93-GT-405
THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS
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Printed in U.S.A.
Copyright © 1993 by ASME
TRANSONIC COMPRESSOR ROTOR CASCADE
WITH BOUNDARY-LAYER SEPARATION:
EXPERIMENTAL AND THEORETICAL RESULTS
R. Fuchs, W. Steinert, and H. Starken
Deutsche Forschungsanstalt fur Luft- and Raumfahrt e.V.
Institut fur Antriebstechnik
Koln, Germany
ABSTRACT
u
A transonic compressor rotor cascade designed for an inlet
x
13
Mach number of 1.09 and 14 degrees of flow turning has been
redesigned for higher loading by an increased pitch-to-chord
ratio. Test results, showing the influence of inlet Mach number
and flow angle on cascade performance are presented and
compared to data of the basic design. Loss-levels of both, the
original and the redesigned higher loaded blade were identical
at design condition, but the new design achieved even lower
losses at lower inlet Mach numbers.
The computational design and analysis has been performed
by a fast inviscid time-dependent code coupled to a viscous
direct/inverse integral boundary-layer code. Good agreement
was achieved between measured and predicted surface Mach
number distributions as well as exit-flow angles.
A boundary-layer visualization method has been used to
detect laminar separation bubbles and turbulent separation
regions. Quantitative results of measured bubble positions are
presented and compared to calculated results.
NOMENCLATURE
velocity
coordinate in chordwise direction
flow angle with reference to circumferential
direction
(3 5stagger angle with reference to circumferential
direction
flow turning (3, — 13
O
boundary layer displacement thickness
SZboundary layer momentum thickness
S,
boundary layer energy loss thickness
w
total
pressure
loss
coefficient
_ (Pu — piz)/(Pu — p^)
or
relaxation factor
SUBSCRIPTS
1
inlet plane far upstream
2
i
in
tr
outlet plane far downstream
inviscid
instability
transition
v
Viscous
AVDR, Q axial-velocity-density-ratio between inlet and outlet of cascade
1c
H,,
H 32
M
M„
n
p
blade chord length
shape factor b,/S z
shape factor 8 ; /62
Mach number
isentropic Mach number = f(p/p„)
iteration number
static pressure
Pi
total pressure
Re
Reynolds number
s/c
pitch to chord ratio
INTRODUCTION
The increase of compressor stage pressure ratios in modern
turbofan-engines leads to supersonic relative inlet Mach numbers. By increasing the inlet Mach number the average Mach
number ahead of the shock waves grows even more and the
shock losses are increasing too. That means boundary layer
separation can occur near design or even at design conditions.
For these highly loaded flow conditions computational methods are required, which can predict accurate surface Mach
Presented at the International Gas Turbine and Aeroengine Congress and Exposition
Cincinnati, Ohio — May 24-27, 1993
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number distributions, boundary layer behaviour and performance parameters like losses and turning. Especially in design
procedures the codes should work as fast and cheap as possible, because many calculations are required to optimize the
cascade geometries for design and off-design flow conditions.
In the investigations described here an Inviscid-Viscous
Interaction (IVI) approach is validated for application in
design systems. A transonic compressor rotor cascade, whose
MCA-blades had been designed in the past by mainly empirical methods, was redesigned using this method for a new
prescribed blade Mach number distribution and increased
pitch/chord ratio. Both cascades had been tested in the same
wind tunnel of DLR Cologne. The test results of the redesigned cascade are presented and compared to the reference
cascade and to computational results.
IVI-Systems are commonly used in cascade computational
analysis. For subsonic flows see for instance Janssens and
Hirsch (1983), for transonic/supercritical applications Barnett
and al. (1990) and for transonic/supersonic applications Calvert (1982). The method used here is a time-dependent inviscid code coupled to a direct or inverse integral boundary layer
code for handling unseparated or separated flow cases. The
inviscid/viscous coupling is modelled by the solid displacement surface method in an iterative manner. In the case of
separated flows a semi invers iteration method with a velocity
coupling model on the limiting streamlines is used.
CASCADE DESIGN
The geometry of the reference cascade L030-4 was also
Selected by the AGARD working group 18 (Schreiber and
Starken, 1984, 1990) as a test case. It is the 45%: blade height
section out of a DFVLR transonic compressor rotor (Dunker
and Hungenberg, 1980, Dunker, 1990). The cascade geometry
was deduced from the MCA-type rotor blade by projecting the
coordinates from the meridional stream surface upon a cylindrical stream surface which crosses the blade centerline. The
blade section was designed for a supersonic inlet Mach number of M 1 =1.09, with a normal shock wave ahead of the cascade entrance, subsonic deceleration in the cascade passage
and a turning angle of 0=12.5 degrees. In the cascade tests the
turning angle was 0=13.5 degrees. Calvert (1983) presented
a comparison of DLR test results and calculations performed
by his IVI-code (Calvert, 1982).
The redesigned cascade, designated here as DLR-TSG89-5.
was designed using the direct 1V1 method which is described
later in this paper and which was used also for test verlfications. The design goal was to find out the loading limits of
an MCA-type blade in a transonic cascade at identical inlet
conditions, stream-tube contraction (AVDR) and flow turning.
The pitch chord ratio was increased up to s/c=0.7 for the new
design instead of 0.62 of the basic one. The blade contour was
changed step by step until the velocity distribution was considered to be favourable. Figure I provides plots of both cascades and the design data.
The blade coordinates can be found in the appendix.
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MCA L030-4
s/c=0.62
DLR TSG 89-5
s/c=0.70
TSG 89-5
L030-4
s/c
6
M,
MT
f2
0
AVDR
0.62
138.51°
1.09
148.66°
0.71
136.17
12.49' / 1 3.5° EXP.
1.212
0.70
138.0°
1.09
148.5°
0.71
134.5`
14.O
1.2
Figure 1. Geometry and design data of (L030-4) cascade and
redesigned cascade (TSG89-5)
CASCADE WIND TUNNEL
The DLR transonic cascade wind tunnel is it continuously
running facility operating in a closed loop. For operation in
the transonic and supersonic range, the upper wall of the test
Section (Figure 2) is slotted and connected to a suction system.
SLOTTED UPPER ENOWALL
WITH SUCTION
SIDEWALL
BOUNDARY
LAYER
SUCTION
FLOW
1/
PROBE
TAILBOARD
WITH
THROTTLE
/
PROBE
N
/ TRANSONIC TAILBOARO
Figure 2. Test Section of the DLR transonic cascade wind tunnel
The suction system is also used to reduce the upstream side
wall boundary layer through protruding slots and to vary the
axial velocity density ratio via slotted side walls. A special
throttle device in the downstream area of the blade row I
necessary, because at some flow conditions at supersonic inlet
velocities the back pressure can be varied independently of the
upstream flow conditions. Also for operation in the transonic
regime the tailboard throttle system is necessary to control and
adjust the upstream flow conditions. The throttle system is
combined with two tailboards hinged to the trailing edges of
,
the outermost blades. The bottom tailboard consists of a closed
box with a slotted surface in which the back pressure is
transferred upstream.
The cascade span is 168mm and 7 blades are mounted
between plexiglas windows in rotatable sidewalls of 2m in
diameter. Periodicity is checked by sidewall pressure taps
24.5mm or half a pitch upstream and downstream of cascade
inlet- and outlet plane. The inlet Mach number is determined
by the inlet total pressure of the settling chamber and the
upstream sidewall static pressures. Because at supersonic
velocity probes would disturb the inlet flow field, the inlet
flow angle 13, is determined by a method presented by Steinert
et al. (1991). This method is based on blade to blade calculations performed at different inlet flow conditions of the
cascade test range. These calculations lead to it correlation
between M. (3, and M,,. where M„ is the local isentropic
Mach number determined at it fixed position in the front part
of ttte suction side. 'fhe correlation yields (3,, it M, and M„
are measured during: the test.
The downstream flow values of static pressure p, total
pressure p,2 and flow angle distribution 132 are measured by
moving a combined probe over more than one blade pitch at
cascade midspan position.
To measure the isentropic Mach number distribution in one
blade passage the third and fourth blade were equipped with
13 pressure taps each at mid-span.
For boundary layer visualization on the profile surfaces an
ink tracing method was used. Coloured ink was introduced
into the boundary layer through one or more pressure taps.
By this method boundary layer separation can be detected. The
extension of the separation region, which means length of the
laminar separation bubble or the turbulent separation region,
was determined in additional tests, introducing ink in it stepw ise manner tap by tap downstream of the incipient separation
locus.
VISCOUS ANALYSIS
The computational method used here is an inviscid-viscous
interaction technique for calculation of the blade-to blade (S I )
flow field. The inviscid part is based on the time-dependent
Euler code of Denton (1982), which includes transonic flows
with shocks and shock losses. The stream tube thickness
(AVDR) was varied linearly between cascade leading and
trailing edge plane in all calculated examples presented. The
viscous part contains both it direct and inverse mode integral
boundary layer code. The direct version of this code is based
on the method of Walz (1969). which uses a two parameter
formulation that are it velocity profile form factor and a
momentum thickness parameter. ]'his method was improved
and inverted by Thiede et al. (1082).
Transition and Separation. Exponential functions of the
shape factor I -I, , are used in the transition criteria of the Thiede
method and can be found in the appendix. Laminar separation
is set at a shape factor I I,, < 1.515. The calculation is continued with attached turbulent boundary layer and assuming zero
laminar separation bubble length. Turbulent separation is set
at it shape factor H,. < 1545 or M > 1.32.
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IVI procedure. On the front part of the blades, as long as
the boundary layers are attached, the inviscid calculation
determines the velocity distribution and the direct mode of the
boundary layer code calculates the new blade shape by adding
the resulting displacement thickness at each mesh point. As
soon as boundary layer separation is expected, caused by
shock boundary layer interaction or rapid deceleration, the
direct mode should become unstable. Then the code switches
to the inverse mode and the velocity distribution is calculated
by an estimated displacement thickness distribution down to
the cascade trailing edge.
Both the inviscid and viscous velocities have to be cotnbined by an inviscid-viscous coupling procedure which is
introduced after every inviscid-viscous iteration loop. In the
method used here, the matching procedure of Carter (1979)
was applied, in which the two resulting velocities at each
surface net point from the inviscid and the inverse viscous
calculation arc coupled by the relation
(51,+ 1[1 i-(i)(u v /u, --- 1 )]
where 5, is the displacement thickness, added to the profile
shape, n is the iteration number. w is a relaxation factor, u, is
the local viscous and u, the inviscid velocity.
Mixing procedure. The final mixing calculation is performed using the flow properties of the trailing edge plane and
solving the conservation equations for mass, momentum and
energy (see Weber et al., 1987). Thereby the trailing edge Flow
values taken from the inviscid and viscous calculation are
changed to constant exit flow properties M2, (3,, p, 2 and the
loss coefficient w
The total pressure distribution in the trailing edge plane
estimated by the inviscid calculation includes both numerical
losses and physical shock losses. Looking at the complex
shock structure in the Schlreren pictures Figure 10 and
Figure 13 it seems impossible to separate the shock losses
from the numerical losses. However due to the lack of a shock
boundary interference loss model in the boundary layer calculation so far, the calculated boundary layer losses are too
low and therefore an overprediction of the losses is avoided.
This was the case in many transonic and supercritical cascade
calculations we performed.
Convergence and computer time. To start the IVI solution
procedure, 300 time steps of the inviscid Euler code are used
before running the boundary layer calculation for the first
time. Every next viscous update is performed after 100 Euler
time steps until convergence is reached. Convergence is
assumed if the change in meridional velocity per cycle at
every mesh point is less than 0.005% of an average velocity
for the whole flow and if the relative change of displacement
thickness S, is less than 4C/.
These criteria lead to total time step numbers between 1700
(design) and 2100 (off design) with it I9x70 calculating grid
and require 2 to 3 minutes on it small mainframe computer
Amdahl 580-58/60. Comparable solutions of a Navier-Stokes
code at our Institute require I to 2 hours on it work station of
similar speed. The recalculation of the inviscid mesh after
every viscous update in the presented solid displacement u - face method is not it costly approach, because a mesh update
of 1330 points requires very little CPU time.
CASCADE PERFORMANCE
• M,= 1.15
° M,= 1.09
❑ M,= 1.02
o M,= 0.92
AVDR=1.20
To make cascade analysis useful for compressor designers, the
main performance values as total pressure loss and flow turning have to be presented over the entire operating range of
inlet Mach number and inlet flow angle.
.20
.18
.16
Influence Of Inlet Mach Number On Total Pressure Losses
The measured variation of the total pressure loss coefficient
with inlet Mach number at design inlet flow angle and design
AVDR are presented in Figure 3 for the redesigned cascade
DLR-TSG99-5 and the reference cascade L030-4 and compared to calculated results for the first one.
.14
U
,-
.12
Q)
o .10
V
W .08
0
0,
=148.5*
AVDR=1.2
❑ Reference L030-4
0 Redesign TSG 89-5
.06
o Predict. TSG 89-5
.04
0.16
3
.02
.00
144
0.12
inlet angle
a)
0.0E
Figure 4. Tested loss versus inlet angle at different inlet Mach
numbers
0.01
The pressure loss coefficients of both cascades measured
at design inlet Mach number and design AVDR are presented
in Figure 5 and compared to calculations for the redesign.
V
ti
0
156
a,
Li
0
-J
❑ Reference L030-4
Redesign TSG 89-5
M,= 1.09
AVDR =1 .20
0
0.8
0.9
1.0
1.1
0
o Predict. TSG 89-5
1.2
.20
Inlet Mach number M,
.18
Figure 3. Tested and predicted loss versus inlet Mach number
3 .16
c
At it constant inlet flow angle the losses increase continuously
with increasing inlet Mach number. This behaviour is mainly
caused by increasing shock strength in front of the cascade
which is resulting in higher shock losses and higher
shock/boundary layer interference losses. Compared to the
original design, the new cascade TSG89-5 offers lower losses
at subsonic and low supersonic inlet velocities, whereas at
design inlet Mach number both loss-levels are of the same
magnitude. The calculation shows good agreement at subsonic
and sonic inlet velocities but lower losses at design conditions.
U
w
0
o
.14
.12
to
a .08
.06
0
n
.04
.02 A
.00 ,i
144
146
Influence Of Inlet Flow Angle On Total Pressure Losses And
Flow Turning
Total pressure loss. The measured loss characteristics of the
new cascade DLR-TSG89-5 are schown in Figure 4 for inlet
flow angle variations and different inlet Mitch numbers.
This figure clearly shows the characteristic narrowing of the
operating range of it transonic cascade with increasing inlet
Mach number. The inlet flow angle range decreases from 9.5
degrees at M, = 0.£i2 to 3.5 degrees at M, = 1.15. At the
design Mach number M, = 1.09 the operating range is of the
order of 5 degrees of incidence.
U
148
r
150
152
inlet angle p
154
156
1
Figure 5. Tested and predicted loss parameter versus inlet angle
The test results of the two cascades are almost identical, but
the predicted loss values are unsatisfactory. The minimum
total pressure losses of 8% can be found at design and at
slightly positive incidences.
4
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1.6
Flow turning. The variation of the flow turning with inlet
flow angle at design inlet Mach number and design AVDR
are presented in Figure 6 .
° ° Experim.
1.4
24
22
20
❑
M,= 1.09
❑ Reference L030-4
AVDR= 1 .20 0 Redesign TSG 89-5
o Predict. TSG 89-5
C
1.0
PS
t
U
0
16
00 0
Q O
0 .0
0
U
14
Q0
12
C
10
.6
Test
Caic.
1.087
1.088
148.4° 148.4°
0.692
0.694
14.4°
13.4°
1.20
1.20
0.081
0.057
1.463
1.462
M
.4
M2
p
8
AVDR
2
6
4
0
2
0
144
SS
1.2
m 18
0)
- calcur.
L
146
148
150
154
152
inlet angle
156
.2
.8
.6
.4
x/chord
1.0
Figure 7. 'rested and predicted Mach number distribution, 0° incidence
p 1
Figure 6. Tested and predicted flow turning versus inlet angle
1.6
At design inlet flow angle both, the design flow turning of
0=13.5° of the cascade 1..03(1-4 and O=14° of the cascade
TS089-5 are well verified test results. The numerically h,
dieted results of the Flow turning of the redesigned cascade
shows similar agreement to the experimental data.
To analyze the total pressure loss development shown in
Figure 5 in more detail, in the following chapters the profile
Mach number distributions at three characteristic inlet flow
angles are presented. The flow angles selected are the design
angle p 1 =148.5°, the positive incidence (3,=151.6° and the
lowest negative incidence (3,=146.5° (incidence =-2°), when
the blade passage gets choked, which is called unique incidence at supersonic inlet velocity. Additionally at corresponding inlet flow angles boundary layer visualization test
results and calculations will be presented.
1.4
❑ v Experim.
-
❑❑
❑
caic.
Ss
1.2
E
C
1.0
U
0
V
°
U
°-
0
.6
C
a)
°'
°°
P,
M2
AVDR
w
P2 /P,
.2
.0
L
v
❑ ❑
v
v
°
PS
M
.4
.0
°°
v v v
e
PROFILE MACH NUMBER DISTRIBUTION
.2
Cale.
Test
1.084
1.084
151.6° 151.6°
0.623
0.661
17.2°
15.7°
1.23
1.23
0.098
0.117
1.529
1.466
.4
.6
.8
1.0
x/chord
Design. A comparison between the tested and calculated
surface Mach number distributions is shown in Figure 7 for
the design values M,=1.09, (3 1 = ] 48.5° and AVDR ( ))=].20.
There is an excellent agreement to be seen for both Mach
number distributions on suction and pressure side. Slight differences at the front part of the pressure surface can be
explained by the course computational mesh in the leading
edge region. The mesh size used in all cases was 70 points in
axial direction with 37 points along the blade surfaces and 19
points in circumferential direction to realize calculation times
as short as possible.
Near Stall. The comparison of the measured and predicted
Mach number distributions at (3 1 =151.6 ° at 3 degrees positve
incidence near stall is shown in Figure 8.
Certain differences between measured and predicted distributions can be seen on the front part of the pressure side and
Figure 8. Tested and predicted Mach number distribution, +3
incidence
0
the rear part of the suction side. Also the calculated turning
angle is 1.5 degree too low. These differences may be caused
by the highly 3-D character of the flow at this positive incidence, which was also observed in the flow pattern of
boundary layer ink injection tests. Although the ink tests
showed no separation in the mean section, in fact it should
be a separated flow case. Because no shock boundary layer
interaction model was applied in the calculation no separation
was predicted there. This should also explain the differences
of the deviation angles in test and calculation. Flow visualhi
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.0
ization by stroboscopic Schlieren video pictures showed also
a remarkebly unsteady flow- and shock behaviour, which alltogether may lead to these different results.
Choking. The comparison of the measured and predicted
Mach number distributions at R 1 =146.7° (unique incidence,
choked passage) is shown in Figure 9.
1.6
❑ v Experim.
Calc.
1.4
1.2
N
❑
LS
°
LS
TS
-c
c
❑
° pO
E
CL
O
o
v
v '
1.0
0
0
SS
Experimental
separation
Exp.
.6
4
lam. sep. bubble
Calc. Test
M1.085 1.083
146.8° 146.7°
0.714 0.721
02
11.2° 11.7
1.13 1.12
AVDR
0.090 0.125
P 2 /P '1.425 1.383
M
0
.2
Figure 10. Schlieren picture at unique incidence Clow condition,
-2° incidence
PS
B.L.
Prediction:
L lam. sep.
T turb. sep
H test
uncertainty
.6
.4
x/chord
.8
1.0
Figtne 9. Tested and predicted Mach number distribution, _ -2°
incidence , tested and predicted boundary layer phenomena indicated
There is as in the design flow case an excellent agreement of
predicted and tested Mach number distributions on both profile surfaces. The supersonic velocities on the front part of the
pressure side indicate clearly that the maximum possible mass
flow is reached. The Schlieren picture in Figure 10 illustrates
this flow condition by showing the two shock system of the
oblique leading edge shock of the incoming flow and the
normal passage shock close downstream of the minimum cross
section of the blade passage.
Opening the throttle moves the passage shock further downstream without influencing the inlet flow anymore. Thereby
the passage shock losses increase due to higher average Mach
numbers ahead of the shock in the diverging passage. In Figure 5 this behaviour is documented in the vertical left branch
of the loss parameter curve at maximum negative incidence.
BOUNDARY LAYER RESULTS
The validation of the boundary layer calculation has been
performed at design and off-design inlet flow angles. The
choking flow angle was chosen for representation of the offdesign flow case because of the better 2D flow character at
this incidence in contrast to the stall flow case as it was
described in the last chapter. The inlet turbulence level of
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2.5% was derived from laser measurements and the inlet
Reynolds number varied from 1.1 * 1(> 6 to 1.3* 10 6 for the tests
and was set 1.1*106 for all calculations.
Choking. In Figure 9 the tested and predicted laminar and
turbulent separation regions are also shown. The results of the
ink injection tests indicate a laminar separation bubble on the
pressure side, extending over the whole shock induced deceleration region from 25%. to 50% of chord. The uncertainty is
one pressure tap distance, which can be seen in Figure 9 and
Figure 12 as the distance between two symbols, which varies
from 5% to 9% of chord length. The incipient laminar separation is very well predicted by the calculation, but because
there is no separation bubble length model implemented in the
boundary layer code until now, the extension of the bubble
could not be predicted. The laminar separation point is interpreted as transition point and the calculation is continued with
reattached turbulent boundary layer.
On the suction side the ink test indicated a separation
starting at the beginning of the shock induced deceleration
without reattachment. The boundary layer calculations showed
good agreement in predicting the laminar separation. But as
on the pressure side, downstream of the laminar separation
point the calculation is continued with an unseparated turbulent boundary layer leading to turbulent separation at 82c/ of
chord length. These deticiences of the boundary layer code in
predicting laminar separation bubbles as well as complete
laminar separation due to shock wave interaction should give
the explanation for the differences in total pressure loss results
in Figure 5. The distributions of the displacement thickness
8, and the shape factors H, 2 and H_, 2 on the suction and pressure side of the profile are shown in Figure 11.
The kink in all curves of Figure 11 indicates the laminar
separation or laminar turbulent transition. The 8, curves (Figure I l top) shows the rapid increase of the boundary layer
displacement thickness behind the shock and in the shock
deceleration region on both surfaces. On the pressure side the
1l 32 distribution (Figure 11 bottom) shows a minimum at 50%.
of chord, indicating that the shock deceleration area is not
large enough to reach the turbulent separation criteria of
H 3 ,= 1.545. The axial distance from the beginning of the
Suction Side
1.6
Pressure Side
❑
1.4
.020
.VLV
Y .015
.015
1.2
.010
.010
E
C 1.0
E .005
.005
U
C
t
U
.0
a .000
.0
.2
.4
.6
.8
1.0
000.0
.2
.4
.6
.8 1.0
N
4
4
3
.2
.4
.6
.8
1.0
Colc.
-M
1.115
f,
147.7°
M z0.719
12.8°
0
AVDR 1 .20
0.062
P 2 /P, 1.489
B.L.
Test
Prediction:
1.110
148.0 ° © lam. sep.
0.700
13.8 °test
1 .21
uncertainty
0.097
1.480
.2
.4
.6
.8
1.0
x/chord
t
Figure 12. Tested and predicted Mach number distribution, =
incidence, increased inlet Mach number M,=1.11 and
tested and predicted boundary layer phenomena
I..
3 1
PSF a^
LS
.0
2
.0
7/
1
LS
SS
7
m
a
0
s
/ ❑
CL .6
0
5
0
U
a
Colo.
U
6
a
Experimental
v Experim. lam. sep. bubble
1.8
I-
0
21
1.7
U
1.6
N
a
- 1
r
exper.
lam. -
bubble
1
1.4
x/chord
x/chord
Fiore 11. Displacement thickness and shape factors. = -2n incidence
laminar separation at x/c=O.25 and the minimum at x/c=O.50
corresponds very µell to the test results of the bubble length
in Figure 9. The identical effect is to be seen in the H i , distribution, but the H:, relative minimum is more intensive than
the H I , relative maximum. This may be a simple method to
predict laminar separation bubble length, but it has to be
I I
confirmed by future tests.
Increased inlet Mach number. Because of the minimum loss
level at design inlet conditions there should he no complete
Figure 13. Schlieren picture at increased inlet Mach number
M,=1.1 1, _ -0.5° incidence
turbulent ,,;paration on the suction side (Figure 5). But the
question should he answered, if an increased inlet Mach
number would prevent the laminar separation from reattachment. Therefore a test was made with an inlet Mach number
of M 1 =1.11 and (3 1 =1421.0 °. The surface Mach number distributions are presented in Figure 12 and the Schlieren picture
in Figure 13 demonstrates the shock system of the same flow
of chord length. The predicted laminar separation point on the
suction side is found slightly further downstream. Again the
bubble length is not predicted as explained before.
'_No pressure side boundary layer tests have been performed
and therefore no comparisons of tested and predicted boundary
layer separation results are possible. The development of displacement thickness 6, and shape factors 11 1 , and FI„ on suction and pressure side is shown in Figure 14.
It can be observed that the shock induced diffusion on the
case.
Again at this increased Mach number a very good agreement
of the predicted and tested Mach number distribution is
apparent. The ink injection test on the suction side of the
profile showed a laminar separation bubble starting at the
beginning of the deceleration at 5W,-,, and reattachment at 65 1%:
suction surface does not cause the Ii,, value to fall below the
turbulent separation criteria of i1=1.545. Again the axial
distance from the start of laminar separation at x/1=0.50 and
the described minimum point at x/1=0.65 correspond very
7
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0
U,
N
face Mach number distributions and overall flow turning. But
the boundary layer analysis clarified the incomplete handling
of the shock boundary layer interaction and separation bubble
structure which resulted in differences in overall loss performance. A method for predicting laminar separation bubble
length has been suggested.
Pressure Side
Suction Side
.020
.020
.015
.015
.010
.010
.005
.005
U
-c
C
N
E
N
u
0
a .000
0
.0 .2
.4
.6
.8
I
1.0
ACKNOWLEDGMENTS
.0
.2
.4
.6
.8
This work was partially supported by Arbeitsgemeinschaft
I-lochtemperatur-Gasturbine AG Turbo, German Bundesministerium fur Forschung and Technologie and German Bundesministerium der Verteidigung. The authors gratefully
acknowledge the permission for publishing the results.
i
1.0
6
6T-
0
U
O
REFERENCES
U
0
0
r
Barnett, M., Hobbs, D.E. and Edwards, D.E., 1990, "lnviscid-Viscous Interaction Analysis of Compressor Cascade Performance", ASME-Paper 90-GT-15
Calvert, W.J., 1982, "An inviscid-viscous interaction treatment to predict the blade-to-blade performance of axial compressors with leading edge normal shock waves", ASME-Paper 92-GT-135
Calvert, W.J., 1983, "Application of an inviscid-viscous
interaction method to transonic compressor cascades", Viscous
Ejkcts in Turbomachines, AGARD-CP-351, pp2/1-2/13
Carter, J.E., 1979, "A New Boundary-Layer Inviscid Interaction Technique for Separated Flow", AIAA-Paper 79-1450
Denton, J.D., 1982, "An Improved Time Marching Method
for Turbomachinery Flow Calculation", ASME-Paper 82-G1'239
Dunker, R.J. and Hungenberg, H.G., 1980, "Transonic Axial
Compressor Using Laser Anemometry and Unsteady Pressure
Measurements", A/AA Journal, Vol.18, No.8 , August 1980
Dunker, R.J. 1990, "Test-Case E/CO-4 Single Compressor
Stage", Test Cases For Computation Of Internal Flows in Aero
Engine Components, AGARD-AR-275, pp.245-285
Janssens, P. and Hirsch, C., 1983, "A Viscid Inviscid Interaction Procedure for Two Dimensional Cascades", Viscous
Effects in Turhomac•hines, AGARD-CP-351, pp.3/I-3/17
Schreiber, H.A. and Starken, H., 1984, "Experimental Cascade Analysis of a Transonic Compressor Rotor Blade Section", ASME Journal cif Engineering for Gas Turbines and
Power, Vol.106, April 1984, pp.288-294
Schreiber, H.A. and Starken, H., 1990, "Test-Case E/CA-4
Low Supersonic Compressor Cascade MCA", Test Cases For
Computation Of internal Flows in Aero Engine Components,
AGARD-AR-275, pp.81-94
Steinert, W., Fuchs, R. and Starken, H., 1991, "Inlet Flow
Angle Determination of Transonic Compressor Cascades•",
ASME Journal of Turboniachinery, Vol.114, No.3
Thiede, P., Dargel, G. and Elsholz, E., 1982, "Viscid-Inviscid Interaction Analysis on Airfoils with an Inverse Boundary
Layer Approach", Recent Contributions to Fluid Mechanics,
W.Haase, ed., Verlag Springer, Berlin
Walz, A., 1969, Boundary Layers of Flow and Temperature,
MIT Press, Cambridge MA.
In
.0
.2
.4
.6
.8
1.0
.0
.4
.6
.8
1.0
1.9
i!
I
0
0
.2
1.8
1.7
1'
e
a
o
1.
U,
1.
1.4
1.6
exper.
lam.
1.5
bubble
.0
.2
.4
.6
x/chord
.8
1.0
1.4
.
6
8 1.
x/chord
Figure 14. Displacement thickness and shape factors, _ -0.5° incidence
well to the test results of the bubble length in Figure 12. This
result confirms the method of predicting laminar separation
bubble length by measuring the axial distance beween "laminar kink" and relative minimum of the calculated H 32 distribution. But additional tests are needed to confirm this method.
CONCLUSIONS
It has been demonstrated, that a fast quasi-3-d inviscid-viscous
interaction code (IVI) is an extremly helpful and economic
tool in a design process, developing cascade blades for a definite blade pressure distribution and the corresponding flow
turning. Applying such a tool it was possible to redesign the
midsection cascade L030-4 of it DLR transonic rotor for
higher loading. The pitch/chord ratio was increased keeping
the same loss level and incidence range at design condition
with lower losses at subdesign inlet Mach numbers. Such a
design, realized in a compressor stage, would help to reduce
the number of blades and th,j,lore costs and weight.
The comparison of prediction and test results at design and
off design conditions showed good agreement for blade sur8
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Weber, A., Faders, M., Starken, H. and Jawtusch. V., 1987,
"Theoretical and Experimental Analysis of a Compressor
Cascade at Supercritical Flow Conditions", ASME-Paper 87-
Coordinates Of The Tested 13 lade
GT-256
APPLNDIX
Transition Criteria
AReo,.rr = Re6,.u.0 - Rea,,m
log ^ 0 Re 6 , ,11 = 4.556 - 76.87(1.670-1{ 3 ,) x.54.
log 1 ARe^,
rru
log 10 ARe^ .1ru
= 1.6435 - 24.2(1.515 -II)
for 1.515_<FI-,<- 1.56
)27 5
= 3.312 - 967.5(1.515 - H) 2715
for 1.56 5 ft 21
.625
Cascade Geometry
Blade chord
c = 70mm
pitch/chord ratio s/c = 0.70
Stagger angle
(3, = 138.0`
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Pressure Side
Suction Side
XP/C'
YP/C
XS/C
YS/C
0.000000 0.001079
0.000000 0.001079
0.003475 -0.003988
0.0021.50 0.003624
0.012482 -0.004814
0.015514 0.005994
0.040001 -0.006858
0.052144 0.01 1841
0.068217 -0.008297
0.088304 0.017280
0.097066 -0.009185
0.124012 0.022326
0.126483 -0.009580
0.159279 0.026988
0.156403 -0.009537
0.194118 0.031279
0.186763 -0.009112
0.228536 0.035204
0.217497 -0.008362
0.262540 0.038768
0.248542 -0.007341
0.296130 0.041973
0.279832 -0.006107
0.329304 0.044816
0.31 1304 -0.004715
0.362052 0.047288
0.394359 0.049378
0.342893 -0.00322 2
0.374534 -0.001683
0.426200 0.051063
0.406164 -0.000154
0.457541 0.052312
0.437718 0.001309
0.488333 0.053085
0.469130 0.002649
0.518511 0.053323
0.547986 0.052951
0.500359 0.003829
0.576659 0.051881
0.531395 0.004842
0.604631 0.050202
0.562236 0.005685
0.632100 0.048086
0.592878 0.006356
0.659201 0.045650
0.623318 0.00685
0.686027 0.042976
0.653553 0.007167
0.712646 0.040120
0.683579 0.007303
0.713394 0.007254
0.739104 0.037125
0.765439 0.034024
0.742993 0.007018
0.772374 0.006592
0.791679 0.030839
0.801534 0.005974
0.817844 0.027589
0.830468 0.005160
0.843952 0.024290
0.859174 0.004147
0.870016 0.020952
0.887648 0.002933
0.896048 0.017587
0.922056 0.014201
0.915887 0.001514
0.948046 0.010799
0.943887 -0.000112
0.971647 -0.001947
0.974026 0.007388
1.000000 0.003972
0.999163 -0.003995