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In the present study, a pore-scale multicomponent lattice Boltzmann method (LBM) is employed for the investigation of the immiscible-phase fluid displacement in a homogeneous porous medium. The viscous fingering and the stable displacement regimes of the invading fluid in the medium are quantified which is beneficial for predicting flow patterns in pore-scale structures, where an experimental study is extremely difficult. Herein, the Shan-Chen (S-C) model is incorporated with an appropriate collision model for computing the interparticle interaction between the immiscible fluids and the interfacial dynamics. Firstly, the computational technique is validated by a comparison of the present results obtained for different benchmark flow problems with those reported in the literature. Then, the penetration of an invading fluid into the porous medium is studied at different flow conditions. The effect of the capillary number (Ca), dynamic viscosity ratio (M), and the surface wettability defined by the contact angle (θ) are investigated on the flow regimes and characteristics. The obtained results show that for M

The vorticity dynamics of a Lamb-like dipole colliding with flat boundaries are investigated for high Reynolds number flows by implementation of the lattice Boltzmann method (LBM). The standard LBM based on the single-relaxation-time collision model suffers from numerical instabilities at high Reynolds numbers. Herein, a regularized collision model is employed for the LBM to preserve the stability and accuracy of the numerical solutions at such flow conditions. The computations are performed for the normal collision of the dipole with the no-slip boundary for several Reynolds numbers in the range of . The results obtained based on the regularized lattice Boltzmann (RLB) method for the statistical flow characteristics like the vorticity field and enstrophy quantity of the dipole-wall collision problem are investigated. The present study demonstrates that the shear-layer instabilities near the wall are responsible for rolling-up of the boundary layer before it is detached from the surface for high Reynolds numbers. This detachment mechanism leads to a viscous rebound and formation of small scale vortices. The shear-layer vortices formed dramatically influence the flow evolution after the collision and result strong enhancement of the total enstrophy of the flow field. By comparing the present results with those of provided by other numerical solutions, it is also concluded that the RLB scheme implemented is robust and sufficiently accurate numerical technique in comparison with the flow solvers based on the Navier-Stokes equations for predicting the statistical features of separated fluid flows even at high Reynolds numbers.

In this paper, several lattice Boltzmann (LB) collision models are evaluated by a comparative study for simulation of incompressible fluid flows with periodic and also with curved wall boundaries. Herein, the single-relaxation-time (SRT) scheme based on the Bhatnagar–Gross–Krook (BGK) approximation, multiple-relaxation-time (MRT), regularized lattice Boltzmann (RLB) and the entropic lattice Boltzmann (ELB) methods are considered. The doubly periodic shear layers flow problem is computed in two different Reynolds numbers to investigate the robustness and performance of the collision operators applied. Efficiency and accuracy of these techniques are also examined by computing the incompressible fluid flows around a circular cylinder at various flow conditions. The predicted results are compared with the experiments and the numerical results performed by other researchers. The present study demonstrates that the SRT model is accurate enough and efficient for simulation of fluid flows with low Reynolds numbers. This scheme, however, suffers from numerical instabilities at moderate Reynolds numbers and requires very fine grid resolutions to remain stable. It is found that the ELB scheme does not sufficiently reduce the numerical oscillation at high Reynolds number flows. This method provides fewer stability benefits while being more computationally expensive. The results obtained show that the MRT and RLB models are stable (in contrast to SRT and ELB) for all the cases considered in the present work even at high Reynolds numbers. In terms of computational efficiency and accuracy, the MRT and RLB schemes are more attractive and provide the results comparable to those of other experimental and numerical methods. The present study suggests that these two techniques based on the implementation of the lattice Boltzmann method are robust, sufficiently accurate and computationally efficient to resolve the flow structures and properties around the practical geometries even at high Reynolds numbers.

A computational technique based on the pseudo-potential multiphase lattice Boltzmann method (LBM) is employed to investigate the collapse dynamics of cavitation bubbles of various liquids in the vicinity of the solid surface with different wettability conditions. The Redlich-Kwong-Soave equation of state (EoS) that includes an acentric factor is incorporated to consider the physical properties of water $({\mathrm{H}}_{2}\mathrm{O})$, liquid nitrogen $(\mathrm{L}{\mathrm{N}}_{2})$, and liquid hydrogen $(\mathrm{L}{\mathrm{H}}_{2})$ in the present simulations. Accuracy and performance of the present multiphase LBM are examined by simulation of the homogenous and heterogeneous cavitation phenomena. The good agreement of the results obtained based on the present solution algorithm in comparison with the available data confirms the validity and capability of the multiphase LBM employed. Then, the cavitation bubble collapse near the solid wall is studied by considering the ${\mathrm{H}}_{2}\mathrm{O}$, $\mathrm{L}{\mathrm{N}}_{2},$ and $\mathrm{L}{\mathrm{H}}_{2}$ fluids, and the wettability effect of the surface on the collapse dynamics is investigated. The obtained results demonstrate that the collapse phenomenon for the ${\mathrm{H}}_{2}\mathrm{O}$ is more aggressive than that of the $\mathrm{L}{\mathrm{H}}_{2}$ and $\mathrm{L}{\mathrm{N}}_{2}$. The cavitation bubble of the water has a shorter collapse time with an intense liquid jet, while the collapse process in the $\mathrm{L}{\mathrm{N}}_{2}$ takes a longer time due to the larger radius of its bubble at the rebound. Also, this study demonstrates that the increment of the hydrophobicity of the wall causes less energy absorption by the solid surface from the liquid phase around the bubble that leads to form a liquid jet with higher kinetic energy. Therefore, the bubble collapse process occurs more quickly for hydrophobic surfaces, regardless of the fluids considered. The present study shows that the pseudopotential LBM with incorporating an appropriate EoS and a robust forcing scheme is an efficient numerical technique for simulation of the dynamics of the cavitation bubble collapse in different fluids.

A three-dimensional (3D) lattice Boltzmann method based on the Allen-Cahn equation (A-C LBM) is employed to study the spreading dynamics of impacting droplets on the hydrophobic flat and textured surfaces. At first, the simulation of the equilibrium state of a droplet and also the impacting droplet spreading on a flat surface are considered at various wetting conditions to examine the accuracy and efficiency of the present numerical technique. The obtained results for these cases show excellent agreement with available theoretical, numerical, and experimental data in the literature that confirms the validity of the A-C LBM employed for simulation of such complex interfacial dynamics. Upon validation, the implemented A-C LBM is applied for investigation of the droplet impingement on the hydrophobic textured surface and the results are compared with those obtained by considering the flat surface. The present study shows that using microscale textures on a hydrophobic surface dramatically reduces the contact area between the impacting droplet and the solid wall due to the momentum redirection phenomenon. Indeed, the hydrophobic surface used with in-plane circular ridges causes the spreading lamella to eject out-of-plane with a liquid bowl shape. This mechanism converts a part of the horizontal momentum of the spreading to the vertical momentum that prevents droplets to have intense interaction. For an impacting droplet at a high Weber number, it is concluded that the geometrical parameters of the ridge dictate the morphology of the spreading on the hydrophobic surface. However, the droplet dynamics at a low Weber number depend on both the texture size and the surface wettability, so that the physical mechanisms of the droplet spreading and lamella ejection dramatically change by variation of these parameters. The obtained results show that when the adhesion force of the substrate is dominant (lower contact angles), the wetting property of the surface plays an effective role than the texture geometry in the formation of the liquid bowl at low Weber numbers. Also, the present study demonstrates the capability of the A-C LBM for the prediction of the studied multiphase flow structures and characteristics with extremely complex interface phenomena.

In this paper, droplet mobility and penetration into a fibrous porous medium are studied considering different physical and geometrical properties for the fibers. An in-depth insight into the droplet imbibition into the fibrous medium is beneficial for improving membrane products in different applications. Herein, a multiphase lattice Boltzmann method is employed as an efficient numerical algorithm for predicting the multiphase flow characteristics and the interfacial dynamics affected by the interaction between the droplet and fibrous substrates considered. This computational technique is validated by comparison of the present results obtained for different benchmark two-phase flow problems with those reported in the literature, which shows good agreement and confirms its accuracy and efficiency. Droplet spreading and penetration into the fibrous porous geometries are then studied considering various porous topologies, intrinsic contact angles, and fiber sizes. This study shows that the intrinsic contact angle has a great influence on the capillary pressure and, consequently, on the droplet imbibition into the porous medium. The droplet easily penetrates the porous substrate by decreasing the intrinsic contact angle of the fibers, and vice versa. It is also concluded that by coating the fibrous porous medium with a narrow layer of thin fibers, the surface resistance to liquid penetration significantly increases. The present results illustrate that the droplet size impacts the directional wicking ability of the fibrous porous structure used in this study. This property should be considered to produce appropriate two-layer membranes for different applications.

A two-dimensional lattice Boltzmann method (LBM) is applied to investigate the use of various equations of state (EoS) for the simulation of liquid–vapor two-phase flow systems with considering the wetting properties, namely the hydrophilic and hydrophobic characteristics, for solid surfaces. The pseudo-potential single-component multiphase Shan–Chen model is used to resolve inter-particle interactions and phase change between the liquid and its vapor. Several EoSs, including the Redlich–Kwong (R–K), Carnahan-Starling (C–S), and Peng–Robinson (P–R) in comparison with the Shan–Chen (S–C) model are considered to study their effects on the numerical simulation results in terms of density ratios, spurious velocities and the contact angle of the two-phase flow with the solid wall. Accuracy and performance of the multiphase LBM by incorporating various EoSs are examined by solving two-phase flow systems at different conditions. Herein, three test cases considered are an equilibrium state of a droplet suspended in the vapor phase, a liquid droplet located on the solid surface, and a liquid droplet motion through a grooved channel with different wetting conditions. The results obtained demonstrate that implementation of the wall boundary condition with the wettability effects significantly impacts the numerical stability of the LBM with the EoSs employed for simulation of liquid–vapor flow problems, particularly at high-density ratio. Simulation of the equilibrium state of a droplet on a surface with considering wettability effects shows that the S–C model, R–K, P–R and C–S EoSs are stable for the maximum density ratio up to ρ l ∕ ρ v = 74 . 6 , 78.9, 4904.4 and 147, respectively. It is defined that the parasitic currents do not increase significantly due to imposing the wetting condition on the solid wall, however, the numerical solutions with considering wettability effects are more sensitive at high-density ratios. The present study demonstrates that the P–R EoS is more stable for simulation of high-density ratio liquid–vapor systems with reasonable spurious currents in the interfacial region for the flow problems with the periodic computational domain. However, with considering the wetting wall boundary condition, the C–S EoS produces less spurious velocity in the interface region, which leads to more precise and stable numerical simulations in comparison with the other EoSs applied for the equilibrium state of a liquid droplet on the solid surface. The results obtained also demonstrate the capability of the multiphase LBM for predicting practical flow characteristics with different EoSs implemented.

In this work, a three-dimensional lattice Boltzmann method is developed for numerical simulation of the fluid flows around the arbitrary geometries in the wide range of Reynolds numbers. For efficient simulation of high Reynolds number flow structures in the turbulent regime, a large eddy simulation (LES) approach with the Smagorinsky subgrid turbulence model is employed. An absorbing boundary condition based on the concept of sponge layer is improved and implemented to damp the vorticity fluctuations near the open boundaries and regularize the numerical solution by significantly reducing the spurious reflections from the open boundaries. An off-lattice scheme with a polynomial interpolation is used for implementation of curved boundary conditions for the arbitrary geometries. The efficiency and accuracy of the numerical approach presented are examined by computing the low to high Reynolds number flows around the practical geometries, including the flow past a sphere in a range of Reynolds numbers from 102 to 104 and flow around the NACA0012 wing section in two different flow conditions. The present results are in good agreement with the numerical and experimental data reported in the literature. The study demonstrates the present computational technique is robust and efficient for solving flow problems with practical geometries.

In the present work, two cavitation modeling strategies, namely the barotropic cavitation model and the transport equation-based model are applied and assessed for the numerical simulation of inviscid cavitating flows over two-dimensional and axisymmetric geometries. The algorithm uses the preconditioned Euler equations employing the interface capturing method for both the cavitation models. A same numerical solution procedure is used herein for discretizing the governing equations resulting from these two cavitation modeling strategies for the assessment to be valid and reliable. A central difference finite-volume scheme employing the suitable dissipation terms to account for density jumps across the cavity interface is shown to yield an effective method for solving the Euler equations. Results for steady inviscid cavitating flows over the NACA0012 and NACA66(MOD) hydrofoils and the hemispherical and ogive head shape bodies are obtained by applying these two cavitation modeling strategies and they are compared with each other for different conditions. A sensitivity study is conducted to evaluate the effects of various numerical and physical parameters involved in each cavitation model on the solution. The advantages and drawbacks of these two strategies for modeling of cavitating flows are also discussed. The present inviscid cavitation results are also compared with the experiments and the other inviscid and viscous cavitation results performed by other researchers and some conclusions are made.

In this work, the implementation of a high-order compact finite-difference lattice Boltzmann method (CFDLBM) is performed in the generalized curvilinear coordinates to improve the computational efficiency of the solution algorithm to handle curved geometries with non-uniform grids. The incompressible form of the discrete Boltzmann equation with the Bhatnagar–Gross–Krook (BGK) approximation with the pressure as the independent dynamic variable is transformed into the generalized curvilinear coordinates. Herein, the spatial derivatives in the resulting lattice Boltzmann (LB) equation in the computational plane are discretized by using the fourth-order compact finite-difference scheme and the temporal term is discretized with the fourth-order Runge–Kutta scheme to provide an accurate and efficient incompressible flow solver. A high-order spectral-type low-pass compact filter is used to regularize the numerical solution and remove spurious waves generated by boundary conditions, flow non-linearities and grid non-uniformity. All boundary conditions are implemented based on the solution of governing equations in the generalized curvilinear coordinates. The accuracy and efficiency of the solution methodology presented are demonstrated by computing different benchmark steady and unsteady incompressible flow problems. A sensitivity study is also conducted to evaluate the effects of grid size and filtering on the accuracy and convergence rate of the solution. Four test cases considered herein for validating the present computations and demonstrating the accuracy and robustness of the solution algorithm are: unsteady Couette flow and steady flow in a 2-D cavity with non-uniform grid and steady and unsteady flows over a circular cylinder and the NACA0012 hydrofoil at different flow conditions. Results obtained for the above test cases are in good agreement with the existing numerical and experimental results. The study shows the present solution methodology based on the implementation of the high-order compact finite-difference Lattice Boltzmann method (CFDLBM) in the generalized curvilinear coordinates is robust, efficient and accurate for solving steady and unsteady incompressible flows over practical geometries.

A high-order compact finite-difference lattice Boltzmann method (CFDLBM) is extended and applied to accurately simulate two-phase liquid-vapor flows with high density ratios. Herein, the He-Shan-Doolen-type lattice Boltzmann multiphase model is used and the spatial derivatives in the resulting equations are discretized by using the fourth-order compact finite-difference scheme and the temporal term is discretized with the fourth-order Runge-Kutta scheme to provide an accurate and efficient two-phase flow solver. A high-order spectral-type low-pass compact nonlinear filter is used to regularize the numerical solution and remove spurious waves generated by flow nonlinearities in smooth regions and at the same time to remove the numerical oscillations in the interfacial region between the two phases. Three discontinuity-detecting sensors for properly switching between a second-order and a higher-order filter are applied and assessed. It is shown that the filtering technique used can be conveniently adopted to reduce the spurious numerical effects and improve the numerical stability of the CFDLBM implemented. A sensitivity study is also conducted to evaluate the effects of grid size and the filtering procedure implemented on the accuracy and performance of the solution. The accuracy and efficiency of the proposed solution procedure based on the compact finite-difference LBM are examined by solving different two-phase systems. Five test cases considered herein for validating the results of the two-phase flows are an equilibrium state of a planar interface in a liquid-vapor system, a droplet suspended in the gaseous phase, a liquid droplet located between two parallel wettable surfaces, the coalescence of two droplets, and a phase separation in a liquid-vapor system at different conditions. Numerical results are also presented for the coexistence curve and the verification of the Laplace law. Results obtained are in good agreement with the analytical solutions and also the numerical results reported in the literature. The study shows that the present solution methodology is robust, efficient, and accurate for solving two-phase liquid-vapor flow problems even at high density ratios.

Cavitating flow through the orifice is numerically solved by implementation of the lattice Boltzmann method. The pseudo-potential single-component multiphase Shan-Chen model is used to resolve inter-particle interactions and phase change between the liquid and its vapor. The effect of surface wettability on the cavity formation and shape is studied by imposing an appropriate wall boundary condition for the contact angle between the liquid-vapor interface and the solid surface. Efficiency of the numerical approach presented is examined by computing the cavitation inception, growth, and collapse for internal cavitating flows over a sack-wall obstacle placed inside a channel and through a convergent-divergent nozzle section. The results obtained demonstrate that hydrophobic walls act as surface nuclei and contribute to the process of cavitation inception even at high cavitation numbers. In contrast, the solid wall with hydrophilic properties shows no contribution to the onset of cavitation in the geometries ...