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Effects of Periodic Wake Passing upon Aerodynamic Loss of a Turbine Cascade
Part II: Time-Resolved Flow Field and Wake Decay Process through the Cascade
Ken-ichi Funazaki and Nobuaki Tetsulca
111111111 19111 11111
Department of Mechanical Engineering
lwate University
Morioka, Japan
Tadashi Tanuma
Keihin Operation
Toshiba Co.
Yokohama, Japan
: axial coordinate
ABSTRACT
This paper. Part II of the study on wake-passing effect upon the
aerodynamic performance of the turbine cascade, demonstrates the
detailed measurements of the time-varying flow field downstream of
the turbine cascade as well as of the moving bars. The experiment
employs a single hot-wire probe to measure pitchwise distributions
of the ensemble-averaged velocity at the blade midspan. The resultant
data consequently provide clear images of the incident bar wakes
that are bowed and directed to the suction side of the blade wake. A
custom-made total pressure probe, instrumented with a miniature
fast-response pressure transducer, are also adopted to understand
time-resolved feature of the wake-affected stagnation pressure fields
downstream of the cascade. Furthermore, a decay process of the bar
wake through the test cascade is examined in detail, which serves
for the discussion related to wake recovery and its impact on the
stage loss.
NOMENCLATURE
wake semi-depth width
Cd
: drag coefficient
C,
it
: axial chord length [m]
: diameter of the wake-generating bar [mm]
: output from hot-wire probe [V]
: wake passing frequency [Hz]
nb
Py
Po
:
:
:
:
yaw coefficient of the probe or index
number of rotation [rpm]
number of wake-generating bar
blade pitch [m]
: stagnation pressure [Pa]
: wake Strouhal number (= jV1dv)
: time [s]
: wake-passing period [s]
TD
: drift function [s]
1./m
: bar moving speed [m/s)
: inlet velocity [m/s1
: relative velocity (m/s]
ensemble-averaged velocity, sampled velocity data
[m/s)
xi ,/
i e
y ,y
: coordinates along the inlet and exit flow direction
: pitchwise coordinate
: coordinates normal to the inlet and exit flow direction
Greeks
a
: absolute flow angle [deg]
: relative flow angle [deg]
: kinematic viscosity [rills]
: vorticity [1/s]
Superscript
: ensemble-averaged value
Subscript
1. 2
: inlet and outlet of the cascade
x,y.z
: axial, tangential and spanwise direction
INTRODUCTION
Part I of the present study dealt with the measurements of the
wake-affected loss of the turbine cascade by use of the pneumatic
five-hole probe. Significant effects of the wake passing upon the
local loss distributions and the resultant loss increases were observed.
It was also shown that the wake passing meaningfully affected the
pitchwise distributions of the exit flow angle, mainly due to the
upward shift of the tip side undertuming. Although these 'results
surely provide aerodynamic designers of turbomachines with useful
information on wake-blade interaction phenomena, a clear image of
the dynamic behaviors of the wake-affected flow field around the
blade row is still lacking, which is very important to understand the
mechanism of the wake-related loss generation or change in the exit
flow angle. In this study, as a companion paper of Part I, time-varying
velocity and stagnation pressure fields disturbed by incident periodic
wakes are investigated by use of a single hot-wire probe and a
custom-made pressure probe instrumented with a fast-response
pressure transducer.
Besides, this paper discusses wake decay process at the upstream
and inside of the blade-to-blade passage. Rotor-stator spacing is an
important and it has been also recognized that the wake decay process
is directly linked to the rotor-stator spacing, affecting aerodynamic
performances of not only neighboring but also far downstream blade
row in nubomachines. Survey of several studies on wake-affected
Presented at the International Gas Turbine & Aeroengine Congress & Exhibition
Indianaporis, Indiana — June 7-June 10, 1999
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turbine cascade or turbine stage (Hodson(1984), Venable et al.
(1998a)(1998b)) reveals that expanding the axial spacing between
rotor and stator tended to reduce aerodynamic loss of the downstream
cascade, which occurred in less drastic manner than expected. Yu
and Lakshiminarayana (1998) executed comprehensive numerical
experiments on a compressor cascade subjected to incoming wakes,
demonstrating that the loss of the cascade was the highest for the
smallest blade row spacing. They also found the existence of the
range of the blade row spacing where the wake-affected cascade loss
became smaller that the sum of the steady-state cawade loss and the
wake mixing loss. This event seems to have a close relationship with
their another finding that the incoming rotor wakes decayed much
faster when the cascade existed at the downstream of the rotor. Yu
and Lakshiminarayana stated that the faster wake decay was caused
by the unsteadiness due to the potential interaction between the
downstream cascade and the incoming wakes. Prior to the study of
Yu and Lalcshiminarayana, similar findings were already reported
by Poensgen and Gallus (1991) , who attributed the faster wake
decay to the flow acceleration and deceleration through the stator
passage. Recently another view on the wake decay process within
the cascade has been given in terms of 'reversible wake recovery
effect' by Adamczyk(1996). Deregel and Tan (1996), Valkov and
Tan (I 998a). This idea of reversible wake recovery as an explanation
for the faster wake decay was originally proposed by Smith (1966)
on a basis of the Kelvin's theorem. The point of the reversible wake
decay effect is that the non-uniform velocity field resulting from the
incoming wakes becomes flattened without any penalty of entropy
production in the cascade passage, in other words, no aerodynamic
loss is generated in this wake-smoothing process. Denton (1993)
also pointed out the possibility of loss reduction due to the wake
recovery effect, however he suggested that the amount of such a loss
reduction might be small if any. In this study wake decay process
was experimentally examined from the viewpoint of not only velocity
field but also the vonicity field associated with the incoming wake
in order to clarify whether any change in wake decay rate or wake
recovery effect could be identified in the present turbine cascade.
Sensor Orientation 1
Uy
Uy
Ux
Figure 1 Two sensor orientations for detecting ensembleaveraged velocity components with a single hot-wire probe
Figure 2 Schematic of the unsteady total pressure probe
A–
cos= a(I k 2
, a – x14
cos 2 a(1– k2)+k2
°M = 40
.(
01 ,
1S + L-
(3)
where the value of k was empirically determined. The quantities
with mean ensemble-averaged values, which were calculated from
100 records as follows:
TEST APPARATUS
Instrumentation and Data Processing
Since detailed explanations on the test apparatus were already
presented in Part I, only some descriptions are hereafter shown on
the instrumentation and data processing for the unsteady
measurements.
A single normal hot-wire probe was used to measure the unsteady
velocity downstream of the moving bars as well as of the cascade.
The technique developed by Fujita and Kovasznay (1968) was
employed in this study. This technique enabled the measurements of
two-dimensional velocity vectors with a single normal hot-wire probe
by rotating the probe around its axis by 90 degree, where the probe
axis was perpendicular to the main stream in the present study. Note
that this so-called multiposition technique provides only time- or
ensemble-averaged flow quantities in principle because of the nonsynchronicity of the data. Figure 1 shows the relationship between
the probe sensor and velocity components at two different sensor
orientations, where the s e represents a specified direction, which
was normally aligned with the design exit flow angle, and y e represents
the direction perpendicular to the x e . In this case the velocity
components were calculated by the following equations,
–
Sensor Orientation 2
m=100,
(4)
k=1
where each of the records contained 2048 words data sampled at 50
kHz by an A/D converter. From the authors' experience, it had been
found that the sample number m = 100 was sufficient to extract the
periodic events out of the measured data in the present test cascade.
Through this condition, about five bar wakes were captured for no
=6 and n =1200 rpm. Uncertainties of the instantaneous velocity
measurement were about 2 %.
Figure 2 shows unsteady total pressure probe used in this study.
This probe was equipped with a fast-response miniature pressure
transducer (Entran, EPI-553-15P) whose diameter was 2.36 mm.
ESTIMATION OF VORT1CITY
Linearized Vorticitv Transport Equation
From the Navier-Stokes equation, the vorticity transport equation
can be derived.
Da)
—=(co ,07)v+vV 2 v
Dr
2(cos 2 a + k 2 sin 2 a)°s
(2)
,
0)=-Vxv ,
(5)
where DID% = apt+(v• V) and v is a velocity vector. The first
term of the right hand side of Eq. (5) represents vorticity production
due to the three-dimensional deformation of vorticity. Because of
2A tan a(cos 2 a+ k 2 sin 2
2
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•••1
the following expression is obtained for vorticity at an arbitrary
location on the steady streamline,
(
q(s)=
j 4),
,
(8)
)
so
where a function tds'irdsl represents a drift function (Lighthill
(1956)). In this ex eme case vonicity associated with the incident
wake is conserved along the steady streamline, so that the wake
location in the flow passage can be spotted by viewing the vonicity. .
Through the above-mentioned approach. Nishiyama and
Funazaki (1984) developed a method to calculate aerodynamic
exciting forces acting on turbine blades subjected to incoming wakes.
By taking advantage of their program, vorticity distributions within
the blade-to-blade passage of the test cascade were calculated and
Figure 3 shows one of those vorticity distributions obtained for S
=0.69. It can be easily understood from this figure that incoming
wakes suffer bow-like deformation when they pass through the
cascade.
Figure 3 Calculated vorticity distribution in the flow passage of
the test cascade for S= 0.69
Upstream of the Cascade
The steady vorticity field associated with the moving bars was
analytically evaluated at the upstream of the test cascade by use of
the correlations derived in Part I. In the relative frame of reference
fixed to the moving bar(xi,y1, wake velocity profile downstream
of the bar W(x t 41 ) can be approximated as follows:
W(xi•YI)=Wt - Aw(xi,yi)
11
= 11 - 2.007( xi
rn exp -On 2)
Yi 2
bin
(9)
jJ
Neglecting the strearnwise gradient of the wake velocity, the vorticity
associated with the bar wake w i can be calculated by the following
equation:
(0,(x,y
aW(xl,yl)
.
)
dYi
d
I
Figure 4 Inlet velocity triangle and cooridinate system to
evaluate the vorticity field at downstream of the cascade
(Mx ,y()
2
(6)
= -2.7821V,( ir
2
71 ii-±exp
Dividing the velocity components into time-averaged and unsteady
parts such as u(x.y.t)=U(s.y)+uls,y,r), and assuming that the
magnitude of the unsteady part is much smaller than that of the
time-averaged part, one can obtain the following linearized vonicity
transport equation,
d
Dr
u +v
a + dx
dy
1/2
tic
d
Onto .vv2(0
0:
b V2 2
-{1n2)(1L)
or in a non-dimensionalized form
the votticity vector u= (0,0.w) and the velocity vector v =(u,v,0)
in two-dimensional flows, the above equation can be reduced to
Dto
—=vV2co
.
( 1 0)
2
i -0.71
x
= -2.782W (— )
bv2 bv2
(II)
2)(2t)
bv2
The maximum of the vorticity magnitude ai l
is found at
ytibv2 = ±1/...ri 2 and using Eq. (8) in Part I it is given by .
4.653 (xi
jilt
(12)
(7)
Eq. (12) provides decay characteristics of the maximum vorticity
within the wake.
Eq. (7) means that the two-dimensional vorticity moves along a
steady streamline with time-averaged flow field experiencing the
diffusion. Provided that the viscous term in Eq. (7) can be neglected,
3
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S=0.34/d= 3
20 <
15 r
ci)
Positive
0.
10
8
Moving
Bar
Velocity
Vectors
0.5
1
t /T
1.5
Negative
....
S=0.34/d=5
• • 44 •
• 444..4.
..... 444 n •
..... .
•••
n4444
0
0.5
1
t /7
1.5
2
n44
.........
Figure 5 Velocity traces and yaw-angle fluctuations from the
design flow angle measured at the downstream of the
moving bars
d5
d = 3 lower :
5 = 0.34 upper :
Figure 6 A snapshot of wake-disturbed inlet velocity field and its
vorticity field estimated by use of Taylor's frozen model d = 5
Downstream of the Cascade
and/or streamwise location of point B. Wake-associated voracity,
, was then determined by taking curl of the above-mentioned
velocity vector, that is,
Rigorously speaking, it was necessary to measure the
instantaneous velocity vectors over the considerably wide area
downstream of the cascade to determine the voracity field. In the
present study, however, the velocity measurement was executed only
along the pitchwise slot. To overcome this difficulty, the idea of
Taylor's frozen model (or Taylor's hypothesis) (Hinze, 1975) was
applied to the data measured at Slot 1 using the following assumptions:
(I) the incident wakes were convected through the passage with the
time-averaged velocity field around the cascade (2) the velocity data
measured at Slot I corresponded to only wake-disturbed flow field
downstream of the cascade. Since vorticity is invariant to the rotation
transformation of coordinate system and the downstream flow field
could be considered almost uniform, the voracity was calculated in
(re,ye)system as shown in Figure 4, where xe was aligned with
the design exit flow direction. Defining Ucx je,yie;r,) as a velocity
vector measured on the point A of Slot at the moment t =
application of Taylor's hypothesis in conjunction with the abovementioned assumptions yielded the following expression for a velocity
vector of the point B on the streamline that passed the point A,
(qr. , yj e •t • = f.J(xl,y1;z i —(x. — xi)/ U•(y.i )) .
r
,
=(d/ax , ,d/dyl .
(14)
A similar procedure was also employed to the flow field upstream
of the cascade to obtain the upstream voracity field, which was
compared with the analytical solution Eq. (10) lately in this paper.
RESULTS
Velocity Measurements and Vorticity
Upstream of the cascade Figure 5 shows some examples of velocity
traces and yaw-angle fluctuations viewed from the design inlet flow
angle that were measured at the downstream of the moving bars,
where S = 0.34. It is clear that the moving bar with larger diameter
(d =5mm) generated more pronounced velocity deficit and yaw-angle
deviation. The maximum yaw-angle deviation was evaluated
in a quasi-steady state manner by use of the following formula that
was derived from the inlet velocity triangle as shown in Figure 4,
(13)
Ai
ce, —a; =
.
(1.1
— 13, +sm -I =7, cos/3, ,
Wake-disturbed flow field downstream of the cascade was finally
determined by changing pitchwise location of the reference point A
4
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(15)
-C I
Eq. (II) at the location of Slot 0 ( x/C„ =-0.03). It follows from
these comparisons that the experimental data matched the theoretical
curves fairly well in terms of peal value and streamwise extent of
the vorticity. In the case of d=5, however one can spot some
discrepancy between the theory and the experiment, probably due to
numerical error or the effect of the intense wake turbulence as seen
in the yaw-angle measurements.
where a superscript • represents a quantity at the wake peak position.
Substitution of U; in Figure 5 into Eq. (13) finally yielded ai=
18.8° for d=3mm and 28.8° for d=5mm, which were meaningfully
larger than the corresponding measured peak values of yaw-angle
deviation. This discrepancy seemed to originate from the
inappropriateness of the quasi-steady state approach in evaluating
4i as well as from possible deterioration of accuracy in the hot-wire
probe measurements inside of the near-bar wake with intense
turbulence. Using those velocity data in Eq. (13) then Eq. (14) one
can obtain a snapshot of the wake-disturbed velocity field and its
vorticity field as shown in Figure 6, where the steady velocity vectors
were subtracted from the calculated velocity field to emphasize the
incoming wake. Note that the bar pitch in this figure adopted here
was only for the direct comparison between the velocity and the
vorticity, and were not to scale. Although wake decay process could
not be reproduced with the frozen model, this snapshot provided a
clear image on the wake spatial extent (at Slot 0 exactly speaking)
as well as on how the incoming wake impacted the cascade. One
can also identify the existence of positive and negative vorticity
regions behind the wake. Vortex-like structure seemed to appear in
the vonicity distribution, however it was a fake caused by a numerical
error in calculating the vonicity. In fact the ensemble-averaging
technique smeared out bar-induced vortical structures that were not
synchronized with the rotation of the wake generator. Figure? shows
streamwise (xi) distributions of the wake vorticity determined from
the estimated velocity vectors for d=3 and d=5, which were
compared with the corresponding theoretical curves calculated by
Downstream of the cascade Figure 8 shows a snapshot of the
wake-disturbed velocity field and its vorticity field at the downstream
of the cascade for d =5. Significant deformation of the incident bar
wake occurred to be bowed when passing through the cascade. The
measured vonicity distribution in this figure looks like the calculated
vorticity distribution shown in Figure 3. It is also clear that the
velocity vectors inside the wake were directed to the suction side of
the blade wake as was expected from the wake transport model
(Kerrebrock and Mikolajczak (1970)). In addition, one can recognize
vortex-like flow structure occurring at the both sides of the wake as
marked by broken circles. The wake velocity vectors near the
suction side of the blade wake were aligned almost against the exit
mean flow U2 . implying the appearance of large velocity decrease
orticityi.
r
d=3
:2000
1500
1
1000
500
0
I
I
,
I
41•41P
•
• 1
•
0
-500
—
-1000
-1500
-2000
,
•
Eq. (11)
Exp.
Wake
I
I
Nelocit9 :
Vectors
1
1
I
iL
0.05
01
xi
02
0.15
d=5
2000
1500
1000
500
z 0
-500
Os
-1000
vac.. .
• %SS .
-1500
• 13.4.4.
• •16.C•••
-2000
o
0.05
0.1
xi
0.15
02
_.
Figure 8 A snapshot of wake-disturbed outlet velocity field and
its vorticity field, showing the appearance of vortex-like flow
structure beside the wake d =3
Figure 7 Comparisons of the theoretical and experimental
vorticity distributions for d = 3 (upper) and d= 5 (lower)
5
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•••••••••• ■ TT v. v a
'Et Met t t
• •`t •N Its T 1
k ,
"."7=3•• ■•
• a ', 1St". •
T • vt •
t• et •• ••••••••■••••.... ',vv.
0.04 - t , t 11
vv.
•
II' f f 41.11 AP flits f • of
-,4
0.02
• - • en, PPPPP ere?
4,74
1;;;;;;;;;;:=1
,fv•
;;;;;;;
/....4afffftl11
fere.
• a
' bfr
•
des
S 4
.j.k
.. aa •aa,
.. aaa
A
ay al
Saab
0.01
0.00 -
..TD(3 ) -
;;1
.,,fftf/ftflittto
0.02-
where TD or Tad is time needed for a fluid particle to drift over the,
distance xi or d with the velocity W . In more general cases where
a fluid particle drift on a steady streamline, one may replace the
time TD with the drift function TA') defined by
.'.'
0.2
0.3
xc 1=1
ds'
C,
u
so w(
t ) 1J11
•
so
te/C,
u,(xTui,
(16)
= ib(s)TD.c
• eve4
:-XI 4
14
e
e
where tp (s) is a drift function non-dimensionalized by time
r
ye,.
..
0. 4
Tac
(= CL IC'x i ) and the integral lower limit s o is placed on the locus of
• • II
-e...Y1t4Iiigualmommece
01
j
the moving bars. Using the drift function. Eq. (6) of Part I and Eq.
(12) can be written as follows:
05
-0.71
'at
0.0.100
0.0300
Am, 2.007 w T
----- • • -
• ...Mt/ /AlIAA AA
.000Eff•ttOf
Vt•
l'OfffPliff,POik
•I
4 _ 4.653( TD.ef 1
ft infliff
fa;
0.0200
<7•-•- g
ke:
a saa•al•ai
0.100
0.200
2.00
0.00
0.30C
xe im)
4.00
velocity
0.400
6.00
0.5 0 0
vectors at the downstream of the cascade
upper :
4=3
lower :
d=5
due to the wake passing. This is rather in contrast to the wake
velocity vectors near the pressure side of the blade wake whose
directions alternate before and past the passage of the incident bar
wake. Figure 9 reveals the difference in the wake-affected velocity
deficit distributions measured at the downstream of the cascade for
d=3 and 4=5. It is evident from this figure that large velocity
deficit region due to the wake tended to pile on the suction side of
the blade wake and such a wake effect was relatively small on the
pressure side of the blade wake. The flow structures of both cases
were similar and pitchwisely biased re-distribution of the incident
bar wake was clearly observed in those cases, however the spatial
extent of the bar wake for 4=5 was much larger than that of 4 =3.
Discussions on wake decay process
Before examining the above-mentioned experimental data, it
seemed necessary to rearrange the expressions for the bar wake
decay given by Eq. (6) of Part I or Eq. (12). In fact, they were not
applicable to the wakes that passed through the non-uniform flow
field around, the turbine cascade unless the governing variable in
those expressions was switched from a relative distance (e.g. xi /d )
to another variable. Looking at Eq. (8) the authors came across the
idea using a drift function instead of the distance. First, xild is
rewritten as follows:
d d/W
(18)
D
Wake decay Velocity deficit aw in Eq. (17) is not a conservative
quantity, so that it seems questionable to apply Eq. (17) to the flow
field around the turbine cascade concerned. Nevertheless, for the
sake of simplicity, the bar wake decay process was first examined
by use of Eq. (17). Since W=76 [m/s], Tot =3.68 x 10-3 [s]. Tad=
3.95x10 -5 [s] for 4=3 and 6.58 x 10 -5 (s] for 4=5. the velocity
deficits at Y2 /13
, 0.5 and 1.0 were expected to be 3.7 [m/s], 4.6
[m/s) and 4.8 [tn/s] for 4=3, and 5.4 [m/s), 6.6 [m/s) and 6.9 [m/s)
for 4r-5, respectively. On the other hand, from the experimental
data as shown in Figure 9 it was found that the velocity deficits
around Y2 /P, = 0.5 and 1.0 were about 4.5 (m/s] and 6 (m/s) for d
=3, while about 6 [m/s3 and 7.5 [m/s] for d=5. Taking account of
the errors involved in the experimental and numerical data, it can be
concluded that the estimations using Eq. (17) yielded similar with
or sightly smaller velocity deficit than the measurements except for
the data obtained very near the blade wakes. Liu and Rodi (1992)
reported nearly the same finding as that in the present study.
Next, wake decay process was examined from the viewpoint of
vorticity. Figure 11 exhibits the wake-induced vorticity profiles for
4=3 and 4=5. Comparisons of these data with the corresponding
inlet vorticity profiles shown in Figure 7 reveal that the wake-induced
vorticity regions expanded and peak values of the vorticity reduced
to about a third of those measured at Slot 0. Figure 12 shows the
pitchwise distributions of the maximum of the vorticity calculated
by using Eq. (18) with the data of the drift function in Figure 10,
which were compared with the experiments. The calculations and
the experiments tended to increase to the suction side of the blade
wake ( Y2 /P =1) in a somewhat similar manner, however the measured
values were much higher than the calculated ones, in particular near
the suction side.
The above investigations gave the authors an impression that
the incident bar wake decayed more slowly when the cascade existed
downstream of the bar than when there was no cascade. This seems
to be in contrast to the numerical or experimental findings in
compressors as mentioned in the introduction of this paper. Although
8.00
Figure 9 Velocity deficit distributions and wake-induced velocity
Xi X i
Tad
1.21
Figure 10 demonstrates the pitchwise variation of the drift function
calculated at the location of Slot I by use of the code developed by
Nishiyama and Funazaki (1984). This figure reveals that a fluid
particle drifting near the blade suction side takes more time to reach
Slot 1 from the cascade inlet than that moving near the blade suction
side, implying that much faster decay of the bar wake could be
identified beside the blade wake pressure side at the downstream of
the cascade.
0.0100
0.0000
(17)
D
an
.AAX.70,0010/0
AAAA AO }fit ft
TD
d
Ta
6
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1000
Drift Function at Slot 1
co
800
o
•
d-3
d5
Exp. (d = 3)
Exp. (d = 5)
•
600
0
400
200
0.2
0.4
0.6
Y
Y
2
P
2
/P
0.8
y
Figure 12 Calculated Vorticity peak values in comparison with
the experimental data
y
recovery effect due to the wake stretching could not be found clearly
in this study. The velocity deficit observed near the pressure side
surely reduced and such a wake reduction seemed to be related to
the wake stretching, however it could not be denied that the wake
reduction was due to the negative jet effect associated with the wake
movement through the passage. Therefore, further investigations are
still needed on this point.
Figure 10 Pitchwise profile of the drift function calculated at
Slot 1
d = 3 mm
Unsteady Measurements of Stagnation Pressure Loss
In the following some discussions are made on experimental
results of wake-affected stagnation pressure loss measured by the
unsteady pressure probe. It should be mentioned here that the authors
have encountered some difficulties related to the sensor, such as
drift of the sensor characteristics, and unfortunately they could not
be fully eliminated in this study. Some practical schemes were adopted
to compensate the measured data for example by subtracting a linear
trend from the original data, which inevitably sacrificed the data
accuracy to some extent through.
Figure 13 demonstrates original and compensated pitchwise
distributions of the time-averaged stagnation pressure loss coefficient
that were measured by the unsteady probe in the no wake condition.
Since the original data exhibited considerable increasing trend from
the left to the right of this figure, such a linear trend was first
subtracted from the data, followed by a slight baseline adjustment of
the data to make a direct comparison with the pneumatic probe data
possible as shown in Figure 13. It followed from this figure that the
unsteady pressure probe yielded similar results to those obtained by
use of the pneumatic probe. Figure 14 is a typical example-of the
unsteady stagnation pressure loss contours on the time-distance
diagram, where the abscissa was time normalized by wake passing
period. In this figure dashed lines represent the areas over which the
loss coefficients became negative (loss reduction) due to the wake
passage. The wake passage obviously brought about loss increase
adjacent to the blade wake suction side, while wake-induced loss
increase was cancelled by the subsequent decrease in loss near the
pressure side of the blade wake. Similar events were also observed
in other test conditions of this study. By checking the relationship
between the unsteady loss and the wake-associated velocity
fluctuations as shown in Figure 9, it was found that the loss increase
occurred when the streamwise velocity decreased and vice versa for
the loss decrease.
1500
1000
500
0
-500
-1000
-1500
0.1
0.2
03
0.4
0.5
Figure 11 Wake-induced vorticity profiles at three pitchwise
locations
upper :
d =3
lower :
d=5
CONCLUSIONS
the coverage of the present measurements was very limited and it
was difficult to draw conclusive statements only from those
measurements, any beneficial phenomena such as reversible wake
Wake-disturbed velocity vectors and stagnation pressure
downstream of the turbine cascade were measured in detail. The
7
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No Wake
probe that the bar-wake passage caused loss increase adjacent
to the blade wake suction side, while wake-induced loss near
the pressure side of the blade wake alternated between increase
and decrease as the wake passed and on average the wakeaffected loss coefficient remained almost the same as the loss
in steady flow .
(3) Checking the relationship between the unsteady loss and the
wake-associated velocity fluctuations revealed that the loss
increase occurred when the streamwise velocity decreased and
vice versa for the loss decrease. These observations led the
authors to the conclusion that the above-mentioned differences
in the unsteady flow behaviors between the suction and pressure
sides of the blade wake nicely explained the biased stagnation
pressure loss distributions downstream of the wake-affected
cascade reported in Part I.
— Original
1.4
—it— Trend eliminated
—c-- Pneumatic Probe
2 0.8
OM
0.4
0.2
0
-1.5
-1
-0.5
0
y / Py
0.5
1
15
REFERENCES
Figure 13 Pitchwise distributions of the time-avegared stagnation
pressure loss coefficient in no wake condition measured by the
unsteady pressure probe
I
1.0
00
I
2.0
I
10
4.0
VT
-1.0
-0.5
0.0
Loss Coefficient
0.5
1.0
Figure 14 Contours of stagnation pressure loss coefficient
measured at Slot 1
S = 0.34 d = 3
wake-associated voracity field was also obtained by use of the Taylor's
frozen model, which was used in conjunction with the velocity data
to examine the decay process of the incident bar wakes through the
cascade. In that case correlations for the wake characteristics were
modified using drift function to estimate the wake decay in the
non-uniform flow field around the cascade. The findings in this
study can be itemized as follows:
(1) The measured wake velocity deficit as well as the peak value
of the voracity measured at the downstream of the cascade
was larger than those estimated using the modified correlations.
In other words the wake decayed more slowly than expected
and no clues showing the effect of reversible wake recovery
were identified in the present study using the turbine cascade.
This was in contrast to the findings in compressor test cases
where upstream rotor wakes decayed much faster when the
stator existed at the downstream.
(2) It followed from the measurements using the unsteady pressure
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Domey, D. J., Dunn, M. G., Haldeman, C. W. and Abhari, R. S.,
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8
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