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.     

气固流化床的离散颗粒运动-碰撞解耦模型与模拟

基于分子动力学和气固两相流体动力学，建立流化床稠密气-固两相离散颗粒运动-碰撞解耦模型，采用硬球模拟方法处理颗粒与颗粒之间的碰撞，及大涡模拟方法处理气相湍流流动．单颗粒运动满足牛顿第二定律，颗粒相和气相相间相互作用的双向耦合由牛顿第三定律确定，数值模拟二维鼓泡流化床内稠密气-固两相流动，得到了气泡的形成、发展及颗粒的流化过程，计算结果表明颗粒弹性恢复系数影响气-固两相流动特性。     

Local thermal nonequilibrium conjugate natural convection heat transfer of nanofluids in a cavity partially filled with porous media using Buongiorno’s model

The natural convection heat transfer in a cavity filled with three layers of solid, porous medium, and free fluid is addressed. The porous medium and free fluid layers are filled with a nanofluid. The porous layer is modeled using the local thermal nonequilibrium (LTNE) model, considering the temperature difference between the solid porous matrix and the nanofluid phases. The nanofluid is modeled using the Buongiorno’s model incorporating the thermophoresis and Brownian motion effects. The governing equations are transformed into a set of nondimensional partial differential equations, and then solved using finite element method in a nonuniform grid. The effects of various nondimensional parameters are discussed. The results showed that the Brownian motion and thermophoresis effects result in significant concentration gradients of nanoparticles in the porous and free fluid layers. The increase in Rayleigh (Ra), Darcy (Da), the thermal conductivity ratios for the solid wall and solid porous matrix, i.e., K_r and R_k, enhanced the average Nusselt number. The increase in the convection interaction heat transfer parameter between the solid porous matrix and the nanofluid in the pores (H) increases the average Nusselt number in the solid porous matrix but decreases the average Nusselt number in the nanofluid phase of the porous layer.     

Numerical Investigation of Heat Transfer by CuO–Water Nanofluid in Rectangular Enclosures

This paper analyzes heat transfer and fluid flow of natural convection in inclined cavity filled with CuO–water nanofluid and differentially heated. Conservation of mass, momentum, and energy equations are solved numerically by a control volume finite-element method using the SIMPLER algorithm for pressure–velocity coupling. The Prandtl number is fixed at 7.02, corresponding to water. Aspect ratio and solid volume fraction are varied from 0.5 to 4 and from 0% to 4%, respectively. The inclination angle is varied from 0° to 90° and used as a control parameter to investigate flow mode-transition and the accompanying hysteresis phenomenon (multi-steady solutions). It is found that the efficiency of heat transfer is improved by the addition of nanoparticles into base fluid; however, there is an optimum solid volume fraction that maximizes the heat transfer rate. Numerical results show also that the diameter of solid particle is an important parameter that affects the heat transfer efficiency; its impact is more important than the concentration itself. Effects of inclination angle on streamlines and on thermal boundary layer are presented. Combined effects of aspect ratio and inclination angle on heat transfer and hysteresis region are analyzed.     

Effect of interfacial nanolayer on the effective thermal conductivity of nanoparticle-fluid mixture

Nanofluids, containing metal or nonmetal particles with nanometer sizes, exhibit much greater thermal conductivity than predictions. It has been proposed that interfacial structures formed by liquid molecule layering might play role. We investigated the impact of this interfacial nanolayer on the effective thermal conductivity of nanofluid. An expression for calculating enhanced thermal conductivity of nanofluid has been derived from the general solution of heat conduction equation in spherical coordinates and the equivalent hard sphere fluid model representing the microstructure of particle/liquid mixtures. The effects of nanolayer thickness, nanoparticle size, volume fraction, and thermal conductivity ratio of particle to fluid have been discussed. The predicted results are in good agreement with some recent available experimental data.     

球形腔式太阳能吸热器性能的数值研究

利用蒙特卡洛光线追踪法分析了6种不同开口比(D/d)的球形腔式吸热器的光学性能,并以光学模拟所得壁面能流作为热分析的边界条件导入CFD软件中,运用CFD软件对6种不同开口比的球形腔式吸热器进行流固耦合传热计算,获得了球形腔式吸热器和内部流体的温度场分布。通过计算球形腔式吸热器的反射光损失、对流热损失和热辐射损失,得到聚光器/球形腔式吸热器系统的光热转化效率为81.9%～84.4%,球形腔式吸热器的最佳开口比1相似文献   

Freezing of water saturated porous media in a rectangular cavity

Results for the freezing of water and of water saturated porous media are reported. Experiments were performed in a rectangular cavity, such that the solid-liquid interface and fluid motion were observed directly. The effects of natural convection and porous media ( spherical glass balls) on the solidification and fluid motion were investigated.     

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.     

Study on boiling heat transfer in liquid saturated particle bed and fluidized bed

An investigation on the effects of solid particles on boiling heat transfer enhancement is performed. The range of particle diameter is from millimeter to nanometer. The experimental results show that boiling heat transfer can be enhanced greatly by adding the solid particle into the liquid whether in fixed particle bed or in fluidized particle bed. The boiling enhancement is closely related to the particle size, the initial bed depth and the heat flux applied. The experiments show that boiling characteristics are greatly changed when a particle layer is put on the heated surface. The major effects of fixed particle bed on nucleate pool boiling heat transfer are the nucleation, bubble moving and thermal conductivity effect. A boiling heat transfer correlation is obtained to predict the boiling heat transfer coefficients in a liquid saturated porous bed. A volumetric convection mechanism of boiling heat transfer enhancement by fluidized particles is proposed. The calculated results from the model suggested in this paper agree reasonably with the experimental values.     

Discussion of proposed mechanisms of thermal conductivity enhancement in nanofluids

Based upon Green–Kubo linear response theory, we use the exact expression for the heat flux vector of the base fluid plus nanoparticle system to estimate the contribution of nanoparticle Brownian motion to thermal conductivity. We find that its contribution is too small to account for abnormally high reported values. The possibility of convection caused by Brownian particles is also found to be unlikely. We have estimated the mean free path and the transition speed of phonons in nanofluid through density functional theory. We found a layer structure can form around the nanoparticles and the structure does not further induce fluid–fluid phase transition in the bulk fluid. By analyzing the compressibility of the fluid, we have also investigated the sound speed in the nanofluid. For the models of an asymmetric hard sphere mixture representing the single spherical nanoparticles and a mixture of rods and hard spheres representing aggregates, both suspended in the fluid, we found that for the very low volume fraction cases, the compressibility changes little. This shows that the speed of phonon transition does not change due to the addition of nanoparticles of either type. Our results indicate that, besides the enhancement due to the high thermal conductivity of nanoparticles themselves, fluid molecules make no evident contribution to the enhancement of thermal conductivity attributable to the presence of the nanoparticles at volume fractions less than 5%.     

Heat transfer in particulate flows with Direct Numerical Simulation (DNS)

A Direct Numerical Simulation (DNS) method has been developed to solve the heat transfer equations for the computation of thermal convection in particulate flows. This numerical method makes use of a finite difference method in combination with the Immersed Boundary (IB) method for treating the particulate phase. A regular Eulerian grid is used to solve the modified momentum and energy equations for the entire flow region simultaneously. In the region that is occupied by the solid particles, a second particle-based Lagrangian grid is used, which tracks particles, and a force density function or an energy density function is introduced to represent the momentum interaction or thermal interaction between particle and fluid. The numerical methods developed in this paper have been validated extensively by comparing the present simulation results with those obtained by others.     

Mixed convection from an isolated spherical particle

A numerical study on mixed convection around a hot spherical particle moving vertically downwards in a still fluid medium has been made. The flow field is considered to be axisymmetric for the range of Reynolds number (based on the diameter and the settling velocity of the particle) considered. A third-order accurate upwind scheme is employed to compute the flow field and the temperature distribution. The form of the wake and the thermal field is analyzed for several values of Grashof number and the Reynolds number. The influence of buoyancy on drag and the rate of heat transfer are studied. At moderate Reynolds number, recirculating eddy develops in the downstream of the sphere. With the rise of surface temperature this eddy collapses and the fluid adjacent to the heated surface develops into a buoyant plume above the sphere. The increase in surface temperature of the sphere delays the flow separation. Our results show that the drag force and the rate of heat transfer strongly depend on Grashof number for the moderate values of Reynolds number. The conjugate heat transfer from the moving sphere is also addressed in the present paper. We have compared our computed solution with several empirical and asymptotic expressions available in the literature and found them in good agreement.     

Influence of relative motion of magnetic field on time‐dependent MHD natural convection flow

The effects of relative motion of magnetic field on unsteady magnetohydrodynamic free convection flow with ramped motion and temperature‐dependent heat source/sink have been analyzed. The motion of the inner cylinder is ramped while the motion of the outer cylinder is fixed. The momentum and energy equations are solved using the well‐known Laplace transform. The time‐domain solution is obtained using the Riemann‐sum approximation method. The influence of the governing parameters on fluid velocity, fluid temperature, volume flow rate, and rate of heat transfer are discussed with the help of line graphs. It is found that Hartmann number has a retarding effect on fluid velocity, skin friction at the outer surface of the inner cylinder, and mass flow rate when the magnetic field is fixed with the fluid and when the velocity of the magnetic field is less than the velocity of the moving cylinder. Whereas, the reverse effect is noticed when the magnetic field is fixed with the moving cylinder.     

Effect of nanoparticles size on thermal performance of nanofluid in a trapezoidal microchannel-heat-sink

This paper deals with spherical nanoparticles size effects on thermal performance and pressure drop of a nanofluid in a trapezoidal microchannel-heat-sink (MCHS). Eulerian–Eulerian two-phase numerical approach is utilized for forced convection laminar, incompressible and steady three dimensional flow of copper-oxide nanoparticles with water as base fluid at 100 to 200 nm diameter and 1% to 4% volume concentration range. Continuity, momentum, energy and volume conservation equations are solved at whole of the computational domain via finite volume method. Obtained results signify that pressure drop increases 15% at Re = 500 and 1% volume concentration while nanoparticles diameter increases from 100 to 200 nm. By increasing volume concentration, nanoparticles size effect becomes more prominent and it is observed that increment rate of pressure drop is intensified for above 150 nm particles diameter. Unlike the pressure drop, heat transfer decreases with an increase in nanoparticles diameter. Also, it is observed that with an increase in nanoparticles diameter, average Nusselt number of base fluid decreases more than that of the nanoparticles and this signifies that base fluid has more efficacy on thermal performance of copper-oxide nanofluid.     

Mixing with time dependent natural convection

Chaotic mixing inside a two dimensional cavity can be achieved with time dependent natural convection if the motion of a fluid is generated by imposing alternating hot and cold wall temperatures. With this set up no moving walls are required to mix the fluid inside the container. In this comment we illustrate this idea by numerically solving the governing equations of natural convection in a two dimensional square cavity with sections of its upper and lower horizontal walls cooled and heated in a periodic manner. These conditions generate a vortex of time dependent intensity that moves its center in a closed loop around the geometrical center of the container. The mixing properties of the flow are illustrated by Lagrangian tracking of a collection of points originally located in a line.     

Adaptive-Network-Based Fuzzy Inference System Analysis to Predict the Temperature and Flow Fields in a Lid-Driven Cavity

Heat transfer behavior in a 2-D square lid-driven cavity has been studied for various pertinent Reynolds and Rayleigh numbers. The lattice Boltzmann method, a numerical tool based on the particle distribution function is applied to simulate a thermal fluid flow problem. Bhatnagar-Gross-Krook (BGK) is combined with the double population thermal Lattice Boltzmann model to solve mixed convection in a square cavity. An adaptive-network-based fuzzy inference system (ANFIS) method is trained and validated using BGK Lattice Boltzmann model results. The results show that the trained ANFIS model successfully predicts the temperature and flow fields in a few seconds with acceptable accuracy.     

A numerical investigation into the charge behaviour of a spherical phase change material particle for high temperature thermal energy storage in packed beds

基于高温相变材料,对填充床储热系统中储热单元球体的储热性能进行了模拟研究.研究了不同传热流体温度和球体直径对球体储热性能的影响规律,对导热为主的相变储热过程与导热和自然对流共同作用的相变储热过程进行了比较分析,同时还探讨了高温辐射换热的影响.结果表明,相变时间随球体直径的增大而增大,随传热流体温度的增大而减小.当考虑相变区域自然对流时,总的相变时间显著减少,和单纯导热相比,完全相变时间缩短了近16%.在导热和自然对流的基础上加上辐射传热后可以看出,辐射换热强化了球体内的传热过程,加快了相变材料的熔化速度,强化了自然对流的作用.     

Passive Laminar Heat Transfer Across Porous Cavities Using the Thermal Non-Equilibrium Model

This work presents a study on laminar free convection within a square cavity filled with a fluid saturated porous medium. Macroscopic flow equations are obtained by volume-averaging local instantaneous continuity and momentum equations. The so-called “two-energy equation model” is used, in which distinct macroscopic equations are applied to the working fluid and the solid material. Transport equations are discretized using the control-volume method and the system of algebraic equations is relaxed via the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm. The effect of Ra_m on Nu_w correctly predicted the enhancement of passive heat transfer across the cavity for increasing Ra_m. Increasing k_s/k_f enhances the conduction transport through the solid material and, consequently, dampens the overall Nusselt number, defined here as the ratio between conduction and convection mechanisms over conduction transport only. Further, results indicate that by increasing the void space within the porous material the overall Nusselt number is reduced rather than increased. Individual contributions to the average Nusselt number indicate that, although convection is enhanced with increasing porosity, the reduction of conduction heat transfer through the solid material is the controlling mechanics for Nu_w as porosity increases. The results herein might contribute to design and optimization of passive heat transfer systems.     

Thermal Dissolution of a Spherical Particle with a Moving Boundary

A numerical problem for mass and energy transport considering thermodynamic equilibrium is solved around a spherical particle in the absence of hydrodynamic effects in a binary solution. The analysis includes the radial convective term generated due to the differences on density between the solid and liquid phases. Because the transport of mass and energy compete in the process, how the rate of dissolution is affected by compositional diffusivity or thermal diffusivity is distinguished. The partial differential equations are discretized with the finite difference method in space, and the resulting set of ordinary differential equations in time is solved by the method of lines. The numerical solution for the thermal dissolution of a spherical particle in a binary melt is compared with heat-balance integral method for small times of the process. The solutions are found to agree for conditions close to the dissolution regime.     

Solution of benard problem with the projection method

The transient convective motion in a two dimensional rectangular cavity driven by vertical temperature gradient is analyzed by the projection method involving a Godunov-type discretization for convective terms. It is shown that the method is sufficient and accurate to predict flow and temperature field. The method may be alternative to some other methods for the solution of thermal problems since its implementation is easy.