无网格法耦合RNGk-ε湍流模型在亚、跨声速翼型黏性绕流中的数值模拟

 基于移动最小二乘无网格方法,耦合RNG (Re-Normalisation Group) k-ε湍流模型求解雷诺平均Navier-Stokes方程。采用AUSM (Advection Upstream Splitting Method)⁺-up迎风格式求解数值通量,应用在高度各向异性点云结构中取得良好结果的点云重构技术结合移动最小二乘法拟合空间导数,并用三阶SSP (Strong Stability Preserving)型Runge-Kutta显式时间推进格式求解离散后的控制方程。在此基础之上,实现了对NACA0012、RAE2822翼型亚、跨声速黏性绕流的数值模拟,给出了翼型表面压力系数分布曲线、不同位置处的平均速度剖面、马赫数等值线等计算结果,并与实验值及相关文献数值模拟结果进行比较,结果吻合较好。表明所发展的结合点云重构技术的无网格方法耦合RNG k-ε湍流模型能够成功模拟翼型亚、跨声速黏性绕流,验证了所提算法的有效性,并拓展了无网格方法求解湍流流动的途径。

Numerical simulation of subsonic and transonic viscous flow around airfoil using meshless method coupled with RNG k-ε turbulent model

In the present paper, the moving least square meshless method is used to solve Reynolds-averaged Navier-Stokes equations with RNG (Re-Normalisation Group) k-ε turbulence model. The flux is calculated by AUSM (Advection Upstream Splitting Method)⁺-up scheme; the moving least square method with cloud of points reconstruction technology, which can obtain good results from highly anisotropic cloud of points, is adopted to fit the spatial derivative, and the third order SSP (Strong Stability Preserving) Runge-Kutta scheme is used for the time advance to solve the discrete format control equation. Based on this, the subsonic and transonic viscous flow field around NACA0012 and RAE2822 airfoils is simulated. According to the numerical simulation results, the pressure coefficient distribution curves of the airfoil surface and the Mach number contours are presented, and the mean velocity profiles of the boundary layer at different locations are also investigated. The simulation results produced by the present work show a good agreement with the experiment results as well as other numerical simulation results, which means the method proposed in the present paper can successfully simulate the subsonic and transonic viscous flow around airfoil and also verify the effectiveness of the algorithm. What''s more, the present work can also expand the way of meshless method to solve the turbulent flow.