A hybrid mesomacroscopic approach has been developed for modeling developed turbulent thermogravitational flows in closed rectangular differentially heated regions. Within the framework of the formulated approach, it is proposed to use the mesoscopic lattice Boltzmann equations to describe gas-dynamical processes, and the macroscopic energy equation solved by the finite difference method for thermodynamic ones. To approximate the Boltzmann equation, simultaneous relaxation and a two-dimensional nine-speed scheme were used. Mathematical simulation was carried out at the Rayleigh number Ra = 1010 and the Prandtl number Pr = 0.71. The influence of the order of approximation of the energy equation on the local heat transfer characteristics has been analyzed. It is found that an increase in the number of computational nodes leads to the smoothing of pulsations in the flow. In this case, the results of numerical simulation agree satisfactorily with the “reference” data obtained by other researchers.
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K. V. Sharma, R. Straka, and F. W. Tavares, Current status of lattice Boltzmann methods applied to aerodynamic, aeroacoustic, and thermal flows, Prog. Aerospace Sci., 115, Article ID 100616, 1–37 (2020).
D. A. Perumal and A. K. Dass, A review on the development of lattice Boltzmann computation of macro fluid flows and heat transfer, Alexandria Eng. J., 54, 955–971 (2015).
A. A. Avramenko, A. I. Tyrinov, I. V. Shevchuk, N. P. Dmitrenko, A. V. Kravchuk, and V. I. Shevchuk, Mixed convection in a vertical circular microchannel, Int. J. Therm. Sci., 121, 1–12 (2017).
H. N. Dixit and V. Babu, Simulation of high Rayleigh number natural convection in a square cavity using the lattice Boltzmann method, Int. J. Heat Mass Transf., 49, 727–739 (2006).
R. Du and W. Liu, A new multiple-relaxation-time lattice Boltzmann method for natural convection, J. Sci. Comput., 56, 122–130 (2013).
N. Frapolli, S. S. Chikatamarla, and I. V. Karlin, Entropic lattice Boltzmann simulation of thermal convective turbulence, Comput. Fluids, 175, 2–19 (2018).
K. V. Sharma, R. Straka, and F. W. Tavares, Natural convection heat transfer modeling by the cascaded thermal lattice Boltzmann method, Int. J. Therm. Sci., 134, 552–564 (2018).
S. R. G. Polasanapalli and K. Anupindi, A high-order compact finite-difference lattice Boltzmann method for simulation of natural convection, Comput. Fluids, 181, 259–282 (2019).
P. Lallemand and L.-S. Lou, Hybrid finite-difference thermal lattice Boltzmann equation, Int. J. Modern Phys. B, 17, 41–47 (2003).
S. Bettaibi, F. Kuznik, and E. Sediki, Hybrid lattice Boltzmann finite difference simulation of mixed convection flows in a lid-driven square cavity, Phys. Lett. A, 378, 2429–2435 (2014).
A. A. Mohamad, Lattice Boltzmann Method, Springer-Verlag London Limited, London (2011).
V. M. Paskonov, V. I. Polezhaev, and L. A. Chudov, Numerical Simulation of Heat and Mass Transfer Processes [in Russian], Nauka, Moscow (1984).
C. Zhuo and C. Zhong, LES-based filter-matrix lattice Boltzmann model for simulating turbulent natural convection in a square cavity, Int. J. Heat Fluid Flow, 42, 10–22 (2013).
N. C. Markatos and K. A. Pericleous, Laminar and turbulent natural convection in an enclosed cavity, Int. J. Heat Mass Transf., 27, 755–772 (1984).
J. Xaman, G. Mejia, G. Alvarez, and Y. Chavez, Analysis on the heat transfer in a square cavity with a semitransparent wall: Effect of the roof materials, Int. J. Therm. Sci., 49, 1920–1932 (2010).
Sh. Chen, H. Liu, and Ch. Zheng, Numerical study of turbulent double-diffusive natural convection in a square cavity by LES-based lattice Boltzmann model, Int. J. Heat Mass Transf., 55, 4862–4870 (2012).
T. Fusegi, J. M. Hyun, and K. Kuwahara, Three-dimensional simulations of natural convection in a sidewall-heated cube, Int. J. Numer. Methods Fluids, 13, 857–867 (1991).
S. Paolucci, Direct numerical simulation of two-dimensional turbulent natural convection in an enclosed cavity, J. Fluid Mech., 215, 229–262 (1990).
P. Wang, Yo. Zhang, and Zh. Guo, Numerical study of three-dimensional natural convection in a cubical cavity at high Rayleigh numbers, Int. J. Heat Mass Transf., 113, 217–228 (2017).
L. D. Landau and E. M. Lifshits, Hydrodynamics [in Russian], Nauka, Moscow (1986).
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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 95, No. 2, pp. 518–525, March–April, 2022.
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Nee, A.É. Hybrid LBGK-FD Model for Studying Turbulent Natural Convection. J Eng Phys Thermophy 95, 508–515 (2022). https://doi.org/10.1007/s10891-022-02506-x
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DOI: https://doi.org/10.1007/s10891-022-02506-x