Direct Numerical Simulation Of Flow Around NACA0012 Airfoil At Low Reynolds Number

Direct numerical simulation(DNS)is a kind of research method of computational fluid dynamics(CFD).It does not need any turbulence model,and directly solves the complete NS equations.It’s often used in the study of turbulence because it can obtain accurate information and fine structures in the flow field.In this paper,the direct numerical simulation method is used to calculate the flow around the NACA0012 airfoil and wing at low Reynolds numbers,and the related properties of turbulence under this condition are studied,which is of great theoretical significance.In the simulation,the space is discretized by the finite difference method of second order accuracy with center difference scheme and the time integral is third order RK-CN method,in which the nonlinear term is advanced explicitly and the linear term is treated implicitly.Fractional step method is adopted since the continuous equation can not be solved by time advance and the second order mixed partial derivative term is specially treated here.In the simulation of three-dimensional,the momentum equations are solved by the factorization method,and the Fast Fourier Transform is used to solve the Possion equation,which both greatly improve the efficiency of the calculation.In this paper,the velocity and vorticity are obtained firstly by calculating the one-dimensional Burgers equation and two-dimensional direct numerical simulation respectively under different Reynolds numbers.These are used to verify the effectiveness of numerical methods and algorithms,and roughly determine the Reynolds number of three-dimensional direct numerical simulations at the same time.The velocity,pressure and vorticity of two-dimensional flow around the airfoil are obtained subsequently under different Reynolds numbers,and the energy variation,kinetic energy dissipation rate,skewness factor and flatness factor of three-dimensional flow are also calculated.The results show that the higher the Reynolds number is,the higher spatial and temporal resolution and the numerical accuracy are needed.The numerical discretization of high order accuracy is necessary for accurate calculation at high Reynolds number.The difference of the velocity variation at different Reynolds numbers are not obvious,but the vorticity of the high Reynolds number increases,the formation and dissipation of the vortex are quite different.In addition,the energy dissipation is slower,and the fluctuation of kinetic energy dissipation rate increases when the Reynolds number is higher.However,the skewness factor and flatness factor have not changed much in the same flow field even at different Reynolds numbers.