Finite Difference Lattice Boltzmann Method Research Articles

Double-diffusive natural convection in an inclined enclosure with heat generation and Soret effect

PurposeThe purpose of this paper is to study numerically thermosolutal natural convection within an inclined rectangular cavity in the presence of Soret effect and heat generation. The enclosure is heated and salted from its long sides with constant but different temperatures and concentrations. The study focuses on the effects of three main parameters which are, the Soret parameter (Sr = 0 and –0.5), the internal to external Rayleigh numbers ratio 0 ≤ R ≤ 80 and the cavity inclination γ, varied from 0° (vertical position) to 60°. The combined effects of these parameters on fluid flow and heat and mass transfer characteristics are examined for the external Rayleigh number RaE = 105, the Prandtl number Pr = 0.71, the buoyancy ratio N = 1, the Lewis number Le = 2 and the aspect ratio of the cavity A = 2.Design/methodology/approachA hybrid lattice Boltzmann-finite difference method (LBM-FD) was used to tackle the problem under consideration. The LBM with the simple relaxation time was used for the fluid flow in the presence of the gravity force, while the temperature and concentration equations were solved separately using an explicit finite-difference technique at the Boltzmann scale.FindingsThe monocellular nature of the flow, obtained for R = 0 is not destroyed by varying the cavity inclination and the Soret parameter but rather by the increase of the parameter R. The Soret parameter and the cavity inclination become perceptible at high values of R. The inclination γ = 60° leads to high mean temperatures compared to the other inclinations. The effect of R on mean concentration is amplified in the presence of Soret effect but limited in the absence of the latter. The negative Soret parameter combined with high internal heat generation and a relatively high inclination is important when the objective is to maintain the fluid at a high concentration of species. The presence of bicellular flow combined with the important elevation undergone by the fluid temperature, makes both the cold and hot walls playing a cooling role with the most important exchanges taking place at the upper part of these walls. The analysis of the mean mass transfer shows that the increase of the inclination may lead to an increase or a decrease of the mass transfer depending on the range of R, in the case of Sr = 0. However, for Sr = −0.5, it is observed that the increase of γ is generally accompanied by a reduction of the mass transfer.Originality/valueTo the best of the authors’ knowledge, the hybrid LBM-FD was not used before to study such a problem. Combined effect of R and inclination may be useful in charging the fluid with species when the objective is to maintain high concentrations in the medium.

Numerical investigation of heat transfer in a power-law non-Newtonian fluid in a C-Shaped cavity with magnetic field effect using finite difference lattice Boltzmann method

The present study aimed to investigate the natural convection heat transfer in a power-law, non-Newtonian fluid under an applied magnetic field inside a C-shaped cavity using the Finite Difference Lattice Boltzmann method (FDLBM). Temperature distribution on the wall on the left side was non-uniform and sinusoidal with the cold wall on the right side. Both top and bottom horizontal walls of the cavity were insulated against heat and mass transfer. The Boussinesq approximation was used due to negligible density variations, making the hydrodynamic field sensitive to the thermal field. Furthermore, the D2Q9 lattice arrangement was used for the density and energy distribution functions‏. This study investigates the effects of the Rayleigh number, exponential function index, aspect ratio, and the Hartmann number on the flow and temperature fields. The results show that the heat transfer rate increases with increasing Rayleigh number. Moreover, it was found that the Nusselt number decreases with increasing power-law index (n) at higher Rayleigh numbers and that an increase in the Hartmann number results in a reduced heat transfer rate. The reduction in the heat transfer rate caused by the increased Hartmann number in the shear thinning fluids was more than that in shear thickening fluids. The Nusselt number decreases with increasing cavity aspect ratio for the Newtonian and shear thinning fluids, whereas for shear thickening fluids, the Nusselt number initially increased and then decreased.

Preconditioned WENO finite-difference lattice Boltzmann method for simulation of incompressible turbulent flows

In this work, a preconditioned high-order weighted essentially non-oscillatory (WENO) finite-difference lattice Boltzmann method (WENO-LBM) is applied to deal with the incompressible turbulent flows. Two different turbulence models namely, the Spalart–Allmaras (SA) and k−ωSST models are used and applied in the solution method for this aim. The spatial derivatives of the two-dimensional (2D) preconditioned LB equation in the generalized curvilinear coordinates are discretized by using the fifth-order WENO finite-difference scheme and an implicit–explicit Runge–Kutta scheme is adopted for the time discretization. For the convective and diffusive terms of the turbulence transport equations, the third-order WENO and second-order central finite-difference schemes are used, respectively. The preconditioning technique along with the local time-stepping method are applied to the WENO-LBM to further accelerate the solution to the converged steady-state condition, and therefore, an accurate and efficient incompressible LB solver is provided for simulating turbulent flows. The accuracy and robustness of the proposed solution method are assessed by computing two test cases: the 2D turbulent flow over a flat plate at Re=1.0×107 and the 2D turbulent flow over a NACA0012 airfoil at Re=6.0×106 and different angles of attack. The present results are compared with the available numerical and experimental results which show excellent agreement. It is demonstrated that the present solution methodology based on the WENO-LBM provides more accurate results of the incompressible turbulent flows and it requires lower number of grid points compared to the traditional (low-order accurate) LB and Navier–Stokes solvers.

Mesoscopic simulation of double-diffusive natural convection and entropy generation of Bingham fluid in an open cavity

In this paper, double-diffusive natural convection, studying Soret and Dufour effects and viscous dissipation in an open cavity filled with Bingham fluid has been simulated by Finite Difference Lattice Boltzmann Method (FDLBM). In addition, entropy generations through fluid friction, heat transfer, and mass transfer has been studied. The problem has been solved by applying the regularized Papanastasiou model. However, the Bingham model without regularizations for some cases have been studied to demonstrate the accuracy of the applied regularization. This study has been conducted for certain pertinent parameters of Rayleigh number (Ra=103, 104 and 105), Bingham number (Bn), Lewis number (Le=2.5, 5 and 10), Dufour parameter (Df=0, 1, and 5), Soret parameter (Sr=0, 1, and 5), Eckert number (Ec=0, 0.001, and 0.01), and the Buoyancy ratio (N=−1, 0.1, 1). Results indicate that the increase in Rayleigh number enhances heat and mass transfer for various Bingham numbers. The rise of Bingham number reduces heat and mass transfer. In addition, the increase in Bingham number enlarges the unyielded zones. The increase in the Lewis number augments mass transfer in different Rayleigh and Bingham numbers, although the enhancement of Lewis number causes heat transfer to drop marginally. The rise of Dufour parameter increases heat transfer gradually. The increase in Soret parameter enhances mass transfer for different Bingham and Rayleigh numbers. The addition of Soret parameter, Dufour parameter and Lewis number do not affect the unyielded zone considerably. The augmentation of the buoyancy ratio number enhances heat and mass transfer at Ra=104 and 105. The rise of buoyancy ratio number alters the unyielded section significantly. The increase in Eckert number influences heat and mass transfer marginally. The augmentation of Rayleigh number enhances different entropy generations and reduces the average Bejan number. The increase in the Bingham number provokes various irreversibilities to drop significantly. The rise of Soret and Dufour parameters enhances the entropy generations due to heat transfer and fluid friction. The rise of Eckert number alters various entropy generations, but the alteration does not follow a specific manner in different studied parameters.

Double-diffusive laminar natural convection and entropy generation of Carreau fluid in a heated enclosure with an inner circular cold cylinder (Part II: Entropy generation)

In this paper, entropy generation of double-diffusive natural convection, studying Soret and Dufour effects and viscous dissipation in a heated enclosure with an inner cold cylinder filled with non-Newtonian Carreau fluid has been simulated by Finite Difference Lattice Boltzmann Method (FDLBM). This study has been conducted for certain pertinent parameters of Rayleigh number (Ra = 104 and 105), Carreau number (Cu = 1, 10, and 20), Lewis number (Le = 2.5, 5 and 10), Dufour parameter (Df = 0, 1, and 5), Soret parameter (Sr = 0, 1, and 5), Eckert number (Ec = 0, 1, and 10), the Buoyancy ratio (N = −1, 0.1, 1), the radius of the inner cylinder (Rd = 0.1 L, 0.2 L, 0.3 L, and 0.4 L), the horizontal distance of the circular cylinder from the center of the enclosure (Ω = −0.2 L, 0 and 0.2 L), the vertical distance of the circular cylinder from the center of the enclosure (δ = −0.2 L, 0 and 0.2 L). Results indicate that the augmentation of Rayleigh number enhances different entropy generations and declines the average Bejan number. The increase in the power-law index provokes various irreversibilities to drop significantly. The rise of Soret and Dufour parameters enhance the entropy generations due to heat transfer and fluid friction. The rise of Eckert number enhances the summation entropy generations. The increase in Lewis number augments the total summation entropy generations gradually. The enhancement of the buoyancy ratio causes the summation entropy generations to increase considerably. The rise of Carreau number declines the total entropy generation gradually. The least value of the total entropy generation in the vertical position of the cylinder occurs at δ = −0.2 L. The increase in the size of the cylinder augments the total entropy generation substantially. The minimum values of the total entropy generations are observed in the center position (δ = 0) in different horizontal positions.

Double-diffusive natural convection and entropy generation of Carreau fluid in a heated enclosure with an inner circular cold cylinder (Part I: Heat and mass transfer)

In this paper, double-diffusive natural convection, studying Soret and Dufour effects and viscous dissipation in a heated enclosure with an inner cold cylinder filled with non-Newtonian Carreau fluid has been simulated by Finite Difference Lattice Boltzmann Method (FDLBM). This study has been conducted for certain pertinent parameters of Rayleigh number (Ra = 104 and 105), Carreau number (Cu = 1, 10, and 20), Lewis number (Le = 2.5, 5 and 10), Dufour parameter (Df = 0, 1, and 5), Soret parameter (Sr = 0, 1, and 5), Eckert number (Ec = 0, 1, and 10), the Buoyancy ratio (N = −1, 0.1, 1), the radius of the inner cylinder (Rd = 0.1 L, 0.2 L, 0.3 L, and 0.4 L), the horizontal distance of the circular cylinder from the center of the enclosure (Ω = −0.2 L, 0 and 0.2 L), the vertical distance of the circular cylinder from the center of the enclosure (δ = −0.2 L, 0 and 0.2 L). Results indicate that the increase in Rayleigh number enhances heat transfer for various studied parameters. The increase in power-law index provokes heat and mass transfer to drop gradually. The increase in the Lewis number declines the mass transfer considerably while causes heat transfer to drop marginally. The heat transfer increases with the rise of the Dufour parameter and the mass transfer enhances as the Soret parameter increases for different Rayleigh numbers. The augmentation of the buoyancy ratio number enhances heat and mass transfer. The increase in Eckert number affects heat and mass transfer; especially, at Ra = 105. The rise of Carreau number causes heat and mass transfer to drop gradually. The movement of the center of the cylinder from the bottom to the top side of the enclosure vertically (δ = −0.2 L, 0 and 0.2 L) decreases heat and mass transfer significantly while the effect of power-law index drops. The increase in the radius of the cylinder enhances heat and mass transfer. The alteration of the center of the cylinder horizontally (Ω) to the left and right sides enhance heat and mass transfer although this augmentation is different in various power-law indexes.

Double-diffusive natural convection and entropy generation of Bingham fluid in an inclined cavity

In this paper, double-diffusive natural convection, studying Soret and Dufour effects and viscous dissipation in a square cavity filled with Bingham fluid has been simulated by Finite Difference Lattice Boltzmann Method (FDLBM). In addition, entropy generations through fluid friction, heat transfer, and mass transfer has been studied. The problem has been solved by applying the regularised Papanastasiou model. This study has been conducted for certain pertinent parameters of Rayleigh number (Ra=103,104 and 105), Bingham number (Bn), Lewis number (Le=2.5, 5 and 10), Dufour parameter (Df=0, 1, and 5), Soret parameter (Sr=0, 1, and 5), Eckert number (Ec=0, 0.001, and 0.01), inclined angle (θ=0, 40, 80, and 120) and the Buoyancy ratio (N=−1, 0.1, 1). Results indicate that the increase in Rayleigh number enhances heat and mass transfer for various Bingham numbers and inclined angles. The alteration of the inclined angle changes heat and mass transfer. In addition, the rise of the inclined angle alter the unyielded zones. The increase in the Lewis number augments mass transfer in different inclined angles while it causes heat transfer to drop marginally at θ=0, 40, and 120. The heat transfer increases with the rise of the Dufour parameter and the mass transfer enhances as the Soret parameter increases for different Bingham numbers and Rayleigh numbers. In some cases, the augmentation of Soret and Dufour parameters alter the behavior of heat and mass transfer against the alteration of the inclined angle. The addition of Soret and Dufour parameters and Lewis numbers do not affect the unyielded zone considerably. The augmentation of the buoyancy ratio number enhances heat and mass transfer. The rise of buoyancy ratio number alters the unyielded section significantly. The increase in Eckert number declines heat transfer, but it has a marginal effect on mass transfer. The augmentation of Rayleigh number enhances different entropy generations and declines the average Bejan number. The increase in the Bingham number provokes various irreversibilities to drop significantly. The rise of Soret and Dufour parameters enhances the entropy generations due to heat transfer and fluid friction. The rise of Eckert number alters various entropy generations, but the alteration does not follow a specific manner in different studied parameters.

A hybrid algorithm of lattice Boltzmann method and finite difference–based lattice Boltzmann method for viscous flows

SummaryIn this paper, a hybrid algorithm of the lattice Boltzmann method (LBM) and the finite difference LBM (FDLBM) is proposed. The conventional LBM is known for its high computational efficiency, whereas the finite difference method can guarantee both the accuracy of the description of the complex geometry and the high resolution of the flow field by a local refined anisotropic body‐fitted mesh. The hybrid algorithm of the LBM and FDLBM takes advantage of the merits of both the methods. Four benchmark flow problems are simulated to verify the hybrid algorithm, namely, the lid‐driven cavity flow, the flow past a static circular cylinder, the flow past an impulsively started cylinder, and the flow past 2 cylinders in tandem configuration. Results from these simulations show that the hybrid method proposed in the present work works very well for viscous flows.

Simulation of natural convection and entropy generation of MHD non-Newtonian nanofluid in a cavity using Buongiorno's mathematical model

In this paper, natural convection and entropy generation of non-Newtonian nanofluid, using the Buongiorno's mathematical model in a cavity in the presence of a uniform magnetic field has been analyzed by Finite Difference Lattice Boltzmann method (FDLBM). The cavity is filled with nanofluid which the mixture shows shear-thinning behavior. This study has been performed for the certain pertinent parameters of Rayleigh number (Ra = 104 and 105), Hartmann number (Ha = 0, 15, 30), buoyancy ratio number (Nr = 0.1, 1, and 4), power-law index (n = 0.4–1), Lewis number (Le = 1, 5, and 10), Thermophoresis parameter (Nt = 0.1, 0.5, 1), and Brownian motion parameter (Nb = 0.1, 1, 5). The Prandtl number is fixed at Pr = 1. The Results indicate that the augmentation of Hartmann number causes heat and mass transfer to drop. The increase in Rayleigh number enhances heat and mass transfer for various power-law indexes. The alteration of the power-law index changes heat and mass transfer. In addition, the rise of Hartmann number declines the shear-thinning behavior. The increase in the Lewis number augments mass transfer while it causes heat transfer to drop. The rise of the Thermophoresis and Brownian motion parameters ameliorate mass transfer and declines heat transfer significantly. The augmentation of buoyancy ratio number enhances heat and mass transfer. The augmentation of the power-law index declines various entropy generations in different Rayleigh numbers and Hartmann numbers. The increase in Hartmann number declines total entropy generation in different Rayleigh numbers. In addition, the rise of Rayleigh number and Hartmann number causes Bejan number to drop in various power-law indexes. The enhancement of the Lewis number provokes the total irreversibility to rise. Further, the total entropy generation increases as the buoyancy ratio number augments. It was shown that the increase in the Brownian motion and Thermophoresis parameters enhance the total irreversibility.

Simulation of natural convection in an inclined polar cavity using a finite-difference lattice Boltzmann method

Natural convection heat transfer in an inclined polar cavity was studied using a Finite-difference lattice Boltzmann method (FDLBM) based on a double-population approach for body-fitted coordinates. A D2G9 model coupled with the simplest TD2Q4 lattice model was applied to determine the velocity field and temperature field. For both velocity and temperature fields, the discrete spatial derivatives were obtained by combining the upwind scheme with the central scheme, and the discrete temporal term is obtained using a fourth-order Runge-Kutta scheme. Studies were carried out for different Rayleigh numbers and different inclination angles. The results in terms of streamlines, isotherms, and Nusselt numbers explain the heat transfer mechanism of natural convection in an inclined polar cavity due to the change of Rayleigh number and inclination angle.

Simulation of natural convection and entropy generation of non-Newtonian nanofluid in a porous cavity using Buongiorno’s mathematical model

In this paper, natural convection of non-Newtonian nanofluid, using the Buongiorno’s mathematical model in a porous cavity has been analyzed by Finite Difference Lattice Boltzmann method (FDLBM) while entropy generations through fluid friction, heat transfer, and mass transfer are analyzed. The cavity is filled with nanofluid which the mixture shows shear-thinning behavior. This study has been performed for the certain pertinent parameters of Rayleigh number (Ra=104 and 105), Darcy number (Da=0.0001,0.001,0.01), Prandtl number (Pr=0.1, 1, and 10), buoyancy ratio number (Nr=0.1, 1, and 4), power-law index (n=0.4–1), Lewis number (Le=1, 5, and 10), Thermophoresis parameter (Nt=0.1, 0.5, 1), and Brownian motion parameter (Nb=0.1, 1, 5). The Prandtl number is fixed at Pr=0.1. Results indicate that the heat and mass transfer augments as Rayleigh number increases. The increase in Darcy number augments heat transfer and declines the mass transfer at Ra=104. The augmentation of Darcy number enhances heat transfer at Ra=105. The increase in power-law index alters heat and mass transfer. The increase in the Lewis number augments mass transfer while it causes heat transfer to drop. The rise of the Thermophoresis and Brownian motion parameters ameliorate mass transfer and declines heat transfer significantly. The augmentation of buoyancy ratio number enhances heat and mass transfer. The increase in Darcy number enhances total entropy generation in different Rayleigh numbers. In addition, the rise of Rayleigh number and Darcy number causes Bejan number to drop in various power-law indexes. The enhancement of the Lewis number provokes the total irreversibility to rise. Further, the total entropy generation increases as the buoyancy ratio number augments. It was shown that the increase in the Brownian motion and Thermophoresis parameters changes the total irreversibility.

An implicit-explicit finite-difference lattice Boltzmann subgrid method on nonuniform meshes

In this paper, an implicit-explicit finite-difference lattice Boltzmann method with subgrid model on nonuniform meshes is proposed. The implicit-explicit Runge–Kutta scheme, which has good convergence rate, is used for the time discretization and a mixed difference scheme, which combines the upwind scheme with the central scheme, is adopted for the space discretization. Meanwhile, the standard Smagorinsky subgrid model is incorporated into the finite-difference lattice Boltzmann scheme. The effects of implicit-explicit Runge–Kutta scheme and nonuniform meshes of present lattice Boltzmann method are discussed through simulations of a two-dimensional lid-driven cavity flow on nonuniform meshes. Moreover, the comparison simulations of the present method and multiple relaxation time lattice Boltzmann subgrid method are conducted qualitatively and quantitatively.

High-order weighted essentially nonoscillatory finite-difference formulation of the lattice Boltzmann method in generalized curvilinear coordinates.

In this work, a high-order weighted essentially nonoscillatory (WENO) finite-difference lattice Boltzmann method (WENOLBM) is developed and assessed for an accurate simulation of incompressible flows. To handle curved geometries with nonuniform grids, the incompressible form of the discrete Boltzmann equation with the Bhatnagar-Gross-Krook (BGK) approximation is transformed into the generalized curvilinear coordinates and the spatial derivatives of the resulting lattice Boltzmann equation in the computational plane are solved using the fifth-order WENO scheme. The first-order implicit-explicit Runge-Kutta scheme and also the fourth-order Runge-Kutta explicit time integrating scheme are adopted for the discretization of the temporal term. To examine the accuracy and performance of the present solution procedure based on the WENOLBM developed, different benchmark test cases are simulated as follows: unsteady Taylor-Green vortex, unsteady doubly periodic shear layer flow, steady flow in a two-dimensional (2D) cavity, steady cylindrical Couette flow, steady flow over a 2D circular cylinder, and steady and unsteady flows over a NACA0012 hydrofoil at different flow conditions. Results of the present solution are compared with the existing numerical and experimental results which show good agreement. To show the efficiency and accuracy of the solution methodology, the results are also compared with the developed second-order central-difference finite-volume lattice Boltzmann method and the compact finite-difference lattice Boltzmann method. It is shown that the present numerical scheme is robust, efficient, and accurate for solving steady and unsteady incompressible flows even at high Reynolds number flows.

Mixed convection of non-Newtonian nanofluid in an enclosure using Buongiorno’s mathematical model

In this paper, mixed convection of non-Newtonian nanofluid, using the Buongiorno’s mathematical model in a cavity has been analyzed by Finite Difference Lattice Boltzmann method (FDLBM). The cavity is filled with nanofluid which the mixture shows shear-thinning behavior. The Prandtl number is fixed at Pr=1. This study has been performed for the certain pertinent parameters of Richardson number (Ri=0.001, 0.01, and 1), buoyancy ratio number (Nr=0.1, 1, and 20), power-law index (n=0.2–1), Lewis number (Le=1, 5, and 10), Thermophoresis parameter (Nt=0.1, 0.5, 1), and Brownian motion parameter (Nb=0.1, 1, 5). Results indicate that the augmentation of the power-law index causes heat and mass transfer to drop at Ri=0.001 and 0.01. The drop of Richardson number from Ri=1 to 0.001 enhances heat and mass transfer for various power-law indexes. The increase in the Lewis number augments mass transfer while it causes heat transfer to drop. The rise of the Thermophoresis and Brownian motion parameters ameliorates mass transfer and declines heat transfer significantly. The augmentation of buoyancy ratio number enhances heat and mass transfer.

Chebyshev collocation spectral lattice Boltzmann method in generalized curvilinear coordinates

Abstract In this work, the Chebyshev collocation spectral lattice Boltzmann method is implemented in the generalized curvilinear coordinates to provide an accurate and efficient low-speed LB-based flow solver to be capable of handling curved geometries with non-uniform grids. The low-speed form of the D2Q9 and D3Q19 lattice Boltzmann equations is transformed into the generalized curvilinear coordinates and then the spatial derivatives in the resulting equations are discretized by using the Chebyshev collocation spectral method and the temporal term is discretized with the fourth-order Runge–Kutta scheme to provide an accurate and efficient low-speed flow solver. All boundary conditions are implemented based on the solution of the governing equations in the generalized curvilinear coordinates. The accuracy and robustness of the solution methodology presented are demonstrated by computing different benchmark and practical low-speed flow problems that are 2D Couette flow between concentric moving cylinders, 2D flow in a gradual expansion duct, 2D regularized trapezoidal cavity flow, and 3D flow in curved ducts of rectangular cross-sections. Results obtained for these test cases are in good agreement with the existing analytical and numerical results. The computational efficiency of the proposed solution methodology based on the Chebyshev collocation spectral lattice Boltzmann method implemented in the generalized curvilinear coordinates is also examined by comparison with the developed second-order finite-difference lattice Boltzmann method that indicates the proposed method provides more accurate and efficient solutions in terms of the CPU time and memory usage. The study shows the present solution methodology is robust and accurate for solving 2D and 3D low-speed flows over practical geometries. Indications are that the solution algorithm based on the CCSLBM in the generalized curvilinear coordinates does not need any filtering or numerical dissipation for stability considerations and thus high accuracy solutions obtained by applying the CCSLBM can be used as benchmark solutions for the evaluation of other LBM-based flow solvers.

A hybrid wavelet-based adaptive immersed boundary finite-difference lattice Boltzmann method for two-dimensional fluid–structure interaction

A second generation wavelet-based adaptive finite-difference Lattice Boltzmann method (FD-LBM) is developed in this paper. In this approach, the adaptive wavelet collocation method (AWCM) is firstly, to the best of our knowledge, incorporated into the FD-LBM. According to the grid refinement criterion based on the wavelet amplitudes of density distribution functions, an adaptive sparse grid is generated by the omission and addition of collocation points. On the sparse grid, the finite differences are used to approximate the derivatives. To eliminate the special treatments in using the FD-based derivative approximation near boundaries, the immersed boundary method (IBM) is also introduced into FD-LBM. By using the adaptive technique, the adaptive code requires much less grid points as compared to the uniform-mesh code. As a consequence, the computational efficiency can be improved. To justify the proposed method, a series of test cases, including fixed boundary cases and moving boundary cases, are invested. A good agreement between the present results and the data in previous literatures is obtained, which demonstrates the accuracy and effectiveness of the present AWCM-IB-LBM.

Behaviors of the wedge-shaped gas-lubricated film using the finite difference lattice Boltzmann method

In this article, the finite difference lattice Boltzmann method (FDLBM) is successfully applied to analyze the hydrodynamic properties of the wedge-shaped gas film lubrication for the high speed micro gas bearings by comparing with the macroscopic methods (solving the modified Reynolds equation coupled with the simplified energy (modified Reynolds equation) and the Navier–Stokes equations coupled with the energy equation). By comparison, it is found that the vertical flow across the gas film can weaken the gas backflow and thus improves the gas film pressure, as the Navier–Stokes equation and FDLBM are used to analyze the wedge-shaped film lubrication. The continuum assumption in the macroscopic methods leads to a larger gas film pressure, compared with the value predicted by the FDLBM. And, the high temperature and speed enlarge this difference between them. Furthermore, the FDLBM provides a good warm-up for the multiscale simulation on the complex flow in the micro gas bearings.

Simulation of natural convection and entropy generation of non-Newtonian nanofluid in an inclined cavity using Buongiorno's mathematical model (Part II, entropy generation)

In this paper, entropy generation of associated with the natural convection of non-Newtonian nanofluid, using the Buongiorno's mathematical model in an inclined cavity has been analyzed by Finite Difference Lattice Boltzmann method (FDLBM). The cavity is filled with nanofluid which the mixture shows shear-thinning behavior. This study has been performed for the certain pertinent parameters of Rayleigh number (Ra = 104 and 105), inclined angle (θ=0°,40°,80°,120°), buoyancy ratio number (Nr=0.1, 1, and 4), power-law index (n=0.4−1), Lewis number (Le=1, 5, and 10), Thermophoresis parameter (Nt=0.1, 0.5, 1), and Brownian motion parameter (Nb=0.1, 1, 5). The Prandtl number is fixed at Pr=1. The Results indicate that the augmentation of the power-law index enhances various entropy generations in different Rayleigh numbers and inclined angles. The lowest total entropy generation was observed in the inclined angle of θ=0° in different Rayleigh numbers. In addition, the highest values of Bejan number was found in the inclined angle of θ=0° in various Rayleigh numbers. The enhancement of the Lewis number provokes the total irreversibility to rise. Further, the total entropy generation increases as the buoyancy ratio number augments. It was shown that the increase in the Brownian motion and Thermophoresis parameters enhance the total irreversibility.

Immersed boundary-finite difference lattice Boltzmann method using the feedback forcing scheme to simulate the incompressible flows

In this study, the immersed boundary-finite difference lattice Boltzmann method (IB-FDLBM) using the feedback momentum forcing scheme is proposed and implemented to simulate 2-D incompressible flows. IB-FBLBM incorporates the immersed boundary method (IBM) into the finite difference lattice Boltzmann method (FDLBM) devised to alleviate shortcomings by using the uniform Cartesian grid of the standard lattice Boltzmann method (LBM). In order to obtain numerical stability while combining IBM with FDLBM, this method utilizes feedback momentum forcing scheme and equilibrium velocity approach to take into account the change of momentum induced by a body force on the immersed boundaries. This approach has the advantages of being simple and easy to implement, and does not require modification of the original governing equations. In order to confirm the applicability and validation of IB-FDLBM, the lid-driven cavity flow with a circular cylinder, the external steady flows around a circular cylinder and external steady flows around a circular cylinder near a plane wall are simulated with a range of Reynolds numbers. The current numerical results are consistent with those of existing researches.

Simulation of double diffusive MHD (magnetohydrodynamic) natural convection and entropy generation in an open cavity filled with power-law fluids in the presence of Soret and Dufour effects (Part I: Study of fluid flow, heat and mass transfer)

In this paper, double diffusive natural convection of non-Newtonian power-law fluids in an open cavity in the presence of a horizontal magnetic field, studying Soret and Dufour parameters has been analyzed by FDLBM (Finite Difference Lattice Boltzmann method). This study has been performed for the certain pertinent parameters of Rayleigh number (Ra = 104 and 105), Hartmann number (Ha = 0, 15, and 30), power-law index (n = 0.6, 1, and 1.4), Lewis number (Le = 2.5 and 5), Dufour parameter (Df = 0, 1, and 5), Soret parameter (Sr = 0, 1, and 5) and the buoyancy ratio (N = −1and 1). Results indicate that the augmentation of the Hartmann number provokes heat and mass transfer to drop for different power-law indexes. As the Soret and Dufour numbers equal zero, the heat and mass transfer decrease with the increment of the power-law index in different Rayleigh numbers for various Hartmann numbers. The heat transfer increases with the rise of the Dufour parameter and the mass transfer enhances as the Soret parameter increases for different power-law indexes and Rayleigh numbers. The augmentation of Soret and Dufour parameters alters the behavior of heat and mass transfer against the change of the power-law index.