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

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2 Introduction to Cooling Methods Combustion gases are 4000 to more than 6000 o F Heat transfer rates from hot-gases to the chamber wall are 0.5 to over 130 BTU/in 2 s A cooling system is needed in order to maintain engine integrity

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

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4 Regeneratively Cooled Rocket Engines

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5 Types of Cooling Channel Rectangular cooling channels

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6 Cooling Channels

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7 High Aspect Ratio Cooling Channels

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

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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

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

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11 Cooling Channel Concepts

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

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13 Propellants H 2 -O 2 RP1 (JET-A) C 12 H 23 -O 2 Methane-LOX CH 4 -O 2 Hydrogen Peroxide

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

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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

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

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17 Modeling Heat Transfer in Regeneratively Cooled Engine Typical Nozzle Broken into a Number of Stations 12 3 n Hot-gas Coolant in

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

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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

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20 n is the station number T GAW and i GAW are adiabatic wall temperature and enthalpy T GW and i GW are gas-side wall temperature and enthalpy h G is the gas-side heat transfer coefficient is constant pressure hot-gas specific heat at reference condition Hot-Gas Side Convective Heat Flux Or

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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

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

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

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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

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

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

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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

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28 One-dimensional wall conduction T GAW T CAW 1/h G A 1/ h F h C A C t/kA

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29 One-dimensional wall conduction T GAW T CAW 1/h G A 1/ h F h C A C t/kA Fin efficiency l 22

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30 Soot Layer Thermal Resistance For engines with hydrocarbon fuel with P c < 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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31 Soot Layer thickness For the converging section: t soot = (A/A t )

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32 Finite Difference Approach

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33 3-D Finite Difference Method

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34 3-D Finite Difference Method i,j,ni+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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35 3-D Finite Difference Method i,j,ni+1,j,n i-1,j,n i,j+1,n i,j,n-1 i,j,n+1 Energy balance for a typical surface node QcQc QrQr

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36 Sample Results of Wall Temperature Distribution for the SSME

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37 Sample Results of Wall Temperature Distribution for the SSME Throat

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

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

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40 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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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).

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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

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43 Cooling Channel Heat Transfer Coefficient for Liquid Hydrogen Where

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

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45 Cooling Channel Heat Transfer Coefficient for RP-1

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46 Cooling Channel Heat Transfer Coefficient for Methane

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47 Heat Transfer Coefficient for Oxygen Where psia

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48 Heat Transfer Coefficient for Fuels as Coolants Fuel Coefficient/Exponent No. of Points Std. Dev. Correl. Coeff.c bcdefgh RP Chem. Pure Propane Commercial Propane Natural Gas All of the above fuels All of the above fuels except Natural Gas

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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.

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50 Entrance Effect

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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

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52 Swilers for Enhancing Heat Transfer

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53 Effects of Surface Roughness

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54 Coolant Pressure Drop

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55 Coolant Pressure Distribution for the SSME

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56 Wall Temperature Distribution Along Axial Direction

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57 Radiation Heat Transfer from Hot-Gases Combustion Gases consist of several radiatively participating species These species are: soot, CO, CO 2, 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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58 Exchange Factors between gas and surface elements r si r x r gi dg i ds i r gj r si dg j ds j

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

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60 Plank-Mean Properties for Water-Vapor

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61 Plank-Mean Properties for CO 2

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62 Plank-Mean Properties for CO

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63 Absorption Coefficient of Soot Where f v is volume fraction of soot C 2 = cm K, n and k are real and imaginary part of index of refraction 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:

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64 Results for a LH2-LO2 Engine (SSME) The specifications of this engine are: Chamber pressure 3027 psia O/F6.0 Contraction ratio 3.0 Expansion ratio 77.5 Throat diameter 10.3 inches PropellantLH2-LO2 CoolantLH2 Total coolant flow rate lb/s Coolant inlet temperature 95R Coolant inlet stagnation pressure 6452 psia Number of cooling channels 430

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65 Effects of radiation on wall heat flux of SSME

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66 Effects of radiation on wall temperature of SSME

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67 Effects of radiation on coolant stagnation temperature of SSME

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68 Effects of radiation on coolant stagnation pressure of SSME

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69 Results for a RP1-LO2 Engine The specifications of this engine are: Chamber pressure2,000 psi O/F (mixture ratio)1.8 Contraction ratio3.4 Expansion ratio7.20 Throat diameter2.6 inch PropellantRP1-LO2 CoolantLO2 Total coolant flow rate lb/s Coolant inlet temperature160°R Coolant inlet pressure3,000 psi Number of cooling channels100 Throat region channel aspect ratio2.5

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

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

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

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

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

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

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76 RTE-TDK Interface 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 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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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.

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

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

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80 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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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

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82 Results for a RP1-LO 2 Engine RP1 as coolant The specifications of this engine are: Chamber pressure2,000 psi O/F (mixture ratio)1.8 Contraction ratio3.4 Expansion ratio7.20 Throat diameter2.6 inch PropellantRP1-LO2 CoolantRP1 Total coolant flow rate lb/s Coolant inlet temperature160°R Coolant inlet pressure1,000 psi Number of cooling channels100 Throat region channel aspect ratio2.5

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

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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

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

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

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

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88 Results for Low Pressure Chamber Chamber pressure450 psia O/F5.8 Contraction ratio3.07 Expansion ratio5.3 Throat diameter8.0 inches PropellantGH2-LO2 CoolantLH2 Coolant inlet temperature50R Coolant inlet stagnation pressure700 psia Total coolant flow rate 15 lb/sec Approximate throat heat flux19 Btu/in 2 -sec Number of cooling channels 240 Throat region channel aspect ratio 5 Channel width step changes at X=3.039 inches X= inches

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89 Low Pressure Chamber (unblocked) T max =723R X= inch T c =91R c = lb/sec

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90 Temperature Profile T max =1188R Closed Open X= inch T c =207R c =0.036 lb/sec 42% reduction in coolant flow rate

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91 Temperature Profile X= Inch T max =1205R Closed Open T c =566R c =0.036 lb/sec 42% reduction in coolant flow rate

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92 Temperature Distribution

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93 Results for High Pressure Chamber Chamber pressure2000 psia O/F5.8 Contraction ratio 3.41 Expansion ratio 6.63 Throat diameter 2.6 inches PropellantGH2-LO2 CoolantLH2 Total coolant flow rate 6.45 lb/sec Coolant inlet temperature50 R Coolant inlet stagnation pressure3200 psia Approximate throat heat flux 77 Btu/in 2 -sec Number of cooling channels 200 Throat region channel aspect ratio Channel width step changes at X=0.947 inches X= inches

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94 T max =1058R X=-0.1 inch T c =122R High Pressure Chamber (unblocked) High pressure chamber 200 cooling channels c =0.032 lb/sec

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95 Temperature Distribution High Pressure, 200 Channels

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96 T max =1479R ClosedOpen X=-0.1 inch Temperature Profile T c =206R High pressure chamber 200 cooling channels c =0.024 lb/sec 25% reduction in coolant flow rate

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97 Temperature Profile T max =1580R ClosedOpen X=-9.38 inch T c =645R High pressure chamber 200 cooling channels c =0.024 lb/sec 25% reduction in coolant flow rate

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98 Results for High Pressure Chamber Chamber pressure2000 psia O/F5.8 Contraction ratio 3.41 Expansion ratio 6.63 Throat diameter 2.6 inches PropellantGH2-LO2 CoolantLH2 Total coolant flow rate 6.45 lb/sec Coolant inlet temperature50 R Coolant inlet stagnation pressure2900 psia Approximate throat heat flux 75 Btu/in 2 -sec Number of cooling channels 150 Throat region channel aspect ratio Channel width step changes at X=0.947 inches X= inches

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99 T max =1211R X=-0.1 inch T c =119R High Pressure Chamber (unblocked) High pressure chamber 150 cooling channels c =0.043 lb/sec

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100 Temperature Distribution High Pressure, 200 Channels

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101 T max =1766R ClosedOpen X=-0.1 inch Temperature Profile T c =206R High pressure chamber 150 cooling channels c =0.031 lb/sec 28% reduction in coolant flow rate

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102 Temperature Profile T max =1738R ClosedOpen X=-9.38 inch T c =651R High pressure chamber 150 cooling channels c =0.031 lb/sec 28% reduction in coolant flow rate

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103 Make two initial guesses for inlet pressures (P i1 and P i2 ) and determine the corresponding exit pressures (P e1 and P e2 ) Evaluate a revised inlet pressure using the following equation: Then use the code to calculate the (exit pressure for ) Is very small? Calculate and If, then and remains unchanged Stop, the results converged, is the inlet pressure. No Yes Design for Inlet Pressure

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104 Design for Aspect Ratio Breaks the cooling channel width interval into a number of increments (i.e. w 1,w 2,w 3,…, w n, where w 1 is the minimum width and w n 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,(w 1,h 1 ), (w 2,h 2 ), … (w n,h n ), from which the most feasible design from manufacturing point can be selected.

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105 Dump Cooling Dump cooling is effective in hydrogen-fueled, low-pressure systems (P c < 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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106 Dump Cooling Schematics

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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 (LH 2, 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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108 Film Cooling Chamber wall T wa T CO Thrust chamber Heat transfer 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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109 Film Cooling (Mixture Ratio Bias)

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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

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111 Correlation for Liquid Film Cooling Where G c Film-coolant weight flow rate per unit area of coolant chamber wall surface, lb/in 2 s G g Combustion gas weight flow rate per unit area of chamber cross section perpendicular to flow, lb/in 2 s Film-cooling efficiency (range from 30% to 70%) hFilm-coolant enthalpy, Btu/lb c plc Average constant pressure specific heat of the coolant in the liquid phase, BTU/lb R c plc Average constant pressure specific heat of the coolant in the vapor phase, BTU/lb R c pg Average constant pressure specific heat of the combustion gases, BTU/lb R T aw Adiabatic wall temperature of the gas, R T wg Gas-side wall temperature and coolant film temperature, R TcoBulk temperature at manifold, R h fg Latent heat of vaporization of coolant, BTU/lb a2V d /V m fb(V g /V d )-1 ffriction coefficient between combustion gases and liquid film coolant V d, V m, V g, axial velocities of combustion gases: at the edge of boundary layer, average and chamber centerline, respectively, ft/s

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112 Correlation for Gaseous-Film Cooling where T aw adiabatic wall temperature of the combustion gases, R T wg maximum allowable gas-side wall temperature, R T co Initial film coolant temperature, R h g gas-side heat transfer coefficient, BTU/in 2 s R G c film-coolant weight flow rate per unit area of cooled chamber wall surface, lb/in 2 s c pvc average specific heat at constant pressure of the gaseous film coolant, BTU/lb R cfilm-cooling efficiency

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113 Transpiration Cooling Coolant is introduced through numerous tiny holes in the inner chamber wall or the wall can be made of porous material T aw T co T wg T wc

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114 Modeling Transpiration Cooling where T aw adiabatic wall temperature, R T wg Gas-side wall temperature, R T co coolant bulk temperature, R G c transpiration-coolant weight flow-rate per unit area of cooled chamber-wall surface, lb/in 2 s G g combustion gas weight flow rate per unit area of chamber cross section perpendicular to flow, lb/in 2 s Pr m mean film Prandtl number Re b bulk combustion-gas Reynolds number

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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

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116 Ablative Cooling

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117 Used for thrust chamber extensions, where pressure stresses are lowest q=h g (T aw -T wg ) Radiation Cooling T wg T aw

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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

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

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