Computational investigation of temperature dependence of speed characteristics of non-stationary gas convection current

About the authors:

Elena M. Sorokina, Senior Lecturer, Affiliate of the Military Education-Research Center Forces «Combined Arms Academy of the Russian Federation Armed Forces» (Tyumen)
Alexandr G. Obukhov, Dr. Sci. (Phys.-Math), Professor, Department of Business Informatics and Mathematics, Industrial University of Tyumen; eLibrary AuthorID, agobukhov@inbox.ru

Abstract:

We consider the full Navier-Stokes equations describing the flow of a compressible viscous heat-conducting gas under gravity. The viscosity and thermal conductivity coefficients are taken to be constant. The functions that are exact analytical solutions of the complete system of Navier-Stokes equations are taken as initial conditions. Specific ratios are suggested as boundary conditions for some initial boundary value problems. The solutions of the complete system of Navier-Stokes equations are solved numerically using an explicit difference scheme in a rectangular parallelepiped. The calculation results of the temperature dependence of the convective flow speed of viscous compressible heat-conducting gas under gravity are presented. It is shown, that the maximum components of the gas flow speed in a convective flow are linearly dependent on the maximum heating temperature of a lower plane of the computational domain. Instantaneous streamlines of the convective flow are built. They essentially depend on the heating temperature.

References:

1. Bautin, S.P. Kharakteristicheskaia zadacha Koshi i ee prilozheniia v gazovoi dinamike [Characteristic Cauchy problem and its applications in gas dynamics]. Novosibirsk: Nauka, 2009. 368 p. (in Russian).

2. Bautin, S.P. Presentation of solutions to the Navier–Stokes equations in the neighborhood of the contact data. Prikladnaia matematika i mekhanika — Applied Mathematics and Mechanics. 1987. V. 51. № 4. Pp. 574-584. (in Russian).

3. Bautin, S.P, Obukhov, A.G. Matematicheskoe modelirovanie razrushitel'nykh atmosfernykh vikhrei [Mathematical modeling of destructive atmospheric vortices]. Novosibirsk: Nauka, 2012. 152 p. (in Russian).

4. Bautin, S.P., Obukhov, A.G. Mathematical modeling and numerical simulation of the flows in the bottom part of the tropical cyclone. Vestnik Tiumenskogo gosudarstvennogo universiteta — Tyumen State University Herald. 2012. № 4. Series «Physical and mathematical sciences. Computer Sciences». Pp. 175–183. (in Russian).

5. Obukhov, A.G. Mathematical modeling and numerical calculations of the currents in the bottom part of the tornado. Vestnik Tiumenskogo gosudarstvennogo universiteta — Tyumen State University Herald. 2012. № 4. Series «Physical and Mathematical Sciences. Computer Sciences». Pp. 183–189. (in Russian).

6. Bautin, S.P., Obukhov, A.G. Mathematical modeling of the bottom part of the ascendant swirling flow. Teplofizika vysokikh temperatur — Thermo Physics of High Temperatures. 2013. V. 51. № 4. Pp. 567-570. (in Russian).

7. Bautin, S.P., Krutova, I.Iu., Obukhov, A.G., Bautin, K.V. Razrushitel'nye atmosfernye vikhri: teoremy, raschety, eksperimenty [Destructive atmospheric vortices: Theorem, calculations, experiments]. Novosibirsk, 2013. 215 p. (in Russian).

8. Bautin, S.P. Tornado i sila Koriolisa [Tornado and the Coriolis force]. Novosibirsk:Nauka, 2008. 96 p. (in Russian).

9. Varaksin, A.Iu., Romash, M.E., Kopeitsev, V.N., Gorbachev, M.A. Thermal modeling of free vortex generation, stability, control. Teplofizika vysokikh temperatur — Thermo Physics of High Temperatures. 2010. V. 48. № 6. Pp. 965-972. (in Russian).

10. Varaksin, A.Iu., Romash, M.E., Kopeitsev, V.N., Gorbachev, M.A. Physical modeling of air tornadoes: some dimensionless parameters. Teplofizika vysokikh temperatur — Thermo Physics of High Temperatures. 2011. V. 49. № 2. Pp. 317-320. (in Russian).

11. Varaksin, A.Iu., Romash, M.E., Kopeitsev, V.N. Tornado [Tornado]. Moscow, 2011. 312 p. (in Russian).

12. Bautin, S.P., Obukhov, A.G. One exact stationary solution of the equations of gas dynamics. Izvestiia vuzov. Neft' i gaz — Proceedings of higher education institutions. Oil and gas. 2013. № 4. Pp. 81–86. (in Russian).

13. Bautin, S.P., Obukhov, A.G. A form of the boundary conditions in the calculation of three-dimensional unsteady compressible viscous heat-conducting gas. Izvestiia vuzov. Neft' i gaz — Proceedings of higher education institutions. Oil and gas. 2013. № 5. Pp. 55–63. (in Russian).

14. Obukhov, A.G., Sorokina, E.M. Mathematical modeling and numerical simulation of three-dimensional convective flow of gas. Izvestiia vuzov. Neft' i gaz — Proceedings of higher education institutions. Oil and gas. 2013. Pp. 57–63. (in Russian).

15. Obukhov, A.G., Abdubakova, L.V. Mathematical modeling of the Earth surface heating. Sb. m-lov VII Mezhdunar. nauch.-praktich. konf. «Fundamental'nye i prikladnye issledovaniia: problemy i rezul'taty» [Collected materials of the 7th Intern. sci. and pract. conf. Fundamental and applied research: problems and results]. Novosibirsk, 2013. Pp. 116-120. (in Russian).