Home

RTE, Rocket Thermal Evaluation

1. eq 4 Calculate hot gas adiabatic wall temperature f Pes icaw Calculate hot gas side heat transfer coefficient he eq 7 Copyright Tara Technologies LLC Pes Pes n ENTE Pes f Pes Los Calculate coolant stagnation enthalpy eq 13 when j gt 1 and eq 14 when j 1 Calculate coolant velocity eq 15 Calculate coolant static enthalpy eq 17 Copyright O Tara Technologies LLC 7 Calculate coolant Reynolds numbers Rec and average Reynolds numbers eqs 18 21 Calculate friction coolant friction factor f eqs 22 23 Calculate viscous and momentum pressure drops eqs 25 27 Evaluate coolant static pressure eq 28 f n sido Determine coolant wall properties Kew Calculate coolant reference enthalpy eq 30 Find coolant reference properties Kex Tex f Pes Find coolant static properties C pa Mes uo Find coolant adiabatic wall enthalpy y eq 31 and adiabatic wall temperature Tr f Pes icy 2 Copyright Tara Technologies LLC 73 Use the conduction subroutine for evaluating wall temperature distribution and heat transfer to the cooling channel at station n q Check wall temperature for convergence T jd lt Calculate coolant entropy and Mach number M 5 f Ps s
2. 2 88 5 40 C Other entrance effect factors for different types of cooling channel entrances reported in 20 are given by 07 n YAS it 0 1 1 E Ty 41 for a 90 bend entrance Taylor 21 suggested the following correction factors 159 Y ASyaldc icd 42 Ent T for straight tube and Copyright O Tara Technologies LLC 23 T pl Es y AS LER 43 T C for a 90 bend entrance Any of the above four correlations can be selected by setting RTE s NAMELIST variable IENT to 1 for equation 40 2 for equation 41 3 for equation 42 and 4 for equation 43 If no number is assigned to IENT then the entrance effect will be neglected Curvature Effect The correction factor for the curvature effect is given by 22 1 20 4 44 Cur CX ave gt 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 The radius of curvature RCURVE must be input through RTE s NAMELIST for every station If no RCURVE value is specified in the input then a large value is assigned to this parameter which corresponds to a straight channel 6 0 Surface Roughness Effect on Heat Transfer Enhancement Itis well known that the surface roughness increases the pressure drop in the cooling channel as well as convective heat transfer The effe
3. cs AcN pcs AcN An average value of variables between stations n and n 1 in equations 25 and 26 are used to improve the accuracy Pressure drop due to change in size of cooling channels contraction or expansion is incorporated through the following equation P cs Y Copyright O Tara Technologies LLC 19 2 C 3 1 for expansion C where i 0 5 0 167 0 125 0 208 for contraction d de de The static pressure at each station is calculated based on the viscous and momentum pressure drops and is given by Pos Pes 7 lar x Ap AP 28 Coolant Wall and Reference Properties Once the coolant static pressure is determined the coolant wall properties which are functions of the static coolant pressure P and wall temperature i e C pcy gt How slow f P CS Toy 29 are evaluated using the coolant properties modules GASP WASP or RP1 It should be noted that the wall temperature is not constant at a given station hence three coolant wall properties which are based on the lower upper and side wall temperatures are determined The reference and adiabatic wall enthalpies at the station are respectively calculated from the following equations 9 beg 05g Fiy 019A s tes 30 and Mr P 31 Tex lco los The adiabatic wall temperature is
4. 0 0095 0 0095 0 0095 0 0095 0 0095 0 0095 0 0095 0 0095 0 0095 0 0095 0 0095 00 0095 0 0095 0 0095 0 0095 0 0095 0 0095 0 0095 0 0095 0 0095 0 0095 CG 0 023 0 023 0 023 0 023 0 023 0 023 0 023 0 023 0 023 0 023 0 023 0 023 0 023 0 023 0 023 0 023 0 023 0 023 0 023 0 023 0 023 0 023 0 023 0 023 0 023 0 023 0 023 0 023 0 023 0 023 0 023 0 023 0 0237 05 023 05023 0 028 70 023 05023 0 023 0 023 0 023 RCURVE 1000000 1000000 1000000 1000000 1000000 1000000 1000000 1000000 1000000 1000000 1000000 2 001 2 001 2 001 2 001 2 001 2 001 2 001 2 001 2 001 2 001 2 001 2 001 1000000 1000000 1000000 1000000 1000000 1000000 1000000 4 002 4 002 4 002 4 002 1000000 1000000 1000000 1000000 1000000 1000000 1000000 ISW 0 0 0 0 0 0 0 0 0 0 0 O 0 0 0 0 0 0 O0 0 O O 0 0 0 0 0 0 0 0 0 O 0 0 0 0 0 0 0 0 O RGHNS 0 000064 0 000064 0 000064 0 000064 0 000064 0 000064 0 000064 0 000064 0 000064 0 000064 0 000064 0 000064 0 000064 0 000064 0 000064 0 000064 0 000064 0 000064 0 000064 0 000064 0 000064 0 000064 0 000064 0 000064 0 000064 0 000064 0 000064 0 000064 0 000064 0 000064 0 000064 0 000064 0 000064 0 000064 0 000064 0 000064 0 000064 0 000064 0 000064 0 000064 0 000064 ISOST IWFLUX 0 OW 0 0 OF 704 40x T0505 70 502 0 0 0 0
5. 01 0 22222539 04 3 0 16937683E 07 0 50061342E 0 31647755E 05 0 66560000E 0 0 00000000 4 ALCLF2 J 6 76AL 1 CL 1 F 2 0 G 300 000 5000 000 100 43135 0 88674544E 01 0 12933319E 02 0 57468796E 06 0 11278419E 09 0 81398154E 14 2 0 12309250E 06 0 15613943E 02 0 34905245E 01 0 23410622E 01 0 36730802E 04 3 0 27577485E 07 0 80570874E 11 0 12197857E 06 0 10346676E 02 0 00000000 4 Copyright O Tara Technologies LLC ZRN S 0 55407820E 01 0 0 45751324 05 0 0 28804219E 08 0 N RN 0 N RO 0 eus 0 ZRO 0 0 ZRO 0 0 END L 0 70451164E 01 38105527E 05 0 0 00000000 2 A 22144395E 02 0 2732797E 06 0 69567648 07 0 2 B 89573629E 01 3414354E 06 0 0 00000000 2 L 0567675E 02 2842745E 06 0 0 00000000 J 6 61ZR No Le 0 0 5 300 000 3225 000 61839353 03 0 29542110 06 0 11784311 09 0 15241430 13 27420654 31087849 11 0 45112020 05 0 13901069 02 J 6 61ZR 1 N 1 0 00000000 34436264E 02 0 0 0 L 0 00000000 70451164E 01 0 00000000 0 38105527E 05 0 34436264E 02 9639763E 01 0 100891E 03 0 2380947E 10 0 C N P o C 0 00000000 45274017E 02 0 0 00000000 0 J12 65ZR O 22 0 00000000 54592264E 02 0 0 00000000 0 0 0 2 65ZR Qu 2 2 65ZR o 2 0 0 5 79537106E 00 0 3311967E 06 0 0 0 5 0 00000000 89573629 01 3414354 06 0 0 0 L 0 00000000 0567675E 02 2842745E 06
6. 20 20 20 20 20 20 20 255 274 28 30 3e 32 34 35 3T 74 74 74 75 75 76 77 77 76 73 01 2 43 83 22 59 T5 225 2 58 42 LTs 76 50 76 76 AN 74 17 13 12 89 94 49 Tl 69 88 1910 195 19 195 19 19 19 19 24 26 28 30 Sis 325 34 354 70 223 63 721 2 34 Tis 72 71 71 2 74 73 73 72 12 71 70 66 99 86 65 94 18 74 45 44 T3 72 15 83 64 76 40 99 2010 1 9 19 1 9 19 19 2 3 26 Zils 29 41 314 33 30 30 34 24 19 24 24 24 24 19 59 251 221 24 24 13 92 16 71 02 18 48 222 88 399 81 69 17 46 2110 18 18 18 18 18 18 18 22 24 25 27 28 29 30 323 33 65 24 66 94 28 58 67 66 67 67 63 87 60 87 225 sd 291 437 06 16 02 22 97 47 83 2210 18 18 18 18 18 Tex 18 22 78 25 239 2 56 274 2 95 31 40 23 26 28 32 64 47 64 64 65 49 65 66 65 67 67 67 67 66 66 66 66 65 62 61 96 19 10 83 16 07 2310 17 17 17 17 17 1 7 17 23 24 254 26 28 239 55 72 29 30 31 62 66 65 70 43 65 26 65 36 63 271 60 65 65 65 64 6
7. A user can fill in engine specifications in designated Excel cells and choose the right engine information from combo boxes Then by clicking on a command button data from the Excel interface would be transferred into RTE s input file Also RTE and its radiation module can be run from Excel RTE provides a number of output files each Copyright O Tara Technologies LLC provide useful information regarding the engine s thermal performance The Graphic postprocessor of RTE is based on Techplot software It produces a number of output files that can be processed by Tecplot for temperature isotherms and graphic results Copyright O Tara Technologies LLC 5 gt Y Q A n ARAS vZB Greek Symbols B AS Ap Ar AQ NOMENCLATURE area correlation factor for heat transfer coefficient specific heat diameter total exchange factor between gas and surface differential elements total exchange factor between two surface differential elements cooling channel surface roughness surface and gas emissive power friction factor gravitational constant 32 2 ft Ib Ib s heat transfer coefficient enthalpy work heat proportionality factor conductivity absorption coefficient scattering coefficient total extinction coefficient total number of axial stations total number of cooling channels pressure Prandtl number heat flux radiative heat transfer at inner surface radius rad
8. Bao Tes tano Re 1 46 where is the insert diameter note that d is always smaller than the cooling channel width Thorsen and Landis measured the heat transfer coefficient for the cooling of water in tubes having tapes with three different helix angles 11 1 16 9 and 26 5 The correction factor for the cooling data is given by G Quer 47 where tan 1 0 004872 tan 0 Swiler inserts in cooling channels result in an increase in pressure drop The correction factor for the swiler pressure drop is given by 1 15 E 49 swiler f y for Re gt 70000 and 1 154 15 7000 Re y 650000 y Quite y m 1 50 yl for Re lt 70000 Copyright Tara Technologies LLC 25 Swilers can be used at stations where heat transfer enhancement is needed by setting ISW 1 in the NAMELIST of RTE If no swiler is used at some stations the ISW must be set to 0 Swiler angles are defined by SANGLE in degrees e g SANGLE 30 Edge Effects The sharp corners of rectangular cooling channels result in an increase in the frictional pressure drop When all four corners are sharp the following correction factor can be used for frictional pressure drop 26 0 1125 1 00875 dm 51 where Ar h w is the aspect ration of the cooling channel In some cases the lower corners of cooling channels are rounded and the upper corners are sharp The correction factor for
9. Hot Gas Side Radiative Properties CHANNEL A R BA Hot gas scattering albedo 0 NRCHB Hot gas extinction coef 1 in 25 Inner surface emissivity 0 3 Lano CHANNEL AR AR ROJAT QNPHIL NPHIC Help on selecting coolant correlation Hendricks Select a coolant correlation Help on User Defined Coolant Coi Coorelation coefficient Reynolds number exponent b Prandtl number exponent c Density ratio exponent d Viscosity ratio exponent 0 6 A Click on the above button for help on the user defined correlation Conductivity ratio exponent 0 2 Specific heat ratio 4 5 Pressure ratio exponent h 0 36 T 14 EE 2 Figure 11 Part of RTE s GUI with help on meshing activated Copyright O Tara Technologies LLC 46 RTE OUTPUTS RTE s main output is printed on unit 5 screen It contains a printout of the input information given in the RTEDATA Next it prints the output nomenclature and the results of the ROCKET subroutine which includes the static chamber pressure the temperature the enthalpy Mach number velocity specific heat ratio and static density of hot gas for all stations Following this the resulting nodal temperature distribution and some hot gas and coolant thermal transport properties for all stations are printed The heat transfer from hot gas to coolant is also given in the output This output is a standard output of RTE which includes the final results for each station
10. Hydrocarbon Rocket Fuels AIAA 84 0512 Niino M Kumakawa A Yatsuyanagi N and Suzuki A Heat Transfer Characteristics of Liquid Hydrogen as a Coolant for the LO2 LH2 Rocket thrust Chamber with the Channel Wall Construction 18Th AIAA SAE ASME Joint Propulsion Conference Cheveland Ohio June 21 23 1982 AIAA paper 82 1107 Taylor M F A Method of Predicting Heat Transfer Coefficients in the Cooling Passages of Nerva and Phoebus 2 Rocket Nozzles NASA TM X 52437 June 1968 Owhadi A Bell K J and Crain B Forced Convection Boiling Inside Helically Coiled Tubes International Journal of Heat and Mass Transfer Vol 11 pp 1779 1793 1968 Norris R H Augmentation of Convection Heat and Mass Transfer American Society of Mechanical Engineers New York 1971 Copyright O Tara Technologies LLC 66 24 25 26 2T 28 29 30 31 32 33 34 35 Date A W Flow in Tubes Containing Twisted Tapes Heating and Ventilating Eng Vol 47 pp 240 249 1973 Thorsen and Landis F Friction and Heat Transfer Characteristics in Turbulent Swirl Flow Subject to Large Transverse Temperature Gradient Journal of Heat Transfer Vol 90 pp 87 89 1968 Handbook of Heat Transfer Fundamentals end Ed Editors Rohsenow Hartnet and Ganic McGraw Hill Book Company 1985 Naraghi M H N Chung B T F and Litkouhi B A Continuous Exchange Factor Method for Rad
11. PEN 95 95 95 95 95 95 94 68 09 67 14 1210 24 24 24 24 24 24 24 32 37 39 40 58 23 45 42 44 89 43 90 46 90 91 91 35 75 92 92 35 319 35 35 35 235 35 41 34 35 54 20 28 90 90 88 95 90 1310 23 295 234 235 2 34 232 2335 315 33 221 36 2 54 21 86 47 45 35 38 40 41 43 92 92 29 91 47 56 75 92 91 91 91 91 74 58 91 90 91 91 Copyright O Tara Technologies LLC 92 92 92 92 92 92 92 66 92 LI 13 66 17 64 08 50 88 89 85 80 95 1410 23 23 23 23 2 3 31 39 41 44 86 86 8134 87 87 88 42 235 42 42 42 42 23 27 Ze 34 36 41 02 42 20 42 42 00 61 18 77 61 81 30 78 22 62 36 95 67 231 87 soL 60 80 83 74 259 2 32 93 1610 22 22 22 22 22 22 22 29 31 34 34 40 91 81 81 82 82 83 23 23 223 3 23 23 23 23 76 40 32 40 35 45 38 46 41 91 96 97 68 40 04 62 22 2397 258 62 56 39 3 275 1710 CQ NO PO PO PO PO PO PO P2 78 44 78 24 58 78 79 T9 TO 22 80 88 os kD 93 54 54 2 54 54 54 54 54 87 45 92 233 119 28 74 18 64 02 85 92 97 72 36 1810
12. Tara Technologies LLC Intern Wall Thk Pas Wth DG DCIN in CCW in 0 05 0 05 0 05 0 05 0 05 0 05 0 05 0 05 0 025 0 025 0 025 0 025 0 025 0 025 0 025 0 025 0 025 0 025 0 025 0 025 0 025 0 025 0 025 0 025 0 025 0 025 0 025 0 025 0 025 0 025 0 05 0 05 0 05 0 05 0 05 0 05 0 05 0 05 0 05 0 05 0 05 0 125 0 125 0 125 0 125 0 125 0 125 0 125 0 125 0 125 0 125 0 125 0 125 0 125 0 125 0 125 0 125 0 125 0 125 0 125 0 134 0 145 0 15 0 156 0 156 0 156 0 156 0 156 0 156 0 156 0 156 0 156 0 156 0 156 0 156 0 156 0 156 0 156 0 156 0 156 0 156 0 156 OOOOOcoooococoooococooooooooooocoooooocooecocoooo Pas H Coat Th Tk Total Thk Land Wt CCH TORT 19 THKN Lc 1 00E 06 1 00E 06 1 00E 06 1 00E 06 1 00E 06 1 00E 06 1 00E 06 1 00E 06 1 00E 06 1 00E 06 1 00E 06 2 001E 00 2 001E 00 2 001E 00 2 001E 00 2 001E 00 2 001E 00 2 001E 00 2 001E 00 2 001E 00 2 001E 00 2 001E 00 2 001E 00 1 00E 06 1 00E 06 1 00E 06 1 00E 06 1 00E 06 1 00E 06 1 00E 06 4 002E 00 4 002E 00 4 002E 00 4 002E 00 1 00E 06 1 00E 06 1 00E 06 1 00E 06 1 00E 06 1 00E 06 1 00E 06 Ch Aspct Ri 96 55 347 Amzirc Platinum Glidcop Inconel 1 Nicraly USER1 Figure C 7 Material selection from combo boxes from RTE s preprocessor Figure C 8 shows the meshing of a wall section at various layers By clicking on the Help on Meshi
13. Tara Technologies LLC 61 INSTALLATION AND EXECUTION INSTRUCTIONS The instruction provided here is to help the user who acquired the source code of RTE and wish to modify the program and generate their executable file The users with RTE s executable can run RTE by using its graphic user interface or typing RTE exe in DOS mode or UNIX systems Typing their executable file can run other supporting files of RTE For example simply typing RTE RAD exe run the radiation module of RTE and typing rtecom exe rte com for UNIX along with required parameter runs RTE TDK interface The easiest way of running RTE is through it Graphic User Interface GUI which is only available for the Windows operating systems Microsoft WINDOWS Operating System RTE and its modules were successfully compiled and executed on Compaq Visual FORTRAN Version 6 The enclosed CD contains the RTE program its supporting modules and typical data files The CD contains the following files rte2002 f RTE main program and its subroutines cet f combustion properties subroutines BONNIE gasp f coolant properties subroutines RTE INP typical RTE input including RTEDATA THERMOSA DAT Thermodynamics properties of hot gases needed in ASCII format only for the first run TRANSSA DAT Transport properties of hot gases needed in ASCII format only for the first run RTE RAD f Program for gas radiation exchange and weight factors calculations After installing these fil
14. The hot gases in the thrust chamber and nozzle form a non homogenous medium hence the extinction coefficient changes with position composition and pressure of hot gases change with axial position If the extinction coefficient K is assumed constant then the transmittance becomes Copyright O Tara Technologies LLC 32 Figure 8 Configuration of surface and gas rings within a nozzle and thrust chamber with throat blockage shadowing Copyright O Tara Technologies LLC 33 T r r e Kon 62 i The limits of integration in equations 57 60 are W ain and Ya and these are the minimum and maximum azimuth angles which ring element j is seen from a point on ring element i The allowable range of y is dictated by the orientation and relative position of the ring position of the ring element pair and blockage effects by the throat Details concerning the determination of the limiting azimuth angles are subsequently presented Geometric consideration of any ring element pair depicted in Figure 8 reveals 2 mA 2 E r r 2r r cosy 63 and for surface ring elements r r cos r cosy 0 x x sin0 64 r r cos r cosy r cos0 x x sin0 65 Where is the angle resting in the r x plane measured from the z axis in the direction of increasing radius onto the backside of element k All surface elements satisfy 2 lt 0 lt
15. Through this procedure the wall temperature and the temperature profile in the blocked channel and the adjacent channel can be calculated To demonstrate RTE s results for a blocked channel case consideration is given to a high pressure chamber blocked paper with 150 and 200 cooling channels The specifications of the engine are Chamber pressure 2000 psia 2000 psia O F 5 8 5 8 Contraction ratio 3 41 3 41 Expansion ratio 6 63 6 63 Throat diameter 2 6 inches 2 6 inches Propellant GH2 LO2 GH2 LO2 Coolant LH2 LH2 Total coolant flow rate 6 45 Ib sec 6 45 b sec Coolant inlet temperature 50 50R Coolant inlet stagnation pressure 200 psia 2900 psia Approximate throat heat flux 77 75 Number of cooling channels 200 150 Throat region channel aspect ratio 5 7 8 6 Channel width step changes at X 0 947 inches X 0 947 inches X 3 906 inches X 3 906 inches The rocket thrust chamber and nozzle contour is shown in Figure 19 with the station locations denoted on the contour The 200 channel chamber was evaluated first In order to allow for the pressure drop across the injector the coolant inlet pressure required was 3200 psia resulting in a pressure drop of 834 psi in the cooling jacket which is relatively Copyright O Tara Technologies LLC 54 high for this chamber pressure However the wall temperature just upstream of the throat is only 1058R which is relatively low for a high pressure chamber showing the effectiveness of H
16. and radiative heat transfer between gases and surfaces of the engine A comprehensive thermal model must account for all of these items RTE Rocket Thermal Evaluation is a comprehensive rocket thermal analysis code that uses a number of existing codes and allows interaction among them via iterative procedures The code is based on the geometry of a typical regeneratively cooled engine similar to that shown in Figures 1 and 2 It uses CET Chemical Equilibrium with Transport Properties 1 2 and GASP 3 4 for the evaluation of hot gas and coolant properties The inputs to this code consist of the composition of fuel oxidant mixtures and flow rates chamber pressure coolant entrance temperature and pressure dimensions of the engine and materials in different parts of the engine as well as the grid generation data This program allows temperature variations in axial radial and circumferential directions and by implementing an iterative scheme it provides a listing of nodal temperatures rates of heat transfer and hot gas and coolant thermal and transport properties The fuel oxidant mixture ratio can be varied along the thrust chamber This feature allows the user to incorporate a non equilibrium model or an energy release model for the hot gas side The mixture ratio along the thrust chamber is calculated using ROCCID 5 ROCket Combustor Interactive Design and Analysis Computer Program ROCCID has been modified to take RTE input and make the m
17. 0 0 0 0 0 O 07007 07 07 07 07 0707707 104 0 0 0 0 0 0 0 0 0 SEND amp CONDDATA NP1 c 1 400 800 900 1100 1650 1 0 0636 0 0617 0 0602 0 0582 0 0551 NP2 6 2 130 300 500 800 1200 1800 2 0 0316 0 018 0 0114 0 00864 0 00744 0 00864 NP3 T3 100 2000 3 7 2 4 0 01254 SEND REACTANTS H 2 000 100 00 0 0 G 298 15 F O 2 000 100 3146 9 L 83 3 O END FINISH SAMPLE OF THERMO DAT FILE THERMO DAT is needed as a separate file if IWFLUX is set to zero WFLUX 0 in amp RTEDATA This file is supplied as an ASCII file THERMOSA DAT If the program is moved to a new operating system THERMOSA DAT must be attached to RTE INP for the first run instead of REACTANT data Then by running RTE the binary format of Copyright O Tara Technologies LLC 83 THERMO DAT will be generated Note that 1f you have received the WINDOWS version of RTE the binary file of THERMO DAT is already a part of the package A partial listing of ASCII format of THERMO DAT is given bellow THERMO 300 000 1000 000 5000 000 L02 67E 0 0 0 0 0 0 6 300 000 5000 000 0 00000 0 25000000E O 0 00000000 0 00000000 0 00000000 0 00000000 2 0 74537496E 03 0 11734026E 02 0 25000000E 0 0 00000000 0 00000000 3 0 00000000 0 00000000 0 74537500E 03 0 11734026E 02 0 00000000 4 AL J 6 79AL 1 0 0 0 G 300 000 5000 000 26 98154 0 25561389E 01 0 10072150E 03 0 68901481E 07 0 20503307E 10 0 22331058E
18. 24998764E 04 0 42170152E 99040245E 05 0 20646994E TM86885 OCT 1984 1018645E 05 0 60008112E 27934880E 05 0 22794623E 38723374 04 0 31068889E 31752127E 06 0 46502768E TM86885 OCT 1984 69480678E 03 0 51475862E 23897053E 05 0 13920631E 4091735E 04 0 30326144E 34391846E 05 0 29520144E TM86885 OCT 1984 20749216E 04 0 24324848E 82600710E 04 0 16032465E 8304585E 04 0 31659144E 32030077E 05 0 15816751E TM86885 OCT 1984 20553653E 04 0 25894132E 60829603E 03 0 16720403E 25434520E 04 0 39610822E 69412155E 05 0 23731702E TM86885 OCT 1984 20721199E 04 0 25236763E 82330148E 04 0 16934280E 68993582E 03 0 12373559E 86556363E 04 0 13809483E Ooo 00 6 CT 6 oO gt gt gt OO 252 6 377 355997 5 012 3 998 3 014 2 00 1 495 1 020 0 997 0 974 0 952 0 93 0591 0 89 0 872 0 853 0 277 0 264 0 252 0 240 0 227 O 205 0 203 0 023 0 015 0 008 0 001 0 000 0 001 0 002 0 003 0 005 0 007 0 009 0 011 92 38 932 46 94 40 93 94 95 95 98 97 97 20 274 96 OUS 97 97 96 65 28 97 96 96 PRO G3 PO ALO 0 80 93 94 83 22 95 86 04 08 89 1110 24 24 24 24 24 24 24 2325 34 38 39 41 43 44 46 96 42 96 95 225 35 53 58 53 39 95
19. 28 2 5 2415s 26 26 255 254 NO No ho PO Po NH Copyright O Tara Technologies LLC 39 89 253 61 12 BU Xo Xo 0 ds O ds to 74 472 69 65 63 61 88 87 86 76 84 28 277 26 2s 255 24 24 NO NO ho PO Po NH 03 24 17 42 88 26 38 89 88 41 94 46 61 58 56 52 vol 49 85 84 83 215 26 26 25 25s 24 24 23 2 3 36 257 ook 82 11 49 46 44 41 39 597 82 80 795 26 25 42 25 24 24 23 NO No ho PO ho NH 22 81 42 44 08 38 89 96 49 24 02 54 2395 22 13 69 42 40 38 35 233 Co 78 78 dus TS 25 254 257 24 2 36 222 79 37 2510 24 2 3 22 22 NO No ho PO Pho NH 85 12 1 5 87 250 02 12 67 94 67 65 63 39 61 22 21 22 20 20 19 87 77 61 57 225 74 32 93 56 20 L9 48 15 19 32 229 26 26 24 423 65 63 61 58 221 21 20 19 ood 21 19 19 18 09 09 05 94 85 45 21 205 28 05 65 93 88 27 24 22 22 20 19 62 75 79 60 58 56 215 20 43 20 1 9 2 34 20 19 18 18 32 18 65 80 19 81 03 68 99 222 21 18 18 16 61 59 30 38 97 55 20 20 19
20. 50 000 500 000 0 500 000 5000 000 O 20 V 200 000 1000 000 0 V 1000 000 5000 000 0 C 200 000 1000 000 0 C 1000 000 5000 000 0 H202 V 50 000 500 000 0 V 500 000 5000 000 0 C 50 000 500 000 0 500 000 5000 000 O O V 50 000 500 000 0 V 500 000 5000 000 0 C 50 000 500 000 0 500 000 5000 000 O OH V 50 000 500 000 0 V 500 000 5000 000 0 C 50 000 500 000 0 C 500 000 5000 000 0 92 V 50 000 500 000 0 V 500 000 5000 000 0 50 000 500 000 0 500 000 5000 000 O LAST END FLUX DAT input file This file is a matrix of heat fluxes for different temperatures and all points along the axial direction of the nozzle Rows of this matrix correspond different locations and its columns are different temperature The first row of this file consists of two integers the first integer gives the number of rows in the matrix number of position points and the second integer gives the number columns number of temperature points The sample FLUX DAT file in the next page has 252 rows and 16 columns Temperatures in this file are from 1000R to 2500R with increments of 100R and positions cover the whole nozzle and thrust chamber 62893503E 59002712 71298372 65015925 12325046E 62902371E 55995219E 63779530E 55942885E 63745095E 52212423E 63757943E 12836605E 88550133E 94668769E 58468518E 14468338E 50651995E 90482890E 62689431E 14029337E 59326745E 53932114E 64852989E 52921368E 730
21. 71 2rrj z 2 MZ 2 XE Qr Xj The minimum and maximum azimuth angles can then be calculated from the following equations VW min COS min 9 TD and Vau ET 72 The direct exchange factors calculated based on the above formulation account for direct exchange of radiation between surface and gas elements To account for multiple reflections and scattering of radiation total exchange factors are introduced The total exchange factor between two elements is defined as the fraction of the radiative energy that is emitted from one element and is absorbed by the other element via direct radiation and multiple reflections and scatterings from surfaces and gas and are calculated using the following equations DSS 1 iss dsgo W ago W fiss dsgo W I dso W gsj 73 Copyright Tara Technologies LLC 35 DVS 1 dggo W des Ly aw fiss dsgo W I dggo W 74 where DSS Ips iS DVS 5 are matrices of total exchange factors from surface and gas axisymmetric rings to surface elements dss dsg las 8 dgs lag j dgg lag rg A are matrices of direct exchange factors between differential surface volume ring elements W 4 and W hw o 4 diagonal matrices of numerical integration weight factors for surface volume ring elements respectively and 5 4 las 2
22. Three FLAG variables are included in the program for printing intermediate iteration results These FLAG variables are IFLAGM for main RTE program intermediate results IFLAGC for COND subroutine intermediate results IFLAGG for GASP and BONNIE subroutines intermediate results When all FLAG variables are zero in RTEDATA the standard output is printed Setting its FLAG variable equal to one prints intermediate results of a subroutine or the main program RTE also produces some files which can be read by TECPLOT a registered software by Amtec Engineering Inc to produce graphs for some important output parameters These files are as follows GRCCH DAT for cooling channel heights versus axial position GRFLUX DAT for wall heat flux versus axial position GRPC DAT for coolant static and stagnation pressures versus axial position GRTEMP DAT for average wall temperature distribution versus axial position These graphs are shown in Figures 13 through 16 Also the code provides data files for contour isotherm plots of temperature distributions similar to that shown in Figure 18 for up to ten stations To get the isotherm plots ISOST in the input file should be set to the station numbers that their plots are needed The program will then provide up to ten files ISOSTI DAT ISOST2 DAT ISOSTIO DAT which can be read by TECPLOT to produce isotherm plots similar to that shown in Figure 9 for the specified station Making a station numb
23. a function of the coolant static pressure and the adiabatic wall enthalpy and is evaluated using the GASP program 3 Note that the Prandtl number in equation 28 is expressed by C poy Hex Pry 2 32 kex where Cpa gt Mex Kex f Pes ley 33 Copyright O Tara Technologies LLC 20 Coolant Heat Transfer Coefficient Calculations A number of built in correlations may be used to evaluate the heat transfer coefficients in the cooling channels These correlations can be activated via the NAMELIST variable ITYPE User specified correlation can be used by setting ITYPE 0 The simplest one is given by the following correlation Dittus Boelter correlation see 8 9 Nu Re Pris 34 This correlation can be used if ITYPE is set to 1 For most supercritical cryogenic fluid flows Hendricks and coworkers suggested a correlation in 14 15 In this correlation the Nusselt number is given by Nu E 0 8 p 04 Nu lt Co Re Pr 35 where Nu y gt y 1 y 1 and oP abr p gt Properties for the above correlation are based on the coolant static temperature To and _ 1 op oT static pressure P The correlation of equation 35 can be used by setting ITYPE 2 Correlations described by equations 34 and 35 give inaccurate results when the coolant is liquid oxygen A correlation specifically for oxygen has been proposed 16 This correlation is given by 0 2 C B k Nu Recs P
24. and ends at their exit Figure 3 shows a counter flow nozzle liner cooling arrangement There are other cooling arrangements where the coolant enters at a point in the middle or the other end of the nozzle liner travels parallel to the hot gas makes a U turn at the exit of nozzle and returns as a counter flow coolant into different cooling channels This arrangement is known as pass and half or wrapped flow cooling The numbering for the pass and half or wrapped coolant flow stations starts at the negative value of the station that coolant flow enters the nozzle liner For example if the coolant flow enters at station 10 the down stream flow the same direction as the hot gas flow the starting point station index is 10 then the next index is 9 8 1 see Figure 4 for details Up to this point the coolant flow is parallel to the hot gas flow The coolant flow makes a U turn from station 1 and moves upstream opposite to the hot gas flow all the way to the last station station n RTE s numerical model starts with the station that coolant enters cooling station 10 for the case shown in Figure 4 The model marches along the cooling channel and at each station the heat picked up by coolant is calculated using the heat balance among several heat transfer modes convection and radiation from hot gases conduction within the chamber and nozzle liner and convection to the coolant In this model the heat transfer between downstream
25. and upstream channels is neglected i e no heat transfer between sections 8 and 8 This assumption will produce reasonable results since the temperature difference between the coolant and hot gas is on the order of 100 times the temperature difference between two adjacent cooling channels This assumption has no effects on the overall heat picked up by the coolant since the heat Copyright O Tara Technologies LLC 11 Coolant transfer from hot gases to the wall at a given station is either picked up by downstream or upstream flows Hot gas flow direction p x 11 10 9 8 2 1 U turn Coolant out manifold Coolant in 10 9 8 d Figure 4 Schematic of a typical pass and half wrapped cooling channel with station numbering The thermodynamic and transport properties of the combustion gases are evaluated using the chemical equilibrium composition computer program developed by Gordon and McBride 1 2 CET Chemical Equilibrium with Transport properties The GASP GAS Properties 3 or WASP Water And Steam Properties 4 programs are implemented to obtain coolant thermodynamic and transport properties For RP1 a separate subroutine is based on properties given in 7 Since the heat transfer coefficients of the hot gas and coolant sides are related to surface temperatures an iterative procedure is used to evaluate heat transfer coefficients and adiabatic wall temperatures The temperature distribution within the wall is de
26. at that station 2 If failure is indicated in the conduction subroutine CONDWCC check dimensions of cooling channels to see 1f the land between cooling channels becomes zero or negative Also check other wall dimensions to make sure that they are consistent Using RTE s preprocessor ensures a user that dimensions of cooling channels are entered correctly 3 Failures in the coolant properties subroutines GASP or WASP are usually caused by low or negative pressure in the cooling channel This is due to small size cooling channels or large coolant flow rate causing a large pressure drop in the cooling channels This problem most likely appears close to the throat area where cooling channels contract Once the coolant passes the throat cooling channels expand causing an increase in coolant pressure and the possibility of negative coolant pressure vanishes For this condition RTE stops running at the Copyright O Tara Technologies LLC 63 station where the coolant runs out of pressure and instructs the user what to do in order to correct the problem 4 Divide by zero in the Reynolds and Prandtl numbers calculations of the main program is caused by very large coolant temperature This can happen if the coolant velocity is very low or the wall temperature is very large The GASP assigns zero to the transport properties of the coolant when its temperature is unrealistically large 5 Very low wall temperature at the inner surface causes
27. coefficients and adiabatic wall temperatures are calculated using equations 3 through 49 Again a new wall temperature distribution based on the most recent heat transfer coefficients and adiabatic wall temperatures is calculated using the finite difference subroutine for heat conduction within the wall This procedure is repeated until the relative difference between the temperature distributions of two consecutive iterations becomes negligibly small After the results for station n converge the coolant Mach number and entropy as functions of static pressure and enthalpy M csc EU CS gt los are evaluated using the GASP or WASP programs Copyright O Tara Technologies LLC 37 Next the coolant stagnation pressure is evaluated based on the coolant entropy and stagnation enthalpy i e Poy Pico 5 The GASP and WASP programs do not have explicit expressions for pressure in terms of entropy and enthalpy Thus an implicit relation for stagnation pressure 1 5 S Poo 1 with the secant method for solving nonlinear equations is used to determine P In the secant method two initial guesses for the stagnation pressures were made P P 20 and P P 20 and the corresponding entropies s and s were determined The secant method s iterative equation is given by P P Pash 76 517 VB where k is the iteration index When equation 76 converges the difference between two consecutive pressures bec
28. computer codes 1 4 for the combustion gases and the coolant The reference enthalpy of the gas side is given by 8 9 iex 0 5 Figs 0 180ligg igs 3 where is a function of gas static pressure and gas side wall temperature Tow and is evaluated using the program given in 1 The gas side adiabatic wall enthalpy 18 calculated using the following equation 8 9 Copyright O Tara Technologies LLC 13 1 3 5 7 los Pray ias e where the gas reference Prandtl number Proy is Cho n 5 Ci gt and koy are functions of P5 and icx Once the gas side adiabatic wall temperature is determined the wall adiabatic temperature is calculated via f Pes Law 6 and using the combustion codes 1 2 The hot gas side heat transfer coefficient ha 1s given by 6 7 0 8 0 3 Pro 7 where C is the gas side correlation coefficient given as input and the Reynolds number is defined by AW Tas Rec se Gs 8 Td u GX Ta f Pes lex 9 Tes f Fs Las 10 Once the hot gas side heat transfer coefficient is determined the wall heat flux can be evaluated via 4 hc 11 Or he In low 12 C Copyright Technologies LLC 14 Later the adiabatic wall temperature and gas side heat transfer coefficient calcu
29. does not need to know the name of an input variable and by simple entering engine information in corresponding cell and selecting proper condition can generate RTE s input file and run the program By clicking on the Generate RTE Input button the input data files RTEDATA CONDDATA and REACTANTS of can be generated Then the user can run the radiation module and RTE by clicking on the corresponding buttons It should be noted that RTE s GUI can only run on a WINDOWS operating system For running the program on a UNIX operating system the input file can be generated using RTE s GUI on a WINDOWS operating system and then upload it to the UNIX machine A more detailed description of RTE s GUI is given in Appendix C Copyright O Tara Technologies LLC 45 N o R 5 m u v x User defined conductivities USER 1 Temperature R_K BTU tA s Hot Gas Radiation IBASRAD Wall Material US ERI Method of heat tranfer evaluati h Enth Diff Closeout Mat Nickel Run RTE What is the status of wall heat AGR Unknown f Coating Mat US ER3 Coolant me rl Propellant LO2 GH2 LO2 6H2 LO2 CH4 decies ll 16 _17 Ch Aspct Swiler Mizture Ratio 18 Ratio YorN 219 3 125 0 000064 1 1607 User defined conductivities USERZ L20 3125 N 0 000064 1 3528 5 8 Coolant Pressure PCO 700 psi Temperature BTUMtA s _21 3 125 0 000064 1 8183 58 Total mass
30. flow of propellant 34 8 Ibis 0 0316 122 3 125 M 0000054 23142 58 0 018 L23 3 125 M 0000054 3 0752 58 0 0114 EQ 3 125 M 0 000064 4 3062 5 8 Cool Flow WC 15 Ibis 0 00864 525 5 000 N 0 000064 6 4775 5 8 Coolant Temperature TCO 50 0 00744 26 5 000 N 0 000064 10 7132 58 Chamber Pressure PGO 450 psi 0 00864 27 5 000 N 0 000064 16 8631 58 Hot Gas Flow rate WGAS 34 8 128 5000 0000064 220382 58 _29 5000 0000064 279862 58 30 5000 M 0000064 34 1953 58 31 5000 0 000064 38 7506 58 Contr Ratio 3 07 292 5 000 M 0 000064 420032 58 Tan Pt 33 5 000 0 000064 43 8885 5 8 Conv Rad Curv 4 002 in 4 002 34 5 000 N 0 000064 16 5633 58 Conv Tangent Point User defined conductivities USERI 35 5000 M 0 000064 485483 58 Angle 25 deg Temperature Ri 5 36 5 000 M 00000654 50 6971 58 Throat US Rad Curv 2 001 100 0 75 4 47 141 v Figure 10 Other parts of RTE s GUI containing various combo boxes and Run RTE button Lb MESHING Land area MPHIL 4 Nodes Channel 3 NRCLO 5 5 CLase aur NRCHB 4 SER 3 prera Outer Surface Condition Outside Boundary Condition etur Comection Dutside Heat Transfer Coff 0 TOP CHANNEL Outer surface emissivity 0 9 AR B NRCHT Outside Temperature 0 Cooling Method ICOOL Regenerativel y z
31. n l i j n l 2 Note that equation 54 is used when hot gas side heat transfer coefficient is known and wall heat flux is evaluated based on the temperature difference i e equation 11 When wall heat flux q is known equation 54 becomes Tee IR q q AQ ASI AS 2 1 1 R VR 1 R MR 1 Ry T R R i j l an i l j n i j ntl i jan l 55 where q is wall heat flux which can be an input of the program or evaluated using equation 12 Finite difference equations for other nodes such as cooling channel interface between two materials and outer surface nodes are included in the program In general the finite difference equations give the temperature of each node at iteration in terms of the temperatures of neighboring nodes and or heat transfer coefficients conductivities hot gas and coolant temperatures at the previous iteration iteration 1 To accelerate convergence the following successive over relaxation formula is used 1 1 o E 56 Copyright O Tara Technologies LLC 30 The most efficient value of for the geometry under consideration here is between 1 7 and 1 9 obtained by a trial and error procedure to minimize the computation time The successive over relaxation equation makes the convergence four times faster than when it is eliminated from the calculation for the configuration considered here It should be noted tha
32. needed for user defined coolant correlation ITYPE 0 exponent of density ratio in equation 39 needed for user defined coolant correlation ITYPE 0 nozzle diameter in for each station emissivity of the outer surface 0 for using temperature difference in calculating wall heat flux equation 11 1 for using enthalpy difference in calculating wall heat flux equation 12 inner surface emissivity convergence criterion for radial and circumferential directions convergence criterion for axial direction outside heat transfer coefficient Btu f s R type of cooling system 1 for regeneratively cooled 2 for radiatively cooled entrance effect correction factor 1 for equation 33 2 for equation 34 3 for equation 35 4 for equation 36 flag variable for printing intermediate results of COND subroutine flag variable for printing intermediate results of GASP and BONNIE subroutines flag variable for printing intermediate results of the main program type of heat transfer at outer boundary 1 for force convection 2 natural convection 3 radiation gas radiation flag 1 for gas radiation 2 no gas radiation station number for which isotherm plots are requested flag for swiler or no swiler for all stations 1 for swiler 0 for no swiler coolant side heat transfer correlation to be used ITYPE 0 for user defined correlation equation 39 ITYPE 1 for the correlation given by equation 34 ITYPE 2 for
33. operating systems before running any case the REACTANT data should be replaced by the ASCII file of THERMO DAT THERMOSA DAT and then run RTE This run will produce the binary form of THERMO DAT TRANS DAT is data for the transport properties of the hot gas species and are taken from reference 1 Similar to the THERMO DAT data file the ASCII form of TRANS DAT data TRANSSA DAT is required for the first run and for the next runs the transport properties are read from TRANS DAT which is a binary file S Equal to 0 for unknown wall heat flux 1 for known wall heat flux and 2 when a matrix of wall heat flux is provided via file flux dat 16 For a maximum of ten stations Copyright O Tara Technologies LLC 43 Note that the ASCII forms of both THERMO DAT and TRANS DAT must be attached to the main data file RTEDATA and REACTANTS for the first run only For the subsequent runs THERMO DAT and TRANS DAT must be removed from the main data file FLUX DAT is needed if WFLUX in RTEDATA is set to 2 RTE expects a matrix of fluxes Often hot gas side boundary layer programs can be used to determine the hot gas side heat fluxes The wall heat fluxes are evaluated along the nozzle and chamber by holding the wall temperature in the hot gas side constant This provides a vector of heat fluxes for various positions along the engine By repeating this for all possible temperatures a number of vectors of heat fluxes can be formed Each of these vectors corr
34. radiation only coolant inlet pressure psia chamber pressure psia critical pressure in equation 39 needed for user defined coolant correlation ITYPE 0 exponent of pressure ratio in equation 39 needed for user defined coolant correlation ITYPE 0 exponent of Prandtl number in equation 39 needed for user defined coolant correlation ITYPE 0 hot gas side wall heat flux Btu in for each station needed if IWFLUX 1 cooling channel radius of curvature in for each station exponent of Reynolds number in equation 39 needed for user defined coolant correlation ITYPE 0 cooling channel surface roughness in percentage of fuel for each station swiler angle in degrees exponent of specific heat ration in equation 39 needed for user defined coolant correlation ITYPE 0 lt Equal to 1 for copper 2 for nickel 3 for soot 4 for NARloy Z 5 for columbium 6 for zirconia 7 for SS 347 8 for amzirc 9 for Platinum 10 for Glidcop 11 for Inconel718 12 for Nicraly 13 for user defined 311 14 for user defined 2 and 15 for user defined 3 Copyright O Tara Technologies LLC 79 TCO TCOAT TGS THKNS OPTO TSTART VISCEXP WC WGAS X coolant inlet temperature R coating thickness in for each station hot gas static temperature R needed if IVFLUX 1 and IGASRAD 1 wall thickness in excluding coating thickness for each station outside temperature R initial guess of wall temperat
35. the RTE Three options are available for the boundary condition at the outside surface radiative natural convective and forced convective boundary conditions For the radiative and convective boundary conditions the outer surface emissivity and convective heat transfer coefficients respectively must be specified The boundary conditions at the inner surface are combined convection and radiation heat transfer from hot gases and other surfaces The convective heat flux for the hot gas side can be specified in the input file This feature allows the user to interface RTE to the other codes for the hot gas side properties and boundary layer analysis The procedure for linking RTE to a hot gas side program will be explained later RTE uses three major subprogram modules hot gas side properties BONNIE which is a modified CET 1 coolant properties GASP WASP and RP1 and conduction subprogram COND Subroutine BONNIE CET is for evaluation of thermodynamic and transport properties of combustion gases A complete description of this subprogram is given in 1 and 2 Subroutine BONNIE is only capable of predicting hot gas properties at equilibrium conditions The combustion in the thrust chamber however is a gradual process and might not reach the equilibrium condition within the thrust chamber As a result of this the model over predicts temperatures close to the injector and a large discrepancy between the computational and experimental tem
36. the combustion gases to freeze on the surface The combustion subroutine BONNIE cannot predict the transport properties of frozen combustion gases and the program may fail by sending an OVERFLOW message Usually this problem occurs at the first station where the coolant temperature is lowest To overcome this problem the user may assign a tiny layer of coating with low thermal conductivity to increase the wall temperature at the inner surface 6 The program has been tested successfully for most commonly used rocket propellants LH2 LO2 and hydrocarbon fuels For propellants with metal components e g LH2 LO2 AL the combustion subroutine over predicts the hot gas temperature causing higher wall and coolant temperature The program will eventually fail due to an excessive coolant temperature The program is not recommended for metallized propellants For any other failure of the program contact its developer at Tara Technologies LLC via e mail mnaraghi Otara technologies com Copyright O Tara Technologies LLC 64 REFERENCES 1 Gordon S and McBride B J Computer Program for Calculation of complex Chemical Equilibrium Compositions Rocket Performance Incident and Reflection Shocks and Chapman Jouquet Detonations NASA SP 270 1971 2 Gordon S McBride B J and Zeleznik F J Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications Supplement I Transport Properties NA
37. the cooling channels is blocked The default mode of RTE when all cooling channels are open due to symmetry of all of the cooling channels at a given station only models one half of a cooling channel a half rib in cross section similar to that shown in Figure 18a In order to perform a thermal analysis for a chamber liner that has a blocked channel the model is represented by two half channels a full rib one side representing a channel that is blocked in which there is no convective cooling while the other side represents the adjacent open channel with coolant flowing in it see Figure 18b In order to show the effects of a blocked cooling channel on the wall temperature profile three different rocket thrust chambers were studied in 34 using RTE interfaced with TDK for hot gas side calculations One chamber was designed to operate at a relatively low chamber pressure 450 psia while the other two chambers were designed to operate at a relatively high chamber pressure 2000 psia The high pressure chambers used in this analysis are modified designs of the high pressure chamber designed and tested at the NASA Glenn Research Center 35 36 The liners for all three chambers are made of copper closed out with nickel incorporating high aspect ratio cooling channels HARCC in their designs The result presented in 34 show that for the blocked channel Copyright O Tara Technologies LLC 52 cases the analysis showed the effec
38. the correlation given by equation 35 ITYPE 3 for the correlation given by equation 36 ITYPE 4 for the correlation given by equation 37 ITYPE 5 for the correlation given by equation 38 2 Equal to O for no intermediate results and 1 for intermediate results Copyright O Tara Technologies LLC 78 IWFLUX IUNIT KTG MAXITER MAXPASS MTCH MTCLO MTCOAT NBLOCK NCC NOFS NPHIC NPHIL NRCHB NRCHT NRCLO NRCOAT OMEGA PCO PGO PCRIT PRESEXP PREXP QW RCURVE REEXP RGHNS RMIX SANGLE SHEXP flag for known or unknown wall heat flux for unknown wall heat flux 1 for known wall heat flux 2 for matrix of wall heat flux FLUX DAT file is needed for this case unit flag 1 for English units and 2 for SI units extinction coefficient in for each station maximum number of iterations at each station maximum number of passes axial marches channel top and bottom portion material close out material coating material number of blocked channels 0 for no blocked channel and 1 for one blocked channel number of cooling channels for each station number of stations number of circumferential nodes within channel area number of circumferential nodes within land area number of radial nodes in channel area bottom portion number of radial nodes in channel area top portion number of radial nodes in close out number of radial nodes in coating hot gas scattering albedo for hot gas
39. the leading edge of the boundary layer NSKIP Number of station to be skipped after XSTART If NSKIP O heat fluxes for all stations after XSTART will be evaluated based on TDK QWI an array of wall heat fluxes Should be equal to zero at the beginning of the run Number of these heat fluxes is equal to the number of stations After the calculation is finished it gives an array of heat fluxes for different stations Copyright O Tara Technologies LLC 104 Sample of CONVERGE DAT Sample CONVERGE DAT at the beginning of the run SCONVERGE ITER 07 ERROR 010000 XSTART 17 80000 NSKIP 0 QW1 2 43 0 SEND Sample CONVERGE DAT at the beginning of the run SCONVERGE ITER 3 ERROR 010000 XSTART 17 80000 NSKIP 0 OW1 3 36077 78935 32674 82563 50660 95934 70223 09922 63991 81184 03034 55929 87093 20585 01301 2556629 70487 81964 93441 10493 38694 11813 09195 51487 04131 19678 47431 78109 76877 439723 10463 94462 77984 61363 59601 BW p pp pp pp pp ip p pp p EE M J 1 1 OY OY OY O I 0 a wa J Copyright O Tara Technologies LLC 105 65873 72459 80522 89900 00498 13227 30026 49020 SEND Running RTE TDK interface For WIN
40. the status of this run Note that if a case with no gas radiation is considered this step can be skipped Finally RTE can be executed by clicking on Run RTE button The results are automatically placed in rte out output file of RTE To have more control on the output and execution of RTE a user may choose to run RTE manually after generated input data files via the preprocessor This can be done by going to the DOS mode changing the directory to where the executable files of RTE are located and simply typing rte rad for running the radiation module or Copyright O Tara Technologies LLC 100 rte2002 gt outputfilename for running RTE UNIX operating system users can generate RTE s input on WINDOWS and then ftp the data file to the UNIX computer Copyright O Tara Technologies LLC 101 APPENDIX D RTE TDK Interface Copyright O Tara Technologies LLC Shell Program for Interfacing RTE and TDK Shell programs based on the flowchart of Figure 1 for both WINDOWS and UNIX are developed for interfacing RTE and TDK These shell programs have two input files inputs of RTE and TDK and two output files outputs of RTE and TDK For the MS WINDOWS operating systems this shell program can be run by typing its executable file rtecom exe in the DOS mode or by double clicking on the executable file RTE s input file must be named rte in or copied onto rte in RTE s input file name is hardwired in the shell program as rte i
41. thermodynamic properties of combustion gas species This file is needed if RTE s own hot gas side calculation is used i e IWFLUX 0 in amp RTEDATA namelist TRANS DAT provides the transport properties of combustion gas species This file is needed if RTE s own hot gas side calculation is used i e IWFLUX 0 in amp RTEDATA namelist TGS DAT is a data file for gas to surface radiation weight and exchange factors This file is needed if hot gas side radiation option is selected TSS DAT is a data file for surface radiation weight and exchange factors This file is needed if hot gas side radiation option is selected NOMENCLATURE FOR RTEDATA NAMELIST CASECODE case code for user distinguish different cases cooling channel heat transfer correlation coefficient for each station hot gas side heat transfer correlation coefficient for each station CCH cooling channel height in for each station CCwP cooling channel width in for each station 19 See Fig 3 for notation Copyright O Tara Technologies LLC 77 CCOLANT DCINP CONDEXP DENEXP DG EM ENTHALPY EPSILON ERROR ERRAX HOI ICOOL IENT IFLAGC IFLAGG IFLAGM IHOUT IGASRAD ISOST ISW ITYPE coolant name e g H2 02 H20 distance between bottom of the cooling channel and inner surface of the nozzle in excluding coating thickness for each station exponent of conductivity ratio in equation 39
42. to these materials the user has an option to input user defined conductivities For user defined conductivities either USER1 USER2 or USER3 must be selected from the material combo boxes Then the corresponding conductivities as functions of temperature can be Copyright O Tara Technologies LLC 95 defined in the tables shown in Figure C 7 There are three tables for user defined thermal conductivity with only two tables shown in the figure Each material s thermal conductivities can be defined as a function of temperature using maximum of ten points Axial Lgth X inches 3 208 2 872 2 009 1 719 1 464 1 347 1 135 1 038 0 947 0 778 0 701 0 452 0 25 0 1 0 000 0 100 0 274 0 506 0 906 1 306 1 706 1 906 2 106 2 306 2 506 2 906 3 106 3 306 3 506 3 706 3 906 4 106 4 506 5 5 5 906 6 106 6 506 7 572 8 35 9 375 Figure C 5 Input data for the geometry of nozzle wall and cooling channel 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 Copyright O
43. typical file for CONVERGE DAT is given in Appendix B CONVERGE DAT has a NAMELIST format which consists of the following variables ITER shell iteration number Initially 21 ERROR convergence criterion for the shell The C shell iteration stops when the difference between wall heat fluxes of two consecutive iterations become smaller than ERROR XSTART coordinate of the boundary layer leading edge When X XSTART the boundary layer heat fluxes are used Otherwise the results of RTE based on equation 7 are implemented NSKIP The BLM option makes the resulting wall heat fluxes close to the leading edge very ustable NSKIP allows the user to skip eliminate heat fluxes close to the leading edge If NSKIP 10 the interface skips 10 rows heat fluxes from the top of the heat flux table TDK RTE DAT QWI wall heat flux Initially 0 At each iteration the resulting wall heat fluxes are written into CONVERGE DAT and are read by TDK RTE at the next iteration to compare with the revised fluxes If the convergence criterion is satisfied the calculation stops otherwise the loop continues At each iteration the writes the resulting wall fluxes and wall temperatures into PLOT DAT This file can be used to plot final results of each iteration A listing of RTE TDK input files is given in Appendix D BLOCKED CHANNEL OPTION AND RESULTS One of the concerns of the rocket designer is what happens to the wall temperature if one of
44. 0 gt W IC Ov NODO SA Copyright O Tara Technologies LLC 5 10 0 40166E 07 47 35 0 71164E 09 47 36 0 75104E 08 47 3 0 13896E 06 47 38 0 27236E 05 47 39 0 57129E 04 47 40 0 12742E 02 47 41 0 26951E 01 47 42 0 20755E 00 47 43 0 25406E 02 47 44 0 20393E 02 47 45 0 69162E 03 47 46 0 19391E 03 47 47 0 40446E 04 Note that the exchange factor data presented here is for an engine with propellant which has a significant gas radiation Copyright O Tara Technologies LLC APPENDIX C WORKING WITH GRAPHIC USER INTERFACE PREPROCESSOR OF RTE Copyright O Tara Technologies LLC RTE s GRAFIC USER INTERFACE GUI PREPROCESSOR RTE s graphic user interface preprocessor is the easiest way to generate a data file and run the program and its radiation module This preprocessor is based on Microsoft s Excel Spreadsheet and has combo boxes and help buttons to facilitate inputting data This file is RTE GUL xls and should be saved in the same directory that all RTE s executable and data files are located RTE GULxls be saved under any other name for example if it is used to generate the Space Shuttle Main Engine data it can be saved as SSME xls or any relevant name that a user chooses It should be noted that the RTE preprocessor can only be used on a Microsoft Windows operating system with Excel UNIX users can use
45. 0 0 0 SAMPLE OF TRANS DAT FILE 2006688E 03 0 0 00000000 3225 000 5000 000 05 22670 0 00000000 0 00000000 0 00000000 0 00000000 0 00000000 300 000 1478 000 23 21880 64686736E 07 0 13004881E 10 43933458E 01 0 81214444E 04 53221009E 00 0 00000000 1478 000 2950 000 23 21880 0 00000000 0 00000000 0 00000000 0 00000000 45274017E 02 0 00000000 2950 000 5000 000 23 21880 0 00000000 0 00000000 0 00000000 0 00000000 54592264E 02 0 00000000 0 000 02 0 28556290E 01 0 86166970E 02 0 53486638E 05 0 000 05 22670 Similar to THERMO DAT transport properties file of hot gas TRANS DAT is needed as a separate file if IWFLUX is set to zero IWFLUX 0 in amp RTEDATA This file is supplied as an ASCII file TRANSSA DAT If the program is moved to a new operating system TRANSSA DAT must be attached to RTE INP for the first run second run after performing the same task for THERMO DAT instead of REACTANT data Then by running RTE the binary format of TRANS DAT will be generated Note that if you have received the WINDOWS version of RTE the binary file of TRANS DAT is already a part of the package A listing of ASCII format of TRANS DAT is given bellow TRANSPORT PROPERTY COEFFICIENTS Q Q lt lt 0 lt A AS m uo s 50 00 500 500 00 5000 50 00 500 500 00 5000 50 00 500 500 00 5000 50 00 500 500 00 5000 50 00 500 500 00 5000 50 00 500 500 00 5000
46. 0 1 inches of the high pressure chamber 200 channels blocked channel and adjacent open channel Closed E Ta 1580R Figure 23 Rib temperature profile at the injector end station x 9 38 inches for the high pressure chamber 200 channels blocked channel and adjacent open channel Copyright O Tara Technologies LLC 58 119 Ta 1211R Figure 24 Rib temperature profile upstream of the throat x 0 1 inches for the high pressure chamber 150 channels unblocked Copyright O Tara Technologies LLC 1143 1075 1007 939 871 804 736 668 600 532 464 396 261 193 39 One blocked channel No blocked channel 10 5 0 5 Axial Position inches Figure 25 Comparison of the maximum wall temperature profile versus axial position for the blocked channel and unblocked channel cases for the high pressure chamber 150 channels Copyright O Tara Technologies LLC 60 T 1674 1582 1490 1398 1306 1214 1122 1020 Tmax 1766R _ Figure 26 Rib temperature profile upstream of the throat x 01 inches for the high pressure chamber 150 channels blocked channel and adjacent open channel Closed Tnax 1738R i Figure 27 Rib temperature profile at the injector end station x 9 38 inches for the high pressure chamber 150 channels blocked channel and adjacent open channel Copyright
47. 0 42 0 4 0 0 0 0 0 130 0 38 0 30 All of the 0 019 0481 04 0 059 0 0019 0 053 0 52 0 11 768 0 28 0 97 above fuels All of the above fuels 0 044 0 76 04 0 0 0 0 0 638 026 0 98 except Natural Gas Table 1 Coefficient and exponents of correlations for hydrocarbon fuels Copyright O Tara Technologies LLC 22 The properties in the above correlations are calculated using the GASP program 3 for H2 O2 etc WASP program 4 for water and RP1 properties routine It should also be noted that there are three coolant heat transfer coefficients and adiabatic wall temperatures They are for the top side and bottom walls of the cooling channel The variable heat transfer coefficient is due to the variable wall temperature in the cooling channel The coolant reference and adiabatic wall enthalpies are also functions of wall temperature and are larger for the surface nodes closer to the bottom of the cooling channel The correlation factors for the heat transfer coefficient C C in equations 34 and 35 are usually equal to 0 023 for most coolants When the coolant is liquid oxygen however a factor of 0 0025 is used in equation 36 Entrance Effect The correlations given by equations 34 39 are for fully developed turbulent flow in a smooth and straight tube channel To include the effect of the entrance region they are multiplied by the following coefficient 20 0 325
48. 02806E 51566598E 64201860E 44556585E 70273668E 53917653E 64854183E 78398875E 75890427E Copyright O Tara Technologies LLC 00 0 59279284E 00 0 35600085E V2C2 GORDON 00 0 65673504E 00 0 18410033E 01 0 17577905E 00 0 22453540E V2C2 GORDON 00 0 43305205E 00 0 23016980E 00 0 43471877E 00 0 23949330E V2C2 GORDON 00 0 67665387E 00 0 24838511E 01 0 11455825E 00 0 30164014E V2C2 GORDON 00 0 69050351E 00 0 46488533E 01 0 17203212E 00 0 14110690E V2C2 GORDON 00 0 21439944E 00 0 62039801E 01 0 56011042E 00 0 49202617E V2C2 GORDON 00 0 87466991E 00 0 84773546E 00 0 74978154E 00 0 16087118E V2C2 GORDON 00 0 81060512E 00 0 12095925E 00 0 10023169E 00 0 23912109E V2C2 GORDON 00 0 87475338E 00 0 84278487E 00 0 29780881E 00 0 49408342E 02 0 03 0 NASA 02 0 02 0 02 0 03 0 NASA 02 0 02 0 02 0 02 0 NASA 02 0 02 0 03 0 03 0 NASA 02 0 03 0 03 0 04 0 NASA 02 0 02 0 02 0 03 0 NASA 02 0 01 0 02 0 03 0 NASA 02 0 02 0 03 0 03 0 NASA 02 0 01 0 02 0 01 0 14545124E 04 0 21849702E 70771415 05 0 27429431E TM86885 OCT 1984 4963183E 04 0 11548638E 27377624 05 0 14926219E 82083093E 03 0 18858575E 5727615E 05 0 24083935E TM86885 OCT 1984 3988573E 04 0 12513079E 60571893E 04 0 70833314E 3985506E 04 0 46873025E 62706766E 04 0 41438921E TM86885 OCT 1984 8585313E 04 0 17199202E 55837133E 04 0 90185688E
49. 1 4244 14 2244 4 5 71 21 87 30 63 85 99 1 5 sal 63 63 75 64 64 64 06 42 07 64 20 92 2410 17 17 17 17 17 1 7 17 21 22 25 26 27 28 29 31 61 61 62 63 34 34 34 34 34 34 34 47 88 24 38 50 18 62 81 99 13 44 78 62 45 62 07 34 13 77 88 278 60 12 80 395 83 87 47 492 2510 dis 17 1 7 17 22 23 24 26 24 30 45 30 28 29 60 61 61 01 01 451 1x E 01 01 01 01 01 23 5 10 48 AS 93 03 14 58 22 60 60 221 2 52 61 62 56 89 07 ont 47 30 82 52 67 55 62 24 i2 O 0 OQ PP O 10 10 10 11 015 018 023 028 854 878 902 926 950 974 998 023 047 2752 10 256 513 758 000 003 95 92 31 497 81 22 29 29 28 28 557 31 30 27 NON OIN ON WW 273 94 93 40 94 84 97 711 15 62 06 02 99 95 94 91 94 93 92 31 28 27 222 43 34 90 92 30 30 1 29 29 54 28 50 26 62 07 02 98 97 291 87 85 82 92 91 59 89 90 30 29 28 27 26 NO No ho PO Po NH 47 68 18 250 293 40 28 34 2315 30 26 29 87 81 87 81 78 76 43 90 88 874 295 28
50. 1 temperature at the entrance to the cooling channel PCO number of stations NOFS type of correlation to be used for coolant heat transfer coefficient ITYPE exponent of Reynolds number exponent of Prandtl number PREXP exponent of density ratio DENEXP exponent of viscosity ratio VISCEXP exponent of conductivity ratio CONDEXP exponent of specific heat ratio SHEXPy pressure ratio exponent PRESEXP critical pressure PCRIT number of blocked channels NBLOCK entrance effect correction factor AENT gas radiation flag IGASRAD initial guess of temperature for the first pass TSTART convergence criterion for conduction in radial and circumferential directions ERROR maximum number of iterations at each station MAXITER convergence criterion for conduction in axial direction ERRAX maximum number of axial passes MAXPASS axial location of stations X heat transfer coefficient correlation factor for hot gas and coolant sides CG amp CC gas side chamber and nozzle diameters DG cooling channel width and height CCW amp CCH distance between the cooling channel bottom and inner surface of the nozzle DCIN wall and coating thickness THKNS amp TCOAT number of cooling channels NCC number of nodes in circumferential NPHIL for land and NPHIC for channel and radial NRCLO NRCHT NRCHB and NRCOAT for close out channel top channel bottom and coating respectively
51. 1 8 10 N 1 8 9 BAULCH 72 A 1 5U Copyright Tara Technologies LLC H2 H2O H 2 2 13 0 0 B 5 15 BAULCH 72 20 H2O O 6 3E12 0 0 1 09 BAULCH 72 LAST THIRD BODY REAX RATE RATIOS M1 25 H 4 H2 10 H20 25 0 25 0H 1 5 02 2 12 5 H 5 H2 17 H20 12 5 0 12 5 0H 6 02 M3 12 5 H 5 H2545 H20 12 5 0 12 5 O0H Ll 02 7 12 5 H 5 H2 5 H20 12 5 0 12 5 0H 5 O2 LAST CARD SODK PRNT 2 7 203 P EN TRANS 200 1 Ey N O IQUI 0 HCK 0 AX 40 IMAXF 1 ND LM FLAG 0 S UJ i w END NISH A E 2 4 4 uu E G nj In addition to RTE and TDK s input files another file is needed to control convergence of wall heat fluxes This file is CONVERGE DAT and has a NAMELIST format Its variables include ITER Iteration number which should be set to 0 before every TDK RTE run During iterations its value indicates iteration number ERROR Convergence criterion iteration stops when relative difference between wall heat fluxes of two consecutive iterations is less than this number XSTART Position of the boundary layer leading edge It is better to set this point behind the injector in order to have stable wall fluxes Note if XSTART is placed after the injectors RTE will be used to calculate heat fluxes for those stations between the injector and
52. 11 Chen N H An Explicit Equation for Friction Factor in Pipe Ind Eng Chem Fundam Vol 18 No 3 pp 296 297 1979 Copyright O Tara Technologies LLC 12 13 14 15 16 17 18 19 20 21 22 23 Ito H Friction Factors for Turbulent Flow in Curved Pipes Journal of Basic Engineering pp 123 134 1959 Moody L F Friction Factors for Pipe Flow Transactions of ASME pp 671 684 1944 Hendricks R C Niino M Kumakawa A Yernshenko V M Yaski L A Majumdar L A and Mukerjee J Friction Factors and Heat Transfer Coefficients for Hydrogen Systems Operating at Supercritical Pressures Proceeding of Beijing International Symposium on Hydrogen Systems Beijing China May 7 11 1985 Kumakawa A Niino M Hendricks R C Giarratano P J and Arp V D Volume Energy Parameters for Heat Transfer to Supercritical Fluids Proceeding of the Fifteenth International Symposium of Space Technology and Science Tokyo pp 389 399 1986 Spencer R G and Rousar D C Supercritical Oxygen Heat Transfer NASA CR 135339 1977 Faith L E Ackerman Henderson H T Heat Sink Capability of Jet A Fuel Heat Transfer and Coking Studies NASA CR 72951 S 14115 1971 Cook R T Advanced Cooling Techniques for High Pressure Hydrocarbon Fueled Rocket Engines 80 1266 Master P A Aukerman C A Deposit Formation and Heat Transfer in
53. 14 2 0 38899208E 05 0 52516077E 01 0 28588767E 01 0 16963453E 02 0 32120695E 05 3 0 27578166 08 0 88926440E 12 0 38853482E 05 0 38750889E 0 0 00000000 4 AL J 6 79AL 1 E 1 0 0 G 300 000 5000 000 26 98154 0 25078778E 01 0 17718291E 04 0 13696497E 07 0 43266360E 0 48066244E 15 2 0 10713754E 06 0 37356724E 01 0 24948978E 01 0 38124702E 04 0 99507420E 07 3 0 10964185E 09 0 43146931E 13 0 10714056E 06 0 37990113E 0 0 00000000 4 AL J 6 79AL 1 E s 0 0 G 300 000 5000 000 26 98154 0 20396369E 01 0 83502844E 03 0 33224315E 06 0 54948566E 10 0 33528088E 14 2 0 33916449E 05 0 84890118E 01 0 26297902E 01 0 43426365E 03 0 34020091E 06 3 0 20861285E 09 0 15032237E 12 0 33727771E 05 0 53309683E 0 0 00000000 4 ALBO2 J 6 66AL 1 B 0 2 0 G 300 000 5000 000 69 779034 0 71722995E 01 0 29780741E 02 0 12431107E 05 0 23188779E 09 0 16041208E 13 2 0 67683682 05 0 99949242E 01 0 23087234E 01 0 18890539E 01 0 20633348E 04 3 0 10251324E 07 0 16941283E 11 0 66482167E 05 0 14463834E 02 0 00000000 4 ALBR J 9 79AL 1 BR 1 0 0 G 300 000 5000 000 106 88554 0 43822424E 01 0 21200707E 03 0 70764447E 07 0 10659018bE 10 0 14830266E 15 2 0 0 57616849E 03 0 37259456E 01 0 34900611E 01 0 45476797E 02 0 81935578E 05 3 0 68666152 08 0 21765058 0 72945306 03 0 78734846 01 0 00000000 4 ALBR3 J 9 79AL 1 BR 3 0 0 G 300 000 5000 000 266 69354 0 96150590E 01 0 44468546E 03 0 19902983E 06 0 39251818 10 0 28427975 14 2 0 52349544E 05 0 13132272E 02 0 62537206E 01 0 1608021
54. 195 1 9 18 18 18 17 NO No ho PO ho NH 04 21 19 PEN 14 14 13 at 595 ST 29s 54 20 19 18 17 64 84 98 09 22 1 9 49 T9 18 45 18 Tis 48 85 dd 77 12 229 12 lt 10 08 07 58 56 54 52x 1 1 1 OO OO XO WOW NO NO ho PO ho NH 44 65 85 98 59 43 07 eb 38 05 74 42 Pus 10 06 05 04 03 e 55 53 51 OY 1 1 OO CO 24 50 279 89 06 04 02 01 00 99 56 2239 54 52 50 OY J 1 CO CO CO 07 62 82 95 62 27 92 60 30 99 40 02 98 97 96 94 88 TGS DAT data file This file is generated by the radiation module of RTE RTE_RAD and contains weight factors of the volume nodes and total exchange factor from gas nodes to surface nodes It begins with the case code assigned in RTEDATA to ensure that RTE reads the right exchange factor numbers If there is a mismatch between the case code of RTEDATA and the radiation exchange factor s case code RTE stops and send a message of the mismatched case code A partial listing of TGS DAT is given below CASECODE 1 0 008839 2 0 008839 3 0 008839 4 0 008839 0 008839 6 0 008368 177 0 001736 178 0 001736 179 0 001736 180 0 001736 181 0 001736 182 0 001736 183 0 001736 184 0 001736 18
55. 2 SHEXP 6 PREXP 0 36 PCRIT 731 IENT 4 IGASRAD 2 TSTART 400 Copyright Tara Technologies LLC 00 CO CO CO 01 00 00 CO CO CO CO 00 00 CO CO 01 O1 O1 01 01 O1 O1 O1 01 O1 O1 aaa CO 81 ERROR 0 1000000E 03 MAXITER 50 ERRAX 0 1000000E 02 MAXPASS 1 NPHIL 4 NPHIC 3 NRCLO 5 NRCHT 5 NRCHB 4 NRCOAT 3 MTCLO 14 13 MTCOAT 15 HOUT 2 HOl 0 EM 0 9 COOL 1 TO 0 OMEGA 0 EPSILON 0 9 SANGLE 30 UNIT 1 EDGE 1 KTG 41 2 5 FLAGM 0 FLAGG 0 FLAGC 0 ENTHALPY 1 3 208 2 872 2 009 1 719 1 464 1 347 1 135 1 038 0 947 0 778 0 701 0 452 0 25 0 1 0 0 1 0 274 0 506 0 29206 1 306 1 706 1 906 2 106 2 306 2 506 2 906 3 106 3 306 3 506 3 706 3 906 4 106 4 506 5 5 5 906 6 106 6 506 7 512 8 35 9 9 375 DG 6 694 6 28 5 154 4 754 4 392 4 226 3 916 3 776 3 64 3 388 3 272 2 902 2 686 2 613 2 6 2 608 2 656 2 746 2 924 3 092 3 264 3 344 34432 4 MALO 3 002 3 77 4 3 96 35294 4 4 022 4 L 4 4 lT 4 236 4 358 4 6 4 666 4 694 4 744 4 8 4 8 4 8 4 8 NCC 150 150 L5051505150 150 150y1505150 150y150 05507 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 1
56. 31 2 Combining equations 57 65 gives the resulting exchange factor expressions V max E 2r r cos0 cosO 45 COS COS r r dss r r Pi i J J 0 P O i Lay 66 r r max _ 2 r cos0 cos0 0 r Ek bcr 67 r r r r ds cos t r dgs r r 2 5 EY 68 2 r V min 69 Copyright Tara Technologies LLC 34 V max r dridx Mos Mu ow Me dgg r r ax 7 r r where tan and 70 rj r r The limiting angles V nin and Y ma remain to be determined The limiting azimuth angles for surface to surface exchange are governed by the configuration and or blocking surfaces It is possible that in many instances the view between ring element pairs is partially obstructed by the throat The blockage angle cos T is evaluated by projecting a line from a point on an emitting ring element denoted by subscript i around the periphery of the blocking body at an axial position such that x is between x and The intersection point between the receiving ring element denoted by subscript and the shadowing produced by the blocking body at x results in a minimum azimuth angle This procedure is repeated for several values of and can mathematically stated as AIDA ae Qo n LU mi
57. 5 0 001736 1 1 0 76654E 00 1 2 0 58044E 01 1 3 0 33586E 02 1 4 0 21049E 03 1 5 0 15036E 04 1 6 0 38147E 04 185 35 0 48987E 09 185 36 0 50041E 08 185 37 0 88018E 07 185 38 0 16163E 05 185 39 0 31476E 04 185 40 0 68707E 03 185 41 0 22496E 01 185 42 0 25675E 01 185 43 0 24126E 01 185 44 0 86659E 00 185 45 0 22498E 00 185 46 0 53916E 01 185 47 0 10362E 01 Copyright O Tara Technologies LLC 89 TSS DAT data file Similar to TGS DAT this file contains weight factors of surface nodes and exchange factors between surface nodes The radiation module of RTE RTE RAD generates this file It begins with the case code assigned in RTEDATA to ensure that RTE reads the right exchange factor numbers If there is a mismatch between the case code of RTEDATA and radiation exchange factor s case code RTE stops and send a message of mismatched case code A partial listing of TGS DAT is given below CASECODE 073592 073592 073592 073592 073592 124826 126371 107213 086943 088059 ND EP Oodd m 083333 083333 020833 020833 020833 020833 020833 0 17160E 11 31344E 10 51322 09 95474 08 22111 06 22806 04 24689 04 48731 05 41 42 43 44 45 46 47 O ODO NR OIT 13283E 0 30072E 0 73070 0 75514 0 12975E 0 18175E 0 69979
58. 50 00 500 500 00 5000 00 0 57664156E 00 0 63946695E 00 0 62665106E 00 0 80309997E 00 0 51572122E 00 0 63895175E 00 0 52513903E 00 0 64819976 00 0 61285983E 00 0 65340841E 00 0 15044605E 00 0 45982942E 00 0 51840229E 00 0 63942307E Copyright O Tara Technologies LLC V2C2 GORDON 00 0 35019433E 00 0 17638455E 00 0 18331584E 00 0 26034111E V2C2 GORDON 00 0 74707840E 00 0 21086915E 00 0 73145794E 00 0 34110542E V2C2 GORDON 00 0 82167119E 00 0 25977551E 01 0 11382256E 00 0 10509052E V2C2 GORDON 00 0 86401891E 00 0 16043078E NASA TM86885 OCT 1984 02 0 47303914E 04 02 0 46773038E 05 02 0 03 0 NASA 02 0 39704839E 04 02 0 03 0 02 0 NASA 02 0 20120034E 05 26842459E 04 04 0 02 0 03 0 NASA 02 0 02 0 2224627E 04 83902096E 03 TM86885 OCT 9719001E 04 9408307E 04 84313328E 05 TM86885 OCT 8475609E 04 5791881E 06 TM86885 OCT 21168247E 04 34528052 03 0 19526199E 0 15133911E 0 25707432E 0 11072852E 1984 0 23318835E 0 14508179E 0 34518423E 0 28934974 1984 0 14747394 0 10943269 0 30431470 0 51358693E 1984 0 24881742E 0 16052082E Coe C 6 04 6 Oo gt o 85 C 50 00 500 00 0 C 500 00 5000 00 0 CO2 V 50 00 500 00 0 V 500 00 5000 00 0 50 00 500 00 O 500 00 5000 00 0 H V 50 00 500 00 0 V 500 00 5000 00 0 C 50 00 500 00 0 C 500 00 5000 00 0 H2 V 50 000 500 000 0 V 500 000 5000 000 0
59. 50 150 150 150 DCIN 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 0 035 CCW 0 05 0 05 0 05 0 05 0 05 0 05 0 05 0 05 0 025 0 025 0 025 0 025 0 025 0 025 0 025 0 025 0 025 0 025 0 025 0 025 0 025 0 025 0 025 0 025 0 025 0 025 0 025 0 025 0 025 0 025 0 05 0 05 0 05 0 05 0 05 0 05 0 05 0 05 0 05 0 05 0 05 CCH 0 125 0 125 0 125 0 1257 0 125 0 1207 101207 0 1257 0 125 05 1257 0 125 0 125 0 125 0 1255 0 125 0 125 0 125 0 125 0 125 0 134 0 145 0 15 0 156 0 156 0 156 0 156 0 156 0 156 0 156 0 156 0 156 0 156 0 156 0 156 0 156 0 156 0 156 0 156 0 156 0 156 0 156 TCOAT 0 O 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 O THKNS 0 36 0 36 0 36 0 36 0 36 0 36 0 36 0 36 0 36 0 36 0 36 0 36 0 36 0 36 0 36 0 36 0 36 0 36 0 36 0 369 0 38 0 385 0 391 0 391 0 391 0 391 0 391 0 391 0 391 0 391 0 391 0 391 0 391 0 391 0 391 04 391 0 391 0 391 0 391 0 391 0 391 eo 0 0095 0 0095 Copyright O Tara Technologies LLC 82 0 0095 0 0095 0 0095 0 0095 0 0095 0 0095 0 0095 0 0095 0 0095 0 0095 0 0095 0 0095 0 0095 0 0095 0 0095 0 0095 0 0095 0 0095
60. 6 CLOSE UP MATERIAL INSULATION THKNS COOLING CHANNEL CCH CCW 2 2 DCIN Sea 52242 COATING DG Figure 6 A half cooling channel cell 1 n R eee IR c1 n R T 1 T jaa R Due E 2 a E _ 53 1 R 1 R 1 R 1 R 1 R 1 R where R R Rz are resistances between node i j n and its six neighboring nodes These resistances are given by Copyright O Tara Technologies LLC 27 1 1 1 n ntl 1 1 1 1 Ash k u i j n 1 1 jon 2 CHE 72 A ia mA 1 A CLOSE OUT l AREA A Z NRCLO 1 1 4 2 2 FT ERES Wo 2 COOLING 2 CHANNEL TOP CHANNEL AREA NRCHT 2 2 CHANNEL AREA 2 COATING LAND CHANNEL AREA AREA NRCOAT NPHIL NPHIC Figure 7 Finite difference grid superimposed on half cooling channel cell 1 A 1 Up Pals As Ln Aye i j l an rAd 1 1 R por M Ase KE RIR i l j n _ 1 1 R 1 1 1 1 ls AS Ru Es Eb Copyright O Tara Technologies LLC 28 5 1 1 is 2A k Jn inu 1 1 R SE 2A E ina i j n l rA9Ar 1 2 rA0Ar 1 2 is the Gauss Siedel iteration index Note that the above equa
61. 7E 01 0 28659758E 04 3 0 23616076E 07 0 73931314E 11 0 51735211E 05 0 26704951E 01 0 00000000 4 ALC J 6 63AL 1 C 5 0 0 6 300 000 5000 000 38 99254 0 41564478 01 0 44692490 03 0 17467040 06 0 34304336 10 0 24772706 14 2 0 0 81606605E 05 0 28915623E 01 0 26422483E 01 0 64465161E 02 0 95892376E 05 3 0 69040805E 08 0 19430779E 0 81929874E 05 0 10254199E 02 0 00000000 4 ALCL J 9 79AL 1 CL 1 0 0 G 300 000 5000 000 62 43454 0 43395271E 01 0 24838874E 03 0 82921852E 07 0 12342319E 10 0 23755818E 16 2 0 75281081E 04 0 25241385E 01 0 31222286E 01 0 59280474E 02 0 10415832E 04 3 0 85551065E 08 0 26722380E 11 0 73075839E 04 0 82402004E 01 0 00000000 4 ALCL J 6 76AL 1 CL 1 E 1 0 G 300 000 5000 000 62 43454 0 46284965E 01 0 34750535E 03 0 22997351E 06 0 24279798E 10 0 26440544E 15 2 0 10220447E 06 0 14172573E 01 0 28698352E 01 0 66534586E 02 0 11327707E 04 3 0 90702974E 08 0 27794640E 0 10259741E 06 0 10006810E 02 0 00000000 4 ALCLF J 6 76AL 1 CL 1 F 1 0 G 300 000 5000 000 81 43294 0 64262622E 01 0 67861168E 03 0 31186392E 06 0 62142379E 10 0 42519573E 14 2 0 60938769E 05 0 30754283E 01 0 32175968E 01 0 14524549E 01 0 23922488E 04 3 0 18621609E 07 0 55903667E 11 0 60305508E 05 0 12258661E 02 0 00000000 4 ALCLF J 6 76AL 1 CL 1 F 300 000 5000 000 81 43294 0 68835905 01 0 70509366 03 0 31366088 06 0 61607310 10 0 44490537 14 2 0 31005990 05 0 84952610 01 0 37341292 01 0 13889043
62. 98 15 C 000300 Hydrogen H 2 100 0 G 298 15 F 9 Hydrogen H 2 100 2154 L 202 7 0 0709 1 JP 5 C 1 H 1 9185 100 5300 L 298 15 F 0 807 5 1 JP 4 1 9423 100 5430 L 298 15 1 Copyright Tara Technologies LLC 80 Methane c1 H 4 100 17895 298 15 9 Methane H 4 100 21390 111 66 4239 1 Methyl C1 H 4 100 57050 L 298 15 78659 alcohol Octane C 8 H 18 100 59740 L 298 15 69849 o 2 100 0 0 G 298 15 o 2 100 3102 L 90 18 1 149 Propane E 3 H 8 100 30372 L 231 08 F Typical data file for two commonly used propellants are given bellow For RP1 02 REACTANTS C 1 000 H 1 9423 100 L 298 O 2 000 100 Lee Bois END For GH2 LO2 REACTANTS H 2 000 100 00 G 298 O 2 000 100 00 L 90 SAMPLE MAIN INPUT FILE FOR RTE RTE INP The main input file of RTE is RTE INP which is read by unit 5 default FORTRAN read unit This file consists if amp RTEDATA and RTECOND namelists and REACTANT data file amp RTEDATA CASECODE HARCC PC2000 COOLANT H2 WC 4 62 WGAS 43 9 RMIX 5 5 5 9 daa an 01 co 24044 01 O1 O1 O1 O1 5 PGO 2000 PCO 2900 TCO 50 NOFS 41 ITYPE 0 NBLOCK 0 REEXP 0 99 PREXP 0 4 DENEXP 0 37 VISCEXP 0 6 CONDEXP 0
63. ARCC in this design The temperature profile for this location is given in Figure 20 The dashed line in Figure 21 shows the average hot gas side wall temperature as a function of axial position for the unblocked channel case This figure also shows that there are step changes in the wall temperature just before and just after step changes in the cooling channel width in the nozzle and chamber respectively at x 1 0 inches and x 4 0 inches Liner Radius inches O N O O o Axial Length inches Figure 19 The high pressure rocket thrust chamber contour showing station locations Copyright O Tara Technologies LLC 55 999 240 882 824 765 707 6418 590 531 473 415 356 298 T 122R ze Tma 1058R 7 Figure 20 Rib temperature profile upstream of the throat x 0 1 inches for the high pressure chamber 200 channels unblocked One blocked channel No blocked channel 10 5 0 5 Axial Position inches Figure 21 Comparison of the maximum wall temperature profile versus axial position for the blocked channel and unblocked channel cases for the high pressure chamber 200 channels Copyright O Tara Technologies LLC 56 The same high pressure chamber was evaluated by running RTE with the blocked channel option In order to maintain the pressure drop of 834 psi for the cooling channel adjacent to the
64. DOWS copy RTE s input file onto rte dat and TDK s input file onto tdk dat Then in DOS mode go to the rte directory and type rtecom exe or double click on rtecom exe The outputs of TDK and RTE will be printed onto rte out and tdk out During the iteration CONVERGE DAT can be viewed for the status of convergence For UNIX systems type the following command rte com rteinputfilename tdkinputfilename rteoutputfilename tdkoutputfilename rte com takes rteinput filename and tdkinput filename for inputs of RTE and TDK respectively The results of each run will be printed onto rteoutput filename for RTE s output and tdkout filename for TDK s output Copyright O Tara Technologies LLC 106
65. Eee E ea Al file Edit a T ptions aa 2RTEDATA VASECODE HARCC PC2000 PART CHE 3E Be 243 2 NOFS del LIVRE 12 NBLOCK 0 IENT ke IGASRAD 2 TSTART 400 ERROR 9 1000000 03 MAXTTER 50 F1 Help Figure C 12 RTE s input file generated by its preprocessor After generating the RTE s input file the selected editor will be invoked and shows a listing of the data file similar to that shown in Figure C 12 The user should scroll over the file to make sure selections are made correctly Special attention should be given to the directory name to ensure that it is the same directory that the executable files of RTE reside in If the directory name is correct then by selecting exit from file list the control returns to the RTE s preprocessor By clicking on Generate RTE s Input the preprocessor generates another data file RTE INP which is directly read by unit 5 of RTE and its radiation module Before running RTE the user should make sure that RTE INP is saved in the same directory that executable files or RTE are located By clicking on Run Radiation Module the exchange factors files of RTE TSS DAT and TGS DAT are generated Note that depending on the speed of your computer and number of stations in the input file running this file can take between one to 30 minutes The DOS window generated after clicking on this button should be checked for
66. Help window for dimensions of cooling channels After entering the number of stations the user can enter station numbers and nozzle wall and cooling channel dimensions in their respective boxes as shown in Figure C5 The user can only enter numbers in those cells with a light blue color Other cells which are darker blue or red colors are protected and their numbers are calculated automatically based on other inputs By making a station number bold RTE will provide isotherm data file for that station which can be read and plotted using TecPlot Up to ten isotherm data files can be generated by RTE do not make more than ten station number bold Some stations in the data of Figure C 5 are identified with different tangent points These tangent point identifications are not used in RTE and are only for identifying different tangent points and they can be eliminated from the input data Note that the maximum allowable number of stations is 61 Additional four columns for swiler surface roughness wall heat flux and O F are in the RTE s preprocessor which is not shown in the Figure C 5 due to space limitation Figure C 6 shows various combo boxes for selecting engine specifications For example for coolant the user can select from the listed coolants that RTE support Material selection offers a listing of 13 built in material conductivities for each layer of the wall which are listed in the main section of the manual see Figure C 7 In addition
67. RAD f Program for gas radiation exchange and weight factors calculations After installing these files the user should compile the FORTRAN files i e rte2002 f cet f and gasp f and link them into an executable file rte exe The user can run the program by simply typing rte exe The following programs and data files are used for linking RTE and TDK rte com Shell program for linking RTE and TDK RTE_TDK f a FORTRAN program for taking RTE BLM DAT or RTE MABL DAT outputs of RTE and inserting wall temperature distribution into TDK input TDK_RTE f a FORTRAN program for taking TDK_RTE DAT an output of TDK and inserting wall heat flux distribution into RTE input CONVERGE DAT typical CONVERGE DAT file TDK DAT typical TDK data file The program was successfully executed for several types of engines under different conditions and provided results which are reasonably close to the experimental data A number of provisions are made in the program to detect possible error in data of unrealistic conditions It is however possible that the program fail under certain conditions The following guidelines may be useful to detect and correct any possible error in the input data 1 For a new case set MAXPASS 1 for the first run Then the program makes one axial pass and prints the results as soon as it finishes calculations for each station If the program fails one can tell exactly at what station the failure has occurred and check the data
68. SA TM 86885 Oct 1984 3 Hendricks R C Baron A K and Peller I C GASP A Computer Code for Calculating the Thermodynamic and Transport Properties for Ten Fluids Parahydrogen Helium Neon Methane Nitrogen Carbon Monoxide Oxygen Fluorine Argon and Carbon Dioxide NASA TN D 7808 Feb 1975 4 Hendricks R C Peller I C and Baron A K WASP A Flexible Fortran IV Computer Code for Calculating Water and Steam Properties NASA TN D 7391 Nov 1973 5 Muss J A Nguyen T V and Johnson C W User s Manual for Rocket Combustor Interactive Design ROCCID and Analysis Compter Program Volumes I and II NASA Contractor Report 1087109 May 1991 6 Nickerson G R Coats D E Dang A L Dunn S S and Kehtarnavaz H Two Dimensional Kinetics TDK Nozzle Performance Computer Program NAS8 36863 March 1989 7 CPIA MA Liquid Propellant Manual Unit 20a September 1997 Chemical Propulsion Information Agency 8 Eckert E R G and Drake R M Analysis of Heat and Mass Transfer McGraw Hill Book Company 1972 9 Bartz D R Turbulent Boundary Layer Heat Transfer from Rapidly Accelerating Flow of Rocket Combustion Gases and of Heated Air Advances in Heat Transfer pp 2 108 1965 10 Colebrook C F Turbulent Flow in Pipes with Particular Reference to the Transition Region Between the Smooth and Rough Pipe Laws Journal of Institute of Civil Engineers Vol 11 pp 133 156 1939
69. USER MANUAL FOR RTE2002 Version 1 A COMPUTER CODE FOR THREE DIMENSIONAL ROCKET THERMAL EVALUATION M H N Naraghi Tara Technologies LLC 3126 Highridge Rd Yorktown Heights NY 10598 www tara technologies com January 2002 ACKNOWLEGMENT The original version of RTE was developed through funding by NASA Lewis research center grant NAG 3 892 and a number of NASA ASEE summer faculty fellowships to the author this code Since the public domain version of the code was release 1991 RTE has been substantially improved through private funds The public domain version of this code can be obtained from NASA Glenn Research Center see NASA s code publication web site http www lerc nasa gov WW W TU Computer Tech Briefs 199 to 1994 htm Copyright O Tara Technologies LLC TABLE OF CONTENTS TOPICS SUMMARY NOMENCLATURE INTRODUCTION NUMERICAL MODEL DESCRIPTION OF THE COMPUTER CODE INPUT FILES OF RTE RTE OUTPUTS HOT GAS SIDE BOUNDARY LAYER ANALYSIS INTERFACE BLOCKED CHANNEL OPTION AND RESULTS INSTALLATION AND EXECUTION INSTRUCTIONS REFERENCES APPENDIX A Flowchart of RTE APPENDIX B Sample inputs APPENDIX C Graphic User Interface Preprocessor of RTE APPENDIX D Interfacing RTE and TDK Copyright O Tara Technologies LLC 101 SUMMARY This manual describes the theoretical model and input output of a computer code for three dimensional thermal analysis of regeneratively cooled rocket thrust c
70. amber shown in Figure 1 and 2 The user specifies the combustion chamber and nozzle wall materials and thicknesses The wall can consist of three layers a coating the channel and the closeout which can be made of different materials The user also specifies the number of cooling channels in the wall For the numerical procedure the rocket thrust chamber and nozzle are subdivided into a number of stations along the longitudinal direction as shown in Figure 3 Copyright O Tara Technologies LLC 9 Coolant LH2 A uu Be Thrust SES Chamber A AA Section Figure 1 Configuration of a typical regeneratively cooled rocket engine Cooling Channels ET N CN gt N Coating Figure 2 Detailed layout of cooling channels in a typical regeneratively cooled rocket engine Copyright O Tara Technologies LLC 10 A AAA AAA AA AAA AAA A PA A AAA f i4 i4 4 4 A A A A Figure 3 A rocket thrust chamber subdivided into a number of stations These stations do not have to be equally spaced in fact it is desirable to put more stations near the throat where the heat flux and temperature gradients are largest The numbering of stations starts with the inlet to the cooling channels
71. blocked channel the mass flow rate of the coolant was reduced to 0 024 Ib sec compared to 0 032 Ib sec per channel for the no blocked channel case a 25 drop in the coolant mass flow The resulting axial average wall temperature profile for the blocked channel and the adjacent open channel is shown in Figure 20 As shown in this Figure the maximum wall temperature occurs at the injector end of the cooling channels Another location of high temperature occurs at x 4 inches where there is a step change in the cooling channel width Figures 22 and 23 show the rib temperature profiles for the peak temperatures in the throat region and injector end locations In order to achieve a chamber design with a lower pressure drop the same chamber was evaluated incorporating 150 cooling channels in the design Although the channel width for the reduced number of channels is larger the aspect ratio in the throat region was held at 6 by increasing the height of the channels relative to the 200 channel case As in the previous cases the chamber was first evaluated with unblocked channels In this case the pressure drop was 587 psi which resulted in a lower coolant inlet pressure of 2900 psia Again the peak wall temperature occurs just upstream of the throat at a value of 1211R 153R higher than the 200 channel case The temperature profile for this location is shown in Figure 24 The dashed line in Figure 25 shows the average hot gas side wall temperature a
72. ce the exchange factors are dependant of gas and surface radiative properties and the geometry of the nozzle they are calculated by running Copyright O Tara Technologies LLC 36 RTE_RAD and the printed into two files TSS DAT and TGS DAT Then RTE reads the exchange factors and use them in equation 75 to evaluate radiative flux for surface nodal points The radiative fluxes as shown in equation 75 are functions of surface temperatures These fluxes are evaluated by an iterative procedure Nodal points in axial direction the same as stations NROW NOES gt 2 d x B Nodal points in radial direction NCLMN Figure 9 Position of surface nodes and gas nodes for the radiation model The combustion properties code given by Gordon and McBride 1 does not provide the radiative properties of combustion gases These properties may be obtained from Ludwig et al 32 and Siegel and Howell 33 For example if the fuel is RP 1 the combustion gas species mole fractions are obtained from the combustion code 1 containing 17 30 CO 33 H20 6 OH 2 5 O2 3 H 7 and 1 5 O Using integrated average value of the absorption coefficients of these species the overall absorption coefficient is found to be 2 5in Iteration and Marching Procedures and Stagnation Coolant Properties Based on the revised wall temperature new hot gas and coolant wall properties heat transfer
73. ct of surface roughness on the pressure drop is incorporated in the fanning friction factor given by equations 22 and 23 Norris 23 suggested a simple empirical correlation for incorporating the effect of surface roughness on the heat transfer coefficient This correlation is given by Nu f Snooi 12 smooth where n 0 68Pr 9 For f f smooth gt 4 0 Norris finds that the Nusselt number no longer increases with increasing roughness Cooling channel roughness is defined by RGHNS for each station in the NAMELIST of RTE The fact that roughness can be varied along the cooling channel allows a user to examine selectively roughening of channel in the area where the most cooling is needed Copyright O Tara Technologies LLC 24 Heat Transfer Enhancement due to Twisted Tapes Inserts In some instances twisted tape inserts swilers can be used to enhance heat transfer in the cooling channel 24 25 A typical twisted tape insert consists of a thin strip that is twisted through 360 per axial distance p Twisted tapes can be described by the twist angle and twist ratio y The helix angle of the tape is related to the twist ratio via tana n 2y Thorsen and Landis 25 recognized that buoyancy effects arising from density variation in the centrifugal field should have an effect on heat transfer They showed that the swirl flow induced buoyancy effect should depend on the dimensionless group Gr Re Gr _ 2d
74. dependent of wall temperature and are only dependent on the cross sectional area of the nozzle the propellant used and chamber pressure Indeed the heat transfer from hot gases to the chamber and nozzle wall will cause very little change in the gas temperature the thermodynamic process dominates the transport process Geometry of the nozzle is inputted into via two variables axial position and the corresponding nozzle diameter do The axial position x is zero at throat positive downstream of the throat and negative upstream of the throat These two variables in the NAMELIST of RTE are defined as X and DG Coolant Properties at the Cooling Channel Entrance On the coolant side the stagnation enthalpy and density at the entrance to the cooling channel are evaluated as functions of the coolant stagnation pressure and temperature icy icy and Peo Peo Peo using the coolant properties modules e g GASP and WASP Axial Marches The model now begins its axial marches passes starting from the first station At the first axial march an initial guess for the wall temperature distribution is made For the next march however the results of temperature distribution for the previous march can be used as an initial guess The hot gas and coolant adiabatic wall temperatures and wall properties can be evaluated at a given station based on the assumed wall temperature distribution using the properties
75. directions types of materials used in different wall layers MTCLO MTCH and MTCOAT for close out channel and coating respectively the boundary condition at the outer surface IHOUT heat transfer coefficient at the outer surface in the case of forced convection 1 outer surface emissivity EM type of cooling system ICOOL outside temperature in the case of convection at the outer surface TO radius of curvature for cooling channel RCURVE gas scattering albedo OMEGA gas extinction coefficient KTG emissivity of inner surface EPSILON swiler angle SANGLE flag for swiler or no swiler at a station ISW edge effect for cooling channel IEDGE cooling channel surface roughness RGHNS flag for units IUNIT flags for detailed outputs of the main program IFLAGM subroutines GASP and BONNIE IFLAGG and subroutine COND IFLAGO flag for using enthalpy difference or temperature difference in calculating hot gas side heat flux ENTHALPY flag for known or unknown wall heat flux s Equal tol 2 3 4 or 5 for equations 34 35 36 37 or 38 respectively Equal to O for user defined correlation equation 39 3 Needed for user defined coolant correlation Equal to 0 for no blocked channel and 1 for one blocked channel d Equal to 1 2 3 or 4 for equations 35 36 37 and 38 respectively Equal to 1 for gas radiation and 2 for no gas radiation Equal to 1 for copper 2 for nickel 3 for s
76. e Reynolds number between the entrance and exit to each station is evaluated 1 e 05 20 0 5 Ree 21 The Reynolds number the cooling channel is within the turbulent flow range hence the Colebrook equation 10 is used to calculate the friction factor This equation is given by e 2 5226 1 2 00 Q2 TF 3 70650 Reg wf This implicit equation very closely approximated by the explicit formula 11 Copyright O Tara Technologies LLC 18 1 1098 Ho mese A SO Vf 3 7065D 7 2 8257 D Re 9 avg Curvature Effect The correlation given by equation 23 is only valid for straight channels To include the curvature effect the friction factor obtained from equation 23 must be multiplied by the curvature factor given by Ito s correlation 12 2 1 20 y t 24 Cur where ro is the hydraulic radius of cooling channel is the radius of curvature The 2 x curvature factor given by equation 24 is valid when Rec a gt 6 otherwise Cur cur 3 1 Pressure Drop Once the friction factors are determined the viscous pressure drop between stations n 1 and n is calculated using Darcy s law 13 which is given by eee Ves tV J AS 25 82 CS CS p 1 and the momentum pressure drop is calculated via Z 26 AcN AcN 8
77. e evaluated do not have to coincide with positions of stations defined in the RTE s input RTE has an interpolation routine that calculates wall heat flux based on the wall temperature and location of the station This feature of RTE can be used by setting IWFLUX 2 and providing another input file FLUX DAT which contains fluxes matrix A sample of FLUX DAT is given in Appendix B Interfacing RTE and TDK s Boundary Layer Module To interface RTE and TDK a shell program is written which allow iterations between RTE and TDK First RTE s internal heat flux calculation equations 6 12 is used to predict wall temperature Then the calculated wall temperature via and RTE and TDK interface program TDK RTE is inserted into input of TDK Then by running TDK with one of its boundary layer modules BLM or MABL the wall heat flux based on TDK s boundary layer module is calculated The heat fluxes for each station are inserted into the input file of RTE via an interface program This cycle is repeated several times until convergence is achieved At each iterative cycle heat fluxes at all stations are compared to those of pervious iteration This iterative calculation stops when the difference between wall heat fluxes of two consecutive iteration become negligibly small The flow chart of this iterative scheme is given in Figure 5 More detailed descriptions of this feature of RTE are presented in HOT GAS SIDE BOUNDARY LAYER ANALYSIS and App
78. e is REACTANT cards that give the chemical composition of the fuel and oxidant A complete description of REACTANT cards is given in 1 The next set is THERMO data that gives the thermodynamic properties for different combustion species These data are valid as long as the gas temperature is between 300 K and 5000 K The last set of data for BONNIE is TRANS data which gives the transport properties namely the viscosities and conductivities of different species Similar to THERMO data TRANS data are valid when the gas temperature is between 300 K and 5000 K When the gas temperature is outside this range a low or high temperature THERMO and TRANS data should be used The ASCII files of THERMO and TRANS data are required for the first run of RTE At the first run BONNIE generates binary files of THERMO and TRANS data files which are used for future runs Subroutines GASP and WASP 3 4 are used for evaluation of the thermodynamic and transport properties of the coolant The GASP subprogram accommodates all commonly used coolants in rockets Sometimes water is used as the coolant for colorimeter experiments In this case the WASP program is used to calculate the thermodynamic and transport properties of the coolant Subroutine COND is used to evaluate the nodal temperature distribution Based on the specified coolant and hot gas heat transfer coefficient and adiabatic wall temperatures or hot gas side wall heat flux This subroutine calculates the n
79. egular outputs RTE produces two output files GAS TEMP DAT which is a table of axial position chamber diameter gas temperature wall heat flux and temperature and RTE BLM DAT and RTE MABL DAT are output files which can be used to interface RTE and TDK The procedure for interfacing RTE and TDK and implementation of these output files will be described in the next section HOT GAS SIDE BOUNDARY LAYER ANALYSIS INTERFACE The convective heat transfer coefficients and heat fluxes for the hot gas side of RTE are evaluated based on adiabatic wall temperature enthalpy correlations 8 9 see equation 3 12 To obtain results based on boundary layer analysis RTE can be linked to a nozzle flow and boundary layer analysis program The procedure for linking RTE to Copyright O Tara Technologies LLC 50 TDK Two Dimensional Kinetics Nozzle Performance Computer Program 6 is described in this section A similar approach may be implemented to link RTE to other nozzle boundary layer analysis programs An iterative procedure for linking RTE to TDK has been devised A flowchart of this procedure is given in Figure 5 Initially the wall fluxes and temperatures are evaluated by running RTE under an unknown wall heat flux condition 1 IWFLUX 0 The wall temperatures calculated by RTE are then used in the inputs of TDK Using one of TDK s boundary layer modules BLM or MABL a new wall heat flux distribution is evaluated The wall heat flux distrib
80. endix D Copyright O Tara Technologies LLC 15 Figure 5 Flow chart of shell program for interfacing RTE and TDK 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 Next attention will be focused on calculating the coolant side properties and heat transfer calculations Copyright O Tara Technologies LLC 16 Coolant Properties For the first station the coolant stagnation enthalpy static pressure and static density are set equal to the stagnation enthalpy pressure and density at the entrance to the cooling channel 1 ico Pes Peo and Pes Pco For the other stations the coolant stagnation enthalpy is calculated via q 4 248 n 13 1 1 C0 0 1 W where AS is the distance between two neighboring stations n 1 and n which is 1 calculated from equation 2 and q is the heat transferred per unit length of the cooling channel from the hot gases to the coolant at station n calculated from the conduction subroutine at iteration 1 For the first iteration at station n q in equation 13 is not known therefore the following equation is used t
81. er bold in RTE s preprocessor the graphic file for that station will be generated Copyright O Tara Technologies LLC 47 Cooling Channel Height in 10 25 0 5 x in Figure 13 Cooling channel height for the SSME engine versus axial position 80 70 60 50 40 Qw BTU in sq 30 20 10 5 0 5 x in Figure 14 Wall heat flux distribution for the SSME engine versus axial position Copyright O Tara Technologies LLC 48 6000 mod 5800 5600 PCS PCO a gt o o Pcs Pco psi al o o 5000 4800 4600 10 5 0 5 x in Figure 15 Static and stagnation pressure distribution for the SSME engine versus axial position 1400 1300 1200 1100 1000 800 10 5 0 5 x in Figure 16 Wall average temperature distribution the SSME engine versus axial position Copyright O Tara Technologies LLC 49 T 1289 39 1225 33 1161 26 1097 2 1033 13 969 067 905 002 840 937 776 872 712 807 648 742 584 677 520 613 456 548 392 483 Figure 17 Temperature distribution for a specified station of an engine A short file showing the summary of results for each station SHRESULTS DAT is also generated The results printed in SHRESULTS DAT include axial position X wall temperature TW wall heat flux QW coolant static pressure PCS coolant stagnation pressure PCO coolant stagnation coolant Mach number In addition to its r
82. es the user should compile the FORTRAN files i e rte f cet f and gasp f and link them into an executable file rte exe The user can run the program by simply typing rte2002 exe To minimize errors in inputting data RTE s graphic user interface can be used By clicking on Run RTE button RTE runs The following programs and data files are used for linking RTE and TDK rtecom exe executable of rtecom f a Shell program for linking RTE and TDK RTE TDK f a FORTRAN program for taking RTE BLM DAT or RTE MABL DAT outputs of RTE and inserting wall temperature distribution into TDK input TDK_RTE f a FORTRAN program for taking RTE DAT an output of TDK and inserting wall heat flux distribution into RTE input CONVERGE DAT typical CONVERGE DAT file TDK DAT typical TDK data file UNIX Operating System RTE and its modules were successfully compiled and executed on an IBM RISC6000 The enclosed CD contains the RTE program its supporting modules and typical data files The CD contains the following files rte f RTE main program and its subroutines Copyright O Tara Technologies LLC 62 cet f combustion properties subroutines BONNIE gasp f coolant properties subroutines RTE INP typical RTE input including RTEDATA THERMOSA DAT Thermodynamics properties of hot gases needed in ASCII format only for the first run TRANSSA DAT Transport properties of hot gases needed in ASCII format only for the first run RTE
83. esponds to constant wall temperatures and their elements give fluxes at different locations along the engine These vectors form columns of the matrix of fluxes in FLUX DAT The first row in FLUX DAT contains two integers The first one is the number of rows locations at which fluxes are given and the second one is the number of columns temperatures at which fluxes are evaluated The second line of FLUX DAT gives temperatures for which wall fluxes are specified starting from the lowest to the highest temperature From the third line on each line gives the x coordinate distance from the throat and the corresponding heat flux for each temperature A sample of FLUX DAT for a typical engine is given in Appendix B Only RTEDATA and CONDDATA provide data for RTE The input data given by REACTANT THERMO and TRANS correspond to the BONNIE subroutine and TSS DAT and TGS DAT are used to evaluate the radiative heat flux at the inner surface Note that for certain types of combustion gases such LHy LO the gas radiation is insignificant and there is no need to include radiation within the chamber Under these conditions IGASRAD in RTEDATA must be set to 2 and TSS DAT and TGS DAT must be excluded from the inputs Radiation Module Input Files When IGASRAD is set to 1 in RTEDATA then the program takes into consideration the hot gas radiation Under this condition the exchange factors as well as weight factors are required for input to RTE T
84. hael L Meyer A Rocket Engine Design for Validating the High Aspect Ratio Cooling Concept Preprint from the 1994 Conference on Advanced Earth To Orbit Propulsion Technology held at NASA Marshall Space Flight Center Huntsville AL May 17 19 1994 Copyright O Tara Technologies LLC 67 36 Mary F Wadel and Michael L Meyer Validation of High Aspect Ratio Cooling in a S9kN 20 000 Ibf Thrust Combustion Chamber AIAA ASME SAE ASEE 3214 Joint Propulsion Conference July 1 3 1996 Lake Buena Vista FL AIAA 96 258 Copyright O Tara Technologies LLC 68 APPENDIX A FLOWCHART OF RTE Copyright O Tara Technologies LLC START Divide the nozzle into m stations Is wall heat flux known Unknown Is matrix of wall heat fluxes given Yes TWFLUX 2 No IWFLUX 0 Calculate hot gas static properties P ics and Mach number for all stations using ROCKET subroutine of CEC Calculate coolant stagnation enthalpy ico and coolant stagnation density pco f Peo Teo using GASP WASP or Copyright Tara Technologies LLC 70 Start pass 1 k 1 Start with station 1 n 1 Em Start iteration 1 G 1 Make an initial guess for the wall temperature distribution at station n use previous pass results when k gt 1 m TWFLUX 1 or 2 1 Calculate reference enthalpy icx eq 3 Calculate adiabatic wall enthalpy
85. hambers and nozzles RTE A unique feature of this code is conjugating all thermal fluids processes in the propulsion system in order to obtain matched results for the thermal field These thermal fluids processes include convection and radiation heat transfer from hot combustion gases to the liner of the engine conduction heat transfer with walls and convection to the coolant RTE uses an iterative marching scheme to match the heat flux and temperature fields of these thermal processes The program uses GASP GAS Properties WASP Water and Steam Properties and a module for properties of RP1 to evaluate coolant flow properties Hence it is capable of handling all commonly used coolants in propulsion systems e g O2 and CET Chemical Equilibrium with Transport Properties code is used for evaluation of hot gas properties The inputs to RTE consist of the composition of fuel oxidant mixtures and flow rates chamber pressure coolant entrance temperature and pressure dimensions of the engine materials and number of nodes in different parts of the engine It allows temperature variations in axial radial and circumferential directions and by implementing an iterative scheme it provides a listing of nodal temperatures rates of heat transfer and hot gas and coolant thermal and transport properties The O F oxidant fuel ratio can be varied along the thrust chamber This feature allows the user to incorporate a non equilib
86. hange factors Values of these exchange factors are functions of the engine geometry and hot gas radiative properties In order to conserve computational time these exchange factors can be evaluated once for a given engine and inputted to the RTE A separate FORTRAN program based on the DEF method 27 31 namely RTE_RAD radiation module of RTE has been developed INPUT FILES OF RTE The main input data file for RTE is called RTE INP which consists of two parts the RTEDATA namelist and reactants information For user defined thermal conductivity an additional namelist CONDDATA is needed Two exchange factor files which contain radiative exchange factors for surface to surface TSS DAT and gas to surface TGS DAT are also needed if the radiative heat transfer option is selected To illustrate the input procedure a sample input for the Space Shuttle Main Engine SSME is presented in Appendix B The three sets of input data in RTE INP file are as follows RTEDATA is the main input data file of RTE RTEDATA has a NAMELIST format and it includes coolant name COOLANT case code for the run CASECODE coolant and total propellant weight flow rate WC amp WGAS percentage of fuel in the mixture at all stations RMIX chamber pressure PGO coolant stagnation pressure and This code can be a character input to recognize the output of RTE This code will be printed on every output of RTE Copyright Tara Technologies LLC 4
87. he exchange and weight factors are read by RTE via two files TSS DAT total exchange factors between surface elements and TGS DAT total exchange factors from volume elements to surface elements RTE s radiation module RTE RAD generates these two files The inputs of RTE RAD are axial position of stations X contour diameter at all stations DG hot gas extinction coefficient KTG and hot gas scattering albedo OMEGA RAD s data is a part of RTEDATA hence to make user s job easy RTEDATA can also be used as the radiation module input data 1 NAMELIST of RTE RAD is the same as RTEDATA Copyright O Tara Technologies LLC 44 Generating RTE s Data Using its Preprocessor RTE can be run in two ways via its Graphic User Interface GUI preprocessor or by typing its executable file name The GUI of RTE is based on Excel which consists of a single data sheet with text boxes combo boxes and help in producing input data see Figures 10 12 for parts of RTE s GUI A user can enter engine specifications and dimensions in appropriate boxes and then by clicking on Generate RTE Input generate the ASCII file of RTE data file Generate RTE Input ws z Radiation Module AAA ls DG in CCW TCOAT in THKNS in 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Figure 10 A portion of RTE s GUI RTE s graphic user interface contains help buttons and it is design to ease generating input data for RTE In fact a user
88. hicle propulsion concepts are to be evaluated in a timely and cost effective manner In the high pressure engines hot gas temperatures are very high they can reach 7000R at the throat area It is therefore essential to be able to estimate the wall temperature and ensure that the material can withstand such high temperature Furthermore an accurate thermal model enables an engine designer to modify the cooling channel configuration for the optimum cooling at high temperature areas It should be noted that the under cooling of an engine would result in catastrophic failure of the engine and over cooling would cause loss of engine performance This loss of performance can be due to the need for a bigger coolant compressor or decreased effective flow area at the throat when the liner temperature is very low larger boundary layer displacement when the liner is over cooled The thermal phenomena in rocket engines involve interactions among a number of processes including combustion in the thrust chamber expansion of hot gases through the nozzle heat transfer from hot gases to the nozzle wall via convection and radiation conduction in the wall and convection to the cooling channel The complexity of the thermal analysis in rocket engines is due to three dimensional geometry coolant and hot gas heat transfer coefficient dependence on the pressure and wall temperature unknown coolant pressure drop and properties axial conduction of heat within the wall
89. ial conduction by allowing for different convergence criterion between the axial and radial and circumferential directions For example in analysis of a thin walled radiatively cooled low pressure engine axial conduction is negligible In this case one might set the convergence accuracy to 5 in the axial direction and 0 1 in the other directions In the case of a thick walled regeneratively Copyright Tara Technologies LLC 38 cooled high pressure engine axial conduction may be significant Thus the accuracy in the axial direction may be set to 0 1 and 0 1 in the other directions DESCRIPTION OF THE COMPUTER CODE RTE Rocket Thermal Evaluation RTE and its radiation module are written in standard FORTRAN The numerical model of RTE is based on the numerical method discussed in the previous section The program provides the temperature distribution in the rocket thrust chamber and nozzle It also calculates the rate of heat transfer to the cooling channel coolant temperature and pressure drop This program can be used for all types of propellants and coolants that are used in regeneratively cooled rockets The conductivities of several rocket engine materials are included in tabular form as functions of temperatures These include Copper Nickel Soot Carbon NASA Z NARloy Z Columbium Zirconia SS 347 Amzirc Platinum Glidcop Inconel718 and Nicraly The user can specify conductivities of up to three materials in the input of
90. iative Analysis of Enclosures with Participating Media Journal of Heat Transfer Trans ASME Vol 110 pp 456 462 1988 Hammad K J and Naraghi M H N Exchange Factor Model for Radiative Heat Transfer Analysis in Rocket Engines AIAA Journal of Thermophysics and Heat Transfer Vol 5 No 3 pp 327 334 1991 Hammad K J Radiative Heat Transfer in Rocket Thrust Chambers and Nozzles M S Thesis Department of Mechanical Engineering Manhattan College 1989 Nunes E M Modi V and Naraghi M H N Radiative Transfer in Arbitrarily Shaped Axisymmetric Bodies with Anisotropic Scattering Media International Journal of Heat and Mass Transfer Vol 43 pp 3275 3285 2000 Nunes E M Naraghi M H N A Model for Radiative Heat Transfer Analysis in Arbitrarily Shaped Axisymmetric Enclosures Numerical Heat transfer Part A Vol 33 pp 495 513 1998 Ludwig C B Malkmus W Reardon J E and Thomson J A L Handbook of Infrared Radiation From Combustion Gases NASA SP 3080 1973 Siegel R and Howell J R Thermal Radiation Heat Transfer Hemisphere Publishing Corporation 3rd Ed 1992 Naraghi M H N Quentmeyer R J Mohr D H Effect of a Blocked Channel on the Wall Temperature of a Regeneratively Cooled Rocket Thrust Chamber AIAA 2001 3406 present in the AIAA ASME SAE ASEE 2001 Joint propulsion Conference Salt Lake City Utah July 8 11 2001 Mary F Wadel Richard J Quentmeyer and Mic
91. ics Calculate coolant stagnation pressure Pog f ico gt Sc No Copyright O Tara Technologies LLC 74 No Yes No Yes Print final results Copyright O Tara Technologies LLC 75 APPENDIX B INPUT NOMENCLATURE AND SAMPLE INPUTS FOR RTE Copyright O Tara Technologies LLC 76 STRUCTURE OF RTE S DATA FILES The main input data of RTE consists of six parts amp RTEDATA amp RTECOND needed only if the user defined conductivity option is chosen REACTANTS FLUX DAT THERMO DAT and TRANS DAT Three files amp RTEDATA amp RTECOND and REACTANTS are attached as a single file to RTE INP which is read by the default read unit of RTE unit 5 amp RTEDATA is a namelist data file which defines all specification of the engine such as nozzle and cooling channel geometry coolant flow rate inlet temperature and pressure amp RTECOND is a namelist file that is only needed if user defined conductivities option is chosen i e negative material code It defines conductivities of up to three user defined materials as function of temperature REACTANT provides information on the fuel and oxidant propellant composition It is needed if the RTE s own hot gas side calculation is used i e IWFLUX 0 in amp RTEDATA namelist FLUX DAT is a matrix of wall heat flux which gives hot gas side heat flux as a function of position and wall temperature This file is needed if IWFLUX 2 THERMO DAT provides the
92. irectories that RTE s preprocessor is not pointed to After clicking on Generate RTE s Input a window similar to that shown in Figure C 11 appears on the screen and requests the name of the file that RTE s input file should be save in After entering a file name and clicking on OK button RTE s input in its namelist format will be generated Help on Meshing Natura Comection D TOP CHANNEL 0 3 AR B NRCHT Hot Gas Side Radiative Properties CHANNEL AR B NRCHE ZA B E COATING LAND CHANNEL AREA AR AR B Help on selecting coolant correlation ROJAT NPHIL NPHIC USER DEFINED Help on User Defined Coolant USER DEFINED Hendricks Oxygen Shell Hines 0 6 0 2 E 0 25 03 Figure C 8 Other parts of RTE s preprocessor for meshing and cooling options Copyright O Tara Technologies LLC 98 Nu C Re Prol Lo Hes Zoe DUCS Ca es ds Es Cus E Pa Figure C 9 User defined coolant correlation input section with help window Generate RTE Input Dos zi Run Radiation Module Run RTE Figure C 10 Command buttons for generating rte input file running radiation module and RTE Save RTE Input Enter file to save as Cancel har CC P2300 Figure C 11 Input box requesting name of the file that RTE s input data should be saved in Copyright Tara Technologies LLC 99 sj
93. it to generate an input data file and upload the resulting file to the UNIX machine WORKING WITH RTE s PREPROCESSOR Loading it into Excel or double clicking on the file can start RTE GUI xls After the file is loaded a message box similar to that shown in Figure C 1 appears Make sure to click Microsoft Excel 2 x Crirtelrte2002 Example 2000 Pc NASA GRC xls contains macros Macros may contain viruses It is always safe to disable macros but if the macros are legitimate you might lose some Functionality i Enable Macros More Info Figure C 1 Microsoft Excel warning message during loading of RTE s GUI on the Enable Macros button The macros are legitimate and virus free After RTE s GUI is loaded a screen similar to that shown in Figure C 2 comes up Scroll bars horizontal and vertical can be used to move around the interface Note that the initial screen can be at a different location of the interface depending on the position of the scroll bars when the file was last saved Make sure to move the horizontal scroll bar to the left of the sheet and vertical scroll bar to the top of the sheet such that the red button with caption Initialize RTE s Pre appears on the top left side of the screen Then click on this red button This initiates the combo boxes and inserts all possible options for these boxes If the initialization is not performed correctly the preprocessor will not work correctly After initializing the prep
94. ius of curvature thermal resistance Reynolds number entropy temperature velocity weight flow weight factor for discrete exchange factor method station position in longitudinal direction angle between a vector normal to the nozzle surface and axial direction length of cooling channel between two stations pressure drop radial mesh size circumferential mesh size Copyright O Tara Technologies LLC gesaneEn Subscripts gt gt lt 09 nr o erp Superscripts A convergence criteria or error limit dynamic viscosity density Stefan Boltzmann coefficient entrance and curvature effect correction factors successive overrelaxation coefficient KyK scattering albedo adiabatic average coolant curvature viscous or friction gas node i node j secant method iteration number momentum related to station n radiation static surface throat wall reference stagnation iteration number iteration number for conduction model related to station n Copyright O Tara Technologies LLC INTRODUCTION Thermal analysis is an essential and integral part in the design of rocket engines The need for thermal analysis is especially important in the reusable engines where an effective and efficient cooling system is crucial in expanding the engine life The rapid and accurate estimation of propulsion system aerothermodyanamic heat loads and thermal protection system effectiveness is required if new ve
95. ixture ratio variable along the thrust chamber Thermal radiation from hot gases within the chamber is also included in the analysis The user has the option of bypassing the hot gas side calculations and Copyright O Tara Technologies LLC directly inputting gas side fluxes This feature is used to link RTE to a boundary layer program for the hot gas side heat flux calculation A shell program was developed to link RTE to a hot gas side program TDK 6 Two Dimensional Kinetics Nozzle Performance Computer Program This shell program runs RTE and TDK in an iterative loop to match wall temperatures and fluxes computed based on the two codes Additionally another feature is devised such that a user can input hot gas side fluxes via a matrix whose rows are axial positions along the chamber and nozzle and columns are different temperatures This manual describes the numerical model and the computer code RTE developed to analyze rocket engine thrust chamber heat transfer characteristics This code can be used to determine the temperature distribution in both regeneratively and radiatively cooled thrust chambers by allowing for temperature variations in the radial circumferential and axial directions NUMERICAL MODEL Overview of the Numerical Model The numerical procedure for the thermal analysis is summarized below A flowchart of this model is given in Appendix A The model is based on the geometry of a typical regeneratively cooled thrust ch
96. lated from equations 6 and 7 or wall heat flux calculated using equations 11 and 12 will be used in the conduction subroutine to evaluate a revised wall temperature distribution It should be noted that the formulation given by equations 7 12 yields an approximate value for the wall heat flux In addition to the formulation given by equation 7 12 the heat fluxes can be input directly at specified station The program then bypasses wall heat flux computations and uses the specified heat fluxes Additionally this feature allows interfacing RTE with a boundary layer module The variable in the NAMELIST of RTE that controls the method of hot gas side calculations is IWFLUX By setting WFLUX 0 equations 3 12 are used to calculate hot gas side fluxes For this case REACTANT compositions data file described in 1 2 are needed If hot gas side wall heat fluxes are known the IWFLUX is set to 1 IWFLUX 1 and an array of wall heat flux QW for every station must be included in the NAMELIST of the RTE If another software is being used for hot gas side computations then the resulting wall heat fluxes can be linked to RTE via a matrix Rows of this matrix represent location along axial direction of the engine and its columns represent various temperature Running the user preferred hot gas side software for a constant wall temperature can generate each column of this matrix It should be noted that positions of points for which heat fluxes ar
97. material 1 conductivity array of material 1 corresponding to temperature array K1 number of temperature points for material 2 NP2 temperature array of material 2 T2 conductivity array of material 2 corresponding to temperature array T2 K2 number of temperature points for material 3 NP3 temperature array of material 3 conductivity array of material 3 corresponding to temperature array T3 K3 All temperatures should be in Rankin and conductivities in Btu s ft R REACTANT describes the chemical composition of the fuel and oxidant propellant In the sample of REACTANT data for RP1 O2 LH2 LO2 and CH4 02 are given in Appendix B REACTANT data is an input to the BONNIE subroutine and a complete description of its format is given in 1 In addition to the main data file which described above RTE requires thermal and transport properties for combustion gases species These properties are provided via the following two files THERMO DAT is data for the thermodynamic properties of the hot gas species A complete list of THERMO data is given in 1 An ASCII form of THERMO DAT named THERMOSA DAT in RTE files is required for the first run of the program Subroutine BONNIE generates a binary form of THERMO DAT which is used in the next runs THERMO DAT in the file package is in binary form suitable for running the executable RTE on a WINDOWS operating systems If RTE is being used in other
98. n The format of RTE s input file is the same as RTE INP file described in Appendix B with IWLFUX set to 0 TDK s input file must be named tdk in and it has a format the same as that described in its manual 6 except that its BLM or MABL namelists must be replaced by the word BLM or MABL respectively Sample input of TDK TITLE HYDROGEN COOLED ENGINE DATA BLM FOR BOUNDARY LAYER DATA SDATA ODE 1 ODK 0 TDE 1 BLM 1 SHOCK 0 IRPEAT 0 IRSTRT 0 NZONES 1 XIC 1 6 NXIC 1 ECRAT 3 4082 ASUB 3 4082 2 1025 1 2648 NASUB 3 ASUP 1 0720 1 7121 3 5315 6 629 NASUP 4 RSI 1 3 1 555 0 77 THETAI 14 5 RI 15 564 THETA 36 868 IWALL 2 RMAX 2 5746 ZMAX 2 4677 IOFF 3 SEND REACTANTS H 2 100 0 0 G 298 15 F O 2 100 3102 0 L 90 56 O 1 149 NAMELISTS SODE T OF T OFSKED 5 80 2000 XP 1 PSIA 0 SEND REACTIONS H H H2 1 6 4E17 N 1 0 0 0 BAULCH 72 A 30U H OH 20 M2 A 8 4E21 2 0 B 0 0 BAULCH 72 A 10U 02 1 9E13 0 0 B 1 79 BAULCH 76 A 100 OH 7 3 62 18 N 1 0 0 0 AR JENSEN 78 B 300 END TBR REAX 02 H OH y Boa 2 2514 No 0 20 B 516 8 BAULCH 72 A 1 5U H2 O H OH
99. nd copies the RTE input data into RTE INP and then starts the iterative loop by running RTE In the first loop RTE performs the hot gas side as well as wall and cooling channel calculations The resulting wall temperature distributions along the axial direction are written into two files BLM DAT and MABL DAT which have the same formats as the NAMELISTS in the MABL or BLM modules of TDK Next the shell program runs an interfacing program RTE TDK This program revises the TDK inputs based on the temperature distribution coming out of RTE i e it inserts the temperature distribution in place of words BLM or MABL TDK is then executed and generates a table of heat fluxes versus axial positions which is written to a file TDK_RTE DAT An interfacing program reads wall heat fluxes from RTE DAT and prints them into the RTE input file consistent with the NAMELIST format of RTE In the second and subsequent iterations RTE runs with a known wall heat flux boundary condition 1 e it bypasses the hot gas side calculations This iterative procedure continues until the relative difference between heat fluxes of two consecutive iterations becomes negligibly UTWFLUX O in the RTE input 18 In place of wall temperature distribution in the TDK input word TEMPERATURES must be inserted Copyright O Tara Technologies LLC 51 small The convergence criterion and the number of iterations are specified in CONVERGE DAT A
100. ng button a window containing meshing nomenclature appears on the screen which can be used to specify the number of nodes at different sections of the wall 1 e NPHIL NPHIC NRCLO NRCHB and NRCOAT Other parts shown in Figure C 8 include outer surface boundary conditions Natural Convection Forced Convection or Radiation method of cooling Regeneratively or Radiatively and coolant side correlation selections Five built in correlations that are discussed in the main part of this manual are available for the user to choose from These correlations can be viewed by clicking on Help on selecting coolant correlation The cells shown if Figure C 9 Copyright Tara Technologies LLC 97 must be filled 1f the USER DEFINED correlation is selected otherwise they are ignored Numbers in these cells are the coefficient and exponents of the user defined correlation that is shown in the help window After all numbers are entered and appropriate selections are made in the combo boxes the user can click on Generate RTE data button to produce the input file of RTE Before clicking on this button make sure appropriate the editor is selected for viewing RTE s input file Three editors are available for viewing the data file DOS Notepad and Word The DOS editor is the most reliable option since it can be called from any directory Notepad and Word in some cases do not show the results since they might be installed in different d
101. nologies LLC 53 high conductivity material As a result this causes the coolant temperature in the channel adjacent to the blocked channel to rise to a level higher than that for the channels further away from the blocked channel region This would result in an increase in coolant Mach number and pressure drop in the adjacent channel assuming the coolant mass flow in that channel is the same as all of the other channels However the pressure drop across the cooling jacket must be equal for all channels Since the pressure drop across the channel adjacent to the blocked channel must be the same as that of the other channels the mass flow in that channel will become less than that of the other channels Therefore in order to calculate the hot gas side wall temperature of the blocked channel and the adjacent channel the mass flow in the adjacent channel must be determined To obtain the mass flow in the cooling channel adjacent to the blocked channel RTE was first run for a given cooling jacket geometry in which there is no blocked channel in order to determine the pressure drop across the cooling jacket Then another case was run using the full rib conduction model in order to obtain the temperature profile in the rib with no cooling on one side and coolant flowing on the other side see figure 18b The mass flow in the adjacent channel is reduced through an iterative scheme until the pressure drop matches that for the case with no blocked channel
102. o evaluate the stagnation enthalpy 1 Wo Fn AS lco lco 14 Note that q in equations 13 and 14 are the heat transfer per unit length of cooling channel at the previous station The coolant velocity is calculated from the following equation W Ves 15 P cs Ac n n n Note that p is set equal to for the first station and for the other stations is evaluated using the GASP WASP programs 3 4 or RP1 subroutine based on the static pressure and enthalpy at the previous iteration 1 e Pes pop ua 16 At the first iteration however it is set equal to the static density of the previous station 1 Pos Pos n l Copyright O Tara Technologies LLC 17 Once the coolant velocity is determined the static enthalpy can be calculated using the following equation Lm c 17 CS 28 1 17 Coolant Friction Factor Calculations In order to determine the coolant friction factor first the Reynolds numbers must be evaluated The coolant static and reference Reynolds numbers respectively are given by R CS Ac 18 and Pew Re Re n n 19 x i Pes Is where is a function of and are calculated using the GASP program 3 the WASP program 4 if the coolant is water or Rp1 subroutine Note also that do is the coolant hydraulic diameter at station To employ a better value for the Reynolds number an averag
103. odal temperatures heat transfer to the coolant and heat transfer from the hot gas Three options are available for the outer surface boundary condition These options are radiation free convection and forced convection boundary conditions This subroutine can take three layers of materials as shown in the rocket wall configuration Figure 3 The thermal conductivities of each layer can be functions of temperature and a successive over relaxation formula is implemented for quick convergence Note that this subroutine has two versions CONDWCC COND With Cooling Channel and CONDNOCC COND No Cooling Channel Subroutine CONDWCC is used when the engine is regeneratively cooled and subroutine CONDNOCC when the engine is radiatively cooled Based on the flowchart given in Appendix A at a given station the program recalculates nodal temperatures coolant pressure thermodynamic and transport properties of the hot gases and coolant for each iteration The iteration continues until the relative difference of nodal temperatures between two consecutive iterations become negligibly small less than e The convergence criteria in this program must be specified in the data file Copyright O Tara Technologies LLC 40 Two convergence criteria can be specified in the input data ERROR is the convergence criterion for iterations at a given station 1 radial and circumferential directions and ERRAX is the convergence criterion for axial marches A s
104. ome negligibly small the coolant stagnation is set equal to the latest value of P The stagnation pressure obtained based on this procedure would automatically satisfy the relation between coolant stagnation and static pressures i e Poo Pos TUN 77 When the coolant is RP1 GASP is not used to determine the coolant properties the above equation is used to determine the coolant stagnation pressure Finally the coolant stagnation temperature is determined based on the coolant stagnation pressure and enthalpy T Peo leo The program then marches axially and performs similar calculations 1 e equations 3 through 43 for all stations Once the results of the last station station m converged the results of this march are compared to those of the previous march If the relative differences between the results of two consecutive marches are less than the axial convergence criterion the program stops otherwise it continues its axial marches until convergence is achieved Setting the axial convergence criterion greater than one or setting the maximum number of passes equal to one can eliminate the effect of axial conduction The method described here i e axial marches along axial direction has several advantages over the direct solution of a three dimensional finite difference formulation First it converges very quickly Second it requires less memory Third it allows the user to control the importance of ax
105. oot 4 for NARloy Z 5 for columbium 6 for zirconia 7 for SS 347 8 for amzirc 9 for Platinum 10 for Glidcop 11 for Inconel718 12 for Nicraly 1 for user definefd 311 2 for user defined 2 and 3 for user defined 3 5 Equal to 1 for forced convection 2 for natural convection and 3 for radiation Equal tol for regeneratively cooled and 2 for radiatively cooled engines 10 Equal to 1 for swiler and 0 for swiler Equal to 0 for no edge effect 1 for two edges and 2 for four edges 12 for English 2 for SI P Equal to 0 for no detailed output and 1 for detailed output 14 Equal to 0 for temperature difference equation 11 and equal to 1 for enthalpy difference equation 12 Copyright O Tara Technologies LLC 42 IWFLUX wall heat flux array along axial direction QW hot gas static temperature TGS QW array is required when IWFLUX is set 1 also TGS is required when both IWFLUX and IGASRAD are set 1 station number for which wall temperature isotherm plots are requested ISOST A sample of RTEDATA data and its nomenclature are given in Appendix B CONDDATA is needed if MTCH MTCLO or MTCOAT is set to 1 2 or 3 CONDDATA defines up to three user defined material conductivities as functions of the temperature profile For each material up to ten temperature points can be defined CONDDATA has a NAMLIST format and it includes number of temperature points for material 1 1 temperature array of
106. peratures is observed in this part of the engine To overcome this problem provisions have been made such that one can input the percentage of fuel burned at each station Using this option a low mixture ratio is assigned to the stations close to the injector and is gradually increased to its actual value at stations closer to the throat The value of mixture ratio at each station depends on the injector and chamber geometries manifold conditions and many other parameters To predict the mixture ratio at each station the user may use ROCCID ROcket Combustor Interactive Design and Analysis Computer Program 5 ROCCID uses state of the art codes and procedures for the analysis of a liquid rocket engine combustor s steady state combustion performance and combustion stability Modifications have been made on Copyright O Tara Technologies LLC 39 ROCCID such that it takes the RTE inputs with constant mixture ratios and produces an input file with variable mixture ratios Details of these modifications will be described later The variable IBCASE controls the output of the BONNIE subroutine When IBCASE 1 the subroutine ROCKET from BONNIE is used to evaluate static temperature and enthalpies of hot gas for all stations When IBCASE 2 and 3 the thermodynamic and transport properties are calculated based on the specified P T and P I respectively The subroutine BONNIE requires three sets of data The first set of data for the BONNIE subroutin
107. radiative heat transfer from hot gases and the surface of the nozzle To evaluate this term the Discrete Exchange Factor DEF method 27 31 and is used The radiation model of RTE is based on the configuration of a typical nozzle shown in Figure 8 In this method radiative exchange between surfaces and or volumes are expressed by four exchange Copyright O Tara Technologies LLC 31 factors between two surface elements dss r r j between a surface and gas elements dsg r T between gas and surface elements dgs r T and between two gas elements dgg r r The equations for these four mechanism of radiative transport is given by see Figure 8 for nomenclature V max 2r ds cosB cosB dss r r J J p p i j 57 r r V min V max 58 2K ridridx cosBt r r dsg r r pod J J j T r r V min 59 V max rds cos D T r r 5 5 J p Mir j A E 60 V min V max r dridx x r r j J J J i Day 2x r r V min where symmetry with respect to the azimuth angle y has been incorporated r denotes the location at which radiation is emitted r j the position at which radiation is received is the angle between the surface normal and the vector connecting r and is the extinction coefficient at node j is the transmittance which can be defined as ear T r r e op
108. rium model or an energy release model for the hot gas side The mixture ratio at each station can be calculated using ROCCID Thermal radiation from hot gases within the chamber is also included in the analysis The exchange factors for radiation calculations are evaluated using an external module RTE RAD Rocket Thermal Evaluation Discrete Exchange Factor which can be input to the main rocket thermal evaluation code This code can be used for both regeneratively and radiatively cooled engines For regeneratively cooled engines the code can be used for one pass as well as pass and half cooling cycles Additionally the blocked channel option allows a user to assess the thermal performance of a regeneratively cooled engine when a cooling channel is blocked The user has the option of bypassing the hot gas side calculations and directly inputting gas side fluxes This feature can be used to link RTE to a boundary layer program for the hot gas side heat flux calculation The procedure for linking RTE to a hot gas side program TDK Two Dimensional Kinetics Nozzle Performance Computer Program is described in this manual RTE is written in Fortran and has been successfully compiled on a number of UNIX systems and Microsoft Windows Shell programs have been developed for UNIX and WINDOWS operation systems to link RTE and TDK To ease inputting the large data sets needed to run the program a Graphic User Interface preprocessor based on Excel is provided
109. rocessor the user should assign a case code to the data file AII outputs of RTE will be marked with this code and helps to separate results of different cases The case code for the example of Figure C 2 is HARCC PC2000 High Aspect Ratio Cooling Channel with a chamber pressure of 2000 psi The next step is to enter the Copyright O Tara Technologies LLC number of stations in the appropriate box RTE s preprocessor has help associated with any input item A help window appears if the mouse is moved on the red spot at the upper right corner of any title box or by clicking on the help buttons provided next to some items that need graphic help Figure C 3 shows the help window for number of stations and Figure C 4 shows the help window for dimensions of cooling channels and wall layers Number of station should be an integer less than or equal to 61 RTE s dimension is limited to 61 stations Figure C 3 A typical interactive help window of RTE Interactive helps are provided for every input item of RTE and a user should ask for them to make sure that data are prepared correctly A text help window disappears when the pointer is moved away from the corresponding cell A graphic help window disappears by clicking on the corresponding help button or window Copyright O Tara Technologies LLC 94 0 15 0 156 0 156 0 156 0 156 0 156 0 156 0 156 lai prEnaTA cOococooooooooooooooooooooooooooo Figure C 4
110. ros Cri Pew 36 pcs Pos Kew Pcs Copyright Tara Technologies LLC 21 where P c 131 4 psia is the critical pressure and low les Tow The oxygen correlation can be used by setting ITYPE 3 When the coolant is the following two correlations can be used see 17 19 0 255 05 Pree 37 for ITYPE 4 and 0 0056Re py G8 for ITYPE 5 The user defined correlation can be used by setting ITYPE 0 where correlation has a general form of d e ff 8 h k C P Ce Re Pr Pes Ucs CS I CS 39 P cw Mew Kow Por The user can specify exponents of the above correlation in the NAMELIST of RTE by setting REEXP b PREXP c DENEXP d VISCEXP e CONDEXP f SHEXP g and PRESEXP h Values of these exponents for some hydrocarbon fuels are reported in 19 and given in Table 1 Coefficient Exponent No of Std Correl Fuel b D E f g h Points Dey Coeff RPI 0 0095 0 99 0 4 0 37 0 6 0 2 6 0 0 36 274 0 16 0 97 0 0068 0 94 0 4 0 0 0 0 0 274 0 20 0 96 Chem Pure 0 011 0 87 0 4 9 6 2 4 0 5 0 26 0 23 79 0 10 0 99 Propane 0 020 0 81 0 4 0 0 0 0 0 79 0 15 0 97 Commercial 034 0 80 0 4 0 24 0 098 0 43 2 1 0 38 285 0 27 0 94 Propane 0 028 0 80 0 4 0 0 0 0 285 0 29 0 93 Natural 0 00069 1 1 04 14 65 63 26 0087 130 016 0 92 Gas 0 0028 1 0 0 4 1 5 6 5 6 4 2 4 0 130 0 16 0 92 3 7
111. s are diagonal matrices of reflectivities and absoptivities for surface ring elements Once the total exchange factors are evaluated using equation 73 and 74 then the radiative heat flux at the n th station is computed using the following energy balance equation 2n m mn A Y w DS S E Y w DG S E SEa 15 j 1 j l E and E are surface and gas emissive powers at station n and are related to their temperatures via E oT 5 E 4K 1 0 0T 8 Note that the first term in the right hand side of equation 75 is the radiative flux at the surface due to emission from other surface elements the second term is due to the radiative flux from gas elements and the last term 1s the radiative heat loss due to emission The present model is benchmarked against a number of exact solutions and solutions that are available for a number of cylindrical problems The results reported in 30 31 show excellent agreement between the results of this model and those published The radiation module of RTE consists of a separate program RTE RAD that only evaluated total exchange factors based on the Discrete Exchange Factor DEF method In this module the nozzle is subdivided into a number of volume and surface nodes as shown in Figure 9 The number of radial nodes is NCLMN which is set to 5 The number of axial nodes is the same as the number of stations The position of axial nodes coincides with that of stations Sin
112. s a function of axial position for the unblocked channel case This figure also shows the step changes in wall temperature just before and just after the step change in the cooling channel width in the nozzle and chamber respectively at x 1 0 inch and x 4 0 inches The same high pressure chamber was evaluated by running RTE with the blocked channel option In order to maintain the pressure drop of 587 psi for the cooling channel adjacent to the blocked channel the mass flow rate of the coolant was reduced from 0 043 Ib sec per channel to 0 031 Ib sec per channel a 28 reduction in the coolant mass flow The resulting average hot gas side wall temperature as a function of axial position for the blocked channel and adjacent open channel is also shown in Figure 25 A maximum wall temperature of 1766R for this case occurs just upstream of the throat and is shown in the temperature profile in Figure26 At the injector end of the cooling channels the maximum wall temperature reached 1738R as shown in Figure 17 The 150 channel design resulted in a conservative axial wall temperature profile with a reasonable pressure drop across the cooling jacket However the peak wall temperatures for the blocked channel case are in a range where severe plastic deformation of the cooling channel on the hot gas side wall could occur Copyright O Tara Technologies LLC 57 Closed Tmax 1479R 7 Figure 22 Rib temperature profile upstream of the throat x
113. t on the wall temperature for the blocked channel and the adjacent open channel The results indicated that there is a significant increase in the hot gas side wall temperature of the blocked channel and the adjacent open channel and a significant reduction in the coolant mass flow in the adjacent open channel The increase in wall temperature due to a blocked channel for the low chamber pressure case was not at a level that would cause significant wall damage However the peak wall temperatures in the blocked channels for the high chamber pressure cases were at levels that could result in severe plastic deformation occurring in the cooling channel hot gas side wall especially for the 150 channel high pressure chamber Adjacent Open Channel Blocked Channel b Figure 18 a One half cooling channel and half rib cross section b One half blocked channel and one half open channel with full rib If one of the cooling channels in a rocket thrust chamber liner is blocked obviously the resulting wall temperature of the blocked channel will be higher than that of the cooled channels However the channel adjacent to the blocked channel will also have a higher wall temperature than the channels further away from the blocked channel region due to conduction of heat from the blocked channel to the adjacent channel This has the effect of reducing the maximum wall temperature in the blocked channel for a liner made of a Copyright O Tara Tech
114. t the finite difference model presented here is only limited to rectangular cooling channels Thermal conductivities in this model are taken as functions of temperatures Conductivities of twelve commonly used materials in regeneratively cooled rocket are built into RTE These thermal conductivities can take an input code number of 1 through 12 The material code for coating channel area and close up are defined by MTCOAT MTCH and MTCLO in the namelist of RTE Figure 8 shows RTE s built in thermal conductivities as functions of temperature User defined materials can be introduced by setting material code 1 2 or 3 a user can defined up to three material conductivities If any of these negative codes are assigned to any layer the corresponding conductivities must be entered as a function of temperature via a separate namelist CONDDATA A complete description of the SCONDDATA namelist is presented in the RTE s input file section 1000 Copper Nickel NARLOYZ Columbium 100 _ LuALLLLULLSALL ALALLALIA LA LI Amzirc 88347 Zirconia Platinum GLIDCOP INCONEL718 NICRALY Conductivity E 4 Btu sec ft R 0 500 1000 1500 2000 2500 Temperature R Figure 8 Built in conductivities in RTE Radiation Heat Transfer Model The radiative heat flux 4 in the nozzle surface energy balance equations consists of
115. termined via a three dimensional finite difference scheme In this method finite difference grids are superimposed throughout the wall at different stations The temperature of each node is then written in terms of temperatures of neighboring nodes the four closest nodes at the same station and two nodes at the neighboring stations The program marches axially from one station to another At each station the Gauss Siedel iterative method is used to obtain convergence for the temperature distribution along the radial and circumferential directions When the axial march is completed comparison is made between the results of the present march and that of the previous one to see if the convergence criteria in the axial direction have been met If it is not met the code starts again at the first station and makes another march along the cooling channels The process continues until convergence is achieved A detailed description of this numerical model is outlined below Geometric Data and Hot Gas Side Equilibrium Properties First the area ratio for each station and the distance between neighboring stations are calculated via the following equations 1 Copyright O Tara Technologies LLC 12 and d D ids ey Rz xX DNE 2 Then the static pressures temperatures enthalpies and Mach numbers for the combustion gases are evaluated using the ROCKET subroutine from 1 It should be noted that these properties are in
116. tion is three dimensional finite difference sguation The Gauss Siedel iteration however is only performed for the nodes on the n station and T ijn and T are kept constant during this iteration The value of T ded from the previous march The conductivity in equation 53 is a function of temperature k k T Similar equations are derived for other nodes boundary nodes and nodes at the interface between two different materials and are being used in the program It should be noted that at the boundary nodes depending on the boundary conditions convective and radiative terms also appear in the nodal balance of energy equation For example for a node at the inner surface of the nozzle the finite difference equation is given by in equation 53 is from the recent march and T Ta oL nl Ro IR 4 544 2 ijn T 1 R 1 R 1 R 1 R 1 R VR R T i j n l R T i j n l 54 where _ 2rA o 1 1 1 1 1 1 1 O i l j n IUD 1 1 1 1 Sur o Kija Kia Copyright O Tara Technologies LLC 29 _ 2 1 R 1 n ntl 1 1 1 1 Ar As Aspa ki i j n i l jon 2 Roz h rAd Ase Agr AS 1 1 Me i j n ASi R 2 z 2 i j n l i jn i j n l et aL ERE in 2 Ar Ar Ar Ar t dd l6 dud A
117. two sharp edge corners is given by 0 0875 0 1125 Ar O aset 1 2 52 The NMELIST variable of for the edge effect is IEDGE Equation 51 is used when IEDGE 2 and equation 52 when IEDGE 1 When IEDGE is 0 or any other number no edge effect correction will be implemented Wall Temperature Distribution Once the heat transfer coefficients and adiabatic wall temperatures for the hot gas and coolant are evaluated a finite difference model is used to re evaluate the wall temperature distribution This model has been specifically developed for three dimensional conduction in a rocket thrust chamber and nozzle as shown in Figure 1 Because of the symmetry of the configuration computations are performed for only one cell see Figure 6 Since no heat is transferred to the two sides of the cell they are assumed insulated A finite difference grid is superimposed on the aforementioned cell as shown in Figure 7 In this program the number of nodes in the radial direction for different layers and in the circumferential direction for the land and channel area must be specified Thus the grid size can vary from one layer to another Each node is connected to four neighboring nodes at the same station It also exchanges heat with its counterpoints at two neighboring stations 1 e stations n 1 and 1 The finite difference equation for a node located in the middle of a material is given by Copyright O Tara Technologies LLC 2
118. uggested value for ERROR is 10 and if the axial conduction is not significant thin wall low pressure engine then the axial conduction is negligible and ERRAX should be set to any number greater than 1 When ERRAX 1 the program makes axial marches iterations and it includes the axial heat conduction in the analysis A reasonable value for ERRAX is 10 Very small values of ERRAX cause excessive numbers of axial marches and in some cases the coolant properties calculated via GASP or WASP subroutines fluctuate about the correct answer without reaching convergence Smaller values of convergence criteria will substantially increase computational time without significantly improving the accuracy of the results To avoid excessive number of iterations the user can specify limits for the number of iterations These limits are MAXITER for maximum number of iterations at each station and MAXPASS for maximum number of axial passes axial marches Listings of the original subroutines BONNIE and GASP are given in references 1 and 2 Major modifications were made to the aforementioned subroutines to conjugate them with the conduction convection and radiation modules of RTE For certain types of fuels e g hydrocarbon fuels radiation from hot gas is significant and the user may include this mode of heat transfer in the thermal analysis by setting IGASRAD 1 in the input file The major part of radiation calculation is the evaluation of total exc
119. ure R exponent of viscosity ratio in equation 39 needed for user defined coolant correlation IT YPE 0 coolant weight flow Ib sec total weight flow of oxidant and fuel Ib sec axial distance from the throat in tive for diverging part tive for converging part 0 for the throat NOMENCLATURE FOR amp CONDDATA NAMELIST conductivities are needed Btu s ft R K2 conductivities are needed Btu s ft R K3 conductivities of material three material code of 3 in amp RTEDATA NP3 conductivities are needed Btu s ft R NP1 number of conductivity points for material one NP2 number of conductivity points for material two NP3 number of conductivity points for material three temperatures for material one R T2 temperatures for material two R T3 temperatures for material three R REACTANT FORMAT conductivities of material one material code of 1 in amp RTEDATA NP1 conductivities of material two material code of 2 in amp RTEDATA 2 This part of the input data provides information on the chemical composition of the propellant The following table provides the name and input format of commonly used propellants in liquid propulsion systems 1 Component Chemical formula Percent Assigned Phase Temp K Fuel F Density columns 1 to 45 46 52 enthalpy L liquid 64 71 Oxid O g cm3 cal mol G Gas 72 73 80 54 62 63 Air N 1 561760 41959 AR 009324 100 28 2 G 2
120. ution is inserted into the RTE inputs This time since the hot gas side heat fluxes are known RTE bypasses all hot gas side calculations e g subroutine BONNIE and hot gas side heat transfer coefficient correlations and calculates the wall temperature distribution The new wall temperature distribution along the axial direction is then input to TDK and a new heat flux distribution is calculated This iterative procedure continues until convergence is reached To automate this iterative process a shell program has been developed This program is a C shell program for the UNIX operating system rte com and a Compaq Visual Fortran System program for MS Windows operating systems RTECOM exe A listing of this program is given in Appendix C The shell program can be executed by typing its name followed by four arguments RTE input data TDK input data RTE output and TDK output filenames Both input data files 1 and TDK input files must end with the word FINISH Note that the user can run TDK with either BLM Boundary Layer Module or MABL Mass Addition Boundary Layer Typical input files for both cases are given in Appendix B Note that in place of a temperature distribution in the TDK input the word BLM or MABL must be inserted depending on the boundary layer option in the TDK input For details of TDK inputs reference should be made to the TDK user manual 6 The shell program first cleans up files from the previous run a

RTE, Rocket Thermal Evaluation

Contents

Download Pdf Manuals

Related Search

Related Contents