A three dimensional analysis of the non-uniform flow around the liquid oxygen (LOX) posts in the Space Shuttle Main Engine (SSME) powerhead was performed to determine possible factors contributing to the failure of the posts. Also performed was three dimensional numerical fluid flow analysis of the high pressure fuel turbopump (HPFTP) exhaust system, consisting of the turnaround duct (TAD), two-duct hot gas manifold (HGM), and the Version B transfer ducts. The analysis was conducted in the following manner: (1) modeling the flow around a single and small clusters (2 to 10) of posts; (2) modeling the velocity field in the cross plane; and (3) modeling the entire flow region with a three dimensional network type model. Shear stress functions which will permit viscous analysis without requiring excessive numbers of computational grid points were developed. These wall functions, laminar and turbulent, have been compared to standard Blasius solutions and are directly applicable to the cylinder in cross flow class of problems to which the LOX post problem belongs

Anderson, P. G.

Farmer, R. C.

English

NASA Technical Reports Server

General Disclaimer 
One or more of the Following Statements may affect this Document 
 
 This document has been reproduced from the best copy furnished by the 
organizational source. It is being released in the interest of making available as 
much information as possible. 
 
 This document may contain data, which exceeds the sheet parameters. It was 
furnished in this condition by the organizational source and is the best copy 
available. 
 
 This document may contain tone-on-tone or color graphs, charts and/or pictures, 
which have been reproduced in black and white. 
 
 This document is paginated as submitted by the original source. 
 
 Portions of this document are not fully legible due to the historical nature of some 
of the material. However, it is the best reproduction available from the original 
submission. 
 
 
 
 
 
 
 
Produced by the NASA Center for Aerospace Information (CASI) 
https://ntrs.nasa.gov/search.jsp?R=19850011052 2020-03-20T20:20:30+00:00Z
I
^-- 3SSG^
(NASA-CE-171344) CAI,JLATICN OF FLOW ABOUT
	 N85-15362
POSTS AND POWERH AD BCDBL Interim Beport
(Continuum, Inc.) 20 p NC Au g/MF A01
CSCL 20D	 Unclas
G3/34 14219
CALCULATION OF FLOW ABOUT POSTS AND POWERHEAD MODEL
Interim Report, Contract NASB-35506
CI-IR-00 79
Prepared For:
National Aeronautics and Space Administration
George C. Marshall Space Flight Center
Marshall Space Flight Center, AL 35812
By:
Peter G. Anderson
Richard C. Farmer
CONTINUUM, Inc.
4. 715 University Drive
Suite 118
Huntsville, AL 35805
4w`	 January '1.,1, 1985
U>
I
CI-IR-00 79
TABLE OF CONTENTS
FORWARD.......................................................2
1. INTRODUCTION ................................................2
1.1	 Background ................................................2
1.2	 Objectives .................................................3
'2.	 SUMMARY ....................................................3
3. HIGH REYNOLDS NUMBER CROSSFLOW ABOUT A CYLn1DER ............. 3
3.1 Introduction ............................ . ................... 3
3.2 Laminar Boundary Layers ...................................... 4
3.3	 Turbulent Boundary Layer ...................................... 4
4. HGM FLOW ANALYSIS ............................................9
4.1	 Introduction ................................................ 9
4.2	 Configuration ...............................................9
4.3	 Flow Conditions at Inlet ....................................... 9
4.4	 Computational Grid ......................................... 10
4.5 Initial and Boundary Conditions ................................. 14
4.6	 Results ..................................................14
S.	 CLOSURE ....................................................15
TABLE OF FIGURES
Figure 3-1 Laminar Boundary Layer on a Flat Plate ....................... 5
Figure 3-2 Turbulent Boundary Layer Calculation ......................... 8
Figure 4. 1 View of Grid From Outside ................................ 11
Figure 4.2 View of Grid From Lside 	 ................................. 12
Figure 4-3 Grids in Plane of Symmetry ................................ 13
Figure 4-4 Averaged Pressure in TAD/Bowl/Tube ........................ 16
Figure 4-5 Pressure Variation Around Bowl ............................. 17
Figure 4-6 Pressure Contours in TAD/Bowl at 0 Degree ................... 18
Figure 4-7 Velocity Contours Midway In Transfer Tube .................... 19
-1-
CI-IR-00 79
FORWARD
This document was prepared by personnel at Continuum, Inc. for NASA-MSFC under
Contract NASB-35506. This document is an interim report on the first year of work
under this contract.
1. INTRODUCTION
1.1 Background
The highly non-uniform flow around the LOX posts in the SSME powerhead has
contributed to a long history of failures of the posts. Both pressure and heating loads
have caused problems which have resulted in undesirable, but necessary, design
modifications such as the use of LOX post flow shields. The geometric complexity of the
LOX post flowfield is enormous; 600 posts are fed by the five hot gas discharge ducts
from the HPFTP and HPOTP. The posts are fluted to modify the structure of the trailing
vortices and are shielded by plates covering pairs of posts in the outermost row. Hot
gases flow along the sides of the injector elements into entry ports which conduct the
flow through an annulus into the main combustion chamber. The region of posts which
are subjected to extreme environments is contained within the region bounded by the
exits of the hot gas transfer ducts, the bottom of the oxidizer manifold, and the space
above the secondary plate. The hydrogen cavity flow between the primary and secondary
plates does not cause severe environments and is not considered further.
Assuming that the flow from the HGM is symmetric about a plane through the center
transfer tube, one-half of the region could be modeled at one time. Even the half-plane
flow would be too complex to provide a direct numerical solution to the flow field of
interest. Continuum has been contracted to address this problem by a phased effort
which first models the flow around a single and small clusters (2-10) of posts, second
models the velocity field in the cross-flow plane, and third models the entire flow region
with a 3-dimensional network-type model. However, the contract has been modified to
include a full 3-D numerical solution of the flow field in the high pressure fuel turbopump
turnaround duct (TAD), hot gas manifold (HGM) and transfer tubes. The results of this
-2-
CI-IR-00 79
effort will be used to define boundary conditions for LOX post analyses.T>	 1.2 Objectives
The following sections discuss the work performed under Phase I of the contract as
modified to reflect the TAD/HGM./Duct analysis. These sections include a presentation
of Continuum's laminar and turbulent boundary layer development in support of the LOX
post study and the results of the 3-D HGM analysis.
2. SUMMARY
Continuum has developed shear stress wall functions which will permit viscous analyses
witbout requiring excessive numbers of computational grid points. These wall functions,
laminar and turbulent, have been compared to standard Blasius solutions and are directly
applicable to the cylinder-in-crossflow class of problems to which the LOX post problem
belongs. The results of this work are presented herein.
Continuum has also performed a full 3-D fluid flow analysis of the HPFTP exhaust
system which consists of the turnaround duct, 2-duct hot gas manifold and the "Version
B" transfer ducts. The results of this analysis are presented in this report.
3. HIGH REYNOLDS NUMBER CROSSFLOW ABOUT A CYLINDER
3.1 Introduction
In order to accurately account for pressure loading and heating to cylinders in crossflow,
like for the LOX posts in the powerhead, a detailed flowfield prediction and suitable wall
boundary conditions are required. It is impractical to resolve the flowfield in the vicinity
of the wall with enough grid points to accurately calculate either the wall friction or
heating, therefore a special wall treatment is required. "Wall functions" are commonly
used to provide the required boundary conditions; however, care must be exercised in
order not to make the wall functions too empirical. The end result is to predictI
-3-
0
CI-IR-00 79
frictional losses from the detailed flow vectors, not from the mean channel flow. The
following procedure was developed and tested with geometrically simple problems to
provide the necessary, CFD tools for powerbead analysis.
3.2 Laminar Boundary Layers
Laminar boundary layers on a flat plate were analyzed with Continuum's VAST code for
constant density and temperature (hence pressure also) conditions. Figure 3-1 shows the
results of these analyses compared to the Blasius solution. A mean lateral velocity was
used as a boundary condition on the free-stream side of the computational region. The
excellent agreement of the VAST solution with the Blasius solution suggests that no
significant artificial viscosity, effects are present in the solution for this case. Notice
that only 15 lateral node points were used for this calculation. Identical results were
obtained for a case run with 11 nodes, only one of which was initially in the boundary
layer. When 7 nodes were used with a step velocity profile a solution was generated, but
the accuracy of this solution w_.s reduced. These results are considered acceptable, and
the use of at least one node in the initial boundary layer is reasonable.
3.3 Turbulent Boundary Layer
For turbulent wall flows, including fully developed pipe flows, for a smooth wall the
following empirical velocity profiles rAre valid.
T
-4-
so
40
U	 &0(fps)
20
10
0
0 1	 2	 3	 4	 5
c
so ,
Y17. 2 tqpuix-
Fig. 3-1 Laminar Boundary Layer an a Flat Plate
-5-
CI-IR-0079
u +	5.5 + 2.5 ln(y+ )	 for y+ > 30	 (3-1)I
u+ _ -3.05 + 5.0 ln(y+)	 for 5 < y + < 30	 (3-2)
u+ = y+	 for y+ < 5
	 (3-3)
where
u
•
u
y
u/u•
(T a w l- 5
(T a /P) 0.5 y/v
Blasius' empirical shear stress relationship is appropriate.
T o = 0.0255 Pu2(v/u•P)0.25
where = R for pipe flow
= 6 for boundary layers
The boundary layer thickness implied by (3-4) and a l/ 7 power-low profile is
6 = 0.376 X/Re0.2
From equation (3-3)
4U) = T0 /P = (u•)2/v
w
(3-4)
(3-5)
(3-6)
In terms of real distance from the wall, equation (3-1) represents most of the boundary
layer, therefore the following computation procedure is suggested. A fictitous wall is
assumed to be 0.0005 feet away from the real wall, and no flow is assumed to occur
between the two walls. Equation (3-1) is valid at .0005 feet from the wall; hence, if u is
calculated with a slip boundary condition, u •
 is determined. Equation (3-6) is used to
-6-
I
ter_--___-- -- —:— . ----
CI-IR-00 79
calculate the velocity gradient at the wall. Since equation (3-1) is not explicit in u * , the
^(r	 approximation
u0 = 0.1662529 u0.867325/(y/\))0.132675 	 (3-7)
is used. These equations determine the velocity gradient and shear stress at the wall.
An eddy viscosity is used to determine both the local shear stress and the variation of
this stress with distance from the wall, y.
where
0
" T = 0.07 u k(FR) + u	 (3-8)
FR = (7/0.39 1 for 0 < (y/R	 < 0.3
FR = 1.0	 for	 ( y/R) > 0.3
Equations ( 3-7) and ( 3-8) and the momentum equations were used to calculate the
turbulent boundary layer over a flat plate between 1 and 2 ft running length over the
plate. A turbulent boundary layer was assumed at the leading edge of the plate. The
flow was air with a free steam velocity of 100 fps (this is an approximate Reynolds
Number of 1A. By adjusting the constants in equations (3-7) and (3-8), the profile at the
end of the plate was predicted to be that shown in Fig. 3-2. The fit is very good,
especially near the wall; the calculated wall shear stress is within 5% of the correct
answer. This procedure is accurate enough to extend its development to more
geometrically complex flows. The reasons for the necessity of adjusting the constants in
equations (3-7) and (3-8) and for the lack of better fit at y's near the free stream side of
the boundary layer are still under investigation.
Research to continue these analyses until cylinders in cross-flow can be accurately
simulated is in progress.
-7-
I100
Input Profile	 ^ r^ +' ' rt
at X-1.0 ftf
i	 Desired Solution at X=2.0 ft.
	
80	 .^	 Computed Profile at X=2.0 ft.
m 60c
w
TLM
U
0
	v 40
	
Smooth Plate
Air
RervlO6
20
	
0 L_	 I
	
0	 0.01	 0.02
	
0.03	 0.04	 0.05	 0.06
Y (Ft.)
Fig. 3-2 Turbulent Boundary Layer Calculation
T
-6-
ICI-IR-0079
4. HGM FLOW ANALYSES
4.1 Introduction
The analysis of the flow environment surrounding the SSME LOX posts requires a
definition of the flow field in the HPFTP transfer tubes exit planes. The exit plane flow
is development by defining the flow conditions immediately downstream of the turbine
and computing the flow field through the turnaround duct, hot gas manifold and transfer
tube. This section discusses the computation of the flow field in the turnaround duct, hot
gas manifold and transfer duct for a two-duct configuration.
4.2 Configuration
The configuration analyzed consisted of the FMOF turnaround duct, the "Phase 3" two-
duct hot gas manifold and the "Version B" transfer tube which includes the flow
separator. The effects of turbine-induced swirl were neglected at the direction of the
customer; hence, a plane of symmetry between the 2 transfer tubes was incorporated.
4.3 Flew Conditions at Inlet
The flow conditions at the inlet to the turnaround duct were specified by the customer.
The fluid in the s7Aem was air at 530°R flowing at M Ibm /sec. The pressure across the
inlet was described by the equation.
P =190.0 0.98 + 0.0441 Sin Z (^)lpsie	 (4-1)2
where ^ is the angular location which ranges from 0 0 between the transfer tubes and
180" on the plane of symmetry on the side fartherest from the transfer tubes. The
velocity profile in the TAD inlet is defined by the equation
-9-
CI-IR-00 79
V = V(1.0 + 0.04 Cosh) 	 (4-2)
where V is the average velocity,
 of any angle ¢ and V is the average velocity over the
entire inlet. The velocity has no cross flow component due to the assumption of no
turbine-induced swirl. The turbulent viscosity was specified as 10,000 times the
molecular viscosity for air.
4.4 Computational Grid
The configuration described in subsection 4.2 was modeled using l0, Td4 nodal grid
points. The grid points depicting tht boundaries of the configuration are shown in Figs.
4-1, 4-2. The struts and posts in the turnaround duct have been darkened in to clarify
their locations. The computational grid in the plane of symmetry at the 0° (between the
transfer tubes) and 18e (far side) positions are shown in Fig. 4-3. The inlet to the
turnaround duct has been artifieally,
 moved upstream to avoid influencing the flow in the
1800
 bend by the prescribed inlet flow conditions. Figures 4-1 through 4-3 illustrate that
all of the salient features of the configuration have been incorporated into the grid.
A>
-10-
0a .-+J
a L
LL O E
O O
u
^ d w
2M h(j; 'OM
D J o
cr
oo'
+a
w
I
4O
m
^WCK
	
IGINAI PAGE
AND 
WHITE PHOTOGRAPH
_11_
}
HM
a
LL
g
N
ro
M
N
G
N
r
O
H
w
v
.rf
H
W
0
s
aj
M
N
1
v
OD
M
w
J
0
in
^l.O
MJ
N
co
H8
W
J(n Z5
Q
i
N
Z
Qa
I
ORIGINAL PAGEP
BLACK AND WHITE PHOTOGRAPH
-12-
IQ
COMPUTATIONAL GRID AT 180 DEC, PLANE OF SYMMETRY
ACTUAL INLET
COMPUTATIONAL GRID AT 0 DEG. PLANE OF SYMMETRY
ACTUAL INLET
FLOW SEPARATOR
Fig. 4-3 Grids in Plane of Symmetry
-13-
I
CI-IR-0079
4.5 lnitia) and Boundary Conditions
The inlet conditions prescribed in subsection 4.3 were applied to the artificially displaced
inlet shown in Fig. 4-3. The viacosity of 10,000 times the molecular viscosity of air
results in a Reynolds Number of 300 to 400 and, hence, laminar flow. Therefore a
laminar parabolic velocity profile was superimposed on the average velocity distributed
defined by Equation _ L.
No-slip boundary conditions were specified for all solid walls and tangency, or free-slip,
boundary conditions were applied to the plane of symmetry. The mass flow rate in the
exit plane of the transfer tube was held fixed at 72 lbm/sec. The total conditions at the
inlet were held fixed, thereby allowing spurious signals to pass upstream and out of the
problem.
4.6 Results
The flowfield for the TAD, HGM and transfer tube described above was computed using
Continuum's VAST code. The problem required 11,000 time steps befure a converged
solution was obtained. The results of the study were presented in detail to the customer
on November 28, 1984. A summary of the results will be discussed in this section.
The total pressure drop through the system is presented is Fig. 4-4 and shows a drop of 18
psi in the 180 bend of the turnaround duct, a 14 psi drop through the struts, and a total
drop through the system of 48 psi. Static pressure drop through the system was about 35
psi. The pressure variation in the circumferencial direction in the HGM bowl inlet is
shown in Fig. 4-5 and indicates a variation of 30 psi. Exactly how much of this result is
affected by the assumed inlet pressure variation (8.38 psi) is unknown but it appears to be
small.
The pressure distribution in the cross section in the plane of symmetry between the
transfer tubes is presented in contour form in Fig. 4-6. The figure sbows significant
pressure drops in the 180 0
 bend of the TAD and through the strutz. The pressure
variation in the bowl is small except in localized areas.
I
-14-
CI-IR-0079
The pressure in the exit plane of the transfer tube varies only about 4 psi, hence, the exit
plane pressure distribution is not presented in this discussion. Instead, velocity contours
in the transfer tube are presented in Fig. 4-7 to show the nonuniform velocity
distribution. A small area of high speed flow appears in the outer and upper portion of
the tube.
Figures 4-4 through 4-7 show large pressure gradients in the turnaround duct and small
pressure gradients in the transfer tube indicating an improved design over the 3 duct
system currently in use.
S. CLOSURE
The analyses of single and multiple LOX posts will be continued. The laminar flow
analysis of the TAD/HGM/transfer tubes was com pleted; the turbulent flow case will' be
analyzed in the next reporting period.
I
I
-is-
i`	 O	 O
N	 M	 R	
^0	 e_
visa
-16-
I
v
F
'-I
3
O
F7
y G
W F
U C
N ^
v
t+
7
F N
U N
z v
w "
a	 a.
z "N ^
z	 '^
z "
o m
x
,c
v
i
eo
M
w
s	 N
fq^
14^
Oco1-1
O	 0
O
o
r
w
G
0
ro
O
co	 4)
w
R.
O
0
rn	 co	 n%0	 Ln
r-I
I	 v Is (I
10o
0o
m
aq
0
u
ro
o•	 r
3
0
q
4
H
C
^-1
N
	
N
H
O
L
G
O
U
J
P
N
a
N
N
a
N
W
i
r ^
m
M
N
rs
W 0
^ d
N ttl^OJ@@@@@@@@@
W Oaf'7G0^'@4^NWtfN@^DtY Qp0^1'^1^nU^^IRlf?It71f?^
a'
W
m +-^NI"7^t'II^^On07dt@+-^N
Z
L
W
2
F'l
N
-18-
rz
O.
O
O
V
O
0
CU
U)0
ttl
Fo
H r
0
0 r
0U r
0
-H0
ci
0
t
F- (f) Lo
" IL IL
to Li. LL
0
-j v 00
iy
LU
M
Z
Ar
^L


Calculation of flow about posts and powerhead model

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server