Lattice Boltzmann Simulation Of Flow Controls

The vortex shedding around the cylinder will cause negative effects such as vortex-induced vibration and noise.Flow control is an effective way to suppress vortex shedding and eliminate vortex-induced vibration.Over the years,two kinds of flow control methods have been proposed based on the experimental phenomena and numerical simulation results.The two methods are active control and passive control.The active control method utilizes external energy to drive the device and equipment,such as forced vibration.The passive control method does not need external force,in fact,the vortex suppression and drag reduction are realized indirectly by using the external environmental factors,which include adding control elements from the outside of the cylinder,such as a splitter plate.From the practical point of view,it is of great significance to the vortex shedding suppression of the cylinder.Based on the above understanding,this paper numerically simulated two kinds of flow controls.One is the flow around a circular cylinder with a splitter plate,and the other is the flow around the oscillating elliptic cylinder.The research results of this paper can help to understand the inner mechanism of vortex shedding.In this paper,both of the two flow control methods work well in controlling the vortex shedding in the cylinder wake,and achieve the purpose of reducing drag force and eliminating vortex induced vibration.In this paper,the large eddy simulation of two-dimensional 9 velocities multi relaxation lattice Boltzmann method is used.The evolution equation can be expressed as:where is the distribution function in the discrete velocity space at time t on each lattice node x.Where M is a matrix which linearly transforms the distribution functions f(x,t)in the discrete velocity space to the velocity moments m(x,t):m = Mf,f = M-1m.M-1 is the inverse matrix of M.S is a diagonal matrix.And m(eq)=Mf(eq)is the equilibrium value of the moment m.The equilibrium distribution functions can be expressed as:where,p is the fluid density,u is the fluid velocity,and is the speed of lattice sound.The particle velocity ea can be written as:where is the lattice speed,and Ax is the lattice length,At is the time step.?? is weighting coefficient:The fluid density and velocity are obtained:The collision matrix is given by S diag(Sp,Se,Se,Sj Sq,sj,Sq,Sv,Sv).In the usual LBM simulations,because p,pu are conserved quantities,the relaxation factors Sp and Sj have no effect on the system and therefore can be assumed any value.sv determines the kinematic viscosity se is related to bulk viscosity.The transformation matrix M is:For large-eddy simulation:Vtotal=v0+Vt,where molecular viscosity V0=UL/Re,and Vt are the turbulent eddy viscosity.In the classical Smagorinsky model,the eddy viscosity is modeled as:,where Cs is Smagorinsky constant determined empirically for each particular flow and ? is the filter size.The magnitude of the large scale strain rate tensor is defined as:Where Sij is the strain rate tensor,The treatment for boundary condition is based on the idea of extrapolation of the non-equilibrium.In this paper,the flow past a cylinder with a splitter plate is simulated firstly,and the flow characteristics and the mechanism of vortex shedding and drag reduction are analyzed.The cylinder is placed near the wall,and the right end of the cylinder is provided with a splitter plate.The circular cylinder and the splitter plate compose a CCSP system.We analyze the sensitivity of two parameters,one is the gap rate G/D,of which the value changed from 0.1 to 3.0,and the other is the Reynolds number Re,of which the value changed from 200 to 400.The influence of gap rate on the vortex shedding is studied,and the critical gap rate corresponding to different Reynolds number is found.When the gap rate is less than the critical one,the vortex shedding alternately disappears completely in the wake region of the CCSP system,and the flow state is stable.It is found that the addition of a splitter plate in the wake region of the cylinder could suppress vortex shedding.Then,the influence of the gap rate on the drag coefficient is studied,and the variation curve of the average drag coefficient and lift coefficient is obtained.The lift drag coefficient decreases with the decrease of the gap rate and the Reynolds number,which indicates that the moving wall and the additional splitter plate have a significant drag reduction effect,and the maximum drag reduction rate is 30%.The numerical simulation of the flow around the oscillating elliptical cylinder is performed secondly.Meanwhile,the influence of the frequency and amplitude of the oscillation on the flow structure is investigated.In the problem of flow around an oscillating cylinder,the "lock-on" is used to describe the synchronization between the vortex shedding frequency and the oscillating frequency of the cylinder.When the frequency of vortex shedding and the excitation frequency of the elliptical cylinder are equal,the state is defined as "lock-on".Otherwise,the non-lock-on state.In this paper,the elliptic cylinder oscillation with Reynolds number Re = 200 is chosen as the basic model.At first,the effect of the oscillating frequency on the vortex shedding is studied when the numerical simulation of the amplitude is 0.2.When the amplitude is fixed,the larger the oscillation frequency is,the more complex the vortex shedding pattern is.And then the effect of oscillation frequency on flow field of flow structure is discussed.The monitoring point in the flow field is set,and the power spectrum analysis of the y-direction velocity is studied.Thus,the lock-on and non-lock-on frequency distribution map is obtained.By comparing of the drag coefficient curve,the oscillation amplitude and oscillation frequency of the lock-on are summed up,and the frequency distribution of the resonance is determined.According to the distribution,the disturbance of the vortex-induced vibration can be realized by changing the amplitude and the oscillation frequency of the cylinder,so as to avoid the occurrence of resonance.This conclusion can be used as a reference for the protection of engineering components from the theoratical perspective.