Numerical simulation of natural convection in an open-ended square cavity filled with porous medium by lattice Boltzmann method

In the present work, natural convection in an open-ended square cavity packed with porous medium is simulated. The double-population approach is used to simulate hydrodynamic and thermal fields, and the Taylor series expansion and the least-squares-based lattice Boltzmann method has been implemented to extend the thermal model. The effect of a porous medium is taken into account by introducing the porosity into the equilibrium distribution function and adding a force term to the evolution equation. The Brinkman–Forchheimer equation, which includes the viscous and inertial terms, is applied to predict the heat transfer and fluid dynamics in the non-Darcy regime. The present model is validated with the previous literature. A comprehensive parametric study of natural convective flows is performed for various values of Rayleigh number and porosity. It is found that these two parameters have considerable influence on heat transfer.     

Numerical study of turbulent double-diffusive natural convection in a square cavity by LES-based lattice Boltzmann model

Turbulent double-diffusive natural convection in a square cavity represents numerous important problems in practice as well as in fundamental. However up to date the study on it is quite sparse and most previous studies just focus on laminar regime. To the best knowledge of the present authors, only several k–? models were developed to investigate turbulent double-diffusive convection and there is no attempt to use Large Eddy Simulation (LES). In order to deepen our knowledge on turbulent double-diffusive convection in a square cavity, we propose a novel LES-based lattice Boltzmann (LB) model to simulate such turbulent convectional flow. Previous LES-based LB models can be recovered from the present model. We find that the symmetry of the fluid circulation becomes broken since the Rayleigh number Ra = 10⁸, although the asymmetry is more clear when Ra ? 10¹⁰. More important, in the present study we find the power-law relationship among the Nusselt (Nu), the ratio of buoyancy forces (N) and the Rayleigh number (Ra) still exists in turbulent regime. The formula among them can be concluded as Nu = a × (Ra × ∣1 ? N∣)^b + c. The values of parameters a, b and c are given in this work.     

Solving transient heat conduction problems on uniform and non-uniform lattices using the lattice Boltzmann method

The lattice Boltzmann method (LBM) has been used to solve transient heat conduction problems in 1-D, 2-D and 3-D Cartesian geometries with uniform and non-uniform lattices. To study the suitability of the LBM, the problems have also been solved using the finite difference method (FDM). To check the performance of LBM for the non-uniform lattices, the results have been compared with uniform lattices. Cases with volumetric heat generation have also been considered. In 1-D problems, the FDM with implicit scheme was found to take more number of iterations and also the CPU time was more. However, with explicit scheme, with increase in the number of control volumes, the LBM was found faster than the FDM. In 2-D and 3-D problems, with increase in the number of control volumes, the LBM was found faster than the FDM. In 2-D problems, number of iterations in the two methods was comparable, while in 3-D problems, the LBM was found to take less number of iterations. The accurate results were found in all the cases.     

Numerical analysis on supercritical natural convection by lattice Boltzmann method

Abstract

One of the main factors affecting the heat transfer efficiency of solar collector is that the ordinary fluid in it is in the state of natural convection. Supercritical fluid is expected to improve the heat transfer efficiency of solar collectors due to its dramatic changes in thermal properties, so it is necessary to carry out the research of natural convection of supercritical fluid. Although researchers have made lots of related experimental investigations, heat transfer mechanism of supercritical natural convection is still unclear. In order to clarify its heat transfer mechanism, this article conducts a numerical analysis for supercritical natural convection applying lattice Boltzmann method, which has been proved to be valid and convenient. Considering the influences of temperature difference and pressure on natural convective heat transfer of supercritical fluid are seldom studied, the relevant researches are carried out in the article. The results imply that pressure of supercritical fluid in solar collectors should be less than 11?MPa so that high heat transfer performance can be obtained. Finally, the correlations of average Nusselt number, Rayleigh number, and pressure are fitted for the convenience of heat transfer calculation.     

Simulating magnetohydrodynamic natural convection flow in a horizontal cylindrical annulus using the lattice Boltzmann method

A numerical study is presented about the effect of a uniform magnetic field on free convection in a horizontal cylindrical annulus using the lattice Boltzmann method. The inner and outer cylinders are maintained at uniform temperatures and it is assumed the walls are insulating with a magnetic field. Detailed numerical results of heat transfer rate, temperature, and velocity fields have been presented for Pr=0.7, Ra=10³ to 5 × 10⁴, and Ha=0 to 100. The computational results show that in a horizontal cylindrical annulus the flow and heat transfer are suppressed more effectively by a radial magnetic field. It is also found that the flow oscillations can be suppressed effectively by imposing an external radial magnetic field. The average Nusselt number increases by increasing the radius ratio while it decreases by increasing the Hartmann number. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21008     

Combined heat transfer of radiation and natural convection in a square cavity containing participating gases

This article deals with analyzing the effect of radiative heat transfer on natural convection heat transfer in a square cavity under normal room conditions. The governing equations of natural convection and radiative transfer are solved simultaneously to obtain the temperature, velocity and heat flux distributions inside the participating medium. The finite volume method has been adopted to solve the governing equations and the discrete ordinates method (DOM) is used to model the radiative transfer in absorbing-emitting media. The radiative–convective model is validated by comparison with test cases solutions from the literature. Then, the effects of Rayleigh number from 10² to 10⁶ and optical thickness in a broad range from 0 to 100 on temperature and velocity distributions and Nusselt numbers are investigated. The results show that even under normal room conditions with a low temperature difference, the radiation plays a significant role on temperature distribution and flow pattern in the cavity. Also, several interesting effects of radiation are observed such as a sweep behavior on the isotherms, streamlines and velocity distributions of the cavity along the optical thickness and a reverse behavior on maximum stream function and convective Nusselt number at different Rayleigh numbers.     

Conjugate natural convection in a square cavity with finite thickness horizontal walls

The effect of conduction of horizontal walls on natural convection heat transfer in a square cavity is numerically investigated. The vertical walls of the cavity are at different constant temperatures while the outer surfaces of horizontal walls are insulated. A code based on vorticity–stream function is written to solve the governing equations simultaneously over the entire computational domain. The dimensionless wall thickness of cavity is taken as 0.1. The steady state results are obtained for wide ranges of Rayleigh number (10³ < Ra < 10⁶) and thermal conductivity ratio (0 < K < 50). The variation of heat transfer rate through the cavity and horizontal walls with Rayleigh number and conductivity ratio is analyzed. It is found that although the horizontal walls do not directly reduce temperature difference between the vertical walls of cavity, they decrease heat transfer rate across the cavity particularly for high values of Rayleigh number and thermal conductivity ratio. Heatline visualization technique is a useful application for conjugate heat transfer problems as shown in this study.     

MHD natural convection in a laterally and volumetrically heated square cavity

A numerical study is presented of unsteady two-dimensional natural convection of an electrically conducting fluid in a laterally and volumetrically heated square cavity under the influence of a magnetic field. The flow is characterized by the external Rayleigh number, Ra_E, determined from the temperature difference of the side walls, the internal Rayleigh number, Ra_I, determined from the volumetric heat rate, and the Hartmann number, Ha, determined from the strength of the imposed magnetic field. Starting from given values of Ra_E and Ha, for which the flow has a steady unicellular pattern, and gradually increasing the ratio S = Ra_I/Ra_E, oscillatory convective flow may occur. The initial steady unicellular flow for S = 0 may undergo transition to steady or unsteady multicellular flow up to a threshold value, Ra_I,cr, of the internal Rayleigh number depending on Ha. Oscillatory multicellular flow fields were observed for S values up to 100 for the range 10⁵-10⁶ of Ra_E studied. The increase of the ratio S results usually in a transition from steady to unsteady flow but there have also been cases where the increase of S results in an inverse transition from unsteady to steady flow. Moreover, the usual damping effect of increasing Hartmann number is not found to be straightforward connected with the resulting flow patterns in the present flow configuration.     

Numerical analysis of convection conduction and radiation using a non-equilibrium model in a square porous cavity

Numerical analysis of heat transfer by convection, conduction and radiation in a saturated porous medium enclosed in a square cavity is investigated using a thermal non-equilibrium model. The flow is assumed to follow Darcy law. The governing partial differential equations are non-dimensionalised and solved numerically using finite element method. The left vertical surface of the square cavity is maintained at an isothermal temperature $T_h$ and the right vertical surface at $T_c$ such that $T_c<T_h$. The top and bottom surfaces of the cavity are assumed to be adiabatic. Results are presented in terms of Nusselt number for fluid, Nusselt number for solid and total Nusselt number, for various parameters such as inter-phase heat transfer coefficient, modified conductivity ratio, radiation parameter and Rayleigh number.     

Conjugate natural convection in air filled tube inserted a square cavity

Numerical analyses of fluid flow and heat transfer due to buoyancy forces in a tube inserted square cavity filled with fluid were carried out by using control volume method in this study. The cavity was heated from the left wall and cooled from the right isothermally and horizontal walls were adiabatic. A circular tube filled with air was inserted into the square cavity. The case that the inside and outside of the tube were filled with the same fluid (air) was examined. Varied solid materials were chosen as the tube wall. Results were obtained for different Rayleigh numbers (Ra = 10⁴, 10⁵ and 10⁶), thermal conductivity ratio of the fluid to the tube wall (k = 0.1, 1 and 10) and different location centers of the tube (c (0.25 ≤ x ≤ 0.75, 0.25 ≤ y ≤ 0.75)). Comparison with benchmark solutions of the natural convection in a cavity was performed and numerical results gave an acceptable agreement. It was found that varied location of the tube center can lead to different flow fields and heat transfer intensities which are also affected by the value of Rayleigh number.     

Effects of slip boundaries on thermal convection in 2D box using lattice Boltzmann method

This work studied the thermal convection under various slip boundary conditions in a 2D box with aspect ratio equal to two. The slip parameter is the normalized tangential momentum accommodation coefficient (TMAC, 0 ? σ ? 1). The results show that the slip boundary conditions of vertical side walls (σ_v) and horizontal plates (σ_h) will affect the pattern selections of the flow and temperature fields. When σ_h < 0.02, the pattern is the one-roll mode for all σ_v. When σ_h ? 0.02 and σ_v ? 0.1, the fluids prefer the two-roll mode where two rolls make the fluids to move upwards in the middle of the box. While σ_h ? 0.02 and σ_v ? 0.2, the fluids prefer the other two-roll mode which makes the fluid to move downwards in the middle of the box.     

Entropy generation for compressible natural convection with high gradient temperature in a square cavity

Entropy generation due to heat transfer and fluid friction irreversibility has been investigated in a square cavity subjected to different side wall temperatures for compressible and incompressible natural convection flows. Based on the obtained velocity and temperature values, the distributions of local entropy generation, average entropy generation and average Bejan number are determined and compared for compressible and incompressible regimes. It is found that the entropy generated for compressible flow always is more than incompressible flow. The study is performed for Ra = 10⁴–10⁸, ε = 0.01(incompressible regime) and 0.6 (compressible regime), Ge = 10⁻⁵ and Pr = 0.7.     

Lattice Boltzmann simulation of natural convection in an open ended cavity

Natural convection in an open ended cavity is simulated using Lattice Boltzmann Method (LBM). The paper is intended to address the physics of flow and heat transfer in open end cavities and close end slots. The flow is induced into the cavity by buoyancy force due to a heated vertical wall. Also, the paper demonstrated that open boundary conditions used at the opening of the cavity is reliable, where the predicted results are similar to conventional CFD method (finite volume method, FVM) predictions. Prandtl number (Pr) is fixed to 0.71 (air) while Rayleigh number (Ra) and aspect ratio (A) of the cavity are changed in the range of 10⁴–10⁶ and of 0.5–10, respectively. It is found that the rate of heat transfer deceases asymptotically as the aspect ratio increases and may reach conduction limit for large aspect ratio. The flow evaluation in the cavity starts with recirculation inside the cavity, as the time proceeds the flow inside the cavity communicates with the ambient.     

Laminar natural convection in an air-filled square cavity with partitions on the top wall

The laminar natural convection in an air-filled square cavity with a partition on the top wall was experimentally investigated. Temperature measurements and flow visualizations were performed for cases with heated and cooled vertical walls (corresponding to a global Grashof number Gr_H of approximately 1.3 × 10⁸) and non-dimensional top wall temperatures θ_T of 0.56 (insulated) to 2.3. Experiments were performed with an aluminum partition with non-dimensional height H_P/H of 0.0625 and 0.125 attached to the top wall at x/H = 0.1, 0.2, 0.4 and 0.6. The blockage effect and/or the thermal effect of the partition resulted in changes to the temperature and flow fields, but were mainly limited to the vicinity of the partition. The partition on the heated top wall resulted in a recirculating flow between the partition and the heated vertical wall. For a given partition height, the structure of this recirculating flow was dependent on the partition location and θ_T. A thermal boundary layer developed along the rear surface of the partition due to the thermal effect of the partition. The ambient temperature outside the boundary layer and Nu near the corner region was affected by the partition height due to the change in the recirculating flow and due to the thermal effect on the rear surface of the partition.     

Double-diffusive turbulent natural convection in a porous square cavity with opposing temperature and concentration gradients

This paper presents results for coupled heat and mass transport under laminar and turbulent flow regimes in porous cavities. Two driving mechanisms are considered to contribute to the overall momentum transport, namely temperature driven and concentration driven mass fluxes. Aiding and opposing flows are considered, where temperature and concentration gradients are either in the same direction or of different sign, respectively. Modeled equations are presented based on the double-decomposition concept, which considers both time fluctuations and spatial deviations about mean values. Turbulent transport is accounted for via a macroscopic version of the k–ε model. Variation of the cavity Nusselt and Sherwood numbers due to changes on N, where N is the ratio of solute to thermal Grashof numbers, is presented. Results indicate that for adding cases, mass and heat transfer across the cavity are enhanced faster than for cases with opposing temperature and concentration gradients. For the conditions here investigated, the use a turbulence model gave results for Nu and Sh that were nearly double when compared with laminar results for the same conditions.     

Estimation of computational grid for thermal convection simulation with lattice Boltzmann method

Accurate, quantitative but not empirical estimation of computational grids helps quickly formulate appropriate computational schemes and shorten the preprocessing of simulations. In this paper, some formulas are proposed to limit a certain range of computational grid N_L for the thermal convection simulations with double distribution function lattice Boltzmann method (DDF-LBM). These formulas are induced from the analysis of relationships among DDF-LBM mathematical limits, mesoscopic physic limits, and flow boundary layer limits, with certain nondimensional parameters Pr, Ra, and Ma. After discussing the essence of the common way in which Ma value is increased to enhance the simulating stability of DDF-LBM, it is confirmed that above formulas also benefit the equivalence between the grid number and increased Ma value. To verify the above formulas, the simulations of Rayleigh–Bénard convection in a square enclosure filled with air at Ra?=?10⁴–10⁸ have been performed. The results coincide well with those in other published references, which suggests the validity of the present study.