Multiple-relaxation-time lattice Boltzmann simulation of free convection and irreversibility of nanofluid with variable thermophysical properties

This numerical study demonstrates heat transfer and irreversibility or entropy generation of non-Newtonian power-law Al2O3-H2O (aluminum oxide-water) nanofluids in a square enclosure using multiple-relaxation-time lattice Boltzmann method accelerated by graphics processing unit computing. In this investigation, the effective thermal conductivity and viscosity are variables, and they depend on the fluid temperature and rate of strain, respectively. The enclosure’s left and right walls are uniformly heated with different temperatures, and the upper and lower walls are thermally adiabatic. There is no valid study and results on non-Newtonian fluid using multiple-relaxation-time lattice Boltzmann method for this configuration and hence the novelty of the present results have been ensured. This paper has formulated and appropriately validated the Newtonian and non-Newtonian natural convection problem with the available numerical results. This study includes a set of comprehensive simulations, showing the effects of these fluids’ natural convection by varying three key parameters: the Rayleigh number, the volume fraction of nanoparticles, and the power-law index on the streamlines, isotherms, local and average Nusselt number as well as the local and total entropy generation. The results show that increasing the volume fraction of the nanoparticles from 0% to 2%, the average rate of heat transfer and the total entropy generation increase 6.5% and 7.4%, respectively, while the Rayleigh number, Ra = 105 and the power-law index n = 0.6.

A unified lattice Boltzmann model and application to multiphase flows

In this work, we develop a unified lattice Boltzmann model (ULBM) framework that can seamlessly integrate the widely used lattice Boltzmann collision operators, including the Bhatnagar–Gross–Krook or single-relation-time, multiple-relaxation-time, central-moment or cascaded lattice Boltzmann method and multiple entropic operators (KBC). Such a framework clarifies the relations among the existing collision operators and greatly facilitates model comparison and development as well as coding. Importantly, any LB model or treatment constructed for a specific collision operator could be easily adopted by other operators. We demonstrate the flexibility and power of the ULBM framework through three multiphase flow problems: the rheology of an emulsion, splashing of a droplet on a liquid film and dynamics of pool boiling. Further exploration of ULBM for a wide variety of phenomena would be both realistic and beneficial, making the LBM more accessible to non-specialists. This article is part of the theme issue ‘Progress in mesoscale methods for fluid dynamics simulation’.

Linear and brute force stability of orthogonal moment multiple-relaxation-time lattice Boltzmann methods applied to homogeneous isotropic turbulence

Multiple-relaxation-time (MRT) lattice Boltzmann methods (LBM) based on orthogonal moments exhibit lattice Mach number dependent instabilities in diffusive scaling. The present work renders an explicit formulation of stability sets for orthogonal moment MRT LBM. The stability sets are defined via the spectral radius of linearized amplification matrices of the MRT collision operator with variable relaxation frequencies. Numerical investigations are carried out for the three-dimensional Taylor–Green vortex benchmark at Reynolds number 1600. Extensive brute force computations of specific relaxation frequency ranges for the full test case are opposed to the von Neumann stability set prediction. Based on that, we prove numerically that a scan over the full wave space, including scaled mean flow variations, is required to draw conclusions on the overall stability of LBM in turbulent flow simulations. Furthermore, the von Neumann results show that a grid dependence is hardly possible to include in the notion of linear stability for LBM. Lastly, via brute force stability investigations based on empirical data from a total number of 22 696 simulations, the existence of a deterministic influence of the grid resolution is deduced. This article is part of the theme issue ‘Progress in mesoscale methods for fluid dynamics simulation’.

A Three-Dimensional Phase Field Based Nonorthogonal Multiple-Relaxation-Time Lattice Boltzmann Method for Interface Tracking

Based on a conservative Allen-Cahn phase field method, a three-dimensional nonorthogonal multiple-relaxation-time (MRT) lattice Boltzmann (LB) model for interface tracking in multiphase flow is proposed in this paper. Different from the traditional MRT LB model, the transformation matrix in the present model is constructed based on a set of nonorthogonal basis vectors to simplify the transformation process between the discrete velocity space and the moment space. Therefore, a higher computational efficiency is achieved by the present model. The present model is developed on two different three-dimensional lattice sets (D3Q19 and D3Q27) to obtain a thorough perspective about the performance of the nonorthogonal matrix. Coupled with the nonorthogonal transformation matrix, simplified discrete source terms are also developed for both two lattice sets to further improve the efficiency of the present model. Numerical tests demonstrate that compared with the traditional MRT LB model, the present model shows a significantly higher computational efficiency and better stability while maintaining a comparable accuracy. It is also found that the D3Q19 nonorthogonal model does not obviously weaken the accuracy of D3Q27 nonorthogonal model while D3Q27 nonorthogonal model dose not decrease the stability of the D3Q19 nonorthogonal model, which is different from the orthogonal model.

Three-Dimensional Weighted Multiple-Relaxation-Time Pseudopotential Lattice Boltzmann Method for Multiphase Flow

The pseudopotential lattice Boltzmann (LB) method has been widely used for simulating multiphase flow due to its concise concept and computational simplicity. In this paper, based on the weighted orthogonal transformation matrix, a three-dimensional (3D) weighted multiple-relaxation-time pseudopotential lattice Boltzmann method (WRMT-LBM) is developed, in which the standard lattice stencil D3Q19 is adopted. Compared with the classical multiple-relaxation-time pseudopotential lattice Boltzmann method (CMRT-LBM) based on the orthogonal transformation matrix, the expressions of the equilibrium density distribution function and discrete force term in moment space are simplified in the present model, which contributes to simplifying the program implementation and improving the computational efficiency. Moreover, an additional discrete source term in moment space compatible with the proposed model is introduced to achieve tunable surface tension. A series of numerical tests are then implemented to investigate the performance of the proposed model. Compared with the CMRT-LBM, the results of the present model can achieve lower spurious velocity and higher computational efficiency while keeping comparable accuracy. Furthermore, using the present model, three benchmark cases, including droplet oscillation, droplet impacting on wall and droplet impact on thin film, are performed to investigate the performance of this model. The numerical results are in good agreement with the analytical solutions or the empirical correlations in the literature, which demonstrates that the present model can simulate the multiphase flow with large density ratio.

MRT-LBM simulation of natural convection in square annulus with a porous coating: Route to chaos

In this work, multiple-relaxation-time lattice Boltzmann method is applied for examining the transient natural convection in a square annulus of circular interior cylinder. This duct is covered by a porous deposit on all interior walls. The Darcy-Brinkman-Forchheimer model is implemented to model the momentum equations in the porous matrix and the Boussinesq assumption is assumed for the buoyancy force term. The influence of Darcy number (10−6 ≤ Da ≤ 10−2), Rayleigh number (103 ≤ Ra ≤ 106), radius ratio of the circular cylinder (0.05 ≤ R ≤ 0.40) and the thickness of the porous layer (0.05 ≤  ≤ 0.15) on natural convection are analysed. The results are reported in the form of streamlines, isotherms and average Nusselt number. In addition, temporal evolution and phase portrait are plotted to examine the unsteady flow at elevated Rayleigh numbers. The results are coherent and show that natural convection develops from stable state to chaotic flow via periodic and quasi-periodic oscillatory regimes as the Rayleigh number increases.