关键词: 超音速喷管, 有限差分法, 矢通量分裂, WENO格式, TVD龙格库塔方法

Abstract: Mathematical modeling of the quasi-one dimensional gas phase flow in a nozzle, which accounted for wall friction and heat transfer, was established through theoretical analysis. Three flux vector splitting methods were used for the characteristic splitting of the aerodynamic equations. The variant form of them was discretized with a finite difference method. Specifically, the spatial and time derivatives were discretized with a fifth-order WENO scheme and a three-step third-order TVD Runge-Kutta method, respectively. The programming, calculations, validation and parameter study were performed based on the Fortran platform. The results showed that the numerical simulation agreed quite well with the experimental data if an appropriate friction correction factor was selected, which verified the availability of the established mathematical model and the adopted numerical methods and algorithms. It was found that as the half expansion angle of the nozzle was enlarged, both the gas velocity and the Mach number at the outlet increased, whereas the outlet static pressure decreased. The increase of the inlet total (or stagnation) temperature led to the significant increase of the outlet gas velocity and the decrease of the corresponding outlet Mach number due to the aggravation of wall friction and heat transfer. The increase of the inlet total (or stagnation) pressure cannot significantly increase the outlet gas velocity. The increase of the wall temperature led to the decrease of both the outlet gas velocity and the outlet Mach number.

Key words: supersonic nozzle, finite difference method, flux vector splitting, WENO scheme, TVD Runge-Kuta method