基于三维特征线理论的曲面激波流场反设计方法

Inverse design method of three-dimensional shocked flow fields based on the theory of three-dimensional characteristic lines

激波流场反设计技术是高超声速乘波布局设计领域的核心技术之一。为了克服传统吻切理论在设计全三维曲面激波流场时的缺陷,本文提出了一种基于三维特征线理论的设计方法。该方法构造了一种包含四条马赫线和一条流线的三维基本单元,发展了用于设计曲面激波流场的阵面推进方法及并行加速方法。通过对Euler方程中微分算子进行特征分解,重构了流场的控制方程,并提出了适用于求解该控制方程的Tikhonov-Lagrange拟合法,实现了三维流场的稳定求解。利用提出的设计方法,分别对高马赫数圆锥激波流场、椭圆锥激波流场、小攻角来流下的圆锥激波流场及由Bezier曲面描述的一般性曲面激波流场算例进行了设计,并与数值模拟结果进行了对比。计算结果表明,当前设计方法实现了对横向压力梯度及攻角引起的三维流动效应的合理求解,其中典型截面的壁面压力及马赫数分布与数值模拟结果相比误差分别小于0.3%和1.7%,且具有较高的并行效率。该设计方法拓展了特征线理论在全三维激波流场反设计领域的应用范围,在高超声速全三维乘波布局设计领域具有重要发展前景。

Shocked-flow-field inverse design technology plays an important role in the design of hypersonic waverider vehicles.A novel design method based on the theory of three-dimensional characteristic lines is developed to overcome the defects of the conventional osculating method in designing three-dimensional shocked flow fields.In this method,a basic cell including four Mach lines and one streamline is constructed,then the corresponding front advancing and parallelization methods are developed.A new set of governing equations are obtained by decomposing the differential operators of the Euler equations,and the Tikhonov-Lagrange curve fitting method is proposed to obtain the corresponding stable solution.Four examples are used to test the numerical stability and accuracy of the method,including the conical shocked flow field,the elliptical shocked flow field,the conical shocked flow field with a small angle of attack,and the shocked flow field with a general shock shape described by the Bezier surface.The results show that the present method has a good performance in predicting the three-dimensional flow effects induced by the transverse pressure gradient and the angle of attack.Compared to the numerical simulation results,the errors of the wall pressure and Mach number distributions are less than 0.3%and 1.7%,respectively,and a high parallelization efficiency is also achieved.The proposed method extends the application of the theory of characteristic lines in the design of three-dimensional shocked flow fields,and has an important development prospect in the design of hypersonic waverider vehicles.