1. business and industrial
2. energy
3. oil

THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS
345 E. 47th St. New York, N.Y. 10017
97-G1-151
The Sodety shall not be responsible for statements or opinions advanced in papers or dieussion at meetings of the Society or of its Divisions or
Sections, or printed in its publications. Dicrutsion is printed only if the paper is published in an ASME Journal. Authorization to photocopy
material for Internal or personal use under circumstanoa not 'offing within the fair use:provisions of the Copyright Act is granted by ASME to
libraries and other users registered with the Copyright Clearance Center (CCC)Transactional Reporting Service provided that the base lee of $0.30
per page is paid directly to the CCC. 27 Congress Street Salem MA 01970. Requests tor special permissiOn or bulk reproduction should be addressed
to CID ASME Technical Publishing Department
Copyright 0 1997 by ASME
All Rights Reserved
. Primed in U.S.A
EXPERIMENTAL AND THEORETICAL STUDY OF DROPLET
VAPORIZATION IN A HIGH PRESSURE ENVIRONMENT
Jorg Stengele
Michael Willmann
111111111111, I11111111111
Sigmar Wittig
Lehrstuhl und Institut far Thermische Stramungsmaschinen
Universitat Karisruhe (T.H.)
Karlsruhe (Germany)
ABSTRACT
Due to the continuous increase of pressure ratios in modem gas
turbine engines the understanding of high pressure effects on the
droplet evaporation process gained significant importance. The precise
prediction of the evaporation time and the movement of the droplets is
crucial for optimum design and performance of modem gas turbine
combustion chambers. Numerous experimental and numerical
investigations have been done already in order to understand the
evaporation process of droplets in high pressure environments. But
until now, all high pressure experiments were carried out with droplets
attached to a thin fiber resulting in the impairment of the droplet
evaporation process due to the suspension unit.
In the present study, a new experimental set up is introduced where
the evaporation of free falling droplets is investigated. Monodisperse
droplets are generated in the upper part of the test rig and fall through
the stagnant high pressure gas inside the pressure chamber. Due to the
relative velocity between droplet and gas, convective effects have to be
considered in this study which are taken into account by experimental
correlations. The droplet diameter and the droplet velocity are
measured simultaneously by means of video technique and a
stroboscope lamp. Detailed measurements with heptane droplets
are presented for different pressures (p = 20 bar, 30 bar and 40 bar),
gas temperatures (T = 550 K and 650 K) and initial diameters
(do = 680 pm, 780 prn and MO um). The experiments were carried out
with single component droplets.
The experimental results are compared with numerical calculations.
For this a theoretical model was developed based on the Conduction
Limit model and the Uniform Temperature model. Good agreement for
all conditions investigated is observed when using the Conduction
Limit model. The Uniform Temperature model predicts incorrectly the
evaporation process of the droplet.
Br
1/(kgK)
cw
m2/s
m/s 2
Mcg
Le
kg/s
Nu
bar
Pr
rd
Re
Sc
Sh
m/s
Greek Symbols:
X
W/(mK)
p
kg/m3
03
,,
-
mass transfer number
mass flow
Nusselt number
pressure
Prandtl number
heat flux
radial coordinate
droplet radius
Reynolds number
time
Schmidt number
Sherwood number
temperature
velocity
distance
mass fraction
thermal conductivity
density
dimensionless radial coordinate
Subscrips:
NOMENCLATURE
Br
-
heat transfer number
specific heat at constant pressure
drag coefficient
droplet diameter
binary gaseous diffusivity
relative change of film thickness
gravity constant
enthalpy of evaporation
Lewis number
ref
droplet
fuel vapor
gas phase
reference
Presented at the International Gas Turbine & Aeroengine Congress & Exhibition
Orlando, Florida — June 2–June 5,1997
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vap
0
0
droplet surface
vaporization
without Stefan flow
Stefan flow included
initial state
Since the distance between the evaporating droplets is large there is
no interaction of the droplets. Due to the relative velocity between
the falling droplet and the stagnant gas, convective effects have to
be taken into consideration by experimental correlations. The
Reynoldsnumber of the free falling droplet varies between 100 and
500 and is, therefore, comparable to conditions occuring in gas turbine
combustion chambers.
The experimental . results are compared with two different droplet
evaporation models. the Conduction Limit and the Uniform
Temperature model. The Conduction Limit model (Law and Sirignano.
1977) assumes a one dimensional radial diffusive transport of heat
within the droplet. The Uniform Temperature model (Faeth. 1977) is
based on an infinite fast mixing process inside the droplet excluding
any temperature gradients inside the droplet. Both models represent
the limiting cases in between the evaporation process of the droplet
takes place.
In order to describe the convective effects, the theory of Abramzon
and Sirignano (1987) is combined with the experimental correlation of
Ranz and Marshall (1952).
INTRODUCTION
The combustion of liquid fuels in gas turbine engines is mainly
influenced by the atomization of the liquid fuel, the motion and
evaporation of the fuel droplets and the mixing of fuel and air. In the
past many experimental and theoretical studies have been done in
order to characterize the behavior of evaporating fuel sprays (Wittig et
al., 1988, Hellmann et al., 1993, Kneer et al., 1990, Kurreck et al.,
1996). They found that exact spray modeling is based on the correct
prediction of both droplet motion and droplet evaporation. Since the
pressure level inside the combustion chambers of gas turbine engines
has continuously increased during the past years reaching or even
exceeding the critical pressure of the fuel used, the present study is
intended to describe the evaporation of droplets in a high pressure
environment by numerical and experimental methods.
Numerous theoretical studies have been carried out describing
droplet evaporation in a high pressure gas (Manrique and Borman.
1969, Hsieh et al., 1991, Curtis and Fare11, 1992, Jia and Cops, 1993,
Stengele et al., (996). They take into account the real gas behavior, the
variation of the thermophysical properties, the non-ideality of the
latent heat of evaporation and the non-ideal phase equilibrium
including the solubility of the ambient gas inside the droplet. These
points are found to be extremely important for the correct prediction of
the droplet evaporation in high pressure environments. Since the
droplet temperature rises with increasing pressures, the unsteady
heating of the droplet affects significantly the droplet evaporation
process under high pressure conditions and steady state evaporation
cannot be obtained. If the pressure and the temperature of the gaseous
environment is sufficiently high, the droplet may reach the critical
point during its evaporation time (Wieber, 1963). These conditions are
reached for example in liquid oxygen combustion systems. Delplanque
and Sirignano (1993) apply new evaporation models in this region,
since the surface tension and the heat of evaporation become zero.
However. Hsieh et al. (1991) found in a theoretical study that for
pentane droplets subcritical models can be used up to 65 bar.
Only few experimental studies have been published describing the
droplet evaporation process in high pressure environments (Madosz et
al., 1972. Kadota and Hiroyasu. 1976 and Olthoff, 1994). In order to
exclude gravity and convective effects on the evaporation process
some experiments on high pressure droplet vaporization were carried
out in microgravity environments (Sato et al.. 1990, Hartfield and
Farrell, 1992). These experiments have been conducted with droplets
attached to a thin fiber resulting in the impairment of the droplet
evaporation process due to the suspension unit. Shih and Megaridis
(1995) have shown that these kinds of experiments will lead to an
overestimation of the liquid evaporation rates and underprediction of
the droplet lifetimes.
The present study introduces a new experimental set-up where the
evaporation of free falling droplets in a stagnant high pressure gas is
investigated. There is no need of a suspension of the droplet and the
evaporation process can be observed without any disturbing influence.
DROPLET EVAPORATION MODEL
The present model describes the evaporation process of an isolated
evaporating droplet in a convective flow field. The flow around the
droplet is assumed to be laminar, since the droplet size is usually at
least one order of magnitude smaller than the turbulent spots in typical
spray applications. Variable thermophysical properties have been used
inside the droplet and the surrounding gas to account for the variation
of temperature and concentration (ICneer et al.. I993a. 1993b). The
correlations necessary to determine the physical properties are listed in
Stengele et al. (1996). The following simplifications are 'assumed in
the model: the droplet evaporates in an inert atmosphere excluding
droplet combustion. The interface between liquid and gas phase is
assumed to be in thermodynamic equilibrium. Radiative heat transfer
is neglected (Lege and Rangel, 1993). Fick's law is used to calculate
mass diffusion. Dufour and Sorel effects are neglected. The
evaporation process is assumed to be spherically symmetric. the
asymmetric convective effects on the evaporation process are included
implicitly in the correlations of Rana and Marshall (1952).
Gas Phase Equation:
In the present model the gas phase is assumed to be quasi-steady.
Delplanque (1993) showed that this assumption is valid for typical
high pressure spray application, since the characteristic time of the
flow around the droplet is much smaller than the droplet lifetime.
Applying the integral solution of the governing equations (Hubbard et
al., 1975) and the extended film theory of Abrarnzon and Sirignano
(1987, 1989) the evaporating mass flow of the droplet and the heat
transfer from the hot environment towards the droplet are calculated as
follows.
The convective effects on the heat and mass transfer of the
evaporating droplet are determined by Eqs. (I) and (2).
Nu . — 2 + Nu " 2
F(13T )
Sh . = 2 +
2
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Sh„ —2
F(B,„ )
( I)
(2)
The flow of the evaporating droplet mass radially outward (Stefan
The drag coefficient is calculated by the correlation of Renksizbulut
and Haywood (1988), where the Stefan flow of the evaporating fuel
radially outward is included. The Reynolds number is calculated again
with the free stream density (Yuen and Chen, 1976).
flow) is described by F(B).
F(B)= (1 +
+ B)
(3)
24
= 036 + 5.48 . Re 4)373 +
c. + B.
The correlations of Ranz and Marshall (1952) are used to calculate
Nuo and Shn in Eqs. (I) and (2).
(12)
Re d
Nu„ = 2 +0.64—Re—d- Pr I13
(4)
After solving Eq. (I I) the position of the evaporating droplet is
determined by integration of Eq. (13).
Sh n = 2 +0.6.11
(5)
dx d
1 Sc u3
=11 0
dt
The evaporating mass flow of the droplet is obtained by integration
of the quasi-steady mass and energy equations.
031
Liquid Phase Equation:
rn„,„ = 2nr4 ps.. 1 Dd..,Sh • In(1+ B.)
•
(6)
In the present paper the Conduction Limit model (Law and
Sirignano, 1977) and the Uniform Temperature model (Faeth. 1977) is
used to describe the heat transport inside the droplet.
The Conduction Limit model assumes that the heat transport within
the droplet is controlled by heat conduction only. The describing
differential equation has to be solved numerically.
k
= 2nrd
Nu s In(1+13.r )
(7)
where B. and Br are the Spalding mass and heat transfer numbers.
•
•I
•
rn•ar, c Pg.rcf
zx
(8)
IIl ••• — T )
I a (
r
Pdcp.d aT
d
at _ r
2 dr
d
)
,
The instantaneous droplet diameter is derived from the mass balance
around the droplet.
(9)
BT
644
•
In contrast to the theory of Abramzon and Sirignano (1987), the
specific heat capacity of the pure vapor is replaced by the specific heat
capacity of the vapor/gas mixture in Eqs. (7) and (9). This will be
confirmed by the subsequent experimental results. The thermophysical
properties necessary are obtained by the 1/2-rule of Renksizbulut and
Yuen (1983). The only exception is the gas density of the Reynolds
number, which is calculated at free stream conditions (Yuen and Chen,
1976). Combining Eq. (6) and Eq. (7) the following relationship is
obtained.
• drd
dt
=_
is —C
U -Lj r2 dr
MvaP
Pair:
422
(15)
0 a2
Since the droplet diameter changes during the evaporation process
due to heating and vaporization, the radial coordinate in the gas phase
and the liquid phase is non-dimensionalized by the instantaneous
droplet diameter. With this transformation the droplet surface is
always located at us = I resulting in a more simple solution procedure
of Eq. (14).
511*
137
+ B riles
—
(10)
—
(16)
r0 (0
With these equations the heat and mass transfer between droplet and
surrounding gas are defined. The calculation procedure starts from Eq.
(6), where the evaporating mass flow of the liquid fuel is calculated.
From this, the ar is determined by Eq. (10). This has to be done
iteratively. Then the total heat transfer from the surrounding gas
towards the droplet is calculated using Eq. (9).
In order to determine the temperature distribution inside the droplet
the following initial and boundary conditions are applied. The initial
temperature within the droplet is uniform. The boundary conditions
result from symmetry at the droplet center and the conservation of
energy at the droplet surface. Both are expressed in terms of Neumann
conditions.
LTH = 0
Pronlet Motion:
The equation of the droplet motion is obtained by the balance of
forces. For reasons of simplicity, the motion of the droplet and the gas
flow is assumed to be one-dimensional. The gravity force and the
buoyancy force are also included, since they affect the evaporation
process of the droplet in the experiments presented here.
du
eI
3Pc
4 pd dd
u (u d — u s )41—Hg
ar
4nrd2
aT
dr
(17)
ref)
=
•
L
(18)
rd
where
is the total Neat flux in Eq. (9) and m np L represents
the latent heat of evaporation.
The Uniform Temperature model assumes an infinite fast mixing
(II)
Pd
3
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The droplets are generated in the upper part of the pressure chamber
and fall down due to gravity through the high temperature stagnant
nitrogen gas. In Fig. 2 the schematic view of the droplet generator is
shown. Due to constant fuel mass flow through a thin glass capillary
tube a droplet is generated at its tip. The diameter of the droplet
increases until the weight of the droplet exceeds the cohesion forces,
the droplet separates from the capillary tube and enters the evaporation
zone. Applying this static technique droplets with a diameter of I mm
or greater can be produced, since the diameter of the capillary can be
decreased only to a certain extend.
With a forced separation the droplet size can be further reduced.
This is realized by a movable droplet generator lifted by a
electromagnet and then released again hitting a stroke device. The
droplet falls off the glass capillary tube and enters the evaporation
zone. With this technique droplets are produced in a diameter range
between 600 gin and 900 gm. If the mass flow through the capillary
tube is constant and the frequency of the up and down movement of
the droplet generator is also constant, monodisperse droplets, i.e.
droplets with identical initial conditions, are produced. Constant
differential pressure between the fuel tank and the pressure chamber is
crucial to obtain constant mass flows. Depending on the frequency and
the mass flow, the distance between the droplets can be adjusted
arbitrarily within distinct boundaries. In the present study, the droplet
distance was more than 100 times the initial droplet diameter,
therefore, any interaction between the evaporating droplets , was
excluded. Inside the cavity surrounding the glass capillary, a
thermocouple element is inserted close to the capillary tip to determine
the initial temperature of the droplet. This temperature is important for
the comparison of the numerical and experimental results. The droplet
generator is cooled by water in order to keep constant the droplet
initial temperature. To avoid blocking by trapped nitrogen. the droplet
generator is vented regularly by means of a valve.
In Fig. 3 an overview of the whole test section is shown including
all temperature and pressure measuring locations. In addition, the
valves, the piping, and the heaters (H I and H 2) and control units are
presented. In order to compensate pressure fluctuations a gas reservoir
was connected to the fuel tank. The pressure difference between fuel
tank and pressure chamber is measured permanently. Before the filling
with nitrogen gas, the test section is evacuated to avoid any residual
oxygen inside the evaporation zone.
vacuum
pump
•
fuel tank
• reservoir
0 temperatom measuring
0 pressure measuring
filter
vent line
Mater and
control unit
to the
exhaust
1.1
vent line
Figure 3: Test section
fuel pipe
RESULTS AND DISCUSSION
The experiments were conducted with heptane droplets for three
different pressures (p = 20 bar, 30 bar and 40 bar), two gas
temperatures (T,. = 550 K and 650 K) and three initial droplet
diameters (dd.0 = 680 gm, 780 gm and 840 gm). The investigation of
less volatile fuel like decane was not practicable, since the initial
droplet size is to large and the evaporation zone in the pressure
chamber is to short. However, the results conducted with heptane are
still applicable and can be expanded to less volatile alcane-fuels.
At p = 40 bar, the critical pressure of the heptane was exceeded by a
factor of 1.5, and at = 650 K, the critical temperature by a factor
of 1.2. The calculated wet bulb temperatures of the droplets in
nitrogen at T. = 550 K and pressures of 20 bar, 30 bar and 40 bar are
426K, 441 K and 451 K. at T., = 650 K and p = 30 bar 460 K. while
the critical temperature of heptane is 540 K. Thus the droplets do not
exceed the critical temperature, or even come close to the critical
temperature, during the evaporation process.
In the following figures, the diameter and the velocity of the droplet
is plotted over the evaporation distance. The symbols indicate the
electromagnet
cooling
water
glass
capillary
Insulating
material
evaporation
zone
Figure 2: Droplet generator
5
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The droplets are generated in the upper part of the pressure chamber
and fall down due to gravity through the high temperature stagnant
nitrogen gas. In Fig. 2 the schematic view of the droplet generator is
shown. Due to constant fuel mass flow through a thin glass capillary
tube a droplet is generated at its tip. The diameter of the droplet
increases until the weight of the droplet exceeds the cohesion forces,
the droplet separates from the capillary tube and enters the evaporation
zone. Applying this static technique droplets with a diameter of I mm
or greater can be produced, since the diameter of the capillary can be
decreased only to a certain extend.
With a forced separation the droplet size can be further reduced.
This is realized by a movable droplet generator lifted by a
electromagnet and then released again hitting a stroke device. The
droplet falls off the glass capillary tube and enters the evaporation
zone. With this technique droplets are produced in a diameter range
between 600 gin and 900 gm. If the mass flow through the capillary
tube is constant and the frequency of the up and down movement of
the droplet generator is also constant, monodisperse droplets, i.e.
droplets with identical initial conditions, are produced. Constant
differential pressure between the fuel tank and the pressure chamber is
crucial to obtain constant mass flows. Depending on the frequency and
the mass flow, the distance between the droplets can be adjusted
arbitrarily within distinct boundaries. In the present study, the droplet
distance was more than 100 times the initial droplet diameter,
therefore, any interaction between the evaporating droplets , was
excluded. Inside the cavity surrounding the glass capillary, a
thermocouple element is inserted close to the capillary tip to determine
the initial temperature of the droplet. This temperature is important for
the comparison of the numerical and experimental results. The droplet
generator is cooled by water in order to keep constant the droplet
initial temperature. To avoid blocking by trapped nitrogen. the droplet
generator is vented regularly by means of a valve.
In Fig. 3 an overview of the whole test section is shown including
all temperature and pressure measuring locations. In addition, the
valves, the piping, and the heaters (H I and H 2) and control units are
presented. In order to compensate pressure fluctuations a gas reservoir
was connected to the fuel tank. The pressure difference between fuel
tank and pressure chamber is measured permanently. Before the filling
with nitrogen gas, the test section is evacuated to avoid any residual
oxygen inside the evaporation zone.
vacuum
pump
•
fuel tank
• reservoir
0 temperatom measuring
0 pressure measuring
filter
vent line
Mater and
control unit
to the
exhaust
1.1
vent line
Figure 3: Test section
fuel pipe
RESULTS AND DISCUSSION
The experiments were conducted with heptane droplets for three
different pressures (p = 20 bar, 30 bar and 40 bar), two gas
temperatures (T,. = 550 K and 650 K) and three initial droplet
diameters (dd.0 = 680 gm, 780 gm and 840 gm). The investigation of
less volatile fuel like decane was not practicable, since the initial
droplet size is to large and the evaporation zone in the pressure
chamber is to short. However, the results conducted with heptane are
still applicable and can be expanded to less volatile alcane-fuels.
At p = 40 bar, the critical pressure of the heptane was exceeded by a
factor of 1.5, and at = 650 K, the critical temperature by a factor
of 1.2. The calculated wet bulb temperatures of the droplets in
nitrogen at T. = 550 K and pressures of 20 bar, 30 bar and 40 bar are
426K, 441 K and 451 K. at T., = 650 K and p = 30 bar 460 K. while
the critical temperature of heptane is 540 K. Thus the droplets do not
exceed the critical temperature, or even come close to the critical
temperature, during the evaporation process.
In the following figures, the diameter and the velocity of the droplet
is plotted over the evaporation distance. The symbols indicate the
electromagnet
cooling
water
glass
capillary
Insulating
material
evaporation
zone
Figure 2: Droplet generator
5
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measured values, and the solid lines represent the calculated values
based on the Conduction Limit model. In the last section the
Conduction Limit and the Uniform Temperature model are compared
with experimental data.
The initial droplet velocity results from the droplet acceleration
between the glass capillary and the entrance of the evaporation zone. It
is for all conditions approximately the same, u d.0 = 0.5 m/s. The initial
droplet temperature rises slightly with higher pressures and higher gas
temperatures. This effect occurs due to the intensified heat transfer
from the evaporation zone towards the droplet generator.
smaller droplet diameters. Towards the end of the evaporation process
there is a steep velocity gradient. In this region the influence of gravity
is negligible.
For all pressure levels investigated, there is an excellent agreement
between the measured and calculated doplet diameter and velocity
distributions.
Variations of Gas Temperature
The calculated and measured results also coincide very well for
different gas temperatures (see Fig. 5). Elevating the gas temperature.
the evaporation distance of the droplet shortens. During the first part
of the evaporation process the velocity increases with higher gas
temperatures resulting from smaller aerodynamic resistance. However.
the following reduction in droplet velocities is much steeper for higher
temperatures due to the faster decrease of the droplet diameter.
Variations of Pressure
A comparison between experimental and theoretical results is shown
in Fig. 4 for different pressures. In this case the gas temperature is
T.. = 550 K. With elevating pressures the evaporation distance and the
velocity of the droplet decreases. This results from the increased
aerodynamic force at higher pressures. For all pressure levels, similar
velocity and diameter distributions are observed. Due to the large
droplet diameters at the beginning of the evaporation process, the
droplet velocity increases quickly to its maximum. The magnitude
depends on the gas pressure, the higher the gas pressurethe lower the
velocity maximum. Passing this point, the droplet velocity decreases
since the aerodynamic resistance exceeds the force of gravity due to
Variations of Initial Droplet Diameters
The decisive influence of the initial droplet diameter on the droplet
evaporation process is shown in Fig. 6. Reducing the initial droplet
diameter by 15 % the evaporation distance shortens more than 30 %.
This follows directly from Godsaves d 2 law (1953). In this case the gas
temperature is T.. = 550 K, the pressure p = 30 bar. As observed
before, experiment and theory agree very well.
1.0
heptane droplet
0.8
•
p = 30 bar
0.6 0.4 0.2.
00
0.0
symbols: experiment
0.2
0.1
0.3
0.4
0.5
0.6
symbols; experiment
115 -
line: Conduction Limit model
line: Conduction Limit model
1.0
0.0
0.0
0.2
0.1
distance (m)
p = 20 bar
= 340 K
A p=30 bar
0.3
0.4
distance [m)
+
Td,0 = 350 K
A
40bar
T. = 550 K
Tcre = 350 K
T - 360 K
•
T = 650K
°
Tc1.0 370 K
Figure 5: Variation of gas temperature
Figure 4: Variation of pressure
6
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0.5
0.6
THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS
345 E. 47th St. New York, N.Y. 10017
97-G1-151
The Sodety shall not be responsible for statements or opinions advanced in papers or dieussion at meetings of the Society or of its Divisions or
Sections, or printed in its publications. Dicrutsion is printed only if the paper is published in an ASME Journal. Authorization to photocopy
material for Internal or personal use under circumstanoa not 'offing within the fair use:provisions of the Copyright Act is granted by ASME to
libraries and other users registered with the Copyright Clearance Center (CCC)Transactional Reporting Service provided that the base lee of $0.30
per page is paid directly to the CCC. 27 Congress Street Salem MA 01970. Requests tor special permissiOn or bulk reproduction should be addressed
to CID ASME Technical Publishing Department
Copyright 0 1997 by ASME
All Rights Reserved
. Primed in U.S.A
EXPERIMENTAL AND THEORETICAL STUDY OF DROPLET
VAPORIZATION IN A HIGH PRESSURE ENVIRONMENT
Jorg Stengele
Michael Willmann
111111111111, I11111111111
Sigmar Wittig
Lehrstuhl und Institut far Thermische Stramungsmaschinen
Universitat Karisruhe (T.H.)
Karlsruhe (Germany)
ABSTRACT
Due to the continuous increase of pressure ratios in modem gas
turbine engines the understanding of high pressure effects on the
droplet evaporation process gained significant importance. The precise
prediction of the evaporation time and the movement of the droplets is
crucial for optimum design and performance of modem gas turbine
combustion chambers. Numerous experimental and numerical
investigations have been done already in order to understand the
evaporation process of droplets in high pressure environments. But
until now, all high pressure experiments were carried out with droplets
attached to a thin fiber resulting in the impairment of the droplet
evaporation process due to the suspension unit.
In the present study, a new experimental set up is introduced where
the evaporation of free falling droplets is investigated. Monodisperse
droplets are generated in the upper part of the test rig and fall through
the stagnant high pressure gas inside the pressure chamber. Due to the
relative velocity between droplet and gas, convective effects have to be
considered in this study which are taken into account by experimental
correlations. The droplet diameter and the droplet velocity are
measured simultaneously by means of video technique and a
stroboscope lamp. Detailed measurements with heptane droplets
are presented for different pressures (p = 20 bar, 30 bar and 40 bar),
gas temperatures (T = 550 K and 650 K) and initial diameters
(do = 680 pm, 780 prn and MO um). The experiments were carried out
with single component droplets.
The experimental results are compared with numerical calculations.
For this a theoretical model was developed based on the Conduction
Limit model and the Uniform Temperature model. Good agreement for
all conditions investigated is observed when using the Conduction
Limit model. The Uniform Temperature model predicts incorrectly the
evaporation process of the droplet.
Br
1/(kgK)
cw
m2/s
m/s 2
Mcg
Le
kg/s
Nu
bar
Pr
rd
Re
Sc
Sh
m/s
Greek Symbols:
X
W/(mK)
p
kg/m3
03
,,
-
mass transfer number
mass flow
Nusselt number
pressure
Prandtl number
heat flux
radial coordinate
droplet radius
Reynolds number
time
Schmidt number
Sherwood number
temperature
velocity
distance
mass fraction
thermal conductivity
density
dimensionless radial coordinate
Subscrips:
NOMENCLATURE
Br
-
heat transfer number
specific heat at constant pressure
drag coefficient
droplet diameter
binary gaseous diffusivity
relative change of film thickness
gravity constant
enthalpy of evaporation
Lewis number
ref
droplet
fuel vapor
gas phase
reference
Presented at the International Gas Turbine & Aeroengine Congress & Exhibition
Orlando, Florida — June 2–June 5,1997
Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 12/29/2014 Terms of Use: http://asme.org/terms
Application of Laser Techniques to Fluid Mechanics. July 9 - 12.
Lisbon, Portugal, Paper 21.5.
obtained when using the Conduction Limit model. In contrast. the
Uniform Temperature model underpredicted the evaporation rate
during the first part of the evaporation process and then overpredicts
the evaporation process of the droplet. This was observed for all
parameter variations presented.
ICneer, R.. Schneider, M., Noll. B., and Wittig, S., 1993. "Effects of
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Transactions of ASME 115, pp. 467 - 472.
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ACKNOWLEDGEMENT
The present study was supported by a grant from the SFB 167 (high
intensity combusters) of the Deutsche Forschungsgemeinschaft which
is gratefully acknowledged.
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Three-Dimensional Reacting Two-Phase Row within a Jet-Stabilized
Combustor," ASME-96-GT-468, Presented on the 'Gas Turbine and
Aeroengine Congress' in Birmingham UK, 10. -13. Juni.
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