Release:

2015, Vol. 1. №1(1)Title:

Numerical simulation of gas convective flow thermodynamic parameters in the annular heating scheme under normal gravity conditions
Authors:
Elena M. Sorokina, Alexandr G. Obukhov

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 complete system of Navier–Stokes equations describing the flow of a compressible viscous heat-conducting gas under the influence of gravity. The coefficients of viscosity and thermal conductivity are assumed to be constant. The initial conditions are set by the functions that are accurate analytical solution of the complete Navier–Stokes equations. For the purposes of this research impermeability and thermal insulation are accepted as boundary conditions. Convective gas flow is initiated by an annular heating of the underlying surface. Solutions of the full Navier–Stokes equations are constructed numerically by an explicit difference scheme in a cube with an edge length of the unit. The article contains the results of calculations for density, temperature and pressure of the convective flow of viscous compressible heat-conducting gas under the influence of gravity. It is shown that the thermodynamic parameters have a complicated structure and essentially depend on the shape of heating, altitude and time of heating. Unsteady convective gas flow is more pronounced in the initial stage of its formation.Keywords:

References:

1. Bautin, S.P. Navier–Stokes equations solutions to in the neighborhood of the contact data // Applied Mathematics and Mechanics. 1987. Vol. 51. Issue 4. Pp. 574-584. (in Russian).

2. Bautin, S.P., Obukhov, A.G. Mathematical modeling of destructive atmospheric vortices. Novosibirsk: Nauka, 2012. 152 p. (in Russian).

3. Bautin, S.P. Obukhov, A.G. Mathematical modeling and numerical simulation of flows in the bottom part of tropical cyclones // Tyumen State University Herald. Physical and Mathematical Sciences. Computer Science. 2012. № 4. Pp. 175–183. (in Russian).

4. Obukhov, A.G. Mathematical modeling and numerical calculations of the currents in the tornado lower part // Tyumen State University Herald. Physical and Mathematical Sciences. Computer Science. 2012. № 4. Pp. 183–189. (in Russian).

5. Bautin, S.P., Obukhov, A.G. Mathematical modeling of the bottom part of the rising swirling flow // High Temperature. 2013. Vol. 51. № 4. Pp. 567-570. (in Russian).

6. Bautin, S.P., Krutova, I.Y., Obukhov, A.G., Bautin, K.V. Destructive atmospheric vortices: Theorem, calculations, experiments. Novosibirsk: Nauka; Ekaterinburg: USURT, 2013. 215 p. (in Russian).

7. Abdubakova, L.V., Obukhov, A.G. Numerical calculation of three-dimensional velocity characteristics of the rising and swirling flow of gas // Proceedings of Higher Educational Institutions. Oil and Gas. 2014. № 3. Pp. 88–94. (in Russian).

8. Obukhov, A.G., Abdubakova, L.V. The numerical calculation of the thermodynamic characteristics of the three-dimensional swirling and rising flow of gas // Tyumen State University Herald. Physical and Mathematical Sciences. Informatics. 2014. № 7. Pp. 157–165. (in Russian).

9. Abdubakova, L.V., Obukhov, A.G. The numerical calculation of the thermodynamic parameters of swirling gas flow initiated by blowing cold vertical // Proceedings of Higher Educational Institutions. Oil and Gas. 2014. № 5. Pp. 57–62. (in Russian).

10. Obukhov, A.G., Barannikova, D.D. Features of the gas flow at the initial stage of the rising and swirling heat flow // Proceedings of Higher Educational Institutions. Oil and Gas. 2014. № 6. Pp. 65–70. (in Russian).

11. Obukhov, A.G., Sorokina, E.M. Mathematical modeling and numerical simulation of three-dimensional convective flow of gas // Proceedings of Higher Educational Institutions. Oil and Gas. 2013. № 6. Pp. 57–63. (in Russian).

12. Sorokina, E.M., Obukhov, A.G. Numerical study of the temperature dependence of the speed characteristics of unsteady convective gas flow // Tyumen State University Herald. Physical and Mathematical Sciences. Informatics. 2014. № 7. Pp. 147–156. (in Russian).

13. Bautin, S.P. Characteristic Cauchy problem and its applications in gas dynamics. Novosibirsk: Nauka, 2009. 368 p. (in Russian).14. Bautin, S.P., Obukhov, A.G. One exact stationary solution of the equations of gas dynamics // Proceedings of Higher Educational Institutions. Oil and Gas. 2013. № 4. Pp. 81–86. (in Russian).

15. Bautin, S.P., Obukhov, A.G. A form of the boundary conditions in the calculation of three-dimensional unsteady compressible viscous heat-conducting gas // Proceedings of Higher Educational Institutions. Oil and Gas. 2013. № 5. Pp. 55–63. (in Russian).