This study simulates pore-scale two-dimensional flows through porous media composed of circular grains with varied pore-scale heterogeneity to analyze non-Darcy flow effects on different types of porous media using the lattice Boltzmann method. The magnitude of non-Darcy coefficients and the critical Reynolds number of non-Darcy flow were computed from the simulation results using the Forchheimer equation. Although the simulated porous materials have similar porosity and representative grain diameters, larger non-Darcy coefficients and an earlier onset of non-Darcy flow were observed for more heterogeneous porous media. The simulation results were compared with existing correlations to predict non-Darcy coefficients, and the large sensitivity of non-Darcy coefficients to pore-scale heterogeneity was identified. The pore-scale heterogeneity and resulting flow fields were evaluated using the participation number. From the computed participation numbers and visualized flow fields, a significant channeling effect for heterogeneous media in the Darcy flow regime was confirmed compared with that for homogeneous media. However, when non-Darcy flow occurs, this channeling effect was alleviated. This study characterizes non-Darcy effect with alleviation of the channeling effect quantified with an increase in participation number. Our findings indicate a strong sensitivity of magnitude and onset of non-Darcy effect to pore-scale heterogeneity and imply the possibility of evaluating non-Darcy effect through numerical analysis of the channeling effect.

In this paper, the lattice Boltzmann method-large eddy simulation (LBM-LES) model was combined with the volume of fluid (VOF) method and used to simulate vortex flow in a typical pump intake. The strain rate tensor in the LES model is locally calculated utilizing nonequilibrium moments based on Chapman–Enskog expansion, and the bounce-back scheme is used for nonslip condition on the solid wall and VOF method for the free surface. The evolution of all kinds of cells on the free surface is based on the mass exchange in the VOF method, i.e., lattice Boltzmann-single phase (LB-SP) free surface model. The introduction of the external force terms is established through adding corresponding expressions on the right of the lattice Boltzmann equation (LBE), and by modifying the velocity. The predicted vortex flow patterns (core location and strength of the vortex) and velocity correlate with the experiments undertaken with the physical model. A comparison of the results demonstrates the feasibility and stability of the model and the numerical method in predicting vortex flows inside pump intakes. The model developed and presented in this paper provides a new analysis method of vortex flow patterns in pump intake from a mesoscopic perspective, enriches the relevant technologies, and makes corresponding contributions to further engineering applications .

Flow past a porous square cylinder, which is constituted by an array of small square cylinders, was studied by simplified and highly stable lattice Boltzmann method (LBM) at Re = 4000. The effects of solid volume fractions (SVF) on the flow structure and important aerodynamic parameters were investigated and the internal fluid was described by phase-averaged method and its interaction with the near region. Several energy-contained Strouhal numbers come up in cylinder arrays, and mass flux through arrays is calculated to estimate the effects of blocking. The average total force on the array is found to decrease monotonically with decreasing SVF, and it has a dramatic drop as SVF decreasing from 0.062 to 0.036. The mass flux of array for SVF = 0.062 is smaller than that of 0.073 due to the stagger arrangement of isolated cylinders. The underlying Reynolds stresses reveal the increase in mean wake length as SVF decreases, and it behaves like the solid one for SVF = 0.132. Comparing with the other SVFs, the shear layer region at SVF = 0.132 indicates a significant decrease of curvature and a linear increase of growth rate, but a nonlinear growth rate for the other SVFs can be observed. The local maximum turbulent kinetic energy (TKE) and vorticity in shear layer region reveal the variation during the initial stages following separation. Moreover, detailed investigations of instantaneous wake dynamics provide an assistance to understand the flow physics of cylinder arrays for different SVF.

We study drag reduction of a uniform flow over a flat surface due to a series of rectangular microgrooves created on the surface. The results reveal that making grooves on the surface usually leads to the generation of secondary vortices inside the grooves that, in turn, decreases the friction drag force and increases the pressure drag force. By increasing the thickness of the grooves to the thickness of the obstacle, the pressure drag increases due to the enhancement of the generated vortices and the occurrence of separation phenomenon and the friction drag reduces due to a decrease of the velocity gradient on the surface. In addition, by increasing the grooves depth ratio, the pressure drag coefficient decreases and the friction drag coefficient increases. However, the impact of the pressure drag coefficient is higher than that of the friction drag coefficient. From a specific point, increasing the groove depth ratio does not effect on decreasing the total pressure drag of the plate. Therefore, creating the grooves in flat surfaces would reduce the total drag coefficient of the plate if the thickness of the grooves does not exceed a specific size and the depth of the grooves is chosen to be sufficiently large. The lattice-Boltzmann method (LBM) is used and the optimal reduction of the drag coefficient is calculated. It is found that for the width ratio equal to 0.19 and the groove depth ratio equal to 0.2548, about 7% decrease is achieved for the average total drag.

To characterize the microflow over a larger range of Knudsen numbers, an improved kinetic equation considering the volume diffusion effect for nonideal gases was presented based on Klimontovich's kinetic equation and Enskog equation-based lattice Boltzmann Bhatnagar–Gross–Krook (LBGK) model. Then, with the modified effective viscosity and the second-order slip boundary condition, a series of numerical simulations of gas flows with different mean Knudsen numbers were carried out based on the proposed model. Compared with the solutions of Navier–Stokes equations, Navier–Stokes equations with different slip boundary conditions, bivelocity hydrodynetics, and experimental data, we found that the present model can be valid up to a Knudsen number of 30. It is also shown that the present model furnishes a better solution in the transitional flow regime (0.1 < Kn < 10). The results not only illustrate that the present model could offer a satisfactory solution to a wider range of mean Knudsen number, but also show the importance of the compressibility and surface-dominated effects in micro gas flows. The improved model provides a promising tool for handling the micro gas flows with complex geometries and boundaries.

To provide porous media substrates that are quick to generate and characterize for lattice Boltzmann analysis, we propose a straightforward algorithm. The method leverages the benefits of the lattice Boltzmann method (LBM), and is extensible to multiphysics flows. Several parameters allow for simple customization. The generation algorithm and LBM are reviewed, and suggested implementation covered. Additionally, results are discussed and interpreted to evaluate the approach. Several verification tools are employed such as Darcy's law, the Ergun equation, the Koponen correlation, a newly proposed correlation, and experimental data. Agreement and repeatability are found to be excellent, suggesting this relatively simple method is a good option for engineering studies.

The local hemodynamic factor plays a vital role in the formation and progression of atherosclerosis. In this study, we simulated pulsatile flow patterns in the three-dimensional stenosed and normal carotid artery bifurcations throughout a cardiac cycle using the multiple-relaxation-time lattice Boltzmann (MRT-LB) method. Additionally, we investigated the time-varied flow rate and its division ratios between the parent and daughter branches, the multidirectionality of the stress field, and the averaged local energy dissipation rate. The results can be used in computational modeling of carotid artery hemodynamics and further investigation of the relationship between hemodynamics and cardiovascular diseases.

Lattice Boltzmann equation with Bhatnagar–Gross–Krook (BGK) model is applied to simulate unsteady laminar flow around a confined square obstacle, in order to study the vortex shedding and their interaction in the flow on the mass transfer in the parietal zone of a channel. The model was tested by comparing to an experimental study via standard particle image velocimetry (PIV). A post-processing was used to well extract instantaneous vortices contained in the flow downstream obstacles. A sensor with zero concentration on the surface is placed on the channel wall to study the effect of wake instabilities on the parietal mass transfer.

In recent years, lattice Boltzmann methods (LBMs) have become popular for solving fluid flow problems of engineering interest. Reasons for this popularity are due to the advantages of this method, which are, for example, the simplicity to handle complex geometries and the high efficiency in calculating transient flows. For the operational reliability and efficiency of pumps and pump systems, the incoming flow conditions are crucial. Since the efficiency and reliability requirements of pumps are rising and must be guaranteed by the pump and plant manufacturer, the flow conditions in pump intakes need to be evaluated during plant design. Recent trends show that pump intakes are built more and more compact, what makes the flow in the intake even more complex and holds a higher risk for unacceptable pump inflow conditions. In this contribution, a numerical scheme for the simulation of pump intake flows based on a lattice Boltzmann-large eddy simulation (LES) approach is presented and the ability of the method to capture the flow phenomena in intake flows is analyzed. Special attention is turned to the potential of the numerical scheme to reproduce the transient vortex behavior of intake flows, which results in a very complex flow structure and is challenging to model numerically.

A three-dimensional (3D), multiphase lattice Boltzmann approach is used to study a pressure-driven displacement flow of two immiscible liquids of different densities and viscosities in a square duct. A three-dimensional, 15-velocity (D3Q15) lattice model is used. The effects of channel inclination, viscosity, and density contrasts are investigated. The contours of the density and the average viscosity profiles in different planes are plotted and compared with those obtained in a two-dimensional (2D) channel. We demonstrate that the flow dynamics in a 3D channel is quite different as compared to that of a 2D channel. We found that the flow is relatively more coherent in a 3D channel than that in a 2D channel. A new screw-type instability is seen in the 3D channel that cannot be observed in the 2D channel.

Lattice Boltzmann method (LBM) is a relatively recent computational technique for fluid dynamics that derives its basis from a mesoscopic physics involving particle motion. While the approach has been studied for different types of fluid flow problems, its application to eddy-capturing simulations of building block complex turbulent flows of engineering interest has not yet received sufficient attention. In particular, there is a need to investigate its ability to compute turbulent flow involving separation and reattachment. Thus, in this work, large eddy simulation (LES) of turbulent flow over a backward facing step, a canonical benchmark problem which is characterized by complex flow features, is performed using the LBM. Multiple relaxation time formulation of the LBM is considered to maintain enhanced numerical stability in a locally refined, conservative multiblock gridding strategy, which allows efficient implementation. Dynamic procedure is used to adapt the proportionality constant in the Smagorinsky eddy viscosity subgrid scale model with the local features of the flow. With a suitable reconstruction procedure to represent inflow turbulence, computation is carried out for a Reynolds number of 5100 based on the maximum inlet velocity and step height and an expansion ratio of 1.2. It is found that various turbulence statistics, among other flow features, in both the recirculation and reattachment regions are in good agreement with direct numerical simulation and experimental data.

The lattice Boltzmann method (LBM) is shown to be equivalent to the Navier-Stokes equations by applying the Chapman-Enskog (C-E) expansion, which has been established by pioneer researchers. However, it is still difficult for elementary researchers. There is no clear explanation of the small parameter ε used in the C-E expansion. There are several expressions for the viscosity coefficient; some are unclear on the relationship with ε. There are two expressions on the LBM evolution equation. Elementary researchers are perplexed as to which is correct. The LBM achieves second order accuracy by including the numerical viscosity within the physical viscosity. This is not only difficult for elementary researchers to understand but also sometimes leads senior researchers into making errors. The C-E expansion of the LBM was thoroughly reviewed and is presented as a self-contained form in this paper. It is natural to use the time step Δt as ε. The viscosity coefficient is expressed as μ∝Δxc(τ − 1/2). The viscosity relationship and the second order accuracy were confirmed by numerical simulations. The difference in the two expressions on the LBM evolution is simply one of perspective. They are identical. The difference between the relaxation parameter τ D for the discrete Boltzmann equation and τ for the LBM was discussed. While τ D is a quantity of time, τ is genuinely nondimensional, which is sometimes overlooked.

Relationship between accuracy and number of velocity particles in velocity slip phenomena was investigated by numerical simulations and theoretical considerations. Two types of 2D models were used: the octagon family and the D2Q9 model. Models have to possess the following four prerequisites to accurately simulate the velocity slip phenomena: (a) equivalency to the Navier–Stokes equations in the N-S flow area, (b) conservation of momentum flow P x y in the whole area, (c) appropriate relaxation process in the Knudsen layer, and (d) capability to properly express the mass and momentum flows on the wall. Both the octagon family and the D2Q9 model satisfy conditions (a) and (b). However, models with fewer velocity particles do not sufficiently satisfy conditions (c) and (d). The D2Q9 model fails to represent a relaxation process in the Knudsen layer and shows a considerable fluctuation in the velocity slip due to the model’s angle to the wall. To perform an accurate velocity slip simulation, models with sufficient velocity particles, such as the triple octagon model with moving particles of 24 directions, are desirable.

Conventional lattice Boltzmann method (LBM) is hyperbolic and can be solved locally, explicitly, and efficiently on parallel computers. The LBM has been applied to different types of complex flows with varying degrees of success, and with increased attention focusing on microscale flows now. Due to its small scale, microchannel flows exhibit many interesting phenomena that are not observed in their macroscale counterpart. It is known that the Navier–Stokes equations can still be used to treat microchannel flows if a slip-wall boundary condition is assumed. The setting of boundary conditions in the conventional LBM has been a difficult task, and reliable boundary setting methods are limited. This paper reports on the development of a finite difference LBM (FDLBM) based numerical scheme suitable for microchannel flows to solve the modeled Boltzmann equation using a splitting technique that allows convenient application of a slip-wall boundary condition. Moreover, the fluid viscosity is accounted for as an additional term in the equilibrium particle distribution function, which offers the ability to simulate both Newtonian and non-Newtonian fluids. A two-dimensional nine-velocity lattice model is developed for the numerical simulation. Validation of the FDLBM is carried out against microchannel and microtube flows, a driven cavity flow, and a two-dimensional sudden expansion flow. Excellent agreement is obtained between numerical calculations and analytical solutions of these flows.

A new and generalized lattice Boltzmann model for simulating thermal two-phase flow is described. In this model, the single component multi-phase lattice Boltzmann model proposed by Shan and Chen is used to simulate the fluid dynamics. The temperature field is simulated using the passive-scalar approach, i.e., through modeling the density field of an extra component, which evolves according to the advection-diffusion equation. By coupling the fluid dynamics and temperature field through a suitably defined body force term, the thermal two-phase lattice Boltzmann model is obtained. In this paper, the theoretical foundations of the model and the validity of the thermal lattice Boltzmann equation method are laid out, illustrated by analytical and numerical examples. In a companion paper ( P. Yuan and L. Schaefer, 2006, ASME J. Fluids Eng., 128, pp. 151–156 ), the numerical results of the new model are reported.

In the previous paper (Part 1) ( P. Yuan and L. Schaefer, 2006, ASME J. Fluids Eng., 128, pp. 142–150 ), the multiphase isothermal lattice Boltzmann equation (LBE) model and single phase thermal LBE (TLBE) model were described. In this work, by combining these two models, the thermal two-phase LBE model is proposed. The coupling of the two models is through a suitably defined body force term. Due to the external nature of this coupling, the new model will have the same stability as the isothermal two-phase model. The applicability of the model is shown by the numerical simulation results of a thermal two-phase flow system in a rectangular channel. Our preliminary studies show that different equations of state, variable wettability, gravity and buoyancy effects, and relatively high Rayleigh numbers can be readily simulated by this new model.