle RRMI throughout a test since each is directly
proportional to RRMI. However, this was shown not to be the case. At higher test pressures the relationship between test pressure and RRMI becomes weaker, Figure 2.6, so
for the minor changes in test pressure during a test no significant difference in drop cycle RRMI was observed. Further, results from the microanalysis of slag from samples
burned at 6.9 MPa, to be discussed later, clearly indicate an extent of reaction of one
indicating that the test was conducted at a pressure sitting in the lower shelf region of
the PICT curve, hence, changes to pressure or temperature do not significantly affect
RRMI as the available fuel is fully combusted.
To evaluate the independence of the drop cycle RRMIs time series plots were
formed, Figures 5.13. There were occasions when a faster than average drop cycle
RRMI was followed by a slower than average drop cycle RRMI and vice versa but
these occurrences were by no means consistent. There were no patterns detected in the
time series plots, hence, the RRMIs of consecutive drop cycles can be assumed to be
independent for all the geometries that were investigated.
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An alternative approach to evaluate the independence of the drop cycle RRMIs is
to plot the ‘next’ drop cycle RRMI versus the ‘current’ drop cycle RRMI. A fast-slowfast drop cycle RRMI pattern would present itself in a linear fashion in the plot. In
Figure 5.14, the data for each geometry is plotted on a single graph. The data lies along
a band from the bottom left to the top right representing the increasing RRMI with
decreasing XA. Within each geometry grouping the data is well scattered. Selected
geometries were plotted individually to clarify the typical data scatter, Figure 5.15.
There were no obvious patterns in the data, but the occasional fast/slow, slow/fast
progression was evident (circled data points). Therefore the time series and drop series
plots are consistent and the drop cycle RRMI data can be considered independent.
Consistency between the data collected from individual rods of the same geometry
was evaluated by forming rod series plots and performing an ANOVA test. Individual
value plots, Figure 5.16, are useful to identify trends and unusual or outlying data.
Individual value plots consisting of limited data (e.g., X2) display a greater variation
between each rod of a single geometry than plots with more data (e.g., X6). The plots
showed that the RRMIs for each rod of the same geometry were similar, except for test
C32 . To quantify this result an ANOVA test was performed.
ANOVA results, presented in Table 5.5, were interpreted using a significance level
of 5%. p-values greater than 0.05 indicate that there is little or no evidence to suggest that the observed differences between the mean RRMI of each rod (for a single
geometry) did not occur by chance. The p-value for only one geometry, C3, was less
than 0.05. This result is attributed to the variation in test pressure among the six C3
tests that were performed since the digital pressure gauge was unavailable at the time.
Test C32 had a substantially lower test pressure than the remaining five C3 tests. The
effect of this lower pressure on the drop cycle RRMIs is evident in Figure 5.16b in
which the data for rod C32 appears to lie lower than the data for the remaining C3
rods. The lower overall RRMI for C32 is likely a result of the extreme outlier indicated
in Figure 5.16b. Data from test C32 was removed and the ANOVA test was repeated
to give a new p-value of 0.19. Based on this result, C32 test data was not included in
further analysis, hence, the summarised C3 data reported in Table 5.4 excludes data
for rod C32 . In summary, there was insufficient evidence to reject the null hypothesis,
hence, the mean RRMIs for the rods of the same geometry are not significantly different. It can therefore be assumed that the rods represent the same population making it
legitimate to combine all drop cycle RRMI data for each geometry to obtain a representative mean and standard deviation for that geometry. These RRMI values are listed
in Table 5.4 in Section 5.2.1.
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D ISCUSSION
Instantaneous RRMI
The position of the SLI for the C2 and C6 geometries is plotted in Figures 5.17
and 5.19, respectively. A ‘wave’ pattern was apparent which suggests that the RRMI
increases over the course of a drop cycle but slows down slightly immediately prior to
drop detachment. This pattern was more distinct for the C2 rods than the C6 rods and
may be attributed to the fact that the drops attached to C6 rods appeared to be more
elongated during a drop cycle and so their contact angle was smaller. At the point of
detachment the attachment geometry of the C2 drops changed more dramatically than
for the C6 drops (see Figures 5.1 and 5.3). The size of the C6 rods enabled subtle
changes in the shape of their SLIs to be observed in more detail than was the case for
the C2 rods. The SLI orientation fluctuated more for the larger rods and this fluctuation explains the lack of repeatability in the instantaneous RRMI pattern during a drop
cycle.
An increasing then decreasing pattern in the instantaneous RRMI is consistent with
previously reported trends [32, 38, 41] and can be explained by the theory initially proposed by DeWit [47]. DeWit attributed the decrease in instantaneous RRMI towards
the end of the drop cycle to a reduced contact area between the molten mass and solid
rod caused by gravitational stretching just prior to drop detachment. As the mass of the
attached drop increases the contact angle between the solid rod and the molten mass
decreases, as seen in Figure 5.1. Hence, the extent to which the drop encompasses the
end of the rod also decreases. Following this logic, slight increases in RRMI just after
drop detachment may be attributed to vertical oscillations in the molten mass as the
molten neck, which is produced during detachment, springs upward to rejoin the remainder of the drop. This motion also increases the contact angle. Vibrations induced
by the retraction and re-incorporation of the molten mass neck into the new attached
drop were evident in high speed video footage of a burning iron rod (T. Steinberg,
Personal Communication, July 21, 2006) and are also observed in a similar context in
the study of dripping from nozzles [149, 150]. The degree to which the drop engulfs
the end of the rod is dependent on rod geometry and gravity level. As the drop grows
its weight increases and the molten mass undergoes significant gravitational stretching
(Figure 5.1g - i). The drop begins to pull down away from the rod, a neck forms and finally, the drop detaches when the surface tension force is no longer able to support the
drop’s weight. During the latter period of the drop cycle it was clear that the drop no
longer engulfs the end of the rod to the same degree as occurred during the main part of
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the drop cycle. The attachment area between the molten mass and solid rod minimises
just prior to drop detachment (Figure 5.1i). This physical phenomena coincides with
the slight periodic decrease in the instantaneous RRMI shown in Figure 5.17. This
behaviour indicates the important effect of contact angle on the RRMI during a drop
cycle. In addition, the result supports the hypothesis that changes in contact angle
caused by rod shape contribute to differences between the RRMIs for rods of differing
geometries.
The instantaneous RRMI is highly dependant on the motion of the molten mass
and activity within its subsystems, in particular the size and shape of the SLI. RRMI
is directly proportional to heat transfer to the solid rod. The fluctuating instantaneous
RRMI during a drop cycle indicates that heat transfer also fluctuates. Heat transfer is
at its peak when the contact angle is the largest and the drop engulfs the rod (larger
SLI), and is minimised when the drop necks prior to detachment reducing the contact
area and the contact angle (smaller SLI). Hence, even small changes in the SLI during
a single test affect the amount of energy transferred to the rod, and subsequently, affect
the RRMI.
6.1.4
RRMI, VFR and Cross-Sectional Area
The variation of drop cycle RRMI and drop cycle VFR as a function of XA is shown
in Figures 5.23a and 5.23b, respectively. In the graphs, the variation in data appears to
increase for the larger XAs, more so for the VFR data. However, variance tests across
shapes for a single XA and across XAs for a single shape indicated that the difference
in variance was not statistically significant at a 95% confidence level. The spread in
data is attributed to the greater amount of data that was collected for the larger XAs,
since the rods melted more slowly. For a similar underlying distribution, if only a few
data points are measured, it is highly likely that these points will lie close to the mean.
However, if many points are measured it is likely that some of the points will lie further
from the mean, in the tails of the distribution. Hence, the data appears to be spread out
even though the variance is similar.
RRMI decreases with increasing XA for the three shapes tested, Figure 5.23a. The
RRMI decreases rapidly for samples of a smaller XA but the RRMI plateaus as the XA
increases. The RRMI trend line asymptotically converges on the x-axis, an artifact of
the power curve regression fit. Current knowledge indicates that as the XA increases,
it will reach a value for which sustained burning will not occur at 6.9 MPa, 6.9 MPa
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will represent the TP for that particular XA. Therefore, the regression fit will be truncated at this point and it is not appropriate to draw conclusions based on extrapolating
the data for large XAs. The regression fit was extrapolated to smaller XAs and its
predictions compared with estimated RRMIs for the small diameter microanalysis test
samples. The regression fit appears to overestimate the RRMIs for these smaller XAs.
However, only one test was performed for these small diameter samples so the result
is not conclusive. Therefore, interpolating data from Figure 5.23a is acceptable but
further testing should be performed in order to gather data for larger and smaller XAs.
The relative difference in the mean RRMI of the rectangular and triangular rods
compared to the mean RRMI of the cylindrical rods is shown in Figure 5.24. Differences in RRMI caused by rod shape are a function of XA. For smaller XAs relative
differences in RRMI are small but as XA increases these differences also increase.
This behaviour was more pronounced for the triangular rods than for the rectangular
rods. The RRMI vs XA plot, Figure 5.23a, supports this finding. The absolute differences between the RRMI of the triangular rod and the RRMI of the cylindrical rod are
similar for all XAs. Since the RRMI is smaller for larger XAs the relative difference
in RRMI between the two shapes increases with XA. Rod dimensions were calculated
to maintain the same XA for all three shapes. Ratios based around the dimensions of
the cylindrical, rectangular and triangular rods give the same result for all the XAs.
Hence, the initial sample geometry cannot be used to explain the increased relative
difference in RRMI between shapes as XA increases. Therefore, the result shown in
Figure 5.24, that the difference in RRMI between the rectangle and triangle, compared
to the cylinder, becomes progressively larger as XA increases must be the result of
changing subsystem geometries, rather than the result of the initial rod geometry.
VFR increases as XA increases. Since the RRMI is effectively an indication of the
volume flux (or mass flux if multiplied by the density), it follows that, if the heat flux
were the same for rods of different XA, their RRMIs should be equal and independent
of XA. If this were the case VFR would increase in a linear fashion. Instead, the data
shows that the rate at which VFR increases actually decreases with increasing XA. This
suggests that heat generation and/or heat transfer becomes limited as the sample’s XA
increases or that some mechanism increases heat loss to the surroundings. Determining
why this is the case has previously been attempted unsuccessfully. Based on the current
work an explanation of why rods with a larger XA burn more slowly than rods with a
smaller XA is proposed.
The filter levels required to provide similar exposure on the video for the X2 and
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X6 rods were 8-stops and 4-stops, respectively. Each stop reduces the level of light that
reaches the camera by half. Therefore, the luminosity of the X6 rods is approximately
16 times less than that of the X2 rods. ND filters do not, however, alter the colour of
the image so the test video is representative of the actual colour of the molten mass and
is not an artifact of filtration. The colour of the drop varies during a drop cycle. The
drop is initially red/orange and becomes a bright white as the molten mass grows. The
colour of the drop also varies with XA. The drops formed on rods with a smaller XA
are a bright white but the drops from on the rods with a larger XA have a predominantly
orange hue, as shown in Figures 5.1, 5.2 and 5.3. The decrease in luminosity and red
colour shift indicate that the surface temperature of the molten mass which is formed
on larger rods is significantly less than that formed on the smaller rods. Hence, the
temperature gradient driving heat transfer to the rod in the case of the larger rods is
significantly reduced, resulting in a slower RRMI. This trend is consistent across the
different shapes that were tested. Since the observed trends between small and large
rods of different shape is consistent, the general burning behaviour of small and large
rods is independent of shape. The change in temperature as a function of XA is coupled
to the VFR. It was shown that as XA increases the VFR also increases. The amount
of material entering the molten mass of the larger rods is an order of magnitude larger
than that entering the molten mass of the smaller rods. The liquid metal enters at the
melting temperature and energy within the molten mass is transferred to heat the metal
up to the reaction temperature. Therefore, a greater amount of energy is used to heat
the liquid iron entering the molten mass in the larger rods. The molten mass of the
larger rods also has a far greater surface area so heat loss to the surroundings is greater.
These two factors may contribute to the lower drop temperature for rods of larger XA.
6.1.5
RRMI and Rod Shape
The summary data presented in Table 5.4 for the cylindrical, rectangular and triangular
rods suggests that their RRMIs differ, however, a statistically significant assessment
of these differences is essential. Mean RRMIs were compared in a pairwise fashion
through a t-test in which 95% confidence intervals were calculated for the difference
in mean RRMI. Confidence intervals, Table 5.6, and their associated p-values, indicate
that the RRMIs for all pairwise shape combinations for the same XA, except one, are
significantly different. This result is based on a significance level of 5%. The intervals
represent the difference between the means and since the intervals do not include zero,
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the null hypothesis, that the population means are equal, is rejected. Therefore, sample
shape significantly affects RRMI.
The sole combination for which a p-value exceeding 0.05 was calculated was for
the R2 and T2 rods. The result indicates that there is no significant difference in the
mean RRMI of R2 and T2 rods at 6.9 MPa. The RRMI of the cylindrical rods was
consistently smaller than the RRMI for the rectangular and triangular rods for all XAs.
The fact that the difference in RRMI between the smallest rectangular and triangular
rods was not significant but became significant for the larger X4 and X6 rods indicates that rod shape is more influential on RRMI for larger XAs. This results supports
the earlier conclusion that the relative difference in the RRMIs of the rectangular and
triangular rods compared to the RRMIs of the cylindrical rods increased with XA, Figure 5.24. Figure 5.24 also demonstrates the deviation of the rectangular and triangular
RRMIs with increasing XA. The greater relative differences in RRMI for larger XAs
is thought to be due in part to the distance between the corners. At a corner SA/V is
locally higher, therefore, heat is transferred into the material across a larger area and
heat loss via conduction to the neighboring solid metal is reduced. The temperature of
the metal at the corner therefore increases at a faster rate and so melts faster than the
metal along an edge or near the middle of the SLI. This causes the area of the SLI to increase locally at the corner. If the corners are too closely spaced these ‘corner effects’
overlap, effectively reducing the contribution of individual corners to the increase in
SLI area. In the test videos the SLI appeared more convex in the corners of the X6 rods
than it did for the X2 rods. This argument could be further explored through quenching
and microanalysis work examining the shape of the SLI.
ANOVA testing was performed to compare the RRMIs of the three shapes simultaneously. The null hypothesis, equal mean RRMIs, and the alternative hypothesis, that
one or more mean RRMIs are different, was evaluated. The calculated p-values for all
XAs were minute. Therefore, the alternative hypothesis was accepted. Although the
ANOVA test indicates that the mean RRMIs for the X2 rods are unequal this result
does not contradict the t-test result from which it was concluded that the mean RRMIs
for R2 and T2 were not significantly different. The ANOVA result simply shows that
the means for all three shapes cannot be considered equal. Tukey’s method was used
to evaluate which of the pairwise comparisons resulted in significant differences. For
the X2 rods differences in the C2 and R2, and, C2 and T2 mean RRMIs are significant but the difference in the R2 and T2 mean RRMIs are not. This result is identical
to the t-test result. The difference between the two approaches is that Tukey’s con125
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siders the confidence limits simultaneously and also provides a conservative estimate
in situations where the samples are of unequal size. Therefore, it can be concluded
that the shape of the cross section effects the RRMI and statistically significant differences in RRMI were found when comparing the RRMIs of cylindrical, rectangular and
triangular rods with XAs ranging from 3.14 mm2 to 28.3 mm2 .
6.1.6
Drop Cycle Times
The drop cycle time represents the time during which heat is transferred from the
molten mass to the solid rod. The drop remains attached to the rod up to the instant
when the gravitation force acting on the drop exceeds the surface tension force holding
the drop to the rod. The circular, rectangular and triangular rods have the same XA but
due to their shape they have different wetted perimeters. The maximum surface tension
force associated with each shape is therefore different. The dynamics of pendant drops
suspended from non-cylindrical tubes/rods is not widely reported but it is reasonable
to assume that drops attached to a uniquely shaped cross section will vary slightly in
regards to their dynamic characteristics (e.g., size/weight/volume/surface area).
The trend in mean drop time between the shapes for X4, X5 and X6 rods was:
DT > DT8 > DT4 .
(6.1)
The drop time obviously relates to the mass of a drop that can be supported by the rod
as well as how quickly this critical size is reached. For each shape there is a finite mass
that can be supported based on the XA and wetted perimeter. The volume of solid metal
melted during a drop cycle was calculated. The drops were assumed to have the same
density so the drop volume was used to represent relative difference in the mass of a
drop. In this approach the mass of incorporated oxygen is neglected since it is deemed
insignificant compared to the mass of metal. The drop volumes for the triangular rods
exceeded those of the cylindrical rod of the same XA. This indicates that either the
triangular rod, with its greater wetted perimeter, was capable of supporting a larger
mass, and/or that a larger SLI contributed a greater adhesion force to support the drop.
The above trend in drop times indicates that the critical drop volume for the triangular
rod, although greater, was reached sooner based on the higher VFR resulting from the
faster RRMI.
The trend in mean drop time between XAs for all shapes was:
DT X2 > DT X4 > DT X6.
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(6.2)
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D ISCUSSION
The mass that can be supported by the rod is proportional to the wetted perimeter.
The ratio of drop volume to perimeter is constant for the various XAs and this finding
supports the work of Hirano et al. [41] who reported that drop volume was proportional
to rod diameter. A shorter average drop time for the larger rods indicates their critical
volume is reached more quickly than the smaller rods. Taking average VFR’s and drop
sizes it follows that the increase in VFR for the large rods is greater than the increase
in their critical drop size, therefore, they form and detach in a shorter period of time.
In terms of heat transfer this means that the larger rods have a shorter period of time
during which heat is transferred into the solid from the molten mass, and this may
contribute to their slower RRMIs.
6.2
Extent of Reaction: Microanalysis
ER is a kinetic parameter which indicates the amount of fuel (metal) that is available
to react in a combustion reaction, to the amount that has reacted. If all the available
metal reacts then the ER equals one (100%). For the system being considered it refers
to the ratio of unreacted (unoxidised) to reacted (oxidised) metal in the molten mass
just prior to drop detachment. Since iron is the metal being investigated the ratio
represents the proportion of melted and resolidified but unreacted iron to that of the
reacted iron (combined oxides: wustite (FeO), hematite (Fe2 O3 ) and magnetite (Fe3 O4 )
or a non-stoichiometric phase (Fex Oy ). During a promoted ignition test, the detached
drops form a conglomerated slag mass at the base of the chamber making it difficult
to distinguish individual drops with any degree of certainty. A representative value of
the ER for individual drops is obtained by considering the slag mass as a whole. It is
assumed that the overall ER should approximate the ER for a single drop.
Although microanalysis on rapidly quenched iron slag has been reported, the testing was conducted at a pressure of 0.69 MPa on 3.2 mm diameter rods [32]. The
samples selected for this work have a range of diameters, 0.25 mm - 6.00 mm, and are
burned at the higher pressure of 6.9 MPa. A range of diameters were tested to provide
insight into why, for similar test conditions, large diameter rods have a lower RRMI
than small diameter rods. Benz et al. [50] proposed a theoretical relationship for ERs
over a range of rod diameters and concluded that the ER decreased with increasing
rod diameter, however, their work was not supported by experimental evidence. This
work was conducted to provide empirical evidence to either support or refute their
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6.2 E XTENT OF R EACTION : M ICROANALYSIS
hypothesis. The hypothesis, that smaller rods have a higher ER, supports the general
observation that for the same test pressure small diameter rods have a faster RRMI
than large diameter rods. If a larger proportion of the melted iron entering the attached
molten mass exothermically reacts this releases more energy which is then transferred
back to the rod causing further melting and a faster RRMI. To qualitatively assess ER
for the various diameter rods, test samples were examined using microanalysis techniques (discussed in Section 2.3).
Polished cross-sectioned surfaces of the quenched slag from rods tested at 6.9 MPa
are shown in Figure 5.27. The slag consisted predominantly of oxidised material and
contained a minor amount of unreacted metal. SEM analysis of the slag revealed that
the unoxidised metal was predominantly palladium, a component of the igniter wire
that was used to initiate the test, rather than iron. The ratio of the mass of the sample
to the mass of the igniter wire increases as the XA of the sample increases, hence, the
palladium is more prominent in the small diameter samples. From these results it is
clear that the ER in all of the high pressure samples was approximately one. Since no
unreacted iron was identified in any of the samples it is concluded that at 6.9 MPa the
ER is independent of rod diameter. The oxide in all of the samples is highly porous
indicating that there is a significant amount of excess incorporated oxygen present
within the molten mass when it detaches. This oxygen, predominantly in the former
of higher iron oxides [44], is then released back into a gas phase when the oxide is
reduced to more stable forms during cooling. This result is consistent with the slag
domes that were formed during the slow cooling and extinguishment of X6 samples,
Figure 5.7.
Testing at a lower pressure was conducted to verify reports that significant amounts
of unreacted iron were present in tests at 0.69 MPa [32,33], inconsistent with the higher
6.9 MPa results obtained here. These low pressure test samples were directly compared
to the high pressure samples to make a judgement regarding the relationship between
ER and test pressure. The samples from low pressure tests at 1.1 MPa, Figure 5.33,
reveal that there is a significant portion of unreacted material in the larger diameter
rods, in contrast to the high pressure samples. Several large deposits of unreacted
iron are identified in the low pressure samples along with a small amount of unreacted
palladium. In the high pressure samples though all unreacted material was identified
as palladium, in the low pressure samples this is not the case. Combining these results
with those previously reported for quenched iron [32] it is clear that test pressure affects
the ER.
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One region of unreacted metal of the ten regions which were identified in the small
diameter low pressure sample contained unreacted iron. This result suggests that ER
is a function of rod diameter at low pressures. Elevated pressure has been proposed to
enhance the incorporation of oxygen at the molten mass surface [26, 44]. This work
has now demonstrated that the increase in available oxygen resulting from an increase
in pressure translates directly to an increase in the ER. This finding is consistent with
the observed increase in RRMI with pressure for rods of the same diameter. As the
pressure increases, more oxygen is incorporated into the molten mass facilitating reactions with the available melted metal, the ER increases, more energy is generated
within the molten mass and this energy is transferred to the solid rod thereby increasing the RRMI. The rate of increase in RRMI with pressure decreases, Figure 2.6. This
is consistent with the finding that at high pressures the ER is one, therefore, further
increases in pressure do not significantly effect the RRMI. Above the critical pressure,
for which ER equals one, further increases in pressure may increase the temperature of
the molten mass causing the RRMI to increase slightly as is observed above 6.9 MPa
for 1 - 3 mm diameter rods, Figure 2.6 [22, 38].
6.3
The Burning Rod System
This section presents a summary of the contribution of this work to the understanding
of a burning rod system. The general qualitative model for burning of iron rods presented in the literature is fairly well accepted [24,26,32,39,41,43–45,79]. The ignition
event transfers heat to the end of the rod, which melts, and under the right conditions
(pressure, temperature, atmosphere) the rod undergoes sustained burning resulting in
a periodic drop-growth-and-detachment cycle. The rod continues to melt only if sufficient energy is transferred to it from the molten mass across the SLI. This energy is
generated by combustion reactions within the molten mass. The oxygen is incorporated into the molten mass from the surroundings to form higher oxides (ferrite ions)
or is dissolved to form an oxygen enriched solution. The rate-limiting mechanism for
this process is debated, however, the presence of excess oxygen in the molten mass led
to the general agreement that heat transfer to the solid rod is rate-limiting.
The RRMI is a direct measure of the rate at which the solid rod is melted and incorporated into the molten mass. Therefore, a faster RRMI signals that, overall, a greater
amount of energy is transferred to the rod per second. The different RRMIs for the
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6.3 T HE B URNING ROD S YSTEM
cylindrical, rectangular and triangular rods, therefore, are best explained by changes to
the subsystems within the attached molten mass as a result of the unique geometries.
These subsystems (see Figure 2.1 include the SLI, a liquid metal (unreacted) zone, the
reaction surface, the product oxide(s) and the gaseous surroundings. These systems
exchange mass and energy at their boundaries, with the size and shape of these boundaries likely changing over the evolution, growth and detachment of the molten mass.
Assuming the same process describes how heat is transferred from the molten mass to
the rod for the different shapes, there are two factors that can lead to the higher RRMIs
observed for the rectangular and triangular rods;
1. Assuming the same heat flux, the surface area across which heat is transferred
(SLI) increases thereby increasing the total energy transferred into the solid rod
per unit time.
2. For the same SLI surface area, the heat flux increases thereby increasing the total
energy transferred into the solid rod per unit time. This increased heat transfer
could be due to higher temperatures within the molten mass perhaps due to a
greater ER.
Quantifying the molten mass temperature and/or ER accurately is clearly a difficult task. Given that the rods have the same XA, are made of the same material and
undergo similar reaction processes, the temperature and ERR are not expected to be
significantly affected by the change in the shape of the sample’s cross section. This
means the cause for the increase in RRMI is an increase in the SLI surface area. This
is clearly observed in the still images for the rectangular and triangular rods in which
the SLI curved upwards at the corners (Figures 5.4, reffig:T6SLIs and 5.6). The larger
SLI results from the higher local SA/V ratio in a corner, which facilitates an increased
rate of heat transfer to this corner. Therefore, a corner will melt at a faster rate creating a convex SLI which has a larger surface area than a planar SLI. These corners
will also alter the dynamic attachment conditions between the molten mass and the
solid rod and thereby affect heat transfer from the molten mass to the solid rod. The
magnitude of the internal corner angle affects heat transfer conditions. This concept is
supported by theoretical considerations of surface tension effects in a corner [151,152].
This ‘corner effect’ changes with XA: for smaller XAs, although the effect was sufficient to account for statistically significant difference in RRMI, the relative differences
in RRMI between the shapes was smaller than for larger XA. The shape of the rod
130
6
D ISCUSSION
changes the contact angle between the molten mass and the solid rod, which will affect
heat transfer. Furthermore, this contact angle is dependent on XA: it was greater in the
smaller rods, and smaller for the larger rods (Figures 5.1, 5.2 and 5.3).
The dependence of ER on the test pressure is consistent with the relationship between RRMI and test pressure. The RRMI increases with increasing pressure and the
ER increases with increasing pressure. Also, the rate at which the RRMI increases,
progressively decreases and this decline likely corresponds to the point at which the
ER equals one. Hence, further increases in pressure do not greatly affect the RRMI.
An ER equal to one indicates that, not only is the oxygen readily available at these
high pressures, but all the available fuel reacts. Wilson and Stoltzfus [26] attributed
the relatively constant RRMI of 3.2 mm rods above 5 MPa to a reaction surface which
was saturated with oxygen. The results of this thesis experimentally show that the
RRMI is dependent on ER which is a function of test pressure. At low pressures, ER
is a function of XA, and this partly explains why rods with a larger XA have a smaller
RRMI for the same pressure, however, an ER argument does not hold for higher pressures since the ER was one for all XAs tested (0.05 - 28 mm2 ). The finding that at
high pressure ER is not a function of XA but at low pressure ER is a function of XA
indicates that the critical pressure, the pressure at which the ER first reaches one, is
a function of XA. These experimental results support the rate-limiting mechanism for
this system to be heat transfer to the solid rod from the molten mass.
131
C HAPTER 7
S TATISTICAL C ONSIDERATIONS IN THE
A NALYSIS OF P ROMOTED I GNITION T EST
DATA
The standard promoted ignition test forms the basis of metals flammability testing,
however, the modelling of test data has only been addressed in a limited fashion [21,
106]. A useful parameter to model in this setting is the reaction probability as a function of test pressure. The reaction probability is defined as the probability (0-1) that a
rod will sustain burning for a sufficient time to be deemed flammable at the pressure
in question for the chosen burn criteria. Logistic regression was identified as a suitable
method for transforming the binary burn/no-burn test data in order to model reaction
probability.
Section 7.1 addresses statistical issues based around the methodology of the standard promoted ignition test. The section also outlines a simple method for evaluating
the confidence interval associated with burn/no-burn test data. Section 7.2 presents an
approach for modeling promoted ignition test data using logistic regression. Logistic
regression models are developed for two standard promoted ignition data sets. The
model fits are evaluated and approximate confidence intervals are developed. The effect of the quantity of data used to generate the models is evaluated as is the effect of
the burn criteria that is used to categorise the burn length data. Section 7.3 discusses
the logistic regression method as applied to promoted ignition test data and outlines the
benefits of the method. In addition, an approach and recommendations are suggested
to easily apply the logistic regression method under the framework of the standard
promoted ignition test.
132
7
7.1
S TATISTICAL C ONSIDERATIONS
Statistical Issues
This section addresses the methodology of promoted ignition testing by examining the
standard test procedure in a statistical context. As mentioned in Chapter 3 the appropriate distribution for modeling the number of burns in a fixed number of independent
trials is the binomial distribution. Thus, it is a straightforward matter to develop exact
confidence intervals which indicate the precision of estimated parameters. In this instance the parameter of interest is the reaction probability. The relationship between
confidence intervals, reaction probability and the number of tests conducted for a single test condition has been previously reported in the literature [91, 110, 153] and is
explored in more detail below.
7.1.1
Standard Test Methodology
The promoted ignition test method is essentially a series of tests conducted at decreasing pressures where the number of tests conducted at a specific pressure is dependent
on the previous test results. The reaction probability, p, is dependent on pressure,
temperature, oxygen concentration and other test variables. In the standard promoted
ignition test method, the major variable of interest is the test pressure as the results are
used to determine pressures at which materials can be safely used. Therefore, in the
following analysis it is assumed that all variables except pressure are constant. The
reaction probability can therefore be written as a function of pressure:
p(X) = Pr(burn|pressure = X).
(7.1)
Let X1 > X2 > X3 > ... > Xk , where Xk represents the first pressure at which no
burns occur in a set of tests. Testing commences at X1 and if the first sample exhibits
self-sustained burning then the next test is conducted at the next lowest scheduled test
pressure in the sequence. Testing is performed in this decreasing series of pressures
and as soon as a burn is obtaining the testing ceases at that pressure and recommences
at the next lowest test pressure. Therefore, the number of tests performed at each
pressure is not always equal. Testing continues in this way until a pressure is reached
(Xk ) at which no burns are detected for a specified minimum number of tests. The
pressure immediately above this pressure, Xk−1 is declared the threshold pressure. It
is therefore desirable that the threshold pressure corresponds to a reaction probability
equal to or less than some arbitrary critical value, for example 5% or 1%, hence, pcrit ≥
133
7.1 S TATISTICAL I SSUES
p(Xk−1 ). Developing confidence intervals for such a sequential analysis is complicated
but it is clear that since more data is acquired in regions where burning is expected this
method does not provide enough information in regions where burning is not expected,
and ultimately, at the pressures where the material is likely to be used. A confidence
interval analysis of test results was performed at individual pressures in a binomial
setting with the following results.
If repeated tests at conducted at specific pressures the results provide an estimates
of the reaction probability, pˆ, for those pressures. For instance, five tests resulting in
burns gives pˆ = 1, three out of five tests resulting in burns gives pˆ = 0.6. Although it
should be noted that according to the standard test method testing recommences at a
lower pressure before multiple burns are obtained at a single pressure. However, considering multiple tests conducted at a single pressure, as the number of tests increases,
the estimated reaction probability approaches the actual reaction probability. In the
context of promoted ignition testing, one must decide on an acceptable risk of having
a burn occur at a pressure below the TP; that is, an acceptable value for the reaction
probability. Functionally, in a test series, if there are any burns, that is, if pˆ ≥ 0, then
the material is deemed flammable at that pressure and testing proceeds at the next lowest test pressure. However, given that we are estimating the probability of an event
occurring, simply attaining five no-burns in a series of five tests does not guarantee
that if a sixth test is conducted, it will also result in a no-burn. The following analysis
explores the range of reaction probabilities that are likely based on the number of tests
performed, the number of no-burn results and the desired confidence level. In this case
the range of reaction probabilities will lie between zero and some upper value, pˆupper .
To gauge whether future tests are also likely to result in no-burns, one must determine the confidence associated with the estimate of pˆ; that is, how confident are we
that we have in fact attained the acceptable reaction probability. Based on the number
of tests conducted, N , and the binary burn and no-burn test data, a confidence interval
for the reaction probability can be established. During a test series for a material, its
TP, by its current definition [16], is identified when several tests are conducted at a
single pressure with all tests resulting in no-burns, the next highest test pressure then
constitutes the TP. Therefore, if N tests are conducted and no burns occur then we
can develop an exact confidence interval for the reaction probability (see Section 3.3)
based on the observed number of burns. The confidence interval takes the form:
(0, pˆupper )
134
(7.2)
7
S TATISTICAL C ONSIDERATIONS
and is obtained so that:
P r(0 < p ≤ pˆupper ) = C
(7.3)
where p lies between zero, the smallest possible reaction probability and an upper
bound, pˆupper . The probability that p lies in the interval is equal to the confidence
level, C (0.90, 0.95, 0.99 etc.).
The number of trials, confidence level and upper reaction probability are all interrelated. In most situations the number of trials is fixed prior to testing, however, it is
more conservative to select an acceptable upper limit for the reaction probability and
an appropriate confidence level and determine the number of tests needed to satisfy
those conditions.
7.1.2
Confidence Intervals and the Standard Test
The relationship between the number of trials, confidence level and reaction probability was explored by fixing two of the three parameters and examining the third. It is
fairly straightforward that increasing the number of trials that are conducted at a single pressure will improve the estimate of reaction probability, with the estimate being
closer to the true value. This effect was investigated quantitatively for confidence levels of 65%, 90%, 95% and 99% as shown in Figure 7.1 in which the upper confidence
limit for reaction probability (ˆ
pupper ), is plotted against the number of trials. The graph
demonstrates that for a given confidence level, as the number of trials increases, the
interval in which the actual reaction probability lies decreases, that is, the lines converge towards the x-axis (x-axis represents a reaction probability of zero). Therefore,
increasing the number of trials increases the precision with which the reaction probability can be estimated (the upper and lower confidence bounds converge). The graph
also demonstrates that the width of the confidence intervals decrease as the confidence
level decreases (less confidence), for the same number of tests. That is, the more confident one is that the reaction probability lies in a given interval, the broader that interval
must be. If one is satisfied with a small confidence level, then the interval may be fairly
narrow.
The minimum number of no-burn test results at a single pressure varies between
standards. NASA-STD-6001 and ASTM G124-951 stipulate five tests, ISO 14624-4
1
ASTM G124-95 is the previous version of ASTM G124-95 (2003).
135
7.1 S TATISTICAL I SSUES
Figure 7.1: Reaction probability versus number of trials for varying confidence levels.
stipulates ten tests. If five tests are conducted and the result for each test is a noburn then based on a 90% confidence level the reaction probability is expected to lie
within (0, 0.37). In other words, if the process were repeated 100 times, the confidence
interval would be expected to contain the actual reaction probability in about 90 of
those cases. For a higher confidence level, 97.5%, the confidence interval widens to
(0, 0.52). For the same number of tests, as the confidence level increases the interval in
which the reaction probability lies also increases. This trend is displayed graphically
in Figure 7.2.
Applying a realistically desirable upper reaction probability of 1%, if five tests are
conducted, all resulting in no-burns, the confidence level is only 5%. Table 7.1 explores
the confidence levels associated with varying upper reaction probability limits for five
and ten tests (Equation 3.34). The table clearly illustrates that based on all no-burn
results for only five or ten tests, the confidence that these results actually imply a low
reaction probability is fairly low.
Given that conducting enormous numbers of tests is cost and time prohibitive, statistical models may be used to capture underlying trends in the data and allow a better understanding of the relationship between reaction probability and test pressure.
Preliminary models can aid in identifying additional testing requirements and/or conditions needed to create more robust models and a better understanding of the flam136
7
S TATISTICAL C ONSIDERATIONS
Figure 7.2: Reaction probability versus confidence level for varying numbers of trials.
Table 7.1: Confidence levels for
promoted ignition tests.
N
pˆupper
(%)
C
(%)
Interval
(0, p
ˆ upper )
5
0.1
0.5
(0,0.001)
5
1
5
(0,0.01)
5
5
23
(0,0.05)
5
10
41
(0,0.1)
10
0.1
1
(0,0.001)
10
1
10
(0,0.01)
10
5
40
(0,0.05)
10
10
65
(0,0.1)
mability of a material in relation to test pressure, geometry, oxygen concentration or
other test parameters. The following section outlines a particular form of statistical
modeling applied to promoted ignition test data.
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7.2 L OGISTIC R EGRESSION M ODELLING
7.2
7.2.1
Logistic Regression Modelling
Results
Logistic regression is a suitable approach for modeling burn/no-burn promoted ignition
test data (Chapter 3). Many variables affect the outcome of a promoted ignition test;
temperature, pressure, oxygen concentration, sample orientation, direction of burning,
material composition including manufacturer and batch differences, diluents and sample dimensions. Logistic regression is commonly used to model outcomes involving a
number of explanatory variables and the method is used to assesses the impact of these
variables on the dependent variable, legitimising the inclusion of, or at least identifying, the ‘significant’ independent variables in the model. With regard to the standard
promoted ignition test, pressure is the variable of interest and in a test series the experimenter typically endeavors to isolate the effect of pressure by keeping all other
variables constant. Hence, for the logistic regression modeling considered, pressure is
the only explanatory variable, simplifying the model considerably.
Burn length data published by Zawierucha et al. [21], from which they presented
the concept of a PICT curve, was used to develop two logistic regression models. The
data was derived from testing of cylindrical samples 100 mm in length and 3.175 mm
in diameter. The authors applied a 30 mm burn criteria (30% for the length of sample
used). The data was selected for a number of reasons: to compare the logistic regression models with the published PICT curves, raw burn length data was published
enabling the effect of different burn criteria on the logistic regression model to be explored and a similar number of tests was performed at each pressure. Also, Zawierucha
et al. present data for two Hastelloy® alloys, C-276 and G-3, so the results demonstrate
the effect of minor alloying constituents on the burning, as captured by the model.
R-Project 2.2.1 [130] was used to estimate the model coefficients (β0 , β1 ). Table 7.2
presents a summary of the R-Project output for Hastelloy® C-276 data based on a 20%
burn criteria. A 20% burn criteria was applied because it lies within the range of burn
criteria reported in the literature. The estimated coefficients are displayed along with
their standard errors, an analysis of deviance table, as well as a covariance matrix.
Residual plots are used in linear regression to assess nonlinearities. Similar plots of
deviance may be useful in the logistic regression setting but in this case there is limited
data for them to be of value in assessing higher order effects. Based on the maximum
138
7
S TATISTICAL C ONSIDERATIONS
likelihood estimated coefficients the fitted model for the data is given by:
pˆ =
e(−8.1050+0.5408×P )
.
1 + e(−8.1050+0.5408×P )
(7.4)
where, P is the test pressure. The fitted probabilities, estimated probabilities given by
burns
) which were input to the software to the generate the model, raw burn length
( no.
total
data and the burn/no-burn data, based on a 20% burn criterion, is presented graphically
in Figure 7.3. The values on the y-axis also represent the percentage of sample burned
in the case of the burn length data. A similar process was followed for Hastelloy® G-3
data. The fitted logistic regression equation is given by:
pˆ =
e(−4.9948+0.5967×P )
1 + e(−4.9948+0.5967×P )
(7.5)
and the results are summarised in Table 7.3 and presented in Figure 7.4.
7.2.2
Evaluation
The model fits are assessed by considering the information in the analysis of deviance
table, Tables 7.2 and 7.3. The null and residual deviance are a measure of the ‘goodness of fit’ of the model, analogous to the ‘sum of squares’ in a linear regression setting. The null deviance represents the model fit using the intercept only, the residual
deviance represents the model fit using the intercept and the slope. The difference between these two values is an appropriate likelihood ratio test statistic with a chi-square
distribution. The smaller the p-value of the test statistic the more significant the pressure is in the model. For Hastelloy® C-276 the p-value of the test statistic is extremely
small, 0.00004, which indicates that the pressure coefficient is significant. The statistical output for Hastelloy® G-3 also indicates that the pressure coefficient is significant,
p-value 0.0005. These results show that the models fit the data well and that pressure
is a suitable and significant predictor variable for modelling reaction probability.
The logistic regression curve has a similar shape to the PICT curve but the method
represents a more formal approach to data analysis. Figure 7.5 is a schematic diagram
based on Zawierucha et al.’s work which highlights important features of the logistic
regression curve. The diagram is based on Hastelloy® C-276 data, Figure 7.3, but
reflects the general features of a logistic regression curve. The schematic diagram
exhibits a lower shelf region at smaller test pressures. In this region no-burn results
were obtained and the reaction probability is low but increases gradually with pressure.
139
7.2 L OGISTIC R EGRESSION M ODELLING
Table 7.2: R-Program logistic model data for Hastelloy® C-276.
Coefficient
Constant
Pressure
Estimate
S.E.
z-value
p-value
95% Conf. Int.
Lower
Upper
-8.1050
0.5408
3.5130
0.2407
-2.307
2.247
0.0210
0.0246
-14.990
0.069
Resid.
df
7
6
Resid.
Deviance
18.3099
1.4226
P(> |Chi|)
Analysis of Deviance Table
df
Deviance
Null
Pressure
1
Covariance Matrix
Intercept
Intercept
12.3412
Pressure
-0.8281
16.8872
-1.220
1.013
0.00004
Pressure
-0.8281
0.0579
Figure 7.3: Logistic regression model and data for Hastelloy® C-276.
140
7
S TATISTICAL C ONSIDERATIONS
Table 7.3: R-Program logistic model data for Hastelloy® G-3.
Coefficient
Constant
Pressure
Estimate
S.E.
z-value
p-value
-4.9948
0.5967
2.9619
0.3409
-1.686
1.750
0.0917
0.0801
-14.990
0.0801
Resid.
df
6
5
Resid.
Deviance
13.2881
1.3407
P(> |Chi|)
Analysis of Deviance Table
df
Deviance
Null
Pressure
1
Covariance Matrix
Intercept
Intercept
23.0498
Pressure
-2.5455
11.9474
95% Confidence Interval
Lower
Upper
0.0005
Pressure
-2.5455
0.2898
Figure 7.4: Logistic regression model and data for Hastelloy® G-3.
141
-1.220
1.013
7.2 L OGISTIC R EGRESSION M ODELLING
At pressures where a combination of burn and no-burn results were obtained, the fitted
reaction probability curve rises sharply, deemed the transition region. Finally, at high
pressures, where test results were typically all burns, the slope of the fitted curve diminishes as the reaction probability approaches one. Two threshold pressures are also
marked in Figure 7.5. The ‘current’ TP is the minimum pressure at which sustained
burning occurred, and the ‘proposed’ TP is the maximum pressure at which no sustained burning was observed. The difference between the fitted reaction probabilities
at these two pressure is indicated. The fitted reaction probability based on the current
definition of threshold pressure is approximately double the reaction probability based
on the proposed definition.
Figure 7.5: Logistic regression schematic diagram based on Hastelloy® C-276 data.
In the logistic regression context the upper and lower shelf regions are the reverse
of those in the PICT curve approach. In the PICT curve the upper shelf region is
associated with lower test pressures since a substantial length of sample remains after
a test. In contrast, in the logistic regression approach the lower shelf region represents a
low reaction probability, and hence, corresponds to lower test pressures. However, this
interpretation could be reversed by modelling the probability of no sustained burning
rather than sustained burning. If the probability of no sustained burning was modelled,
the ratio of interest is ( no−burns
), which, for low pressures, would be close to one, and
no. total
142
7
S TATISTICAL C ONSIDERATIONS
for high pressures, would approach zero, similar to the PICT curve.
Burn criteria ranging from 10% to 100% have been reported in the literature so
logistic regression models were fitted using different burn criteria. The burn length
data for Hastelloy® C-276 was categorised into burns and no-burns by applying three
different burn criteria; 10%, representative of the two-drop burn length [102], 20%
and 30%. Figure 7.6 displays the fitted probabilities for each model together with the
burns
), which change based on
estimated probabilities used to generate the model, ( no.
total
the burn criteria. A similar approach was taken for Hastelloy® G-3 data, but only
10%, 20% and 25% burn criteria were applied, Figure 7.7. A burn criteria equal to
or exceeding 30% was not applied because it resulted in complete separation of the
data. That is, there was no overlap in burn/no-burn results for the same pressure. In
the tested pressure range less than or equal to 10.35MPa, all results for Hastelloy®
G-3 were no-burns and in the tested pressure range greater than or equal to 13.8 MPa,
all the results were burns. For similar reasons, a burn criterion of 50% or higher was
not applied to Hastelloy® C-276 data, in this case quasi-complete separation occurred,
meaning that there was a single pressure at which both burns and no-burns occurred.
At 17.25 MPa both burns and no-burns were obtained but below this pressure only noburns were observed and above this pressure the results were all burns. The maximum
likelihood estimates (β’s) are highly dependent on the available data [154,155]. If there
is a wealth of data in the regions of the curve where the probability changes rapidly
(the transition region), better estimates can be obtained. Alternatively, complete and
quasi-complete separation of data result in either non-existent maximum likelihood
estimates or estimates that are not appropriate [156].
Figures 7.6 and 7.7 present fitted reaction probabilities in the form of the typical
logistic regression s-shaped curve. As the pressure increases the reaction probability
increases, slowly at first (lower shelf region), then rapidly (transition zone) and finally
it tapers towards a reaction probability of one and further increases in pressure do not
affect reaction probability (upper shelf). The transition region typically narrows as the
burn criteria increases . For smaller burn criteria, the transition regions extends across
a broader range of test pressures, since, at low pressures, the burn length data is no
longer classified as only no-burns but is a mixture of burns and no-burns. Conversely,
as the burn criteria is increased, the transition regions becomes narrower. The curve
effectively becomes a step function when the burn criteria causes quasi-complete of
complete separation of the data. A this point logistic regression is no longer possible
for the reasons outlined above.
143
7.2 L OGISTIC R EGRESSION M ODELLING
The cases of quasi-complete and complete separation are interesting in that, functionally, the pressure at which separation occurs represents a TP. Below this pressure,
no-burns are obtained, and above this pressure, burns are obtained. For example, complete separation of the data occurs based on a burn criteria of 60% for Hastelloy® C276 data and 35% for Hastelloy® G-3 data. Under these criteria the TP, the minimum
pressure which resulted in a burn, is 20.7 MPa for Hastelloy® C-276 and 13.8 MPa for
Hastelloy® G-3. However, if the same burn length data is interpreted using a logistic
regression model based on a 20% burn criteria, 20.7 MPa and 13.8 MPa are associated
with fitted reaction probabilities exceeding 90%. If the TP is considered the maximum
pressure that does not support self-sustained burning (‘proposed’ definition), the TPs,
based on complete separation of data, for Hastelloy® C-276 and Hastelloy® G-3 are
17.25 MPa and 10.35 MPa, respectively. From the fitted probability curve developed
for the 20% burn criteria these pressures correspond to reaction probabilities exceeding
60%. Therefore, although high burn criteria may enable one to distinguish pressures
where burning was observed and pressures where no-burning was observed, high burn
criteria are less conservative. Realistically, the existence of a threshold pressure which
defines a transition from only burns to only no-burns is unlikely. This situation represents a reaction probability of zero below the TP and a reaction probability of one
above the TP. However, the data explored in this section suggests that this is not the
case, and a more informative characterisation of the transition region is obtained when
quasi and complete separation are avoided.
Burn criteria should not be selected to achieve quasi/complete separation. Instead,
the burn criteria should be based on engineering principles by considering the amount
of energy the ignition event transfers to the sample. If the length of sample that melts
and burns is within the region deemed to be affected by ignition, then melting and burning beyond this point would result if the material were flammable at the test pressure.
This is the principle underlying the 2-drop burn criteria and ASTM G124-95 (2003)
stipulates that self-sustained burning occurs when the sample is consumed “beyond
the point at which the promoter influences the combustion of the material” [16]. The
length of this ignition affected region may vary depending on the material properties
of the sample, for example conductivity, and further work is required to quantitatively
evaluate the ignition event so that suitable burn criteria may be enforced and uniformly
adopted.
144
7
S TATISTICAL C ONSIDERATIONS
Figure 7.6: Logistic regression model developed using 10%, 20% and 30% burn criteria applied to Hastelloy® C-276 data.
Figure 7.7: Logistic regression model developed using 10%, 20% and 25% burn criteria applied to Hastelloy® G-3 data.
Confidence intervals for the regression coefficients and the fitted reaction probability were calculated. Confidence intervals for the maximum likelihood estimates,
given in Tables 7.2 and 7.3, were calculated based on Equation 3.27 [131]. The confidence interval for the reaction probability was also evaluated. The approach is based
on large sample assumptions which are reasonable for the data sets that were used but
145
7.2 L OGISTIC R EGRESSION M ODELLING
Figure 7.8: Logistic regression model and confidence intervals for Hastelloy® C-276
promoted ignition data.
of course, more data would be beneficial (refer to Chapter 3 for the relevant theory and
equations).
Confidence intervals for the reaction probability were obtained for the Hastelloy®
C-276 model based on a 20% burn criteria (Figure 7.3). At a pressure of 9.5 MPa the
fitted reaction probability is 0.05. The 95% confidence interval for the reaction probability at this pressure is (0.004, 0.424), from Equation 3.30. Data was generated, based
on the ratio of (burns/no. tests) to simulate ten tests at each pressure for the purpose
of investigating the change in confidence interval for the fitted reaction probability.
For ten tests the span of the 95% confidence interval at a 0.05 reaction probability decreased to (0.012, 0.185), and for twenty tests the confidence interval decreased further
to (0.019, 0.124). The fitted reaction probability and confidence intervals are plotted
in Figure 7.8. It is clear that as the number of tests increases the confidence intervals
converge towards the fitted probability curve.
A similar analysis was performed based on the logistic regression model for Hastelloy® G-3 and targeting a fitted reaction probability of 0.05, which corresponds to a
pressure of 3.45 MPa. For the raw data the endpoints of the 95% confidence interval
were (0.001, 0.663), for ten tests the interval became (0.009, 0.240) and for twenty
tests this decreased to (0.015, 0.157). Figure 7.9 displays the fitted reaction probabil146
7
S TATISTICAL C ONSIDERATIONS
ity and confidence intervals over the tested pressure range and the confidence interval
curves display similar converging behaviour as the number of tests increases.
Figure 7.9: Logistic Regression Model and Confidence Intervals for Hastelloy®G3
Promoted Ignition Data.
The 95% confidence interval for the fitted probability decreases as the number of
tests increase (see Figures 7.8 and 7.9). An interesting feature of the confidence interval plots was that the confidence interval widened at the tails of the fitted probability
curve when the original data was used. This is a common feature in confidence or prediction interval plots. The curve in the middle of the pressure range is better defined
since it data is available for pressures on both sides, whereas, in the tails there is little
or no data on one side. Furthermore, in the tails of the probability curve, where the
reaction probability is close to zero or one, a huge number of tests would be required to
definitively conclude that the reaction probability is indeed almost zero or almost one.
In the transition region a few tests resulting in both burns and no-burns is sufficient to
identify the test pressure as being situated within the transition region. However, in the
upper or lower shelf region, a few burns or no-burns, respectively, simply suggests that
the test pressure could be close to the upper or lower shelf region, but not necessarily
within it. This analysis not only reaffirms the need for further testing if one wants to
improve the confidence in their data, it also demonstrates the value of testing on both
sides of a pressure of interest in order to gain information about the reaction probability
at that pressure.
147
7.3 D ISCUSSION
7.3
Discussion
It is worth reflecting on the method with which data is generated in the standard promoted ignition test. The method involves testing at a pressure and decreasing the
pressure, in intervals, until a sufficient number of no-burn results are observed. At this
point testing ceases, driven by economic considerations. Depending on the interval
between consecutive test pressures the testing may stop prematurely. In this approach,
a greater amount of data is generated at conditions for which burning is expected and
the material is considered flammable, rather than at pressures at which the material
is ultimately considered non-flammable, the same conditions to which the material
will presumably be exposed in practice. Therefore, there is a greater certainty that
the material is flammable for the flammable pressure region than non-flammable for
the non-flammable pressure region. It would seem more appropriate that this scenario
be reversed to accumulate more data in the non-flammable regions, based on the way
data is used by engineers, and considering the logistic regression modelling analysis
presented here. The test procedure itself is a particularly important consideration in
relation to the definition of TP. If the TP is defined conservatively as the maximum
pressure at which self-sustained burning does not occur, and above which burning is
experienced it would certainly be far more appropriate to perform tests for an increasing sequence of pressures. A test method based on a series of increasing pressures
raises the issue of the minimum number of no-burns that should be obtained before
testing commences at a higher pressure. This is an issue which should be explored in
future work and it may be the case that a minimum number of tests (e.g., 5) should
be performed at each scheduled pressure. Once a pressure is reached for which a burn
is observed testing should be repeated until the minimum number of tests have been
performed. Repeated tests at higher pressures should also be performed in order to
characterise the lower shelf and transition region. That is, to assess whether the lower
shelf region gradually/rapidly merges into the transition region and whether the transition region is narrow or broad. Further testing at the highest test pressure resulting
in no-burns could be conducted in order to gather more data, and therefore increase
the confidence of the results. Given that this is not the approach adopted and that
there is often a greater amount of data for flammable regions it would be useful to
use this data rather than base judgements on the data from a single test pressure in the
non-flammable region. For this reason a modelling approach is befitting.
The major benefit of the logistic regression method over the current practise of ob148
7
S TATISTICAL C ONSIDERATIONS
taining a designated number of no-burn test results is that it successfully models an
increasing reaction probability with pressure. This contrasts to the standard interpretation of test data which focusses on a threshold pressure without considering the reaction probability associated with that threshold pressure. Information about the reaction
probability is important to engineers and designers as it provides them with a broader
picture of the risks associated with different materials at a range of pressures. The
method quantifies these risks through reaction probability which is more useful than
the simple concept of ‘low’ or ‘high’ risk. Burn length and burn/no-burn data simply
provide raw information informing users of the pressures at which samples sustained
burning and those at which they did not. By combining this data across all the tested
pressures and applying the logistic regression method a model can be developed from
which judgements can be made regarding a material’s flammability. The model is most
suitable when the same number of tests were performed at each test pressure. Although
this is not the situation described by the standard test method repeated tests are sometimes performed, as was the case for the particular data sets chosen. Furthermore, the
recommended changes to the test method suggest that repeated tests are performed regardless of the burn/no-burn outcome. Confidence intervals can be established for the
fitted reaction probability and based on the level of risk that a designer or engineer is
prepared to accept, the users can decide on the combination of materials and pressures
with which they are prepared to operate. From this exploration of logistic regression
as a feasible alternative to the current methods for interpreting test data the following
approach is recommended:
1. Burn length data should be collected and recorded during a promoted ignition
test series. This forms the raw data which is transformed into binary burn/noburn data by an appropriate burn criteria.
2. Plot the length of rod burnt against pressure.
3. Convert the burn length data into burn/no-burn data using an appropriate burn
criteria.
4. Enter the pressure, burn/no-burn data and the number of tests into a statistical
software package capable of performing logistic regression.
5. Plot the fitted reaction probability against pressure on the same axes as the
burns
burn/no-burn data and the estimated reaction probability, ( no.
), to assess the
total
fit of the model.
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7.4 S UMMARY AND C ONCLUSIONS
6. Calculate confidence intervals for the fitted probability based on the approach
outlined in Chapter 3. The confidence intervals indicate the expected range of
reaction probabilities that would occur based on the chosen confidence level.
7. Based on the reaction probability and confidence interval curves experimenters
can target pressures that may benefit from further testing.
Data collection is most critical at the pressures between the lower shelf and transition region. The lower shelf region represents pressures where sustained burning is
very improbable, therefore, it is important to accurately identify the upper limit for the
pressures in this region. This can easily be done based on an acceptable value for the
reaction probability. This value may depend on the organisation and the application for
which the material is being considered. The ASTM G124-95 (2003) definition of TP
places it within the transition region since it represents the minimum pressure at which
sustained burning occurs. In the suggested alternative definition, the TP would be located on the border of the lower shelf and transition regions, at the maximum pressure
at which burning is not sustained. This is a far more conservative approach. If the focus
of testing is on identifying the maximum pressure which does not sustain burning then
extensive data at pressures which result in burning is not important as it is assumed
that as the pressure increases the probability of achieving a burn also increases and
so the material would be unsafe to use at those pressures. Therefore, testing should
concentrate of the pressures at which no-burns occur, specifically around the transition between the lower shelf and transition regions. If logistic regression modelling
is to be applied then the curve in the lower shelf and transition regions will be better
characterised by including some data from pressures at which the material sustained
burning.
7.4
Summary and Conclusions
This chapter illustrated deficiencies in the current promoted ignition test methodology.
The practise of testing in a sequence of decreasing pressures results in a large amount
of burn data. Although this data aids in identifying the regions where burning occurs,
the regions where no-burning occurs are of far greater interest to the engineer. If a
TP physically existed such that, above the pressure burns would only ever be obtained
and below the pressure no-burns would only ever be obtained, the current approach
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S TATISTICAL C ONSIDERATIONS
would be sufficient, however, realistically, as the pressure increases the probability
that a sample will burn also increases. It has been demonstrated that this increase
in probability can be successfully modelled using logistic regression. The logistic
regression method is a formal approach to data analysis and provides end users with a
better understanding of the relationship between reaction probability and pressure than
simply looking at burn/no-burn data in a ‘good’/‘bad’ fashion. The logistic regression
method quantifies the risk, based on the test pressure, for a given material.
A preliminary investigation of the relationship between reaction probability, confidence levels and the number of tests performed was presented. Binomial confidence
intervals were developed using burn/no-burn data at individual pressures. Figures 7.1
and 7.2 and Table 7.1 quantitatively clarified the lack of confidence associated with
small sample sizes for low reaction probabilities. The figures indicated that as the number of samples increases, the width of the confidence interval, for the same confidence
level, decreases. Therefore, the upper limit of reaction probability also decreases. In
addition, the work showed that if the targeted reaction probability is at a relatively low
1%, which equates to a risk of sustained burning of 1%, and only five or ten tests are
conducted, the confidence level is a mere 5% or 10%, respectively. Therefore, if only
a few tests are conducted and only no-burn results are obtained, the likelihood that the
pressure at which those results were obtained actually corresponds to a low reaction
probability is extremely small.
The logistic regression curves that were formulated successfully model the transition between low reaction probabilities at low pressures and high reaction probabilities
at high pressures. The method takes into account all the available data, both burns
and no-burns, to produce a picture of a material’s flammability as a function of pressure. The method was shown to be a useful exploratory tool to determine appropriate
burn criteria and to reflect on the effect that the choice of burn criteria has on the fitted reaction probabilities. Smaller burn criteria resulted in broader transition regions
and the transition between the lower shelf and transition regions was not well defined.
Alternatively, larger burn criteria, 20% and 25% presented a relatively conservative approach whilst still capturing the lower shelf, transition and upper shelf regions. It was
noted that if too large a burn criteria is applied this will result in complete separation
of the data, that is, pressures at which only burns occur and pressures at which only
no-burns occur. Although this sounds like the perfect solution, since it represents a
true TP, the approach is based on a high burn criteria which is non-conservative. Furthermore, complete separation of data does not aid in quantifying and characterising
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7.4 S UMMARY AND C ONCLUSIONS
the reaction probability in relation to pressure. The work demonstrates that confidence
intervals can be developed for the fitted reaction probability, and that these confidence
intervals, like all confidence intervals, decreases as the number of samples increases.
The work demonstrates that increasing the number of samples from three to ten significantly decreases the width of the confidence intervals. The graphs also indicate
that the confidence intervals are smaller at pressures for which there was data on either
side of the particular pressure. These pressures generally correspond to the transition
region rather than the tails of the curve. Since the point between the transition and
lower shelf regions represents an appropriate and conservative TP it is recommended
that data collection be targeted at these pressures.
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C HAPTER 8
S UMMARY
8.1
Summary
A critical review of literature revealed that sample geometry can have a significant
effect on the TP and the RRMI of a material. TP and RRMI are two key parameters
obtained from the standard promoted ignition test. These tests are performed using
samples of a standard geometry: 3.2 mm diameter cylindrical rods or 3.2 × 3.2 mm
square rods. The results of these standard tests are used to develop relative rankings
of the flammability of different metallic materials. These relative rankings can then be
used to assess the oxygen compatibility of metallic materials to be used within oxygen
systems. It has been shown that sample geometry affects the oxygen compatibility
ranking of materials based on TP and RRMI. The review also explored the statistical
modelling of the binary data produced from materials testing. The research highlighted
the statistical nature of the promoted ignition test and presented the concept of an
experimentally derived curve for modelling burn length data. Logistic regression was
presented as a method with which to extend this approach in order to model the binary
burn/no-burn promoted ignition test data.
Promoted ignition tests were conducted on mild steel rods with five different XAs
ranging from 3 - 28 mm2 . In order to isolate the effect of the shape of the rod on the
RRMI cylindrical, rectangular and triangular rods of equal XA were studied. It was
found that the cylindrical rods had the smallest RRMI for all the XAs tested while the
triangular rods consistently had the fastest RRMI. The differences in RRMI between
each of the shapes were found to be statistically significant at the 95% confidence level
for all but one (X2) of the XAs tested. This work revealed for the first time the effect of
rod shape on the RRMI of burning metal rods. In addition, the research demonstrated
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8.1 S UMMARY
that the differences in the RRMIs for different shapes increase with increasing XA.
The work also demonstrated that RRMI decreases as XA increases in a similar fashion
for the non-standard rectangular and triangular rod geometries, as for the commonly
tested cylindrical rod.
To qualitatively evaluate how much metal was burning in the formed drops, promoted ignition tests were conducted on wires and rods with XAs ranging from 0.05 28 mm2 . The slag produced during these tests was quenched in a water bath to produce
post-test samples representative of the actual phases, and their relative amounts, that
are present during burning. This work was performed to qualitatively assess the ER
as a function of test pressure and rod diameter. Microanalysis of the quenched slag
indicated that ER was dependent on pressures. Testing at 6.9 MPa resulted in complete burning of all available iron, and therefore, an ER of one was confirmed. This
contrasted to the slag from testing at 1.1 MPa which contained a significant amount of
unreacted iron. At the low pressure ER was dependent on rod diameter. Small diameter rods had an ER of approximately one and the larger rods had an ER less than one.
The high pressure test results further demonstrated that the rod diameter did not significantly affect ER. Based on these findings it can be concluded that 6.9 MPa exceeded
(or was equal to) some critical pressure at which 100% burning of the melted metal
first occurred. It was proposed that the ER is directly related to the changing RRMI as
a function of test pressure reported in the literature. For a constant diameter, as the test
pressure increases, the ER increases and consequently the RRMI increases. When the
pressure reaches a level corresponding to an ER of one, the RRMI plateaus.
In addition to the experimental work undertaken, the statistical modelling of promoted ignition test data was evaluated. ‘Reaction probability’, representing the probability that a sample will sustain burning, is a function of the test pressure and was used
to describe the results. Confidence intervals for a series of no-burn test results were
explored to understand the limitations arising from the current test method. It was
shown that, based on low reaction probabilities, 1% and 5%, that the associated confidence levels based on five tests were 5% and 23%, respectively, or from ten tests were
10% and 40%, respectively. An alternative approach was described whereby the promoted ignition test data for all tested pressures is used to generate a model of reaction
probability as a function of test pressure using logistic regression. The benefit of this
approach was demonstrated by considering two data sets, obtained from the literature,
from promoted ignition tests on Hastelloy® C-276 and Hastelloy® G-3. The approach
improves upon past methods used to describe this data by using the burn/no-burn data
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S UMMARY
to generate probabilities that the sample will burn. Logistic regression models and
associated confidence intervals for reaction probability were discussed by varying the
burn criteria and the number of tests. This work also resulted in a better understanding
of the reaction probabilities and confidence levels associated with test data leading to
recommendations for an improved test methodology.
The major objectives of this thesis were to: 1) investigate the relationship between
sample geometry, RRMI and ER and 2) to explore the analysis of promoted ignition test data through statistical modelling. These objectives have been successfully
achieved through the work presented.
8.2
Conclusions
This thesis contributes a number of significant findings to the field of metals combustion. Conclusions resulting from this work are listed below and are categorised as
‘scientific’ or ‘industry related’.
Scientific
• RRMI is a function of rod shape. Statistically significant differences (95%) were
found between cylindrical, rectangular and triangular rods with the same XA,
RRMIT > RRMIR > RRMIC . The differences are due to corner effects (locally
high SA/V) including increased local melting creasing an increased SLI area
leading to enhanced heat transfer to the corner. Though perhaps indicative of the
SLI area, XA is not equal to the area across which heat is transferred to the rod.
• RRMIs for rods of different shape (but the same XA) become more dissimilar as
XA increases, relative to the standard cylindrical rod geometry.
• Instantaneous variations exist in the RRMI over a drop cycle due to changes
in the contact angle between the molten mass and the solid rod. The RRMI
increases during the first part of the drop cycle and decreases slightly just prior
to drop detachment.
• The drop cycle basis for calculating the RRMI is an improvement on the global
average method typically used since it enables accurate means, standard errors
and confidence intervals for the RRMI to be calculated. It also provides insight
155
8.2 C ONCLUSIONS
into relative changes in RRMI that may occur throughout a test (on a drop cycle
basis).
• ER is a function of both pressure and XA. At 6.9 MPa, ER was approximately
one for all XAs tested and at 1.1 MPa the ER was a function of XA with higher
ERs associated with smaller XAs.
• The relationship between ER and pressure is consistent with the accepted relationship between RRMI and pressure. Increases in RRMI with pressure correlate
to an increasing ER. At the pressure corresponding to an ER of one (critical pressure), the RRMI plateaus. Increases in RRMI above this critical pressure is not
a result of an increase in ER and may be due to other effects such as an increase
in system temperature.
• Molten mass surface temperature is a function of XA. Temperature increased as
XA decreased. The change in temperature is due to the mass flux of metal into
the molten mass, which is dependent on XA.
• Five or ten promoted ignition tests resulting in no-burns, recommended in standard test methods, have associated confidence levels of 5% and 10%, based on a
1% reaction probability. These numbers are obtained from a simple method for
calculating exact confidence intervals based on the binomial distribution once a
reaction probability is selected.
• Logistic regression suitably models the reaction probability as a function of test
pressure. The fitted reaction probability and associated confidence intervals can
be determined and are shown to decrease dramatically when the number of tests
at a single pressure is increased from three to ten.
Industry Related
• It is recommended that ASTM G124-95 (2003) and NASA-STD-6001 are updated to reflect the minimum of ten no-burn tests at a single pressure adopted in
ISO 14624-4.
• Organisations must specify a reaction probability based on the level of risk they
are prepared to accept. It is recommended that the confidence levels for test data
be presented in test reports. Confidence levels can be easily calculated based on
the number of tests conducted once the reaction probability is specified.
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• Burn lengths should be reported in all test reports so that data can be easily
interpreted and applied by other organisations/interested parties.
• It is recommended that the procedure in ASTM G124-95 (2003) be modified. It
would be more informative to conduct tests by an increasing series of pressures
in order to generate a greater quantity of data at pressures where the material
will ultimately be used. A minimum of five no-burns should be obtained before moving onto the next highest test pressure. Testing may cease after three or
four pressures resulting in burns have been identified. This enables the transition
between the lower shelf and the transition region to be far better characterised.
Data collection should concentrate on the pressure range between the lower shelf
and the transition region. If this is not possible due to economic or human factors, once the lower shelf region is identified additional testing at these lower
pressures should be performed (minimum of 10 tests).
• It is recommended that a logistic regression model be derived from promoted
ignition test data. A simple procedure for developing the model is outlined. The
models can then be used to assess the reaction probability for different pressures
in light of an organisation’s accepted level of risk.
• Threshold pressure should be redefined as the maximum pressure at which ten
no-burns are sustained. Alternatively the pressure corresponding to an acceptable reaction probability could be identified and treated as the threshold pressure.
• It is recommended that the square rod sample geometry be changed from 3.2 ×
3.2 mm to 2.84 × 2.84 mm in order to keep the XAs of the cylindrical and square
rods equal.
• Square rods are acceptable in the current standard promoted ignition test considering the small XA of the samples.
• Relative differences in RRMI due to sample geometry were minimal for small
XAs but this was not the case for larger XAs. Therefore, the RRMIs from promoted ignition tests of larger cylindrical rods may underestimate the RRMIs of
components or samples of different shape, even if the components or sample
have the same XA.
• It is recommended that oxygen components should be designed to avoid corners
if possible. The locally high SA/V ratio of a corner may facilitate ignition, and
157
8.3 F UTURE W ORK
will certainly enhance burning if ignition occurs. These experimental results
have proved the intuitive concept applied in industry.
8.3
Future Work
A number of areas relating to this work would benefit from future work.
It would be useful to develop a 2D or 3D transient heat transfer model of the burning process. This would be a complex task and is dependent on knowledge of the
reaction chemistry during burning. To aid in identifying the elements that are present
during burning it may be beneficial to consider real-time spectroscopic analysis of the
burning molten mass. In addition to accurately predicting the RRMI, a 2D or 3D heat
transfer model may also be useful in identifying TP by simulating the effect of a localised heat input to the system at various pressures. A suitable first step in this process
would be to form a 2D or 3D model of heat transfer into the solid rod from the molten
mass based on a fixed boundary condition equal to the melting temperature.
Further testing could be conducted to quantify the relationship between aspect ratio
and RRMI in the case of rectangular rods. This work showed that the SLI is not directly
proportional to the rod perimeter since the rectangular rods have a larger perimeter
than the triangular rods, yet their RRMIs were slower. The rectangle is an interesting
geometry and it is predicted that, for the same XA, its RRMI will vary depending on
the aspect ratio. The ratio used in this study was 3:1, but as the aspect ratio increases,
the RRMI should also increase, since the shape approaches that of an infinitesimally
thin flat sheet. As the aspect ratio decreases, the geometry approaches a square shape
and the RRMI is expected to decrease. Understanding the effect of aspect ratio on
RRMI will help to relate standard test geometries to actual geometries found in real
engineering systems. Promoted ignition testing of other geometries would also be a
valued contribution to the community, particularly testing of thin samples given the
lack of data present in the literature.
It is recommended that a study of sample geometry in relation to TP be conducted
to assess the effect of the shape of a rod for equal XAs. Although the rod shape affects
the RRMI it is not expected that TP will be affected but testing should be performed to
verify this hypothesis. The TP of the standard cylindrical and square sample geometries should be compared for a range of materials.
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S UMMARY
The microanalysis work should be expanded to thoroughly investigate and quantify
the relationship between ER, test pressure, XA and RRMI. The low and high pressure
work in this thesis showed that test pressure clearly affects the ER. By performing tests
over a range of pressures the critical pressure which corresponds to an ER of one can be
identified and the relationship between ER and pressure will be better characterised.
This testing could be performed for different sample geometries. It has been shown
that as the pressure increases the RRMI also increases, but there exists a pressure above
which further increases in pressure do not result in significant increases in RRMI. This
work showed that the increase in RRMI is linked to the increasing ER with increasing
pressure but this behaviour should be explored more thoroughly. By measuring the
RRMI and ER the relationship between ER and RRMI could be determined for various
pressures. The microanalysis techniques applied in this work could be applied to build
a detailed 3D image of the slag by analysing multiple cross sections. XRD analysis
techniques could also be used to quantitatively assess ER. However, one would first
have to determine a suitable method for crushing the samples without further oxidation
reactions occurring, in order to obtain a representative sample for analysis.
The statistical modelling approach introduced in this work should be further explored to investigate the reaction probabilities associated with current TPs. Further
work should also be undertaken to demonstrate how a modification in the test procedure (i.e., more data in the lower shelf region) greatly increases confidence levels
for a given reaction probability. Various organisations should be approached to obtain access to existing test data sets for analysis via the logistic regression model. In
doing so, the relative differences in reaction probability between the current and proposed definition of burn criteria may be further explored. It would also be useful to
expand the model to include other independent parameters, for instance, temperature
and oxygen concentration. A draft proposal for a revised version of ASTM G124-95
(2003) which presents the logistic regression method as a suggested means of test data
analysis should be prepared.
It is recommended that technical papers on the effect of sample geometry on RRMI,
the logistic regression method for promoted ignition data analysis and the microanalysis results presented in this thesis be prepared. The papers should draw particularly on
the industry related conclusions of the thesis to be of greatest immediate direct benefit
to the metals combustion community.
159
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177
Appendices
178
A PPENDIX A
E LECTRICAL S YSTEMS
A.1
Test Procedure
The following is the test procedures for the electrical aspects of the combustion chamber test system (refer to Figure A.1):
1. Ensure all batteries are fully charged.
2. Ensure the Arm and Trigger Switches are OFF/OPEN.
3. Ensure the Data Trigger Switch is ON/CLOSED.
4. Switch the 12V circuit ON.
5. Switch the 5V Regulator, RDAS and Igniter Switches ON.
6. Switch on the Digital Display.
7. Vent and fill the oxygen chamber as per pneumatic system procedure.
8. Initiate Video Camera Recording.
9. Initiate pressure data acquisition by switching the Data Trigger to OFF/OPEN
10. Switch the 24V circuit ON.
11. Switch the Arm switch to ON/CLOSED.
12. To initiate test, switch the Trigger switch to ON/CLOSED.
13. After ignition switch the Arm and Trigger switches OFF/OPEN.
179
A.2 C OMPONENTS
14. After the test switch the 24V circuit OFF.
15. Connect the RDAS and video camera to the PC and download data.
16. Switch the Digital Display OFF.
17. Switch the 12V circuit, 5V Regulator, RDAS, Igniter switches OFF.
A.2
Components
The following is a list of important electrical components and their various functions:
24V Battery
Powers the igniter circuit via 2 × 12V 13Ah Genesis Lead Acid Batteries connected in series(G13EP).
12V Battery
Powers the data acquisition equipment and the igniter circuit relay via a 12V
Battery Warehouse Battery (FNC 1270).
Signal Conditioner
Powers the pressure transducer whilst amplifying and conditioning the incoming signal via a Dataforth Isolated Analog Signal Conditioner (SCM5B38-01)
mounted on a Dataforth Analog I/O Backpanel (SCMPB04-2).
Digital Display
Outputs a digital pressure reading from the output of the signal conditioner and
is independently powered by a built in 9V battery.
RDAS
Records the test pressure via a Classic AED Rocket Data Acquisition Board.
Relay
High power relay array and heat sink formed by five solid state relays connected
in parallel. Once triggered on the control side (12V circuit) the relay closes the
24V circuit leading to the combustion chamber.
180
A
E LECTRICAL S YSTEMS
Capacitors
The capacitors (2 × 1F 20VDC Aerpro Capacitors (AP806) connected in series)
deliver current to the igniter terminals to trigger instantaneous ignition once the
relay is closed.
Resistor
The resistor provides added protection to the battery (RS Components 1R 300W
5%).
Combustion Chamber
The combustion chamber is fitted with two igniter feed-throughs in its base to
which the igniter circuit is connected.
Reset Switch
The reset switch allows the RDAS to be reset if it was switched ON while the
Data Trigger Switch was OPEN. The data trigger switch must be CLOSED when
the RDAS is switched on or else data acquisition will fail.
Data Trigger
This pull switch initiates pressure data acquisition when OPENED.
181
A.3
Figure A.1: Electrical Schematic Diagram of the Combustion Chamber Test System.
Electrical Schematic Diagram
A.3 E LECTRICAL S CHEMATIC D IAGRAM
182
A PPENDIX B
P RESSURE G AUGE C ALIBRATION
Pressure Gauge: Sensotec Model TJE (0 - 20.7 MPa)
Table B.1 contains the calibration data for the pressure transducer. Data was generated using a dead weight pressure gauge tester. The pressure column represents the
pressure to which the gauge was exposed and the voltage column provides the output voltage after signal conditioning. The data is plotted in Figure B.1. Equation B.1
relates pressure (MPa) to output voltage (V).
PM P a = 4.12 × V − 0.24
Pressure
(MPa)
0.10
1.48
2.86
4.24
5.62
7.00
8.38
9.75
(B.1)
Voltage
(V)
0.08
0.42
0.75
1.08
1.42
1.75
2.09
2.43
Table B.1: Calibration Data.
Figure B.1: Pressure Transducer Calibration Curve.
183
A PPENDIX C
P NEUMATIC S YSTEMS
C.1
Test Procedure
The following are test procedures associated with filling and venting the combustion
chamber test system (refer to Figure C.1):
1. Seal the combustion chamber.
2. Ensure MV3 is set to the oxygen cylinder side.
3. Open BV2.
4. Adjust Reg.2 to a pressure slightly higher than the desired pressure.
5. Adjust PRV1 to the desired pressure.
6. Open MV5 and purge the combustion chamber to a minimum of pressure of 1.7
MPa. Close MV5.
7. Open MV6 and vent the combustion chamber. Close MV6.
8. Repeat steps 5-6 twice more.
9. Open MV5 and fill the combustion chamber to the desired test pressure. Close
MV5.
10. Fully reduce PRV1.
11. Open MV4 and vent the oxygen lines.
12. Commence test.
13. After the test open MV6 and vent the combustion chamber. Close MV6.
184
C.2
Figure C.1: Pneumatic Schematic Diagram of the Combustion Chamber Test System.
Pneumatic Schematic Diagram
C
185
P NEUMATIC S YSTEMS
A PPENDIX D
P ROMOTED I GNITION T EST DATA USED FOR
L OGISTIC R EGRESSION A NALYSIS
186
D
P ROMOTED I GNITION T EST DATA
USED FOR
L OGISTIC R EGRESSION
A NALYSIS
Table D.1: Hastelloy® G-3 Data [21].
20%1
Burn NoBurn
30%2
Burn NoBurn
Material
Test
Pressure
(MPa)
Oxygen
(%)
Fraction
Burned
(%)
Hastelloy G-3
Hastelloy G-3
3.45
3.45
≥99.7
≥99.7
0
12
0
2
0
2
Hastelloy G-3
Hastelloy G-3
Hastelloy G-3
6.9
6.9
6.9
≥99.7
≥99.7
≥99.7
7
9
23
1
2
0
3
Hastelloy G-3
Hastelloy G-3
Hastelloy G-3
8.6
8.6
8.6
≥99.7
≥99.7
≥99.7
4
26
30
2
1
0
3
Hastelloy G-3
Hastelloy G-3
10.35
10.35
≥99.7
≥99.7
18
21
1
1
0
2
Hastelloy G-3
Hastelloy G-3
Hastelloy G-3
13.8
13.8
13.8
≥99.7
≥99.7
≥99.7
92
91
100
3
0
3
0
Hastelloy G-3
Hastelloy G-3
Hastelloy G-3
20.7
20.7
20.7
≥99.7
≥99.7
≥99.7
91
93
100
3
0
3
0
Hastelloy G-3
Hastelloy G-3
Hastelloy G-3
34.5
34.5
34.5
≥99.7
≥99.7
≥99.7
90
93
100
3
0
3
0
1
2
A 20% burn criteria was applied to obtain burn/no-burn data for the logistic regression models.
The 30% criteria is presented as it was the burn criteria applied in [21] for a 100 mm sample
length.
187
P ROMOTED I GNITION T EST DATA USED FOR L OGISTIC R EGRESSION A NALYSIS
Table D.2: Hastelloy® C-276 Data [21].
20%1
Burn NoBurn
30%2
Burn NoBurn
Material
Test
Pressure
(MPa)
Oxygen
(%)
Fraction
Burned
(%)
Hastelloy C-276
Hastelloy C-276
Hastelloy C-276
3.45
3.45
3.45
≥99.7
≥99.7
≥99.7
0
5
7
0
3
0
3
Hastelloy C-276
Hastelloy C-276
6.9
6.9
≥99.7
≥99.7
7
17
0
2
0
2
Hastelloy C-276
Hastelloy C-276
Hastelloy C-276
10.35
10.35
10.35
≥99.7
≥99.7
≥99.7
7
9
12
0
3
0
3
Hastelloy C-276
Hastelloy C-276
Hastelloy C-276
12.1
12.1
12.1
≥99.7
≥99.7
≥99.7
10
20
39
1
2
1
2
Hastelloy C-276
Hastelloy C-276
Hastelloy C-276
13.8
13.8
13.8
≥99.7
≥99.7
≥99.7
12
17
35
1
2
1
2
Hastelloy C-276
Hastelloy C-276
Hastelloy C-276
17.25
17.25
17.25
≥99.7
≥99.7
≥99.7
7
25
57
2
1
1
2
Hastelloy C-276
Hastelloy C-276
Hastelloy C-276
20.7
20.7
20.7
≥99.7
≥99.7
≥99.7
93
95
100
3
0
3
0
Hastelloy C-276
Hastelloy C-276
34.5
34.5
≥99.7
≥99.7
90
100
2
0
2
0
1
2
A 20% burn criteria was applied to obtain burn/no-burn data for the logistic regression models.
The 30% criteria is presented as it was the burn criteria applied in [21] for a 100 mm sample
length.
188