Development of Tools for Thermodynamic Calculation of Rocket Engine Characteristics using the Julia Programming Language

Authors: Belov G.V. Published: 20.12.2021
Published in issue: #4(139)/2021  

DOI: 10.18698/0236-3941-2021-4-80-93

Category: Power Engineering | Chapter: Heat Engines  
Keywords: combustion products, rocket fuel, thermodynamic modeling

The experience in developing an algorithm and a program for the thermal-chemical calculation of the characteristics of a rocket engine is presented. The program is written in Julia. To calculate the equilibrium composition of combustion products the freely distributed library Ipopt is used. The program is interfaced to the database on thermodynamic properties of individual substances IVTANTERMO. For the convenience of processing, the information on thermodynamic properties is stored in two text files of a special form. The program has been developed using the simplest working process model according to which the flow is one-dimensional, the product flow is adiabatic, there are no friction losses, the product flow is equilibrium, and the speed of condensed particles is equal to the gas flow speed. Ratios for calculating the derivatives of composition, as well as equilibrium values of heat capacity and sound velocity are given. The text of the program can be used in the study process and can easily be adapted to more complex models of the rocket engine workflow. The calculation results obtained using the developed program are in good agreement with the results of TERRA calculations. The execution time of one calculation for a four-element fuel, which includes the determination of the combustion products characteristics in the chamber, the critical cross section and at the nozzle cross section, varies in the range of 3--5 s


[1] Ze’dovich Ya.B., Polyarnyy A.I. Raschety teplovykh protsessov pri vysokoy temperature [Calculation of thermal processes at high temperature]. Moscow, NII no. 1 Publ., 1947.

[2] Huff V.N., Morrell V.E. General method for computation of equilibrium composition and temperature of chemical reactions. NACA Technical report 2113. Washington, NACA, 1950.

[3] Huff V.N., Gordon S., Morrell V.E. General method and thermodynamic tables for computation of equilibrium composition and temperature of chemical reactions. NACA Technical report 1037. Washington, NACA, 1951.

[4] Donegan A.J., Farber M. Solution of thermochemical propellant calculations on a high-speed digital computer. J. Jet Propuls., 1956, vol. 26, no. 3, pp. 164--171. DOI: https://doi.org/10.2514/8.6950

[5] Villars D.S. A method of successive approximations for computing combustion equilibria on a high speed digital computer. J. Phys. Chem., 1959, vol. 63, no. 4, pp. 521--525. DOI: https://doi.org/10.1021/j150574a016

[6] Gordon S., Zeleznik F.J. A General IBM 704 or 7090 сomputer рrogram for computation of chemical equilibrium compositions, rocket performance, and Chapman --- Jouguet detonations. NACA Technical report D-1454. Washington, NAСA, 1962.

[7] Glushko V.P., ed. Termodinamicheskie i teplofizicheskie svoystva produktov sgoraniya. T. 1 [Thermodynamic and thermophysic properties of combustion products. Vol. 1]. Moscow, AN SSSR Publ., VINITI Publ., 1971.

[8] Sinyarev G.B. Universal’nyy metod resheniya sistemy uravneniy dlya opredeleniya ravnovesnogo sostava rabochego tela [Universal method of solving equation system for determination of equilibrium composition of a working body]. V: Nekotorye voprosy mekhaniki [In: Some issues of mechanics]. Moscow, Oborongiz Publ., 1962, pp. 80--106 (in Russ.).

[9] Sinyarev G.B., Slyn’ko L.E., Trusov B.G. Metod, universal’nyy algoritm i programma termodinamicheskogo rascheta mnogokomponentnykh geterogennykh sistem [Method, universal algorithm and program for thermodynamic computation of multicomponent heterogeneous systems]. Moscow, Bauman MHTU Publ., 1978.

[10] Sinyarev G.B., Vatolin N.A., Trusov B.G., et al. Primenenie EVM dlya termo-dinamicheskikh raschetov metallurgicheskikh protsessov [Using computer for thermodynamic calculations of metallurgic processes]. Moscow, Nauka Publ., 1982.

[11] Gordon S., McBride B.J. Computer program for calculation of complex chemical equilibrium compositions and applications. P. 1. Analysis. NACA Technical report archive 19950013764. Washington, NACA, 1994.

[12] Wachter A., Biegler L.T. On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math. Program., 2006, vol. 106, no. 1, pp. 25--57. DOI: https://doi.org/10.1007/s10107-004-0559-y

[13] Dunning I., Huchette J., Lubin M. JuMP: a modeling language for mathematical optimization. SIAM Rev., 2017, vol. 59, no. 2, pp. 295--320. DOI: https://doi.org/10.1137/15M1020575

[14] Belov G.V. Calculation of equilibrium composition of complex thermodynamic systems using Julia language and Ipopt library. Herald of the Bauman Moscow State Technical University, Series Instrument Engineering, 2021, no. 3 (136), pp. 24--45 (in Russ.). DOI: https://doi.org/10.18698/0236-3933-2021-3-24-45

[15] Belov G.V., Dyachkov S.A., Levashov P.R., et al. The IVTANTHERMO --- online database for thermodynamic properties of individual substances with web interface. J. Phys.: Conf. Ser., 2018, vol. 946, art. 012120. DOI: https://doi.org/10.1088/1742-6596/946/1/012120

[16] Belov G.V., Trusov B.G. Termodinamicheskoe modelirovanie khimicheski reagiruyushchikh system [Thermodynamic modelling of reacting chemical systems]. Moscow, Bauman MSTU Publ., 2013.