Two-dimensional free convection flow simulations on a square cavity through the use of lattice boltzmann equation method
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Convection is a key phenomenon found in different atmospheric and industrial applications. This work presents the numerical simulation of flow in a cavity which has been heated on one wall, in laminar regime, with Rayleigh numbers (Ra) of 103 ≤ Ra ≤ 106 and a Prandtl number of Pr = 0.7, through the lattice Boltzmann equation method -LBE. This technique has proven to be very efficient and powerful in computational fluid dynamics -CFD- (Y. W. Know, 2006). The flow velocity is calculated based on the use of density distribution function in the model D2Q9 -, with two dimensions and nine velocities. Temperature readings are obtained through the model D2T5 -, with two dimensions and five temperatures. The new thermal model used showed to be stable, and the results are highly accurate compared to the experimental and numerical results obtained through other CFD methods.
Numerical simulation, Lattice Boltzmann equation, natural convectionSimulación numérica, ecuación de Boltzmann en redes, convección natural
CHEN, Y.; OHASHI, H. y AKIYAMA, M. A. Thermal lattice Bhatnagar-Gross-Krook model without nonlinear deviations in macrodynamic equations. Physical Review E. 1994; vol. 50, núm. 4, pp. 2776-2783.
D’ORAZIO, A.; MASSIMO, C. y GIAN PIERO, C. Application to natural convection enclosed flow of a lattice Boltzmann BGK model coupled with a general purpose thermal boundary conditions. International Journal of Thermal Sciences. 2004, vol. 43, pp. 575-586.
DAZHI, Y.; RENWEI, M.; LI-SHI, L. y WEI, S. Viscous flow computations with the method of lattice Boltzmann equations. Progress in Aerospace Sciences. 2003, vol. 39, núm. 5, pp. 329-367.
FILIPPOVA, O. y PANEL, D. A novel BGK approach for low Mach number combustión. Journal of Computations Physics. 2000, vol. 158, núm. 2, pp. 139-160.
FLOREZ, S. E.; CUESTA, I. y SALUEÑA, C. Flujo de Poiseuille y la cavidad con pared móvil calculado usando el método de la ecuación de lattice Boltzmann. Ingeniería & Desarrollo. 2008, vol. 1, núm. 24, pp. 117-132.
GUO, Z.; SHI, B. y ZHENG, C. A coupled lattice BGK model for the Boussinesq equations. International Journal for Numerical Methods in Fluids. 2002, vol. 39, pp. 325-342.
HE, X.; CHEN, S. y DOOLEN, G. D. A novel thermal model for the lattice Boltzman method in incompresible limit. Journal of Computational Physics. 1998, vol. 146, núm. 1, pp. 282-300.
HIGUERA, F. J. y JIMÉNEZ, J. Boltzmann approach to lattice gas simulation. Europhysics Letters. 1989, vol. 9, núm. 7, pp. 663-668.
KNOW, Y. W. Development of coupling technique for LBM and FEM for FSI application. International Journal for Computer-Aided Engineering and Software. 2006, vol. 23, núm. 8, pp. 860-875.
KUZNICK, F.; VAREILLES, J.; RUSAOUEN, G. y KRAUSS, G. A double-population lattice Boltzmann method whit non-uniform mesh for the simulation of natural convection in square cavity. International Journal of Heat and Fluid Flow. 2007, vol. 28, pp. 862-870.
KUZNIK, F.; VAREILLES, J.; RUSAOUEN, G. y KRAUSS, G. Application to natural convection enclosed flows of a lattice Boltzmann BGK model coupled with a general purpose thermal boundary conditions. International Journal of Thermal Sciences. 2004, vol. 43, pp. 575-586.
QUIAN, Y.; D’HUMIERES, D. y LALLEMAND P. Lattice BGK models for Navier-Stokes Equation. Europhysics Letters. 1992, vol. 17, pp. 479-84.
QUIAN, Y. H. y ORSZAG, S. A. Lattice BGK models for Navier-Stokes equation: non-linear deviation in compressible regimes. Europhysics Letters. 1993, vol. 21, pp. 255-259.