# Mathematical Numerical Simulation of Fire Vortices

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

Release:

2017, Vol. 3. №2

Title:
Mathematical Numerical Simulation of Fire Vortices

Authors:

For citation: Barannikova D. D., Obukhov A. G. 2017. “Mathematical Numerical Simulation of Fire Vortices”. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, vol. 3, no 2, pp. 60-71. DOI: 10.21684/2411-7978-2017-3-2-60-71

Darya D. Barannikova, Senior Lecturer, Department of Algebra and Mathematical Logic, Tyumen State University; d.d.barannikova@utmn.ru

Alexandr G. Obukhov, Dr. Sci. (Phys.-Math), Professor, Department of Business Informatics and Mathematics, Industrial University of Tyumen; eLibrary AuthorID, agobukhov@inbox.ru

Abstract:

This article considers mathematical numerical simulation of a swirling flow of air around a smoothly heated vertical cylindrical region under the action of gravity and Coriolis. The mathematical model is the complete system of nonlinear differential Navier-Stokes equations. It is a differential form of the basic laws of conserving momentum, mass, and energy. In addition, the authors take into account the basic laws of thermodynamics and the dissipative properties of the viscosity and thermal conductivity of a compressible viscous polytropic gas. The complete system of Navier-Stokes differential equations is solved numerically and the constancy of the viscosity coefficients and the thermal conductivity coefficient is taken into account. The initial conditions are functions that describe the gas at rest in the gravitational field. These functions represent an exact solution of the above system of differential equations. All gas-dynamical parameters — density, temperature, pressure, and three components of the velocity of gas particles are calculated for different time instants in the initial stage of air flow formation. Instantaneous streamlines corresponding to the particle trajectories in the emerging flow are constructed. A negative direction of the twisting of the air flow, which occurs when the vertical cylindrical region is heated, is established.

Keywords:

References:

1. Bautin S. P., Krutova I. Yu. 2012. “Zakrutka gaza pri plavnom stoke v usloviyakh deystviya sil tyazhesti i Koriolisa” [The Swirling of Gas in a Smooth Flow under the Conditions of Gravity and Coriolis Forces]. Thermophysics of High Temperatures, vol. 50, no 3, pp. 473-475.
2. Bautin S. P., Krutova I. Yu., Obukhov A. G. 2015. “Zakrutka ognennogo vikhrya pri uchete sil tyazhesti i Koriolisa” [The Twisting of a Fiery Vortex When Gravity and Coriolis are Taken into Account]. Thermal Physics of High Temperatures, vol. 53, no 6, pp. 961-964. DOI: 10.7868/S0040364415050038
3. Bautin S. P., Obukhov A. G. 2012. Matematicheskoe modelirovanie razrushitel'nykh atmosfernykh vikhrey [Mathematical Modeling of Destructive Atmospheric Vortices]. Novosibirsk: Nauka.
4. Bautin S. P., Obukhov A. G. 2013. “Ob odnom vide kraevykh usloviy pri raschete trekhmernykh nestatsionarnykh techeniy szhimaemogo vyazkogo teploprovodnogo gaza” [On a Form of Boundary Conditions in the Calculation of Three-Dimensional Unsteady Flows of a Compressible Viscous Heat-Conducting Gas]. Izvestiya Vuzov. Oil and gas, no 5, pp. 55-63.
5. Bautin S. P., Obukhov A. G. 2013. “Odno tochnoe statsionarnoe reshenie sistemy uravneniy gazovoy dinamiki” [One Exact Stationary Solution of the System of Equations of Gas Dynamics]. Izvestiya Vuzov. Oil and gas, no 4, pp. 81-86.
6. Bautin S. P., Deryabin S. L., Krutova I. Yu., Obukhov A. G. 2017. Razrushitel'nye atmosfernye vikhri i vrashchenie Zemli vokrug svoey osi [Destructive Atmospheric Vortices and the Rotation of the Earth Around Its Axis]. Yekaterinburg: USURT.
7. Bautin S. P. 2008. Tornado i sila Koriolisa [Tornado and the Coriolis Force]. Novosibirsk: Nauka.
8. Varaksin A. Yu., Romash M. E., Kopeytsev V. N., Gorbachev M. A. 2014. “O vozmozhnoy generatsii ognennykh vikhrey bez ispol'zovaniya prinuditel'noy zakrutki” [On the Possible Generation of Fiery Vortices without the Use of Forced Twist]. Reports of the Academy of Sciences, vol. 456, no 2, pp. 159-161. DOI: 10.7868/S0869565214140102
9. Varaksin A. Yu., Romash M. E., Kopeytsev V. N. 2011. Tornado [Tornado]. Moscow: Fizmatlit.
10. Nalivkin D. V. 1984. Smerchi [Tornadoes]. Moscow: Nauka.
11. Nalivkin D. V. 1969. Uragany, buri i smerchi. Geograficheskie osobennosti i geologicheskaya deyatel'nost' [Hurricanes, Storms and Tornadoes. Geographical Features and Geological Activity]. Leningrad: Nauka.
12. Obukhov A. G., Barannikova D. D. 2014. “Osobennosti techeniya gaza v nachal'noy stadii formirovaniya teplovogo voskhodyashchego zakruchennogo potoka” [Peculiarities of Gas Flow in the Initial Stage of the Formation of a Thermal Ascending Swirling Flow]. Izvestiya Vuzov. Oil and gas, no 6, pp. 65-70.
﻿