High Rayleigh Number Natural Convection Inside 2D Porous Enclosures Using the Lattice Boltzmann Method
01 Jun 2011-Journal of Heat Transfer-transactions of The Asme (American Society of Mechanical Engineers)-Vol. 133, Iss: 6, pp 062501
TL;DR: In this article, a lattice Boltzmann method was employed to investigate natural convection inside porous medium enclosures at high Rayleigh numbers, and the effect of the form drag on the Nusselt number was studied by using a form drag modified Rayleigh number Ra C (extended from Ra m ).
Abstract: Lattice Boltzmann method (LBM) is employed to investigate natural convection inside porous medium enclosures at high Rayleigh numbers. Volume averaged porous medium model is coupled with the lattice Boltzmann formulation of the momentum and energy equations for fluid flow. A parallel implementation of the single relaxation time LBM is used, which allows the porous medium modified Rayleigh number Ra m to be as high as 10 8 . Heat transfer results in the form of the enclosure averaged Nusselt number Nu are obtained for higher modified Rayleigh numbers 10 4 ≤Ra m ≤ 10 8 . The Nu values are compared with values in the absence of the form drag term. The form drag due to the porous medium is found to influence Nu considerably. The effect of the form drag on Nu is studied by using a form drag modified Rayleigh number Ra C (extended from Ra m ). Utilizing the results for Nu in the high Ra m range, a correlation is proposed between Nu and Ra C for Darcy numbers 10 ―6 ≤ Da ≤ 10 ―2 , encompassing the non-Darcy flow regime.
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References
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TL;DR: An overview of the lattice Boltzmann method, a parallel and efficient algorithm for simulating single-phase and multiphase fluid flows and for incorporating additional physical complexities, is presented.
Abstract: We present an overview of the lattice Boltzmann method (LBM), a parallel and efficient algorithm for simulating single-phase and multiphase fluid flows and for incorporating additional physical complexities. The LBM is especially useful for modeling complicated boundary conditions and multiphase interfaces. Recent extensions of this method are described, including simulations of fluid turbulence, suspension flows, and reaction diffusion systems.
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Abstract: This introduction to convection in porous media assumes the reader is familiar with basic fluid mechanics and heat transfer, going on to cover insulation of buildings, energy storage and recovery, geothermal reservoirs, nuclear waste disposal, chemical reactor engineering and the storage of heat-generating materials like grain and coal. Geophysical applications range from the flow of groundwater around hot intrusions to the stability of snow against avalanches. The book is intended to be used as a reference, a tutorial work or a textbook for graduates.
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TL;DR: A lattice Boltzmann model is developed which has the ability to simulate flows containing multiple phases and components and is highly efficient to compute on massively parallel computers.
Abstract: A lattice Boltzmann model is developed which has the ability to simulate flows containing multiple phases and components. Each of the components can be immiscible with the others and can have different mass values. The equilibrium state of each component can have a nonideal gas equation of state at a prescribed temperature exhibiting thermodynamic phase transitions. The scheme incorporated in this model is the introduction of an interparticle potential. The dynamical rules in this model are local so it is highly efficient to compute on massively parallel computers. This model has many applications in large-scale numerical simulations of various types of fluid flows.
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