Internal Flow of a Rocket Engine Nozzle Calculated Through One-Dimensional Equilibrium
Keywords:
Chemical equilibrium, Rocket engine design, Internal flow, Rocket nozzles, Transport propertiesAbstract
Modeling of the internal flow of a nozzle is a vital step in the design of a rocket engine. This study focuses on providing an in-depth examination of a thermochemical rocket engine’s operation through chemical equilibrium. The computation extends to cover both gaseous and condensed species, as well as phase transitions, offering a comprehensive understanding of the engine’s behavior. Notably, this research introduces the ability to freeze the composition at any chosen point within the nozzle, allowing for tailored modeling to specific engine conditions and enhancing its versatility as a tool for analysis and design. Moreover, the study takes an additional step by calculating the transport properties along the nozzle. Special note is made of the difference between equilibrium and frozen variables. By integrating equilibrium composition, condensed species, and transport properties, this research exemplifies a holistic approach to analyzing and optimizing the performance of thermochemical rocket engines, with several illustrative examples showcasing the capabilities of the program.
References
Al Kady MA (2013) Numerical simulation of nozzle flow with chemical equilibrium. ARPN J Eng Appl Sci 8(5). https://www.researchgate.net/publication/256731890_Numerical_Simulation_of_Nozzle_Flow_with_Chemical_Equilibrium
Bac J, Bagheera PA (1984) Ballistic thermodynamic code. Paper presented 3rd International Gun Propellant Symposium. Picatinny Arsenal; Dover, USA.
Belov GV (1998) Thermodynamic analysis of combustion products at high temperature and pressure. Propell Explos Pyrotech 23(2):86-89. https://doi.org/10.1002/(SICI)1521-4087(199804)23:2<86::AID-PREP86>3.0.CO;2-2
Brinkley SR (1947) Calculation of the equilibrium composition of systems of many constituents. J Chem Phys 15(2):107-110. https://doi.org/10.1063/1.1746420
Brown ED (1995) An introduction to PROPEP, a Propellant Evaluation Program for personal computers. J Pyrotech (1):11-18. https://www.jpyro.co.uk/wp-content/uploads/j01_11_htfsr.pdf
Browne HN, Williams MM, Cruise DR (1960) The theoretical computation of equilibrium compositions, thermodynamic properties and performance characteristics of propellant systems. NAVWEPS Report 7043, TP 2434. China Lake; Naval Ordnance Test Station.
Burkhardt H, Sippel M (2004) Kerosene vs methane: a propellant tradeoff for reusable liquid booster stages. J Spacecr Rockets 41(5). https://doi.org/10.2514/1.2672
Cooper D (2016) ProPep3. [accessed Jul 30 2025]. http://www.rimworld.com/loggerusb/propep3/intro.html
Cowperthwaite M, Zwisler WH (1974) TIGER computer program documentation. Publication AD/A-002 791. Menlo Park: Stanford Research Institute. https://apps.dtic.mil/sti/pdfs/ADA002791.pdf
Cowperthwaite M, Zwisler WH (1982) Thermodynamics of nonideal heterogeneous systems and detonation products containing condensed Al2O3, Al, and C. J Phys Chem 86(5):813-817. https://doi.org/10.1021/j100394a044
Cox CF, Cooper D (1994) General solution procedure for flows in local chemical equilibrium. AIAA J 32(3). https://doi.org/10.2514/3.12016
Cruise DR (1964) Notes on the rapid computation of chemical equilibria. J Phys Chem 68(12):3797-3802. https://doi.org/10.1021/j100794a044
Cruise DR (1979) Theoretical computations of equilibrium compositions, thermodynamic properties, and performance characteristics of propellant systems. China Lake: Naval Weapons Center. https://apps.dtic.mil/sti/citations/ADA069832
Dobbs JL, Grubelich MC (2001) Instructions and changes to the NEWPEP thermochemical code. SAN2001-1074. Albuquerque: Sandia National Laboratories. https://doi.org/10.2172/782591
Filipović M, Kilibarda N (2000) Calculation of complex chemical equilibrium compositions of composite rocket propellants combustion products. J Serb Chem Soc 65(11):803-810. https://doi.org/10.2298/jsc0011803f
Filipović M, Kilibarda N (2001) The calculation of theoretical energetic performances of composite rocket propellants. J Serb Chem Soc 66(2):107-117. https://doi.org/10.2298/jsc0102107f
Freedman E (1973) BLAKE – A ballistic code based on TIGER. Paper presented International Symposium on Gun Propellants. Picatinny Arsenal; Dover, USA. https://apps.dtic.mil/sti/tr/pdf/ADA353385.pdf
Freedman E (1982) BLAKE – A thermodynamics code based on TIGER: users guide and manual. Report ARBRL-TR-02411. Aberdeen Proving Ground: U.S. Army Ballistic Research Laboratory. https://doi.org/10.21236/ADA121259
Freedman E (1998) BLAKE – A thermodynamics code based on TIGER: users guide to the revised program. Report ARLCR-422. Adelphi: Army Research Laboratory. https://doi.org/10.21236/ADA353385
Gordon S (1971) Calculation of theoretical equilibrium nozzle throat conditions when velocity of sound is discontinuous. AIAA J 9(1):179-182. https://doi.org/10.2514/3.6142
Gordon S, McBride BJ (1976) Computer program for calculation of complex chemical equilibrium compositions, rocket performance, incident and reflected shocks, and Chapman-Jouguet detonations. Interim Revision. NASA SP-273 https://ntrs.nasa.gov/api/citations/19780009781/downloads/19780009781.pdf
Gordon S, McBride BJ (1994) Computer program for calculation complex chemical equilibrium compositions and applications: I. Analysis. NASA RP-1311. https://ntrs.nasa.gov/api/citations/19950013764/downloads/19950013764.pdf
Gordon S, Zeleznik FJ (1962) Thermodynamic extrapolation of rocket performance parameters. ARS J 32(8):1195-1202. https://doi.org/10.2514/8.6243
Gordon S, Zeleznik FJ (1963) A general IBM 704 or 7090 computer program for computation of chemical equilibrium compositions, rocket performance, and Chapman-Jouguet detonations. Supplement I. Assigned area-ratio performance. NASA TN D-1737. https://ntrs.nasa.gov/api/citations/19630012282/downloads/19630012282.pdf
Gordon S, Zeleznik FJ, Huff VN (1959) A general method for automatic computation of equilibrium compositions and theoretical rocket performance of propellant. NASA TN-D-132. https://ntrs.nasa.gov/api/citations/19980223618/downloads/19980223618.pdf
Huff VN, Gordon S (1950) Tables of thermodynamic functions for analysis of aircraft-propulsion systems. NACA TN 2161. [accessed Jul 30 2025]. https://ntrs.nasa.gov/api/citations/19930083112/downloads/19930083112.pdf
Huff VN, Gordon S, Morrell VE (1951) General method and thermodynamic tables for computation of equilibrium composition and temperature of chemical reactions. NACA TR-1037. https://ntrs.nasa.gov/api/citations/19930091090/downloads/19930091090.pdf
Koch EC, Weiser V, Webb R (2011) Review on thermochemical codes. NATO MSIAC Report O-138, Brussels, Belgium. [accessed Jul 30 2025]. https://www.msiac.nato.int/publication/o-138-review-on thermochemical-codes/McBride BJ, Gordon S (1961) Thermodynamic functions of several triatomic molecules in the ideal El Word en Word ahora sí que yagas state. J Chem Phys 35(6):2198-2206. https://doi.org/10.1063/1.1732232
McBride BJ, Gordon S (1967) Fortran IV Program for calculation of thermodynamic data. NASA TN D 4097. [accessed Jul 30 2025]. https://ntrs.nasa.gov/api/citations/19670025863/downloads/19670025863.pdf
McBride BJ, Gordon S (1996) Computer program for calculation complex chemical equilibrium compositions and applications: II. Users manual and program description. NASA RP-1311. https://ntrs.nasa.gov/api/citations/19950013764/downloads/19950013764.pdf
McBride BJ, Gordon S, Reno MA (1993) Coefficients for calculating thermodynamic and transport properties of individual species. NASA TM-4513. https://ntrs.nasa.gov/api/citations/19940013151/downloads/19940013151.pdf
McBride BJ, Heimel S, Ehlers JG, Gordon S (1963) Thermodynamic properties to properties to 6000 30K for 210 substances involving the first 18 elements. NASA SP-3001. https://ntrs.nasa.gov/api/citations/19630013835/downloads/19630013835.pdf
Morgan MS, Silverman J, Webber WT (1956) The theoretical specific thrust of a rocket motor for the C-H N-0-F system. J Jet Propuls 26(10):874-877. https://doi.org/10.2514/8.7151
Morrell GV (1951) General method and thermodynamic tables for computation of equilibrium composition and temperature of chemical reactions. NACA TR-1037. https://ntrs.nasa.gov/api/citations/19930091090/downloads/19930091090.pdf
Noläng B (1983) Application of equilibrium computations to chemical vapour transport and related systems (EKVI code) (doctoral dissertation). Uppsala: Uppsala University
Schneider D, Génin C (2017) Numerical model for nozzle flow application under liquid oxygen/methane hot-flow conditions. AIAA J 34(1). https://doi.org/10.2514/1.B36611
Smith WR, Missen RW (1968) Calculating complex chemical equilibria by an improved reaction adjustment method. Can J Chem Eng 46(4):269-272. https://doi.org/10.1002/cjce. 5450460411
Tanaka K (1986) Detonation properties of high explosives calculated by revised Kihara-Hikita equation of state. Paper presented 8th Symposium (International) on Detonation. United States Office of Naval Research; Albuquerque, USA. https://cir.nii.ac.jp/crid/1570291224167737344
Terzic J, Zecevic B, Catovic A, Serdarevic-Kadic S (2011) Prediction of internal ballistic parameters of solid propellant rocket motors. Probl Mechatron Armament Aviat Saf Eng 2:7-26. https://bibliotekanauki.pl/articles/403510.pdf
Tizón Pulido JM, Jenaro de Mencos G (2018) Propulsio´n de misiles ta´cticos. Madrid: Garceta Grupo Editorial. https:// www.garceta.es/catalogo/libro.php?ISBN=978-84-1728-925-6
Van Hooser KP (2011) Space shuttle main engine – The relentless pursuit of improvement. AIAA J. https://doi.org/10.2514/6.2011-7159
Villars DS (1959) A method of successive approximations for computing combustion equilibria on a high speed digital computer. J Phys Chem 63(4):521-525. https://doi.org/10.1021/j150574a016
White WB, Johnson SM, Dantzig GB (1958) Chemical equilibrium in complex mixtures. J Chem Phys 28(5):751-755. https://doi.org/10.1063/1.1744264
Wieberson W, Zwisler W, Seely L, Brinkley S (1968) TIGER computer program documentation: I. Theoretical and mathematical formulations for the Tiger computer program. Report Z106. Menlo Park: Stanford Research Institute.
Wong F, Gottlieb J, Lussier L-S (2007) Chemical equilibrium mixture computations for energetic material combustion in closed vessels, Paper presented 4th Workshop on Pyrotechnic Combustion Mechanisms. International Pyrotechnics Society; Pfinztal, Germany. https://apps.dtic.mil/sti/pdfs/ADA432904.pdf
Zeleznik FJ, Gordon S (1960) An analytical investigation of three general methods of calculating chemical-equilibrium compositions. NASA TN-D-473. https://ntrs.nasa.gov/api/citations/19980228202/downloads/19980228202.pdf
Zeleznik FJ, Gordon S (1962a) A general IBM 704 or 7090 computer program for computation of chemical equilibrium compositions, rocket performance, and Chapman-Jouguet detonations. NASA TN-D-1454. https://ntrs.nasa.gov/api/citations/19620007372/downloads/19620007372.pdf
Zeleznik FJ, Gordon S (1962b) Calculation of detonation properties and effect of independent parameters on gaseous detonations. ARS J 32(4). https://doi.org/10.2514/8.6080
Zeleznik FJ, Gordon S (1968) Calculation of complex chemical equilibria. Ind Eng Chem 60(6):27-57. https://doi.org/10.1021/ie50702a006
Downloads
Published
Issue
Section
License
Copyright (c) 2025 Nicolás de Jong Cantariño, Juan Manuel Tizón Pulido
This work is licensed under a Creative Commons Attribution 4.0 International License.
This work is licensed under a Creative Commons — Attribution 4.0 International — CC BY 4.0. Authors are free to Share (copy and redistribute the material in any medium or format) and Adapt (remix, transform, and build upon the material for any purpose, even commercially). JATM allow the authors to retain publishing rights without restrictions.
