高超声速飞行器外形热流密度分布计算的高精度方法研究

为提高高超声速条件下飞行器表面热环境的计算精度,发展了高精度算法WCNS-E-5,并开展了热流密度分布的数值计算研究.该算法采用的是五阶精度加权显式非线性格式,结合四阶精度的二阶偏导数差分近似、四阶精度的边界格式,同时还对网格偏导数及温度梯度也离散为四阶精度.通过求解三维Navier-Stokes方程,数值研究了高超声速飞行器外形如钝锥和双椭球体的物面热流密度分布.模拟结果表明,这种保证全流场高精度的WCNS-E-5得到的流场图像清晰、真实.与通常的二阶算法MUSCL对比,WCNS-E-5具有更高的流线分辨率,获得的热流密度更接近于实验测得分布.

Study of Heat Flux Distributions over Hypersonic Vehicle Configurations with High-order Accurate Algorithm WCNS-E-5

The high-order algorithm of WCNS-E-5 is developed in this paper to improve the calculational accuracy when the aerodynamic heating predictions over hypersonic vehicles are needed. WCNS-E-5 consists of fifth-order weighted explicit nonlinear scheme for the inviscid term of Navier-Stokes equations, fourth-order accurate scheme for the viscous term, the corresponding fourth-order boundary scheme and fourth-order difference discretization for gild partial derivatives and temperature partial derivative. Then WCNS-E-5 is used to solve three-dimensional Navier-Stokes equations and the heat flux distributions over vehicles in the hypersonic viscous flow are studied. The vehicle configurations are simplified as blunt cone and double ellipsoid. The solutions ensuring overall high-order accuracy in the flow field show that the contours are smooth and clear without spurious oscillations. Compared with second-order algorithm MUSCL, WCNS-E-5 owns the feature of higher resolution, and the calculated heat flux distribt,tions are more conformed to the experimental data.