一种求解透平叶栅三维流场的高精度TVD格式

本文提出了一种应用三阶精度Chakravarthy-OsherTVD格式求解环形透平叶栅三维定常流场的隐式近似因子分解方法。控制方程为柱座标速度分量表示的任意曲线座标系下的三维欧拉方程。采用Beam-Warming近似分解, 对隐式项进行迎风差分, 得到了时间精度为一阶、空间精度为5点三阶的隐式格式。算例对5点三阶和5点二阶精度的格式进行了比较。表明空间三阶精度隐格式对计算结果没有明显改进, 但收敛残差有较大降低。 

A HIGH-ORDER ACCURACY TVD EULER SOLVER FOR 3D FLOWS IN TURBINE CASCADES

Abstract A third order accuracy implicit approximate factorized TVD code is developed using Chakravarthy-Osher scheme to solve the steady flows in annular turbine cascades.The governing equation is the 3D Euler equations in arbitary curvilinear coordinate systems in terms of cylinder coordinate system velocity components.Beam-Warming factorization and upwind difference are adopted to discretize the implicit term,and the explicit one is discretized by Chakravarthy-Osher TVD numerical fluxes.The boundary condition is obtained from extrapolation.The resulted algebraic equations are tridiagonal block matric system and solved by sweeping in each direction.So the scheme is a 5 point implicit AF scheme of first order temporal and third order or second order spacial accuracy depending on the two TVD factors.Two examples are presented,the first verifies the calculation of third order scheme with a low speed wind tunnel experiment,the second compares the third order scheme with the second order one.The examples indicate that the code results in numerical solutions agree with the experiment,and the third order scheme has little difference from the second order one in the solutions,but it decreases the convergent residual greatly.Also it is showed that the two schemes do not agree with each other very well in the throat of the cascade where the flow velocity is equal to the local sound speed.