超声速流场的流线-特征线坐标变换与应用

Conversion and Application of Streamline-Characteristic Coordinate System Conversion in Supersonic Flows

关键词:  弯曲激波  坐标变换  超声速流场  特征线  流线

Key words:  Curved shock waves  Coordinate conversion  Supersonic flowfield  Characteristics  Streamlines

摘要:

为了求解二维平面弯曲激波波后流场，讨论并发展了一系列基于流线-特征线坐标系变换的流场代数计算方法。该系列方法依据二维平面流场中气流角、静压沿特征线近似不变的特点，可快速求解平面弯曲激波波后流场。其中，等气流角近似法适合模拟流线轨迹，等静压近似法适合求解波后流场参数。在此基础上，又提出了一种改进的等气流角-等静压混合方法用于计算弯曲激波波后流场。和特征线法对比，等气流角-等静压混合法计算得到的流场基本特征与特征线法得到的结果相同，在来流马赫数Ma=6和Ma=4情况下误差分别仅为0.5%和0.15%，证实了该方法在求解二维平面弯曲激波流场中的适用性。

Abstract:

In order to solve the two-dimensional planar flowfield behind the curved shock，a series of algebraic methods are acquired at the streamline-characteristic coordinate system. The main idea is that flow angle and static pressure are approximately constant along each characteristic line. In contrast to the Method of Characteristics，the method of constant flow angle is good at calculating the streamline trajectory while the method of constant static pressure is proper for solving the flowfield parameters. A combined method named MCFP，Method of Constant Flow-angle and Pressure，is afterwards proposed to better solve the two-dimensional planar flowfield behind the curved shock. For a relatively large Mach number range，the flowfield calculated by the MCFP method is in good agreement with the MOC's. The error at incoming Mach number 6 is 0.5% and the error at incoming Mach number 4 is 0.15%，which demonstrates the applicability of the MCFP method.