MODELING THE EVOLUTION OF WHIRL STRUCTURES IN A SUPERSONIC GAS STREAM
https://doi.org/10.32362/2500-316X-2018-6-5-45-54
Abstract
With the help of mathematical modeling methods we studied the evolution of whirl structures moving in a gas behind a shock wave front. This shock wave is defined by the Hugoniot relations. The Hugoniot relations allow finding the parameters of the gas behind the shock wave front, if the Mach number and gas parameters before the pressure jump are known. We developed a parallel algorithm and a numerical code for solving 2D gas dynamics equations. We made numerical simulations that modeled the shock wave interaction with whirl structures of different configurations (single whirl, two whirls with different directions of their vectors). We demonstrated the results of test simulations in a supercomputer with a different number of processors. It was shown that using 40 processors allows decreasing the duration of a test simulation approximately by the factor of 30. We described the results of the calculation of interaction of one/two whirls with the incident wave and the reflected waves. The gas dynamics parameters at the moment t = 0 were set with the help of Bernoulli law. Besides, we made a comparison with a similar program based on another algorithm (particle-in-cell method). It was shown that the interaction of two whirls with opposite directions does not lead to their compensation, but the interaction area (turbulent zone) has a complicated shape. The possibility of natural experiments with the help of a shock tube and a laser shock tube is discussed in the article. Such research would allow comparing the experimental data with the results of numerical simulations and developing more complicate models of the turbulent motion.
About the Authors
I. G. Lebo
MIREA - Russian Technological University
Russian Federation
Russian Federation
A. I. Simakov
MIREA - Russian Technological University
Russian Federation
Russian Federation
References
1. Zworykin V.D., Lebo I.G. The use of the potent KrF-laser for a research of supersonic currents of gas and development of hydrodynamic instabilities in stratified mediums. Kvantovaya elektronika (Quantum Electronics). 2000; 30(6): 540-544. (in Russ.)
2. Samarskiy A.A., Mikhailov A.P. Mathematic Modeling. Moscow: Nauka-Fizmatlit Publ., 1997. 316 p. (in Russ.)
3. Lebo I.G., Akzholov M.Zh. Model operation of interaction of a shockwave with vortex structures in gas. Vestnik MGTU MIREA. 2015; (2-7): 240-250. (in Russ.)
4. Madera A.G., Akzholov M.Zh., Lebo I.G. Modeling of development of processes "convection plus heat conductivity" in air near the processor. Trudy NIISI RAN (Proceed. of the Research Institute for System Studies RAS). 2013; 3(1): 90-93. (in Russ.)
5. Belotserkovskiy O.M., Davydov Yu.M. The large particles method in the gas dynamics. Moscow: Nauka Publ., 1982. 391 p. (in Russ.)
6. Lebo I.G., Tishkin V.F. Research of hydrodynamic instability in problems of laser thermonuclear synthesis. Moscow: Fizmatlit Publ., 2006. 304 p. (in Russ.)
7. Harten A. On a class of high resolution total-variation-stable finite-difference schemes. SIAM J. Numeric Anal. 1984; 21(1): 1-23.
8. Vyaznikov К.V., Тishkin V.F., Favorskiy А.P. Construction of monotone difference schemes of a higher order of approximation for systems of hyperbolic equations. Matematicheskoe modelirovanie (Mathematic Modeling). 1989; 1(5): 95-98. (in Russ.)
9. Ladonkina M.E. Numerical modeling of turbulent mixing with use of high-performance systems: diss. … Ph.D. (Physics and Mathematics). Moscow, 2005. 157 p. (in Russ.)
10. Fundamentals of Gas Dynamics. Editor Howard W. Emmons. Princeton, New Jersey: Princeton University Press, 1958.
11. Dmitriev O.A., Krivets V.V., Lebo I.G., Simakov A.I., Titov S.N., Chebotareva E.I. Modeling of development of hydrodynamic instability when passing a wave of compression through the contact surface of two gases. Matematicheskoe modelirovanie (Mathematic Modeling). 2013; 25(8): 22-32. (in Russ.)
12. Zel'dovich Ya.B., Raizer Yu.P. Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena. Moscow: Nauka Publ., 1966. 687 p. (in Russ.)
13. Akzholov M.Zh., Dmitriev O.A., Lebo I.G., Madera A.G. Comparison of calculations of distribution of shock waves in gases, executed according to the ENS programs and NUT_2D. Trudy NIISI RAN (Proceed. of the Research Institute for System Studies RAS). 2014; 4(1): 58- 61. (in Russ.)
14. Goloviznin V.M., Karabasov S.A., Kondakov V.G. Synthesis of the scheme of CABARET on two-dimensional orthogonal grids. Matematicheskoe modelirovanie (Mathematical Modeling). 2013; 25(7): 103-136. (in Russ.)
15. Zworykin V.D., Lebo I.G. The use of the potent KrF-laser for a research of supersonic currents of gas and development of hydrodynamic instabilities in stratified mediums. Kvantovaya elektronika (Quantum Electronics). 2000; 30(6): 540-544. (in Russ.)
Review
For citations:
Lebo I.G., Simakov A.I. MODELING THE EVOLUTION OF WHIRL STRUCTURES IN A SUPERSONIC GAS STREAM. Russian Technological Journal. 2018;6(5):45-54. (In Russ.) https://doi.org/10.32362/2500-316X-2018-6-5-45-54
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