Cascaded Lattice Boltzmann Method Research Articles

Cascaded lattice Boltzmann simulation of Newtonian and non-Newtonian mixture nanofluids with variable thermophysical properties in a cavity with vertical heat radiator

The central moments-based cascaded lattice Boltzmann method (CLBM) for then Newtonian and non-Newtonian Buongiorno’s model mixture nanofluids (CuO, ZnO, Al2O3-water) has been implemented and applied in a square chamber with a vertical heat radiator using accelerated graphics processing unit (GPU) computing through compute unified device architecture (CUDA) C/C++ platform. Due to the higher numerical stability, the CLBM is a superior numerical tool to the raw moments-based MRT-LBM (multiple-relaxation-time lattice Boltzmann method). Three different models for the viscosity and thermal conductivity of the nanofluids: (i) the Binkmann model for the constant viscosity and the Maxwell model for the constant thermal conductivity (ii) Binkmann and Maxwell model with temperature dependent Brownian motion and (iii) Corcione model with non-Newtonian fluid where the temperature and strain rate determine the nanofluid effective thermal conductivity and viscosity, have been used. The enclosure’s upper and bottom walls are thermally adiabatic, but the left and right walls are uniformly cold. A vertical heater is immersed in the middle position of the cavity. The benchmark results for non-Newtonian, Newtonian, and nanofluids for the various computational domains are used to validate the current code adequately. The Bingham number (Bn), the Rayleigh number (Ra), and The volume fraction of the nanoparticles (ϕ) are the three key parameters that are varied in this investigation to demonstrate the effects of natural convection on the isotherms, streamlines, isolines of nanoparticle volume fractionation, yielded and unyeilded zone, and average Nusselt number (Nu¯). The Brownian motion effects of the nanoparticles augmented the average rate of heat transfer and the use of the Bingham nanofluids reduced the heat transfer enhancement. For the CuO-water nanofluid, the augmentation of the rate of heat transfer is 15.42% from ϕ=0 to 4% while Ra=106 and the corresponding heat transfer enhancement for the ZnO-water nanofluid is 11.11%. For the Bingham fluid, the rate of heat transfer increases 7% from Ra=105 to Ra=106 while ϕ=2% and Bn=0.3. The findings can be applied to optimize automotive radiator systems, which are crucial for maintaining engine temperature.

Generalized interpolation-supplemented cascaded lattice Boltzmann method for noise radiated from a circular cylinder

Flow past a stationary or vibrating body usually leads to intense noise radiation. In order to study this problem via direct simulations, a cascaded lattice Boltzmann method (CLBM) is developed in the moving frame of reference, and implemented in a body-fitted grid using the generalized interpolation-supplemented particle streaming. A far-field perfectly matched layer is also incorporated so as to avoid sound reflection. The proposed generalized interpolation-supplemented cascaded lattice Boltzmann method (GICLBM) is then validated through numerical experiments concerning fixed and forced oscillating circular cylinders, in terms of forces exerting on the cylinder, wall stress, near-field flow dynamics, and far-field sound radiation. Very good consistency is observed for all quantities discussed therein with previous benchmark tests. Furthermore, the noise radiated from a circular cylinder undergoing vortex-induced vibration (VIV) is investigated using the GICLBM, providing interesting results. Firstly, at a mass ratio of m⁎=2, the flow and vibration dynamics are found to be dependent on the Mach number, and the critical value is found to be approximately Ma=0.1. Secondly, through comparisons with scenarios involving a fixed cylinder and a forced vibrating cylinder, it is noted that the VIV generates significantly more complicated sound sources including monopole and drag dipole. Thirdly, in the lock-in condition, the increase in the reduced velocity only alters the magnitude of the radiated sound pressure but not the directivity. Through this study, a high-fidelity, efficient, and relatively simple framework for fluid-structure-sound interactions is proposed.

Direct simulations of external flow and noise radiation using the generalized interpolation-supplemented cascaded lattice Boltzmann method

Direct simulations of external flow and the associated noise radiation are studied by an improved lattice Boltzmann method, i.e., the generalized interpolation-supplemented cascaded lattice Boltzmann method (GICLBM). In this method, the cascaded collision scheme is used to improve the numerical stability of the conventional collision schemes, and the generalized interpolation approach is used in the particle streaming process so as to allow a non-uniform and body-fitted mesh partition. With that, both near- and far-field flow dynamics and noise radiation are resolved simultaneously. In order to capture sound waves, the perfectly matched layer is also implemented so as to avoid waves reflecting to and polluting the inner acoustic field. Moreover, a novel index technique is developed for the GICLBM to enable implicit streaming, which brings an efficient memory reduction. Three cases are then performed to showcase the feasibility, accuracy, extensibility, and efficiency of the present framework, including flow past a square cylinder, flow past an elliptic cylinder, and flow past a NACA 0012 airfoil, each implemented with a type of body-fitted mesh. Both the fluid dynamic and noise radiation are found to be in good agreement with results using the Navier–Stokes solvers. This study demonstrates the potential of the GICLBM for accurately and efficiently simulating external problems as well as sound generation and propagation.

Three-dimensional lattice Boltzmann simulations for droplet impact and freezing on ultra-cold superhydrophobic surfaces

Droplet impact and freezing on cold surfaces is a widely encountered multi-physical phenomenon involving droplet deformation and the liquid–solid phase change. Due to its complexity in nature, it is challenging to simulate the three-dimensional (3D) droplet impact and freezing process. Furthermore, due to the limitation of experimental techniques, it is not easy to experimentally investigate the impact of liquid droplets on ultra-cold superhydrophobic surfaces, which is crucial in some applications. Thus, in the present work, a 3D lattice Boltzmann (LB) method is developed to simulate the droplet impact and freezing on an ultra-cold superhydrophobic surface, in which an enhanced cascaded LB method is used to solve the multiphase flow field, and a multi-relaxation-time scheme is applied to solve the liquid–solid phase change model. The previous experimental results are numerically reproduced, proving that the present model can satisfactorily describe the droplet impact and solidification. The surface temperatures have no significant influence on droplet spreading. However, during the droplet retraction, a rim of ice first appears near the three-phase contact line, and then, the droplet bottom will completely solidify into ice. The occurrence of solidification at the bottom of the droplet will lead the droplet to break at a lower impact velocity, which can only be observed at a high Weber number on the room-temperature superhydrophobic surface. In addition, the effects of surface temperatures and Weber numbers on the evolution of spreading factors and space-averaged heat flux are also quantitatively analyzed in detail.

An enthalpy-based cascaded lattice Boltzmann method for solid-liquid phase-change heat transfer

• The CLB method is extended to simulate solid-liquid phase-change problems. • The unphysical numerical diffusion can be effectively eliminated by the CLB method. • The CLB method can achieve better numerical stability due to the enhanced Galilean invariance. In this paper, a cascaded lattice Boltzmann (CLB) method for investigating solid-liquid phase-change heat transfer is developed. In the CLB method, the enthalpy methodology is adopted to capture the solid-liquid phase interface implicitly. Mesoscopically, the enthalpy is defined as the basic evolution variable of the CLB equation of the temperature field so as to consider the phase-change effect in simulations without iteration procedure, and to achieve this purpose, the cascaded collision process is artfully designed by modifying the shifting procedure. Numerical results demonstrate that the enthalpy-based CLB method can serve as an accurate and reliable numerical tool for simulating solid-liquid phase-change heat transfer.

Strongly coupled peridynamic and lattice Boltzmann models using immersed boundary method for flow-induced structural deformation and fracture

To simulate the dynamics of structural deformation and fracture caused by fluid-structure interactions accurately and efficiently, a strong coupling between the peridynamic model and the lattice Boltzmann method using the immersed boundary method is developed here. In this novel method, the peridynamic model predicts structural deformation and fracture, the cascaded lattice Boltzmann method serves as the flow solver, and the immersed boundary method is to enforce a no-slip boundary condition on the fluid-solid interface. The strong coupling is achieved by adding velocity corrections for the fluid and solid phases simultaneously at each time step, which are calculated by solving a linear system of equations derived from an implicit velocity correction immersed boundary scheme. Therefore, this new scheme based on the immersed boundary method eliminates the need to iteratively solve the dynamics of the fluid and solid phases at each time step. The proposed method is rigorously validated considering the plate with a pre-existing crack under velocity boundary conditions, the sedimentation of an elastic disk, the cross-flow over a flexible beam, and the flow-induced deformation of an elastic beam attached to a rigid cylinder. More importantly, the structural deformation, crack formation, and fracture due to interaction with the fluid flow are captured innovatively.

Mesoscopic simulation of three-dimensional pool boiling based on a phase-change cascaded lattice Boltzmann method

In this paper, a three-dimensional (3D) cascaded lattice Boltzmann method (CLBM) is implemented to simulate the liquid–vapor phase-change process. The multiphase flow field is solved by incorporating the pseudopotential multiphase model into an improved CLBM, the temperature field is solved by the finite difference method, and the two fields are coupled via a non-ideal equation of state. Through numerical simulations of several canonical problems, it is verified that the proposed phase-change CLBM is applicable for both the isothermal multiphase flow and the liquid–vapor phase-change process. Using the developed method, a complete 3D pool boiling process with up to hundreds of spontaneously generated bubbles is simulated, faithfully reproducing the nucleate boiling, transition boiling, and film boiling regimes. It is shown that the critical heat flux predicted by the 3D simulations agrees better with the established theories and correlation equations than that obtained by two-dimensional simulations. Furthermore, it is found that with the increase in the wall superheats, the bubble footprint area distribution changes from an exponential distribution to a power-law distribution, in agreement with experimental observations. In addition, insights into the instantaneous and time-averaged characteristics of the first two largest bubble footprints are obtained.

Numerical simulations of convection heat transfer in porous media using a cascaded lattice Boltzmann method

Convection heat transfer in porous media is a universal phenomenon in nature, and it is also frequently encountered in scientific and engineering fields. An in-depth understanding of the fundamental mechanism of convection heat transfer in porous media requires efficient and powerful numerical tools. In this paper, a cascaded lattice Boltzmann (CLB) method for convection heat transfer in porous media at the representative elementary volume (REV) scale is presented. In the CLB method, the flow field is solved by an isothermal CLB model with the D2Q9 lattice based on the generalized non-Darcy model, while the temperature field is solved by a temperature-based CLB model with the D2Q5 lattice. The key point is to incorporate the influence of the porous media into the CLB method by introducing the porosity and heat capacity ratio into the shift matrices. The effectiveness and practicability of the present method are validated by numerical simulations of several heat transfer problems in porous media at the REV scale. It is shown that the present method for convection heat transfer in porous media is second-order accurate in space. Moreover, in comparison with the Bhatnagar-Gross-Krook lattice Boltzmann method, the present method has sufficient tunable parameters and possesses better numerical stability.

An accuracy analysis of the cascaded lattice Boltzmann method for the 1D advection-diffusion equation

An accuracy analysis of the cascaded lattice Boltzmann method for the 1D advection-diffusion equation

Numerical Modelling of Microchannel Gas Flows in the Transition Flow Regime Using the Cascaded Lattice Boltzmann Method.

In this article, a lattice Boltzmann (LB) method for studying microchannel gas flows is developed in the framework of the cascaded collision operator. In the cascaded lattice Boltzmann (CLB) method, the Bosanquet-type effective viscosity is employed to capture the rarefaction effects, and the combined bounce-back/specular-reflection scheme together with the modified second-order slip boundary condition is adopted so as to match the Bosanquet-type effective viscosity. Numerical simulations of microchannel gas flow with periodic and pressure boundary conditions in the transition flow regime are carried out to validate the CLB method. The predicted results agree well with the analytical, numerical, and experimental data reported in the literature.

Numerical investigation of the cascaded central moment lattice Boltzmann method for non-Newtonian fluid flows

We present a cascaded lattice Boltzmann (LB) method based on central moments and multiple relaxation times for the simulation of the non-Newtonian fluid flows. In this regard, we consider nonlinear constitutive relations for the power law fluids encompassing shear thinning and shear thickening characteristics and the Bingham fluids that model fluids with yield behavior. This involves local adjustment of the relaxation times during the collision step for the second order moments, which are related to the magnitude of the shear rate. The latter is related to the second invariant of the strain rate tensor whose components are computed locally based on non-equilibrium moments. Such relations also account for the additional corrections needed to eliminate the cubic velocity errors arising from the aliasing effects associated with the standard lattices to enable simulations of non-Newtonian flows with high fidelity. We then perform the validation of the resulting method for a variety of non-Newtonian flow problems, including the lid driven cavity flow, flow over a cylinder and a pair of cylinders in a tandem configuration. Results demonstrate accurate solutions, second order grid convergence and improvements in numerical stability to enable higher Reynolds number computations of non-Newtonian fluid flows achieved with the use of the cascaded LB method when compared to other collision models.

A cascaded phase-field lattice Boltzmann model for the simulation of incompressible, immiscible fluids with high density contrast

In this work, a conservative phase-field model for the simulation of immiscible multiphase flows is developed using an incompressible, velocity-based, cascaded lattice Boltzmann method (CLBM). Extensions are made to the lattice Boltzmann (LB) equations for interface tracking and incompressible hydrodynamics, proposed by Fakhari et al. [1], by performing relaxation operations in central moment space. This was motivated by the work of Fei et al. [2,3], where promising results from such a transformation were observed. The relaxation of central moments is defined in a reference frame moving with the fluid, while the existing multiple-relaxation time [4,5] scheme performs collision in a fixed frame of reference. Moreover, the derivations make use of continuous, Maxwellian distribution functions. As a result, the CLBM enhances the Galilean invariance and stability of the method when high lattice Mach numbers are evident. The cascaded scheme has been previously used in the literature to simulate multiphase flows based on the pseudo-potential model, where it allowed for high density and viscosity contrasts to be captured [6,7]. Here, the CLBM is implemented within the phase-field framework and is verified through the analysis of a layered Poiseuille flow. The performance of the CLBM is then investigated in terms of spurious currents, Galilean invariance and computational efficiency. Finally, the work of Fakhari et al. [1] is extended by validating the model’s ability to capture the relation between surface tension and the rise velocity of a planar Taylor bubble, in both stagnant and flowing fluids. New counter-current results indicate that the rise velocity model of Ha-Ngoc and Fabre [8] also applies in this regime.

A multi-physics peridynamics-DEM-IB-CLBM framework for the prediction of erosive impact of solid particles in viscous fluids

In this paper, a new fully-resolved framework capable of capturing the fundamental physics of particle–fluid interactions, the collision of particles with solid surfaces, and the resulting damage is proposed. A coupled DEM-IB-CLBM, consisting of a discrete element method (DEM), an immersed boundary (IB) method, and a cascaded lattice Boltzmann method (CLBM), is used to fully resolve the interaction of the particles with the surrounding viscous fluid. The peridynamics theory is then implemented and used to predict the impact damage to the target material. This framework is validated by comparing the trajectory of a particle–wall collision event in a viscous fluid with the previous results in the literature. Furthermore, the variation of the restitution coefficient with the impact velocity is in a good agreement with the available experimental results. The influence of multiple impacts and the resulting surface damage on the fluid dynamics of the system is investigated. It is demonstrated that the method correctly predicts the expected effects of multiple collisions and impact angle variations on the surface damage.

Role of higher-order Hermite polynomials in the central-moments-based lattice Boltzmann framework.

The cascaded lattice Boltzmann method decomposes the collision stage on a basis of central moments on which the equilibrium state is assumed equal to that of the continuous Maxwellian distribution. Such a relaxation process is usually considered as an assumption, which is then justified a posteriori by showing the enhanced Galilean invariance of the resultant algorithm. An alternative method is to relax central moments to the equilibrium state of the discrete second-order truncated distribution. In this paper, we demonstrate that relaxation to the continuous Maxwellian distribution is equivalent to the discrete counterpart if higher-order (up to sixth) Hermite polynomials are used to construct the equilibrium when the D3Q27 lattice velocity space is considered. Therefore, a theoretical a priori justification of the choice of the continuous distribution is formally provided for the first time.

Cascaded Lattice Boltzmann Method application in forced and natural convection

Lattice Boltzmann Method is applied to forced and natural convection heat transfer from the tube banks. Hot tubes are cooled by flowing or passive air. Two Reynolds numbers (Re = 80 and Re = 1600) and two Rayleigh numbers (Ra = 103 and Ra = 105) of the corresponding heat transfer regime are studied. The method itself is based on the recently derived cascaded collision operator not only for the fluid flow but also for the temperature field. Using this method and moderate space resolution of the lattice we were able to obtain stable and bounded simulations for the non-trivial geometry.

Cascaded lattice Boltzmann method for thermal flows on standard lattices

In this paper, a thermal cascaded lattice Boltzmann method (TCLBM) is developed in combination with the double-distribution-function (DDF) approach on the standard D2Q9 lattice. A density distribution function relaxed by the cascaded scheme based on central moments is employed to solve the flow field, and a total energy distribution function relaxed by the BGK scheme is used to solve the temperature field. The two distribution functions are coupled naturally to provide a new TCLBM. In this method, the viscous heat dissipation and compression work are taken into account, the Prandtl number and specific-heat ratio are adjustable, and the external force is considered directly without the Boussinesq assumption. The TCLBM is validated by numerical experiments of the thermal Couette flow, low-Mach number shock tube problem, Rayleigh-Bénard convection, and natural convection in a square cavity with a large temperature difference. The simulation results agree well with the analytical solutions and/or results given by previous researchers.

Laser-induced alteration of microstructural and microscopic transport properties in porous materials: Experiment, modeling and analysis

Porous materials are of great importance in various industrial applications. Microscopic modifications in the pore structures of these materials can change their functional behavior. We treat Indiana limestone by lasers to modify its pore structures microscopically. Microcomputed tomography (micro-CT) of the treated samples reveal that pulsed Nd:YAG laser with energy 330 mJ increases open porosity of limestone by 15% and almost doubles the total porosity. This laser increases the limestone pore connectivity by 460%. High power CO2 laser increases the open porosity by 20% but it reduces the pore connectivity of limestone. Our findings show that pulsed laser beams induce high increase in porosity and connectivity. 3D pore scale modeling using Cascaded lattice Boltzmann method (CLBM) on a D3Q27 model shows that regions treated by pulsed Nd:YAG lasers exhibit enhanced fluid transport efficiency compared to untreated regions. The obtained results successfully demonstrate that lasers can be used to induce a well controlled heat transfer in porous materials directly enhancing their morphometric characteristics and microscopic fluid transport behavior.

Numerical study of the particle sedimentation in a viscous fluid using a coupled DEM-IB-CLBM approach

At low terminal Reynolds numbers Re=2–10, there are multiple asymmetrical principal movement states for the sedimentation of a pair of particles in a channel filled with a viscous fluid. The main emphasis of this work is to investigate the formation process of these states and the effect of the natural rotation on the process when particles are released symmetrically. The flow field around each particle is fully resolved with an Immersed Boundary Method (IBM) coupled with the Cascaded Lattice Boltzmann Method (CLBM). An improved algorithm is developed to couple IBM with CLBM which can fully exploit the Graphics Processing Unit (GPU) for parallelisation. The collision between particles is handled with the Discrete Element Model (DEM). The approach is validated considering the sedimentation of a single particle released asymmetrically and also the Drafting–Kissing–Tumbling (DKT) problem of two particles.The trajectories of particles corresponding to different principal movement states are determined for the sedimentation of a pair of particles released symmetrically in a long narrow channel. By analysing the trajectories, it is found that particles go through two distinct symmetry breaking phenomena, a sudden lateral migration that leads to asymmetrically moving centres, and (or) a divergent oscillation that leads to a zero phase lag between the fundamental frequencies of oscillating particles. Since particle's lateral movement and natural rotation display a strong coherence of nearly 1.0 over a transitional oscillatory period, the trajectories of particles without rotational degree-of-freedom are then considered to determine the impacts of natural rotation on the principal movement states. It is shown that the lateral migration can still take place even after removing the rotational degree-of-freedom. However, the divergent oscillation disappears, which makes particles move in a steady oblique or horizontal structure and leads to a smaller terminal Reynolds number.

A cascaded lattice Boltzmann model for thermal convective flows with local heat sources

A cascaded central moment based lattice Boltzmann (LB) method for solving low Mach number thermal convective flows with source terms in two-dimensions in a double distribution function framework is presented. For the passive temperature field, which satisfies the convection diffusion equation (CDE) with a source term to represent internal/external local heat source, a new cascaded collision kernel is presented. Due to the use of a single conserved variable in the thermal energy equation, the cascaded structure in its collision operator begins from the first order moments and evolves to higher order moments. This is markedly different from the collision operator for the fluid flow equations, constructed in previous work, where the cascaded formulation starts at the second order moments in its collision kernel. A consistent implementation of the spatially and temporally varying source terms in the thermal cascaded LB method representing the heat sources in the CDE that maintains second order accuracy via a variable transformation is discussed. The consistency of the thermal cascaded LB method including a source term for the D2Q9 lattice with the macroscopic convection–diffusion equation is demonstrated by means of a Chapman–Enskog analysis. The new model is tested on a set of benchmark problems such as the thermal Poiseuille flow, thermal Couette flow with either wall injection or including viscous dissipation and natural convection in a square cavity. The validation study shows that the thermal cascaded LB method with source term is in very good agreement with the analytical solutions or numerical results reported for the benchmark problems. In addition, the numerical results show that our new thermal cascaded LB model maintains second order accuracy.

Consistent forcing scheme in the cascaded lattice Boltzmann method.

In this paper, we give an alternative derivation for the cascaded lattice Boltzmann method (CLBM) within a general multiple-relaxation-time (MRT) framework by introducing a shift matrix. When the shift matrix is a unit matrix, the CLBM degrades into an MRT LBM. Based on this, a consistent forcing scheme is developed for the CLBM. The consistency of the nonslip rule, the second-order convergence rate in space, and the property of isotropy for the consistent forcing scheme is demonstrated through numerical simulations of several canonical problems. Several existing forcing schemes previously used in the CLBM are also examined. The study clarifies the relation between MRT LBM and CLBM under a general framework.