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FINAL REPORT 

ANALYSIS OF INTERNAL FLOWS 

RELATIVE TO THE SPACE SHUTTLE 

MAIN ENGINE 

30 December 1987 

Contract NAS8-35984 

Prepared for 

NATIONAL 

BY 

AERONAUTICS AND SPACE ADMINISTRATION 

MARSHALL SPACE FLIGHT CENTER, AL 358 12 

4800 Bradford Blvd., Huntsville, AL 35807 
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FOREWORD 

This report was prepared by personnel of the Computational 

Mechanics Section of Lockheed's Huntsville Engineering Center. 

It constitutes final documentation of efforts performed under 

Contract NAS8-35984 for NASA-Marshall Space Flight Center. 

The NASA-MSFC Contracting Officer's Representative for 

this research study was Hr. G.A. Wilhold, ED31. 

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Section 

FOREWORD 

1 GENERAL DESCRIPTION 

2 CFD CAPABILITIES DEVELOPMENT 

2.1 Introduction 

2.2 Code Description 

2.3 Code Modification 

2.4 Test Case Results 

3 LOX MANIFOLD ANALYSIS 

3.1 Introduction 

3.2 Two-Phase Oxygen FLOW 

3.3 Solution Methods 

3.4 The COBRA/TRAC Code 

3.5 Propellant Properties 

4 SUMMARY AND CONCLUSIONS 

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CONTENTS 

5 REFERENCES 

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1. INTRODUCTION 

One of the problem areas in the design of the Space Shuttle Main Engine 

(SSNE) is in the second stage rotor in the high pressure fuel turbopwnp 

(HPFTP). Cracks have developed on the blade shank, apparently due to thermal 

stresses generated by strong thermal gradients. It is generally believed that 

the offending thermal gradients are caused by cold liquid hydrogen flowing 

directly over, and thus over-cooling, the aft side of the shank. A schematic 

of the current second stage rotor and platform seal region is shown in Fig. 

1-1. The cold liquid hydrogen flows through the labyrinth seal into the 

cavity on the aft side of the second stage rotor and through the gap between 

the blade platform and platform seal, thus strongly cooling the aft side of 

the blade shanks. A proposed remedy for this problem is to divert the cold 

flow away from the blade shank region by means of a mechanical barrier or by 

providing a bypass for the cold flow through the labyrinth seal. A possible 

flow diverter and coolant bypass configuration is shown in Fig. 1-2. 

The primary objective to the first task originally described by NASA-MSFC 

was to perform a three-dimensional CFD analysis for the flow environment in 

the region shown in Fig. 1-1 as well as that in Fig. 1-2, showing the base 

line flow diverter configuration, and to compare these results. Subsequently 

alternate diverter geometries were to be investigated to determine the optimum 

system design. 

A second distinctly different task was to perform an unsteady, threedimensional liquid oxygen (LOX) manifold analysis to describe the flow and 

phase distribution of oxygen as the main oxidizer value to the fuel preburlrdL 

is opened. A CFD model would be provided for accurate description of the twophase flow of oxygen in these passages so that the unsteady flow rates through 

the preburner injection elements can be simulated. 

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Fig. 1-1 Schematic of SSME Fuel Side Second Stage 

Turbine Rotor REgion and Coolant Flow 

Fig. 1-2 Schematic of SSUE Fuel Side Second Stage Turbine Rotor 

Region Showing Modified Aft Platform Seal with Flow 

Diverter and Coolant Bypass 

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Shortly after commencement of efforts on the flow diverter task described 

above, NASA-HSFC engineers abandoned the flow diverter concept. The contracting officer's representative for this contract redirected efforts as 

follows. 

the Lockheed Computational Mechanics staff cooperate with the SSHE computational staff at NASA-HSFC in developing and providing for NASA numerical capabilities for accurate analysis of much of the internal flows related to the 

SSHE. 

CFD techniques should be used, which appropriate CFD codes are available, and 

what modifications to the codes would be necessary for application to the SSHE 

problem. Efforts and results for this redirected work are described in 

Section 2 of this report. 

In lieu of performing the flow diverter analysis it was directed that 

This would involve consulting with the NASA CFD personnel as to which 

Efforts under the LOX manifold task were performed under a subcontract to 

the Software Engineers Consultants, Analysis (SECA) engineering firm of 

Huntsville, Ala. Description of work performed under this subcontract is 

described in Section 3 of this document. 

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2. CFD CAPABILITIES DEVELOPMENT 

2.1 INTRODUCTION 

Since the Mach number for most of the internal fluid flows to the SSME are 

below 0.2, it was decided, by the Contracting Officer's Representative, that an 

incompressible Navier-Stokes flow solver is the appropriate methodology to seek 

in a CFD code. An additional requirement is that the discrete solver in the 

code be implicit in nature. 

boundary effects which could be responsible for undesirable separation and recirculation regions. 

tional grid points are placed very close to the walls. 

nodal spacing would adversely affect the usefulness of an explicit code 

because of the CFD limitation. 

This is important for proper resolution of viscous 

Such phenomena are more accurately detected when computaThis extremely small 

Several numerical methods have been developed (Refs. 1 through 6) to solve 

the incompressible Navier-Stokes equations in three-dimensional body-fitted 

coordinate systems. That which differs in these methodologies is the procedure for finding the pressure field so that the flow field is as close to 

divergence-free as possible. 

culty in solving incompressible flow problems numerically. The techniques of 

Refs. 1, 2, and 3 employ the pseudocompressibility approach. This is a timeiterative scheme which generates the pressure field so that the continuity 

equation is satisfied when a steady state solution is reached. 

employed in Refs. 4, 5, and 6 utilize a successive pressure-velocity correction 

scheme for ensuring that the continuity equation is satisfied. 

equation for pressure correction is used which is derived approximately froAh& 

both the continuity and momentum equations. 

(Semi-Implicit Method for Pressure-Linked Equations). 

Satisfying this requirement is the main diffiMethods 

Here a Poisson 

They are called SIMPLE methods 

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Much information was gathered from the scientific literature and individuals with experience in using codes based on both of these solution techniques. In general it was found that for similar FORTRAN coding structures 

the speeds, in CPU seconds per iteration per node, for both is comparable. A 

fundamental difference between the pseudocompressibility and the SIHPLE codes 

is that the former uses finite difference techniques whereas the latter uses 

finite or control volume techniques. This difference allows the pseudocompressiblity coding to be much less storage intensive. 

reason that this approach was selected as the one to pursue. 

It was for this 

2.2 CODE DESCRIPTION 

Much success (Refs. 7 and 8) had been enjoyed by the INS3D (Ref. 3) code. 

Thus it was the one chosen to obtain, learn, modify, and apply to SSME internal 

flowfield investigations. A basic unedited flow solver version of the INS3D 

source code was obtained from NASA-Ames. This version provides for inclusion 

of a turbulence model subroutine but does not contain one. At the time the 

code was acquired no user's manual was available but one has subsequently been 

documented (Ref. 9). This NASA document contains a detailed description of 

the code and its methodology. We present here a very brief description. 

0 INS3D is a three-dimensional fluid dynamics code for computing steady 

state incompressible flow fields in arbitrary fixed geometries. 

finite difference solution procedure employs an implicit, approximate 

factorization scheme (Refs. 10 and 11) to solve the three-dimensional 

Navier-Stokes equations in primitive variables form. 

The 

0 The formulation uses a three-dimensional coordinate transformation 

from Cartesian to general curvilinear coordinates. 

solution is based on the pseudocompressibility method. 

stresses are uncoupled from the implicit scheme and are lagged by one 

time step to facilitate implementing any form of eddy viscosity 

turbulence model which the user chooses. 

admissible are no slip, inflow, outflow, and periodic. 

The pressure 

The Reynolds 

Explicit boundary conditions 

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INS3D has been verified by computing fundamental fluid dynamics problems 

such as the flow through a channel (Ref. 3), flow over a backward-facing step 

(Ref. 121, and flow over a circular cylinder (Refs. 3 and 12). Threedimensional cases include flow over an ogive cylinder (Ref. 131, flow through 

a rectangular duct (Ref. 3). wind-tunnel-inlet flow (Ref. 141, cylinder-wall 

juncture flow, and flow through multiple posts mounted between two plates 

(Refs. 15 and 16). 

This is a very robust Navier-Stokes solver but is by no means designed to 

be a general code to be used by the uninitiated for application to an arbitrary 

problem. 

application to symmetry boundaries. 

to the code are required, and as mentioned previously, the user must supply an 

eddy viscosity subroutine for turbulence modeling. 

Grid generation is user supplied as are flow field initialization and 

For multiple zoning major modifications 

2.3 CODE MODIFICATION 

Several modifications were implemented into the basic INS3D source code 

obtained from NASA-Ames, of these only two are of significance to be reported 

here. 

A subroutine for determining the value of the eddy viscosity at each node 

was added. Because of the convoluted geometries generic to the internal SSME 

structure a simple algebraic model was chosen. In much of the flow passages 

strong curvature effects are present, and as a result of the rapid turning of 

the fluid, the balance between strong pressure gradients and centrifugal 

forces dominate the evolution of the flow. It follows that although turbulent 

mixing is present it plays a secondary role in the physics of what is 

happening. It thus appears that the accuracy of the numerical technique used 

for solving the fluid dynamic equations is of paramount importance and will 

yield reliable predictions even with a relatively simple turbulence model. 

The particular model chosen (Ref. 17) is a Prandtl-Van Driest mixing 

length type in which the eddy viscosity is proportional to the local vorticity. 

The mixing length is a function of the distance from a wall, and for the types 

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of channel flows of relevance here, of the distance to the position of minimum 

vort.icity. This kind of turbulence model is not difficult to code and has 

demonstrated surprisingly good agreement with experimental measurements in 

geometries like those found in the SSME (Ref. 18). 

A second modification effected to the basic INS3D source code was an 

explicit multi-zone or multi-block procedure. 

is true for most codes, is structured such that computations are preformed in 

a transformed curvilinear coordinate space, where the range of all three coordinates is from zero to one. Thus the calculations are actually done on a 

three-dimensional cube or block. 

tations performed on two or more such blocks while preserving the physics 

which needs to be communicated between blocks or zones. 

The methodology of the code, as 

Multi-blocking is a method of linking compuThe procedure adopted is an explicit method (Ref. 7) which works well for 

subsonic flows and lends itself to straight forward coding. The actual coded 

scheme assumes that at least two planes of nodes in connected zones be in 

common. 

directions for both zones must be coincident. If positions of nodes in these 

two planes for each zone are not coincident in the remaining curvilinear 

directions, linear interpolation between nearest neighbors is used to obtain 

flow variables from one zone to the other. 

In each plane the nodal distribution in one of the curvilinear 

Giving the forgoing geometric requirement the solution methodology is 

simple. 

to time step N in Zone 1 flow variables are either transferred or interpolated 

to the inlet coincident plane of Zone 2. 

the time step sweeping in Zone 2. After this is done, flow variables are 

obtained on the second common plane of Zone 1 from a similar equating or interpolating procedure. 

reached in both zones. Typically, the two-block procedure requires front A 5 

to 2.0 times the number of numerical iterations as would be required if both 

zones were solved as a single block. 

For a two-zone computation the following would be used. Subsequent 

These values are held fixed during 

This process is repeated until a converged solution is 

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2.4 TEST CASE RESULTS 

Initial computations performed with the INS3D code were accomplished 

using the CRAY-XHP at the NASA-Ames research facility. Subsequently, NASA-HSFC 

obtained its own CRAY-XHP and we were required to transfer the code to HSFC and 

devote the necessary time required to get INS3D operational on this system. 

Accomplishing this task demanded considerable effort because of differences in 

the front end machine and comunications network. 

A two-dimensional geometry was generated having the dimensions of the 

FHOF version of the SSME/HGH fuel side turnaround duct. The computational 

grid, shown in Fig. 2-1, contained 3861 nodes and employed a grid stretched to 

both walls. This grid was used for almost all of the test cases, both laminar 

and turbulent, single and multi-block. 

Results for laminar flow at a Reynolds number of 1,000 are presented in 

Fig. 2-2. Because of the two-dimensional nature of this flow the fluid is 

seen to accelerate near the inner wall around the turn and a large separated 

region is seen to have developed on the downstream side of the turn. 

results can be compared to those for a turbulent flow computation at a 

Reynolds number of 1,000,000 using the turbulence model described in Section 

2.2. These results are displayed in Fig. 2-3. 

These 

Multi-blocking test cases were first performed on a grid with the same 

nodal distribution as shown in Fig. 2-1 but used as a straight two-dimensional 

duct or channel. The two overlapped planes between the two zones was placed 

at mid-channel. Results of this computation are compared in Fig. 2-4. Both 

single and multi-block computations were carried to the same level of convergence. 

Additional multi-blocking experiments were carried out using the turnaround 

duct geometry where the two overlapped planes from each block or zone wert: 

placed in the most precarious position just at the end of the 180-deg turn. 

These results are displayed for comparison in Figs. 2-5 through 2-9. 

There is essentially no discernable difference in the results. 

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Fig. 2-1 Two-Dimensional Computation Grid for Testing 

Modifications Made to INS3D Code 

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/ 

Fig. 2-3 Velocity Vectors (Top), Velocity Magnitude Contours, 

and Static Pressure Contours (Bottom) for Turbulent 

Flow at Re = lo6 Using INS3D 

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SINGLE BLOCK TWO BLOCK 

Fig. 2-4 Comparison of Velocity Vectors and Velocity Contours 

for Single and Multi-Block Cases in Straight Duct for 

Laminar Flow at Re = 500 with Blocking at Mid Channel 

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SINGLE BLOCK 

TWO BLOCK 

Fig. 2-5 Comparison of Velocity Vectors for Single and Multi-Block 

Cases in 2-D Turnaround Duct for Laminar Flow at Re = 500 

with Blocking at Downstream Position of 180-deg Turn 

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Fig. 2-6 Comparison of Velocity Contours for Single and Multi-Block 

Cases in 2-D Turnaround Duct for Laminar Flow at Re = 500 

with Blocking at Downstream Position of 180-deg Turn 

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SINGLE BLOCK 

TWO BLOCK 

Fig. 2-7 Comparison of Pressure Contours for Single and Hulti-Block 

Cases in 2-D Turnaround Duct for Laminar Flow at Re = 500 

with Blocking at Downstream Position of 180-deg Turn 

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TAD PRESSURE COEFFICIENT 

ALONG INNER 8 OUTER WALL 

SINGLE ZONE CFISE 

1200 ITERATIONS 

0 - INNER HALL 

0 - OUTER WALL 

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0 1.0 2.0 3.0 1.0 5.0 6.0 7.0 8.0 9.0 10.0 

DISTRNCE ALONG INNER 8 OUTER HALL 

Fig. 2-8 Single Block Results for the Linear Distribution 

of Pressure Along Inner and Outer Wall of 2-D 

Turnaround Duct for Case of Re = 500 

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0 - INNER WALL 0 - OUTER WALL 

Fig. 2-9 Multi-Block Results for the Linear Distribution 

of Pressure Along Inner and Outer Wall of 2-D 

Turnaround Duct for Case of Re = 500 

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The static pressure distribution for any of these calculations is the 

most sensitive diagnostic for convergence as well as for comparison of 

solutions. Thus we present in Figs. 2-8 and 2-9 a plot of the pressure along 

the inner and outer wall for both single and two-block computations. The two 

curves for each lie directly on top of each other. 

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3. LOX MANIFOLD ANALYSIS 

3.1 INTRODUCTION 

The preburners of the Space Shuttle Main Engine still experience serious 

problems with respect to cracking of LOX posts and the frisbee in the inlet 

manifolds. 

blade cracking in the high pressure fuel turbopump. 

these problems is the extreme thermal environments caused by startup and shutdown of the engine. A detailed transient analysis of these flows is necessary 

in order to help alleviate these problems. 

Operation of the fuel preburner creates flows which cause turbine 

The most likely cause of 

Operation of the fuel preburner is initiated by opening propellant control 

valves and igniting the flow with the augmented spark igniter (ASI). 

figuration of the FPB is shown in Fig. 3-1. The flow passage from the fuel 

preburner oxidizer valve (FPOV) into the oxidizer manifold above the interpropellant plate is shown in this figure, and a cross-sectional view of this 

passage is presented in Fig. 3-2. The oxidizer flow to the AS1 is supplied 

from a bleed line from the FPOV. The FPOV is shown in Fig. 3-3. The valves 

which control this flow are shown schematically in Fig. 3-4; notice that there 

is not a separate fuel control valve for each preburner. 

and oxidizer manifolds enter the FPB combustor through the injector faceplate, 

the layout of which is shown in Fig. 3-5. These figures were taken from Refs. 

19 and 20. 

The conFlows from the fuel 

The object of this study was to perform an unsteady, three-dimensional 

LOX manifold analysis to describe the flow and phase distribution of oxygen as 

the main oxidizer valve to the FPB is opened. 

model was developed to describe the filling and chill down of the LOX manifold. 

A computational fluid dynamics 

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ORIGINAL PAGE IS 

OB POOR QUAWTY 

AS1 INJECTORIC1IAMRER~ AS, n 

FROhl PRI:I3URNER 

FUEI. SUPI’1,Y DUCT 

I N T E R P R O PE LLA 

ELEMENTS (264) 

CIA N IF0 I,D 

I N T ER I:A C I: 

(WELDED ) 

PRERURNER LINER 

EXTENSION 

TO IIICtI-PRESSURE FACE PLATE 

I‘UEI, TURHOI’UMI’ 

AND 1IO‘l’-CAS MANIF0I.D 

Fig. 3-1 SSME Fuel Side Preburner Configuration 

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POOR QUALITY 

Fig. 3-2 Schematic for Cross-Section of Flow Passages of LOX Through 

Manifold and Interpropellant and Plate Above Fuel Side Preburner 

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ORIGINAL PAGE r% 

D! PooR QUALWY 

Sealing System 

,am-.-, 

Fig. 3-3 SSME Fuel Preburner Oxidizer Valve Assembly and Sealing System 

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$243 ,POOR QUALITY 

low Pressure Low Preuuri OKldlxer 

OKldkOf Preburner 

Fuel Preburner 

Chamber Coolanl Valve (HPOTP) 

Fig. 3-4 SSME Schematic Showing Entire Gas FLOW Path 

and Positions of Fuel and Oxidizer Control Valves 

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ORIGINAL PAGE IS 

DE POOR QUALIX 

Hydrogen Injection Holes Primary Inject ion Elernen t 

Fig. 3-5 Schematic of SSHE Fuel Preburner Injection Faceplate Layout 

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Downstream boundary conditions were established to couple the manifold flow to 

the preburner flow so that the simultaneous operation of these two components 

could be simulated. 

necessary so that the unsteady flow rates through the injectors can be simulated. 

Detailed modeling of the phase state of the oxygen is 

This report described the results of this study. 

3.2 TWO-PHASE OXYGEN FLOW 

The initial transient flow of LOX into the oxidizer manifold involves the 

flow of a cryogenic liquid into motor hardware at ambient temperature, hence 

the initial oxidizer flowing into the fueled preburner is GOX. 

matically model this two-phase flow process, the individual phase conservation 

equations written in the conventional manner for each point in space must be 

volume and time averaged. Whitaker (Ref. 21) and Slattery (Ref. 22) have presented a rigorous derivation of such equations for the simultaneous description 

of three phases. 

phase and surface balance equations to describe interfacial transfer. Ishii 

(Ref. 23) and others have presented suitably averaged equations for two phases 

as a "two-fluid model." 

phases, a simplified "diffusion model" is obtained. Particulate flow in solid 

rocket motor plumes is modeled with a diffusion model. 

(Ref. 24) have corrected the pressure terms in Ishii's derivation to arrive at 

the equation set given below. These equations implicitly include the interfacial area separating the two phases. 

sufficient to predict such topological information. For the present, 

empirically determined flow regimes must be postulated to describe flow 

topology. The governing equations are stated as follows: 

To matheThe equation set consists of conservation equations for each 

If the flow is dilute with respect to one of the 

Harlow and Amsden 

Current modeling capabilities are not 

(ai di V.} -1 t + (a. 1 di Vi Vi}a + ai {P}R = Mi - Fi 

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where i = vapor, liquid; a is the volume fraction of the phase, d is density; 

V_ is velocity vector; e is internal energy; P is pressure. Braces with 

subscripts indicate appropriate partial differentiation with respect to the 

subscript, t for time or R for the position vector. 

exchange of mass and energy, respectively. Momentum exchange is separated 

into a part due to mass exchange, H, and a part due to friction and other 

forces, F. The interfacial exchange terms are functions of the principal 

variables and the interfacial area. 

functions is not critical to the solution method used to solve the equations, 

hence many representations of transport may be modeled. The only limitation 

is that these exchange rates vary slowly with respect to the inviscid terns on 

the left-hand side of the equations. 

control the complexity required of the numerical solution. 

has been recently reviewed by Stewart and Wendroff (Ref. 25). 

G and L are interfacial 

The exact specification of the exchange 

The left-hand side of the equations 

Such methodology 

A solution of ten equations is required for a three-dimensional problem; 

one for each phase for energy and the three momentum equations, one for the 

volume fraction of one phase (the volume fractions must sum to unity), and one 

for pressure (implying a thermal equation of state for the mixture). 

time scales associated with specific classes of physical behavior must be considered in obtaining numerical solutions; these scales characterize interphase 

exchanges, sonic propagation, and fluid convection. Filling of the LOX manifold may be assumed to have interphase exchanges and pressure propagations 

which are in equilibrium with convective phenomena controlling the flow. 

Stewart and Wendroff's review identified two codes as being very useful for 

this type of problem: the TRAC code of Liles and Reed (Ref. 26) and an 

approximate implicit code developed by Spalding which is used in the PHOENICS 

code (Ref. 27). The method of Liles and Reed will be further evaluated for 

application to the LOX manifold filling analysis because it has been widely 

used in the nuclear industry. 

cretizations on staggered grids. Algebraic manipulations of the conservation 

equations and linearizations of the difference equations result in a pressure 

equation which contains all of the spatial coupling in the code. 

pressure values are obtained the remaining variables are simply calculated. 

Three 

The TRAC code uses finite difference disOnce updated 

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Current versions of this program are available from Los Alamos National 

Laboratory and are being requested through NASA. 

will be discussed in Section 4 of this report, but first other solution 

methods will be presented. 

Further details of this code 

3.3 SOLUTION HETHODS 

If there were no velocity lag between the phases, it was shown by Stewart 

and Wendroff that the mixture sound speed is less than that of either of the 

pure phases. This implies that a computational fluid dynamic method which is 

efficient for either compressible or incompressible flow could be expected to 

solve the two-phase flow equations. 

istic directions based on sonic velocity of the fluid to determine an integration algorithm, and since ALFA is currently being developed to treat both 

compressible and incompressible flow, the code should also solve the two-phase 

Since SECA's ALFA code utilizes characterflow equations, even when there is velocity lag. The TRAC code has been 

requested by NASA but is not yet available to SECA; therefore, the ALFA code 

was evaluated for solving the LOX manifold transient problem. 

ALFA is an explicit, unsteady Navier-Stokes solver developed from a 

finite-element point of departure, so that geometry and grid generation can be 

conveniently separated from the solution advancement portion of the program. 

Boundary condition and flow initialization definitions are also separated into 

distinct steps in the calculations. ALFA is structured such that initial flow 

property specification, integration/iteration analysis and outputting are 

treated in a modular fashion. 

propagate pressure signals only in the characteristic directions. This is the 

program of choice to describe the combusting flow in the FPB. 

module is the only one which would require modification to describe the 

two-phase flow of oxygen. 

The integration algorithm is biased to 

The integrator 

The two-fluid model recommended in the previous section is seen to contain 

a single pressure at a given point which describes both fluids. This is a 

physically realistic assumption, but we shall show that is does impact the 

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solution methodology. 

single phase flows may be revealed by considering the following onedimensional, simplified system of conservation laws. 

Other solution restrictions which are present even in 

where U and F are n-component column vectors. 

linearized by considering F to be a function of U. 

The system can be quasiwhere A(U} is the Jacobian matrix, 

hyperbolic at this point, if there exists a similarity transformation such that 

The system of equations is 

Q-’ A Q = M 

where H is a diagonal matrix. 

If the eigenvalues are real, a computational algorithm can be devised which 

propagates pressure waves such that physically unrealistic signals are not 

generated. 

The elements of M are the eigenvalues of A. 

The eigenvalues calculation just presented is utilized in SECA’s ALFA 

code to provide a stable, efficient unsteady solution. If the two-fluid 

system of equations with one pressure possesses real eigenvalues, the ALFA 

code methodology would be expected to solve the model equations. Wendroff 

(Ref. 25) performed the eigenvalue determination for the one-dimensional, 

unsteady two-fluid conservation equations and found four real eigenvalues and 

two complex eigenvalues. This demonstrates that the current ALFA methodology 

is not appropriate for this application without modification. 

Wendroff (Ref. 25) did not perform the eigenvalue determination to devise 

a computational algorithm, but to determine if the problem was ill-posed. 

Although the problem is ill-posed, two of the real eigenvalues do tend to give 

the system pressure wave propagation properties similar to those of gases. 

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Furthermore, interfacial phenomena involving friction and the assumed behavior 

of relative velocity and equality of pressure may be used to make the model 

become well-posed. 

on this two-phase flow problem, but, since the TRAC methodology apparently 

works the problem in a satisfactory manner, further code development does not 

appear worthwile. It should be mentioned that artificial viscosity or dissipation which may be present in the numerical solution method may be sufficient 

to make the problem well-posed and avoid the difficulty just described. Regardless of whether or not suitable modifications can be made, the ALFA code 

will require further development for use in describing the LOX flashing in the 

fuel preburner manifold; therefore, TRAC should be used for near term studies. 

Thus modifications could be made to utilize the ALFA code 

In addition to a solution methodology for the left-hand side of the twofluid equations, the interface transfer terms must be specified, and heat 

transfer within the solid walls of the LOX manifold calculated. All of these 

factors are already included in the TRAC code presented in the next section. 

3.4 THE COBRA/TRAC CODE 

The COBRAITRAC code (Ref. 28) was developed by the Pacific Northwest 

Laboratory of the Battelle Hemorial Institute to predict the thermal-hydraulic 

response of nuclear reactor coolant systems to break loss-of-coolant accidents 

and other anticipated transients. 

three-dimensional, two-fluid, three-field equations for two-phase flow in a 

reactor vessel and the heat transfer within solid walls using COBRA-TF. 

three fields are the vapor field, the continuous liquid field, and the liquid 

drop field. 

the analysis. 

Laboratory (Ref. 26). The effort which was devoted to the development of this 

computational tool both at Battelle and Los Alamos was substantial; therefore, 

the conversion of this model from one describing waterlsteam to one describing 

The code is used to solve the compressible 

The 

The primary reactor system is modeled with the TRAC portion of 

The TRAC technology was developed at the Los Alamos National 

LOX/GOX flow is well justified. 

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To utilize the COBRA/TRAC code, physical models of the mass exchange 

across the phase boundaries must be specified. 

face topology included in the code is one developed by Dukler for vertical 

flow in pipes. 

because the effect of gravity on the liquid phase creates severe complications. 

These correlations will be assumed to be valid for the LOX manifold analysis. 

Their validity will be ascertained after some experience is developed in using 

the code. 

would cause the GOX and LOX densities to differ much less than water/steam 

densities. Nevertheless, all of the flow regimes in the code are expected to 

be required to treat the GOX/LOX flow. 

and 3-7 taken from Ref. 28 for adiabatic and hot walls, respectively. The 

correlation equations contained in COBRAITRAC will be assumed to be valid for 

oxygen when oxygen properties are used in place of those for water. The 

computed void fraction is used to shift from one flow regime to another. 

The flow map to define interA similar treatment for horizontal flows is not available 

This is not a gross assumption because the cold GOX temperatures 

These regimes are shown in Figs. 3-6 

Heat transfer within solid walls is treated with a nodal network model and 

convective and/or boiling heat transfer correlations; these will be utilized. 

The gap conductance and radiant exchange models will not be required. 

quench front model will be useful in describing the LOX flashing. 

The 

The use of the COBRA/TRAC code is expected to greatly enhance the 

capability to simulate the transient behavior of the FPB startup and shutdown 

when coupled to the ALFA code for describing the propellant flow within the 

FPB combustor. The major remaining requirement is the correct specification 

of the physical properties of the propellant for these flow regimes. 

3.5 PROPELLANT PROPERTIES 

The physical properties for oxygen will be taken from the following 

sources. Liquid thermodynamic and transport properties from Ref. 29, gaseous 

thermodynamic properties from Ref. 30, and transport properties from Ref. 13. 

Liquid hydrogen properties are from Ref. 32. Transport properties are from 

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SMALL BUBBLES 

LIQUID 

DISPERSED 

AT A 

IN 

VOlUME 

- 

FRACTION OF 0.2 

... .. *e. 

.. * .. .. .* 

** . . *. * *. 

* * ** . .* . 

* .. 

... *. 

.. . *- 

*. * . .. ’ 

e 

0 

00 

0 0 

0 0 

e s 

FILM I FILM MI ST FLOW 

C HU RN-TU RBULENT FLOW 

SLUG FLOW 

DISPERSED BUBBLY FLOW 

Fig. 3-6 Schematic Showing Normal Regimes in a Two-Phase Flow I 

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O0 .). 0 

0 

0 

eo 0 :j 0 

0 

0 

t 

0 

0 

0 0 

0 

0 

0 0 

. .o 

eow 0 

0 

0 

ooo 

00 0 

00 

oo 0 

6 

E - 

\ - 4 

LMSC-HEC TR F225770 

:ALLING FILM REGIME 

3UENCH FRONT LOCATION 

D I S PERSED DROPLET FLOW 

DROPS DE-ENTRAIN AND 

BREAK UP ON GRID SPACER 

LIQUID CHUNK (LIQUID ~ 

SATURAlED) 

INVERTED ANNULAR FLOW 

(LI QU I D SU BCOOLED 1 

QUENCH FRONT LOCATION 

NORMAL FLOW REG1 NES 

Fig. 3-7 Schematic Showing Two-Phase Flow Regimes for Case of Hot Wall FLOW 

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F225 7 70 

the same source as for oxygen. 

volume expansivity for oxygen (Ref. 29) appears to have the wrong sign. Most 

substances expand when heated; LOX is not an exception. The magnitude of the 

values given in the NBS technical note agree with those given by Rowlinson 

(Ref. 331, but the signs do not. 

tables to calculate the speed of sound tables; hence the sound speeds are too 

high. These data are not used directly in the COBRA/TRAC code, but the 

apparent error should be anticipated. 

The only discrepancy noted to date is that the 

The NBS TN uses the signs given in the 

The COBRA/TRAC code uses tables of property data which must be created 

from the cited references for LOXIGOX. This code also uses temperatures as 

flags for certain calculations; these flags must be changes to reflect oxygen 

properties. 

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4. SUMMARY AND CONCLUSIONS 

Cooperative efforts between the Lockheed-Huntsville Computational 

Mechanics Group and the NASA-MSFC Computational Fluid Dynamics staff (ED321 

has resulted in improved capabilities for numerically simulating incompressible 

flows generic to the Space Shuttle Main Engine. 

documented CFD code has been obtained, modified, and applied to laminar and 

turbulent flows of the type occurring in the SSHE Hot Gas Manifold. 

code has been installed on the NASA-IISFC CRAY-XMP computer system and is 

currently being used by NASA engineers. 

A well established and 

The INS3D 

Studies to perform a transient analysis of the FPB have been conducted. 

The COBRA/TRAC code is recommended for simulating the transient flow of oxygen 

into the LOX manifold. Property data for modifying the code to represent LOX/ 

GOX flow has been collected. The ALFA code has been developed and recommended 

for representing the transient combustion in the preburner. 

will couple through transient boundary conditions to simulate the startup 

and/or shutdown of the fuel preburner. 

NAS8-37461, to implement this modeling effort. 

These two codes 

SECA is currently conducting a study, 

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2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

11. 

5. REFERENCES 

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581-590. 

Kwak, D., J.L.C. Chang, S.P. Shanks, and S. Chakravarthy, "An Incompressible Navier-Stokes FLOW Solver in Three-Dimensional Curvilinear 

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Vanka, S.P., B.C-J. Chen, and W.T. Sha, "A Semi-Implicit Calculation 

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Shyy, W., S.S. Tong, and S.M. Correa, "Numerical Recirculating Flow 

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8, 1985, pp. 99-113. 

Maliska, C.R., and G.D. Raithby, **A Method for Computing Three-Dimensional 

Flows Using Non-Orthogonal Boundary-Fitted Coordinates," Int. J. for Num. 

Meth. Fluids, Vol. 4, 1984, pp. 519-537. 

Chang, J.L.C., and D. Kwak, **On the Method of Pseudo Compressibility for 

Numerically Solving Incompressible Flows," AIM Paper 84-0252, 1984. 

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

Flow Simulation Method and its Application to the Space Shuttle Main 

Engine, Part 1, Laminar Flow," AIM Paper 85-0175, 1985. 

Rogers, S.E., D. Kwak, and J.L.C. Chang, "INS3D - An Incompressible NavierStokes Code in Generalized Three-Dimensional Coordinates," NASA TM-100012, 

November 1987. 

Beam, R.M., and R.F. Warming, "An Implicit Finite-Difference Algorithm for 

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1976, pp. 87-110. 

Briley, W.R., and H. McDonald, "Solution of the Three-Dimensional Compressible Navier-Stokes Equations by an Implicit Technique. Proceedings 

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Dynamics, Lecture Notes in Physics," Vol. 35, Springer Verlag, New York, 

1975, pp. 105-110. 

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12. Rogers, S.E., D. Kwak, and U.K. Kaul, "On the Accuracy of the Pseudo 

Compressibility Method in Solving the Incompressible Navier-Stokes 

Equations," Awl. Math. Mod., Vol. 11, 1987, pp. 35-44. 

13. Zilliac, G., "A Computational/Experimental Study of the Flow Around a Body 

of Revolution at Angle of Attack," NASA Tn-88329, 1986. 

14. Champney, J.M., T.J. Coakley, and U.K. Kaul, "Incompressible Viscous Flow 

Simulations of the NFAC Wind !Gunnel," ATM-FR-25-012, 1986. 

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

Separation and Horseshoe Vortex System," AIM Paper 85-0182, 1985. 

16. Rogers, S.E., D. Kwak, and U.K. Kaul, **A Uumerical Study of ThreeDimensional Incompressible Flow Around Multiple Posts," AIM Paper 

86-0353, 1986. 

17. Chang, 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 I1 - Turbulent Flow," AIM Paper 85-1670, 1985. 

18. Chang, J.L.C., "A Study of Turbulent Flow in an Axisymmetric Diffusion 

Duct," Fifth SSME CFD Working Group Meeting, Huntsville, Ala., 21 April 

1987. 

19. Anon., "SSME Orientation (Part A-Engine)," Contract NAS8-27980, Rocketdyne 

Division, Rockwell International, Canoga Park, Calif., October 1982. 

20. David, D., "Space Shuttle Engine Study, Vol. 11, Interim Report," Contract 

8-36176, Aerojet Technical Systems Co., Sacramento, Calif., April 1985. 

21. Whitaker, S., Adv. in Heat Transfer, Vol. 13, 1981, pp. 119-203. 

22. Slattery, J.C., Momentum, Enerw, and Mass Transfer in Continua, McGrawHill, New York 1972. 

23. Ishii, M., Thermo-Fluid Dynamic Theory of Two-Phase Flow, Eyrolles, 1975. 

24. Harlow, F.H., and A.A. Amsden, J. of Cow. Phys., Vol. 17, 1975, pp. 19-52. 

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363-409. 

26. Liles, D.R., and W.H. Reed, J. of Cow. Phys., Vol. 26, 1978, pp. 390-407. 

27. Spalding, D.B., "The Numerical Computation of Multi-Phase Flows," to be 

published, 1984. 

28. Thurgood, M.H., et al., WUREG/CR-3046, PNL-4385, Vol. 1, Battelle Memorial 

Institute, Richland, Wash., 1983. 

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29. Anon., NBS Technical Note 384. 

30. Stull, D.R., and H. Prophet, NSRDS, NBS 37, 1971. 

31. Svehla, R.A., NASA TR R-132. 

32. McCarty, R.D., and L.A. Weber, NBS TI 617, April 1972. 

33. Rowlinson, J.S., Liquids and Liquid Mixtures, 2nd ed., Butterworth, 

London, 1969. 

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