Mathematical Numerical Simulation of Fire Vortices

About the authors:

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.

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