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.     

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.     

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.     

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     

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.     

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.     

Effects of Magnetic Field and Inclination on Natural Convection in a Cavity Filled with Nanofluids by a Double Multiple-Relaxation-Time Thermal Lattice Boltzmann Method

Abstract

The present study numerically investigates the magneto-hydrodynamic flow and heat transfer of copper (Cu)-water nanofluids in an inclined cavity with one heat and one cold source. Simulations have been done via double multiple-relaxation-time thermal lattice Boltzmann method. Impacts of Hartmann number, Rayleigh number, inclination angle and the volume fraction of nanoparticles on the fluid flow and heat transfer performance are illustrated in terms of streamlines, isotherms, local, and average Nusselt numbers. Outputs demonstrate that the average Nusselt number decreases remarkably first as the inclination angle increases and then the average Nusselt number increases continuously and approaches a maximum value at a certain inclination angle for high Rayleigh numbers. In addition, the position where the average Nusselt number is maximized moves toward the lower inclination angle with increasing the Hartmann number for high Rayleigh numbers.     

封闭方腔自然对流换热的研究

论述和分析了封闭方腔自然对流换热的研究进展,研究了采用商业软件FLUENT对此模拟的方法以及换热规律研究的可行性,所获得的数值模拟结果与研究文献做了对比分析,其模拟结果是正确的,由此表明:采用FLUENT软件通过数值模拟方法不仅能获得封闭腔自然对流换热的结果,还能研究其换热规律,是解决封闭腔自然对流换热的有效工具。     

Lattice Boltzmann Simulation of Natural Convection in a Differentially Heated Square Enclosure Containing Heat Generating Low‐Prandtl Number Fluid

Lattice Boltzmann simulations were conducted for the free convective flow of a low‐Prandtl number (Pr = 0.0321) fluid with internal heat generation in a square enclosure having adiabatic top and bottom walls and isothermal side walls. The problem of free convection with volumetric heat source has represented itself in connection with advanced engineering applications, such as water‐cooled lithium–lead breeder blankets for nuclear fusion reactors and liquid metal sources of spallation neutrons for subcritical fission systems. A single relaxation time (SRT) thermal lattice Boltzmann method (LBM) was employed. While applying SRT, a D2Q9 model was used to simulate the flow field and temperature field. Results have been obtained for various Rayleigh numbers characterizing internal and external heating from 10³ to 10⁶. Flow and temperature fields in terms of stream function and isotherms in the enclosure were predicted for these cases. The temperature of the fluid in the enclosure was found higher than the heated wall temperature at high values of internal Rayleigh numbers. The internal heat generation affected the rate of heat transfer significantly as two convection loops are observed in the enclosure. The average Nusselt number at the heated and cold wall was determined for all the cases.     

二阶全展开ETG有限元方法在方腔自然对流模拟中的应用

应用二阶全展开ETG有限元方法离散求解N-S方程和能量方程,并以零初值方腔自然对流问题为例进行了数值模拟。计算了不同瑞利数条件下方腔自然对流的流场和温度场,最终达到的稳态结果与标准数值解符合很好,并且较好地反映了流场和温度场的时间演化过程,特剐是捕捉到了分叉前后流场中涡结构的变化。结果表明二阶全展开ETG有限元方法有较好的稳定性和较高的精度,在计算温度场和流场的时间演化过程方面有一定优点。     

Simulation of Thermal Radiation Effects on MHD Free Convection in a Square Cavity Using the Chebyshev Collocation Spectral Method

This article deals with the application of the Chebyshev collocation spectral method (CSM) to the analysis of thermal radiation effects on magnetohydrodynamics free convection in a square cavity. The improved projection scheme, which is based on the spectral methods, is applied to treat the coupling of the velocity and the pressure. The radiative transfer equation is angularly discretized by discrete ordinates method with an SRAP_N quadrature scheme, and then solved by CSM using the same grid system as in solving the flow field. Streamlines, isotherms, and Nusselt number are analyzed for the effects of various parameters, such as inclination angle of the magnetic field, Hartmann number, optical thickness, and scatter albedo.     

Lattice Boltzmann Simulation of Turbulent Natural Convection in Tall Enclosures Using Cu/Water Nanofluid

In this article, Lattice Boltzmann simulation of turbulent natural convection with large-eddy simulations (LES) in a square cavity, which is filled by water/copper nanofluid, has been investigated. The present results are validated by the consequences of an experimental research at Pr = 0.71 and Ra = 1.58 × 10⁹. Calculations are performed for high Rayleigh numbers (Ra = 10⁷–10⁹), low volume fractions of nanoparticles (0 ≤ ? ≤ 0.06), and three aspect ratios (A = 0.5, 1, and 2). In this investigation, we present that large-eddy turbulent nanofluid flow is modeled by the Lattice Boltzmann method (LBM) with a clear and simple statement. Effects of nanopartcles are displayed on streamlines, isotherm counters, local Nusselt number, and average Nusselt number. The average Nusselt number enhances with the augmentation of the nanoparticles volume fractions in the base fluid for multifarious aspect ratios and the Rayleigh numbers. Heat transfer declines with the increase in the aspect ratios in the base fluid, but the effects of nanopaticles are dissimilar for various aspect ratios at different Rayleigh numbers.     

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.     

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.     

Natural Convection Heat Transfer Enhancement in a Square Cavity Periodically Cooled from Above

The present article reports numerical results of natural convection within an air filled square cavity with its horizontal walls submitted to different heating models. The temperature of the bottom horizontal surface (hot temperature) is maintained constant, while that of the opposite surface (cold temperature) is varied sinusoidally with time. The remaining vertical walls are considered adiabatic. The parameters governing the problem are the amplitude (0 ≤ a ≤ 0.8) and the period (τ ≥ 0.001) of the variable temperature, the Rayleigh number (10³ ≤ Ra ≤ 7 × 10⁶), and the Prandtl number (Pr = 0.71). In constant cooling conditions (a = 0), up to three different solutions (monocellular flow MF, bicellular vertical flow BVF, and bicellular horizontal flow BHF) are obtained. Their existence ranges are delineated and, in the limits of the existence range of each solution, the transitions observed are identified and described. In the variable cooling conditions, the effect of the amplitude and the period of the exciting temperature on fluid flow and heat transfer is examined in the case of the MF, and BHF for specific values of Ra. Results are presented in terms of Ψ _max (t), Ψ _min (t), Nu(t) and streamlines, heatlines, and isotherms during the evolutions of selected flow cycles. In comparison with the constant heating conditions, it is found that the variable cooling temperature could lead to a drastic change in the flow structure and the corresponding heat transfer, especially at specific low periods of the cold variable temperature. This leads to a resonance phenomenon characterized by an important increase in heat transfer by about 46.1% compared to the case of a constant cold temperature boundary condition.     

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...     

Evaluation of Turbulent Models for Natural Convection of Compressible Air in a Tall Cavity

Numerical simulation of turbulent natural convection of compressible air in a tall cavity is carried out. In order to evaluate the accuracy of turbulent models, various turbulent models are applied to solve the natural convection in a tall cavity that has different temperatures imposed on two opposing vertical walls. For the large-eddy simulation (LES) model, Smagorinsky subgrid scale (SGS) and dynamic Smagorinsky SGS are also applied to the same cases in order to investigate the differences in temperature and velocity caused by different turbulent models. It is found that the k–? model has a high accuracy of predicting velocity distribution at various sampled lines by comparing with experimental data at Rayleigh number of 2.03 × 10¹⁰ and 3.37 × 10¹⁰, while the LES model has good performance in predicting temperature distributions.     

一维热扩散方程的格子Boltzmann方法分析

针对一维热扩散方程的数学特点,建立了热扩散方程离散速度模型,构造了其平衡态分布函数,采用Chapman-Enskog展开和多尺度技术,构建了用于求解一维热扩散方程的D1Q3模型,进行了验证性数值实验。实验结果表明,模型的数值解与文献的解析解吻合良好,其两者的误差随网格细化而大幅度减小,从而说明了本文构建的格子Boltzmann模型可用于求解一维热扩散方程。     

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.