低耗散TVD格式及叶轮机内低马赫数流动模拟

推导了条件化预处理矩阵在守恒变量下的形式,以及三维任意曲线坐标系下的相应的系统特征值与特征矩阵。根据预处理技术修正了任意曲线坐标下的Harten-TVD格式,得到低耗散TVD格式,并讨论了抑制了压力速度失耦的方法。分别使用修正后低耗散格式与未修正的格式,对高负荷低压涡轮叶栅T106内低速流动:进口马赫数分别为0.1,0.01和0.001,进行数值模拟。计算表明,未修正格式不能得到有意义的结果,而修正后的低耗散格式,即使在极低的马赫数流动下,也工作良好。同时可以注意到:对于无粘流动,三种进口马赫数条件下,流场内等压线分布几乎是一致的。 

Low Diffusion TVD Schemes and Simulation of Low Mach Number Flow in Turbomachinery

The preconditioning matrix in conservation variables was derived from the primitive variables of pressure and entropy,and the resultant eigenvalues and eigenvectors of the preconditioned system were deduced in three dimensional curvilinear coordinates.Specially,the feature matrix given in three dimensional curvilinear coordinates was simple and could be inversed in any case.Then,the low diffusion Harten-TVD scheme in the curvilinear coordinates was obtained based on preconditioning,and the method enforcing the pressure/velocity coupling was discussed.Using schemes with and without preconditioning,low-pressure turbine blade T106 at low Mach number flow,i.e.inlet mach numbers were 0.1,0.01,0.001 respectively,was simulated.The convergence histories were considered firstly.It could be noticed that the convergence rate increased obviously with preconditioning.The convergent results indicate that low diffusion scheme with preconditioning can recover features of low mach flow but scheme without preconditioning can't.The reason was that the modified eigenvalues of preconditioned system were proportional to the particle velocity approximately,not acoustic velocity,that agreed with real flow characters in low speed flows.However,high convergence rate and high accuracy were gained because of low diffusion and low equation stiffness.It was also noticed that the distribution of equi-pressure contours for these three inlet mach numbers were almost undistinguishable for inviscid flow.