NASA 

Technicd Memorandum 88928 

USAAVSCOM 

Technical Report 86-C-36 

, 

A Method for Calculating Turbulent 

Boundary Layers and Losses in the 

Flow Channels of Turbomachines 

I 

Lawrence F. Schumann 

Propulsion Directorate 

U. S. Army Aviation Research and Technology Activity-AVSCOM 

Lewis Research Center 

Cleveland, Ohio 

(UASA-Tfl-88926) A METHOD FOR CALCULATING N87- 1% 44 

'IUBBULENT BOUNDARY LAYEES ANC LOSSES IN THE 

FLOH CHANNEL3 Ok IURBCHACHINES [NASA) 17 p i CSCL OlA Unclas 

G3/02 43337 

Prepared for the 

32nd International Gas Turbine Conference and Exhibition 

sponsored by the American Society of Mechanical Engineers 

Anaheim, California, May 31-June 4, 1987 

. . 

1 
A METHOD FOR CALCULATING TURBULENT BOUNDARY LAYERS AND LOSSES IN THE FLOW CHANNELS OF TURBOMACHINES 

Lawrence F. Schumann 

Propulsion Directorate 

U.S. Army Aviation Research and Technoloqy Acitivity - AVSCOM 

Lewis Research Center 

Cleveland, Ohio 44135 

ABSTRACT 

An interactive inviscid core flow-boundary layer 

method is presented for the calculation of turhomachine 

channel flows. For this method, a one-dimensional 

inviscid core flow is assumed. The end-wall and blade 

surface boundary layers are calculated usinq an inte2 gral entrainment method. The boundary layers are 

% assumed to be collateral and thus are two-dimensional. 

& The boundary layer equations are written in a streamline coordinate system. The streamwise velocity profiles are approximated by power law profiles. 

Compressibility is accounted for in the streamvise 

direction hut not in the normal direction. 

Equations are derived for the special cases of 

conical and two-dimensional rectangular diffusers. 

For these cases, the assumptions of a one-dimensional 

core flow and col 1 ateral boundary layers are Val id. 

Results using the method are compared with experiment 

and good quantitative agreement is obtained. 

NOMENCLATURE 

Ah 

Ag 

A1-A3 

a 

B 

b 

C f 

cP 

Pr C 

unblocked flow area = (1 - B) Aq 

qeometric area 

terms in velocity gradient equation 

speed of sound 

blockage 

passage height 

skin friction coefficient 

specific heat at constant pressure 

pressure recovery coefficient, 1 P-P 

p1; - p1 

D 

01-0, 

F 

H1 

HZ 

K1-K3 

Kt 'Ky 

I. 

M 

MU 

m 

m 

P 

PSTD 

Re 

Rg 

r 

S 

T 

TSTD 

1 

d i f f user throat d i amet er 

terms in velocity gradient equation 

entrainment function 

1 shape factor, - 

6-6 

&2 

shape factor, - 

&2 

terms in area equation 

curvature terms 

diffuser length 

relative Mach number, W/a 

wheel speed Mach numher, U/a 

exponent in velocity profile 

mass flux 

pressure 

standard pressure, 101 325 N/m 

Reynold's number 

qas constant 

radius 

entropy 

t einper ature 

standard temperature, 288.2 K 
t 

U 

W 

X 

Y 

Z 

a 

6 

Y 

6 

61 

62 

e 

x 

u 

P 

T 

Q 

w 

tangential coordinate 

wheel speed 

relative velocity 

streamline coordinate 

normal coordinate 

blade number 

angle between meridional stream 

axis of rotation 

angle between re1 ati ve velocity 

meridional plane 

specific heat ratio 

boundary layer thickness 

channel divergence angle 

orewhi r 1 

coefficient of vi scosi ty 

density 

shear stress 

r 

entropy function, 

rotational speed 

ine and 

vector and 

\ ") 'e dY 

Subscripts: 

A spanwise direction 

e edge of boundary layer 

r radial direction 

t,T tangential direction 

W wall 

X streamline direction 

Y normal direction 

3 channel inlet 

2 channel exit 

Superscripts 

I absolute total conditions 

relative total conditions I, 

2 

INTRODUCTION 

In the preliminary design of turbomachinery it 

is necessary to estimate the losses in the individual 

components. For rotors, stators and impellers, this 

is usually done by usinq empirical correlations for 

channel losses (e.q., skin friction, diffusion, etc. 

(1-4)). 

done by empirically relating the diffuser pressure 

recovery coefficient to the diffuser geometry and 

inlet flow conditions (5,i). 

estimating these losses would be to calculate the 

surface boundary layers and from these obtain a massaveraged estimate of channel losses. However, many of 

the present methods for calculating boundary layers 

(e.g., the code, BLAYER, ref. 7) are not ideally 

suited for calculating the boundary layers in turbomachine flow channels. 

F i r s t o f all, most boundary layer codes are 

written for external flows, thus, they require a 

specification of the free-stream velocity distribution. 

For internal flows, the velocity distribution is not 

known apriori and thus must be determined by an iterative procedure along with the continuity equation for 

the assumed inviscid core flow. This can be a very 

time consuming procedure especially for preliminary 

design calculations where several levels of iteration 

must be performed. 

two-dimensional flows along flat surfaces and thus 

ignore any coordinate curvature terms (i .e., metrics). 

This can lead to large errors for some internal channel flows in which the channel end walls are converqing or diverging; e.g., nozzles and diffusers. 

There have been several methods proposed to calculate the performance of straiqht-wal led, rectangular 

type diffusers (4-%). 

dimensional in nature (i.e., they ignore end-wall 

effects) and are limited to the computation of incompressible, straight center-line diffuser flows. These 

methods are highly developed and predict the performance of this class of diffusers very well even into 

the stalled regions of the diffuser maps. However, 

since all these methods are iterative, viscousinviscid interaction methods, their running times can 

be much longer than that of the method proposed here. 

This could make them unsuitable for use in compressor 

preliminary design codes. 

entrainment method for calculating the flow fields in 

turbomachines has been developed. 

taneously calculates the free-stream velocity distribution from an assumed one-dimensional core flow 

continuity equation together with the equations 

describing the surface boundary layers. 

one pass through the flow channel is required thereby 

making the method very fast. The primary assumptions 

made for the boundary layer calculations are that the 

flow is basically two-dimensional and that the boundary layer profile can be described by a power law. 

The exponent in the power law is allowed to vary as 

prescribed by the equations cf motion. 

ity is accounted for in the streamline direction hut 

not in the direction normal to the flow surfaces. 

Turbulent flow is assumed everywhere usinq the semiempirical Ludwieg-Tillman relation for skin friction. 

Approximate methods for calculatinq through regions of 

fully-developed or separated flows are also presented. 

Comparisons are made with experimental data for the 

cases of conical and rectangular diffusers and good 

agreement is demonstrated for cases where no separation is indicated. Fair agreement is demonstrated in 

separated regions of the flow. 

For diffusers (conical, rectangular) this is 

i A more riqorous way of 

Also, most boundary layer codes are written for 

These methods are all twoFor these reasons, a noninterative integralThe method simulThus, only 

Compressibil- 
METHOD OF ANALYSIS Normal Momentum 

The method of analysis used to calculate the flqw 

surface boundary layers in the channel is an inteqralentrainment method. The method is similar to that 

used for the calculation of end-wall boundary layers 

in Ref. 12. For this analysis, the core flow is 

assumed to be one-dimensional and is described by the 

one-dimensional continuity and momentum equations. 

Two-Dimensional Boundary Layer Method 

The followinq assumptions are made for this 

anal ys i s : 

(1) The flow is steady and turbulent everywhere 

(2) The fluid is a perfect gas 

(3) The flow in the bour,dary layers is twodimensional, i.e., there is no crossflow component of 

velocity. 

collateral, i.e., the flow angle, 6, is constant 

throuqh the boundary layer. 

(4) The channel flow surfaces are adiabatic 

(5) There is no density variation in the direcTherefore, the boundary layers are also 

tion normal to the channel boundaries althouqh the 

density is allowed to vary in the streamline direction, i.e., p = p(x). This approximation seems to 

work well for Mach numbers up to 1.0 and slightly 

beyond (12). For high supersonic flows, some other 

formulation would have to be used. 

(6) The boundary layer velocity profile in the 

streamline direction may be described by the power-law 

equa t ion 

where We, 6, and m are functions of distance along 

a streamline, x, only. The power law approximation 

adequately predicts pressure recovery up to separation, 

althouqh the actual profile deviates from the power 

law approximation more significantly as separation is 

approached. 

To completely solve the problem, the boundary 

layer thickness, 6, and the boundary layer exponent, 

m, for each surface boundary layer calculated; the 

free-stream velocity, We; and the free-stream pressure, density and temperature must be determined. 

Thus, a total of (4 + 2n) equations must be solved 

where n is the number of surface boundary layers. 

If a streamline coordinate system is chosen (with 

x in the streamline direction, y in the normal to 

the wall direction, and t in the crossflow direction 

completing the orthogonal triad), the boundary layer 

equations for motion can be written as follows: 

Continuity 

Momen t um 

aWX a WX ap 1 

OW, ax + pwY ay - prW2 sin a cos = - - + -- ax r ay 

(3) 

(4 

In Eq. (Z), the curvature term, Ky, is defined as the 

curvature of the normal coordinate, y, in the 

t = constant plane and the curvature term, Kt, is 

defined as the curvature of the tanqential coordinate 

t, in the y = constant plane. The normal coordinate 

is assumed to be everywhere normal to the flow. 

boundary layer with the additional assumption that Kt, 

Ky, a, 6 and r are indepevlent of the normal 

coordinate, y; the followinq equations result: 

If Eqs. (2) and (3) are inteqrated throuqh the 

(5) 

- pr6w2 sin a cos B = - 6 - ax xw (6) 

Equation (3) can also be evaluated for the isentropic 

core flow which results in the following equation 

One additional unknown was added in the integration of 

Eq. (3), i.e., the normal velocity at the edqe of the 

boundary layer, Wye, as shown in Eq. (6). This can 

be modelled using Head's entrainment relation as was 

demonstrated in Ref. 12. The resultinq relation is 

g i ven by 

Using the velocity profile from Eq. (1) and performing 

the indicated differentiations and inteqrations, 

Eqs. (5) to (8) can be combined to yield the following 

equations 

sin a COS B 2 r Mu - (KY + Kt) (10) 

Equations (9) and (10) can be solved if the variation 

in free stream velocity, We, is known. A detailed 

derivation of equations similar to Eqs. (9) and (10) 

is shown in the Appendix to Ref. 12. 

In order to solve these equations, the skin friction coefficient, cf, and the entrainment function, 

F, must be evaluated. The skin friction coefficient 

is obtained from the Ludwieg-Tillman relation which is 

3 
-0.268 e- Cf = 0.246 ReG 

2 

where 

The entrainment function is a funct 

boundary layer shape factor and was 

to be given by 

H2 = 1 + 2m. 

0.653 

F = 0.0306 (&) 

on only of a 

shown in Ref. 12 

(12) 

The variation in the free stream velocitv, We, 

can be determined if a one-dimensional core flow is 

assumed. 

from the continuity equation for the core flow which 

can he written 

In this case, the velocity can he determined 

A = pWeAb 

where Ab represents the unblocked channel area 

normal to the flow. 

ing Eq. (13) results in the equation 

Using the results from Eq. (7) and differentiatThe static temperature of the core flow can be 

determined from the energy equation for the core flow 

which is 

where 

- T" = T' 1 - 2cp 

The static pressure and density can then be determined 

from either Eq. (7) and the equation of state for the 

core flow, or from the isentropic relations for the 

core flow. These equations toqether with Eq. (14), 

and Eqs. (9) and (10) written for each boundary layer, 

then provide the (4 + 2n) equations needed to solve 

the channel flow field. 

Fully Developed and Separated Flow 

When the boundary layers from opposite walls of 

a channel merge, an isentropic core flow no lonqer 

exists and the flow is said to be fully developed. In 

this case, the thin shear layer assumption used in the 

derivation of Eqs. (2) to (4) is no longer valid. 

However, it would be useful to carry out the calculations after the flow becomes fully developed. In 

order to do this, some simplifyinq assumptions must 

be made. These are as follows: 

approximately the fully deveioped flow field. 

Although this is consistent with Prandtl's mixinq 

length theory of turbulence; in reality, it is not 

valid due to a nonzero shear stress qradient at the 

centerline. 

With these assumptions and the fact that the 

entrainment function equals zero (as can be seen from 

(1) The boundary layer Eqs. (2) to (4) describe 

(2) The centerline of the flow remains isentropic. 

the definition in Eq. (8)), and the boundary layer 

thickness equals half the channel height, Eqs. (9) 

and (14) can be solved as before. 

the calculation beyond an indicated point of houndary 

layer separation. This point is usually determined bv 

a limiting value of the shape factor, 

Once again, the boundary laycr Eqs. (2) to (4) become 

invalid when the boundary layer separates. Also, the 

assumed power 1 aw profiles cannot accurate1 y d e s c r i h e 

a separated flow. However, calculations show that the 

pressure recovery and losses can be reasonably nredicted usinq some simplifyinq assumptions. 

as follows: 

law profile remain valid for separated flow. 

It yo1.11d also be useful to be able to continue 

H7 = 1 + 2m. 

These are 

(1) The boundary layer Eqs. (2) to (4) and ooww 

(2) The skin friction coefficient qoes to zero. 

(3) The entrainment function reaches a limiting 

value chosen to be the value at the separation point. 

(4) The shape factor is allowed to increase 

beyond the separation point. 

With these assumptions, the calculations can proceed beyond points of separation or fully developed 

flow. 

Loss Calculations 

Since the flow is assumed to be two-dimensional. 

the losses can be determined by a simple mass averaqing procedure. Since the channel exit static pressure 

is determined in the solution of the boundary layer 

flow, all that is needed is a static enthalpy correspondinq to a mass-averaqed flow in the channel in 

order to calculate the mass-averaqed entropy rise from 

the equation 

PA 

APPLICATIONS OF THE METHOD 

The method has been applied to the cases of 

conical and rectangular diffusers. In these cases, 

the assumptions of a one-dimensional core flow and 

collateral boundary layers are valid at least for 

nonseparated flows. 

Conical Diffuser 

The basic geometry of a conical diffuser is shown 

in Fig. 1. In order to solve Eqs. (9), (10) and (14), 

the cross-sectional area, Ab, and the curvatures, 

Ky and Kt, must be determined. The flow area is 

assumed to lie on a spherical segment as shown which 

is approximately everywhere normal to the flow. The 

unblocked flow area is then given by 

and the area term in Eq. (14) becomes 

4 
2 K --+K - 2-x 1 x 

The curvature terms for this case are qiven by 

(20) 1 sin e K =K --=- y t-x r 

Then for this case, since Mu = 0, and 

dsl m d6 + 6 dm 

aj;-=1.ma;; (1 + m)2- a;; 

Eq. (14) becomes 

1 dWe A1 

We dx - D1 ---- 

(21) 

(2 + 3 K161) 2 2 Cf - 2Klm F + K1(l + 2m) X where A - - 1- 

2 Ill = (1 - Me)(l + K161) + 2K161(l + m)(l + 2m) 

Equations (9) and (10) complete the system of 3 

equations in 3 unknowns (We,m,6). The equations are 

solved using a fourth-order Runge-Kutta technique (13). 

Results using this method have been compared wxh 

experimental data from a wind-tunnel diffuser section 

(14) and with data for conical diffusers (5). 

Fiqures 2 to 4 show comparisons of velocity profiles, 

static pressure coefficients, and displacement thicknesses at the exit of the cross-leq diffuser of 

Ref. 14 for three different inlet Reynold's numbers 

and Mach numbers. In all cases the agreement is qood. 

For these cases, the boundary layers remained attached 

according to the analysis. Figures 5(a) to (d) shows 

comparisons of pressure recovery coefficient for several arbitrary cases of inlet Mach number, blockaqe, 

and cone angle for the conical diffuser data of 

Ref. 5. Almost all of the data lie in a reqion where 

the flow would be expected to be separated according 

to the analysis. 

experiment and analysis is still fair. 

However, the agreement between 

Rectangular Diffuser 

The geometry for a rectangular diffuser is shown 

in Fia. 6. For this case. the boundary layers in the 

tangential (blade to blade) and spanwise (hub to 

shroud) directions cannot be assumed to be equal due 

to the fact that the initial boundary layer thicknesses may be unequal and the flow may become fully 

developed in one direction only. 

and spanwise boundary layers must be calculated separately. However, the core flow is still assumed to 

be one-dimensional. 

Thus, the tanqential 

The unblocked flow area for this case is qiven by 

Ab = (b - 261A)(2ex - 261~) (231 

and the term in Eq. (12) becomes 

d61T d61A 

-K3-K 2TT-Kl-Z1 d% 

Ab dx 

where 

(24) 

2 K- 1 - Ib - PalA) 

1 K1T' 2 - (ex - 6 

e K1T) 3 - (ex - 6 

The curvature terms for the tangential boundary layers 

are given by 

(25) 

K = -; 1

y x Kt=O 

The curvature terms for the spanwise boundary layers 

are given by 

(26 

K =O; Kt=y 1 

Y 

Equation (14) can then be expressed 

dWe AI + A2 + A, 

Tdx= D1 + D 

where AI = -2K24FT - 2K m 2 F 

1AA 

J 

- (27 

Equations (9) and (10) written for both the tangential 

and spanwise boundary layers then complete the system 

of 5 equations in 5 unknowns (We,mA,6A,lITr,6~). 

Results using this method have been compared 

with experimental data for rectanqular diffusers (6). 

A comparison of calculated and experimental pressure 

coefficients for several arbitrary cases of inlet Mach 

number, blockage, and divergence angle, e, is shown 

in Fig. 7(a) to (d). The cases shown correspond to an 

inlet aspect ratio of one; however, the method is 

applicable for any arbitrary inlet aspect ratio. 

cases were calculated assuminq equal boundary layer 

thicknesses and exponents on the inlet vane surfaces 

and end walls. 

between calculation and experiment even thouqh the 

calculations indicate that almost all of the data 

shown lie in a region where the flow would be 

separated. 

CONCLUSIONS 

The 

The results show fair aqreement 

An analytical method has been developed to calculate boundary layers and losses in turbomachine 

flow channels. 

compared with experimental data for the special cases 

of conical and rectangular diffusers. Good arlreement 

is demonstrated for the flow regimes where the analysis indicates no separation. Fair agreement is 

Results using this method have been 

5 
demonstrated for the pressure coefficients calculated 

in the separated regions of the flow. 

Since the method is a noninterative inteqral 

inethod, it is very fast coinpared to other methods of 

analysis. Thus, it can be easily adapted for use in 

preliminary design or off-desiqn codes for turbomachinery components. 

REFERENCES 

1. Galvas, M.R., "Analytical Correlation of Centrifugal Compressor Design Geometry for Maximum Efficiency with Specific Speed," NASA TN D-6729, 1972. 

2. Crouse, J.E., and Gorrell, W.T., "Computer Proqram 

for Aerodynamic and Bladinq Desiqn of Multistaqe 

Axial-Flow Compressors," NASA TP-1946, 1981. 

3. Glassman, A.J., "Computer Proqram for Desiqn 

Analysis of Radial-Inflow Turbines," NASA TN 

~-8164, 1976. 

4. Glassman, A.J., "Computer Proqram for Preliminary 

Design Analysis of Axial-Flow Turbines," NASA TN 

5. Dolan, F.X., and Runstadler, P.W. Jr., "Pressure 

D-6702, 1972. 

Recovery Performance of Conical Diffusers at Hiqh 

Subsonic Mach Numbers," NASA CR-2299, 1973. 

6. Runstadler, P.W., Jr., "Pressure Recovery Performance of Straight-Channel, Sinqle-Plane Oiverqence 

Diffusers at High Mach Numbers," Rept. N-88, Crear 

Inc., Hanover, NH, (USAAVLABS-TR-69-56, 

AD-865300), Oct. 1969. 

7. McNally, W.D., "FORTRAN Program for Calculating 

Compressible Laminar and Turbulent Boundary Layers 

in Arbitrary Pressure Gradients," NASA TN D-5681, 

,1970. 

8. Bardina, J., Lyrio, A., Kline, S.J., Ferziqer, 

J.H., and Johnston, J.P., "A Prediction Method for 

Planar Diffuser Flows," ASME Journal of Fluids 

Engineering, Vol. 103, 1981, pp. 315-371. 

9. Ghose, S., and Kline, S.J., "The Computation of 

Optimum Pressure Recovery in Two-Dimensional Diffusers," ASME Journal of Fluids Engineerinq, 

Vol. 100, pp. 419-426. 

10. Woolley, R.L., and Kline, S.J., "A Procedure for 

Computation of Fully Stalled Flows in TwoDimensional Passages,'' ASME ,Journal of Fluids 

Engineering, Vol. 100, pp. 180-186. 

11. Ashjaee, J., and Johnston, J.P., "Straight-Walled, 

Two-Dimensional Diffusers-Transitory Stall and 

Peak Pressure Recovery," ASME Journal of Fluids 

Engineering, Vol. 102, pp. 275-282. 

Calculations Procedure for Turbulent Flows in it 

12. Schwann, L.F., "A Three-Dimensional Axisyrninetric 

Radial Vaneless Diffuser," Journal of Enqineerinq 

for Gas Turbines and Power, Vol. 108, No. 1, 

Jan. 1986, pp. 118-124. 

13. White, F.M., Visous Fluid Flow, NcGraw Hill, New 

York, 1974. 

14. Shyne, R.J., Moore, R.D., and Boldrnan, D.R., 

"Comparison of Analytical and Experiments Performance of a Wind-Tunnel Diffuser Section," NASA 

TM-88795, 1986. 

6 
INLET 

STATION 1 

EXIT 

STATION 2 

+L -I 

FIGURE 1. - CONICAL DIFFUSER GEOMETRY. 
0 DATA (REF. 10) 

ANALYSIS 

1 .o 

.8 

.6 

1 .o 

.8 

F z 

.6 

.4 

ReD = 2.76~10 

Mi = ,292 

.4 

0 .05 .10 .15 .20 .25 

Y/r 

FIGURE 2.- BOUNDARY LAYER VELOCITY PROFILES AT EXIT OF 

. 1 SCALE CROSSLEG DIFFUSER. 
.4 

.3 

.2 

.1 

0 

-.l 

DATA (REF. 10) J 

- 

0 

-- ANALYSIS /’ 

ReD = 6.10~10~ 

Mi = .325 

-1 

0 .5 1.0 1.5 2.0 2.5 

Y/rl 

FIGURE 3.- PRESSURE RECOVERY COEFFICIENTS IN .1 SCALE 

CROSSLEG DIFFUSER. 
.03 

* 02 

- 

0 DATA (REF. 10) 

ANALYSIS 

6 ReD = 6.10~10 

fl1 = ,325 

0 

.03 r 

.02 I 

.03 

0 * 

.02 

.Ol L I 

0 .5 1 .o 1.5 2.0 2.5 

x/r 

FIGURE 4. - DISPLACEMENT THICKNESSES IN . 1 SCALE CROSSLEG 

DIFFUSER. 

i 
.8 

.7 

.6 

.5 

.4 

.7 

n 

V 

.6 

.5 

*4 

.3 

0 

:' E/ 28 DATA (REF. 5) ANALYSIS 

0 

40 

8' 

120 

0 

0 

A 

4 8 12 16 

L/D 

(B) Mi = .6, B1 = .12. 

20 

FIGURE 5. - PRESSURE RECOVERY COEFFICIENTS FOR VARIOUS 

CONICAL DIFFUSERS. 
r 

:: j 

.5 

,4 n 

u 

.7 

.6 

.5 

.4 

n 0 

--- 

28 DATA (REF. 5) ANALYSIS 

fA 

I 0 o/ 

I /- 00 
INLET 

STATION 1 

EXIT 

STATION 2 

f LOW 

I)- 

+----L-----i 

FIGURE 6.- RECTANGULAR DIFFUSER GEOMETRY. 
.8 

.7 

.6 

.5 

0, 

V 

.4 

28 DATA (REF. 6) ANALYSIS 

6' 0 

- 80 0 

1 oo 

----- 

A --- 

I 

(A) M = .6. B = .06. 

.7 r 

.6 

.5 - 

J 

2 6 10 14 18 24 

L/W1 

(B) fl1 = .6, B1 = .12. 

FIGURE 7.- PRESSURE RECOVERY COEFFICIENTS FOR VARIOUS 

RECTANGULAR DIFFUSERS , 
.8 

I 

.7 

"7 100 A --e 

.6 

.5 

r 

28 DATA (REF. 6) ANALYSIS 

----- 

.7 

.6 

.5 

.4 

2 

J 

6 10 14 1/w1 

(D) Mi = 1.0, B1 = .12. 

F IGURE 7. - CONCLUMD. 

18 24 
2. Government Accession No. 1. No. NASA TM-88928 

USAAVSCOH-TR-86-C-36 

4. Tltle and Subtitle 

7. Key Words (Suggested by Authoas)) 

Turbomachine flow; Conical diffuser; 

Rectangular diffuser; Turbulent boundary 

layer; Entrainment method; Compressible 

flow 

A Method for Calculating Turbulent Boundary Layers 

and Losses in the Flow Channels of Turbomachines 

18. Distribution Statement 

Unclassified - unlimited 

STAR Category 02 

7. Author@) 

Lawrence F. Schumann 

9. Security Classlf. (of this report) 20. Security Classif. (of this page) 21. No. of pages 

Unclassified Unclassified 

0. Performing Organization Name and Address 

22. Price' 

NASA Lewis Research Center and Propulsion Directorate, 

U.S. Army Aviation Research and Technology Activity - 

AVSCOH, Cleveland, Ohio 44135 

National Aeronautics and Space Administration 

Washington, D.C. 20546 and U.S. Army Aviation 

Systems Comnand, St. Louis, Ho, 63120 

2. Sponsoring Agency Name and Address 

5. Supplementary Notes 

3. Recipient's Catalog No. 

5. Report Date 

8. Performing Organization Code 

505-62-21 

8. Performing Organization Report No. 

E-3264 

IO. Work Unit No. 

If. Contract or Grant No. 

13. Type of Report and Period Covered 

Technical Memorandum 

14. Sponsoring Agency Code 

Prepared for the 32nd International Gas Turbine Conference and Exhibition 

sponsored by the American Society of Mechanical Engineers, Anaheim, California, 

Hay 31 - June 4, 1987. 

8. Abstract 

An interactive inviscid core flow-boundary layer method Is presented for the 

calculation of turbomachine channel flows. For this method, a one-dimensional 

inviscid core flow is assumed. The end-wall and blade surface boundary layers 

are calculated using an integral entrainment method. The boundary layers are 

assumed to be collateral and thus are two-dimensional. The boundary layer equations are written in a streamline coordinate system. The streamwise velocity 

profiles are approximated by power law profiles. 

for in the streamwise direction but not in the normal direction. Equations are 

derived for the special cases of conical and two-dimensional rectangular diffusers. For these cases, the assumptions of a one-dimensional core flow and 

collateral boundary layers are valid. Results using the method are compared 

with experiment and good quantitative agreement is obtained. 

Compressibility is accounted