Computation of Turbulent Natural Convection in a Rectangular Cavity with the Lattice Boltzmann Method

A numerical study of a turbulent natural convection in a rectangular cavity with the lattice Boltzmann method (LBM) is presented. The primary emphasis of the present study is placed on investigation of accuracy and numerical stability of the LBM for the turbulent natural-convection flow. A HYBRID method in which the thermal equation is solved by the conventional Reynolds-averaged Navier-Stokes equation (RANS) method while the conservation of mass and momentum equations are resolved by the LBM is employed in the present study. The elliptic-relaxation model is employed for the turbulence model and the turbulent heat fluxes are treated by the algebraic flux model. All the governing equations are discretized on a cell-centered, nonuniform grid using the finite-volume method. The convection terms are treated by a second-order central-difference scheme with the deferred correction method to ensure accuracy and stability of solutions. The present LBM is applied to the prediction of a turbulent natural convection in a rectangular cavity and the computed results are compared with the experimental data commonly used for the validation of turbulence models and those by the conventional finite-volume method. It is shown that the LBM with the present HYBRID thermal model predicts mean velocity components and turbulent quantities which are as good as those by the conventional finite-volume method. It is also found that the accuracy and stability of the solution is significantly affected by the treatment of the convection term, especially near the wall.     

MHD Turbulent and Laminar Natural Convection in a Square Cavity utilizing Lattice Boltzmann Method

In this study, the lattice Boltzmann method was used to solve the turbulent and laminar natural convection in a square cavity. In this paper a fluid with Pr = 6.2 and different Rayleigh numbers (Ra = 10³, 10⁴,10⁵ for laminar flow and Ra = 10⁷, 10⁸,10⁹ for turbulent flow) in the presence of a magnetic field (Ha = 0, 25, 50, and 100) was investigated. (Results show that the magnetic field drops the heat transfer in the laminar flow as the heat transfer behaves erratically toward the presence of a magnetic field in a turbulent flow. Moreover, the effect of the magnetic field is marginal for a turbulent flow in contrast with a laminar flow.The greatest influence of the magnetic field is observed at Ra = 10⁵ from Ha = 0 to 100 as the heat transfer decreases significantly.     

Comparative Analysis of Thermal Models in the Lattice Boltzmann Method for the Simulation of Natural Convection in a Square Cavity

In this article, a comparative analysis of thermal models in the lattice Boltzmann method for the simulation of natural convection in a square cavity is presented. A hybrid method, in which the thermal equation is solved by the Navier-Stokes equation method while the mass and momentum equations are solved by the lattice Boltzmann method (LBM), is introduced and its merits are explained. All the governing equations are discretized on a cell-centered, nonuniform grid using the finite-volume method. The convection terms are treated by a second-order central-difference scheme with a deferred-correction method to ensure accuracy of solutions. The resulting algebraic equations are solved by a strongly implicit procedure. The hybrid method is applied to the simulation of natural convection in a square cavity and the predicted results are compared with the benchmark solutions given in the literatures. The predicted results are also compared with those by the double-population LBM and by the Navier-Stokes equation method. In general, the present hybrid method is as accurate as the Navier-Stokes equation method and the double-population LBM. The hybrid method shows better convergence and stability than the double-population LBM. These observations indicate that this hybrid method is an efficient and economic method for the simulation of incompressible fluid flow and heat transfer problems involving complex geometries.     

A Multiple-Relaxation-Time Lattice Boltzmann Model for Natural Convection in a Hydrodynamically and Thermally Anisotropic Porous Medium under Local Thermal Non-Equilibrium Conditions

To investigate the natural convective process in a hydrodynamically and thermally anisotropic porous medium at the representative elementary volume(REV) scale, the present work presented a multiplerelaxation-time lattice Boltzmann method(MRT-LBM) based on the assumption of local thermal non-equilibrium conditions(LTNE). Three sets of distribution function were used to solve the coupled momentum and heat transfer equations. One set was used to compute the flow field based on the generalized non-D...     

Numerical Investigation of the Magnetic Field Effects on the Entropy Generation and Heat Transfer in a Nanofluid Filled Cavity with Natural Convection

This paper presents a numerical investigation of the entropy generation and heat transfer in a ferrofluid (water and 4% Fe₃O₄ nanoparticles) filled cavity with natural convection using a two phase mixture model and control volume technique. The effect of applying a nonuniform magnetic field on the entropy generation and heat transfer in the cavity and also the interaction of magnetic force and the buoyancy force are investigated. Based on the obtained results, applying a magnetic field will enhance the heat transfer mechanism. Furthermore, by applying the nonuniform magnetic field on the ferrofluid filled cavity with natural convection, the total entropy generation is decreased considerably at higher Rayleigh numbers. Therefore, applying a magnetic field can be considered as a suitable method for entropy generation minimization in order to have high efficiency in the system.     

Lattice Boltzmann Modeling of Thermal Explosion in Natural Convection Conditions

Lattice Boltzmann (LB) computational code developed by the authors is used to simulate the development of thermal explosion in reactive mixtures subjected to convection. The work demonstrates an LB modeling application to reactive flows by considering practically important combustion and fire research problem. The problem of convection-affected thermal explosion is of particular interest from both theoretical and practical points of view. Critical conditions for convection-affected thermal explosion are found in the range of Rayleigh numbers 10³–10⁸.     

Numerical Simulation of Natural Convection in a Triangle Cavity Filled with Nanofluids Using Tiwari and Das' Model: Effects of Heat Flux

In this article, we present a fully higher‐order compact (FHOC) finite difference method to investigate the effects of heat flux on natural convection of nanofluids in a right‐angle triangle cavity, where the left vertical side is heated with constant heat flux both partially and throughout the entire wall, the inclined wall is cooled, and the rest of walls are kept adiabatic. The Darcy flow and the Tiwari and Das’ nanofluid models are considered. Investigations with four types of nanofluids were made for different values of Rayleigh numbers with the range of 100 ≤ Ra ≤ 50,000, size of heat flux as 0.1 ≤ ε ≤ 1.0, enclosure aspect ratio as 0.5 ≤ AR ≤ 2.0, and solid volume fraction parameter of nanofluids with the range of 0% ≤ ? ≤ 20%. Results show that the average heat transfer rate increases significantly as particle volume fraction and Rayleigh numbers increase, and the maximum value of average Nusselt number is obtained by decreasing the enclosure aspect ratio. The results also show that the average heat transfer decreases with an increase in the length of the heater. Furthermore, multiple correlations in terms of the Rayleigh numbers and the solid volume fraction of four types of nanoparticles have been established in a general form.     

Lattice Boltzmann Simulation of Natural Convection in an Inclined Square Cavity with Spatial Temperature Variation

In this paper, natural convection heat transfer in an inclined square cavity filled with pure air (Pr = 0.71) was numerically analyzed with the lattice Boltzmann method. The heat source element is symmetrically embedded over the center of the bottom wall, and its temperature varies sinusoidally along the length. The top and the rest part of the bottom wall are adiabatic while the sidewalls are fixed at a low temperature. The influences of heat source length, inclination angle, and Rayleigh number (Ra) on flow and heat transfer were investigated. The Nusselt number (Nu) distributions on the heat source surface, the streamlines, and the isotherms were presented. The results show that the inclination angle and heat source length have a significant impact on the flow and temperature fields and the heat transfer performance at high Rayleigh numbers. In addition, the average Nu firstly increases with γ and reaches a local maximum at around γ = 45°, then decreases with increasing γ and reaches minimum at γ = 180° in the cavity with ? = 0.4. Similar behaviors are observed for ? = 0.2 at Ra = 10⁴. Moreover, nonuniform heating produces a significant different type of average Nu and two local minimum average Nu values are observed at around γ = 45° and γ = 180° for Ra = 10⁵ in the cavity with ? = 0.2.     

Lattice Boltzmann Simulation of Natural Convection in a Square Cavity with Linearly Heated Wall(s)

In this study, the lattice Boltzmann method is used in order to investigate the natural convection in a cavity with linearly heated wall(s). The bottom wall is heated uniformly and the vertical wall(s) are heated linearly, whereas the top wall is insulated. Investigation has been conducted for Rayleigh numbers of 10³ to 10⁵, while Prandtl number is varied from 0.7 to 10. The effects of an increase in Rayleigh number and Prandtl number on streamlines, isotherm counters, local Nusselt number and average Nusselt number are depicted. It has been observed that the average Nusselt number at the bottom wall augments with an increase in Prandtl number.     

Effects of Heating Location and Size on Natural Convection in Partially Heated Open-Ended Enclosure by Using Lattice Boltzmann Method

Natural convection heat transfer in an square enclosure, consisting of a partially heated west wall with east end open to ambient, is investigated numerically by using an in-house computational fluid dynamics solver based on thermal lattice Boltzmann method. In particular, the influences of Rayleigh number (10³–10⁶), heating location (bottom, middle, and top) on west wall, and dimensionless heating length (0.25–0.75) on momentum and heat transfer characteristics of air are presented and discussed. The streamline patterns show bifurcation at the lowest Rayleigh number for bottom and middle heating, whereas at the highest Rayleigh number, all heating positions yield bifurcation and elongation of flow patterns with a secondary vortex near the lower side of open end. The middle and bottom heating locations show a linear increase in Nusselt number with heater size, whereas inverse dependence is seen for top heating. The maximum heat transfer is observed in the case of middle heating. As expected, average Nusselt number increased with increasing Rayleigh number. Finally, the functional dependence of the average Nusselt number on flow governing parameters (Rayleigh number and heating length) for different heating locations is presented as a simple predictive empirical relationship.     

Lattice Boltzmann Method Based Simulation of Natural Convection in Partially Open Enclosure

A thermal lattice Boltzmann method‐based analysis was performed to numerically investigate the heat transfer by natural convection from an enclosure with a large vertical side opening. The height of the opening was less than the enclosure height and the vertical wall opposite to the opening was maintained at constant temperature. A parametric study was carried out for different values of Rayleigh number (Ra) ranging from 10³ to 10⁵ with air as the working fluid for three opening sizes and three opening locations. The Prandtl number was fixed at 0.71 and the enclosure aspect ratio was also fixed at 2 in all calculations. With Boussinesq approximation, the temperature distribution and stream functions in the enclosure were predicted. The profile of the normal velocity component at the opening location was determined. The opening size affects the stratification and recirculation pattern within the enclosure. The average Nusselt number at the heated wall was determined for all cases. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21110     

Numerical Investigation of the Entropy Generation Due to Natural Convection in a Partially Heated Square Cavity Filled With Nanofluids

A comprehensive numerical investigation has been carried out on the heat transfer performance and entropy generation within a rectangular cavity containing nanofluid. The cavity consists of two heat sources located on the bottom and a side wall. The effects of influential parameters including type and concentration of nanoparticles, radius of corner, width and thickness of heaters, heater distance from corners and aspect ratio of the enclosure were studied. The results showed that the Nusselt number enhanced by increasing the aspect ratio of the cavity, the distance of heaters from the corners, and concentration of nanoparticle and applying Cu as nanoparticle while it reduced by increasing the radius of the corner and the width and thickness of the heat sources. The entropy generation was found to be profoundly minimized by lowering the Rayleigh number. In addition, the entropy generation was attenuated by increasing the Eckert number, corner radius, the distance from the corner and concentration of nanoparticles and using Al₂O₃ as nanoparticle. On the other hand, increasing the aspect ratio of the cavity, width and thickness of the heaters augmented the entropy generation. Interestingly, the entropy generation of the system was lowered by just increasing the distance of one heater from the corner, whereas increasing the thickness and width of one heater resulted in larger entropy generation. This study provides valuable insight into the change in the amount of heat transfer and entropy by altering the geometry as well as fluid properties.     

Numerical Investigation of Natural Convection in an Enclosure Filled with Porous Medium Under Magnetic Field

In this study, natural convection in an enclosure filled with a fluid-saturated porous medium in a strong magnetic field is investigated numerically. Two physical models are considered. One is heated from the bottom and cooled from the top (Model A), and the other is heated from the left side vertical wall and cooled from the opposite wall (Model B). An electric coil is set below this enclosure to generate a magnetic field. The Brinkman-Forchheimer extended Darcy model is used to solve the momentum equations, and the energy equations for the fluid and solid are solved with the local thermal nonequilibrium (LTNE) model. The linkage between velocity and pressure is handled with the SIMPLE algorithm. Computations are performed for a range of Darcy number from 10^?5 to 10^?1, Rayleigh number from 10³ to 10⁵, and magnetic force parameter γ from 0 to 100. The results show that the magnetic force has significant effect on the flow field and heat transfer in the fluid-saturated porous medium.     

A Hybrid Lattice Boltzmann and Finite-Volume Method for Melting with Convection

A hybrid lattice Boltzmann and finite-volume model is proposed to solve the natural-convection-controlled melting problem. The lattice Boltzmann method (LBM) is applied to solve the velocity field, while the temperature field is obtained by the finite-volume method (FVM). The D2Q9 model and finite-difference velocity gradient boundary condition are used in the LBM and the SIMPLE algorithm with QUICK scheme is employed in the FVM. An interfacial tracking model based on energy balance at the interface is applied to obtain the location of the solid–liquid interface. The results from the present hybrid method are validated with experimental results, and good agreement is obtained.     

Simulation of Natural Convection in the Presence of Volumetric Radiation Using the Lattice Boltzmann Method

This article deals with the application of the lattice Boltzmann method (LBM) to the analysis of natural convection in the presence of volumetric radiation in a square cavity containing an absorbing, emitting, and scattering medium. Separate particle distribution functions in the LBM are used to calculate the density and velocity fields and the thermal field. The radiative term of the energy equation is computed using the finite-volume method. Streamlines, isotherms, and Nusselt number are analyzed for the effects of different parameters such as Rayleigh number, convection-radiation parameter, extinction coefficient, and scattering albedo.     

Numerical Prediction of Natural Convection Occurring in Building Components: A Double-Population Lattice Boltzmann Method

In this article, a double-population thermal lattice Boltzmann method is proposed to solve the problem of the heated cavity with imposed temperatures. This family of problems can be considered as a test model for building physics application. A Taylor series expansion- and least-square-based lattice Boltzmann method (TLLBM) has been implemented in order to use a non-uniform mesh. This allowed us to investigate, at reasonable computational cost, the laminar and transitional flow fields (10³ ≤ Ra ≤ 10⁸). The numerical results, concerning the heat and mass transfers in the cases tested, are in good agreement with those from the literature. In order to demonstrate the possibilities of the method described in the article, applications are described covering double-skin facades and solar collectors or local heaters.     

Natural Convection in an Enclosure with a Partially Active Magnetic Field

Chaotic natural convection flow of a molten gallium in a square enclosure with the upper and lower surfaces being insulated was studied by two-dimensional numerical simulation. Constant temperatures are imposed along the left and right walls of the enclosure with a volumetrically heated enclosure. In addition, a nonuniform partially active magnetic field is applied in a vertical direction. The flux lines spread out into a fringing field so the effective cross-sectional area of the gap is larger than that of the pole face. A chaotic regime is considered under steady state boundary condition. This study was done for an internal Rayleigh number of 10⁷, external Rayleigh number of 10⁵, and Prandtl number of 0.024. The study covers various magnet pole effect widths of 1/4, 1/2, and 3/4 from enclosure width and the magnetic field strength ranges 0.0 ≤ B _o  ≤ 10 Tesla. The transport equations for continuity, momentum, and energy are solved. The numerical results are reported for the effect of the partially active magnetic field on the velocity vectors, counters of temperature, streamline, and heat transfer coefficient. The numerical study shows that a magnetic field is damping chaotic oscillation behavior and decreases the amplitude of oscillation. Also, at a certain magnetic field strength the chaotic flow tend to becomes periodic flow at certain amplitude and frequency, and at high magnetic field strength the flow in the square enclosure flow tends to become steady laminar flow with stable average Nusselt number values; so, the random oscillation behavior disappeared. The effect of a nonuniform magnetic field tends to push the fluid to flow away from magnetic field region.     

The Use of Thermal Lattice Boltzmann Numerical Scheme for Particle-Laden Channel Flow with a Cavity

In this article, particle-laden flow in a channel with heated cavity has been investigated. Calculations were performed using a point force scheme for particle dynamics, while the process of fluid renewal was modeled using the double-population thermal lattice Boltzmann method. Point-particle formulation accounts for the finite-size dispersed phase and the forces acting on the particles were modeled through drag force correlations. Two-way interactions of solid-fluid calculation were considered by adding an external force term for feedback that forced particles in the evolution of fluid distribution function. The method was first validated with steady state flow in a channel with cavity in the presence and absence of a heat source. It was then applied to mixed convection flow laden with particles at various Grashof numbers. The particle dispersion characteristics were examined in detail, where the particle removal rate from cavity upon cavity aspect ratio was emphasized. The effect of the Reynolds number on particle distribution was further investigated numerically by varying the speed of inlet flow into the channel.     

Natural Convection in a Nanofluids-Filled Portioned Cavity: The Lattice-Boltzmann Method

Numerical simulation of natural convection in a nanofluids-filled partitioned square cavity is presented. Two independent solvers, an in-house LBE-BGK code and the commercially available software CFD-ACE, are used to achieve this goal. While the partitioning plates are generating heat at a uniform temperature, the vertical walls are isothermally cooled allowing for the removal of the internally generated heat with the horizontal walls being adiabatic. While the particle volume fraction is kept constant at 5%, the effective Rayleigh number, the length, and the orientation of the partition have been parametrically varied from 10³–10⁷, 0.25H–0.75H, and horizontal to vertical, respectively.     

Optimal Natural Convection Heat Transfer Improvement by Combining Periodic Heating Temperature,Cavity Inclination,and Nanofluid

Natural convection within a square inclined cavity filled with Al₂O₃–water nanofluid is investigated numerically. The temperature of the cooled surface is maintained constant, while that of the opposite surface (heating temperature) is varied sinusoidally in time. The remaining walls are considered adiabatic. The parameters governing the problem are the amplitude and the period of the variable temperature, the Rayleigh number, the inclination of the cavity, and the solid volume fraction. A substantial enhancement of heat transfer is obtained by combining the beneficial effects of the variable heating temperature (via its period and amplitude), the inclination of the cavity, and the nanoparticles fraction. In comparison with the constant heating conditions, it is found that both the variable heating temperature and the inclination of the cavity may lead to drastic changes in the flow structure and the corresponding heat transfer. The resonance phenomenon, observed for critical periods of the exciting temperature, is amplified by adding Al₂O₃ nanoparticles to the base fluid.