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**THERMAL ANALYSIS OF LIQUID ROCKET ENGINES**

Mohammad H. Naraghi Department of Mechanical Engineering Manhattan College Riverdale NY 10471

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**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

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**Chamber and Nozzle Cooling Techniques**

Regenerative cooling Dump cooling Film cooling Transpiration cooling Ablative cooling Radiation cooling

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**Regeneratively Cooled Rocket Engines**

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**Types of Cooling Channel**

Rectangular cooling channels

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Cooling Channels

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**High Aspect Ratio Cooling Channels**

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

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**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

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**Tubular Cooling Channel**

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

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**Cooling Channel Concepts**

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**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

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**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

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**Coolants Liquid Hydrogen Liquid Oxygen Water RP1 (JET-A) Methane**

Hydrogen Peroxide

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**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

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**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

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

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**Typical Cross-Section of Nozzle**

Due to symmetry calculation can be performed for a half cooling channel.

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**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

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**Hot-Gas Side Convective Heat Flux**

Or 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

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**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

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**Hot-Gas Side Convective Heat Transfer Coefficient**

Dittus-Bolter correlation

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**Hot-Gas Side Convective Heat Transfer Coefficient**

Bartz correlation Is correction factor for property variation across the boundary layer

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**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

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**CFD Results, Static Temperature for the Regen Part of the SSME**

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**Comparison Between Heat Fluxes Based on Various Methods for the SSME**

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**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

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**One-dimensional wall conduction**

TCAW 1/hFhCAC t/kA 1/hGA TGAW

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**One-dimensional wall conduction**

TGAW TCAW 1/hGA 1/hFhCAC t/kA Fin efficiency l 2

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**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

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**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

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**Finite Difference Approach**

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**3-D Finite Difference Method**

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**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

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**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

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**Sample Results of Wall Temperature Distribution for the SSME**

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**Sample Results of Wall Temperature Distribution for the SSME Throat**

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

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

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**Coolant Flow Convection**

Two approaches can be used for coolant flow analysis: One dimensional flow and heat transfer Multidimensional CFD analysis

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**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).

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**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

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**Cooling Channel Heat Transfer Coefficient for Liquid Hydrogen**

Where

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**Cooling Channel Heat Transfer Coefficient for RP-1**

Shell correlation Rocketdyne correlation

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**Cooling Channel Heat Transfer Coefficient for RP-1**

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**Cooling Channel Heat Transfer Coefficient for Methane**

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**Heat Transfer Coefficient for Oxygen**

psia Where

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**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

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**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.

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Entrance Effect

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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

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**Swilers for Enhancing Heat Transfer**

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**Effects of Surface Roughness**

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Coolant Pressure Drop

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**Coolant Pressure Distribution for the SSME**

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**Wall Temperature Distribution Along Axial Direction**

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**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

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**Exchange Factors between gas and surface elements**

rsi r x rgi dgi dsi rgj dgj dsj

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**Total Exchange Factors Account for wall reflection and gas scattering**

Wall heat flux at station n

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**Plank-Mean Properties for Water-Vapor**

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**Plank-Mean Properties for CO2**

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**Plank-Mean Properties for CO**

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**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

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**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

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**Effects of radiation on wall heat flux of SSME**

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**Effects of radiation on wall temperature of SSME**

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**Effects of radiation on coolant stagnation temperature of SSME**

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**Effects of radiation on coolant stagnation pressure of SSME**

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**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

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

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

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**Effects of radiation on the wall temperature of the RP1-LOX engine**

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**Effects of radiation on the coolant temperature of the RP1-LOX engine**

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

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

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**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

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**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.

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

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Why Stanton Number? for the SSME at Different Wall Temperatures

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

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**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

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**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

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

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**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

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

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**Cooling Channel Maximum Wall Temperature for RP1 Cooled Case (with 0**

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

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**Some Results Low-pressure chamber**

High pressure chamber with 200 cooling channels High pressure chamber with 150 cooling channels

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**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

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**Low Pressure Chamber (unblocked)**

X= inch Tc=91R c= lb/sec Tmax=723R

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**Temperature Profile X=-0.618 inch Open Closed c=0.036 lb/sec**

42% reduction in coolant flow rate Tc=207R Tmax=1188R

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**Temperature Profile X=-17.781 Inch Open Closed c=0.036 lb/sec**

42% reduction in coolant flow rate Tc=566R Tmax=1205R

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**Temperature Distribution**

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**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

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**High Pressure Chamber (unblocked)**

200 cooling channels X=-0.1 inch Tc=122R c=0.032 lb/sec Tmax=1058R

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**Temperature Distribution High Pressure, 200 Channels**

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**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

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**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

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**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

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**High Pressure Chamber (unblocked)**

150 cooling channels X=-0.1 inch Tc=119R c=0.043 lb/sec Tmax=1211R

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**Temperature Distribution High Pressure, 200 Channels**

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**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

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**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

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**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

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**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.

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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.

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**Dump Cooling Schematics**

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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.

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**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.

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**Film Cooling (Mixture Ratio Bias)**

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**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

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**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

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**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

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**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

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**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

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**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

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Ablative Cooling

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**Radiation Cooling q=hg(Taw-Twg)**

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

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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

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**Software TDK, Software Engineering Associates, Inc. seainc.com**

RTE, Tara Technologies, LLC, tara-technologies.com Fluent, fluent.com

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