Research And Application Of Lattice Boltzmann Method Based Algorithm For Fluid-Structure Interaction

With the development of modern theory of computation and computational devices,Computational Fluid Dynamics(CFD)has been applied increasingly in the field of engineering.Compared with the sound velocity in fluid,the velocity is always small in realistic applications.Therefore,it is always in the field of low speed flow.In these situations,incompressibility is always introduced to simplify the Navier-Stokes(NS)equations.Inspite of the improvement of computational resource in the past decades,there are still challenges to solve NS equations numerically.Firstly,because of the introduction of incompressibility,the pressure of the fluid flow acts as the Lagrangian multiplier to enforce the incompressibility.To get the pressure of the fluid flow,considerable resource is needed to solve the relating elliptic equation and such treatment limits the efficiency of CFD model.Secondly,with the increase of velocity,convection becomes dominant.Therefore,convection terms in NS equations must be discretized carefully to keep the numerical stability of the model.Finally,because of the spacial discretization in the whole field,the computational cost of CFD model is large.Accelaration is always needed to improve the efficiency of the model.Considering the mentioned facts,development of robust flow solver with high efficiency is desirable for its application in engineering.To remedy the issues to evaluate the pressure of fluid flow and improve the efficiency of traditional CFD models,the newly developed lattice Boltzmann method(LBM),which is based on the assumption of weak compressibility of fluid,has attracted more and more attentions from researchers because of its unique numerical scheme,simple numerical implementation and ease of parallel computation.It has been shown that the numerical performance and efficiency of the model are satisfactory for a wide range of problems.Based on standard LBM model,flow solver with 9 velocities in two dimensions(D2Q9)and 19 velocities in three dimensions(D3Q19)has been developed to simulate the fluid flow numerically.Multiple Relaxation Time(MRT)model is introduced in the process of particle collision to improve the numerical stability.Based on the local refinement of computational grid,adaptive multi-scale LBM model has been built to reduce the computational cost.Parallel version of the code has been carried out to accelerate the simulation and to improve the efficiency of the model.To deal with Fluid-Structure Interaction(FSI)in engineering,numerical model has been built for rigid body and deformable body.Quaternion is introduced to describe the location of the rigid body.For deformable body with simple geometrical characteristics,finite difference model is used to solve the dynamic equation in Lagrange form.For complex deformable body,co-rotation scheme is introduced to consider the nonlinear behaviour caused by its large deformation.To achieve the coupling between the response of structure and fluid flow,Immersed Boundary Method(IBM)is assembled in the model with weak coupling strategy.Base on the flow solver in 3D,hydrodynamic characteristics of square heaving plate with opening have been tested.The numerical results show that the hydrodynamics of the heaving plate are not sensitive to the shape of the opening.Dependency of the hydrodynamics on the opening ratio,distribution of the opening and spacing of the double plates has been observed.There are optimal opening ratios with which the heaving plates obtain more damping.Based on the developed FSI solver,hydrodynamic behaviour of tandem arranged flapping flexible foils in uniform flow has been analysed.Numerical results show that,compared with single flapping flexible foil,the flow is rich and complex for tandem foils.With different gap distance and phase difference in heave motion,the deformation characteristics of the foils are different.Complex deformation leads complex flow around the foils.The trailing foil affects the propulsive performance of the leading foil by its interaction with the wake flow of the leading foil.There are optimal phase differences with which the propulsive performance of the leading foil is better and the enhancement is weakened with increase of gap distance.The trailing edge vortex of the leading foil contributes to the propulsive performance of the trailing foil.It is shown that the hydrodynamic behaviour of the trailing foil is not sensitive to the gap distance.