THERMAL ANALYSIS OF LIQUID
ROCKET ENGINES
Mohammad H. Naraghi
Department of Mechanical Engineering
Manhattan College
Riverdale NY 10471
1
Introduction to Cooling Methods
• Combustion gases are 4000 to
more than 6000oF
• Heat transfer rates from hot-gases
to the chamber wall are 0.5 to over
130 BTU/in2s
• A cooling system is needed in
order to maintain engine integrity
2
Chamber and Nozzle Cooling
Techniques
•
•
•
•
•
•
Regenerative cooling
Dump cooling
Film cooling
Transpiration cooling
Ablative cooling
Radiation cooling
3
Regeneratively Cooled Rocket Engines
Coolant (LH2)
A
GH2
Thrust
Chamber
A
AA Section
4
Types of Cooling Channel
Rectangular cooling channels
5
Cooling Channels
6
High Aspect Ratio Cooling
Channels
7
A rocket chamber nozzle made of a
copper alloy with machined cooling
channels (no closeout)
8
Tubular Cooling Channel
Chamber jacket
The number of coolant tubes required is a function of
the chamber geometry, the coolant weight flow rate per
unit tube, the maximum allowable tube wall stress,
and fabrication consideration
9
Tubular Cooling Channel
Chamber jacket
Tubular cooling channel configuration at throat area
(parts of nozzle with small diameter)
10
Cooling Channel Concepts
Close-up
Bonding material
Coating
Tubular Channels
Truncated Oval Channels
Collant injection nozzles
Increased hot-gas side surface area
Cooling channel with transpiration injection
11
Wall Materials
Wall:
Close-out:
Coating:
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Copper
NARloy-Z
SS-347
Glidcop
Inconel718
Amzirc
Columbium
SS-347
Nickel
Copper
Monel
Platinum
Nicraly
Soot
Zirconia
12
Propellants
• H2-O2
• RP1 (JET-A) C12H23-O2
• Methane-LOX CH4-O2
•Hydrogen Peroxide
13
Coolants
• Liquid Hydrogen
• Liquid Oxygen
• Water
• RP1 (JET-A)
• Methane
•Hydrogen Peroxide
14
Issues in Designing Cooling Passages
• Keeping nozzle and wall temperatures
below material limits
• Keep pressure drop reasonable
• Overcooling is detrimental to engine
performance
• Coolant exit condition be suitable for
injector or running a turbo pump
15
Modes of Heat Transfer
Convection and radiation from
combustion gases (hot-gases).
All these modes of heat transfer must be conjugated
16
Modeling Heat Transfer in
Regeneratively Cooled Engine
Typical Nozzle Broken into a Number of Stations
Hot-gas
Coolant in
n
3
2
1
17
Typical Cross-Section of Nozzle
INSULATION
NICKEL
Due to symmetry calculation
can be performed for a half
cooling channel.
COOLING
CHANNEL
COPPER
18
COATING
DG
Convection from Hot-Gases
• The first step is to determine hot-gas
thermodynamics and transport properties
• CEA (Chemical Equilibrium with Applications)
code can be used to evaluate the hot-gas
properties. This program is a public domain code
and can be downloaded from NASA Glenn’s site:
http://www.grc.nasa.gov/WWW/CEAWeb/
• Typical results of CEA with rocket option for the
SSME
19
Hot-Gas Side Convective Heat Flux
qn  hGn (TGAWn  TGWn )
Or
qn 
hGn
c pGX
(iGAWn  iGW n )
n
n is the station number
TGAW and iGAW are adiabatic wall temperature and enthalpy
TGW and iGW are gas-side wall temperature and enthalpy
hG is the gas-side heat transfer coefficient
c pGX is constant pressure hot-gas specific heat at reference condition
20
Adiabatic Wall Temperature (Enthalpy)
The reference enthalpy of the gas side, is given by
(Eckert):
iGX n  0.5(iGWn  iGS n )  0.180(iG0n  iGS n )
The adiabatic wall enthalpy (Bartz and Eckert)
iGAWn  iGS n  (PrGX n ) (iG0n  iGS n )
1/ 3
Subscripts S and 0 represent static and stagnation conditions
21
Hot-Gas Side Convective Heat
Transfer Coefficient
Dittus-Bolter correlation
hGn 
Re GX n
CGn k GX n
d Gn
Re GX n
4WG TGS n

d Gn  GX n TGX n
CG  0.023
0.8
PrGX n
0.3
PrGX n 
c pCX n  GX n
kGX n
22
Hot-Gas Side Convective Heat
Transfer Coefficient
Bartz correlation
 C  G0.02c p
G0
hGn   0G.2 
0.6

 Dt  PrG 0
 PC g c 0.8  Dt  At 0.9


  

*
 c  Rcurv .  A 



 Is correction factor for property variation across the boundary layer

1
 1 TWG

 2 T0
  1 2  1 
M n   
1 


 2
CG  0.026
0.68
  1 2 
1  2 M n 
23
Computational Methods for Hot-Gas
Heat Flux Calculations
• Boundary Layer analysis using available codes,
such as TDK (Two Dimensional Kinetics)
• TDK has two boundary layer modules (BLM,
Boundary Layer Module, and MABL, Mass
Addition Boundary Layer)
• MABL can be used for transpiration cooling
• Computation time for TDK is approximately two
minutes
• CFD codes
24
CFD Results, Static Temperature for
the Regen Part of the SSME
25
Comparison Between Heat Fluxes Based
on Various Methods for the SSME
120
Wall Heat Flux (BTU/sec-in 2)
RTE_TDK
100
CFD
Method A
Method B
80
Bartz
BLM
60
40
20
x=0 (Throat)
0
-15
-10
-5
0
Axial location (inches)
5
10
26
Wall Conduction Models
Two approaches can be used for wall
conduction:
• Simple one-dimensional heat conduction
• Two or Three-dimensional
finite-difference or finite-element
methods
27
One-dimensional wall conduction
TCAW
1/hFhCAC
t/kA
1/hGA
TGAW
28
One-dimensional wall conduction
TCAW
Fin efficiency
1/hFhCAC
l
t/kA
2
1/hGA
TGAW
tanh( ml )
F 
ml
TGAW  TCAW
qn 
1 /  F hC AC   t / kA  1 / hG A
hC
m
k
29
Soot Layer Thermal Resistance
For engines with hydrocarbon fuel with Pc < 1500 psi
30
From Modern Engineering for Design of Liquid-Propellant Rocket Engines, D. K. Huzel and D. H. Huang
Progress in Astronautics and Aeronautics, Vol. 147, 1992
Soot Layer thickness
For the converging section:
tsoot = 0.0041213(A/At) + 0.0041023
tsoot = 0.01234
1<A/At<2
2<A/At
For the diverging section:
tsoot = -0.0000442(A/At)2 + 0.0011448(A/At) + 0.0070920
1<A/At<12
tsoot=0.01445
12<A/At
tsoot are in inches
31
Finite Difference Approach
Cooling Channels
p
u
se
INSULATION
NICKEL
o
Cl
Coating
COOLING
CHANNEL
COPPER
COATING
DG
32
3-D Finite Difference Method
CLOSE-OUT
AREA
(NRCLO)
COOLING
CHANNEL
TOP CHANNEL
AREA (NRCHT)
BOTTOM
CHANNEL AREA
(NRCHB)
COATING
AREA
(NRCOAT)
LAND
AREA
(NPHIL)
CHANNEL
AREA
(NPHIC)
33
3-D Finite Difference Method
i,j+1,n
i,j,n-1
Energy balance for a
typical middle node
i-1,j,n
i,j,n
i+1,j,n
i,j,n+1
i,j-1,n
Ti l 11, j ,n / R1  Ti ,l j 11,n / R2  Ti l 11, j ,n / R3  Ti ,l j 11,n / R4  Ti , j ,n1 / R5  Ti , j ,n1 / R6
Ti ,l j ,n 
1 / R1  1 / R2  1 / R3  1 / R4  1 / R5  1 / R6
r
R1 
r S in, j 1,n  S in, ,jn 1

r
R3 
r S in, j 1,n  S in, ,jn 1



 1
1


l 1
 k l 1
k
i
,
j
,
n
i
1, j , n

 1
1


l 1
 k l 1
k
i
,
j
,
n
i
1, j , n









R2 
r
r 

n 1, n
n , n 1
r 
 S i , j  S i , j
2 

R4 


 1
1

 l 1
l

1
k
 i , j ,n k i , j 1,n
r
r 

n 1, n
n , n 1
 r   S i , j  S i , j
2 







 1
1


l 1
 k l 1
 i , j ,n k i , j 1,n
34




3-D Finite Difference Method
i,j+1,n
i,j,n-1
Energy balance for a
typical surface node
i-1,j,n
i,j,n+1
i,j,n
i+1,j,n
Qc Qr
Ti ,l j ,n  [Ti l 11, j ,n / R1  Ti ,l j 11,n / R2  Ti l 11, j ,n / R3  Ti ,l j 11,n / R4  Ti , j ,n 1 / R5  Ti , j ,n1 / R6 
Qc  Qr ] /(1 / R1  1 / R2  1 / R3  1 / R4  1 / R5  1 / R6 )
m
 (S in, j 1,n  S in, ,jn1 ) sin  n  m 2

Qr 
  wsl E sl DSl S n   wgl E gl DGl S n  E sn 
4
l 1
 l 1

35
Sample Results of Wall Temperature
Distribution for the SSME
36
Sample Results of Wall Temperature
Distribution for the SSME Throat
37
Sample Results of Wall Temperature Distribution for an Engine with PassT
and-half Tubular Cooling Channels Y
993
936
879
821
764
707
650
593
535
478
421
364
307
249
192
X
Z
Z=29.7"
Z=12.53"
Z=10.53"
Z=1.04"
Throat
Z=-17.4"
Z=-5.39"
Two pass section
Entrance of coolant
38
Sample Results of Wall Temperature Distribution for an
Engine with Pass-and-half Tubular Cooling Channels
39
Coolant Flow Convection
Two approaches can be used for coolant flow
analysis:
• One dimensional flow and heat transfer
• Multidimensional CFD analysis
40
Coolant Flow Convection
• One-dimensional channel flow with variable
cross-section for calculation pressure drop.
• Heat transfer to coolant is evaluated based on the
heat transfer coefficients calculated using
Nu=f(Re,Pr) correlations.
• GASP (Gas Properties) and WASP (Water and
Steam Properties) are used for evaluating coolant
properties (these programs are public domain
codes).
41
Variables Effecting Coolant Convection
•
•
•
•
•
•
•
Surface roughness
Entrance effect
Curvature effect
Using swilers
Cooling channel contraction and expansion
Pressure drop
Cooling channel tolerance and blocked channel
42
Cooling Channel Heat Transfer
Coefficient for Liquid Hydrogen
Nu
0.8
0.4
 CCn Re Pr
Nu r
Where
Nu r  
1 
 
 T
0.55
P
  1   TW  TS 
 P 


1  T  

  P 
 
   T
43
Cooling Channel Heat Transfer
Coefficient for RP-1
Shell correlation
Nu  0.255Re
0.582
CS
0.554
CS
Pr
Rocketdyne correlation
Nu  0.0055Re
0.95
CX
0.4
CX
Pr
44
Cooling Channel Heat Transfer
Coefficient for RP-1
Nu  Cc Re
0.95
0.4
Pr
2500
Nusselt Number (Nu)
2000
Experimental
Cc=0.0055
Cc=0.0109
Cc=0.0077
1500
1000
500
0
0
40000
80000
Re
0.95
Pr
0.4
120000
160000
45
Cooling Channel Heat Transfer
Coefficient for Methane
Nu  Cc Re
1800
0.95
0.4
Pr
1600
Experimental
CC=0.031
CC=0.023
CC=0.025
Nusselt Number (Nu)
1400
1200
1000
800
600
400
200
0
0
5000
10000
15000
20000
25000
Re0.95Pr0.4
30000
35000
40000
45000
50000
46
Heat Transfer Coefficient for
Oxygen
 cp
Nu  CCn ReCS Pr 
 cp
 CS
0.4
CS
Where
PCri  731.4
 PCri

 PCS




0.2
 k CS

 k CW
  CW

  CS
psia
iCW  iCS
cp 
TCW  TCS
47



Heat Transfer Coefficient for
Fuels as Coolants
Nu CS
  CS
 CCn Re Pr 
  CW
b
CS
Fuel
c
CS



d
  CS

  CW



e
 k CS

 k CW



f
 cp

 cp
 CS
Coefficient/Exponent




g
 PCS

 PCri



h
No. of
Points
Std.
Dev.
Correl.
Coeff.
cc
b
c
d
e
f
g
h
RP1
0.0095
0.0068
0.99
0.94
0.4
0.4
0.37
0
0.6
0
-0.2
0
-6.0
0
-0.36
0
274
274
0.16
0.20
0.97
0.96
Chem. Pure
Propane
0.011
0.020
0.87
0.81
0.4
0.4
-9.6
0
2.4
0
-0.5
0
0.26
0
-0.23
0
79
79
0.10
0.15
0.99
0.97
Commercial
0.034
0.028
0.80
0.80
0.4
0.4
-0.24
0
0.098
0
-0.43
0
2.1
-0.38
0
285
285
0.27
0.29
0.94
0.93
Natural
Gas
0.00069
0.0028
3.7
1.1
1.0
0.42
0.4
0.4
0.4
1.4
1.5
0
-6.5
-6.5
0
6.3
6.4
0
2.6
2.4
0
0.087
0
0
130
130
130
0.16
0.16
0.38
0.92
0.92
0.30
All of the above
fuels
0.019
0.81
0.4
-0.059
0.0019
0.053
0.52
0.11
768
0.28
0.97
All of the above
fuels except
Natural Gas
0.044
0.76
0.4
0
0
0
0
0
638
0.26
0.98
Propane
48
Coking Characteristics of RP1
1000
o
Coolant wall temperature ( F)
900
Temerature limit line
800
700
600
Velocity limit line
500
400
300
Rectangular channel, no coking
V=70 ft/s
Heated tube, coking
Heated tube, no coking
200
0
50
100
150
200
250
300
350
400
Coolant Velocity - (ft/s)
Range of Conditions Tested During RP1 Cooling
Claflin, S.E., and Volkmann, J.C., “Material; Compatibility and Fuel Cooling Limit
Investigation for Advanced LOX/Hydrocarbon Thrust Chambers,” AIAA 90-2185,
AIAA/SAE/ASME/ASEE 26th Joint Propulsion Conference, Orlando, FL, 1990.
49
Entrance Effect


  S i ,i 1 

 2.88 i 1
 dC

n




n
 Ent.
 Ent .
 TW
 
 Tb



0.325

 n
1.59 / 
S i , i 1 / d C n


 i 1

 Ent.
0.7
  n

   S i ,i 1 
  TW
 1   i 1
  Tb
  dC
n

 

 

0.1 
 

 






50
Curvature Effect
 Cur .

 rCn
 Re CX Avg . 

R

Cur .n






2




1 / 20
where rC is the hydraulic radius of cooling channel, RCur . is the radius of
curvature, the sign (+) denotes the concave curvature and the sign (-)
denotes the convex one
51
n
n
Swilers for Enhancing Heat
Transfer
Gr 2d Cn  T TCW  TCS tan

2
di
Re
 swiler

Gr 

 F 1  0.25

Re


tan 
F  1  0.004872
d i 1  tan2 
2


52
Effects of Surface Roughness
 f
Nu
 
Nu smooth  f smooth



n
n  0.68Pr
0.215

 1  e 1.1098

e
5
.
0452
5
.
8506

 2.0 log

log



0.8981 
 2..8257 D 
 3.7065D Re CX Avg .

Re
f
CX Avg .



1
53
Coolant Pressure Drop

PCS n  PCS n1  PCS n1,n
P
CS n 1, n
P

CS n 1, n M

f
fn

8g c
  P
f
  CS n   CS n 1

 dC  dC
n
n 1


2
 
  AC N n 1   AC N n
 WC 2

 g
 c

CS n1,n M


 VCS  VCS 2 S n 1,n
n 1
 n





1
1


  A N    A N  
CS C
n 1 
 CS C n
54
Coolant Pressure Distribution for the SSME
Coolant Static and Stagnation Pressure (psi)
7000
6500
Static
Stagnation
6000
Cooling Channel
entrance x=8.238 in
5500
5000
4500
4000
3500
Cooling channel
exit x=-14.469 in
Throat (x=0)
3000
-15
-10
-5
0
5
10
Axial distance from the throat (in)
55
Wall Temperature Distribution Along
Axial Direction
1600
TW, RTE_TDK (D & S)
TW, RTE_TDK (Hendricks)
Wall Temperature (R)
Wang, CFD
1200
800
x=0 (Throat)
400
-15
-10
-5
0
Axial Distance From Throat (in)
5
10
56
Radiation Heat Transfer from
Hot-Gases
• Combustion Gases consist of several radiatively
participating species
• These species are: soot, CO, CO2, and water vapor
• HITRAN and HITEMP database can be used to
evaluate absorption coefficients
• Properties of the radiatively participating species
are spectral, consisting of a large number of band
• A Plank-mean approach can be used to evaluate
absorption factors
57
Exchange Factors between
gas and surface elements
 max
dss(ri , r j ) 

2r j ds j

cos  i cos  j (ri  r j )
ri  r j
 min
2
rgi
dgi
d j
rsi
dsg(ri , r j ) 
2kt j rj drj dx j  max cos  i (ri  r j )



 max
dgs(ri , r j ) 
r j ds j
2

 min
dgg(ri , r j ) 
ri  r j
min
2
 (ri  r j )  e
d j
x
cos  j (ri  r j )
ri  r j
2


min
 kt ri r j
ri  r j
rgj
d j
rsi
kt j rj drj dx j  max  (ri  r j )
2
dsi
2
d j
dgj
dsj
r

58
Total Exchange Factors
Account for wall reflection and gas scattering
 
  dss  dsg W I  dss W  dgsα
DGS  I  dgg W  dgsI  ρW dss  dsg W I  dgg W  dgs α


1
DSS  I  dss  dsg0 Wg I  dgg0 Wg dgs ρWs
1
1
0
g
0
1
0
g
1
s
0
g
0
g
-1
g
Wall heat flux at station n
qr ,n 
2 nr  m
mnr
w
j 1
DS j S n Es , j   wg , j DG j S n E g , j  Es ,n
s, j
j 1
Esn  T
4
sn
E g j  4K tl (1   0 )Tg4j
59
Plank-Mean Properties for Water-Vapor
0.6
0.5
0.4
Ka/P (cm bar)
-1
HITEMP
HITRAN
0.3
0.2
0.1
0
0
500
1000
1500
T, K
2000
2500
3000
60
Plank-Mean Properties for CO2
0.4
0.35
ka/P (cm bar)
-1
0.3
HITEMP
HITRAN
0.25
0.2
0.15
0.1
0.05
0
0
500
1000
1500
T, K
2000
2500
3000
61
Plank-Mean Properties for CO
0.04
0.035
Ka/P (cm bar)
-1
0.03
HITEMP
HITRAN
0.025
0.02
0.015
0.01
0.005
0
0
500
1000
1500
T (K)
2000
2500
62
3000
Absorption Coefficient of Soot
When engines running with rich hydrocarbon fuels soot is present
in the combustion gases.
As of today little is known about the nature of the production,
Destruction, shape and size distribution. An approximate value
of soot absorption coefficient can be obtained via:
ka  3.72 f vC0T / C2
Where fv is volume fraction of soot
36nk
C0  2
2
2
2 2
(n  k  2)  4n k
C2=1.4388 cm K, n and k are real and imaginary part of index of
63
refraction
Results for a LH2-LO2 Engine
(SSME)
The specifications of this engine are:
Chamber pressure
O/F
Contraction ratio
Expansion ratio
Throat diameter
Propellant
Coolant
Total coolant flow rate
Coolant inlet temperature
Coolant inlet stagnation pressure
Number of cooling channels
3027 psia
6.0
3.0
77.5
10.3 inches
LH2-LO2
LH2
29.06 lb/s
95R
6452 psia
430
64
Effects of radiation on wall heat
flux of SSME
110
No Radiation
With Radiation, HITRAN
With Radiation, HITEMP
Wall Heat Flux (Btu/in2s)
100
90
80
70
60
50
40
30
20
-15
-10
-5
0
5
10
Axial Position (in)
65
Effects of radiation on wall
temperature of SSME
Wall Surface Temperature (R)
1600
1400
1200
1000
No Radiation
With Radiation HITRAN
With Radiation HITEMP
800
600
-15
-10
-5
0
Axial Position (in)
5
10
66
Coolant Stagnation Temperature (R)
Effects of radiation on coolant
stagnation temperature of SSME
700
No radiation
With Radiation, HITRAN
With Radiation, HITEMP
600
500
400
300
200
100
-15
-10
-5
0
Axial Position (in)
5
10
67
Effects of radiation on coolant
stagnation pressure of SSME
7000
Coolant Stagnation Pressure (psi)
6500
6000
With Radiation, HITEMP
With Radiation, HITRAN
No Radiation
5500
5000
4500
4000
-15
-10
-5
Axial Position (in)
0
5
10
68
Results for a RP1-LO2 Engine
The specifications of this engine are:
Chamber pressure
O/F (mixture ratio)
Contraction ratio
Expansion ratio
Throat diameter
Propellant
Coolant
Total coolant flow rate
Coolant inlet temperature
Coolant inlet pressure
Number of cooling channels
Throat region channel aspect ratio
2,000 psi
1.8
3.4
7.20
2.6 inch
RP1-LO2
LO2
32.893 lb/s
160°R
3,000 psi
100
2.5
69
Effects of radiation on the thermal
characteristics of a RP1-LOX engine
10
Liner radius (in)
8
6
4
2
0
-10
-8
-6
-4
-2
0
2
4
Axial location (in)
70
Effects of radiation on the wall heat
flux of the RP1-LOX engine
50
45
40
No radiation
35
QW, BTU/s in2
With Radiation HITEMP
30
25
20
15
10
5
0
-10
-5
Axial location (in)
0
5
71
Effects of radiation on the wall
temperature of the RP1-LOX engine
1400
1200
TW (R)
1000
800
No Radition
With Radition HITEMP
600
400
200
-10
-5
0
5
Axial location (in)
72
Effects of radiation on the coolant
temperature of the RP1-LOX engine
450
400
Coolant temperature, R
No Radiation
With Rdiation HITEMP
350
300
250
200
150
-10
-5
0
5
Axial location, in
73
Effects of radiation on the coolant stagnation
pressure of the RP1-LOX engine
3000
Coolant stagnation pressure, psi
2900
2800
2700
2600
No radiation
With radiation
2500
2400
2300
-10
-5
0
Axial location, in
5
74
Effects of radiation on the coolant Mach
number of the RP1-LOX engine
0.35
0.3
No radiation
With Radiation, HITEMP
Coolant Mach number
0.25
0.2
0.15
0.1
0.05
0
-10
-5
Axial location, in
0
5
75
Start
Run RTE with its internal
heat flux model
RTE-TDK Interface
Run RTE-TDK interface
program and print wall
temperatures into TDK input
Run TDK
RTE can be replaced by
any wall conduction and
coolant flow code.
TDK can be replaced by
any hot-gas combustion
and convection code
Run TDK-RTE interface program
and print wall heat fluxes into RTE
input
Run RTE with known
wall flux option
Run RTE-TDK interface program and print wall
temperatures into TDK input. Also, check for
convergence
Convergence?
No
Yes
STOP
76
Procedure for Linking TDK and
RTE
This new procedure for linking TDK and RTE is
based on a lookup table of Stanton numbers
that is generated by TDK.
qw
e U eSt 
h adbw  h w
77
Why Stanton Number?
120.00
2
Wall flux (BTU/s in )
100.00
TW=540R
TW=750R
TW=1000R
TW=1250R
TW=1500R
80.00
60.00
40.00
20.00
0.00
-10.00
-5.00
0.00
5.00
10.00
15.00
20.00
25.00
30.00
35.00
40.00
Axial distance from throat (inch)
Wall Flux Distribution for SSME for Five Wall Temperature Generated by TDK
78
Why Stanton Number?
3.5
3
TW=540R
TW=750R
TW=1000R
TW=1250R
TW=1500R
ρeUeSt
2.5
2
1.5
1
0.5
0
-10.00
-5.00
0.00
5.00
10.00
15.00
20.00
25.00
30.00
35.00
40.00
Axial distance from throat (inch)
St
forthe
at Different Wall Temperatures
eU eSSME
79
Why Stanton Number?
18
Percent of relative difference for flux and ρeUeSt at TW=750R and TW=1500R
16
Relative difference %
14
12
QW
10
ρeUeSt
8
6
4
2
0
-10.00
-5.00
0.00
5.00
10.00
15.00
20.00
25.00
30.00
35.00
40.00
Axial distance from throat
Percentage of Relative Difference of Wall Heat Flux and
Between Maximum (1500R) and Minimum (540R) Wall Temperature
for the SSME
80
Flowchart of TDK-RTE Interaction
TDK input with
RTE=.TRUE.
Run TDK
Standard
TDK output
Table of  eU e St
Run RTE
RTE input with
OVERRIDE=
.TRUE.
Resulting wall
temperature distribution
and coolant properties
81
Results for a RP1-LO2 Engine
RP1 as coolant
The specifications of this engine are:
Chamber pressure
O/F (mixture ratio)
Contraction ratio
Expansion ratio
Throat diameter
Propellant
Coolant
Total coolant flow rate
Coolant inlet temperature
Coolant inlet pressure
Number of cooling channels
Throat region channel aspect ratio
2,000 psi
1.8
3.4
7.20
2.6 inch
RP1-LO2
RP1
32.893 lb/s
160°R
1,000 psi
100
2.5
82
Effects of radiation on the thermal
characteristics of a RP1-LOX engine
10
Liner radius (in)
8
6
4
2
0
-10
-8
-6
-4
-2
0
2
4
Axial location (in)
83
Temperature Distribution of the NASA’s RP1/LOX
Engine with RP1 Used as Coolant (without coating)
High coolant wall temperature at z=-1.3” results in coking
84
Temperature Distribution of the NASA’s RP1/LOX Engine with RP1
Used as Coolant (with 0.002” zirconia coating)
85
Cooling channel maximum wall temperature (R)
Cooling Channel Maximum Wall Temperature for RP1
Cooled Case (with 0.002 inch Zirconia coating)
1100
1050
1000
950
900
850
800
750
700
650
600
-10
-8
-6
-4
-2
0
2
4
Axial distance from throat (in)
86
Some Results
• Low-pressure chamber
• High pressure chamber with 200
cooling channels
• High pressure chamber with 150
cooling channels
87
Results for Low Pressure Chamber
Chamber pressure
O/F
Contraction ratio
Expansion ratio
Throat diameter
Propellant
Coolant
Coolant inlet temperature
Coolant inlet stagnation pressure
Total coolant flow rate
Approximate throat heat flux
Number of cooling channels
Throat region channel aspect ratio
Channel width step changes at
450 psia
5.8
3.07
5.3
8.0 inches
GH2-LO2
LH2
50R
700 psia
15 lb/sec
19 Btu/in2-sec
240
5
X=3.039 inches88
X=-4.158 inches
Low Pressure Chamber (unblocked)
X=-0.618 inch
Tc=91R
mc=0.0625 lb/sec
89
Tmax=723R
Temperature Profile
Closed
Open
X=-0.618 inch
mc=0.036 lb/sec
42% reduction in
coolant flow rate
Tc=207R
Tmax=1188R
90
Temperature Profile
Closed
Open
X=-17.781 Inch
mc=0.036 lb/sec
42% reduction in
coolant flow rate
Tc=566R
91
Tmax=1205R
Temperature Distribution
1400
One blocked channel
No blocked channel
Wall Temperature (R)
1200
1000
800
600
400
200
-20
-15
-10
-5
0
5
10
Axial Position (inches)
92
Results for High Pressure Chamber
Chamber pressure
2000 psia
O/F
5.8
Contraction ratio
3.41
Expansion ratio
6.63
Throat diameter
2.6 inches
Propellant
GH2-LO2
Coolant
LH2
Total coolant flow rate
6.45 lb/sec
Coolant inlet temperature
50 R
Coolant inlet stagnation pressure 3200 psia
Approximate throat heat flux
77 Btu/in2-sec
Number of cooling channels
200
Throat region channel aspect ratio 5-7.8
Channel width step changes at
X=0.947 inches
X=-3.906 inches
93
High Pressure Chamber (unblocked)
High pressure chamber
200 cooling channels
X=-0.1 inch
Tc=122R
mc=0.032 lb/sec
Tmax=1058R
94
Temperature Distribution
High Pressure, 200 Channels
1800
One blocked channel
No blocked channel
1600
Wall Temperature (R)
1400
1200
1000
800
600
400
200
-10
-5
0
Axial Position (inches)
5
95
Temperature Profile
High pressure chamber
200 cooling channels
X=-0.1 inch
mc=0.024 lb/sec
Closed
Tmax=1479R
Open
Tc=206R
25% reduction in
coolant flow rate
96
Temperature Profile
High pressure chamber
200 cooling channels
X=-9.38 inch
Closed
Tmax=1580R
Open
Tc=645R
mc=0.024 lb/sec
25% reduction in
coolant flow rate
97
Results for High Pressure Chamber
Chamber pressure
2000 psia
O/F
5.8
Contraction ratio
3.41
Expansion ratio
6.63
Throat diameter
2.6 inches
Propellant
GH2-LO2
Coolant
LH2
Total coolant flow rate
6.45 lb/sec
Coolant inlet temperature
50 R
Coolant inlet stagnation pressure 2900 psia
Approximate throat heat flux
75 Btu/in2-sec
Number of cooling channels
150
Throat region channel aspect ratio 5-7.8
Channel width step changes at
X=0.947 inches
X=-3.906 inches
98
High Pressure Chamber (unblocked)
High pressure chamber
150 cooling channels
X=-0.1 inch
Tc=119R
mc=0.043 lb/sec
Tmax=1211R
99
Temperature Distribution
High Pressure, 200 Channels
One blocked channel
2000
No blocked channel
1800
Wall Temperature (R)
1600
1400
1200
1000
800
600
400
200
-10
-5
0
Axial Position (inches)
5
100
Temperature Profile
High pressure chamber
150 cooling channels
X=-0.1 inch
Closed
Tmax=1766R
Open
Tc=206R
mc=0.031 lb/sec
28% reduction in
coolant flow rate
101
Temperature Profile
High pressure chamber
150 cooling channels
X=-9.38 inch
Closed
Tmax=1738R
Open
Tc=651R
mc=0.031 lb/sec
28% reduction in
coolant flow rate
102
Design for Inlet Pressure
Make two initial guesses for inlet pressures
(Pi1 and Pi2) and determine the corresponding exit
pressures (Pe1 and Pe2 )
Evaluate a revised inlet pressure using the following
equation:
P P
Pi 3  Pi1  ( Pe  Pe1 )
i2
i1
Pe 2  Pe1
Then use the code to calculate the (exit pressure for )
Is
Pe  Pe3
Pe
Yes
very small?
Stop, the results
converged, Pi 3 is the
inlet pressure.
No
Calculate h1  Pe3  Pe1 and h2  Pe3  Pe2
If h1  h2, then Pi 2  Pi 3 and Pi1 remains unchanged
If h2  h1, then Pi1  Pi3 and Pi 2 remains unchanged
103
Design for Aspect Ratio
Breaks the cooling channel width interval into a number
of increments (i.e. w1,w2 ,w3 ,…, wn, where w1 is the
minimum width and wn is the maximum width).
For each width value a procedure similar to that shown
before will be used to determine the corresponding
cooling channel height that yields the desired surface
temperature at the throat. The resulting output will be n
possible solutions,(w1,h1) , (w2,h2), … (wn,hn), from
which the most feasible design from manufacturing
point can be selected.
104
Dump Cooling
• Dump cooling is effective in hydrogen-fueled,
low-pressure systems (Pc < 100 psi) or in nozzle
extension of high-pressure hydrogen systems.
• A small amount of the total hydrogen flow is
diverted from the main fuel-feed line, passed
through cooling passage, and ejected.
• The heat transfer mechanism is similar to that of a
co-current regenerative cooling.
• The coolant, in dump cooling, becomes
superheated as it flows toward the nozzle exit,
where it is expanded overboard at reasonably high
temperatures and velocities, thus contributing
105
some thrust.
Dump Cooling Schematics
LH2 entering
cooling
channels
High velocity H2
106
Film Cooling
• Porous wall materials, or slots and holes provided
in thrust-chamber walls, serve to introduce a
coolant.
• The coolant is usually a fuel (LH2, RP1, etc.)
• Because of the interaction between coolant film
and combustion gases, as a result of heat and mass
transfer, the effective thickness of the coolant film
decreases in the direction of flow.
• Additional coolant is injected at one or more
downstream chamber stations.
• In most engine, film cooling can be achieved by
injection of fuel toward the chamber wall through
peripheral orifices in the injector.
107
Film Cooling
Heat transfer
W fuel
TCO
Twa
Thrust chamber
Chamber wall
Exclusive film cooling has not been applied for major
operational rocket engines. In practice, regenerative
cooling is nearly always supplemented by some sort of film
cooling.
108
Film Cooling (Mixture Ratio Bias)
Periphial orifice injecting fuel only
109
Calculation of wall heat flux
• Correlations are available to evaluate
adiabatic wall temperature with film cooling
• TDK with MABL (Mass Addition
Boundary Layer)
• CFD modeling
110
Correlation for Liquid Film Cooling
Gc
1
h
 
Gg c a(1  bc pvc / c pg )
Where
Gc
Gg
Film-coolant weight flow rate per unit area of coolant chamber wall surface, lb/in2 s
Combustion gas weight flow rate per unit area of chamber cross section
perpendicular to flow, lb/in2 s
c pvc (Taw  Twg )
h
c
Film-cooling efficiency (range from 30% to 70%)
c plc (Twg  Tco )  h fg
h
Film-coolant enthalpy, Btu/lb
cplc
Average constant pressure specific heat of the coolant in the liquid phase, BTU/lb R
cplc
Average constant pressure specific heat of the coolant in the vapor phase, BTU/lb R
cpg
Average constant pressure specific heat of the combustion gases, BTU/lb R
Taw
Adiabatic wall temperature of the gas, R
Twg
Gas-side wall temperature and coolant film temperature, R
Tco
Bulk temperature at manifold, R
hfg
Latent heat of vaporization of coolant, BTU/lb
a
2Vd/Vmf
b
(Vg/Vd)-1
f
friction coefficient between combustion gases and liquid film coolant
Vd, Vm, Vg, axial velocities of combustion gases: at the edge of boundary layer, average and
111
chamber centerline, respectively, ft/s
Correlation for Gaseous-Film Cooling
Taw  Twg
Taw  Tco
where
Taw
Twg
Tco
hg
Gc
cpvc
c
e

hg


 Gc c pvc c





adiabatic wall temperature of the combustion gases, R
maximum allowable gas-side wall temperature, R
Initial film coolant temperature, R
gas-side heat transfer coefficient, BTU/in2 s R
film-coolant weight flow rate per unit area of cooled
chamber wall surface, lb/in2 s
average specific heat at constant pressure of the gaseous film
coolant, BTU/lb R
film-cooling efficiency
112
Transpiration Cooling
Combustion gases
Taw
Twg
Coolant Flow
Tco
Twc
Coolant is introduced through numerous tiny holes in the inner
chamber wall or the wall can be made of porous material
113
Modeling Transpiration Cooling
G 


37  c   Re b 0.1 
G 
Taw  Tco 


0,1
 1  1.8Reb   1 1  e  g 

Twg  Tco 






where
Taw
Twg
Tco
Gc
Gg
Prm
Reb

 37  Gc Reb 0.1 Prm 
e  Gg 





adiabatic wall temperature, R
Gas-side wall temperature, R
coolant bulk temperature, R
transpiration-coolant weight flow-rate per unit area of cooled chamber-wall
surface, lb/in2 s
combustion gas weight flow rate per unit area of chamber cross section
perpendicular to flow, lb/in2 s
mean film Prandtl number
bulk combustion-gas Reynolds number
114
Ablative Cooling
• Good for booster and upper-stage application
• Firing duration from a few seconds to many
minutes
• Limited to chamber pressures of 300 psi or less
• When assisted by film cooling can be used for
chamber pressures up to 1000 psi
• Pyrolysis of resins contained in the chamberwall material does the cooling
115
Ablative Cooling
Ablative Liners
Insulation and
Bonding
High Strength
Outer Shell
116
Radiation Cooling
Used for thrust chamber extensions, where pressure stresses are lowest
Taw
Radiation to
surroundings
Covection
heat from
combustion
gases
4
q   (Twg4  Tsur
.)
q=hg(Taw-Twg)
Twg
hg (Taw  Twg )   (T  T )
4
wg
4
sur .
117
References
• From Modern Engineering for Design of
Liquid-Propellant Rocket Engines, D. K.
Huzel and D. H. Huang Progress in
Astronautics and Aeronautics, Vol. 147, 1992
• home.manhattan.edu/~mohammad.naraghi/rte/rte.html
118
Software
• TDK, Software Engineering Associates, Inc.
seainc.com
• RTE, Tara Technologies, LLC,
tara-technologies.com
• Fluent, fluent.com
119