Twist around heating gas cylinder taking into account the forces of gravity and coriolis

Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy


Release:

2015, Vol. 1. №1(1)

Title: 
Twist around heating gas cylinder taking into account the forces of gravity and coriolis


About the authors:

Sergei P. Bautin, Dr. Sci. (Phys.-Math.), Professor, Department of Higher and Applied Mathematics, Snezhinsk Physic Institute of the National Research Nuclear University MEPhI; sbautin@usurt.ru

Irina Yu. Krutova, Cand. Sci. (Phys.-Math.), Head of the Department of Higher and Applied Mathematics, Snezhinsk Physic Institute of the National Research Nuclear University MEPhI; iykrutova@mephi.ru

Abstract:

The paper studies a system of equations of gas dynamics under the action of gravity and Coriolis for ideal polytropic gas. A special characteristic Cauchy problem has been put; the solution of the problem describes the motion of air in a gravitational field with continuous heating of a vertical cylinder located in it. It is proved that under the condition of analyticity of input data, the problem has the only analytical solution presented as a convergent series. The analysis of the first coefficients of the series showed that as the cylinder is heated, there appears circumferential motion of gas in the air twisted in the negative direction in the Northern Hemisphere, and in the positive direction in the Southern Hemisphere. The established facts are mathematical justification for fire vortex twist direction.

References:

1. Bautin, S.P. Tornado and Coriolis force. Novosibirsk, 2008. 96 p. (in Russian).

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

3. Bautin, S.P., Krutova, I.Yu., Obukhov, A.G., Bautin, K.V. Destructive atmospheric vortices: theorems, calculations, experiments. Novosibirsk, 2013. 216 p. (in Russian).

4. Bautin, S.P. Characteristic Cauchy problem and its applications in gas dynamics. Novosibirsk, 2009. 368 p. (in Russian).

5. Bautin, S.P., Krutova, I.Yu. A problem about a smooth flow with the variables r, t as a standard Cauchy problem // UrGUPS Bulletin. 2011. Vol. 1(10). Pp. 4–13. (in Russian).

6. Bautin, S.P., Krutova, I.Yu. A problem about a smooth gas flow with the variables t, r, φ, χ taking into account gravity and Coriolis // Issues of applied mathematics and mechanics. 2011. Vol. 95(178). Pp. 17–43. (in Russian).

7. Bautin, S.P., Krutova, I.Yu. Twisting of smooth gas under the action of gravity and Coriolis forces // Thermophysics of High Temperatures. 2012. Vol. 20. № 3. Pp. 473–475. (in Russian).

8. Bautin, S.P., Krutova, I.Yu. Twisting of smooth gas flow under the action of gravity and Coriolis Forces // High Temperature. 2012. Vol. 50, № 3. Pp. 444-446.

9. Bautin, S.P. Cauchy characteristic problem for quasi-linear analytic system // Differential Equations. 1976. Vol. 12. № 11. Pp. 2052–2063. (in Russian).

10. Varaksin, A.Yu., Romash, M.E., Kopeitsev, V.N., Taekin S.I. On physical modelling of air votices in laboratory conditions // Thermophysics of High Temperatures. 2008. Vol. 46. № 6. Pp. 957–960. (in Russian).

11. Varaksin, A.Yu., Romash, M.E., Kopeitsev, V.N. Tornado-like gas-solid flow // The 6th Int. Symp. on Multiphase Flow, Heat Mass Transfer and Energy Conversion. AIP Conference Proc. 2010. Vol. 1207. Pp. 342–347.

12. Varaksin, A.Yu., Romash, M.E., Kopeitsev, V.N. Effect of Net Structures on Wall-Free Non-Stationary Air Heat Vortices // Int. J. Heat Mass Transfer. 2013. Vol. 64. Pp. 817–828.

13. Varaksin, A.Yu., Romash, M.E., Kopeitsev, V.N. On the issue of influencing air vortices behaviour // Thermophysics of High Temperatures. 2009. Vol. 47. № 6. Pp. 870–876. (in Russian).

14. Varaksin, A.Yu., Romash, M.E., Kopeitsev, V.N. On the possibility of visualizing air vortex modeling // Thermophysics of High Temperatures. 2010. Vol. 48. № 4. Pp. 617–622. (in Russian).

15. Varaksin, A.Yu., Romash, M.E., Kopeitsev, V.N., Gorbachev, M.A. Physical modeling of air vortices: nondimensional parameters // Thermophysics of High Temperatures. 2011. Vol. 49. № 2. Pp. 317–320. (in Russian).

16. Varaksin, A.Yu., Protasov, M.V. Teplitskiy, Yu.S. On the choice of particle parameters for visualizing and diagnostics of free concentrated air vortices // Thermophysics of High Temperatures. 2014. Vol. 52. № 4. Pp. 581–587. (in Russian).

17. Varaksin, A.Yu. Particle clustering in turbulent and vortex-type two-phase flows // Thermophysics of High Temperatures. 2014. Vol. 52. № 5. Pp. 777–796. (in Russian).

18. Bautin, K.V., Bautin, S.P., Makarov, V.N. Empirical verification of a possibility to create an airflow twisted under the action of Coriolis forces // UrGUPS Bulletin. 2013. № 2(18). Pp. 27–33. (in Russian).

19. Nalivkin, D.V. Hurricanes, storms and vortices. Geographic characteristics and geological activity. Leningrad, 1969. 487 p. (in Russian).

20. Nalivkin, D.V. Vortices. Moscow, 1984. 112 p. (in Russian).

21. Varaksin, A.Yu., Romash, M.E., Kopeitsev, V.N., Gorbachev, M.A. On a possibility of fire vortex generation without the application of forced swirling // Proceedings of the Academy of Sciences. 2014. Vol. 456. № 2. Pp. 159–161. (in Russian).

22. Obukhov, A.G., Barannikova, D.D. Gas flow parameters on the initial stage of twisted upward heat flow formation // Proceedings of Higher Educational Institutions. Oil and Gas. 2014. № 6. Pp. 65–70. (in Russian).

23. Bautin, S.P., Obkhov, A.G. One explicit stationary solution of the system of equations of gas dynamics // Proceedings of Higher Educational Institutions. Oil and Gas. 2013. № 4. Pp. 81–86. (in Russian).

24. Ovsyannikov, L.V. Lectures on fundamentals of gas dynamics. Moscow; Izhevsk, 2003. 336 p. (in Russian).