Lattice Boltzmann Simulation Of The Flows Around Bluff Body

The present thesis covers two main parts: the theoretical research of Lattice Boltzmann Method, and the simulation of the flows around bluff body using Lattice Boltzmann method.1. The model of Lattice Boltzmann MethodThe lattice Boltzmann method (LBM) has recently become an available method for computational fluid dynamics (CFD). Unlike conventional methods based on macroscopic continuum equation, the LBM starts from microcosmic kinetic equations. The kinetic nature brings certain advantages over conventional numerical methods, such as its algorithmic simplicity, easy handing of complex boundary conditions, and programming easily. We introduce the foundation of Lattice Boltzmann model exhaustively with two-dimensional nine-velocity (D2Q9) incompressible lattice Boltzmann model.For two-dimensional nine-velocity (D2Q9) incompressible lattice Boltzmann model, the Boltzmann equation can be discretized in space x and time t intoIn the above equation, e_α(α=0,1,…8) is the particle velocity in the a direction, f_α( x,t)is the density distribution function along theαdirection, f_α^(eq)(x,t) is its corresponding equilibrium state, x is the spatial position vector, and t is the time,τis the dimensionless relaxation time andδ_t is time step. The equilibrium distribution function of D2Q9 model is: in the above equation, whenα=0,ω_α=4/9; else whenα=1,3,5,7,ω_α=1/9; elseα=2,4,6,8时,ω_α=1/36.Equation (1) can be computed by the following two steps, where f|^<sub>αdenote the post-collision state of the distribution function. One can notice that the collision is completely local and the distribution function of a lattice is only affected by neighboring ones in the streaming step.Now we give a computational method of force evaluation in the Lattice Boltzmann method involving curved geometry:Consider an arbitrary curved wall which separates the solid region from the fluid region. Let x_w, x_f and x_b be the intersections of the boundary with various lattice links, the boundary node in the fluid region, and that in the solid region, respectively. Then,Δcan be It is well understood that the bounce-back boundary condition defined as satisfies the no-slip boundary condition with second-order accuracy at the location ofΔ=1/2.On the boundary it is important for us to define distribution function at x bin order to get the value at x f.To construct based upon some know information in the surrounding, Chapman-Enskog expansion for post- collision distribution function on the right-hand side of Eq. (3b) is carried out on the boundary. It has been proved that a second-order accurate no-slip boundary condition can be achieved by this method.Using the momentum-exchange method, the total force on the boundary can be computed with:2. Simulation of Flow around bluff body with LBMFor the simulation of flows around bluff body, firstly, we use D2Q9 model to investigate the case of flow around a cylinder. We present the streamlines, drag coefficients, lift coefficients, vorticity contours,Strouhal numbers etc. Secondly, we investigate the case of flow around a cylinder with a board behind it, we also present the streamlines, lift coefficients, Strouhal numbers etc. and compare them with the former results. Moreover, we investigate again with various Re and various length of the board. Afterwards, we investigate the case of flow around a cylinder with two boards which have the angel 90 between them. And also we give the lift coefficients, Strouhal numbers etc. At last, we list all the results together and analyze them.