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Journal ArticleDOI

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.
Citations
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Journal ArticleDOI
TL;DR: A comprehensive review of the lattice Boltzmann (LB) method for single-phase and solid-liquid phase-change heat transfer in porous media at both the pore scale and representative elementary volume (REV) scale is presented in this paper.

155 citations

Posted Content
TL;DR: In this paper, the basic principles of the lattice gas automata and lattice Boltzmann automata were introduced and their applications to pattern formation in chemical reaction-diffusion systems, multiphase fluid flows and polymeric dynamics were discussed.
Abstract: The recent development of the lattice gas automata method and its extension to the lattice Boltzmann method have provided new computational schemes for solving a variety of partial differential equations and modeling chemically reacting systems. The lattice gas method, regarded as the simplest microscopic and kinetic approach which generates meaningful macroscopic dynamics, is fully parallel and can, as a result, be easily programmed on parallel machines. In this paper, we introduce the basic principles of the lattice gas method and the lattice Boltzmann method, their numerical implementations and applications to chemically reacting systems. Comparisons of the lattice Boltzmann method with the lattice gas technique and other traditional numerical schemes, including the finite difference scheme and the pseudo-spectral method, for solving the Navier-Stokes hydrodynamic fluid flows will be discussed. Recent developments of the lattice gas and the lattice Boltzmann method and their applications to pattern formation in chemical reaction-diffusion systems, multiphase fluid flows and polymeric dynamics will be presented.

107 citations

Book ChapterDOI
01 Jan 2013
TL;DR: In this article, the authors focus on the first law of thermodynamics in a porous medium and assume that heat conduction in the solid and fluid phases takes place in parallel so that there is no net heat transfer from one phase to the other.
Abstract: In this chapter we focus on the equation that expresses the first law of thermodynamics in a porous medium. We start with a simple situation in which the medium is isotropic, and where radiative effects, viscous dissipation, and the work done by pressure changes are negligible. Very shortly we shall assume that there is local thermal equilibrium so that T s = T f = T, where T s and T f are the temperatures of the solid and fluid phases, respectively. More complex situations will be considered in Section 6.5. Here we also assume that heat conduction in the solid and fluid phases takes place in parallel so that there is no net heat transfer from one phase to the other.

71 citations

Journal ArticleDOI
TL;DR: The problem of convection in a fluid-saturated porous medium is reviewed with a focus on ‘vigorous’ convective flow, when the driving buoyancy forces are large relative to any dissipative forces in the system.
Abstract: The problem of convection in a fluid-saturated porous medium is reviewed with a focus on 'vigorous' convective flow, when the driving buoyancy forces are large relative to any dissipative forces in the system This limit of strong convection is applicable in numerous settings in geophysics and beyond, including geothermal circulation, thermohaline mixing in the subsurface and heat transport through the lithosphere Its manifestations range from 'black smoker' chimneys at mid-ocean ridges to salt-desert patterns to astrological plumes, and it has received a great deal of recent attention because of its important role in the long-term stability of geologically sequestered CO2 In this review, the basic mathematical framework for convection in porous media governed by Darcy's Law is outlined, and its validity and limitations discussed The main focus of the review is split between 'two-sided' and 'one-sided' systems: the former mimics the classical Rayleigh-Benard set-up of a cell heated from below and cooled from above, allowing for detailed examination of convective dynamics and fluxes; the latter involves convection from one boundary only, which evolves in time through a series of regimes Both set-ups are reviewed, accounting for theoretical, numerical and experimental studies in each case, and studies that incorporate additional physical effects are discussed Future research in this area and various associated modelling challenges are also discussed

36 citations

Journal ArticleDOI
TL;DR: In this paper, an analytical approach and the interpolation-supplemented lattice Boltzmann method (ISLBM) were used to quantify convective and diffusive transport during CO2 dissolution.
Abstract: In this study, we use an analytical approach and the interpolation-supplemented lattice Boltzmann method (ISLBM) to quantify convective and diffusive transport during CO2 dissolution. In the first step, we use a turbulence analogy and the ISLBM to determine the relationship between the Rayleigh number (Ra) and the ratio of the pseudo-diffusion coefficient to the molecular diffusion coefficient (D*D). We then use experimental data from two oil samples, condensate and crude oils, to validate the obtained relationship between D*D and Ra. We also use the Sherwood number (Sh) and total mixing and diffusive transport curves to analyze different periods during CO2 dissolution for condensate and crude oils. We focus, in particular, on how Ra affects the characteristics of density-driven fingers and the convection field. Our results show that there is a logarithmic trend between D*D and Ra. Analysis of the total mixing and diffusive curves indicates that the CO2 dissolution process can be divided into three distinct periods, namely, diffusive transport, early convection, and late convection. We find that more than 50% of the ultimate CO2 dissolution occurs in the early convection period. We also show that the analytical results obtained for the critical time and critical depth at the onset of convection is in good agreement with those of the ISLBM. After the onset of convection, the formation of initial fingers leads to enhanced convective transport, with marked implications for the concentration variance and mixing rate.

31 citations

References
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01 Jan 1952

6,655 citations

Journal ArticleDOI
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.

6,565 citations

Book
01 Jan 1992
TL;DR: In this paper, an 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.
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.

5,570 citations

Journal ArticleDOI
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.

2,719 citations