1. THERMAL ANALYSIS OF LIQUID ROCKET ENGINES
Mohammad H. Naraghi
Department of Mechanical Engineering
Manhattan College
Riverdale NY 10471

2. 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

3. Chamber and Nozzle Cooling Techniques
Regenerative cooling
Dump cooling
Film cooling
Transpiration cooling
Ablative cooling
Radiation cooling

4. Regeneratively Cooled Rocket Engines

5. Types of Cooling Channel
Rectangular cooling channels

6. Cooling Channels

7. High Aspect Ratio Cooling Channels

8. A rocket chamber nozzle made of a copper alloy with machined cooling channels (no closeout)

9. 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

10. Tubular Cooling Channel
Chamber jacket
Tubular cooling channel configuration at throat area (parts of nozzle with small diameter)

11. Cooling Channel Concepts

12. Wall Materials Copper NARloy-Z SS-347 Glidcop Inconel718 Amzirc
Coating:
Wall:
Close-out:
Copper
NARloy-Z
SS-347
Glidcop
Inconel718
Amzirc
Columbium
SS-347
Nickel
Copper
Monel
Platinum
Nicraly
Soot
Zirconia

13. H2-O2 RP1 (JET-A) C12H23-O2 Methane-LOX CH4-O2 Hydrogen Peroxide
Propellants
H2-O2
RP1 (JET-A) C12H23-O2
Methane-LOX CH4-O2
Hydrogen Peroxide

14. Coolants Liquid Hydrogen Liquid Oxygen Water RP1 (JET-A) Methane
Hydrogen Peroxide

15. 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

16. Modes of Heat Transfer Coolant convection Conduction within the wall
Convection and radiation from
combustion gases (hot-gases).
All these modes of heat transfer must be conjugated

17. Modeling Heat Transfer in Regeneratively Cooled Engine Typical Nozzle Broken into a Number of Stations 1 2 3 n
Hot-gas
Coolant in

18. Typical Cross-Section of Nozzle
Due to symmetry calculation
can be performed for a half
cooling channel.

19. 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:
Typical results of CEA with rocket option for the SSME

20. Hot-Gas Side Convective Heat FluxOr
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
is constant pressure hot-gas specific heat at reference condition

21. Adiabatic Wall Temperature (Enthalpy)
The reference enthalpy of the gas side, is given by (Eckert):
The adiabatic wall enthalpy (Bartz and Eckert)
Subscripts S and 0 represent static and stagnation conditions

22. Hot-Gas Side Convective Heat Transfer Coefficient
Dittus-Bolter correlation

23. Hot-Gas Side Convective Heat Transfer Coefficient
Bartz correlation
 Is correction factor for property variation across the boundary layer

24. 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

25. CFD Results, Static Temperature for the Regen Part of the SSME

26. Comparison Between Heat Fluxes Based on Various Methods for the SSME

27. 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

28. One-dimensional wall conduction
TCAW
1/hFhCAC
t/kA
1/hGA
TGAW

29. One-dimensional wall conduction
TGAW
TCAW
1/hGA
1/hFhCAC
t/kA
Fin efficiency l 2

30. Soot Layer Thermal Resistance
For engines with hydrocarbon fuel with Pc < 1500 psi
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

31. Soot Layer thickness For the converging section:
tsoot = (A/At) <A/At<2
tsoot = <A/At
For the diverging section:
tsoot = (A/At) (A/At)
1<A/At<12
tsoot= <A/At
tsoot are in inches

32. Finite Difference Approach

33. 3-D Finite Difference Method

34. 3-D Finite Difference Method
i,j,n
i+1,j,n
i-1,j,n
i,j-1,n
i,j+1,n
i,j,n-1
i,j,n+1
Energy balance for a
typical middle node

35. 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
i+1,j,n
i,j,n+1 Qr Qc

36. Sample Results of Wall Temperature Distribution for the SSME

37. Sample Results of Wall Temperature Distribution for the SSME Throat

38. Sample Results of Wall Temperature Distribution for an Engine with Pass-and-half Tubular Cooling Channels

39. Sample Results of Wall Temperature Distribution for an Engine with Pass-and-half Tubular Cooling Channels

40. Coolant Flow Convection
Two approaches can be used for coolant flow
analysis:
One dimensional flow and heat transfer
Multidimensional CFD analysis

41. 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).

42. 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

43. Cooling Channel Heat Transfer Coefficient for Liquid Hydrogen
Where

44. Cooling Channel Heat Transfer Coefficient for RP-1
Shell correlation
Rocketdyne correlation

45. Cooling Channel Heat Transfer Coefficient for RP-1

46. Cooling Channel Heat Transfer Coefficient for Methane

47. Heat Transfer Coefficient for Oxygen
psia
Where

48. Heat Transfer Coefficient for Fuels as Coolants
Coefficient/Exponent
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
0.37
0.6
-0.2
-6.0
-0.36
274
0.16
0.20
0.97
0.96
Chem. Pure Propane
0.011
0.020
0.87
0.81
-9.6
2.4
-0.5
0.26
-0.23 79
0.10
0.15
Commercial
Propane
0.034
0.028
0.80
-0.24
0.098
-0.43
2.1
-0.38
285
0.27
0.29
0.93
Natural
Gas
0.0028
3.7
1.1
1.0
0.42
1.4
1.5
-6.5
6.3
6.4
2.6
0.087
130
0.38
0.92
0.30
All of the above fuels
0.019
-0.059
0.0019
0.053
0.52
0.11
768
0.28
All of the above fuels except Natural Gas
0.044
0.76
638
0.98

49. Coking Characteristics of RP1
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 , AIAA/SAE/ASME/ASEE 26th Joint Propulsion Conference, Orlando, FL, 1990.

50. Entrance Effect

51. Curvature Effect
where is the hydraulic radius of cooling channel, is the radius of curvature, the sign (+) denotes the concave curvature and the sign (-) denotes the convex one

52. Swilers for Enhancing Heat Transfer

53. Effects of Surface Roughness

54. Coolant Pressure Drop

55. Coolant Pressure Distribution for the SSME

56. Wall Temperature Distribution Along Axial Direction

57. 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

58. Exchange Factors between gas and surface elements
rsi r x
rgi
dgi
dsi
rgj
dgj
dsj

59. Total Exchange Factors Account for wall reflection and gas scattering
Wall heat flux at station n

60. Plank-Mean Properties for Water-Vapor

61. Plank-Mean Properties for CO2

62. Plank-Mean Properties for CO

63. 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:
Where fv is volume fraction of soot
C2= cm K, n and k are real and imaginary part of index of refraction

64. Results for a LH2-LO2 Engine (SSME)
The specifications of this engine are:
Chamber pressure psia
O/F
Contraction ratio
Expansion ratio
Throat diameter inches
Propellant LH2-LO2
Coolant LH2
Total coolant flow rate lb/s
Coolant inlet temperature 95R
Coolant inlet stagnation pressure psia
Number of cooling channels

65. Effects of radiation on wall heat flux of SSME

66. Effects of radiation on wall temperature of SSME

67. Effects of radiation on coolant stagnation temperature of SSME

68. Effects of radiation on coolant stagnation pressure of SSME

69. Results for a RP1-LO2 Engine
The specifications of this engine are:
Chamber pressure 2,000 psi
O/F (mixture ratio)
Contraction ratio
Expansion ratio
Throat diameter inch
Propellant RP1-LO2
Coolant LO2
Total coolant flow rate lb/s
Coolant inlet temperature 160°R
Coolant inlet pressure 3,000 psi
Number of cooling channels 100
Throat region channel aspect ratio 2.5

70. Effects of radiation on the thermal characteristics of a RP1-LOX engine

71. Effects of radiation on the wall heat flux of the RP1-LOX engine

72. Effects of radiation on the wall temperature of the RP1-LOX engine

73. Effects of radiation on the coolant temperature of the RP1-LOX engine

74. Effects of radiation on the coolant stagnation pressure of the RP1-LOX engine

75. Effects of radiation on the coolant Mach number of the RP1-LOX engine

76. RTE-TDK Interface RTE can be replaced by any wall conduction and
Start
Run RTE with its internal heat flux model
Run RTE-TDK interface program and print wall temperatures into TDK input
Run TDK
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?
Yes No
STOP
RTE-TDK Interface
RTE can be replaced by
any wall conduction and
coolant flow code.
TDK can be replaced by
any hot-gas combustion
and convection code

77. 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.

78. Why Stanton Number?
Wall Flux Distribution for SSME for Five Wall Temperature Generated by TDK

79. Why Stanton Number?
for the SSME at Different Wall Temperatures

80. Why Stanton Number?
Percentage of Relative Difference of Wall Heat Flux and
Between Maximum (1500R) and Minimum (540R) Wall Temperature
for the SSME

81. Flowchart of TDK-RTE Interaction
TDK input with RTE=.TRUE.
Run TDK
Standard TDK output
Table of
Run RTE
RTE input with OVERRIDE=
.TRUE.
Resulting wall temperature distribution and coolant properties

82. Results for a RP1-LO2 Engine RP1 as coolant
The specifications of this engine are:
Chamber pressure 2,000 psi
O/F (mixture ratio)
Contraction ratio
Expansion ratio
Throat diameter inch
Propellant RP1-LO2
Coolant RP1
Total coolant flow rate lb/s
Coolant inlet temperature 160°R
Coolant inlet pressure 1,000 psi
Number of cooling channels 100
Throat region channel aspect ratio 2.5

83. Effects of radiation on the thermal characteristics of a RP1-LOX engine

84. 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

85. Temperature Distribution of the NASA’s RP1/LOX Engine with RP1 Used as Coolant (with 0.002” zirconia coating)

86. Cooling Channel Maximum Wall Temperature for RP1 Cooled Case (with 0
Cooling Channel Maximum Wall Temperature for RP1 Cooled Case (with inch Zirconia coating)

87. Some Results Low-pressure chamber
High pressure chamber with 200 cooling channels
High pressure chamber with 150 cooling channels

88. Results for Low Pressure Chamber
Chamber pressure psia
O/F
Contraction ratio
Expansion ratio
Throat diameter inches
Propellant GH2-LO2
Coolant LH2
Coolant inlet temperature 50R
Coolant inlet stagnation pressure 700 psia
Total coolant flow rate lb/sec
Approximate throat heat flux 19 Btu/in2-sec
Number of cooling channels
Throat region channel aspect ratio
Channel width step changes at X=3.039 inches
X= inches

89. Low Pressure Chamber (unblocked)
X= inch
Tc=91R
c= lb/sec
Tmax=723R

90. Temperature Profile X=-0.618 inch Open Closed c=0.036 lb/sec
42% reduction in
coolant flow rate
Tc=207R
Tmax=1188R

91. Temperature Profile X=-17.781 Inch Open Closed c=0.036 lb/sec
42% reduction in
coolant flow rate
Tc=566R
Tmax=1205R

92. Temperature Distribution

93. Results for High Pressure Chamber
Chamber pressure psia
O/F
Contraction ratio
Expansion ratio
Throat diameter inches
Propellant GH2-LO2
Coolant LH2
Total coolant flow rate lb/sec
Coolant inlet temperature 50 R
Coolant inlet stagnation pressure 3200 psia
Approximate throat heat flux Btu/in2-sec
Number of cooling channels
Throat region channel aspect ratio
Channel width step changes at X=0.947 inches
X= inches

94. High Pressure Chamber (unblocked)
200 cooling channels
X=-0.1 inch
Tc=122R
c=0.032 lb/sec
Tmax=1058R

95. Temperature Distribution High Pressure, 200 Channels

96. Temperature Profile High pressure chamber 200 cooling channels
X=-0.1 inch
c=0.024 lb/sec
25% reduction in
coolant flow rate
Closed
Open
Tc=206R
Tmax=1479R

97. Temperature Profile High pressure chamber 200 cooling channels
X=-9.38 inch
c=0.024 lb/sec
Closed
Open
25% reduction in
coolant flow rate
Tmax=1580R
Tc=645R

98. Results for High Pressure Chamber
Chamber pressure psia
O/F
Contraction ratio
Expansion ratio
Throat diameter inches
Propellant GH2-LO2
Coolant LH2
Total coolant flow rate lb/sec
Coolant inlet temperature 50 R
Coolant inlet stagnation pressure 2900 psia
Approximate throat heat flux Btu/in2-sec
Number of cooling channels
Throat region channel aspect ratio
Channel width step changes at X=0.947 inches
X= inches

99. High Pressure Chamber (unblocked)
150 cooling channels
X=-0.1 inch
Tc=119R
c=0.043 lb/sec
Tmax=1211R

100. Temperature Distribution High Pressure, 200 Channels

101. Temperature Profile High pressure chamber 150 cooling channels
X=-0.1 inch
c=0.031 lb/sec
Closed
Open
28% reduction in
coolant flow rate
Tc=206R
Tmax=1766R

102. Temperature Profile High pressure chamber 150 cooling channels
X=-9.38 inch
Closed
Open
c=0.031 lb/sec
28% reduction in
coolant flow rate
Tc=651R
Tmax=1738R

103. 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:
Then use the code to calculate the (exit pressure for ) Is
very small?
Stop, the results converged, is the inlet pressure.
Yes No
Calculate and
If , then and remains unchanged

104. 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.

105. 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 some thrust.

106. Dump Cooling Schematics

107. 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.

108. Film Cooling Heat transfer Twa Thrust chamber TCO 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.

109. Film Cooling (Mixture Ratio Bias)

110. 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

111. Correlation for Liquid Film Cooling
Where
Gc Film-coolant weight flow rate per unit area of coolant chamber wall surface, lb/in2 s
Gg Combustion gas weight flow rate per unit area of chamber cross section perpendicular to flow, lb/in2 s
Film-cooling efficiency (range from 30% to 70%)
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 chamber centerline, respectively, ft/s

112. Correlation for Gaseous-Film Cooling
where
Taw adiabatic wall temperature of the combustion gases, R
Twg maximum allowable gas-side wall temperature, R
Tco Initial film coolant temperature, R
hg gas-side heat transfer coefficient, BTU/in2 s R
Gc film-coolant weight flow rate per unit area of cooled chamber wall surface, lb/in2 s
cpvc average specific heat at constant pressure of the gaseous film coolant, BTU/lb R
c film-cooling efficiency

113. Transpiration Cooling
Taw
Twg
Twc
Tco
Coolant is introduced through numerous tiny holes in the inner
chamber wall or the wall can be made of porous material

114. Modeling Transpiration Cooling
where
Taw adiabatic wall temperature, R
Twg Gas-side wall temperature, R
Tco coolant bulk temperature, R
Gc transpiration-coolant weight flow-rate per unit area of cooled chamber-wall
surface, lb/in2 s
Gg combustion gas weight flow rate per unit area of chamber cross section
perpendicular to flow, lb/in2 s
Prm mean film Prandtl number
Reb bulk combustion-gas Reynolds number

115. 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 chamber-wall material does the cooling

116. Ablative Cooling

117. Radiation Cooling q=hg(Taw-Twg)
Used for thrust chamber extensions, where pressure stresses are lowest
Taw
q=hg(Taw-Twg)
Twg

118. 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

119. Software TDK, Software Engineering Associates, Inc. seainc.com
RTE, Tara Technologies, LLC, tara-technologies.com
Fluent, fluent.com