final report ncc3-719 centrifugal compressor …
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Final ReportNCC3-719
CENTRIFUGAL COMPRESSOR AEROELASTICANALYSIS CODE
submitted to
National Aeronautics and Space Administration
Glenn Research Center at Lewis Field
Cleveland, Ohio
Dr. Theo G. Keith, Jr.
Distinguished University Professor
Dr. Rakesh Srivastava
Senior Research Associate
Department of Mechanical Industrial and Manufacturing EngineeringThe University of Toledo
Toledo, Ohio 43606
CENTRIFUGAL COMPRESSOR AEROELASTIC
ANALYSIS CODE
Introduction
Centrifugal compressors are very widely used in the turbomachine industry where low mass flow
rates are required. Gas turbine engines for tanks, rotorcraft and small jets rely extensively on
centrifugal compressors for ragged and compact design. These compressors experience
problems related with unsteadiness of flowfields, such as stall flutter, separation at the trailing
edge over diffuser guide vanes, tip vortex unsteadiness, etc., leading to rotating stall and surge.
Considerable interest exists in small gas turbine engine manufacturers to understand and
eventually eliminate the problems related to centrifugal compressors. The geometric complexity
of centrifugal compressor blades and the twisting of the blade passages makes the linear methods
inapplicable. Advanced computational fluid dynamics (CFD) methods are needed for accurate
unsteady aerodynamic and aeroelastic analysis of centrifugal compressors. Most of the current
day industrial turbomachines and small aircraft engines are designed with a centrifugal
compressor. With such a large customer base and NASA Glenn Research Center being the lead
center for turbomachines, it is important that adequate emphasis be placed on this area as well.
Currently, this activity is not supported under any project at NASA Glenn.
Centrifugal compressors experience essentially the same problems associated with unsteadiness
as axial compressors. Separated flows lead to a significant drop in performance. Problems
associated with stall futter lead to blade loss that further deteriorates the performance. Because
of the complex shape, a CFD based aerodynamic solver is needed to accurately calculate the
unsteady airloads. Further, since the primary instability is either stall flutter or surge, the
aeroelastic solver requires viscous analysis capabilities.
A viscous aeroelastic or unsteady aerodynamic analysis capability will help design safer, lighter
and more reliable engines. Because of a more accurate estimate of the unsteady aerodynamic
forces improved blades can be designed that will help move instability boundaries away from the
engine operating range. The increased safety margin will allow operation at higher efficiencies
resulting in lower fuel consumption and reduction in exhaust gas pollutants such as CO2, NOx
andhydrocarbons.A betterbladedesignwill reduceor eliminatetheflutter andforcedresponse
problemsresultingin lower maintenancecostsandlessrisk of bladefailure.
Currentlythereareno viscousaeroelasticanalysiscodesfor centrifugalcompressorgeometries
availableto industryusers. Industry,especiallythe small enginemanufacturers,areextremely
interestedin obtaing the capability of unsteadyaerodynamicand aeroelasticanalysesof
centrifugal compressor. Under the cooperative agreement with NASA (NCC3-719),
developmentof a tool basedon a viscous aerodynamicanalysiscode, TURBO [1], wasundertakento addressthis shortcoming and provide industry userswith a robustaeroelastic
_,,_h,_;_codefor ....,,,_,,,.4_,,,,,_,_,,,_,_,,,compressors, r,,.._,L_.... m" funding by almost 50 percent for the last two,.AA l _4.x ,_ olto
years of the project and unforeseen additional code modifications, restricted us from completely
accomplishing the final objective. However, significant progress was made in developing an
unsteady aerodynamic solver applicable to impeller geometry. The TURBO-AE code [2], an
aeroelastic analysis code for axial turbomachinery geometry, based on the TURBO code, was
successfully modified for analysis of centrifugal impellers with and without splitters. The code
was validated by applying it to a Low Speed Centrifugal Compressor (LSCC) geometry. Results
showed good agreement with measured data. Also, the modifications made to the code were
furnished to researchers at Mississippi State University (MSU), the developers of the TURBO
code, to incorporate the modifications into later versions of the code.
Accomplishments
The goal of this effort was to suitably modify and extend the capabilities of the TURBO-AE
aeroelastic code for application to centrifugal compressors. The TURBO-AE code is a viscous
aeroelastic program for axial turbomachinery components. It has been developed with funding
from the AST program. Further development of the TURBO-AE code is continuing with
funding from the Ultra Efficient Engine Technology (UEET) and the Quiet Aircraft Technology
(QAT) programs. The modified TURBO-AE code was applied to the LSCC geometry for
validating the code modifications.
The TURBO and the TURBO-AE codes have been developed for axial flow turbomachinery
configurations and as such possess several inherent assumptions that would not allow a solution
of a centrifugal geometry. The codes, for example, assume the flow to be predominantly in the
axial direction with the in-flow and out-flow boundaries being nearly perpendicular to the flight
direction. This assumption is used to simplify the inlet and exit boundary conditions. Also, the
orientationof the boundary plane is used in defining the deformations to simulate the blade
vibrations. This dependence on the orientation of the exit plane had to be modified to make the
code compatible with centrifugal compressor geometry. Further, the interpolations of mode
shapes from structural to aerodynamic grids assume the blades to be more or less planar. This is
not the case for centrifugal compressors, which require a more sophisticated interpolation
program. Also, since the basic grid layouts are significantly different from the axial flow
geometry, dynamic grid deformation routines - used to simulate blade flexibility, had to be
modified as well.
aa_u_.latcu withI1_ t'_ _.¢ ".o U I. S _,_ bl,l.l 0 .LJ JL _..*eJ %_" %.' t" , 0 _..- ¥ _v.qL (_LI K./LII_'ID_,,n e the ..... of ,h; .... ;,_,-, ....... 1 ,,,_,,,,- problems were encountered
coding issues. For example, the code did not have the capability of using multiple blocks per
blade passage. This became an issue with larger grids. Further, the coding did not permit leading
or trailing edges to have different indices for different blades. This prohibited the analysis of
impellers with splitter blades. Both of these issues required significant code modifications that
were not anticipated at the beginning of the work. Because of reductions in funding, all of the
required modifications could not be completed. However, in the following, tasks that were
accomplished during the project will be described.
Code Modifications
The following major modifications were made to the TURBO-AE code to allow for the analysis
of a centrifugal impeller.
Flow Initialization: TURBO code initializes the flowfield based on the starting condition for the
flow condition. If a flow solution is available, it is used to initialize the flowfield for further
analysis. In the absence of an existing solution, the flowfield is initialized with uniform far field
conditions. For axial flow configuration the flow through the turbomachine is primarily axial,
however, for the centrifugal machines the flow turns by 90 deg with the exit flow being dis-
charged with a significant radial velocity component. Initializing the flow with uniform axial
flow field caused numerical problems in starting the analysis. This required modification of flow
initialization for the centrifugal impeller geometry. The modifications were made by initializing
the flow conditions to be parallel to the hub and casing and normal to blade passage at each flow
location, keeping the total flow conditions the same as the farfield conditions. The passage nor-
mal was determined by taking the area normal of the plane formed at the constant/-plane. How-
ever, no account was made for the pressure rise due to radial displacement because of change of
radial location in the flow path.
Splitter Geometry: Significant effort was required to adapt the coding to handle a splitter blade.
Most CFD codes inherently assume the/-indices for leading and trailing edges for all blades to
be same for a blade row. This built-in assumption within the TURBO-AE code had to be modi-
fied in order to enable the analysis of geometries with splitter blades. Further, the TURBO-AE
code solves the flowfield of one blade passage with the blade surfaces located at the two ends of
the passage. This meant that the leading and trailing edge indices for the two surfaces across the
same passage needed to differ from one another. This flexibility of indices has implications on
the application of the surface or fluid passage boundary condition since the indices define the.... ,,In
t.,UUUsolid _,,,-e.... of the blades. This required __Az¢.,z _ _:_:,':. ............ ,.u,.,._n_ _,_,_-,-,_., portions of the to allow
for blade passage and surface dependent solid surface definition and indices.
Another significant modification dictated by the need for handling splitter geometry was the fact
that the grid for one blade passage would be too large and thereby poses a problem with com-
puter resources. Consequently, the original passage had to be split into at least two passages.
The TURBO code assumed that a single blade passage constituted a single analysis block. This
required modifying the code to allow for the analysis of multiple blocks per blade passage. Sig-
nificant effort was required in making modifications to the code to permit this change. The modi-
fications were restricted to two blocks per blade passage to keep the modifications to a mini-
mum. More blocks per passage would have required modifying the boundary layer application
routines resulting in significantly more code modifications. Multiple blocks per passage re-
quired modifications to boundary condition applications, performance calculations, distance to
wall calculation for viscous analysis, and so forth.
Exit Boundary: The most significant modifications were required for the implementation of exit
boundary conditions. The TURBO code applies characteristics boundary conditions at the exit
plane in Cartesian coordinates. The exit grid plane is assumed to be normal to the x-axis to sim-
plify the boundary conditions. For a radial machine, neither the exit plane is normal to x-axis,
nor is it Cartesian. This required the development of characteristic boundary conditions in radial
coordinates simplified by the assumption of the exit plane grid being in the radial plane.
For subsonic exit flow boundary conditions, four characteristics are extrapolated from inside the
flow domain with the fifth characteristic being fixed at the boundary. For a supersonic exit
boundary, all five characteristics are extrapolated from inside the domain. The characteristics at
the boundary are obtained as follows
4
lWkln+l=(Wk/nT)b _, J )b
-A k_k
d)
where, W k is the characteristic, J is the Jacobian, Vz is the time step, A k is the eigenvalue, n
is the iteration counter, and subscript b refers to the boundary. For the five characteristics -WkJ
and g- are defined as followsJ
W 2
k _ u x andJ
W3 - -u 0 andJ
4 lp____0
Wk_ 1 p
J _f2 +Ur
Wk5 1( p
j - 4_p0c °
g__L2=0J
g3 UrU0
J r
/and 4'i 1i i-_ u_ _u_-xPPoCo
Urt and rPlT- ra(u --ooco
where, u x , u r, and u 0 are velocity components in the axial, radial and tangential directions,
respectively, 13 is the fluid density, p is the pressure, c is the speed of sound, r is the radius,
and 5' is the gas constant. The subscript 0 refers to reference quantities.
For a subsonic exit boundary condition application, the exit static pressure is fixed based on the
pressure ratio of the operating condition and the first four characteristics are extrapolated to the
boundary using Eq.(1). The characteristic values are converted to primitive variables using he
definition provided above. For a supersonic exit boundary all five characteristics are extrapo-
lated. The primitive variables obtained in cylindrical coordinates at the exit plane are then con-
vened back to the Cartesian coordinates.
Post Processing: A significant effort was also devoted to developing post processing capabilities
in order to compare the calculated results with measured data. Fluid velocity and blade surface
pressure have been measured at various locations with measurement planes being normal to the
mean flow direction. This required development of interpolation routines to transfer calculated
flow properties from the aerodynamic grid onto the plane of measurement. Since the flow path
is highly three-dimensional, special attention had to be paid to finding the correct set of points
from which to interpolate. Further, the measured static surface pressure has been reduced to ac-
count for the centrifugal force exerted on the fluid. In order to compare the pressure with meas-
ured data, the following normalization was used based on the formulation described in Ref. [3]
Y
/ 2r2/Pr p h-_- y-1- (2)
Pstd P std h
where, Pr is the reduced pressure, Pstd is a reference pressure, p is the calculated pressure, h
is enthalpy, co is the rotational speed, and r is the radius.
The code modifications to TURBO were made in modular form without disturbing the original
computational capabilities.
A grid generation program entitled TIGER [6] was also evaluated for use with grid generation of
a centrifugal geometry. However, the program was found to be difficult and cumbersome to use
for grid generation of LSCC. This program was abandoned in favor of a grid generation
program available at NASA Glenn.
MSU researchers are currently involved in developing a parallel version of the TURBO code.
The modifications made to the TURBO-AE code were forwarded to researchers at MSU to
import the appropriate modifications into the parallel code. This will enable industry users to
employ one code for various turbomachinery applications.
Code Validation
The modified code was tested and validated for aerodynamic analysis capability by applying the
code to analyze the Low Speed Centrifugal Compressor (LSCC). This compressor impeller has
been thoroughly tested in a NASA Glenn wind tunnel [4], and provides for an excellent test case
to verify and validate the modified code for performance calculations.
The LSCCis anaxial flow impeller with 20 blades,tip diameterof 1.524m anda backsweep
angleof 55deg.Theimpellerwastestednearits designedoperatingpointwith amassflow of 30
kg/sanda rotationalspeedof 1,862rpm.Thetestconditionsweresuchthattheflow wasentirely
subsonicthroughthe impeller.The testwasconductedusinga vanelessdiffuser that generated
an axisymmetricoutflow boundarycondition,desirablefor CFD analysisof an isolatedbladerow. The analysisusingthemodifiedTURBO-AE codewascarriedout usinga grid with 129
grid points in the flow direction(m-direction),61 grid pointsbetweenthe hub and the casing
(span-direction),and41 grid pointsin theblade-to-bladedirection(tht-direction).Becauseof theb_au_passagein thesiT,_._of th,_..._e,-d, -,,_ _,._,j _,_ ,.,,._.... ,.,,,,,,.,., out using two grid "'-_'-_u,u_._per ' "-
blade-to-blade direction.
Figure 1 shows the impeller analyzed with pressure contours on its solid surfaces. The casing of
the impeller is not shown for sake of clarity. Comparison of blade surface static pressure is
shown in Figure 2. The pressure was normalized using Eq.(2) for comparison with experimental
data. This normalization removes the pressure rise due to increase in the radius as the fluid
travels from the leading edge to the trailing edge and provides the pressure variation because of
blade passage diffusion. Very good agreement of the surface pressures with measured data was
found. Also, shown on this figure is the comparison of performance characteristics of the
impeller as compared with experimental measurements. Once again excellent agreement was
obtained.
Figures 3 through 10 show comparisons of the velocity distributions. Comparisons are shown for
the variation of the three velocity components (axial, radial, and tangential) normalized by the
impeller tip speed at three span locations. The variation is shown for the blade passage at each
streamwise location with suction surface being at 0 and pressure surface being at 100 on the
horizontal axis. Flow velocity predictions were found to be in good agreement with measured
values, however the comparisons of the velocities in the wake were found to possess only
qualitative agreement. It is believed that the differences in the wake velocities were due to the
use of the Baldwin-Lomax turbulence model in the code. This turbulence model does not
accurately capture the characteristics of the blunt trailing edge of the blades. This resulted in the
calculated flow leaving the surface at a slightly different angle than experimentally observed.
Nevertheless, overall the agreement of the flow velocity was found to be good.
7
Concluding Remarks
A viscous analysis code applicable to centrifugal impeller geometry was developed and validated
using experimental data. The code was developed by modifying the TURBO-AE code, which is
applicable to axial flow turbomachinery components. The exit flow boundary conditions were
developed and implemented in the TURBQ-AE code along with several other modifications.
Significant effort was expended to modify the code architecture to allow analysis with multiple
blocks per blade passage and to allow for different i-indices for the leading and trailing edges of
different blades. Predicted values manifested good agreement with measured data of surface
pressure, performance quantities, and velocity components. However, the comparison of velocity
distribution in the wake was found to be fair to poor, espccially in the area near the casing. It was
determined that the differences in the wake velocity predictions were primarily due to the
inadequacy of the Baldwin-Lomax turbulence model. It is suggested that the k-e turbulence
model be added to the code to improve the velocity predictions. Also, further validation of a
high-speed impeller geometry should be carried out.
References
1. Janus, J. M., "Advanced Three-Dimensional CFD Algorithm for Turbomachinery," Ph.D.
Dissertation, Mississippi State University, May 1989.
2. Bakhle, M., Srivastava, R., Keith, T. Jr., Stefko, G. L., "A 3D Euler/Navier-Stokes
Aeroelastic Code for Propulsion Applications," A!AA Paper 97-2749, 33rd Joint Propulsion
Conference and Exhibit at Seattle, WA, July 1997.
3. Rautaheimo, P., Salminen, E., Siikonen, T., "Numerical Simulation of the Flow in the
NASA Low-Speed Centrifugal Compressor", Report 119, Helsinki University of
Technology, Helsinki, Finland.
4. Hathway, M. D., Chriss, R. M., Strazisar, A. J., and Wood, J. R., "Laser AnemometerMeasurements of the Three-Dimensional Rotor Flow Field in the NASA Low-Speed
Centrifugal Compressor.
5. Skoch, G. J., Prahst, P. S., Wernet, M. P., Wood, J. R., and Strazisar, A. J., "Laser
Anemometer Measurements of the Flow Field in a 4:1 Pressure Ratio Centrifugal Impeller",
NASA TM 107541, June 1997.
6. Shih, Ming-Hsin and Chen Yen-Sen, "TIGER Grid Generation Code," Final Technical
Report for NASA Contract Number NAS-3-2775, ESI-TR-97-07, September 1997.
Calculated: Adlab. Eff.=0.916, Mass Avg. Temp Ralio=1.041, Energy Avg. Press. Ratlo=1.138Measured: Adlab. Eff.=0.922, Mass Avg. Temp Ratlo=1.042, Energy Avg. Press. Ratio=1.141
1r
098
098
Q.0 92
ng
068
-- TURBO I
l " "="_!
span=5%
I I025 05
m/m=
I I075 I
09
o96
a.0, 92
09
088
Span=49%
I I0.25 05
m/m,_73
1
o98
098
092
-- TURBO
• MeemlltKI
09
089
Span=94%
lr
098
0.96
_.0 94
O,.092
0.9
0.86
I -- = ._JP,,BO ]
I " --==1
Span=20%
I I0 2.5 05
m/m=
I I075 1
1
098
096
l 094
a.
088
TURBO
• MeetZUl,lZd
•
Span=79%
I I025 05
m/m,070
1
o.ge
095
:i
o 93.
o.9
0Be
TURBO
Span=98%
I I I I o2s os o?s
o25 o5 o7s , m/m=m/m,
Figure 2. Comparison of blade surface static pressure for the LSCC at design condition at
various span locations.
10
03S f 0
m=-O 038, s=20 '/o
02S[
Cht
016 f o
m=-O 038, s=20 '/o
= o_ t ' I
o%[ " L ; 'o gtht
032 J_J
thl
012
.... ./. -. )°°9
_t
m= 0 038, s=50%
2o ' " ' & ' io ' ,L
03,¢
o3e
.o _8
)-04
• m=-O 038, s=50%
•o " Jo '. ,o'o_t
°_I°'2 m=-O 038, s=90% oo.....
\ "
_t
m=-O 038, s=90%
tht
•a 4S
m=-O 038, s=90%
\I, /
_t
Figure 3. Comparison of axial, tangential and rotational velocity components in blade passage at
3.8 percent of chord length upstream of the blade at 20, 50 and 90 percent span stations. ----
Measured velocities, -- predicted TURBO predicted velocities.
11
O5
04
m=O.03, s=20%
/03! z.... ; , ,o r , , ,_ ,
tht
,,=
m=O.03, s=50%
oe
_5
_4
_3
az
o_
m=O.03, s=90%
.[)
c
lht
m=O.03, s=20% ....
-02
i [ .... -03
11 .04
,I
.05
' '_ _ 'o , '_ ' Io ' ,_ ....tht
m=O.03, s=50%
Q2
3
: -_ " ------ - _ ..... -- -_ _ "_r -'_- - _-o_.
05
' 'o ' " ' _' ' Io ' ,'o -°'mt
m=O.03, s=90% ....
_3
-04
Tm=O.03, s=20%r
I
J _I o
tht
m=O.03, s=50%
m=O.03, s=90%
, / ° , 10 , / , / _ I ° , / , slo , / ,
thl lht
,_o
Figure 4. Comparison of axial, tangential and rotational velocity components in blade passage at
3.8 percent of chord length downstream of leading edge of the blade at 20, 50 and 90 percentspan stations. ---- Measured velocities, -- predicted TURBO predicted velocities.
12
• . .. m
O7
OB
05
)O4
m=0.396, s=20%
.... Jo • • jo' ,,_Ult
03
o i_
a
m=0.396, s=50%
tht
m=0.396, s=90%
'o ' • ' 'o ' 'o _,_otht
m=0.396, s=20%
"--= • • _-- _--_Q-IIIN
tht
,'oo
15
I
)a5
o
_5
m=0.396, s=50%
4-*
IDDtht
)
m=0.396, s=90%
o
o15
.o._
m=0.396, s=20%
F
°_f , , . ......o o 5o so _oo
tht
.o3
)-04_
OS
"01
_2
_04
_5
i 2_ k _Q i _ i _0 i !_
tht
m=0.396, s=90%
mt tht
Figure 5. Comparison of axial, tangential and rotational velocity components in blade passage at
39.6 percent of chord length downstream of blade leading edge 20, 50 and 90 percent spanstations. ---- Measured velocities, m predicted TURBO predicted velocities.
13
a3
O2
01
05
04
O3
O2
01
=
o
-01
m=0.644, s=20%
Ult
• m=0.644, s=50%
1 • 4_ _ _ a_e_ I_jB'j_,
20 _o SO eO t O0
tht
O5
-O5
O5
_3
_2
m=0.644, s=20%
mt
m=0.644, s=50%
tht
I
I i i_o
o_
02
-03
0
o2
03
-04
-0_
,. -. _m=0"644' s=90% °_I m_°644' s=90%
/
.oa
' Io ' 41o ' Io ' II_ ' ?o oI , I , I , I , I , ', I _o ....o zo ao so ao i• t _t
m=0.644, s=20%
Ult
m=0.644, s=50% i" r-"
I
I
I /
II
b_t
m=0.644, s=90%
, , , ,,o , _,o , , , ,_oO'tt
Figure 6. Comparison of axial, tangential and rotational velocity components in blade passage at
64.4 percent of chord length downstream of blade leading edge at 20, 50 and 90 percent span
stations. ---- Measured velocities, m predicted TURBO predicted velocities.
14
O3
02
01
m=0.852, s=20%
•o . ?o • • , ,_
-0
m=0.852, s=20%
- = _
tht
.01
-o2
.03
-O4
-O5
oB_
m=0.852, s=20%
,o .,o ,_ . • ,_
O7"5
oS
025
5
a25
-o5
• m=0.852, s=50%
tht
OO
O_
_ O3
o15
m=0.852, s=50%
L 'e-_4
, /o , - ,o _,o,_otht
-03
_o45
-oe
_o't5
m=0.852, s=50% ,'I
-o,_ , ,o . :o /o . ,_o_t
m=0.852, s=90%
I I
M _h
' " ' 'o ' 1o ' : ' ,_°_t
Figure 7. Comparison of axial, tangential and rotational velocity components in blade passage at
85.2 percent of chord length downstream of blade leading edge at 20, 50 and 90 percent span
stations. ---- Measured velocities, -- predicted TURBO predicted velocities.
15
o_
O2
o
_ o_
04
m=0.960, s=20%
_ ' " ' " ' io ' ,_tht
°"--_ m=0.960, s=20%
02
'101 r i
:l
-o ' Jo ' 2o ' _ ' Io ' ,__t
-O3
oa,_
•og i
m=0.960, s=20% 1
,F
kr
_o I _ ' _ B _ I _
Ult
o°il m=0.960, s=50% o.,°_
o h 2lo , / , efo , / r ,_0 O_
m=0.960, s=50%
' :o ' " ' 'o ' _', ,,t_o
tht
-03
-0 75
-og
•1 05 _
mt
oa
oe
. 04
_e
m=0.960, s=90% t _'°,I, -. m=0.960,,, s=90% ...._o_
II
m=0.960, s=90%
I t
" ' ,'= ' ,'= ' ,' ' ,o'o_t
Figure 8. Comparison of axial, tangential and rotational velocity components in blade passage at
96 percent of chord length downstream of blade leading edge at 20, 50 and 90 percent span
stations. ---- Measured velocities, -- predicted TURBO predicted velocities.
16
°' Im=1.081, s=20%005
_ ,, ,+,; +
.ol r_,'
I, . , ,o , . . ,o , ,tht
0275
025
O225
+02
0175
015_
m=1.081, s=20%
• *_ -o +75
_,t/ / +• ill +i
_, .0575
-OB
tht
I'_ m=1.081, s=20%
/ _"m. "+" +"_"+_
t_t
oi
015
42
m=1.081, s=50% _ °°I "'"""m=1.081, s=50% .o,
0275 I ! -o ,I._.
.... +.q( t
, 21 I 10 I 10 , / ' 11 ...... I0 ' /0 ' 20 , / ° I _fO i ,_o oo_
bht f_
., m=1.081, s=50%
' _'o ' "o ' 'o ' ,' ,_'oUlt
oa
os
O4
=
OZ
0
-o1
m=1.081, s=go% =_ii! m=1.081 , s=90% i "'°°''
• = • : _ o -orI
' "o ' _o ' 'o ' 'o ' ,'.......... °'tht _t
m=1.081, s=90%
' " ' '= ' 'o ' +' ' I_ofllt
Figure 9. Comparison of axial, tangential and rotational velocity components in blade passage at
8.1 percent of chord length downstream of blade trailing edge at 20, 50 and 90 percent span
stations. ---- Measured velocities, -- predicted TURBO predicted velocities.
17
oi
Do5
.oi
o05
.005
5]
.o i
.o 15
o2
, os
o os
ol
.a_s
"m=1.094, s=20%
Ult
m=1.094, s=50%
= = =---!...
IL__,
°_"I m=1.094, s=20% o,_
°o.._Ii,::' ''""=%°
.... ; ' Io ' ; ' ,'o ' 'Ult
m=1.094, s=50 %
o2e _ _ 045
tht
m=1.094, s=90% °"
Y I' :+,: _oo
' _ ' I, ' ,=o ' Io ' ,,_o °"
-O4
m=1.094, s=90%
_t
r_ m=l 094, S=20%
, / ° , / ° , _ , I , ?oo
tht
m=1.094, s=50%
_t
m=1.094, s=90%
/ / \' _ 1o ' Io ' elo ' ,Io
fJlt
Figure 10. Comparison of axial, tangential and rotational velocity components in blade passageat 9.4 percent of chord length downstream of blade trailing edge at 20, 50 and 90 percent spanstations. ---- Measured velocities, -- predicted TURBO predicted velocities.
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