An immersed boundary-lattice Boltzmann method for single- and multi-component fluid flows

International audienceThe paper presents a numerical method to simulate single-and multi-component fluid flows around moving/deformable solid boundaries, based on the coupling of Immersed Boundary (IB) and Lattice Boltzmann (LB) methods. The fluid domain is simulated with LB method using the single relaxation time BGK model, in which an interparticle potential model is applied for multi-component fluid flows. The IB-related force is directly calculated with the interpolated definition of the fluid macroscopic velocity on the Lagrangian points that define the immersed solid boundary. The present IB-LB method can better ensure the no-slip solid boundary condition, thanks to an improved spreading operator. The proposed method is validated through several 2D/3D single-and multi-component fluid test cases with a particular emphasis on wetting conditions on solid wall. Finally, a 3D two-fluid application case is given to show the feasibility of modeling the fluid transport via a cluster of beating cilia

Computing the force distribution on the surface of complex, deforming geometries using vortex methods and Brinkman penalization

The distribution of forces on the surface of complex, deforming geometries is an invaluable output of flow simulations. One particular example of such geometries involves self-propelled swimmers. Surface forces can provide significant information about the flow field sensed by the swimmers, and are difficult to obtain experimentally. At the same time, simulations of flow around complex, deforming shapes can be computationally prohibitive when body-fitted grids are used. Alternatively, such simulations may employ penalization techniques. Penalization methods rely on simple Cartesian grids to discretize the governing equations, which are enhanced by a penalty term to account for the boundary conditions. They have been shown to provide a robust estimation of mean quantities, such as drag and propulsion velocity, but the computation of surface force distribution remains a challenge. We present a method for determining flow- induced forces on the surface of both rigid and deforming bodies, in simulations using re-meshed vortex methods and Brinkman penalization. The pressure field is recovered from the velocity by solving a Poisson's equation using the Green's function approach, augmented with a fast multipole expansion and a tree- code algorithm. The viscous forces are determined by evaluating the strain-rate tensor on the surface of deforming bodies, and on a 'lifted' surface in simulations involving rigid objects. We present results for benchmark flows demonstrating that we can obtain an accurate distribution of flow-induced surface-forces. The capabilities of our method are demonstrated using simulations of self-propelled swimmers, where we obtain the pressure and shear distribution on their deforming surfaces

An improved volumetric LBM boundary approach and its extension for sliding mesh simulation

The lattice Boltzmann method (LBM) has been emerging as a promising alternative CFD approach for complex fluid flows. With LBM, no-slip/free-slip wall boundary conditions are implemented via straightforward particle bounce-back/specular reflections on a solid surface, thus enable the use of Cartesian grid for accurate boundary representation. For curved boundary that is commonly encountered with complex geometry, available point-wise based LBM extrapolation/interpolation boundary schemes can not guarantee the exact hydrodynamic flux conditions. To address this fundamental issue, a volumetric LBM boundary scheme was proposed in 1998, which ensures an exact treatment of hydrodynamic fluxes on solid surface and establishes a generic framework for realizing hydrodynamic boundary conditions on curved surface. This dissertation presents the development of an improved volumetric LBM boundary scheme. The basic idea is when reflecting (scattering) back the fluid particles from solid boundary, particles should be distributed in the affected volume according to local flow information rather than uniformly as in the original volumetric LBM boundary formulation. To realize this, a scattering correction procedure is formulated and added to the originally proposed volumetric LBM boundary scheme framework. In particular, the procedure redistributes the surface scattered particles based on local velocity variation. As a result, it reduces the solution dependence on actual boundary location/orientation with respect to the computational grid, demonstrates an improved order of accuracy for flow solutions with arbitrarily located boundary. Accuracy of this approach has been demonstrated on typical flow benchmark problems that involve curved boundaries. In the second part of this dissertation, the proposed volumetric LBM boundary scheme is extended to sliding-mesh interface condition for flow simulation involving rotating geometries. A volumetric LBM sliding-mesh interface scheme couples the flow solutions on both sides of sliding interface, and conserves the mass and momentum flux across it. Accuracy of this scheme is demonstrated by performing a LBM-sliding mesh simulation of flow past a rotating propeller

A vorticity based model and its application to flow around an impulsively started cylinder

An improved model of VIScous Vorticity Equation (VISVE) in 2-D is proposed and implemented in this thesis. Based on the original model, non-orthogonal terms have been included in this model in order to apply to meshes with skewness. A surface pressure model has been designed in order to predict the time evolution of pressure and force. Parallelization has been implemented in the code to shorten the computational time cost. The proposed method is applied to an impulsive started cylinder, which is a classic unsteady separated flow in 2-D. New griding has been created in order to apply to the cylinder geometry. Results are correlated with published experimental and numerical data. The flow patterns were captured in the converging solution. Grid independence and sufficiency of the computational domain are evaluated.Mechanical Engineerin

The Diffuse Bounce Back Lattice Boltzmann Method and its Applications on the Study of Fluid-Particle Interactions

Fluid-structure interaction is very broadly seen and widely used in many industrial, engineering and environmental processes. The lattice Boltzmann method has been preferred for simulating particulate flows due to its advantages of easy implementation, micro- and mesoscopic physical insights and parallel algorithm. Both sharp and diffuse boundary treatments are studied to recover curved and moving boundaries on structured orthogonal grids for the lattice Boltzmann method. These methods can describe curved boundaries more accurately and more smoothly than the naive staircase approximation. However, to improve the order of velocity accuracy and to reduce the fluctuation of force, either interpolation or additional momenta have been introduced to the collision step of lattice Boltzmann equation. In this dissertation, a new boundary scheme based on diffuse geometry is proposed for lattice Boltzmann method. The scheme is named Diffuse Bounce Back-Lattice Boltzmann Method (DBB-LBM) and is derived by directly incorporating the bounce back condition into the weak form of the propagation step of discretized Boltzmann equation. The new method does not change the collision operator. Therefore it can be easily combined with other fluid models that modify the collision step, such as multi-phase flow model, turbulence model, non-Newtonian model, etc. Although diffuse boundary is introduced, this scheme recovers exact bounce back condition at sharp boundary limit, regardless of the shapes and motions of the boundaries. Numerical tests show that the velocity accuracy of this method is second order. Under the Diffuse Bounce Back scheme, the boundary force can be simply recovered by taking the first moment of the boundary term. This treatment to boundary force is natural and does not require the calculation of momentum exchange. The new boundary force model is able to recover the drag coefficient of cylinder flows at different Reynolds numbers correctly. In moving boundary problems, the fluctuation of force can be reduced compared to traditional sharp boundary conditions because it does not require extrapolation to fulfill the unknown information of the newly generated fluid nodes around the boundaries. The validated force model can be applied to fluid-particle interaction problems to study the behavior of particle in various flows, including the inertial migration of particle in the Taylor Couette flow. In this dissertation, the background and applications of fluid-structure interaction are first introduced. Descriptions of previously published models for fluid-structure interaction are expanded upon afterwards. Detailed inspiration and derivation for the new DBB-LBM scheme are explained, and several benchmark problems are initiated to test and validate its accuracy, performance of mass conservation and the effect of different parameters and factors. The force model proposed within the framework of DBB-LBM is then introduced and applied to the cylinder flow benchmark problem for validation. A complete fluid-particle interaction model is built upon the Diffuse Bounce Back boundary scheme, the moment force model, the Velocity Verlét Integration of Newton’s Equations of Motion, together with the models for internal and external forces like gravity and repulsion. The combination is tested by a series of problems including particle in Couette flow, particle in Poiseuille flow, and the drafting, kissing and tumbling of two falling particles. The trajectories of the particles are consistent with the reported data in previous publications. The proposed boundary scheme is finally applied to the 3D Taylor Couette flow simulations with and without particles, in order to study the flow regimes at different Taylor numbers and the behaviors of inertial particle migration under these flow structures

IMMERSED BOUNDARY-FINITE DIFFERENCE LATTICE BOLTZMANN METHOD USING TWO RELAXATION TIMES

ABSTRACT It is known that velocity fields computed by using an immersed boundary-lattice Boltzmann method (IB-LBM) with a single-relaxation time (SRT) show unphysical distortion when the relaxation time, τ, is high. The authors proposed an immersed boundary-finite difference lattice Boltzmann method (IB-FDLBM) using SRT to predict liquid-solid flows. In simulations with IB-FDLBM, numerical errors in the velocity fields appear as in IBLBMs when τ is high. A two-relaxation time (TRT) collision operator is therefore implemented into IB-FDLBM in this study to reduce numerical errors at high τ. Simulations of circular Couette flows show that the proposed method gives accurate predictions at high τ, provided that the magic parameter, which is a function of the relaxation times, is less than unity. In addition, predicted drag coefficients of a circular cylinder and a sphere at low Reynolds numbers show reasonable agreements with theoretical solutions and measured data