TVD格式在超音速喷管三维粘性流动求解中的应用

Application of TVD Scheme in Computation of Three Dimensional Viscous Flows in a Supersonic Nozzle

详细给出了任意三维曲线坐标系中Ｎｏｖｉｅｒ－Ｓｔｏｋｅｓ方程的对流项ＴＶＤ格式的构造过程，建立了数值求解三维粘性流动的计算方法，应用该方法对三维超音速喷管中有激波及无激波情况下的两种工况的层流流场进行了数值求解，并与实验做了对比。结果表明本文建立的计算方法具有较高的精度，同时也证明ＴＶＤ格式具有分辩率高，稳定收敛等优点，为进一步开展叶栅流场及紊流的研究打下了基础。

In this paper, a TVD scheme for solving the conductive terms of the Navier Stokes equations in three dimensional arbitrary curvilinear coordinate system was constructed and a numerical method for calculating three dimensional viscous flows was presented in details. The method was applied to the prediction for the laminar flow fields with shock and shock free in a three dimensional supersonic nozzle, and it was shown from the comparison between the computational and experimental results that the method proposed in this paper has a higher accuracy. Moreover, the TVD scheme was demonstrated to have high resolution for shock wave capturing and good numerical stability and convergence. The present work provides a sound base for the further study on turbulent flows in the three dimensional supersonic nozzle as well as in turbomachinery cascades.