Narrow Results

The natural convection problem in a square cavity filled with heterogeneously porous medium is solved by lattice Boltzmann method. The temperature distribution is fully coupled with the fluid velocity through relaxation time. The present calculated results are in good agreement with available published data. It is found that the porosity of porous media near the walls has significant influence on the heat transfer, and the porosity of middle porous medium has little influence on the natural convection. It is of particular interest for thermal management in electronic packages, since it can reduce the space of air.

This paper reports a study of the ability of an improved LBM in replicating acoustic interaction. With a BGK model with two relaxation times approximating the collison term, the improved LBM is shown not only able to recover the equation of state, but also replicates the specific heat ratio, the fluid viscosity and thermal conductivity correctly. With these improvements, the recovery of full set of unsteady compressible Navier-Stokes equations is possible. Two complex aeroacoustic interaction problems, namely the interaction of three fundamental aeroacoustic pulses and scattering of short wave by a zero circulation vortex, are calculated. The LBM solutions are compared with DNS results. In the first case it has been shown that the improved LBM is as effective as the DNS in simulating aeroacoustic interaction of three pulses. Both methods obtain essentially same results using same truncated domains. In the scattering problem, LBM is able to replicate the directivity of scattered acoustic wave from the vortex but it does not accurately reproduce the symmetry as calculated using DNS.

A lattice Boltzmann model using upstream finite volume scheme has been employed in the investigation of bifurcation and transition of flow through suddenly-expanded channels. To enhance the stability and accuracy of simulation, a fifth-order Runge–Kutta method is used for the time-marching and upwind biasing factors based on pressure are used as flux correctors in the lattice Boltzmann equation. In the range of Reynolds numbers investigated, the laminar flow through the expansion underwent a symmetry-breaking bifurcation. The critical Reynolds number evaluated from the experiments and the simulations were compared to other values reported in the literature. Comparisons are found to be quantitatively accurate. Furthermore, the results show that the critical Reynolds number decreases with increasing channel expansion ratio. At a fixed supercritical Reynolds number, the location at which the jet first impinges on the channel wall grows with the expansion ratio.

Monolithic columns have attracted much attention as a novel platform for high throughput analysis, but there is little information about the fluid profile in the flow channels. In this paper, we presented our approach for the fluid simulation in column chromatography by the lattice Boltzmann method (LBM). To simulate the monolithic column system, the calculation domain was modeled by the 3D channel flow through sphere obstacles. Several types of porous structure were used, with uniform and nonuniform pores. Based on the simulations results, we discussed fluid flow and pressure variation for the optimization of the suitable structure for HPLC system.

The main goal of the present study is to investigate the heat transfer enhancement in a channel partially filled with an anisotropic porous block (Porous Foam) using the lattice Boltzmann method (LBM). Combined pore level simulation of flow and heat transfer is performed for a 2D channel which is partially filled with square obstacles in both ordered and random arrangements by LBM which is not studied completely in the literature. The effect of the Reynolds number, different arrangements of obstacles, blockage ratio and porosity on the velocity and temperature profiles inside the porous region are studied. The local and averaged Nusselt numbers on the channel walls along with the respective confidence interval and comparison between results of regular and random arrangements are presented for the first time. For constant porosity and block size, the maximum value of averaged Nusselt number in the porous block is obtained in the case of random arrangement of obstacles. Also, by decreasing the porosity, the value of averaged Nusselt number is increased. Heat transfer to the working fluids increases significantly by increasing the blockage ratio. Several blockage ratios with different arrangements are checked to obtain a correlation for the Nusselt number.

Many rheological properties of blood, along with transport properties of blood cells can be captured by means of modeling blood through its main constituents, red blood cells (RBCs) and plasma. In the current work, we present a fully resolved two-dimensional model for blood suspension flow, employing a discrete element model (DEM) for RBCs and coupling it to a lattice Boltzmann method (LBM) fluid solver using the immersed boundary method (IBM). We identify an efficient computationally reduced mesoscopic representation of cells and flow, still able to recover essential physics and physiological phenomena. Our model is found to agree quantitatively with experimental findings. The Fåhræus–Lindqvist effect and shear thinning is recovered, while the thickness of the cell-free layer (CFL) matches the observations. In addition, we investigate the tank-treading frequency of a single RBC in shear flow along with the transition from tumbling to tank-treading, also matching experimental data.

In this work, a multiple relaxation time (MRT) extension of the recently introduced constant speed kinetic model (CSKM) is proposed. The CSKM, which is an entropic kinetic model and based on unconventional entropies of Burg and Tssalis, was introduced in [A. Zadehgol and M. Ashrafizaadeh, J. Comput. Phys.274, 803 (2014)]; [A. Zadehgol Phys. Rev. E91, 063311 (2015)] as an extension of the model of Boghosian et al. [Phys. Rev. E68, 025103 (2003)] in the limit of fixed speed continuous velocities. The present extension improves the stability of the previous models at very high Reynolds numbers, while allowing for a more convenient orthogonal lattice. The model is verified by solving the following benchmark problems: (i) the lid driven square cavity and (ii) the Kelvin–Helmholtz instability of thin shear layers in a doubly periodic square domain.

The aim of this paper is investigating the forced convection heat transfer in a channel with transverse rectangular cavities using the lattice Boltzmann method (LBM) which is not available in the literature yet. The effects of the Reynolds number (100–400), cavity aspect ratio ($\mathrm{\text{AR}}=0.25$, 0.5, 1.0), distance of cavities from each other ($S^{\prime }=0,2,4,6$) in fixed depth of cavity ($A^{\prime }=0.5$) on the velocity and temperature profiles are studied. Moreover, the flow patterns such as deflection and re-circulation zone inside the cavities are obtained. The local and averaged Nusselt numbers on the channel walls are achieved. The results show that the channel with cavities achieves heat transfer enhancements relative to the smooth channel. For the constant cavity aspect ratio, the maximum value of averaged Nusselt number in the channel is obtained in the case of $S^{\prime }=2$. Heat transfer to the working fluids increases significantly by increasing the aspect ratio. The existed results are used to ascertain the validity of the numerical code and excellent agreement between results was found.

In this work, application of the recently introduced constant speed kinetic model (CSKM) [A. Zadehgol and M. Ashrafizaadeh, J. Comp. Phys.274 803, (2014); A. Zadehgol, Phys. Rev. E91, 063311 (2015)] in simulating fluid flow through porous media is explored. Discrete forms of Tsallis and Burg entropy functions were first introduced by Boghosian et al. [Phys. Rev. E$68$, 025103, (2003)], in the context of lattice Boltzmann model (LBM). In the CSKM, the virtual particles are concentrated on n-dimensional (nD-) spheres centered at the computational nodes. Using continuous forms of the unconventional entropies of Burg, $h\sim logf$ (for 2D), and Tsallis, $h\sim f^{1-\frac{2}{n}}$ (for nD with $n\ge 3$), the CSKM extends the work of Boghosian et al., in the limit of fixed speed continuous velocities. In this work, the second-order accuracy, efficiency, and thermodynamic consistency of the 2D- and 3D-projections of the 4D-CSKM are explored and numerically verified.

A numerical investigation is carried out to analyze the flow patterns, drag and lift coefficients, and vortex shedding around a square cylinder using a control circular bar upstream and downstream. Lattice Boltzmann method (LBM) was used to investigate flow over a square cylinder controlled by upstream and downstream circular bar, which is the main novelty of this study. Compared with those available results in the literature, the code for flow over a single square cylinder proves valid. The Reynolds number (Re) based on the width of the square cylinder ($D$) and diameter of circular bar ($d$) are 100 for square cylinder, 30 and 50 for different circular bars. Numerical simulations are performed in the ranges of $1\le L∕D\le 5$ and $1\le G∕D\le 5$, where $L$ and $G$ are the center-to-center distances between the bar and cylinder. Five distinct flow patterns are observed in the present study. It is found that the maximum percentage reduction in drag coefficient is 59.86% by upstream control bar, and the maximum percentage reduction in r.m.s. lift coefficient is 73.69% by downstream control bar. By varying the distance ratio for the downstream control bar, a critical value of distance ratio is found where there are two domain frequencies.

In this study, lattice Boltzmann method (LBM) simulation is performed to investigate laminar forced convection of nanofluids in a horizontal parallel-plate channel with three rectangular cavities. Two cavities are considered as located on the top wall of the channel and one on the bottom wall. The effects of the Reynolds number (100–400), the cavity aspect ratio (AR = 0.25, 0.5), the various distances of the cavities from each other ($X_c^{\prime }$) at different solid volume fractions of nanofluids ($\varphi =0-0.05$) on the velocity and the temperature profiles of the nanofluids are studied. In addition, the flow patterns, i.e. the deflection and re-circulation zone inside the cavities, and the local and averaged Nusselt numbers on the channel walls are calculated. The results obtained are used to ascertain the validity of the written numerical code, which points to the excellent agreement across the results. The results show that, as the solid volume fraction of nanofluids is enhanced, the transfer of heat to working fluids increases significantly. Further, the results show that the maximum value of the averaged Nusselt number in the channel is obtained at $X_c^{\prime }=0.1204$ for AR = 0.5 and $X_c^{\prime }=0.1024$ for AR = 0.25. The interval [0.1224, 0.1304] is the best position for the second cavity. It is concluded that the results of this paper are very useful for designing optimized heat exchangers.

Recently, various ways are investigated to augment heat transfer in different applications such as porous ceramic domain. Adding nanoparticles to fluid is the best operational way to increase the conduction of fluids. In this paper, migration of nanofluid inside a porous duct under the impact of magnetic force is scrutinized. LBM is applied to present comprehensive parametric analysis for various concentrations of nanofluid, Hartmann, Reynolds, and Darcy numbers. Outputs illustrate that Nu augments with improve of Lorentz forces. Augmenting Da significantly enhances the convective flow in our model.

Lattice Boltzmann method (LBM) was used to simulate two-dimensional MHD Al₂O₃/water nanofluid flow and heat transfer in an enclosure with a semicircular wall and a triangular heating obstacle. The effects of nanoparticle volume fraction ($0\le \varphi \le 0.05$), Rayleigh number $(10^4\le Ra\le 10^6)$, Hartmann number $(0\le Ha\le 60)$ and heating obstacle position (Cases 1–7) on flow pattern, temperature distribution and rate of heat transfer were investigated. The results show that with the enhancing Rayleigh number, the increasing nanoparticle volume fraction and the reducing Hartmann number, an enhancement in the average Nusselt number and the heat transfer appeared. The effect of Ha on the average Nu increases by increasing the Ra. It can also be found that the action of changing the heating obstacle position on the convection heat transfer is more important than that on the conduction heat transfer. The higher obstacle position in Cases 6 and 7 leads to the small value of the average Nusselt number. Moreover, the effect of Ha on average Nu in Case 1 at $Ra=10^6$ is more significant than other cases because the flow pattern in Case 1 is changed as increasing Ha.

Marangoni surface tension forcing soap film is numerically solved by Lattice Boltzmann Method (LBM). A delicate false force term in the LBM equation is proposed to describe the Marangoni forcing soap film. The validity of LBM is elucidated by the linear theory of surface tension profile as a function of the vertical position of the soap film. The effect of thickness on the statistical behaviors of the Marangoni forcing soap film is discussed from three aspects: the energy spectrum, energy transfer and intermittency. It is found that the scaling behavior of energy spectrum is independent of the scaling constant of thickness $\alpha$ where the range of $\alpha$ is from 0.2 to 0.3. The scaling behavior of energy spectrum is $k^{-5∕3}$, which is in accordance with the Kraichnan theory in the inverse cascade. In the large-scale range, the energy flux cascades to the small scale which is called as a forward cascade process. In this scale range, more energy flux cascades to the small scale when the value of $\alpha$ becomes larger. On the contrary, the backward cascade is involved in the small-scale range of the thinned film where more energy transfers to the large scale as the value of $\alpha$ is smaller. The intermittency measured by PDF of the velocity increment exists in the turbulent soap film. The universal scaling law of the velocity structure function is identical with the 3D S-L intermittency model and our 2D intermittency theory.

In this paper, effects of nondimensional distance between two square cylinders on the dissipation characteristics of the complex flow are investigated. The viscosity entropy generation rates around two serial square cylinders and the lift coefficient are analyzed to fully reveal the statistical features of the flow dissipation. Numerical results mainly show that the major viscosity entropy generation rate appears in the shear intersection region of the main flow and local stationary vortex. The viscosity entropy generation rate increases with increasing nondimensional distance ($S^{\ast }$). The increasing slope of the viscosity entropy generation rate at a range of $S^{\ast }\le 2$ is greater than that of $2\le S^{\ast }\le 5$. It is also found that the viscosity entropy generation rate is kept as a constant when the nondimensional distance $S^{\ast }$ is greater than 5. At $S^{\ast }\ge 5$, the effect of downstream square cylinder becomes negligible on the viscosity entropy generation rate. The fluctuating amplitude increases with increasing the nondimensional distance $S^{\ast }$. The high-frequency peak is ascribed to the strong vortex shedding around the downstream square cylinder, and the low-frequency peak is ascribed to the weak vortex shedding around the up square cylinder at $S^{\ast }=1$. Although our focus is mainly on the complex flow around two square cylinders, this work demonstrates the viscosity entropy generation rate with increasing nondimensional distance, which provides nice physical insight into understanding the local flow dissipation characteristics around the two serial square cylinders.

In this paper, the forced convection heat transfer of Ag–MgO/water hybrid micropolar nanofluid in a channel is studied numerically which the top wall of channel is smooth and bottom of it is in stairway form. The lattice Boltzmann method (LBM) is used for solving the fluid flow and heat transfer equations. The effects of Reynolds numbers ($Re=100$–400), volume fraction of nanofluid ($\varphi =0$, 0.01 and 0.02) and stairway aspect ratio ($a∕H=0.1$, 0.2 and 0.3) on the velocity, temperature and local and average Nusselt number profiles are investigated. The results show that by incrementing the Reynolds number and solid volume fraction and decreasing the $a$/$H$ simultaneously, the average Nusselt number increases.

This paper contains natural convection of Ag–MgO/water micropolar hybrid nanofluid in a hollow hot square enclosure equipped by four cold obstacles on the walls. The simulations were performed by the lattice Boltzmann method (LBM). The influences of Rayleigh number and volume fraction of nanoparticle on the fluid flow and heat transfer performance were studied. Moreover, the effects of some geometric parameters, such as cold obstacle height and aspect ratio, were also considered in this study. The results showed that when the aspect ratio is not large ($\mathrm{\text{AR}}=0.2$ or 0.4), at low Rayleigh number (10³), the two secondary vortices are established in each main vortex and this kind of secondary vortex does not form at high Rayleigh number (10⁶). However, at $\mathrm{\text{Ra}}=10^6$, these secondary vortices occur again in the middle two vortices at $\mathrm{\text{AR}}=0.6$, which is similar to that at $\mathrm{\text{Ra}}=10^3$. At $\mathrm{\text{AR}}=0.2$, the critical Rayleigh number, when the dominated mechanism of heat transfer changes from conduction to convection, is 10⁴. However, the critical Rayleigh number becomes 10⁵ at $\mathrm{\text{AR}}=0.4$ or 0.6. When the cold obstacle height increases, the shape of the vortices inside the enclosure changes due to the different spaces. Besides, at $\mathrm{\text{Ra}}=10^6$, for different cold obstacle heights, the location of the thermal plume is different, owing to the different shapes of vortices. Accordingly, the average Nusselt number increases by increment of the Rayleigh number, nanoparticle volume fraction, cold obstacle height and aspect ratio.

The coupling of numerical methods in different scales is of great significance in the investigation of intricate multiscale phenomena. This work develops a dynamic coupling approach based on domain decomposition by combining the mesoscale lattice Boltzmann method (LBM) and microscale molecular dynamics (MD) simulations. In the proposed scheme, a two-way concurrent exchange of information between different scales has been achieved. At the atomistic scale, the fluid dynamics are modeled through the particle-based MD method on the framework of the open large-scale atomic/molecular massively parallel simulator (LAMMPS). While at the coarse scale, the fluid system is simulated utilizing the LBM approach, which relies on the collision and streaming of the particles constrained in discretized lattices, adhering to the conservation laws of mass and momentum. The exchange of velocity distributions between the two scales was handled. The accuracy and efficiency of the proposed coupling scheme were validated through simulations of the classic Poiseuille and Couette flows. The obtained results show that satisfactory agreement against pure MD results has been achieved. Moreover, a notable improved efficiency as high as 92.8% has been observed for the coupling scheme in comparison to MD simulations. Due to the inherent parallelism of LBM and MD, the proposed coupling scheme exhibits great potential for extended application in studying complex multiscale phenomena with dynamic coupling between different scales.

A new optimization strategy based on system performance optimization life cycle (SPOLC) is introduced for high-performance lattice Boltzmann simulations of three-dimensional decaying isotropic turbulence. This strategy improves the performance of turbulent flow simulations in periodic boxes at different resolutions using the lattice Boltzmann method (LBM). The strategy improves the performance by modifying the lattice Boltzmann model, mathematical representation, computational algorithm, software implementation, and computing hardware utilization. The modifications include: (1) Establishing the slice concept as a logical grouping layer added to the LBM, applying an aggregation–disaggregation mechanism, enabling two-dimensional (2D) operation on the three-dimensional (3D) model, (2) improving lattice data access pattern by using an alternative one-dimensional (1D) array for numerical representation instead of the 3D cubic representation, (3) major reduction in memory access iterations by switching from function-wise iteration method to lattice-wise iteration method by applying code fusion to the streaming, velocity and collision model functions and iterations, (4) applying process parallelization and data vectorization, (5) achieving a much more efficient utilization of modern compute units by increasing the adaption of stream processing model. Furthermore, a correctness validation process has been applied by conducting lattice-wise value comparisons between the proposed solution output and the original implementation output. Simulations of decaying isotropic turbulence at resolutions ranging from $32^3$ to $512^3$ using the LBM are carried out for these purposes. Calculations are performed on two systems with distinct specifications, to validate the effectiveness and portability of the SPOLC strategy. The calculation times are significantly reduced after applying the SPOLC strategy on S1 with the lattice Boltzmann relaxation time $\tau =0.503$ by over $69\%$ compared to S2’s original time, increasing to $95.47\%$ at higher resolutions. Different features of the flow fields are depicted and their characteristics are discussed. Thin tubes are visualized, and the energy spectra are studied. All fields are initialized by a forced turbulent field simulated in a previous study using the LBM.

In this paper, a CFD parallel adaptive algorithm is self-developed by combining the multi-block Lattice Boltzmann Method (LBM) with Adaptive Mesh Refinement (AMR). The mesh refinement criterion of this algorithm is based on the density, velocity and vortices of the flow field. The refined grid boundary is obtained by extending outward half a ghost cell from the coarse grid boundary, which makes the adaptive mesh more compact and the boundary treatment more convenient. Two numerical examples of the backward step flow separation and the unsteady flow around circular cylinder demonstrate the vortex structure of the cold flow field accurately and specifically.