Numerical algorithm for solving the problem of modeling the dynamics of a large-scale thermal
DOI:
https://doi.org/10.26577/JMMCS-2018-4-564Keywords:
large-scale thermal, Lattice Boltzmann Method, D3Q27Abstract
The article presents research results on dynamics of large-scale thermals influenced by buoyancy
force, turbulent mixing and adiabatic expansion. Mathematical model is based on the Navier –
Stokes equations, the continuity equation, and the total energy equation. Numerical simulation
realized by finding solution of three dimension Lattice Boltzmann Equations appling D3Q27 model.
First approximation of the solution of Boltzmann equation leads to the hydrodynamic Navier –
Stokes equation.Numerical verification of the algorithm was carried out using benchmark Poiseuille
flow problem. A number of numerical experiments were carried out, with different initial conditions
for temperature and density inside and outside the large-scale thermal.The dependence of the
height of cloud rise on the initial temperature was obtained. Dynamics of the temperature field
propagation is given for an initial value of 1800 ◦ K at the time instant of 5 s, 15 s, and 35 s.
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26. Chen C.K., Chang S.C., Sun S.Y. "Lattice Boltzmann method simulation of channel flow with square pillars inside by the field synergy principle", CMES-Comput. Model. Eng. Sci. (2007), 203–215.
27. Yang Y.T., Chang S.C., Chiou C.S. "Lattice Boltzmann method and large-eddy simulation for turbulent impinging jet cooling", International Journal of Heat and Mass Transfer(2013), 543-553.
28. Zhang J. "Lattice Boltzmann method for microfluidics: models and applications", Microfluid. Nanofluid(2011), 1–28.
29. Guo Z., Zhao T.S. "Lattice Boltzmann model for incompressible flows through porous media", Phys.Rev.E.(2002), 036304.
30. Kuwata Y., Suga K. "Large eddy simulations of pore-scale turbulent flows in porous media by the lattice Boltzmann method" International Journal of Heat and Mass Transfer(2015), 143-157.
31. Chang S.C., Hsu Y.S., Chen C.L. "Lattice Boltzmann simulation of fluid flows with fractal geometry: an unknown-index algorithm", J.Chin.Soc.Mech.Eng.(2011), 523–531.
2. Garbaruk A.V., Strelec M.H., Travin A.K., Shur M.L "Sovremennye podhody k modelirovaniju turbulentnosti: ucheb. posobie" [Modern approaches for modeling of turbulencce](SPb, Izd-voPolitehn. un-ta, 2016),234 s.
3. Assylzhan Kizbayev, Dauren Zhakebayev, Ualikhan Abdibekov, Askar Khikmetov, "Mathematical modeling of electron irradiation of oil”, Engineering Computations(2018),pp.1998-2009.
4. Abdibekov S., Zhakebayev D., Karzhaubayev K., Abdibekov U., "Large eddy simulation the evolution of the cloud explosion of a launch vehicle", VYChISLITELNYE TEHNOLOGII (2018),7-17 p.
5. Zhumagulov B.T., Zhakebaev D.B., Abdibekov U.S., "Matematicheskoe modelirovanie vyrozhdenija jenergii turbulentnosti na osnove gibridnogo metoda"[Mathematical modeling of turbulence energy by gibrid model], Vestnik NIA RK № 3(2018), 9-15 p.
6. Ben-Nasra O., Hadjadj A., Chaudhurib A., Shadloo M.S. "Assessment of subgrid-scale modeling for large-eddy simulation of a spatially-evolving compressible turbulent boundary layer", Computers and Fluids (2017), 144-158 p.
7. Meneveau C., Katz J. Scale-invariance and turbulence models for large eddy simulation, Annu. Rev. Fluid Mech(2000), 1-32 p.
8. You D., Moin P. A dynamic global-coefficient subgrid-scale eddy-viscosity model for large-eddy simulation in complex geometries, // Physics of Fluids. – 2007. – Vol. 19, No. 6. –065110.
9. Oran E.S., Boris J.P. Numerical Simulation of reactive flow (Cambridge University Press, 2001), 550 p.
10. Grinstein F.F., Margolin L.G., Rider W.J. Implicit Large Eddy Simulation(Cambridge University Press, 2007), 577 p.
11. Spalart P.R. "Strategies for turbulence modeling and simulations" , Int. J. of Heat and Fluid Flow (2000), 252-263 p.
12. Onufriev A.T. "Teorija dvizhenija vihrevogo kol'ca pod dejstviem sily tjazhesti. Podyem oblaka atomnogo vzryva"[Theorem of movement of vortex ring by influence of boynce forces], Prikladnaja mehanika i tehnicheskaja fizika(1967), 3-15 p.
13. Kudrjashov N.A. "Vlijanie vjazkosti i teploprovodnosti na vsplyvanie termika pod dejstviem sil plavuchesti" [Humid viscosity and heat capacity of thermals](Moskva: Nauka, 1985), 135 p.
14. Dovgalyuk Y.A., Zatevakhin M.A., Stankova E.N. "Numerical Simulation of a Buoyant Thermal Using the Turbulence Model", Journal of applied Meteorology 33 (1994): 1118-1126
15. Sinjab, I. M., Robertson, J. A., Connon Smith, R. "The dissipation factor in contact binaries revisited," Monthly Notices of the Royal Astronomical Society 244 (1990):619
16. Hazlehurst, J. "The dissipation factor in contact binaries," Astronomy and Astrophysics 145 (1985): 481-488
17. Brandenburg A., Hazlehurst J. "Evolution of highly buoyant thermals in a stratified layer," Astronomy and Astrophysics 370 (2001): 1092-1102
18. Zhaoli G., Chaguang Z., Baochang S. "Thermal lattice Boltzmann equation for low Mach number flow," Physical Review E 75 (2007): 036704
19. Woods L.C. "An Introduction to the Kinetic Theory of Gases and Magnetoplasmas," Oxford University Press (Oxford: 1993)
20. Kruger, T., Kusumaatmaja, H., Kuzmin, A., Shardt, O., Silva, G., Viggen, E. M. "The Lattice Boltzmann Method," Springer 215 (2017): 35
21. Chang S.C., yang Y.T., Chen C.K., Chen W.L. "Application of the lattice Boltzmann method combined with large-eddy simulations to turbulent convective heat transfer" International Journal of Heat and Mass Transfer (2013), 338-348 p.
22. Pradhan A., Yadav S. "Large Eddy Simulation using Lattice Boltzmann Method based on Sigma Model", Procedia Engineering (2015), 177-184 p.
23. Sagaut P. "Toward advanced subgrid models for Lattice-Boltzmann-based Large-eddy simulation: Theoretical formulations" Computers and Mathematics with Applications (2010), 2194-2199 p.
24. Grunau D., Chen S., Eggert K. "A lattice Boltzmann model for multiphase fluid flows", Phys. Fluids. (1993), 2557–2562 p.
25. Amirshaghaghi H., Rahimian M.H., Safari H., Krafczyk M. "Large Eddy Simulation of liquid sheet breakup using a two-phase lattice Boltzmann method", Computers and Fluids(2018), 93-107 p.
26. Chen C.K., Chang S.C., Sun S.Y. "Lattice Boltzmann method simulation of channel flow with square pillars inside by the field synergy principle", CMES-Comput. Model. Eng. Sci. (2007), 203–215.
27. Yang Y.T., Chang S.C., Chiou C.S. "Lattice Boltzmann method and large-eddy simulation for turbulent impinging jet cooling", International Journal of Heat and Mass Transfer(2013), 543-553.
28. Zhang J. "Lattice Boltzmann method for microfluidics: models and applications", Microfluid. Nanofluid(2011), 1–28.
29. Guo Z., Zhao T.S. "Lattice Boltzmann model for incompressible flows through porous media", Phys.Rev.E.(2002), 036304.
30. Kuwata Y., Suga K. "Large eddy simulations of pore-scale turbulent flows in porous media by the lattice Boltzmann method" International Journal of Heat and Mass Transfer(2015), 143-157.
31. Chang S.C., Hsu Y.S., Chen C.L. "Lattice Boltzmann simulation of fluid flows with fractal geometry: an unknown-index algorithm", J.Chin.Soc.Mech.Eng.(2011), 523–531.
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How to Cite
Zhakebayev, D. B., Moisseyeva, Y., Hrebtov, M. Y., & Tsoy, N. V. (2019). Numerical algorithm for solving the problem of modeling the dynamics of a large-scale thermal. Journal of Mathematics, Mechanics and Computer Science, 100(4), 88–102. https://doi.org/10.26577/JMMCS-2018-4-564
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Applied Mathematics
