基于黎曼不变量的P-M流动边界条件分析

Analysis of Boundary Condition in Prandtl-Meyer Flow Based on Riemann Invariants

P-M(Prandtl-Mayer)流动是一种基本的二维定常超声速平面无旋流动,未引入黎曼不变量时,其特征线理论或传统的Prandtl-Meyer膨胀波求解过程都没有直观显示出壁面边界条件对流场参数的影响方式和途径.本文从流线坐标系下的二维定常气体动力学方程和无旋条件出发,直观地得到了蕴涵壁面边界条件的两个黎曼不变量,通过分析两个黎曼不变量沿流场不同特征线族的携带和传播,详细阐明了初始条件和边界条件对P-M流场参数的影响过程.得到了固壁边界上每一点对流场参数皆有影响,且这种影响是沿该点发出的特征线通过黎曼不变量传播到流场内部的直观结论.

Prandtl-Meyer（P-M） flow is a basic two-dimensional steady supersonic plane irrotational flow. Before introduction of Riemann invariants, the solution process of characteristic line theory or traditional Prandtl-Meyer ex- pansion wave theory does not directly show the influence way of wall boundary condition on flow field parameters. Based on the two-dimensional steady gas dynamics equations and irrotational conditions in streamline coordinates, two Riemann invariants implication of the wall boundary conditions are intuitively obtained. Through the analysis of carry- ing and spreading of two Riemann invariants along different characteristic line family in the flow fields, the process of effects on P-M field parameters of the initial condition and boundary conditions is elaborated. The results show that each point of the solid wall boundary have effects on the flow field parameters, and these effects are spread to the inte- rior of flow field by the Riemann invariant along the characteristic line issued from the point.