I -A .' 

. .. 

I 

I 

I 

I 

I 

I 

I 

LMSC-HEC TR F225800 

Duct Flow Nonuniformities - 

Effect of Struts in SSME HGM II+ 

- Interim Report 

25 January 1988 

Contract NAS8-37359 

(NASA-CR- 179285) DUCT FLOW NON UNIFOR RIT IES : N88-22296 

EFFECT OF STRUTS IN SSHE HGU II[+) Interim 

Report (Lockheed 8issiles and Space Co. 1 

36 P CSCL 20D Unclas 

I 

I G3/34 0137324 

Prepared for I 

I 

1 

I 

I 

I 

I 

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION 

MARSHALL SPACE FLIGHT CENTER, AL 35812 

BY 

Roger Burke 

I h&shs & siplillcle amaaw fmHuntsville Engineering Center 

4000 Bradford Blvd., Huntsville, AL 35007 
 ~~ ~~~ ~ 

 

LHSC-HEC TR F225800 

FOREWORD 

This report documents interim numerical results obtained 

by personnel of the Computational Mechanics Section at 

Lockheed's Huntsville Engineering Center under Contract 

NAS8-37359, "Duct Flow Nonuniformities Study." 

The NASA-HSFC Contracting Officer's Representative for 

this study is Dr. Paul K. McConnaughey, ED32. 

I 

I 

'I 

ii 

0677C 

LOCKHEED-HUNTSVILLE ENGINEERING CENTER 
Section 

FOREWORD 

1 INTRODUCTION 

2 APPROACH 

3 

4 

5 

Figure 

2.1 General Description 

2.2 Multiple-Zone Method 

2.3 Grid 

2.4 Boundary Conditions 

2.5 Turbulence Model 

RESULTS 

CONTENTS 

3.1 Two-Dimensional Computations 

3.1.1 Laminar 

3.1.2 Turbulent 

3.2 Three-Dimensional Computations 

CONCLUDING REMARKS 

REFERENCES 

LIST OF FIGURES 

SSME Powerhead Configuration 

Strut and Post Assembly 

Zonal Boundary Treatment Scheme 

Mesh System Around Two-Dimensional Strut 

Two-Zone Grid Used in Multi-Zone Calculation 

Strut with Upper and Lower Annulus Surfaces 

Mixing Length Regimes for Internal Flow 

~~ ~~ 

LMSC-HEC TR F225800 

iii 

LOCKHEED-HUNTSVILLE ENGINEERING CENTER 

Page 

ii 

1 

4 

4 

4 

7 

9 

11 

15 

15 

15 

19 

22 

29 

32 

Page 

1 

3 

5 

6 

8 

10 

14 
~ 

LHSC-HEC TR F225800 

1 

I 

E 

I 

Figure 

8 

9 

10 

11 

12 

13 

14 

15 

16 

17 

8 

8 

18 

CONTENTS (Concluded) 

Velocity Contours for Two Block Two-Dimensional Simulation 

of Two Struts with (Bottom) and Without Posts 

Static Pressure Contours for Two Block Two-Dimensional 

Simulation of Two Struts with (Bottom) and Without Spacers 

Included 

Velocity Vectors Along Selected Nodal Lines in Region 

Between Two Struts Showing Effect of Spacer Simulation 

Hidway Between Them 

Velocity Vectors Behind Strut for Two-Dimensional Laminar 

Calculation Showing Recirculation Region 

Velocity Contours at Time Step of 1.0 for Two-Dimensional 

Laminar Flow at 10-deg Angle of Attack 

Velocity Contours for Two-Dimensional Turbulent Flow at 

Zero (Top) and 10-deg Angle of Attack 

Velocity Vectors Behind Strut for Two-Dimensional Turbulent 

Flow at Zero (Top) and 10-deg Angle of Attack 

Simulated Oil Flow Streamlines at Upper (Top) and Lower 

Annulus Surf aces 

Particle Traces 

Velocity Vectors Behind Strut Hidway Between Lower and 

Upper Annulus Surf aces 

Computational Grid Showing Revised Geometry 

iv 

LOCKHEED-HUNTSVILLE ENGINEERING CENTER 

Page 

16 

17 

18 

20 

21 

23 

24 

25 

27 

28 

31 
LHSC-HEC TR F225800 

Dlt!KXNU PAGE IS 

POOR QIJALITY 

1. IblTRODUCTIOI 

This study consists of an analysis of flow through the Space Shuttle Main 

Engine (SSHE) Hot Gas Manifold (HGM) for the purpose of understanding and 

quantifying the flow environment and, in particular, the flow through a region 

of structural supports located between the inner and outer walls of the HGH. 

The primary task of the study, as defined by NASA-HSFC, is to assess and 

develop the computational capability of analyzing detailed three-dimensional 

flow through the HGM support strut region to be incorporated into a full fuelside HGH analysis. 

available experimental results. 

Secondarily, computed results are to be compared with 

Figure 1 shows the SSME powerhead configuration. The turbine is run by a 

hot gas, produced in the preburner by burning the fuel at high pressure and 

high temperature. Having performed work on the turbine, this gas enters an 
LWSC-HEC TR F225800 

annular turnaround duct (TAD), which changes the direction of the mean flow by 

180 deg. The gas then passes through an assembly of struts and posts before 

diffusing into a fuel bowl. The gas flows from the fuel bowl into the main 

injector through several transfer ducts. 

flow to be practically incompressible, with a Mach number of less than 0.12. 

The high gas temperature causes the 

A more detailed picture of the strut-post assembly is seen in Fig. 2a, 

which presents an idealized cross-sectional view of the TAD, with the flow 

direction normal to the plane of the paper. 

perspective, with the flow direction in the plane of the paper. 

Figure 2b shows a different 

As a first step toward simulating the three-dimensional viscous, turbulent 

flow in the HGM strut region, two simplified test geometries were investigated, 

and will be the major focus of this interim report. These geometries consist 

of two-dimensional flow around a strut, and three-dimensional flow around a 

strut in an annulus. 

A multi-zone procedure was implemented to calculate two-dimensional laminar 

flow over two struts placed in parallel, with each strut confined to a separate 

computational zone. Details of the approach used to numerically simulate these 

flow fields are contained in Section 2. 

and discussed in Section 3, and concluding remarks are outlined in Section 4. 

Both laminar and turbulent calculations were performed. 

Computational results are presented 

2 

LOCKHEED-HUNTSVILLE ENGINEERING CENTER 
LHSC-HEC TR F225800 

a. Idealized Top View of TAD Strut an9 Post Assembly 

(Flow direction is normal to plane of paper.) 

STRUT POST 

FLOW DIRECTION 

b. View A, with Flow Direction in Plane of Paper 

Fig. 2 Strut and Post Assembly 

3 

LOCKHEED-HUNTSVILLE ENGINEERING CENTER 
LMSC-HEC TR F225800 

2. APPROACH 

2.1 GENERAL DESCRIPTION 

Computations were performed using the INS3D code for incompressible threedimensional flow which was developed by Kwak et al. (Ref. 1). The code solves 

the full three-dimensional incompressible Navier-Stokes equations, using a 

pseudo-compressibility approach to handle the pressure. 

a detailed description of the INS3D methodology. 

Reference 1 provides 

2.2 MULTIPLE-ZONE METHOD 

The calculations in this study were performed on the NASA-Ames Cray X-Np 

418, which has a maximum allowable CPU memory of approximately four million 

words. A full three-dimensional, viscous simulation of the flow in the HGH 

strut region will require more computational mesh points than can be handled 

by this size of storage, thus necessitating the use of a multiple-zone method. 

In this method, the solution is obtained by dividing the computational domain 

of interest into several zones, generating the grid for each zone separately, 

then solving the equations of motion in each zone to update the interior 

points. The points at the interface between zones are updated using a zonal 

boundary treatment which ensures smooth continuation of the solution between 

zones. Various zonal boundary strategies have been proposed (Ref. 2 and 3). 

The approach used in this study consists of a simple double-plane overlapping, 

as described by Chang et al. (Ref. 4) and Holst et al. (Ref. 5). 

As an illustration of the zonal boundary treatment scheme, Fig. 3 shows a 

double-plane overlapping of two zones; the grid points of zone 1 are designated 

by circles, while those of zone 2 are marked by diamonds. 

lines of zone 1 Cj-1 and j) are seen to overlap with the first two lines 

The last two grid 

4 

LOCKHEED-HUNTSVILLE ENGINEERING CENTER 
C 

I 

I 

I 

1 

I 

I 

1 

1 

I 

I 

8 

8 

I 

I 

1 

I 

I 

1 

~ -~ 

LMSC-HEC TR F225800 

: 

Zone 2 

123 

v 

5-2 J-1 J 

Zone 1 

AR-88-022 

Fig. 3 Zonal Boundary Treatment Scheme 

5 

LOCKHEED-HUNTSVILLE ENGINEERING CENTER 
8 

t 

I 

U 

I 

1 

1 

I 

I 

8 

LMSC-HEC TR F225800 

Fig. 4 Mesh System Around Two-Dimensional Strut 

6 

LOCKHEED-HUNTSVILLE ENGINEERING CENTER 
LMSC-HEC TR F225800 

I 

1 

8 of zone 2. 

gration scheme, the values of the variables at the first line of zone 2 are 

set equal to the updated values of line j-1 in zone 1. Next, the interior 

points of zone 2 are computed, and the newly calculated values on line 2 in 

zone 2 are used to update line J in zone 1. 

one-to-one correspondence exists between the nodes in each zone, which will be 

the case for the calculations discussed here. In situations where a coarse 

grid overlaps with a finer grid, an interpolation process is required to carry 

the information from one grid to another (Refs. 4 and 5). Such an interpolation routine will be necessary to multi-block the computational zones 

containing the struts with the relatively lower density grid of the TAD. 

Upon updating the interior nodes of zone 1 using the INS3D inteThis procedure assumes that a 

2.3 GRID 

The test geometry grids used in the calculations presented here were 

generated using the Lockheed algebraic grid generation code. 

strut has a 3:l length-to-width ratio. The distance between struts is four 

strut widths. The turnaround duct (TAD) is modeled as an annulus with an inner 

radius of 6.5 and an outer radius of 8.5 strut wiJths. These dimensions do not 

coincide with those of the strut assembly in the HGH; the actual dimensions 

will be incorporated into the final computations. 

The test geometry 

I 

I 

1 

1 

8 

Figure 4 shows the C-type mesh system around the two-dimensional strut. 

The x-y Cartesian coordinate system is oriented so that x is in the streamwise 

direction. 

lines extending away from the strut. 

calculations is presented in Fig. 5. The two zones are seen to overlap one 

another by a double line of nodes. Computations are first performed on grid 1, 

and then on grid 2, with the zonal interface being treated as discussed 

in Section 2.2. 

There are 201 grid lines wrapped around the strut with 26 grid 

The two-zone grid used in the multi-zone 

7 

LOCKHEED-"TSVILLE ENGINEERING CENTER 
LnSC-HEC TR F225800 

-Zone 1 

It 

Fig. 5 Two-Zone Grid Used in Multi-Zone Calculations 

8 

LOCKHEED-HUNTSVILLE ENGINEERING CENTER 

____________~ ~ 
LMSC-HEC TR F225800 

The grid modeling a three-dimensional strut in an annulus contains 31 

planes in the vertical (z) direction. In each annular plane the grid has the 

same configuration as the two-dimensional grid, resulting in a total of 162006 

grid points for the three-dimensional geometry. 

of the grid in the vicinity of the strut indicating all no-slip surfaces in 

the geometry. 

Figure 6 shows that portion 

For both the two-dimensional and three-dimensional grid the inlet plane 

is located a distance of 12 strut widths ahead of the strut. The exit plane 

is 18 strut widths downstream of the strut trailing edge. 

2.4 BOUNDARY CONDITIONS 

Explicit boundary conditions are used in the calculations. No-slip conditions are applied on the strut and annulus surfaces. The pressure on these 

surfaces is determined by requiring that the normal pressure gradient be zero, 

i.e., 

where ^n represents the direction normal to a wall. 

Conditions for the downstream boundary are the most difficult to provide. 

and they require careful specification to avoid numerical instabilities and 

nonconvergence. 

the manner prescribed by Chang et al. (Ref. 4). In this approach, a secondorder upwind extrapolation is first used to update the velocities normal to 

the exit plane. 

the inlet mass flux. 

velocities is then determined to ensure conservation of momentum flux at the 

outflow. 

The downstream values of pressure and velocity are updated in 

Next, these updated velocities are mass-weighted to conserve 

A new pressure corresponding to these mass-weighted 

9 

LOCKHEED-HUNTSVILLE ENGINEERING CENTER 
LMSC-HEC TR F225800 

ORIGINAC PXGE IS 

OF POOR QUALIm 

Fig. 6 Strut with Upper and Lower Annulus Surfaces 

10 

LOCKHEED-HUNTSVILLE ENGINEERING CENTER 
LHSC-HEC TR F225800 

Periodic boundary conditions are applied at the lateral boundaries to 

simulate the effect of a row of struts, such as exists in the HGM. The posts, 

which are located midway between successive struts (Fig. 2b) are treated as noslip boundary nodes. To date, the posts have been included in two-dimensional 

laminar calculations only. 

pressure and velocity is assumed known and held fixed at the inlet. 

three-dimensional calculation of a strut in an annulus, a uniform static 

pressure is held fixed at the inlet. 

held constant, with the velocity magnitudes being derived from a power law 

formulation in the vicinity of the inner and outer no-slip surfaces. 

For the two-dimensional computations uniform static 

For the 

The velocity profile at the inlet is also 

2.5 TURBULENCE MODEL 

A Baldwin-Lomax turbulence model (Ref. 6) was used to parameterize the 

turbulent shear stresses for the two-dimensional flow around a strut. In this 

approach, an eddy viscosity (p ) is calculated for an inner and an outer 

region. 

Driest formulation 

t 

The eddy viscosity for the inner region is based on the Prandtl-Van 

2 = Pa IWl ( ’ t inner 

where 

and T is the wall shear stress. The magnitude of the vorticity iwl is 

given by 

W 

The eddy viscosity for the outer region is given by 

- 

(’t) - “cp Fwake Fkleb outer 

n 

LI 

wake max max Or ‘wk ‘max ‘dFmax. where F is the smaller of Y F 

11 

(2) 

(5)‘ 

LOCKHEED-HUNTSVILLE ENGINEERING CENTER 
I 

I 

I 

1 

8 

I 

I 

I 

I 

1 

I 

8 

1 

I 

I 

I 

II 

I 

I 

~~ - ~ 

LHSC-HEC TR F225800 

is the maximum value of the expression Fmax 

in a profile and Y is y at that point. Also 

max 

1.0+5.5 ( yCkleb/Ymx) ‘1 Fkleb(Y)= [ 

(6) 

(7) 

The quantity U 

velocity in a given profile. 

values: A+ = 26, C 

is the difference between the maximum and minimum values of d 

The constants are assigned the following 

= 1.6, Ckleb = 0.3, Cwk = 0.25, and K = 0.0168. 

CP 

- -- 

As discussed by Hehta et al.(Ref. 7) the above formulation gives ut = 0.0 

in the wake region when the wake is symmetric, because the Van Driest damping 

function, Eq. (2), depends on the vorticity on the centerline of the wake, 

which has the value of zero. 

the length scale equation to give 

Mehta et al.correct for this error by modifying 

with 

xb 1 + 0.0 if x < 

(X - %)/L otherwise! (9) 

% is the x location of the strut trailing edge, and L is the length of the 

strut. 

In the outer region, the definition of F(y) is replaced by 

The eddy viscosity is determined at every point using Eqs. (2) and (5). The 

smaller of the two values is then used in the governing equations. 

12 

LOCKHEED-HUNTSVILLE ENGINEERING CENTER 
I 

I 

I 

I 

I 

I 

1 

I 

I 

1 

I 

I 

I 

I 

1 

I 

I 

I 

I 

LMSC-HEC TR F225800 

The turbulence model for the flow around a three-dimensional strut in an 

annulus is obtained by combining the Baldwin-Lomax model for flow around a 

two-dimensional strut described above with an approach similar to that of 

Chang et al. (Ref. 4) for flow in the HGH. In their analysis, which did not 

include the presence of struts, Chang et a1 adopted an extended Prandtl-Karman 

mixing length theory, with the mixing length (a) given as 

(11) 

N 

where z = z/d. 

d is some characteristic reference length scale which serves to divide the 

internal flow region into two zones. Figure 7 shows this approach applied to 

a two-dimensional channel flow. The terms d and d are the reference length 

scales measured from wall 1 and wall 2, respectively. In zone 1, d is used in 

Eq. (111, and 2 and z are computed based on wall 1. In zone 2, d is used 

in Equation 11, and 2 and z 

been proposed for 4, including the centerline of the flow domain, location of 

maximum velocity, and location of minimum vorticity (du), which is the length 

scale proposed by Chang et al. 

the reference length scale. 

1 2 

1 + 

2 + 

are computed based on wall 2. Various ideas have 

The calculations presented here also use du as 

The eddy viscosity in the three-dimensional strut in an annulus calculation is calculated first by computing pt according to Eqs. (2) through (101, 

which assumes that the strut is the only length scale. Next, v is computed 

using Eq. (11). which assumes that the upper and lower annulus surfaces are the 

only scales, and ignores the presence of the strut. The smaller of the two 

values of vt is then taken as the final value of the eddy viscosity. 

idea of calculating two separate eddy viscosities and then taking the smaller 

of the two values was applied by Gorski et al. (Ref. 8) to the problem of a 

wing on a single flat plate. 

a strut between two walls. 

t 

This 

It has been extended here to include the case of 

13 

LOCKHEED-HUNTSVILLE ENGINEERING CENTER 
LHSC-HEC TR F225800 

Zone 2 

Zone 1 

c 

Fig. 7 Mixing Length Regimes for Internal Flow 

14 

LOCKHEED-HUNTSVILLE ENGIIEERING CENTER 
I 

I 

I 

1 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

I 

m 

m 

m 

LMSC-HEC TR F225800 

3. RESULTS 

This section presents the laminar and turbulent numerical calculations 

for two-dimensional flow around a strut, and three-dimensional flow around a 

strut in an annulus. 

routine PLOT3D, which was developed at NASA-Ames Research Center (Ref. 9). 

The results were produced using the graphical display 

3.1 TWO-DIMENSIONAL COMPUTATIONS 

Two-dimensional laminar and turbulent computations for flow around a strut 

were performed. The Reynolds number (based on strut width) was 500 for the 

6 laminar case and 1.9 x 10 for the turbulent case. 

calculations was to work out errors in the boundary and initial condition 

routines, experiment with the Baldwin-Lomax turbulence model, and develop the 

capability to perform multi-block calculations, which will be necessary in 

simulating the flow in the complete three-dimensional HGM strut region. 

The main purpose of these 

3.1.1 Laminar 

Figures 8 and 9 present velocity and pressure contours for a two-zone 

laminar calculation of flow around two struts, with each zone representing one 

strut. Two cases are considered, one without posts between the struts, and 

one where the posts are included. 

zero degrees. 

The angle of incidence in both cases is 

As discussed previously, the posts are simulated by treating two lines 

of nodes on the overlapping nodal planes as no-slip boundary nodes. Velocity 

vectors in the region of a post treated in this manner are presented in Fig. 

10. 

15 

LOCKHEED-HUNTSVILLE ENGINEERING CENTER 
MSC-HEC TR F225800 

Fig. 8 Velocity Contours for Two Block Two-Dimensional Simulation 

of Two Struts with (Bottom) and Without Posts 

16 

LOCKHEED-HUNTSVILLE ENGINEERING CENTER 
LMSC-HEC TR F225800 

Fig. 9 Static Pressure Contours for Two Block Two-Dimensional Simulation 

of Two Struts with (Bottom) and Without Spacers Included 

17 

LOCKHEED-HUNTSVILLE ENGINEERING CENTER 
LMSC-HEC TR F225800 

I 

E 

I 

I 

I 

I 

I 

B 

m 

Fig. 10 Velocity Vectors Along Selected Nodal Lines in Region Between Two 

Struts Showing Effect of Spacer Simulation Midway Between Them 

18 

LOCKHEED-"TSVILLE ENGINEERING CENTER 
LMSC-HEC TR F225800 

Periodic boundary conditions are applied at the outer lateral boundaries 

of each zone to simulate the effect of a row of struts, or struts alternating 

with posts. 

periodic nature, with a period length of four strut widths. 

The results in Figure 8 and 9 are seen to exhibit the expected 

Velocity vectors in the region immediately behind the strut, for the case 

without posts, are shown in Fig. 11. Two symmetric recirculation regions have 

developed, one on either side of the strut centerline. The length of the recirculation region is approximately two and a half strut widths. 

The calculations discussed so far have been for zero angle of incidence. 

In addition to this, single block computations around a strut were performed 

with a 10-beg angle of attack. 

unsteady; this can be seen in Fig. 12, which shows the velocity contours at 

non-dimensional time step intervals of 1.0. Results at a Reynolds number of 

SO did not display this unsteady appearance. 

Results to date indicate that the flow is 

3.1.2 Turbulent 

6 Single block turbulent computations (Re = 1.9 x 10 1 around a twodimensional strut were performed at zero and 10-deg angle of incidence. 

Baldwin-Lomax turbulence model was used to parameterize the turbulent shear 

stresses. Periodic boundary conditions were applied at the lateral boundaries. 

The grids used in the laminar computations discussed above were modified to 

obtain a finer resolution near the strut surface. The average value of y 

at the first line of nodes above the strut was approximately ten. A more 

refined grid would undoubtedly have provided better resolution of the nearsurface flow field. However, as mentioned previously, the main purpose of the 

two-dimensional computations was to experiment with the implementation of 

various aspects of the numerical procedure as a first step toward the complete 

three-dimensional flowfield simulation. As such, a value of y = 10 is 

considered adequate for present purposes. 

A 

4- 

+ 

19 

LOCKHEED-HUNTSVILLE ENGINEERING CENTER 
t 

I 

I 

1 

I 

1 

I 

I 

I 

R 

E 

8 

I 

I 

8 

8 

I 

I 

I 

LMSC-HEC TR F225800 

--/ -- 

Fig. 11 Velocity Vectors Behind Strut for Two-Dimensional 

Laminar Calculation Showing Recirculation Region 

20 

LOCKHEED-HUNTSVILLE ENGINEERING CENTER 
LMSC-HEC TR F225800 

Fig. 12 Velocity Contours at Time Step of 1.0 for Two-Dimensional 

Laminar Flow at 10-deg Angle of Attack 

21 

LOCKHEED-HUNTSVILLE ENGINEERING CENTER 
LHSC-HEC TR F225800 

V+@ure 13 shows the velocity contours around a strut for zero and 10-deg 

angle-of-attack. 

cases is presented in Fig. 14. The size of the recirculation region is 

considerably smaller than for the laminar case (Fig. 11). As compared with 

the laminar 10-deg angle-of-attack results, the turbulent 10-Beg angle-ofattack results did not show any noticeable unsteadiness in the velocity 

contours. 

Velocity vectors in the near wake region for each of these 

3.2 THREE-DIMENSIONAL COMPUTATIONS 

6 Laminar (Re = 500) and turbulent three-dimensional (Re = 1.9 x 10 1 

calculations were performed to simulate the three-dimensional flow around a 

strut in an annulus, as shown in Fig. 6. This kind of flow, which occurs when 

an obstruction is placed within an approaching boundary layer, is typically 

referred to as wing-body junction or corner flow. 

feature is a horseshoe vortex system that is caused by steep adverse pressure 

gradients set up at the junction of the obstruction (in this case the strut) 

and the body (i.e., the annulus). As a result of these pressure gradients, 

the vorticity in the oncoming boundary layer wraps around the obstruction in a 

characteristic horseshoe shape, with each leg having vorticity of opposite 

rotational sense. 

Perhaps its most dominant 

Both the laminar and turbulent results displayed essentially the same 

flowfield features, including the presence of the characteristic horseshoe 

vortex system. Because of this, and because of their greater relevance to the 

HGH flow field, only the turbulent computations will be discussed here. 

average value of y on the first plane of grid points above the strut was 

approximately seven. On the lower and upper annulus surfaces the average 

value was about 1.5. 

The 

+ 

Figure 15 shows simulated oil flow lines on the lower and upper annulus 

surfaces, respectively. The oil flow lines are seen to diverge and wrap around 

the strut in the characteristic horseshoe shape. 

horseshoe vortex system for the lower annulus surface is about the same as that 

of the upper surface. 

The size and shape of the 

22 

LOCKHEED-HUNTSVILLE ENGINEERING CENTER 
~~ 

LMSC-HEC TR F225800 

Fig. 13 Velocity Contours for Two-Dimensional Turbulent Flow 

at Zero (Top) and 10-deg Angle of Attack 

23 

LOCKHEED-HUNTSVILLE ENGINEERING CENTER 
LMSC-HEC TR F225800 

-- f 5 

U 

Fig. 14 Velocity Vectors Behind Strut for Two-Dimensional Turbulent 

Flow at Zero (Top) and 10-deg Angle of Attack 

24 

LOCKHEED-HUNTSVILLE ENGINEERING CENTER 
LHSC-HEC TR F225800 

11 E 

I 

-IS -i.o +'.s io 6.5 i.r i.s L U 

Fig. 15 Simulated Oil Flow Streamlines at Upper (Top) 

and Lower Annulus Surfaces 

25 

LOCKHEED-HUNTSVILLE ENGINEERING CENTER 
LHSC-HEC TR F225800 

BLgure 16 presents particle traces for particles released at various 

ahead of the strut. Two spiraling vortex systems are observed behind 

the strut; one system is associated with the lower annulus surface, and the 

second with the upper surface. 

is due to the asymmetry of the annulus geometry. 

been found for laminar flow of a cylinder on a flat plate (Ref. 10). 

The difference in size between the two systems 

A similar phenomenon has 

Velocity vectors in the near-wake region of the strut midway between the 

annulus walls are presented in Fig. 17. The size of the recirculation region 

is approximately the same as for the turbulent flow around a two-dimensional 

strut, discussed earlier in Section 3.1. 

26 

LOCKHEED-HUNTSVILLE ENGINEERING CENTER 

~~~ 
I 

8 

I 

1 

I 

I 

9- 

IN 

~~~~ 

LHSC-HEC TR F225800 

Fig. 16 Particle Traces 

27 

LOCKHEED-HUNTSVILLE ENGINEERING CENTER 
1 

I 

~~ ~- 

LHSC-HEC TR F225800 

1 

I 

Fig. 17 Velocity Vectors Behind Strut Midway Between 

Lower and Upper Annulus Surfaces 

28 

LOCKHEED-HUNTSVILLE ENGINEERING CENTER 
USC-HEC TR F225800 

4. CONCLUDING REHARKS 

'Chis interim report has presented a numeral study, using the IWS3D flow 

solver, of laminar and turbulent flow around two-dimensional strut, and threedimensional flow around a strut in an annulus. 

used to calculate two-dimensional laminar flow around two struts in parallel, 

with each strut represented by one computational block. 

lations were performed for turbulent flow around a two-dimensional strut, 

using a Baldwin-Lomax turbulence model to parameterize the turbulent shear 

stresses. 

A multi-block procedure was 

Single block calcuA modified Baldwin-Lomax model was applied to the case of a threedimensional strut in an annulus. The results displayed the essential features 

of wing-body flows, including the presence of a horseshoe vortex system at the 

junction of the strut and the lower annulus surface. A similar system was 

observed at the upper annulus surface. 

The test geometries discussed here were useful in developing the capability to perform multiblock calculations, and to simulate turbulent flow 

around obstructions located between curved walls. Both of these skills will 

be necessary to model the three-dimensional flow in the strut assembly of the 

SSME . 

Work is now in progress on performing a three-dimensional two block 

turbulent calculation of the flow in the turnaround duct (TAD) and strutlfuel 

bowl juncture region. The grid for the TAD will comprise one computational 

zone and will be joined, using a two-plane overlap multiblock technique, to 

the strut/bowl grid, which will be a second computational zone. 

will be considered with periodic boundary conditions to simulate a row of 

Only one strut 

29 

LOCKHEED-HUNTSVILLE ENGINEERING CENTER 
LMSC-HEC TR F225800 

stmtg. 

vpFi(rk$,on of the cross-sectional area aft of the strut. 

shown in Fig. 18, which presents the revised strut grid. Later computations 

will incorporate a more detailed simulation of the fuel bowl, as well as the 

effect of the transfer ducts. 

As a first step, the fuel bowl will be simulated by a streamwise 

This variation is 

30 

LOCKHEED-HUNTSVILLE ENGINEERING CENTER 
LMSC-HEC TR F225800 

31 

9 

-0 

LOCKHEED-HUNTSVILLE ENGINEERING CENTER 
LMSC-HEC TR F225800 

5. REFERENCES 

1. Kwak, D., J.L.C. Chang, S.P. Shanks, and S.R. Chakravarthy, "A ThreeDimensional Incompressible Navier-Stokes Flow Solver Using Primitive 

Variables," AIM Journal, Vol. 24, 1986, pp. 390-396. 

2. Hessenius, K.A., and M.M. Rai, "Applications of a Conservative Zonal 

Scheme to Transient and Geometrically Complex Problems," Computers and 

Fluids, Vol. 14, No. 1, 1986, pp. 43-58. 

3. Walters, R.W., J.L. Thomas, and G.F. Switzer, "Aspects and Applications of 

Patched Grid Calculations," AIM 86-1063, AIM/ASME 4th Fluid Mechanics, 

Plasma Dynamics and Lasers Conference, Atlanta, Ga., 12-14 May 1986. 

4. Chang, J.L.C., D. Kwak, S.C. Dao, and R. Rosen, "A Three-Dimensional 

Incompressible Flow Simulation Method and Its Application to the Space 

Shuttle Main Engine, Part I - Laminar Flow," AIM-85-0175, AIM 23rd 

Aerospace Sciences Meeting, Reno, 14-17 January 1985. 

5. Holst, T.L., U. Kayivak, K.L. Gundy, S.D. Thomas, J.L. Flores, and N.M. 

Chanderjian, "Numerical Solution of Transonic Wing Flows Using an Euler/ 

Navier-Stokes Zonal Approach," AIM-85-1640, AIM 23rd Aerospace Sciences 

Meeting, Reno, 14-17 January 1985. 

6. Baldwin, B.S., and H. Lomax, "Thin Layer Approximation and Algebraic Model 

for Separated Turbulent Flows," AIM Paper 78-257, Huntsville, Ala., 

January 1978. 

7. Mehta, U., K.C. Chang, and T. Cebeci, "A Comparison on Interactive Boundary 

Layer and Thin-Layer Navier-Stokes Procedures," Numerical Physical Aspects 

of Aerodynamic Flows 111, ed. T. Cebeci, Springer-Verlag, 1986. 

8. Gorski, J.J., T.R. Govindran, and B. Lakshminarayana, "Computation of 

Three-Dimensional Turbulent Shear Flows in Corners," AIM Journal, Vol. 

23, NO. 5, 1985, pp. 685-692. 

9. Buning, P.G. and J.L. Steger, "Graphics and Flow Visualization in Computational Fluid Dynamics," Proceedings of the AIM 7th Computational Fluid 

Dynamics Conference, Cincinnati, 1985. 

10. Kaul, U.K., D. Kwak, and C. Wagner, "A Computational Study of Saddle Point 

Separation and Horseshoe Vortex Systems," AIM-85-0182, AIM 23rd Aerospace Sciences Meeting, Reno, 14-17 January 1985. 

32 

LOCKHEED-HUNTSVILLE ENGINEERING CENTER