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.