Lattice Boltzmann simulation of natural convection heat transfer in eccentric annulus

In this article, the natural convection flow in eccentric annulus is simulated numerically by Lattice Boltzmann Model (LBM) based on double-population approach. A numerical strategy presents for dealing with curved boundaries of second order accuracy for both velocity and temperature fields. The effect of vertical, horizontal, and diagonal eccentricity at various locations is examined at Ra = 10⁴ and σ = 2. Velocity and temperature distributions as well as Nusselt number are obtained. The results show that the average Nusselt number increases when the inner cylinder moves downward regardless of the radial position. The validation with previous studies shows that double-population approach can evaluate the velocity and temperature fields in curved boundaries with a good accuracy.     

Lattice Boltzmann simulation of mixed convection heat transfer in a corrugated wall cavity utilizing water‐based nanofluids

In the present study, the effects of Cu and CuO nanoparticles' presence on mixed convection heat transfer in a lid‐driven cavity with a corrugated wall are investigated using the lattice Boltzmann method. The boundary fitting method with second‐order accuracy at both velocity and temperature fields is used to simulate the curved boundaries in the LBM. The problem is investigated for different Richardson numbers (0.1–10), volume fractions of nanoparticles (0–0.05), curve amplitudes (0.05–0.25), and phase shifts of corrugated wall (0–270) when the Reynolds number is equal to 25. The volume fraction of added nanoparticles to the water‐based fluid is less than 0.05 to make dilute suspensions. Results show that adding nanoparticles enhances the rate of heat transfer. It is found that nanoparticles have significant effects on both fluid flow and heat transfer of the mixed convection, especially for low Richardson numbers. A comparison between Cu and CuO nanoparticles shows the Cu nanoparticles have a better effect on heat transfer enhancement for all tested conditions. The results also represent the effective role of a corrugated wall on the rate of nanofluid heat transfer. It is observed that increasing the wavy wall's amplitude leads to a decrease of the average Nusselt numberfor a high Richardson number. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21024     

Lattice Boltzmann simulation of substrate flow past a cylinder with PSB biofilm for bio-hydrogen production

Based on hydrogen production by photosynthetic bacteria (PSB) in biofilm bioreactor, in the present study, a substrate solution with specific inlet concentration flowing past a circular cylinder with biochemical reaction in an attached thin PSB biofilm is numerically simulated by applying the lattice Boltzmann method (LBM). A non-equilibrium extrapolation method is employed to handle the velocity and concentration curved boundary. The model is validated by available theoretical and numerical results in terms of the drag and lift coefficients and concentration profiles. The good agreement demonstrated that LBM is an effective method to simulate nonlinear biochemical reaction systems with curved boundary. The velocity profile and concentration distributions of the substrate and hydrogen are determined, and the effect of Reynolds number on mass transfer characteristics is also discussed by introducing Sherwood number. The simulation results show that for both the substrate and product the concentration extension along X- and Y-directions decrease with increasing Reynolds number. The highest hydrogen concentration is obtained at the back of the cylinder. Furthermore, increasing Reynolds number results in decreasing substrate consumption efficiency, while hydrogen yield almost keeps a steady value.     

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.     

Lattice Boltzmann simulation of natural convection heat transfer in an elliptical-triangular annulus

A numerical study for steady-state, laminar natural convection in a horizontal annulus between a heated triangular inner cylinder and cold elliptical outer cylinder was investigated using lattice Boltzmann method. Both inner and outer surfaces are maintained at the constant temperature and air is the working fluid. Study is carried out for Rayleigh numbers ranging from 1.0 × 10³ to 5.0 × 10⁵. The effects of different aspect ratios and elliptical cylinder orientation were studied at different Rayleigh numbers. The local and average Nusselt numbers and percentage of increment heat transfer rate were presented. The average Nusselt number was correlated. The results show that by decreasing the value of aspect ratio and/or increasing the Rayleigh number, the Nusselt number increases. Also the heat transfer rate increases when the ellipse positioned vertically.     

Lattice Boltzmann simulation of natural convection and heat transfer from multiple heated blocks

This study is aimed to investigate the natural convection heat transfer from discrete heat sources (similar to heated microchips) using Bhatnagar‐Gross‐Krook lattice Boltzmann method via graphics process unit computing. The simulation is carried out separately for three and six heated blocks model for different Rayleigh numbers and fixed Prandtl number, $Pr=0.71$ (air). The uniformly heated blocks are placed at the bottom wall inside a rectangular enclosure. The enclosure is maintained by the cold temperature at its left and right walls. The top and bottom surface is maintained by adiabatic conditions apart from the regions where blocks are attached to the bottom wall. The numerical code is validated with the benchmark heat transfer problem of side‐heated square cavity as well as with an experimental study for one discrete heat source. The rate of heat transfer is presented in terms of the local Nusselt and average Nusselt number for each block. It is found that the heat transfer rate becomes maximized in the leftmost and rightmost blocks due to the adjacent cold walls. It is found that the number of blocks and their positions play a substantial role in determining their collective performance on the heat transfer rate.     

Lattice Boltzmann simulation of natural convection in tall enclosures using water/SiO2 nanofluid

Natural convection in enclosures using water/SiO₂ nanofluid is simulated with Lattice Boltzmann method (LBM). This investigation compared with other numerical methods and found to be in excellent agreement. This study has been carried out for the pertinent parameters in the following ranges: the Rayleigh number of base fluid, Ra = 10³-10⁵, the volumetric fraction of nanoparticles between 0 and 4% and aspect ratio (A) of the enclosure between 0.5 and 2. The thermal conductivity of nanofluids is obtained on basis of experimental data. The comparisons show that the average Nusselt number increases with volume fraction for the whole range of Rayleigh numbers and aspect ratios. Also the effect of nanoparticles on heat transfer augments as the enclosure aspect ratio increases.     

Lattice Boltzmann simulation of mixed convection in an inclined cavity with a wavy wall

In the present study, the effect of inclination on mixed convection heat transfer and fluid flow in a lid‐driven cavity with a wavy wall is investigated using the lattice Boltzmann method. The double‐population approach with second‐order accuracy at velocity and temperature fields is used to simulate the curved boundary in the lattice Boltzmann method. The problem is investigated for different Richardson numbers (0.1 ≤ Ri ≤ 10), curve amplitudes (0.05 ≤ A ≤ 0.25), and inclination angles (0 ≤ θ ≤ 180) when the Reynolds number is equal to 100. Results show that the inclination phenomenon has important effects on both flow and temperature fields at high Richardson numbers. It is also found that the inclination loses its role on mixed convection heat transfer from the wavy wall by the increase of the curve amplitude of the wavy wall for all Richardson numbers. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21005     

Lattice Boltzmann simulation of heat conduction problems in non‐isothermally heated enclosures

A numerical study following the lattice Boltzmann method (LBM) is performed to solve transient heat conduction problems with and without volumetric heat generation/absorption in 2D and 3D Cartesian geometries. Uniform lattices are considered for both geometries. To validate the correctness of LBM, a finite difference method (FDM) is also used to solve the 2D problem without heat generation/absorption and results are compared with that of LBM. For both 2D and 3D geometries one of the walls is heated and cooled with a sinusoidal function and the rest of the walls are cooled isothermally. Effects of amplitude of the sinusoidal function and volumetric heat generation/absorption on temperature profiles are analyzed. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20406     

Lattice Boltzmann simulation of nanofluid in lid-driven cavity

Lattice Boltzmann Method is applied to investigate the mixed convection flows utilizing nanofluids in a lid-driven cavity. The fluid in the cavity is a water-based nanofluid containing Cu, Cuo or Al₂O₃ nanoparticles. The effects of Reynolds number and solid volume fraction for different nanofluids on hydrodynamic and thermal characteristics are investigated. The effective thermal conductivity and viscosity of nanofluid are calculated by Chon and Brinkman models, respectively. The results indicate that the effects of solid volume fraction grow stronger sequentially for Al₂O₃, Cuo and Cu. In addition the increases of Reynolds number leads to decrease the solid concentration effect.     

Lattice Boltzmann simulation of MHD mixed convection in a two‐sided lid‐driven square cavity

In this paper the effects of a magnetic field on mixed convection flow in a two‐sided lid‐driven cavity have been analyzed by the lattice Boltzmann method (LBM). The Hartmann number varied from Ha = 0 to 100. The study has been conducted for different Richardson numbers (Ri) from 0.01 to 100 while the direction of the magnetic field was investigated in the x‐direction. Consequences demonstrate that the heat transfer augments with an increment of the Richardson number for different Hartmann numbers for two cases. The heat transfer declines with the growth of the magnetic field for various Richardson numbers for two cases. The difference between the values of heat transfer for the two cases at variant parameters is negligible but the trend of fluid flow for the two cases is multifarious. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20402     

Simulation of laminar flow and convective heat transfer in conduits filled with porous media using Lattice Boltzmann Method

In the present work, laminar flow and convective heat transfer between two parallel plates of a conduit were simulated using Lattice Boltzmann Method (LBM). The conduit core was filled with a porous medium fully and partially. The effect of porous medium was considered by introducing the porosity into the equilibrium distribution. Viscous and inertia flow resistance effects of porous medium were incorporated in the form of force terms in the Boltzmann's equation. To simulate the temperature field, a simplified thermal lattice BGK model with doubled population method was employed. Comparing the results of the present study to the analytical solutions, a reasonable agreement was observed. The effects of various parameters like Darcy number, porous medium thickness, etc. on the conduit thermal performance were investigated. It was found that all these parameters had significant influence on thermal performance of the channel in certain conditions.     

液滴在化学非均匀表面上铺展的格子Boltzmann方法模拟

采用格子Boltzmann方法模拟二维液滴在非均匀表面上的铺展。非均匀表面由两块面积相等但润湿性不同的均匀表面拼接而成,左半部分为亲水表面(θeq=35.00°),右半部分为疏水表面(θeq=115.00°)。液滴初始为圆形,位于亲疏水表面交界处。由于表面两侧平衡接触角θeq相差较大,铺展的Young驱动力FY=γlg(cosθeq-cosθD)有显著差异,因而液滴左右呈现出不同的铺展规律。模拟结果显示,铺展可分为三个阶段:第一阶段,液滴向两侧铺展直至疏水侧铺展速度为0,但亲水侧铺展速度始终快于疏水侧;第二阶段,整个液滴向亲水侧运动,直到液滴右侧到达亲疏水表面交界处;第三阶段,液滴在亲水表面铺展直至平衡。当液滴初始位于亲水侧或疏水侧,且其质心与亲疏水表面交界处的横向距离小于50lu时,液滴呈现出三种不同铺展形式,然而由于亲水侧更大的Young驱动力,最终的平衡液滴均位于亲水侧。     

流体动力学的格子Boltzmann方法及其具体实现

格子气自动机和格子Ｂｏｌｔｚｍａｎｎ方法的迅速发展提供了一类求解流体力学问题的新方法，本文中，我们介绍了格子Ｂｏｌｔｚｍａｎｎ方法，解决了格子气方法中的缺点，通过选择适当平衡分布及其参数，导出了Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程，并得到了声速一粘性系数，最后在微机上模拟了平面平板中无障碍物流问题及绕矩形障碍块的流动问题，表明该模型有格子气方法及其它的数值方法所没有的优点，计算更精确和直观。     

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 analysis of gas tightness of seals in pSOFCs based on Lattice Boltzmann Method simulation

To better understand the leakage mechanism of compressive seals in planar solid oxide fuel cells (pSOFCs), a theoretical method of leakage prediction is proposed that combines three numerical techniques. The Lattice-Boltzmann method was introduced to simulate the nonlinear flow in rough wall interfacial gaps due to its flexibility when dealing with flow problems related to complex boundaries. A numerical three-dimensional (3D) rough-surface generation technique was applied for the geometry configuration of interface gaps, and finite element analysis was adopted for micro-contact mechanics of single asperities to determine the gap height under stress. Based on this method, the 3D flow characteristics of the gas in interface gaps were numerically studied, and two important dimensionless flow factors (the flow factor Φ_σ of roughness and the flow factor Φ_h of height) were proposed. All numerical results were fitted as dimensionless criteria for calculating the interface leakage rate. These criteria can be directly used to predict the leakage rate of a given compressive seal under specific working conditions without relying on any experimental empirical formula. Furthermore, leakage rate predictions were compared to existing experimental data and good agreement was obtained, corroborating the accuracy of the method. In addition, the effects of influencing parameters on leakage according to the rate-temperature relationship were discussed. Several important conclusions were drawn to guide the design of compressive seals for pSOFC.     

Solution of transient heat transfer in graded-material fins of varying thickness under step changes in boundary conditions using the Lattice Boltzmann Method

Graded materials (GM) possess superior thermo-mechanical properties, which are not feasible to obtain with homogeneous materials (HM), and hence in this paper, the transient response of a longitudinal fin of varying geometry made up of GM is reported. The temperature-dependent convection coefficient and heat generation parameters are considered to account for real-world high-temperature applications of fins. Fin material properties such as density and specific heat remain constant while thermal conductivity is assumed to vary axially based on four different physically possible variations namely, linear, quadratic, power, and exponential variations. The typical nonlinear differential equation obtained for fins was solved by using a mesoscopic scale-based particle tracking method called the Lattice Boltzmann method. The Lattice Boltzmann solver has been implemented in form of an in-house MATLAB code and validated with existing results, thereafter it is developed for solving the foregoing problems. The results obtained are reported for rectangular, triangular, convex, and concave profiles under step change in base temperature and base heat flux. The performance of graded fins is investigated in terms of time required to attain steady-state and fin tip temperature which are inherent design parameters in the case of the transient fin. Inhomogeneity index and profile function have a significant effect on the performance of fin in terms of resistance to heat flow. Hereby, in comparison with HM fins, GM fins have lower resistance to heat flow irrespective of fin profiles. Concurrently, comparative analysis for fins of different profiles made of HM and GM is also done to facilitate the designer in selecting the most appropriate fins.     

Lattice Boltzmann simulation of tree-shaped fins enhanced melting heat transfer

Abstract

A thermal lattice Boltzmann model is developed to simulate the melting process with natural convection in a cavity filled with tree-shaped solid fins, in which the velocity field and temperature field distribution functions are considered. The present model incorporates the total enthalpy and a free parameter in the equilibrium distribution function to handle conjugate heat transfer. The results indicate that natural convection of liquid phase change material (PCM) plays a significant role in the melting heat transfer of PCM. Increasing the number of branching levels leads to a more rapid melting process, and selecting appropriate bifurcation angle has more efficient heat transfer performance.     

A numerical study of natural convection heat transfer in a vertically eccentric spherical annulus

The results of a numerical investigation of the natural convection process between isothermal vertically eccentric spheres with hotter inner core, are being presented. The Grashof and the Prandtl numbers have been kept constant at 4×10⁴ and 10 respectively. Eccentricities varying from −0.75 to +0.75 have been studied. From the numerical solution, it is possible to explain the average results obtained previously for the regime where the steady crescent flow pattern exists. Negative eccentricities have been found to enhance convection while positive eccentricities have the reverse effect. Results also show that heat transfer actually increases slightly for very high positive eccentricities where conduction plays an important role.     

重力场下通道内毛细上升过程的格子Boltzmann模拟

采用格子Boltzmann方法中Shan-Chen伪势模型对重力场下通道中液体毛细上升过程进行了数值模拟,得到其流场分布,分析了通道个数、通道宽度与通道放置角度对通道内液柱上升过程的影响。数值结果表明,不同个数的通道毛细抽吸的最终高度差异不大,但通道个数对每个通道内液体毛细上升过程有一定影响。在重力场下,通道内液体沿通道方向的毛细上升长度随着通道倾斜角度的增大而增大,液柱稳定的竖直高度先增大后减小。