Multi-block Lattice Boltzmann Method Research Articles

Study of unsteady separated fluid flows using a multi-block lattice Boltzmann method

PurposeNumerical simulations are performed for studying the vorticity dynamics of a dipole colliding with the wall in a bounded flow and the wake structure and separated flow properties past a circular cylinder at the values of Reynolds numbers.Design/methodology/approachThe near wake statistics of separated fluid flows are investigated by using the lattice Boltzmann method (LBM) in a two-dimensional framework. A multi-block technique is applied to accurately resolve the flow characteristics by the grid refinement near the wall and preserve the stability of the numerical solution at relatively high Reynolds numbers.FindingsThe results show that the rolling-up of the boundary layer occurs due to the shear-layer instabilities near the surface which causes a boundary layer detachment from the wall and consequently leads to the formation of small-scale vortices. These shear-layer vortices shed at higher frequencies than the large-scale Strouhal vortices which result in small-scale high-frequency fluctuations in the velocity field in the very near wake. The present study also demonstrates that the efficiency of the multi-block LBM used for predicting the statistical features of flow problems is comparable with the solvers based on the Navier-Stokes equations.Practical implicationsStudying the separated flow characteristics in aerospace applications.Originality/valueApplying a multi-block lattice Boltzmann method (LBM) for simulation of separated fluid flows at high-Reynolds numbers. Studying of the near wake statistics of unsteady separated fluid flows using the multi-block LBM. Comparison of flow characteristics obtained based on the LBM with those of reported based on the Navier-Stokes equations.

Two-dimensional numerical model for predicting fouling shape growth based on immersed boundary method and lattice Boltzmann method

Fouling and ash deposition are important problems for the heat exchangers. The numerical models are efficient ways to understand the fouling processes and guide the design of heat exchangers. Because the shape of the fouling layer can influence the flow and heat transfer, modeling the shape change of the fouling layer is essential for the numerical models. In this work, a new numerical model based on the immersed boundary method is proposed for 2D fouling processes. The flow is modeled by a multiblock lattice Boltzmann method with a fixed Eulerian mesh, and the fouling layer is represented by an immersed boundary with Lagrangian points. The shape change of the fouling layer can be carried out by deforming the immersed boundary, while keeping the mesh of flow simulation unchanged. The particle motion, deposition models and a time ratio for fouling time scale are also included in the model. The particle depositions on a single row of tube and tube bundles with different tube shapes are simulated by the proposed model as examples. The influences of particle size and flow velocity on the particle deposition on windward and leeward sides of a circular tube are analyzed. As for the tube bundles, the elliptical tube can reduce the fouling rate. The evolution of the shape of the fouling layer can be obtained by the proposed model.

ICCM2016: The Implementation of Two-Dimensional Multi-Block Lattice Boltzmann Method on GPU

A straightforward implementation of the Multi-Block Lattice Boltzmann Method (MB-LBM) on a Graphics Processing Unit (GPU) is presented to accelerate the simulation of fluid flows in two-dimensional geometries. The algorithm is measured in terms of both accuracy and efficiency with the benchmark cases of the lid-driven cavity flow and the flow past a circular cylinder, and satisfactory results are obtained. The results show that the performance on GPU becomes even better with the amount of data increasing. Moreover, the arrangement of the computational domain has a significant effect on the efficiency. These results demonstrate the great potential of GPU on the MB-LBM, especially when dealing with massive data.

A multi-block adaptive solving technique based on lattice Boltzmann method

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

A multi-block lattice Boltzmann method for the thermal contact resistance at the interface of two solids

In the present paper, a patching type multi-block lattice Boltzmann method is adopted to predict the thermal contact resistance (TCR) at the interface of two solids. The rough surfaces of contact materials are reconstructed based on the fractal theory and the contact pressure is obtained based on the plastic deformation model. The accuracy of the patching type multi-block lattice Boltzmann method is validated by some benchmarks. After validations, effects of the contact pressure, roughness, thermal conductivity of contact material, thermal conductivity of interstitial medium, temperature and radiation on TCR are investigated. The results show that: the TCR decreases when the contact pressure increases, but increases with the root-mean-square roughness; the TCR of two contact aluminums decreases faster than that of stainless steels when contact pressure increases; a higher thermal conductivity of contact materials leads to a smaller TCR; when the thermal conductivity of interstitial medium is close to zero or the gap is in vacuum, the TCR is much larger than that filled with air, especially at low contact pressure; at the high temperature, the contribution of the radiation to the TCR becomes appreciable if the thermal conductivity of the interstitial medium is low. Especially when the gap is in vacuum, the contribution of radiation on the TCR cannot be neglected.

Analysis and numerical tests of lifting relations to reconstruct LBM distribution functions for coupling simulations

The reconstruction operator (RO), which calculates the distribution functions of the lattice Boltzmann method (LBM) by the macroscopic variables, is important for the information exchange in the coupling simulation between LBM and macroscopic numerical methods. In the present work, different ROs are derived based on the first- and second-order expansions. The derivations show that the second-order ROs can conserve the momentum but the first-order ROs fail. The first-order models can be modified to guarantee the momentum conservation. The numerical tests are employed to evaluate the precisions of different models. The results demonstrate that the multiple-relaxation-time LBM is more stable than the single-relaxation-time LBM, and the first-order models are more stable than the second-order models. The second-order models give better reconstructions of the non-equilibrium parts of the distribution functions than the first-order models. However, the modified first-order models have similar accuracy to the second-order models when they are employed as boundary conditions or used in coupling simulations. Therefore, the second-order models are suggested for the initial conditions. The modified first-order models are suggested for the boundary conditions and the coupling simulations. Moreover, CPU time for coupling simulation decreases with the increase of the ratio between the time steps of finite volume method and LBM, and an optimized time ratio exists to minimize the errors. Finally, the flow past a porous medium is simulated by both the coupling methods and the multi-block LBM. The results show that the coupling methods are more efficient when using a large time step for the finite volume method.

Propulsive performance of a passively flapping plate in a uniform flow

Propulsive performance of a passively flapping plate in a uniform viscous flow has been studied numerically by means of a multiblock lattice Boltzmann method. The passively flapping plate is modeled by a rigid plate with a torsion spring acting about the pivot at the leading-edge of the plate, which is called a lumped-torsional-flexibility model. When the leading-edge is forced to take a vertical oscillation, the plate pitches passively due to the fluid-plate interaction. Based on our numerical simulations, various fundamental mechanisms dictating the propulsive performance, including the forces on the plate, power consumption, propulsive efficiency and vortical structures, have been studied. It is found that the torsional flexibility of the passively pitching plate can improve the propulsive performance. The results obtained in this study provide some physical insights into the understanding of the propulsive behaviors of swimming and flying animals.

Numerical analysis of lamination effect in a vortex micro T-mixer with non-aligned inputs

In the present study, the lamination effect in a micro T-mixer with non-aligned inputs on the mixing index has been investigated numerically in four different cases. The multi-block lattice Boltzmann method has been implemented for the flow field simulation and the second order upwind finite difference scheme has been used to simulate mass transfer. Reynolds numbers includes in the range of 10 ≤ Re ≤ 70. The simulation results show that the lamination effect in the mixer inputs, despite of its simple design, causes the interface of two fluids to increase and also to make the vortex effect stronger in the confluence of two fluid streams that increases the mixing index considerably. Of four lamination cases included for the mixing input, the maximum mixing index is for the vertical and asymmetrical lamination at the Reynolds number of 70 that is equal 0.689 and the minimum mixing index is for the horizontal and asymmetrical lamination at the Reynolds number of 10 that is equal 0.198.

Viscous flow past a collapsible channel as a model for self-excited oscillation of blood vessels

Motivated by collapse of blood vessels for both healthy and diseased situations under various circumstances in human body, we have performed computational studies on an incompressible viscous fluid past a rigid channel with part of its upper wall being replaced by a deformable beam. The Navier–Stokes equations governing the fluid flow are solved by a multi-block lattice Boltzmann method and the structural equation governing the elastic beam motion by a finite difference method. The mutual coupling of the fluid and solid is realized by the momentum exchange scheme. The present study focuses on the influences of the dimensionless parameters controlling the fluid–structure system on the collapse and self-excited oscillation of the beam and fluid dynamics downstream. The major conclusions obtained in this study are described as follows. The self-excited oscillation can be intrigued by application of an external pressure on the elastic portion of the channel and the part of the beam having the largest deformation tends to occur always towards the end portion of the deformable wall. The blood pressure and wall shear stress undergo significant variations near the portion of the greatest oscillation. The stretching motion has the most contribution to the total potential elastic energy of the oscillating beam.

Natural convection around a pair of hot and cold horizontal microtubes at low Rayleigh numbers

Natural convection around a pair of hot and cold horizontal microtubes in a relative large square enclosure was numerically studied using multi-block Lattice Boltzmann method (LBM). Five typical arrangements of the tube pair were made by placing the hot tube at various positions relative to the cold tube, such as side-by-side with, above or under. The hot and cold horizontal microtubes were put at the middle of a horizontal square enclosure. No slip flow conditions were given for all of the tube and the enclosure walls. Constant temperature conditions were given for the hot and cold tubes, respectively, and the adiabatic condition for the square enclosure. The computational code was validated by performing a benchmark case of a single hot isothermal horizontal microtube in the closed cold square cavity. A simple experimental loop was set up in order to make a comparison with the obtained numerical results. Two stainless microtubes with outer diameter of 1.00 mm were used for heat transfer test with a counter-current arrangement. The inlet water temperatures through the hot and cold microtubes were separately controlled by two water baths. The numerical simulated range of Rayleigh number is Ra < 1500. A correlation of Nusselt number with Rayleigh number was proposed based on the numerical results, which is in general agreement with the obtained experimental data.

Computation of transitional flow past a circular cylinder using multiblock lattice Boltzmann method with a dynamic subgrid scale model

Lattice Boltzmann method (LBM) is a kinetic based numerical scheme for the simulation of fluid flow. While the approach has attracted considerable attention during the last two decades, there is a need for systematic investigation of its applicability for complex canonical turbulent flow problems of engineering interest, where the nature of the numerical properties of the underlying scheme plays an important role for their accurate solution. In this paper, we discuss and evaluate a LBM based on a multiblock approach for efficient large eddy simulation of three-dimensional external flow past a circular cylinder in the transitional regime characterized by the presence of multiple scales. For enhanced numerical stability at higher Reynolds numbers, a multiple relaxation time formulation is considered. The effect of subgrid scales is represented by means of a Smagorinsky eddy-viscosity model, where the model coefficient is computed locally by means of a dynamic procedure, providing better representation of flow physics with reduced empiricism. Simulations are performed for a Reynolds number of 3900 based on the free stream velocity and cylinder diameter for which prior data is available for comparison. The presence of laminar boundary layer which separates into a pair of shear layers that evolve into turbulent wakes impose particular challenge for numerical methods for this condition. The relatively low numerical dissipation introduced by the inherently parallel and second-order accurate LBM is an important computational asset in this regard. Computations using five different grid levels, where the various blocks are suitably aligned to resolve multiscale flow features show that the structure of the recirculation region is well reproduced and the statistics of the mean flow and turbulent fluctuations are in satisfactory agreement with prior data.

Numerical studies on locomotion perfromance of fish-like tail fins

Flapping plates of typical fishlike tail shapes are simulated to investigate their locomotion performance using the multi-block Lattice Boltzmann Method (LBM) and Immersed Boundary (IB) method. Numerical results show that fishlike forked configurations have better locomotion performance compared with unforked plates. Based on our results, the caudal fin in carangi-form mode has greater thrust, and the lunate tail fin in thunniform mode has higher efficiency. These findings are qualitatively consistent with biological observations of fish swimming. Analysis of wake topology shows that the wake of the forked plate consists of a chain of alternating reverse horseshoe-like vortical structures. These structures induce a backward jet and generate a positive thrust. Moreover, this backward jet has a more favorable direction compared with that behind an unforked plate.

An efficient immersed boundary-lattice Boltzmann method for the hydrodynamic interaction of elastic filaments

We have introduced a modified penalty approach into the flow-structure interaction solver that combines an immersed boundary method (IBM) and a multi-block lattice Boltzmann method (LBM) to model an incompressible flow and elastic boundaries with finite mass. The effect of the solid structure is handled by the IBM in which the stress exerted by the structure on the fluid is spread onto the collocated grid points near the boundary. The fluid motion is obtained by solving the discrete lattice Boltzmann equation. The inertial force of the thin solid structure is incorporated by connecting this structure through virtual springs to a ghost structure with the equivalent mass. This treatment ameliorates the numerical instability issue encountered in this type of problems. Thanks to the superior efficiency of the IBM and LBM, the overall method is extremely fast for a class of flow-structure interaction problems where details of flow patterns need to be resolved. Numerical examples, including those involving multiple solid bodies, are presented to verify the method and illustrate its efficiency. As an application of the present method, an elastic filament flapping in the Kármán gait and the entrainment regions near a cylinder is studied to model fish swimming in these regions. Significant drag reduction is found for the filament, and the result is consistent with the metabolic cost measured experimentally for the live fish.

Fundamentals of migrating multi-block lattice Boltzmann model for immiscible mixtures in 2D geometries

This paper proposes an extension scheme for the application of the single phase multi-block lattice Boltzmann method (LBM) to the multiphase Gunstensen model, in which the grid is refined in a specific part of the domain where a fluid–fluid interface evolves, and the refined grid is free to migrate with the suspended phase in the flow direction. The method is applicable to single and multiphase flows, and it was demonstrated by simulating a benchmark single phase flow around a 2D asymmetrically placed cylinder in a channel and for investigating the shear lift of 2D neutrally buoyant drop in a parabolic flow.

Locomotion of a passively flapping flat plate

Locomotion of a passively flapping flat plate has been studied numerically by means of a multiblock lattice Boltzmann method. A flexible plate is modelled by a rigid plate with a torsion spring acting about the pivot at the leading edge of the plate. A dynamic model of this kind is called a lumped-torsional-flexibility model. When the leading edge is forced to heave sinusoidally, the plate pitches passively and propels itself in the horizontal direction as a result of the fluid–plate interaction. We have investigated various aspects of the mechanics behind the behaviour of the flapping plate, including the periodic- and non-periodic-flow states, the spontaneous motion of the plate, vortical structure and how they compare to similar propulsion systems in animals. In the periodic-flow regime, two dynamical responses of the passively pitching plate (forward and backward movements) are observed. Which movement will occur depends only on the frequency ratioFof the natural frequency of the system and the heaving frequency associated with the lumped torsional flexibility. It is found that the plate will select the forward movement whenF&gt; 1 and the backward movement whenF≤ 1. In the forward-movement regime, analysis of the dynamical behaviours and propulsive properties of the passively pitching plate indicates that the torsional flexibility can remarkably improve the propulsive performance. In addition, four kinds of vortex structures in the near wake are identified, which mainly depend on the forward speed of the plate. Finally the forward movement is compared to the flapping-based locomotion of swimming and flying animals. The results obtained in this study are consistent with the observations and measurements of swimming and flying animals; thus, they may provide physical insights into understanding of the propulsive mechanisms of the flapping wings and fins of animals.

Numerical simulation of capsule deformation in simple shear flow

The transient deformation of two-dimensional non-circular and three-dimensional non-spherical capsules in simple shear flow is studied numerically, using the hybrid immersed boundary and multi-block lattice Boltzmann method recently proposed by the present authors. The capsules are modeled as Newtonian liquid drops enclosed by elastic membranes; the liquids inside and outside the capsule have the same physical properties. The present results show important different behaviors between two-dimensional and three-dimensional capsules in shear flow. For two-dimensional non-circular capsules without considering the membrane bending rigidity, or considering the bending with the minimum bending-energy configurations (shapes at which the bending-energy has a global minimum) being uniform-curvature shapes, the capsules will always achieve the steady tank treading motion (a capsule deforms to a steady shape with a steady inclination and the membrane rotates around the liquid inside). However, for three-dimensional non-spherical capsules without membrane bending rigidity, such a steady mode does not exist; with the shear rate decreasing, the three-dimensional capsules’ motion changes from swinging mode (a capsule undergoes periodic shape deformation and inclination oscillation while its membrane is rotating around the liquid inside) to flipping mode. The deformation of two-dimensional capsules, with their initial non-circular shapes taken as the minimum bending-energy configurations, is also considered. It is quite interesting to find such two-dimensional capsules behave qualitatively similar to three-dimensional capsules: there is a swinging-to-flipping transition induced by lowering the shear rate.

Aerodynamic performance due to forewing and hindwing interaction in gliding dragonfly flight

Aerodynamic performance due to forewing and hindwing interaction in gliding dragonfly flight has been studied using a multiblock lattice Boltzmann method. We find that the interactions between forewing and hindwing effectively enhance the total lift force and reduce the drag force on the wings compared to two independent wings. The interaction mechanism may be associated with the triangular camber effect by modulating the relative arrangement of the forewing and hindwing. The results obtained in this Brief Report provide physical insight into the understanding of aerodynamic behaviors for gliding dragonfly flight.

Flow patterns in the sedimentation of an elliptical particle

We study the dynamics of a single two-dimensional elliptical particle sedimenting in a Newtonian fluid using numerical simulations. The main emphasis in this work is to study the effect of boundaries on the flow patterns observed during sedimentation. The simulations were performed using a multi-block lattice Boltzmann method as well as a finite-element technique and the results are shown to be consistent. We have conducted a detailed study on the effects of density ratio, aspect ratio and the channel blockage ratio on the flow patterns during sedimentation. As the channel blockage ratio is varied, our results show that there are five distinct modes of sedimentation: oscillating, tumbling along the wall, vertical sedimentation, horizontal sedimentation and an inclined mode where the particle sediments with a non-trivial orientation to the vertical. The inclined mode is shown to form a smooth bridge between the vertical and horizontal modes of sedimentation. For narrow channels, the mode of sedimentation is found to be sensitively dependent on the initial orientation of the particle. We present a phase diagram showing the transitions between the various modes of sedimentation with changing blockage ratio of the channel.

Multi-block Lattice Boltzmann method: Extension to 3D and validation in turbulence

In this paper, a multi-block method is applied to 3D problems. In this application, interpolation schemes are carefully addressed to avoid the inconsistency when information is transferred from coarse to fine blocks. Two test cases are employed to assess information transfer scheme and accuracy improvement with respect to grid refinement.