斜激波总压损失率极小值理论解与物理意义

Theoretical solutions and physical significances for minimum ratio of total pressure loss by oblique shock

以法向马赫数作为激波强度表征量,对斜激波关系式进行重新推导,得到了穿过激波总压损失率极小值的理论解。控制方程表达式为激波角对物面角的线性函数。依据斜激波总压损失率极小值解析公式,首先,绘制了针对超声速流总压损失率应用的楔形角-激波角-马赫数的斜激波效率图。其次,通过生成斜激波三维总压损失率等值线图,呈现了总压损失率在楔形角-激波角-特征马赫数空间上的分布规律。此外,利用斜激波效率图,揭示了等总压损失率条件下马赫数与激波角的对称双解现象。

Theoretical solutions for the minimum ratio of total pressure loss are derived based on the oblique shock relation and a definition of the strength by using normal Mach number for an oblique shock.First,the governing equation for the minimum ratio of total pressure loss is formulated as a linear function of the shock angle and the corresponding deflection angle. Second,based on the analytical formulae,a new oblique shock efficiency diagram regarding the deflection angle,the shock angle and the upstream Mach number is generated,For applications of the total pressure loss,the line for minimum ratio of total pressure loss is mapped on the diagram Then a three-dimensional contour graph is proposed to study the distribution on ratio of total pressure loss in terms of the deflection angle,the shock angle and the characteristic Mach number.Third,according to the oblique shock efficiency diagram,solutions for the upstream Mach number and the corresponding shock angle are obtained.For the same ratio of total pressure loss,these solutions have symmetrical double values properties in their domain.