The Generalized Tensor Model for Numerical Investigation of Combustion and Flow Processes in Liquid Rocket Engine Chamber



Liquid Rocket Engine, Combustion and Flow Processes, Generalized Tensor Model


Combustion and flow thermogasdynamics is one of the most sophisticated computational stages in liquid rocket engine (LRE) design. A considerable amount of different methodologies used to conduct the thermogasdynamic analysis of the combustion and flow process and obtain the accurate estimates of the parameters of the LRE chamber is known, currently, in rocket and space sciences. However, the development of a generalized mathematical model that would have a capability of being applied for any unique combustion case by, hence, yielding reliable results and, nevertheless, be efficient in any application still remains to be an issue. The following paper considers the development of a generalized tensor model the application of which for any desired propellant configuration yields unique results. In addition considered the application of the mentioned model at significant nozzle sections. Moreover the current paper, also, considers an approach based on the specific area in order to compute the parameters at the nozzle throat. The uniqness of this approach is based on the fact, that the outcoming results appear to be more accurate than the ones obtained using convential approaches. The paper accurately summarizes the application of the generalized tensor model based on an example problem which involves the combustion of liquid methane with liquid oxygen.


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Author Biography

Parviz Shahmurad Abdullayev

Parviz Shahmurad Abdullayev (1967). In 1984 he entered to the Leningrad Mechanics Institute (Baltic State Technical University, Saint Petersburg, Russia) and in 1990 he completed the institute in Flight Vehicles Engines (Liquid Rocket Engines) field. In 2003, he was appointed as the Head of the Flight Vehicles and Aviation Engines Department of the National Aviation Academy and has been working at this job until now. He defended the Ph.D. thesis (2001) at the Saint Petersburg Civil Aviation Academy (Russia) and the D.Sc. thesis (2014) at the National Aviation Academy. Author of 94 scientific papers and theses, 3 patents and 5 books. His current research interest include mathematical modeling of aircraft and rocket engines (aviation gas turbine engines, liquid propellant rocket engines), thermo-gas-dynamics of jet engines, diagnostics with soft computing and machine learning


[1] V.Ye. Alemasov, A.F. Dregalin, and A.P. Tishin, Theory of Rocket Engines. A Textbook for High Schools, Ed. V.P. Glushko., Moscow, Mashino-stroeniye, 1989.
[2] V.Ye. Alemasov, A.F. Dregalin, A.P. Tishin, V.A. Khudyakov, and V. N. Kostin. Thermodynamic and thermophysical properties of combustion products. A guide in 10 volumes. Under the scientific. by the hand of V.P. Glushko, USSR Academy of Sciences, Moscow, VINITI, Volume 1., 1971-1976.
[3] L.V. Gurvich, I.V. Veits, V.A. Medvedev, G.A. Bergman, V.S. Yungman, G.A. Khachkuruzov, V.S. Iorish, O.V. Dorofeeva, E.L. Osina, P.I. Tolmach, I.N. Przheval’skii, I.I. Nazarenko, N.M. Aristova, E.A. Shenyavskaya, L.N. Gorokhov, A.L. Rogatskii, M.E. Efimov, V.Ya. Leonidov, Yu.G. Khait, A.G. Efimova, S. E.Tomberg, A.V. Gusarov, N.E. Khandamirova, G.N. Yurkov, L.R. Fokin, L.F. Kuratova, and V.G. Ryabova. Thermodynamic Properties of Individual Substances. in 4 volumes, Eds. V.P. Glushko et al., A guide in 4 volumes, Nauka, M. 1978-1982.
[4] A.A. Dorofeev, Fundamentals of Thermal Rocket Engines Theory - Theory, Calculation and Design, 3rd edition, A Textbook for High Schools, Moscow, MSTU named after E.E. Bauman, 2014.
[5] G. P. Sutton, and O. Biblarz, Rocket Propulsion Elements, 9th ed., Wiley, 2016.
[6] V. Chan, and L. Alborzfar, Principles of Chemical Equilibrium. Available: https://chem.libretexts. org, [Accessed: June 5, 2019].
[7] S.C. Chapra, and R.P. Canale, Numerical Methods for Engineers. 7th ed., New York: McGraw Hill Education, 2015.
[8] P.R. Young, Molar Stoichiometry in Chemical Equations. Available:, [Accessed: June 5, 2019].
[9] A.A. Gurtovoi, S.I. Batishev, Y.V. Demianenko, and A.M. Sushkov, Mathematical modeling. Thermodynamic Computation of Combustion and Flow Processes. Voronezh, 2015. (in russian).
[10] Yu.A. Bulygin, A.V. Kretinin, V.S. Rachuk, and S.V. Faleev, Calculation of the thermal state of the liquid propellant rocket engine, A Textbook for High Schools, Editor V.P. Kozelkov, VSTU, Voronej, 1997.
[11] A.A. Gurtovoy, A.V. Ivanov, G.I. Skomorokhov, and D.P Shmatov. Calculation and design of LPRE aggregates, A Textbook for High Schools, Voronezh, VSTU, 2016.
[12] J.M. Bonnie, J.Z. Michael, and G. Sanford Coefficients for Calculating Thermodynamic Properties of Individual Species. Glenn Research Center, NASA TP-2002-211556, NASA Glenn Cleveland, Ohio, USA. 2002.
[13] S. Gordon, and B. McBride, Computer Program for Complex Chemical Equilibrium Compositions and Applications, Part 1. Analysis, NASA RP 1311, 1994.
[14] B.J. Cantwell Aircraft and Rocket Propulsion, AA283 course, Stanford University, Stanford, California, Available: Material/, [Accessed: March 25, 2019].
[15] S. Gordon, and B.J. McBride, Computer Program for Calculation of Complex Chemical Equilibrium Compositions, Rocket Performance, Incident and Reflected Shocks, and Chapman-Jouguet Detonations, NASA SP-273, NASA (Spec. Publ.), Interim Revision, March, 1976.
[16] A.P. Vasiliev, V.M. Kudryavtsev, V.A. Kuznetsov, V.D. Kurpatenkov, A.M. Obelnitsky, V.M. Polyaev, and B.Y. Poluyan, Fundamentals of the theory and calculation of liquid rocket engines. Textbook. Edited by V.M. Kudryavtsev. Moscow, High School, 3rd edition, 1983.
[17] G.V. Belov, and B.G. Trusov, Thermodynamic modeling of chemically reacting systems. Moscow, Publ. MSTU named after E.E. Bauman, 2013.
[18] N.A. Brykov, K.N. Volkov, V.N. Emelyanov, and, I.V. Teterina, Flows of Ideal and Real Gases in Channels of Variable Cross Section with Unsteady Localized Energy Supply. Journal of Computational methods and programming, T.18, N1, Available:, [Accessed: February 25, 2021].
[19] M.R. Colonno, E. Van der Weide, and J.J. Alonso, “The Optimum Vacuum Nozzle: an MDO Approach”, Proc. of the 46th AIAA Aerospace Sciences Meeting and Exhibit, AIAA 2008-911, Reno, Nevada, 7-10 January 2008.
[20] L. Fu, S. Zhang, and, Y. Zheng, Design and Verification of Minimum Length Nozzles with Specific/Variable Heat Ratio Based on Method of Characteristics, International Journal of Computational Methods, V.13, N.06, 2016. [Online]. Available: 10.1142/S0219876216500341/, [Accessed: February 25, 2021].
[21] J. Kestin, Influence of Variable Specific Heats on the High-speed Flow of Air, A.R.C. Technical Report, C.P. No.33 (13.176), London his majesty’s stationery office, Polish University College, 1950.
[22] T. Zebbiche, Stagnation temperature effect on the supersonic axisymmetric minimum length nozzle design with application for air, Adv. Space Res. 48 (10), 2011, p.1656–1675.
[23] J.J. Anderson, Modern Compressible Flow: With Historical Perspective. New York: McGraw-Hill Book Company, 1982. pp.260-305.
[24] P. Abdullayev and N. Abdulla, “The LRE Design System Using a New Thermo-Gas-Dynamic Calculation Method”. Journal of Aeronautics and Space Technologies. Vol.12, No 2, p.171-183, July 2019.
[25] P.Sh. Abdullayev and N.P. Abdulla, “To the question of the thermodynamic design of the LRE chamber”, Journal of Aerospace technic and technology, National Aerospace University «Kharkiv Aviation Institute», Ukraine, Kharkiv, No 8 (160), p.28-38, August 2019.
[26] M.V. Silyutin, Developing an electronic reference book on thermogasodynamic properties of rocket engine fuel combustion products taking into account non-ideal character of the working process, Vestnik of the Samara State Aerospace University named after Academician S.P. Korolev, (2), p.14-23, 2009 [Online]. Available: /vestnik/article/view/653/653, [Accessed: November 30, 2021].
[27] I.A. Klepikov, Choice of energetic and mass characteristics of main rocket engines fueled by liquefied natural gas, Habilitation Dissertation, NPO Energomash, Moscow, 2005.
[28] A.I. Kuzin, V.S. Rachuk, A.S. Koroteev, B.I. Katorgin, I.A. Smirnov, V.V. Vakhnichenko, S.N. Lozin, P.A. Lekhov, A.I. Semenov, A.V. Ievlev, A.F. Efimochkin, I.A. Klepikov, A.A. Likhvantsev, V.I. Petrov, A.M. Romashkin, Yu.G. Gusev, A.G. Yakovlev, “Substantiation of rocket fuel components choice for propulsion units of the reusable space-rocket system's first stage”, Aviakosmicheskaya tekhnika i tekhnologiya Journal, N.1, p.19-55, April 2010.




How to Cite

N. Abdulla and P. S. Abdullayev, “The Generalized Tensor Model for Numerical Investigation of Combustion and Flow Processes in Liquid Rocket Engine Chamber”, JAST, vol. 16, no. 1, pp. 15–40, Jan. 2023.