超音速喷管内准一维气相流动建模与数值模拟

Modeling and numerical simulation of quasi-one dimensional gas phase flow in a supersonic nozzle

通过理论分析建立考虑壁面摩擦和换热影响的喷管内气相准一维流动数理模型,在气动方程组矢通量分裂基础上,采用有限差分方法对其变体形式进行离散,空间导数采用五阶精度WENO格式,时间导数采用三阶精度三步TVD龙格库塔方法,在Fortran平台上进行编程和计算,进行模型方法验证和参数研究。结果表明,在适当选取摩擦修正因子时,数值模拟与实验数据吻合较好,验证了数理模型、数值计算与求解方法的有效性。喷管半扩张角增大时,出口气流速度和马赫数增大,而静压减小;进口总温提高时,出口速度显著升高,但由于壁面摩擦和换热加剧,相应的出口马赫数会减小;进口总压提高时,出口气流速度并不显著增大;壁面温度升高时,出口气流速度和马赫数均减小。

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.