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The intrinsic permeability is a crucial parameter to characterise and quantify fluid flow through porous media. However, this parameter is typically uncertain, even if the geometry of the pore structure is available. In this paper, we perform a comparative study of experimental, semi-analytical and numerical methods to calculate the permeability of a regular porous structure. In particular, we use the Kozeny-Carman relation, different homogenisation approaches (3D, 2D, very thin porous media and pseudo 2D/3D), pore-scale simulations (lattice Boltzmann method, Smoothed Particle Hydrodynamics and finite-element method) and pore-scale experiments (microfluidics). A conceptual design of a periodic porous structure with regularly positioned solid cylinders is set up as a benchmark problem and treated with all considered methods. The results are discussed with regard to the individual strengths and limitations of the used methods. The applicable homogenisation approaches as well as all considered pore-scale models prove their ability to predict the permeability of the benchmark problem. The underestimation obtained by the microfluidic experiments is analysed in detail using the lattice Boltzmann method, which makes it possible to quantify the influence of experimental setup restrictions., Deutsche Forschungsgemeinschaft, Projekt DEAL

Solid–liquid phase change has been widely used in practice, but most of the existing literature focuses on Newtonian phase change materials, and there are few studies on power-law phase change mate...

In this paper, a phase-field-based lattice Boltzmann model for ternary fluid flows is proposed, where the conservative Allen-Cahn equation for ternary fluids is employed to track the interface of fluids. A time derivative term is introduced to the LB equation for the conservative Allen-Cahn equation and a forcing distribution function is used to the LB equation for the Navier-Stokes equations. The computational accuracy and capability of this proposed model are verified by benchmark cases related to stationary droplets, spreading of a liquid lens, and phase separation of a ternary mixture fluid. Moreover, a wetting boundary scheme based on the framework of the lattice Boltzmann method applicable to ternary fluid flows is developed. This model performs well in eliminating the undesired numerical artifact after considering the wettability effect. Typical wettability problems are simulated to verify the applicability of the wetting boundary scheme, including the spreading of binary droplets and compound droplets on the surface. The numerical results of static contact angles and spreading length show a good fit of the data to the theoretical results within the scope of permissible error. Furthermore, the reliability of this wetting boundary condition for the dynamic case is verified by modelling the motion of the compound droplets subjected to the shear flow on the substrate. This boundary scheme performs well for the motion of ternary fluids with a small and large density ratio. In conclusion, the phase-field-based lattice Boltzmann model for ternary fluid flows considering the wetting effect has good applicability for modelling the ternary fluid flows at a density ratio of 1000.

Fully resolved numerical simulations of a micron-sized spherical particle residing on a surface with large-scale roughness are performed by using the Lattice–Boltzmann method. The aim is to investigate the influence of surface roughness on the detachment of fine drug particles from larger carrier particles for transporting fine drug particles in a DPI (dry powder inhaler). Often the carrier surface is modified by mechanical treatments for modifying the surface roughness in order to reduce the adhesion force of drug particles. Therefore, drug particle removal from the carrier surface is equivalent to the detachment of a sphere from a rough plane surface. Here a sphere with a diameter of 5 μm at a particle Reynolds number of 1.0, 3.5 and 10 are considered. The surface roughness is described as regularly spaced semi-cylindrical asperities (with the axes oriented normal to the flow direction) on a smooth surface. The influence of asperity distance and size ratio (i.e. the radius of the semi-cylinder to the particle radius, Rc/Rd) on particle adhesion and detachment are studied. The asperity distance is varied in the range 1.2

The application of grooved surface structure is an emerging and effective means in turbulence flow control. However, for a realistic configuration, the global flow field described directly by simple application of massive grids makes it unfeasible to simulate. In this paper, a boundary surrogate model reproducing the effect of microscopic near-wall region is proposed to improve computational efficiency. The surrogate model trained with Lattice Boltzmann Method (LBM) considering the rarefied effect based on real micro/nanoflow field is new among literature, which accurately shows flow characteristics of the micro/nano structure. With this approach, numerical simulations via Reynolds-averaged Navier Stokes equations with modified wall boundary condition are performed in subsonic and transonic flow. The results show that micro/nano grooved surface structure has the effect of delaying transition from laminar to turbulence, thus reducing the skin friction significantly. Analysis of turbulence intensity and turbulence kinetic energy shows that the near-wall flow field of grooved airfoil is more stable compared with that of the smooth airfoil. The reducing rate of maximum turbulent intensity reaches 13.39%. The paper shows a perspective for further application of micro/nano groove structure to turbulence flow control in aircraft design by providing an accurate and efficient simulation method.

In turbines, kinetic energy is transferred to the shaft then converted into a rotational motion to move a generator, so having a good design in the efficiency of turbines is important. Studies show that the efficiency of turbines in the presence of shafts has not been investigated so far. Therefore, our main goal in this study is to investigate the effect of shaft presence on the final efficiency of the hydro turbine. In this paper, the flow of fluid passing through the channels around the sharp leading edge cylinders in a tunnel is simulated using Lattice Boltzmann Method (LBM). Fluid streamlines stability, flow velocity rate, and pressure coefficient in channels with different shapes at assembly gaps of 2, 1.75, and 1.5 m have been investigated. The studied channels are considered in seven Airfoil-like shapes, Reverse Airfoil-like, hyperbola, Triangle, Triple triangle, Hexa triangle, and trapezoidal. The results show that the pressure coefficient in all channels decreases by increasing assembles gaps. On the other hand, reducing the pressure coefficient in the channel leads to cavitation. Cavitation causes erosion at the tip of the hydro turbine blades and reduces the life of the turbine. Therefore, the pressure coefficient is one of the most important parameters that depend on the assembly gap. Finally, the result shows that installing Hyperbola channels with an assembly gap of 1.75 m has the best performance in simulated hydro turbines.

In this paper, a novel model to investigate leakage of gaseous working fluid in pressured devices with lubricating oil was created with Lattice Boltzmann method and Shan-Chen multiphase model. A method to adapt actual pressure-density relation into the lattice via a self-adapting timestep and simplify the simulation of compressible fluid was developed. A model to simulate two-phased leakage with lubricating oil was created with a combination of Shan-Chen model and passive scalar model. The model can realize the phase distribution simulation in the leakage field without causing the pressure and the inter-phase interactions to overlap. This model is also able to be combined with other multiphase models. After a group of preliminary tests of the model, the characteristics of phase distribution and leakage were investigated qualitatively. Five types of phase distribution in the simulation results were classified, which are: uniformed distribution, sphered drips, gas channel, blocked channel and slug bubbles. The results of simulations show good conformance with actual leakage patterns. Preliminary discussions about the leakage features are made upon the results. However, these simulation results are only qualitative and cannot show the quantitative features in leakages. More experimental investigations should be carried out to realize correlations to the model.

In this study, a free energy model of the Lattice Boltzmann Method (LBM) is performed to simulate the motion, deformation, and decomposition of a droplet in the presence of electrohydrodynamic flow in porous media. To simulate the multi-phase flow in the presence of dielectric current by using the LBM, three distribution functions are used. To implement the free energy mode of HCZ, two equilibrium distribution functions are considered, one for solving the Navier-Stokes equation and the other for solving the Cahn-Hillard equation. Initially, the ability of the code to apply surface tension is tested by using the Laplace law and the droplet release test. Results show that there is a linear relation is between surface tension and κ which is a parameter in the HCZ model. The results show that the present numerical program is capable of modeling the regulated surface tension force as well. Then, the Rayleigh–Taylor instability simulation is used to evaluate the code's ability to apply volume forces. Also, the obtained results of the written numerical program are in good agreement with the numerical results of other valid references. Obtained results show that the difference between droplet deformation measured by numerical method and Taylor function is less than 2%. After modeling the droplet motions to investigate the droplet deformation, two electric fields are inserted into the droplet with reverse directions of each other. Then, by various tests, it is shown that at a given potential difference the droplet breaks down after much deformation and is divided into smaller droplets. The decomposition of droplets in a pre-mixed emulsion is a common technique to produce the monodisperse droplets. The presence of monodisperse droplets in an emulsion improves the physical properties of polymer from the science expert's perspective. The results of this study are used to improve the quality of polymer components.

Sedimentation of particle suspensions in a channel flow into a cavity is analysed numerically using a lattice Boltzmann method coupled with a discrete element method. The work focuses on the entrapment of particles inside a confined cavity and the particle dynamics after entrapment. A close examination of the particle motions reveals three distinct dynamic behaviours: i) resuspension, ii) circulation in the central vortex and iii) deposition to the rear edge of the cavity. The effects of fluid inertia, particle density and cavity size on the infiltration and resuspension behaviours are systematically investigated. The results show that decreasing the Reynolds number, and increasing the length and depth of the cavity all lead to an increase in the trap efficiency. Three distinctive regimes with respect to the trap efficiency were then identified by deriving an empirical dimensionless trap number Tp: a resuspension regime when Tp 2.5.

The innovation of this paper is hybrid heat transfer simulation of two different multi-phase nanofluid simultaneously between two 3D enclosures under heat flux boundary condition. This present work with arrangement of different shape of mounted obstacles effects has practical applications such as energy storage systems. Velocity and temperature fields of fluid flow are modeled based on the D3Q19, Lattice Boltzmann Method. Nanoparticle volume fraction, temperature fields, mean and local velocity in 24 cases of enclosures with 5, 7 and 9 obstacles in hot zone and 10, 14 and 18 obstacles in hot and cold zones have been investigated for arrangement rectangular, circle, vertical and horizontal ellipse obstacles. rates of mean temperature in each enclosure have been analyzed. The results presented that minimum of fluid velocity in left enclosure was in 0.4 y / L 0.5 , and maximum was in 0.15 y / L 0.25 and 0.7 y / L 0.85 . Also, maximum and minimum of mean temperature in left enclosure on the wall ( y = 0 ) were in enclosures with 9 rectangular obstacles in hot zones that was equal to 48.37 °C (%8.3) and 10 horizontal ellipse obstacles in hot and cold zone that was equal to 45.03 °C (%0.8), respectively.

Direct ink writing (DIW), as an additive manufacturing method, can effectively mould ceramic parts. The single screw extruder is used here to extrude viscous SiC slurry. The deposits caused by the low viscosity and the agglomerations resulting from the nonuniform mixing, form the obstacles in the channel, which affect the normal theoretical flow of the slurry, and interaction with other printing parameters. Therefore, it is necessary to explore the effect mechanism of the obstacles on the flow. The obstacles are always irregular, which makes it difficult to directly analyse them. The irregular geometries are always composed of linear and/or arcuate elements; therefore, the obstacles can be simplified into regular geometries. In the previous work, linear elements have been analysed first. As the continuous work, arcuate elements are investigated in the current research. To conduct the required simulations, an improved MRT LBM (multiple relaxation time lattice Boltzmann method) with a pseudo external force is proposed. The above numerical method is combined with the rheological model to analyse cases with two obstacles, and the obtained results are used to reveal the general mechanism in cases with multiple obstacles. The results show that the central angles, radii, and positions of the obstacles are important factors affecting the flow. To obtain a stable and controllable slurry flow, it is recommended that the central angle and the radius should be small enough. The number of obstacles should be minimized, and the position of the last obstacle is expected to be far away from the outlet to avoid the negative velocity. In addition, the adjacent obstacles should maintain a certain distance to ensure the full development of the vortex and avoid affecting the following obstacles or back vortices.

Coffee-ring patterns are typical phenomena in evaporation-driven nanoparticles suspended (NPs-laden) droplet. However, NPs motion in droplet fails to exhibit characteristic patterns such as coffee-ring formation in lattice Boltzmann (LB) framework. With features of density diffuse interface, new interfacial schemes composed of density gradient force and interfacial force are proposed and coupled in LB-LE model. They offer a solution to well modulate the NPs dynamics in liquid-vapor interface as droplet deforms and evaporates. In the following simulations of one droplet and multi-droplets evaporation, typical coffee-ring pattern is obtained for one droplet evaporation with hysteresis window 5°

Purpose This paper aims to explore the mechanism of the slip phenomenon at macro/micro scales, and analyze the effect of slip on fluid flow and heat transfer, to reduce drag and enhance heat transfer. Design/methodology/approach The improved tangential momentum accommodation coefficient scheme incorporated with Navier’s slip model is introduced to the discrete unified gas kinetic scheme as a slip boundary condition. Numerical tests are simulated using the D2Q9 model with a code written in C++. Findings Velocity contour with slip at high Re is similar to that without slip at low Re. For flow around a square cylinder, the drag is reduced effectively and the vortex shedding frequency is reduced. For flow around a delta wing, drag is reduced and lift is increased significantly. For Cu/water nanofluid in a channel with surface mounted blocks, drag can be reduced greatly by slip and the highest value of drag reduction (DR) (67.63%) can be obtained. The highest value of the increase in averaged Nu (11.78%) is obtained by slip at Re = 40 with volume fraction φ=0.01, which shows that super-hydrophobic surface can enhance heat transfer by slip. Originality/value The present study introduces and proposes an effective and superior method for the numerical simulation of fluid/nanofluid slip flow, which has active guidance meaning and applied value to the engineering practice of DR, heat transfer, flow control and performance improvement.

Purpose The purpose of this study is the identification of the best method to apply the body force in the lattice Boltzmann method (LBM). In the simulation of mixed convection, especially for large Richardson number flows in a square cavity. Design/methodology/approach First, three methods for applying the body force were compared to each other in the LBM. Then, an LBM-based code was written in the FORTRAN language using these three methods. Next, that code was used to simulate natural/mixed convection in a two-dimensional cavity to evaluate the methods for applying the body force. Finally, the optimum way for applying the body force was used for the simulation of free convection heat transfer in a concentric annulus with Rayleigh number in a range of 1,000 to 50,000, and mixed convection heat transfer in a concentric annulus with Rayleigh number in a range of 10,000 to 50,000 and Reynolds number in a range of 100 to 400. Findings Mixed convection heat transfer was simulated in a two-dimensional cavity with Richardson number in a range of 0.0001 to 100. The results which were obtained in low Richardson number flows have shown good adaptation to the available data. However, the results of large Richardson number flows, for example, Ri = 100, have shown a significant difference to the available data. Investigations revealed that this difference was due to the method of applying the body force. Therefore, the choice of the best way to apply the body force was investigated. Finally, for the large Richardson number flows, the best method to apply the body force has been identified among the several techniques. Originality/value To the authors’ knowledge, the effects of methods for applying the body force were not investigated in the cavities mixed convection, even though there are numerous investigations conducted on mixed convection with the LBM. In this study, the effects of techniques to apply the body force were investigated in large Richardson number flows. Finally, the best method to apply the body force is distinguished between several techniques for the large Richardson number mixed convection flows.

In this research work, numerical simulations were conducted to examine the effect of baffles on flow activity in a stirred tank bioreactor fitted with two six-blade Rushton turbines, at Reynolds number (Re) = 40,000. The lattice Boltzmann method (LBM) was used as a numerical technique to discretize the flow domain. Large Eddy Simulation (LES) method was applied for turbulence modeling. The small-scale turbulent structures were resolved by using the conventional Smagorinsky subgrid-scale (SGS) model. The action of the reactor components (i.e., cylindrical wall, baffles, shaft, and Rushton turbines) on the flow field were obtained by using the immersed boundary (IB) method. The simulations were performed for three different geometries of stirred tank reactors, differentiated based on the impeller clearance. The study shows the impact of baffles on all the three employed geometries. For each of the geometries, simulations were performed with and without the baffles. A uniform, cubic computational grid of $$150^{3}$$ lattice nodes was constructed for the simulation. The computer code was developed for performing the simulation. The complexity of the geometry and different physical processes involved make the simulation more challenging and time-consuming. Thus, to get the results in an adequate time, the computer code was parallelized to run on a multicore Graphical Processing Unit (GPU) platform. The results are demonstrated in the form of phase average flow velocities as well as in turbulent properties, with validation from the available experimental data reported in the literature.

The swelling behavior of IPN hydrogel tablets in the shape of cuboid or rectangular parallelepiped tablets in contact with buffer solutions at different pH and temperature conditions were estimated by a three-dimensional multiple-relaxation-time lattice Boltzmann (LB) model. Adsorption isotherms were obtained experimentally for tablets of IPN hydrogel formulation immersed in buffer solution at 298.15 and 310.15 K at pH equal to 4.48, 7.25, and 8.225, and those of copolymer hydrogel formulation at 298.15 K at pH equal to 4.48, 7.25, and 8.225. A computational method based on an LB model is used to simulate the hydrogels swelling, employing dimensionless units of length and mass. The discretization error estimation of the computational simulations was calculated by the grid convergence index method. Excellent correlations were achieved between the computational data and experimental values of mass swelling percentage, achieving coefficients of determination equal to or higher than 0.993 for the finest grids. The equilibrium diffusion coefficient at low pH values is higher than at large pH values. The simulations allowed us to estimate the equilibrium diffusion coefficient for each case; a qualitative property of the polymer, and to observe how the inner regions of a sample are hydrated in the time domain, both of which cannot be done experimentally.

The purpose of the present work is to investigate the effect of the angle of application of magnetic field in two types of uniform and non-uniform on the nanofluid flow characteristics and natural convection heat transfer in the presence of uniform heat generation. This numerical study was performed using multi relaxation time lattice Boltzmann method (MRT-LBM). The D2Q9 and D2Q5 grid arrangements were used to simulate the flow and temperature fields, respectively. The results show that in all cases, increasing the strength of magnetic field (the Hartmann number) reduces the average Nusselt number, which increases with increasing the heat generation coefficient. Applying a magnetic field horizontally results in an average of about 15% lower Nusselt number compared to the vertical. Increasing the strength of magnetic field (the Hartmann number) and the average Nusselt number is achieved by periodically applying a magnetic field instead of applying a uniform one. As the aspect ratio of the cavity increases, the non-uniform effect of applying a magnetic field becomes more apparent.

In this study, the lattice Boltzmann method was used to simulate the three-dimensional intrusion process of liquid water in the gas diffusion layer (GDL) of a polymer electrolyte membrane fuel cell (PEMFC). The GDL was reconstructed by the stochastic method and used to investigate fiber orientation's influence on liquid water transport in the GDL of a PEMFC. The fiber orientation can be described by the angle between a single fiber and the in-plane direction; three different samples were simulated for three different fiber orientation ranges. The simulated permeability correlated well with the anisotropic characteristics of reconstructed carbon papers. It was concluded that the fiber orientation had a significant effect on the liquid invasion pattern in the GDL by changing the pore shape and distribution of the GDL. The results indicated that the stochastically reconstructed GDL, taking into account the fiber orientation, better demonstrates the mass transport properties of the GDL.

A four-way coupling CFD-DEM model is originally developed in this work to investigate the sedimentation of adhesive particles in viscous fluids. In this model, the particles are traced by the discrete element method based on the JKR contacting theory, and the fluid flow is resolved by the lattice Boltzmann method combining with large eddy simulation. Three benchmark problems are first investigated to validate the LBM-LES-DEM scheme, and then the sedimentations of non-adhesive and adhesive particles are further discussed in detail. Results indicate that the drafting-kissing-tumbling process identified during the settling of non-adhesive particles is significantly different from that of adhesive ones, and separation will not happen if the vdW adhesion between particles becomes strong enough. Moreover, the settling of adhesive particles is found to be faster than non-adhesive ones, and this can be reasonably interpreted by the agglomeration effect that takes place during the settling of adhesive particles.

Porous particle flow is universal in nature and industry. However, in previous numerical simulations, porous particles have usually been assumed to be solid. It is necessary to study the flow and heat-transfer characteristics around porous particles because they are greatly different from those of impermeable particles. In this study, two-dimensional steady flow and heat transfer around and through a porous particle with a constant temperature placed in a cold fluid were numerically investigated. The effects of the Reynolds number (Re) and Darcy number (Da) on the flow and heat-transfer characteristics were investigated in detail. The investigated ranges of the parameters were 10 ≤ Re ≤ 40 and 10−6 ≤ Da ≤ 10−2. It is sophisticated to simulate porous particles with traditional simulation methods because of their complicated structure. Therefore, the lattice Boltzmann method was used to solve the generalized macroscopic governing equations because of its simplicity. The drag coefficient decreased with increasing Re or Da, but the decrease was not prominent in the range 10−6 ≤ Da ≤ 10−4. The heat-transfer efficiency of the front surface was much stronger than that of the rear surface. The heat-transfer efficiency between the particle and the fluid increased with increasing Re or Da. However, for 10−6 ≤ Da ≤ 10−4, the increase was not prominent and the heat-transfer enhancement ratio was slightly larger than one. Furthermore, the effect of Da became more prominent at larger Re. In addition, new correlations for the drag coefficient and surface-averaged Nusselt number were obtained based on the simulated results.

In the present paper, nanofluid mixed convection is investigated in a square cavity with an adiabatic obstacle by using the Lattice Boltzmann method (LBM). This enclosure contains Fe–ethylene-glycol nanofluid and three constant temperature thermal sources at the left wall and bottom of the enclosure through a lateral wall. The fluid is incompressible, laminar, and Newtonian. The obtained results are presented in the constant Ra = 104 and a Pr = 0.71 for different Ri = 0.1, 1, and 10. The effects of the slope of the enclosure, volume fraction of nanoparticles $$\left( \varphi \right)$$ φ , the location of adiabatic obstacles, and nanoparticle diameter in the fluid are investigated on the value of heat transfer. A change in the attack angle of the enclosure leads to changes in the movement distance for fluid between hot and cold sources and passing fluid through case E, which affects the flow pattern strongly. In each attack angle, on colliding with an obstacle, the fluid heat transfers between two sources, which leads to uniform heat transfer in the enclosure. By increasing the velocity of the lid, the Richardson number decreases leading to improvement of the convective heat transfer coefficient and Nusselt number enhancement. The results so obtained reveal that by augmenting $$\varphi$$ φ value the effect of Richardson number reduction can augment Nusselt number and the amount of absorbed heat from the hot surface. Consequently, in each state where a better flow mixture and lower depreciation of fluid velocity components, due to the penetration of lid movement and buoyancy force, occurs higher heat transfer rate is accomplished. Furthermore, it is shown that when Ri = 0.1, the effect of cavity angle is more important but when Ri = 10, the effect of the position of obstacle is more visible.

Purpose The lattice Boltzmann simulation of fluid flow in partial porous geometries with curved porous-fluid interfaces has not been investigated yet. It is mainly because of the lack of a method in the lattice Boltzmann framework to model the hydrodynamic compatibility conditions at curved porous-fluid interfaces, which is required for the two-domain approach. Therefore, the purpose of this study is to develop such a method. Design/methodology/approach This research extends the non-equilibrium extrapolation lattice Boltzmann method for satisfying no-slip conditions at curved solid boundaries, to model hydrodynamic compatibility conditions at curved porous-fluid interfaces. Findings The proposed method is tested against the results available from conventional numerical methods via the problem of fluid flow through and around a porous circular cylinder in crossflow. As such, streamlines, geometrical characteristics of recirculating wakes and drag coefficient are validated for different Reynolds (5 ≤ Re ≤ 40) and Darcy (10−5 ≤ Da ≤ 5 × 10−1) numbers. It is also shown that without applying any compatibility conditions at the interface, the predicted flow structure is not satisfactory, even for a very fine mesh. This result highlights the importance of the two-domain approach for lattice Boltzmann simulation of the fluid flow in partial porous geometries with curved porous-fluid interfaces. Originality/value No research is found in the literature for applying the hydrodynamic compatibility conditions at curved porous-fluid interfaces in the lattice Boltzmann framework.

Particle suspensions form a fundamental yet complex component of many scientific and engineering endeavours. This paper proposes a numerical coupling between the lattice Boltzmann and discrete element methods that resolves particle suspensions exposed to thermal influences due to temperature-dependent fluid viscosity and conjugate heat transfer between components. Validation of the model was performed via the study of the relative viscosity of suspensions. This numerically corroborated the proposed temperature-dependence of the relative viscosity of suspensions. The model was finally used to interrogate the macroscopic behaviour of sheared suspensions at a range of solid volume fractions. This demonstrated changes in suspension flow behaviour due to temperature related effects. Future work based on these results would examine how particle properties could be modified to exacerbate and control temperature-based phenomena potentially leading to improvements in domains such as industrial material processing and manufacture.

Background Droplet impact on a superhydrophobic cylinder differs from that on a flat surface. After bouncing, once re-touch takes place, the contact time τc would increase, which is unfavorable for some applications. The increased τc may strongly depend on the Weber number and radius ratio, R*, of cylinder to droplet. Methods The impact is investigated via lattice Boltzmann method simulations. The particular emphasis is placed on re-touch rebound patterns and τc. Significant findings Rebound patterns and τc both strongly depend on a combined parameter, α=We/R*, characterizing the asymmetry of droplet spreading and retraction. As α increases, upward rebound and stretched breakup take place sequentially for the first bouncing, whereas rebound patterns change as intact re-touch rebound and separate re-touch rebound for the second bouncing. Increasing α enhances the asymmetry, which promotes the first rebound, thereby reducing τc regardless of rebound patterns. The enhanced asymmetry also accelerates rebound and thus reduces τc in the separate re-touch rebound regime, whereas it hinders rebound, leading to a significantly increased τc. The power-law correlations of τc vs α are developed for the first and second bouncing. Besides, a method is proposed to suppress or prevent the re-touch, which is proven to effectively reduce τc.

The dynamic behavior of liquid droplets on a reconstructed real gas diffusion layer (GDL) surface with the inertial effect produced by the three dimensional (3D) flow channel is investigated using an improved pseudopotential multiphase model within the unified lattice Boltzmann model (ULBM) framework, which can realize thermodynamic consistency and tunable surface tension. The microstructure of the GDL (Toray-090) including carbon fibers and polytetrafluoroethylene (PTFE) is reconstructed by a stochastic and mixed-wettability model. The critical force formulation for the Cassie-Wenzel transition of a droplet on GDL surface is derived. The effects of inertia and contact angles on the liquid droplet transport process on a reconstructed real GDL surface with a 3D flow channel are investigated. The results show the normalized center-of-mass coordinate X may enter the channel wall area or fluctuate around the initial position. With increased inertia applied on the droplet, the normalized center-of-mass coordinate Y grows faster and the normalized center-of-mass coordinate Z decreases. It is found by the ULBM for the first time that the liquid droplet is pushed back into the GDL by inertial effect. With the increase of inertia and the decrease of contact angle of GDL, both the droplet penetration depth in GDL and the droplet invasion fraction increase. The droplet invasion fraction in GDL is up to 30%.

In vascular targeted therapies, blood-borne carriers should realize sustained drug release from the luminal side towards the diseased tissue. In this context, such carriers are required to firmly adhere to the vessel walls for a sufficient period of time while resisting force perturbations induced by the blood flow and circulating cells. Here, a hybrid computational model, combining a Lattice Boltzmann (LBM) and Immersed Boundary Methods (IBM), is proposed for predicting the strength of adhesion of particles in narrow capillaries (7.5 $\mu \mathrm{m})$ traversed by blood cells. While flowing down the capillary, globular and biconcave deformable cells ( $7 \mu \mathrm{m}$ ) encounter $2 \mu \mathrm{m}$ discoidal particles, adhering to the vessel walls. Particles present aspect ratios ranging from $0.25$ to $1.0$ and a mechanical stiffness varying from rigid $(\mathrm{Ca}=0)$ to soft $\left(\mathrm{Ca}=10^{-3}\right)$. Cell-particle interactions are quantitatively predicted over time via three independent parameters: the cell membrane stretching $\delta p$; the cell-to-particle distance $r$, and the number of engaged ligand-receptor bonds $N_{\mathrm{L}}$., Comment: arXiv admin note: text overlap with arXiv:1907.00080

Churning loss and lubrication performance are key issues that need to be considered for the efficiency of electric vehicle reducers. In this article, a 3D transient computational fluid dynamics mod...

In this work, the capability of a multiphase lattice Boltzmann method (LBM) based on the pseudopotential Shan-Chen (S-C) model is investigated for simulation of two-phase flows through porous media at high-density and high–viscosity ratios. The accuracy and robustness of the S-C LBM are examined by the implementation of the single relaxation time (SRT) and multiple relaxation time (MRT) collision operators with integrating the forcing schemes of the shifted velocity method (SVM) and the exact difference method (EDM). Herein, two equations of state (EoS), namely, the standard Shan-Chen (SC) EoS and Carnahan-Starling (CS) EoS, are implemented to assay the performance of the numerical technique employed for simulation of two-phase flows at high-density ratios. An appropriate modification in the forcing schemes is also used to remove the thermodynamic inconsistency in the simulation of two-phase flow problems studied at low reduced temperatures. The comparative study of these improvements of the S-C LBM is performed by considering an equilibrium state of a droplet suspended in the vapor phase. The solver is validated against the analytical coexistence curve for the liquid-vapor system and the surface tension estimation from the Laplace Law. Then, according to the results obtained, a conclusion has been made to choose an efficient numerical algorithm, including an appropriate collision operator, a realistic EoS, and an accurate forcing scheme, for simulation of multiphase flow transport through a porous medium. The patterns of two-phase flow transport through the porous medium are predicted using the present numerical scheme in different flow conditions defined by the capillary number and the dynamic viscosity ratio. The results obtained for the nonwetting phase saturation, penetration structure of the invading fluid, and the displacement patterns of two-phase flow in the porous medium are comparable with those reported in the literature. The present study demonstrates that the S-C LBM with employing the MRT-EDM scheme, CS EoS, and the modified forcing scheme is efficient and accurate for estimation of the two-phase flow characteristics through the porous medium.

In the present work, a numerical algorithm based on a combination of the lattice Boltzmann method (LBM) and the improved smoothed profile method (iSPM) has been proposed to study the motion of one, two and many circular particles in a non-Newtonian fluid. At first, the velocity profile of the non-Newtonian fluid at various power law indexes (n) was analyzed and the findings were compared with the numerical results of the previous works. Then, the motion of one circular cylinder and the hydrodynamic interactions between two particles in a shear flow were investigated. It was observed that Reshear, p had no important impact on the rotation of a single cylinder. In the two particles interaction, increasing the shear rate caused the particles to tumble on each other more closely and during a longer time. Therefore, the effective viscosity of a particulate suspension was considered for different Reynolds numbers and solid volume fractions, showing a satisfactory agreement with the previously published data. The results, therefore, showed that inertia increased the particles contribution to the effective viscosity of the suspension.

We numerically study the translocation dynamics of double emulsion drops with multiple close-packed inner droplets within constrictions. Such liquid architectures, which we refer to as HIPdEs (high-internal phase double emulsions), consist of a ternary fluid, in which monodisperse droplets are encapsulated within a larger drop in turn immersed in a bulk fluid. Extensive two-dimensional lattice Boltzmann simulations show that if the area fraction of the internal drops is close to the packing fraction limit of hard spheres and the height of the channel is much smaller than the typical size of the emulsion, the crossing yields permanent shape deformations persistent over long periods of time. Morphological changes and rheological response are quantitatively assessed in terms of the structure of the velocity field, circularity of the emulsion, and rate of energy dissipated by viscous forces. Our results may be used to improve the design of soft mesoscale porous materials, which employ HIPdEs as templates for tissue engineering applications.

Purpose This study aims to employ a modern numerical approach for conducting the simulations, which uses the smoothed-profile lattice Boltzmann method. Two separate distribution functions for flow and temperature fields are used to solve the Navier–Stokes equations in the most efficient manner. In addition, the Koo–Kleinstreuer–Li model is used to calculate the dynamic viscosity and thermal conductivity in the desired volume fractions, and the effect of Brownian motion is taken into consideration. Design/methodology/approach Nowadays, because of enhanced global price of oil and critical issue of global warming, a significant demand for using renewable energy exists. The solar energy is one of the most popular forms of renewable energy. The solar collector can be used to collect and trap the energy received from the sun. The present work focuses on introducing and investigating a parabolic-trough solar collector. Findings To analyze all hydrodynamic and thermal views of the solar collector, the structure of nanofluid stream, distribution of temperature, local dissipations because of flow and heat transfer, volumetric entropy production, Bejan number vs Rayleigh number and volume fraction are presented. Also, three different configurations for profile of solar receiver are designed and studied. Originality/value The originality of the present work is in using a modern numerical approach for a well-known application. Also, the effect of Brownian motion is taken into account which significantly enhances the accuracy.

In this article, transient response of triangular longitudinal fin with internal heat generation under step change in (i) base temperature and (ii) base heat flux assuming is reported. The convecti...

A hybrid model has been developed for the analysis of the process of combined mass and heat transfer in closed rectangular cavities under the conditions of volumetric radiation of a medium. Within the framework of the formulated method, hydrodynamics is described by the mesoscopic lattice Boltzmann method, and the macroscopic equations of energy and concentration are described by the method of finite differences. To calculate the radiation flux, use was made of approximation of an optically thick layer. Based on the results of mathematical modeling, it has been established that accounting for radiation heat transfer results in an increase of the incidence angle of thermal stratification and the formation of external secondary flows. The convective Nusselt number decreases as the radiation parameter rises. On the other hand, it has little effect on the mass transfer rate.

Purpose This paper aims to investigate the influence of droplet infiltration and sliding on the deposition size and make a uniform deposition by controlling the interaction between droplets, using the three-dimensional lattice Boltzmann method (LBM) based on the actual working condition. Design/methodology/approach D3Q19 Shan-Chen LB approach is developed and optimized based on the metal droplet deposition. The Carnahan-Starling equation of state and transition layers are introduced to maintain the greater stability and low pseudo velocities. In addition, an additional collision term is adopted to implement immersed moving boundary scheme to deal with no-slip boundaries on the front of the phase change. Findings The numerical results show that the new¬ incoming droplet wet and slide off the solidified surface and the rejection between droplets are the reasons for the deviation of the actual deposition length. The total length of the longitudinal section negatively correlates with the deposition distance. To improve the dimensional accuracy, the deposition distance and repulsion rate need to be guaranteed. The optimal deposition distance is found to have a negative linear correlation with wettability. Originality/value The numerical model developed in this paper will help predict the continuous metal droplet deposition and provide guidance for the selection of deposition distance.

Purpose The purpose of this paper is to study the flow field characteristics of the micro-scale textured bearing surfaces using the lattice Boltzmann method based on the microscopic dynamics of the fluid. Design/methodology/approach Considering the inertia effects and the micro-scale effects, the models of a single micro-scale texture unit cell with different shapes and different film thickness ratios are established. The influence of pressure difference between inlet and outlet of the unit cell on flow characteristics is studied. Findings The surface pressure distribution, flow patterns and pressure contours in the flow field are obtained. The results reveal that the pressure difference has a significant influence on the characteristics of the micro-textured flow field. Originality/value The results have certain guiding significance for further step investigation on microscopic lubrication mechanism of the water-lubricated polymer bearings.

Purpose This paper aims to analyze the effect of absorber’s geometry and operating fluid on the thermal and hydrodynamic behaviors of a solar collector. Two different profiles are proposed for the absorber which is wavy and flat. Also, the inner tube of HTF (i.e. heat transfer fluid) is considered as single and double. The solar collector is filled with hybrid nanofluid of SiO2-TiO2/ ethylene glycol (EG) which its thermal conductivity and dynamic viscosity are measured using KD2 Pro and Brookfield LVDV III Ultra; respectively, in the temperature range of 30°C to 80°C and nanoparticle concentration in the range of 1.5% to 3.5%. Design/methodology/approach Among the solar collector, the parabolic-trough solar collector is one of the most efficient models for extracting solar thermal power. A parabolic trough solar collector with two different models of absorbers and included with two models of inner HTF tube is proposed. Findings The corresponding regression equations are derived versus temperature and volume fraction and used in the numerical process. For the numerical process, the thermal lattice Boltzmann method manipulated with a single-node curved scheme is used. Also, in the final step, the second law analysis is carried out in local and volumetric forms. The influential factors are Rayleigh number, the concentration of hybrid nano-powder and the structure of absorber profile. Originality/value The originality of the present work is combining a modern numerical method (i.e. double-population lattice Boltzmann method) with experimental observation on characteristics of SiO2-TiO2/EG nanofluid to analyze the thermal performance of parabolic trough solar collector.

In this paper, the process of a drop rebounding from a hydrophobic and chemically heterogeneous surface is investigated using the multiphase lattice Boltzmann method. The bounce behavior of drops is dependent on the degree of hydrophobicity and heterogeneity of the surface. When the surface is homogeneous, the drop rebounds vertically and the height increases with the enhancement of the surface hydrophobicity. For the heterogeneous surface with two different hydrophobic parts, the drop rebounds laterally toward the lower hydrophobic side. Because the high hydrophobic side exerts the stronger unbalanced Young's force on the contact line compared with the low hydrophobic side, the difference of the forces results in the asymmetrical rebound. A phase diagram displays the rebound numbers of a drop impacting on the various chemically homogeneous and heterogeneous surfaces. A simply quantitative estimation is made to predict the rebound heights and flying times through the contact angles of the surface. This work promotes the understanding of the rebound mechanism of a drop impacting on a chemically heterogeneous surface and provides a guiding strategy for the precise control of the lateral behavior of rebounding drops by hydrophobic and heterogeneous surfaces.

In this paper, the lattice Boltzmann method (LBM) has been employed to explore the permeability and internal fluid flow behavior of the gas diffusion layer (GDL). Three different non-uniform porosity distributions are designed as linear type, stepped type, and transitional type and compared with constant porosity samples. Results show that the linear porosity gradient distribution leads to higher permeability values compared with the other two types. For samples with total porosity of 0.65 and 0.75, optimal porosity gradient distributions bring about an enhancement of permeability have been found. The impact of porosity gradient distribution on the velocity field is presented. Dependencies of permeability with porosity and tortuosity are demonstrated through several fitted equations.

In the conventional representative elementary volume-scale models, details of fluid movement, thermal transfer and mass transport in the porous media are relatively hard to capture, while the understanding of them is crucial in many diverse engineering and environmental applications such as running nuclear power facilities or pollutant diffusion in soil environment. In this paper, a pore-scale lattice Boltzmann method (LBM) modeling of double diffusion systems in saturated porous media is developed to investigate the role played by pore structure in the behavior of salt finger phenomena together with their fluid flow mechanism. An iterative source-correction immersed boundary method is developed to describe the solid skeleton with different boundary conditions for velocity field, heat transfer, and mass transport, respectively. The natural convection in a vertical annulus and the conjugate heat transfer problem in a two-layer horizontal annulus are employed to verify the accuracy and the applicability of the immersed boundary method for Dirichlet-type, Neumann-type and conjugate heat transfer boundary conditions, respectively. Comparisons between the present results and existing investigation show a very good agreement and demonstrate that the double diffusive process in porous media can be predicted with a good accuracy by the proposed model. Subsequently, the instability evolution process of salt finger-type of double diffusive convection in porous media is investigated, with a focus on the structure and behavior of salt fingers and the kinetic energy evolution. The obtained simulation results show that in saturated porous media, relatively large vertical mass fluxes can be generated even if the density distribution is of dynamical stability.

Anodic porous transport layer (PTL) plays a pivotal role in the performance of the polymer electrolyte membrane (PEM) water electrolyser. In this study, Shen-Chen Lattice Boltzmann Method (SC-LBM) is implemented to study the invasion patterns (IP) of O2 in a water saturated anodic PTL. Multiphase flow patterns in anodic PTL obtained with the LBM simulations are validated with the experiment results. Simulations are conducted for varied Capillary number (Ca) and Bond number (Bo) to study the competitiveness between the capillary, viscous forces and gravity. A dimensionless number ( φ ) is defined to develop a set of optimized parameters to enhance O2 removal. The O2 saturations along the normalized length reveal importance of void space microstructure in PTL. Thus, positive and negative porosity gradients are implemented from catalyst layer (CL) to water flow channel to understand invasion patterns. The results inspire to consider a random micro porous layer (MPL) near the CL to minimize the accumulation of O2. Such parametric analysis and pore structure studies is a promising technique for the optimisation of the O2 removal process.