Interpolated Bounce-back Scheme Research Articles

Direct numerical simulation of three-dimensional particle-laden thermal convection using the Lattice Boltzmann Method

In thermal multiphase flows, the modulation in the heat transfer rate due to the presence of finite-size solid particles attract growing interest in recent years. This study focuses on developing a robust and efficient simulation method for particle-laden Rayleigh-Bénard convection. The present work utilizes the double distribution function-based thermal lattice-Boltzmann method (TLBM), which enables successful simulations of multiphase fluid-thermal interactions. The no-slip boundary of the moving solid particles is handled by the interpolated bounce-back scheme. Additionally, Galilean invariant momentum exchange and heat exchange approaches are employed for hydrodynamic force and heat transfer calculation at the solid boundaries. The accuracy of the current method is verified with several benchmark cases, including three-dimensional single-phase Rayleigh-Bénard convection, as well as the settling of hot and cold spherical particles in a three-dimensional enclosure. Furthermore, we explore the modulation of Rayleigh-Bénard flows due to the presence of freely moving finite-size particles. The simulations are conducted on a distributed memory cluster with a 3D domain decomposition technique facilitated by the MPI library. A brief discussion on the parallel performance of the simulations is provided for both particle-laden and single-phase flow scenarios. Finally, the effects of finite-size solid particles on the overall heat transfer efficiency and modulation to the flow field in three-dimensional particle-laden turbulent Rayleigh-Bénard convection are discussed. The results show that addition of solid particles results in a moderate increase in the overall Nusselt number, and this enhancement is mainly due to the increased heat flux transported by the particles.

The influence of particle density and diameter on the interactions between the finite-size particles and the turbulent channel flow

Understanding the influence of different particle parameters on the two-way interactions between the particles and wall-bounded turbulence is important in many natural phenomena and engineering applications. In this work, particle-resolved direct simulation of particle-laden turbulent channel flow is performed based on the mesoscopic lattice Boltzmann method (LBM), and the particle–fluid interface is treated using the interpolated bounce back scheme. The friction Reynolds number (Reτ) of the single phase turbulent channel flow is 180, and the particle volume fraction is fixed at 1%. Three particle–fluid density ratios and three particle diameters are considered, and five particle-laden simulations are performed to investigate the influence of particle density and diameter on the interactions between the particles and the carrier turbulence. Results show that the streamwise velocity of the solid phase is larger than that of the fluid phase in the near-wall region, and the velocity difference between the two phases decreases with increasing particle density, but increases with increasing particle diameter. The probability density functions (PDFs) of particle velocity and angular velocity depend on the distance between the particles and the wall, but the PDFs of particle acceleration and angular acceleration are not spatially dependent. The distribution of particle Reynolds number follows the Gamma distribution within the buffer region and viscous sublayer. The solid phase concentration is high in the near-wall region, and the largest solid-phase concentration in this region occurs in the case with particles of intermediate density. Particles with different parameters would lead to different modulation to the carrier flow. Then, two aspects of the turbulence modulation are explored, i.e., the streamwise velocity and the turbulent kinetic energy (TKE). The presence of finite-size particles typically increases the streamwise velocity in the near-wall region and reduce the streamwise velocity outside this region. The trend is similar for TKE, but the TKE attenuation mainly occurs in the buffer region. The modulation to the streamwise velocity is analyzed using the streamwise momentum balance equation. It is found that the streamwise velocity modulation is dominated by the weighted Reynolds stress, but the different modulation in the near-wall region is due to the difference in weighted particle-induced stress, whereas the different modulation outside the near-wall region is due to the change in weighted Reynolds stress. Through TKE budget analysis, it is found that the enhancement of the total TKE source in the viscous sublayer increases with increasing particle density and diameter and the attenuation of total TKE source in the buffer region increases with increasing particle density and diameter, which is consistent with the TKE modulation for different cases.

Unsteady aerodynamic simulations by the lattice Boltzmann method with near-wall modeling on hierarchical Cartesian grids

Near-wall modeling for large-eddy simulation (LES) based on the lattice Boltzmann method (LBM) is applied to the unsteady aerodynamic simulations around the tandem cylinders and the 30P30N three-element high-lift airfoil using hierarchical Cartesian grids. The near-wall modeling of the inner turbulent boundary layer is essential for LES to accurately calculate the high Reynolds number wall-bounded turbulent flow with a reasonable calculation cost. Therefore, near-wall modeling for LES has been studied within the framework of the Navier–Stokes equations. However, LBM-based modeling is still in its early developing stage because of the LBM’s calculation algorithm using distribution functions on a non-body fitted Cartesian grid, and further developments are needed regarding the applicability to flow simulations around arbitrary complicated shapes that appear in the actual engineering field. In this study, aerodynamic simulations around tandem cylinders are conducted using the proposed near-wall modeling that reproduces the profiles of the turbulent boundary layer in turbulent channel flow simulations on a non-body-fitted Cartesian grid. The same benchmark problem is also calculated using the non-slip wall boundary condition (interpolated bounce-back scheme) for comparison. Those calculation results are validated through the comparisons with the available experimental measurements, and the effectiveness of the proposed near-wall modeling to high Reynolds number wall-bounded turbulent flow simulations around objects with curvilinear surfaces is demonstrated. Followed by the tandem cylinders, the aerodynamic simulation around the 30P30N three-element high-lift airfoil is also conducted in order to demonstrate the applicability to more complicated shapes. The simulation result shows that the proposed method can stably calculate the relatively complicated configuration such as the high-lift airfoil, and the potential of the proposed method to unsteady aerodynamic simulations around arbitrary complicated shapes is demonstrated.

Numerical Simulations of Flows in a Cerebral Aneurysm Using the Lattice Boltzmann Method with the Half-Way and Interpolated Bounce-Back Schemes

Lattice Boltzmann simulations and a velocity measurement of flows in a cerebral aneurysm reconstructed from MRA (magnetic resonance angiography) images of an actual aneurysm were carried out and the numerical results obtained using the bounce-back schemes were compared with the experimental data to discuss the effects of the numerical treatment of the no-slip boundary condition of the complex boundary shape of the aneurysm on the predictions. The conclusions obtained are as follows: (1) measured data of the velocity in the aneurysm model useful for validation of numerical methods were obtained, (2) the numerical stability of the quadratic interpolated bounce-back scheme (QBB) in the flow simulation of the cerebral aneurysm is lower than those of the half-way bounce-back (HBB) and the linearly interpolated bounce-back (LBB) schemes, (3) the flow structures predicted using HBB and LBB are comparable and agree well with the experimental data, and (4) the fluctuations of the wall shear stress (WSS), i.e., the oscillatory shear index (OSI), can be well predicted even with the jaggy wall representation of HBB, whereas the magnitude of WSS predicted with HBB tends to be smaller than that with LBB.

Direct numerical simulations of turbulent periodic-hill flows with mass-conserving lattice Boltzmann method

The multi-relaxation time lattice Boltzmann method is used to perform direct numerical simulations of laminar and turbulent pressure-driven flows within a channel with hill-shape periodic constriction for the first time. The simulations are conducted on a graphics processing unit cluster with two-dimensional domain decomposition to accelerate the computation. The hill-shape boundary is represented using the interpolated bounce back scheme. However, the scheme generates mass leakage across the boundary, which is more pronounced in the turbulent flow regime, and this may produce diverging solutions for turbulent flows. The mass leakage due to the local mass imbalance along the curved boundary is solved by modifying the distribution functions locally or globally, and both predict similar velocity distributions. Since the global correction method is more computing time-consuming, the local correction method is adopted. The present numerical implementation’s capability is first validated by performing direct numerical simulations of turbulent channel flow at Reτ = 180, and the current predicted results agree well with the benchmark solutions. Direct numerical simulations are further conducted for the turbulent flow over the periodic hill at Reh = 2800. Both the mean velocity and turbulent stress compare favorably with the benchmark solutions. The present simulation also correctly predicts the turbulence splatting effect near the windward hill. Both phenomena are in good accordance with the benchmark solutions.

Particle-resolved direct numerical simulation of collisions of bidisperse inertial particles in a homogeneous isotropic turbulence

A particle-resolved study of a collision system composed of heavy particles and light particles in a homogeneous isotropic turbulence has been performed. Direct numerical simulations (DNS) of this system were conducted using lattice Boltzmann method (LBM). The effects of hydrodynamics on the collision particles were accounted by directly resolving the flow around finite-size particles with an interpolated bounce-back scheme. A large-scale stochastic forcing scheme was implemented within the mesoscopic multiple-relaxation-time LBM approach to maintain turbulence intensity at targeted levels. Both kinematic and dynamic collision kernels were evaluated to study the correlation of total collision events and turbulent kinetic energy (TKE) dissipation rate. The results show that collisions between particles increase with the increase of TKE dissipation rate as radial relative velocities between particles increase with it. It is found that the dynamic collision kernels do not match with the kinematic collision kernels which is derived from point-particle method. Quantitatively, they were approximately 4 to 10 times smaller than the corresponding dynamic collision kernels. Therefore, it is not reasonable to estimate the kinematic collision kernel in particle-resolved simulations as its rationales are not valid. However, the collision behavior can still be accounted for by means of the dynamic collision kernel since it is obtained from the direct statistical analysis of the collision events.

Lattice Boltzmann simulations of magnetic particles in a three-dimensional microchannel

A lattice Boltzmann model for magnetic particles in a fluid is established, in which both hydrodynamic and magnetic interactions are fully coupled. The interpolated bounce back scheme is adopted to describe the fluid-particle interaction. We combine the implicit particle velocity updated scheme and the modified momentum-exchange method to make the algorithm stable and also maintain the Galilean invariance. Moreover, MPI + OpenMP hybrid programming mode is used for parallel computing. The model is validated by numerical simulation of the sedimentation of a particle in a tank. We investigate the motion of magnetic particles in a microchannel with carrier fluid under the uniform magnetic field and hybrid magnetic field, and then the magnetic particles flow through a variable-section microchannel is studied. The results indicate that the structures formed by magnetic particles can be regulated by controlling the external magnetic field and flow field; besides, the more ordered structures have more influence on the fluid flow.

A comparative study of immersed boundary method and interpolated bounce-back scheme for no-slip boundary treatment in the lattice Boltzmann method: Part II, turbulent flows

In the first part of this study [1], we compared the performances of two categories of no-slip boundary treatments, i.e., the interpolated bounce-back schemes and the immersed boundary methods in a series of laminar flow simulations within the lattice Boltzmann method. In this second part, these boundary treatments are further compared in the simulations of turbulent flows with complex geometry to provide a next-level assessment of these schemes. Two non-trivial turbulent flow problems, a fully developed turbulent pipe flow at a low Reynolds number, and a decaying homogeneous isotropic turbulent flow laden with a large number of resolved spherical particles are considered. The major problem of the immersed boundary method revealed by the present study is its incapability in computing the local velocity gradients inside the diffused interface, which can result in significantly underestimated dissipation rate and viscous diffusion locally near the particle surfaces. Otherwise, both categories of the no-slip boundary treatments are able to provide accurate results for most of turbulent statistics in both the carrier and dispersed phases, provided that sufficient grid resolutions are used. The criteria of sufficient grid resolutions for each examined flow are also addressed in this document.

A comparative study of immersed boundary method and interpolated bounce-back scheme for no-slip boundary treatment in the lattice Boltzmann method: Part I, laminar flows

The interpolated bounce-back schemes and the immersed boundary method are the two most popular algorithms in treating a no-slip boundary on curved surfaces in the lattice Boltzmann method. While those algorithms are frequently implemented in the numerical simulations involving complex geometries, such as particle-laden flows, their performances are seldom compared systematically over the same local quantities within the same context. In this paper, we present a systematic comparative investigation on some frequently used and most state-of-the-art interpolated bounce-back schemes and immersed boundary methods, based on both theoretical analyses and numerical simulations of four selected 2D and 3D laminar flow problems. Our analyses show that immersed boundary methods (IBM) typically yield a first-order accuracy when the regularized delta-function is employed to interpolate velocity from the Eulerian to Lagrangian mesh, and the resulting boundary force back to the Eulerian mesh. This first order in accuracy for IBM is observed for both the local velocity and hydrodynamic force/torque, apparently different from the second-order accuracy sometime claimed in the literature. Another problem of immersed boundary methods is that the local stress within the diffused fluid-solid interface tends to be significantly underestimated. On the other hand, the interpolated bounce-back generally possesses a second-order accuracy for velocity, hydrodynamic force/torque, and local stress field. The main disadvantage of the interpolated bounce-back schemes is its higher level of fluctuations in the calculated hydrodynamic force/torque when a solid object moves across the grid lines. General guidelines are also provided for the necessary grid resolutions in the two approaches in order to accurately simulate flows over a solid particle.

Numerical simulations of flows in cerebral aneurysms using the lattice Boltzmann method with single- and multiple-relaxation time collision models

Lattice Boltzmann simulations of flows in TOF-MRA-based cerebral aneurysm models are carried out using the single-, two- and multiple-relaxation time collision models, SRT, TRT and MRT, to investigate the effects of the collision model on predicted velocity fields in the aneurysms. The non-Newtonian characteristics of blood are accounted for by using the Casson model, whereas a simulation with the Newtonian viscous stress model is also carried out to investigate the effects of the viscous stress model on predicted velocity and wall shear stress distributions. Four cerebral aneurysm models are used in the simulation. The shapes of cerebral arteries are extracted from TOF-MRA data as STL meshes, and the level set function representing the artery wall is reconstructed from the STL mesh data. By making use of the level set function in the interpolated bounce-back scheme, the complex structures of arteries having aneurysms can be easily dealt with in the LB framework. As a result, the following conclusions are obtained: (1) the SRT can give reasonable predictions comparable to the MRT, provided that the spatial resolution is high enough; otherwise numerical errors can be large and numerical instabilities take place, (2) numerical errors in velocity is apt to take place in the near aneurysm wall region due to a small velocity scale, (3) although the TRT is less stable than the MRT, predictions of the TRT under stable numerical conditions are almost the same as those of the MRT, and (4) although the Bingham number effect on the flow structure is small, the mean wall shear stress may change over several percent, depending on the configuration of the aneurysm and the main blood flow, by neglecting the non-Newtonian nature of blood.

LBM study of aggregation of monosized spherical particles in homogeneous isotropic turbulence

Direct numerical simulations of an aggregation system composed of monosized spherical particles in homogeneous isotropic turbulence have been performed using Lattice Boltzmann method (LBM). The effects of hydrodynamics on the aggregation process were considered by directly resolving the disturbance flows around finite-size solid particles using an interpolated bounce-back scheme. A nonuniform time-dependent large-scale stochastic forcing scheme was implemented within the mesoscopic multiple-relaxation-time LBM approach to maintain turbulence intensity at targeted levels. To simulate particle interactions, the non-contact surface force and the contact force were taken into account using the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory and the soft-sphere model, respectively. This interface-resolved direct numerical simulation (IR-DNS) combined with the well-known DLVO theory was employed to obtain an insight into the aggregation process of micron-size particles. Specifically, the model was used to study the effects of solid volume fraction on aggregate growth. Aggregates of larger sizes formed in local regions of higher concentration of particles due to higher encountering probability between particles. The effects of aggregating particles of different volume fractions on the statistically stationary homogeneous isotropic turbulent flow were investigated. It was found that the presence of particles attenuated the turbulent kinetic energy at large scales and augmented the kinetic energy at the small scales. This effect is more apparent with increasing volume concentration of particles.

Control of wakes and vortex-induced vibrations of a single circular cylinder using synthetic jets

This paper presents a study on active control of the wakes and one-dimensional vortex-induced vibrations (VIVs) of a single circular cylinder using a pair of synthetic jets (SJs) at a low Reynolds number Re=100. To facilitate this study, a lattice Boltzmann method based numerical framework is established, in which the multi-block scheme and the overlap-mesh approach with improved information exchange mechanisms are used to balance the computational accuracy and efficiency, and the interpolated bounce-back scheme and a corrected momentum exchange scheme are adopted for accurate force evaluation. Two configurations are considered. In the first configuration, the cylinder is fixed, on which a pair of SJs is implemented and operates in phase. Effects of the SJ pair on the cylinder wake are investigated in a systematical way, with the focus placed on the SJ׳s momentum coefficient, frequency and position. Simulation results indicate that the Kármán vortex street formed behind the cylinder can be effectively suppressed when the SJ pair operates with sufficiently high momentum coefficient, at a frequency close to the cylinder׳s natural vortex shedding frequency, and is placed in the quarter arc edge of the cylinder׳s leeward side. In the second configuration, the same cylinder is allowed to oscillate in the cross-flow direction under the excitation of asymmetrically shedding vortices as well as the constraint of a spring. It is well demonstrated that this one-dimensional VIV of the cylinder can be successfully suppressed by the use of SJ control. Due to stronger vortex shedding induced by increased relative motion between the cylinder and its surrounding flow, however, not all the cases that perform complete wake suppression on the fixed cylinder are able to completely suppress the VIVs of the oscillating cylinder. Through the present study, details about SJ-controlled flow around the cylinder and in the wake are also revealed.

Implementation issues and benchmarking of lattice Boltzmann method for moving rigid particle simulations in a viscous flow

In this work, we revisit implementation issues in the lattice Boltzmann method (LBM) concerning moving rigid solid particles suspended a viscous fluid. Three aspects relevant to the interaction between flow of a viscous fluid and moving solid boundaries are considered. First, the popular interpolated bounce back scheme is examined both theoretically and numerically. It is important to recognize that even though significant efforts had previously been devoted to the performance, especially the accuracy, of different interpolated bounce back schemes for a fixed boundary, there were relatively few studies focusing on moving solid surfaces. In this study, different interpolated bounce back schemes are compared theoretically for a moving boundary. Then, several benchmark cases are presented to show their actual performance in numerical simulations. Second, we examine different implementations of the momentum exchange method to calculate hydrodynamic force and torque acting on a moving surface. The momentum exchange method is well established for fixed solid boundaries, however, for moving solid boundaries there are still open issues such as unphysical force fluctuations and Galilean invariance errors. Recent progress in this direction is discussed, along with our own interpretations and modifications. Several benchmark cases, including a particle-laden turbulent channel flow, are used to demonstrate the effects of different modifications on the accuracy and physical results under different physical configurations. The third aspect is the refilling scheme for constructing the unknown distribution functions for the new fluid nodes that emerge from the previous solid region as a particle moves relative to a fixed lattice grid. We examine and compare the performance of the refilling schemes introduced by Fang et al. (2002), Lallemand and Luo (2003), and Caiazzo (2008). We demonstrate that improvements can be made to suppress force fluctuations resulting from refilling.

Numerical study on dynamic sorting of a compliant capsule with a thin shell

Sorting compliant capsules is an interesting research topic. In this paper, a simple bifurcated micro-channel is used to sort the particles with different rigidities. The behavior of a compliant particle inside the channel is investigated numerically. The fluid flow and the particle’s deformation are solved by Lattice Boltzmann Method (LBM) and Lattice Spring Model (LSM), respectively. The fluid and solid solvers are coupled through interpolated bounce-back scheme. Two benchmark problems are used to validate our method. One is the motion of a compliant capsule in a channel and the other is the deformation of a capsule inside a simple shear flow. The results are quantitatively consistent with those in literature. By taking advantage of the rotating of capsules in shear flow, a simple distinguished bifurcated micro-channel is proposed to sort capsules with different rigidities. In this micro-channel, the initial offset and shear stress induce the rotating and lateral migration of the capsule and flux ratio is determined by the outlet pressures. The competition between the effect of initial offset and flux ratio contributes to the sorting mechanism. Compared to other micro-channels with different geometrical models, present one is more convenient and may be more efficient to screen the microcapsule we want.

A Comparison Between the Interpolated Bounce-Back Scheme and the Immersed Boundary Method to Treat Solid Boundary Conditions for Laminar Flows in the Lattice Boltzmann Framework

In this paper, the interpolated bounce-back scheme and the immersed boundary method are compared in order to handle solid boundary conditions in the lattice Boltzmann method. These two approaches are numerically investigated in two test cases: a rigid fixed cylinder invested by an incoming viscous fluid and an oscillating cylinder in a calm viscous fluid. Findings in terms of velocity profiles in several cross sections are shown. Differences and similarities between the two methods are discussed, by emphasizing pros and cons in terms of stability and computational effort of the numerical algorithm.

Ghost-fluid-based boundary treatment in lattice Boltzmann method and its extension to advancing boundary

A ghost-fluid-based boundary treatment in lattice Boltzmann method (GF-LBM) proposed by Tiwari and Vanka (2012) is one of the complex boundary treatment in fluid flow computation. In this paper, this treatment is developed to multi-relaxation-time LBM and further discussed with validation. It is found that, in case of stationary and sliding boundary such as Taylor–Couette flow, this treatment is superior to other bounce-back-based treatment. However, a defect in the density conservativeness is found due to the prediction of the density at image point under a non-penetration condition. Authors improve the treatment by using the normal moment relation followed by the validation. Next, the treatment is extended to other moving boundary problem such that the boundary advances with stepping over the computational grids. It is found that, this treatment is comparable to the second-order interpolated bounce-back scheme, and its precision depends on node numbers considered in each treatment. GF treatment is found to have high precision especially at curved boundary in motion.

Non-body-fitted Cartesian-mesh simulation of highly turbulent flows using multi-relaxation-time lattice Boltzmann method

This paper presents a lattice Boltzmann method (LBM) based study aimed at numerical simulation of highly turbulent and largely inclined flow around obstacles of curved geometry using non-body-fitted Cartesian meshes. The approach features (1) combining the interpolated bounce-back scheme with the LBM of multi-relaxation-time (MRT) type to enable the use of simple Cartesian mesh for the flow cases even with complex geometries; and (2) incorporating the Spalart–Allmaras (SA) turbulence model into LBM in order to represent the turbulent flow effect. The numerical experiments are performed corresponding to flows around an NACA0012 airfoil at Re=5×105 and around a flat plate at Re=2×104, respectively. The agreement between all simulation results obtained from this study and the data provided by other literature demonstrates the reliability of the enhanced LBM proposed in this paper for simulating, simply on Cartesian meshes, complex flows that may involve bodies of curved boundary, high Reynolds number, and large angle of attack.

Lattice Boltzmann simulation of turbulent flow laden with finite-size particles

The paper describes a particle-resolved simulation method for turbulent flow laden with finite size particles. The method is based on the multiple-relaxation-time lattice Boltzmann equation. The no-slip boundary condition on the moving particle boundaries is handled by a second-order interpolated bounce-back scheme. The populations at a newly converted fluid lattice node are constructed by the equilibrium distribution with non-equilibrium corrections. MPI implementation details are described and the resulting code is found to be computationally efficient with a good scalability. The method is first validated using unsteady sedimentation of a single particle and sedimentation of a random suspension. It is then applied to a decaying isotropic turbulence laden with particles of Kolmogorov to Taylor microscale sizes. At a given particle volume fraction, the dynamics of the particle-laden flow is found to depend mainly on the effective particle surface area and particle Stokes number. The presence of finite-size inertial particles enhances dissipation at small scales while reducing kinetic energy at large scales. This is in accordance with related studies. The normalized pivot wavenumber is found to not only depend on the particle size, but also on the ratio of particle size to flow scales and particle-to-fluid density ratio.