高超声速无粘流场的推进计算

SPACE-MARCHING CALCULATIONS OF HYPERSONIC INVISCID FLOWFIELD

本文将文[1]中用于时间相关法计算的NND格式推广到定常超声速流动的空间推进计算,采用二步的预测、校正方法保证了推进方向的二阶精度,可以证明,这种二阶精度的NND格式具有TVD性质,是MacCormack二步显式格式的推广。本文首先将格式应用于二维平板上斜激波反射流场的推进计算,以检验格式捕捉激波的能力,同时研究了不同的通量分裂方法对格式捕捉激波能力的影响,得到了相当满意的结果。在此基础上,计算了航天飞机简化外形的身部超声速流场,给出了M_∞=10,α=0°,和M_∞=5,α=5°两种状态的部分结果,计算结果清楚地描绘了由于气流在机翼附近受到强烈压缩而产生的内嵌激波与外激波相交的复杂流场结构,与文[7]相比,流场结构更为清晰。

NND scheme, presented by Prof. Zhang hanxin of CARDC and used for time-dependent calculations before, has been generalized into the predictor-corrector two step, two order scheme in space-marching calculations in this paper. It possesses TVD property, It has been proved that it is an extension of MacCormack's two step explicit scheme. In order to check out the shock-capturing properties of this scheme, we consider the problem of regular reflection of an oblique shock wave on the flat plate, and study the effects of different flux splitting method, such as Warming and Steger, van Leer, et al. , on the capability of shock-capturing, the results of numerical experiments are satisfactory. Then, the scheme is used in space-marching calculations of hypersonic inviscid flowfield of modified space shuttle orbiter, some results of M∞ = 10, α = 0° and M∞=5, α=5° have been showed in this paper. The numerical results show clearly the interaction of body shock wave and wing shock wave, the flowfield structure of shock interaction region obtained in this paper is more clear than that in [7].