Numerical Method for Calculating Plane Flows of Viscous Gas in a Cylinder
https://doi.org/10.30932/1992-3252-2023-21-4-1
Abstract
To solve scientific, technological and environmental problems in the field of road transport, it is necessary to develop new mathematical models. At this stage of development of internal combustion engines and their parts, it is necessary to model complex hydrodynamic technologies. This necessities revealing different forms of liquid and gas flows with arbitrary initial and boundary conditions for the region under consideration.
The work is devoted to modelling a turbulent flow over a plate located in a cylinder. Reynolds-averaged Navier-Stokes equations were used as a mathematical model of the flow. Turbulent viscosity was calculated using the one-equation Spalart-Allmaras turbulence model. To solve the system of hydrodynamic equations, the finite difference method was used. A numerical method for calculating plane flows of viscous gas in a cylinder using turbulence models is presented. Suitable options were selected based on physical assumptions used to develop the models.
Recommendations have been developed on the possibility of using the considered turbulence models.
About the Authors
A. Kh. Zakirov
National University of Uzbekistan named after Mirzo Ulugbek
Uzbekistan
Uzbekistan
Zakirov, Asqar Kh., Ph.D. (Physics and Mathematics), Associate Professor at the Department of Mechanics and Mathematical
Modelling
Tashkent
F. Kh. Nazarov
National University of Uzbekistan named after Mirzo Ulugbek
Uzbekistan
Uzbekistan
Nazarov, Farrukh Kh., PhD (Physics and Mathematics), Senior Researcher at the Institute of Mechanics and Seismic Stability of
Structures, Senior Lecturer at the Department of Mechanics and Mathematical Modeling
Tashkent
References
1. Petrichenko, R. M. Physical basis of intra-cylinder processes in internal combustion engines [Fizicheskie osnovy vnutritsilindrovykh protsessov v dvigatelyakh vnutrennego sgoraniya]. Leningrad, Publ. house of Leningrad university, 1983, 244 p.
2. Mashkur Mahmud, A. Mathematical model of gas dynamics and heat transfer processes in the intake and exhaust systems of internal combustion engines. Ph.D. (Eng) thesis [Matematicheskaya model protsessov gazodinamiki i teploobmena vo vpusknoi i vypusknoi sistemakh DVS. Diss. kand. tekh. nauk]. St. Petersburg, SPbGPU publ., 2005, 189 p.
3. Khmelev, R. N. Study of the influence of gas-dynamic processes on functioning of internal combustion engines. Ph.D. (Eng) thesis [Issledovanie vliyaniya gazodinamichekikh protsessov na funktsionirovanie DVS. Diss. kand. tekh. nauk]. Tula, TSU publ., 2002, 144 p.
4. Yuan, C., Xu, J., Feng, H. In-cylinder heat transfer and gas motion of a free-piston diesel engine generator. Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, 2017, Vol. 231, Iss. 8, pp. 739–752. DOI: 10.1177/0957650917717627 [restricted access].
5. Sharoglazov, B. A., Farafontov, M. F., Klementiev, V. V. Internal combustion engines: theory, modelling and calculation of processes [Dvigateli vnutrennego sgoraniya: teoriya, modelirovanie i raschet protsessov]. Chelyabinsk, SUSU publ., 2005, 403 p. [Electronic resource]: https://lib.susu.ru/ftd?base=SUSU_METHOD&key=000305263&dtype=F&etype=.pdf. Last accessed 17.05.2023.
6. Strelets, M. Kh., Shur, M. L. Methods of scaling the compressibility in calculating stationary flows of a viscous gas at arbitrary Mach numbers. USSR Computational Mathematics and Mathematical Physics, 1988, Vol. 28, Iss. 2, pp. 254–266. DOI: https://doi.org/10.1016/0041-5553(88)90237-6.
7. Garbaruk, A. V., Strelets, M. Kh., Shur, M. L. Modelling turbulence in complex flow calculations [Modelirovanie turbulentnosti v raschetakh slozhnykh techenii]. St.Petersburg, Publ. house of Polytechnic University, 2012, 88 p. ISBN: 978–5–7422–3349–7.
8. Kavtaradze, R. Z., Onishchenko, D. O., Zelentsov, A. A., Kadyrov, S. M., Aripdzhanov, M. M. Computational and experimental study of influence of piston’s and sleeve’s thermal insulation on formation of nitrogen oxides in combustion products of high-speed diesel. Vestnik MGTU im. N. E. Baumana. Ser. «Mashinostroenie», 2011, Iss. 4 (85), pp. 83–102. [Electronic resource]: https://www.elibrary.ru/item.asp?id=17228197&ysclid=lnd7dt9l8p367078437. Last accessed 17.05.2023.
9. Sedov, L. I. Plane problems in hydrodynamics and aerodynamics [Ploskie zadachi gidrodinamiki i aerodinamiki]. Moscow, Nauka publ., 1980, 448 p.
10. Gurevich, M. I. The theory of ideal fluid jets [Teoriya strui idealnoi zhidkosti]. Moscow, Nauka publ., 1979, 536 p.
11. Khamidov, A. A. Plane and axisymmetric problems on jet flow of an ideal compressible fluid [Ploskie i osesimmetrichnie zadachi o struinom techenii idealnoi szhimaemoi zhidkosti]. Tashkent, Fan publ., 1978, 140 p.
12. Mazo, A. B. Modelling of turbulent incompressible fluid flows [Modelirovanie turbulentnykh techenii neszhimaemoi zhidkosti]. Kazan, KSU publ., 2007, 106 p. [Electronic resource]: https://www.researchgate.net/publication/320466159. Last accessed 17.05.2023.
13. Bruyatskiy, E. V., Kostin, A. G., Nikiforovich, E. I., Rozumnyuk, N. V. Method for numerical solution of Navier-Stokes equations in velocity–pressure variables. Prikladna gidromekhanika, 2008, Vol.10, Iss. 2, pp. 13–23.
14. Zakirov, A. Kh. Study of the flow of compressible gas with a free jet in a cylinder/ In: Proceedings of the International Conference «Modern problems of applied mathematics and mechanics: theory, experiment and practice». Novosibirsk, 2011. [Electronic resource]: http://conf.nsc.ru/files/conferences/niknik‑90/fulltext/40557/49562/Zakirov%20A.pdf. Last accessed 17.05.2023.
15. Zakirov, A. Kh. Numerical modelling of separated fluid flow in a cylinder. In: XXVI All-Russian Seminar with international participation on jet, separated and unsteady flows: Materials of reports. St. Petersburg, June 27–July 1, 2022. St. Petersburg, Baltic State Technical University, 2022, pp. 89–90. [Electronic resource]: https://elibrary.ru/item.asp?id=49818567&pff=1. Last accessed 17.05.2023.
16. Spalart, P. R., Allmaras, S. R. A One-Equation Turbulence Model for Aerodynamic Flows. AIAA 1992–439, 30th Aerospace Sciences Meeting and Exhibit. January 1992. Published online 17.08.2012. DOI: https://doi.org/10.2514/6.1992-439.
17. Patankar, S. V. Numerical Heat Transfer and Fluid Flow. Taylor and Francis, 1980. 214 p. ISBN: 9780070487406.
18. MacCormack, R. W. The Effect of Viscosity in Hypervelocity Impact Cratering. Journal of Spacecraft and Rockets, 2003, Vol. 40, Iss. 5, pp. 757–763. [Reprinted from AIAA paper 69–354, 1969]. Published online 23.05.2012. DOI: https://doi.org/10.2514/2.6901.
19. Tannehill, J. C., Anderson, D. A., Pletcher, R. H. Computational fluid mechanics and heat transfer. [Edition in Russian]. In 2 vol. Vol. 1. Transl. from English. Moscow, Mir publ., 1990, 382 p. ISBN: 5-03-001927-8
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For citations:
Zakirov A.Kh., Nazarov F.Kh. Numerical Method for Calculating Plane Flows of Viscous Gas in a Cylinder. World of Transport and Transportation. 2023;21(4):6-11. https://doi.org/10.30932/1992-3252-2023-21-4-1
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