Investigating the Dependence of the Energy Characteristics of the Ascending Swirling Air Flow on the Vertical Purge Velocity

About the authors:

Roman E. Volkov, Postgraduate Student, Department Algebra and Mathematical Logic, University of Tyumen; email@romanvolkov.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 paper, using numerical experiments, aims to establish the nature of the changes in the speed and energy characteristics of the swirling air flow that forms when it leaves the stationary mode, and with a sudden step-like decrease in the vertical blowing speed.

The authors use the complete system of Navier-Stokes equations to describe complex non-stationary three-dimensional flows of a compressible viscous heat-conducting gas. This system of nonlinear equations is a differential form of recording the basic laws of conservation of mass, momentum, and energy. In addition, it takes into account the laws of thermodynamics and the action of gravity and Coriolis.

In the case of constant values of the coefficients of viscosity and thermal conductivity, functions that determine the exact solution of the complete system of Navier-Stokes equations are taken as initial conditions for describing the corresponding flows of a compressible viscous heat-conducting gas.

For the density on all six faces of the calculated parallelepiped, the condition of continuity of the flow is stated. The boundary conditions for the components of the gas velocity vector correspond to the non-flow conditions for the normal component of the velocity vector, and the symmetry conditions for the other two components of the velocity vector. For the temperature on all six faces, the conditions for thermal insulation are specified.

The numerical solution of the complete system of Navier-Stokes equations made it possible to establish the nature of the change in the velocity and energy characteristics of the ascending swirling airflow initiated by a vertical blow through a pipe 5 meters in diameter when it leaves the stationary regime. The results of numerical simulation of a smooth transition to a stationary mode of a lower energy level are given with a stepwise decrease in the velocity of a vertical purge as well as a complete stoppage of the vortex flow.

The results of the calculations allow us to give meaningful recommendations for a large-scale full-scale experiment on creating an artificial tornado.

References:

1. Abdubakova L. V., Obukhov A. G. 2014. “Chislennyy raschet skorostnykh kharakteristik trekhmernogo voskhodyashchego zakruchennogo potoka gaza”. Izvestiya vuzov. Neft’ i gaz, no 3, pp. 88-94.
2. Bautin S. P., Obukhov A. G. 2012. “Matematicheskoe modelirovanie i chislennyy raschet techeniy v pridonnoy chasti tropicheskogo tsiklona”. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, no 4. pp. 175-182.
3. Bautin S. P., Obukhov A. G. 2013. “Matematicheskoe modelirovanie pridonnoy chasti voskhodyashchego zakruchennogo potoka”. Teplofizika vysokikh temperature, no 51. pp. 567-570. DOI: 10.7868/S0040364413020038
4. Bautin S. P., Obukhov A. G. 2012. Matematicheskoe modelirovanie razrushitel’nykh atmosfernykh vikhrey [Mathematical Modeling of Destructive Atmospheric Vortices]. Novosibirsk: Nauka.
5. Bautin S.P., Obukhov A. G. 2013. “Ob odnom vide kraevykh usloviy pri raschete trekhmernykh nestatsionarnykh techeniy szhimaemogo vyazkogo teploprovodnogo gaza”. Izvestiya vuzov. Neft’ i gaz, no 5. pp. 55-63.
6. Bautin S. P., Obukhov A. G. 2013. “Odno tochnoe statsionarnoe reshenie sistemy uravneniy gazovoy dinamiki”. Izvestiya vuzov. Neft’ i gaz, no 4, pp. 81-86.
7. Bautin S. P. 1987. “Predstavlenie resheniy sistemy uravneniy Nav’e-Stoksa v okrestnosti kontaktnoy kharakteristiki”. Prikladnaya matematika i mekhanika, no 51, pp. 574-584.
8. 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 Rotation of the Earth around Its Axis]. Yekaterinburg: UrGUPS.
9. Bautin S. P., Krutova I. Yu., Obukhov A. G., Bautin K. V. 2013. Razrushitel’nye atmosfernye vikhri: teoremy, raschety, eksperimenty [Destructive Atmospheric Vortices: Theorems, Calculations, and Experiments]. Novosibirsk: Nauka; Yekaterinburg: Izd-vo UrGUPS.
10. Volkov R. E., Obukhov A. G. 2016. “Metod rasparallelivaniya algoritma chislennogo resheniya polnoy sistemy uravneniy Nav’e-Stoksa”. Izvestiya vuzov. Neft’ i gaz, no 2, pp. 92-98.
11. Volkov R. E., Obukhov A. G. 2016. “Parallel’nye vychisleniya v issledovaniyakh zavisimosti gazodinamicheskikh parametrov voskhodyashchego zakruchennogo potoka gaza ot skorosti produva”. Izvestiya vuzov. Neft’ i gaz, no 1, pp. 92-97.
12. Obukhov A. G. 2012. “Matematicheskoe modelirovanie i chislennye raschety techeniy v pridonnoy chasti tornado”. Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy, no 4. pp. 183-188.