二维可压缩自由剪切层的理论分析

本文从"二维可压缩自由剪切层存在相对稳定的大尺度拟序涡结构,流场应该满足什么样的条件"这样一个反问题出发,应用常微分方程奇点理论对NS方程进行了分析,维持大尺度拟序涡结构的条件是流场内有交替出现的能量不平衡点,鞍点是温度极大值点,结点是温度极小值点;压缩性增加抑制了结点的生成和持续,是导致可压缩自由剪切层厚度增长速度比不可压情况变小的机理;得到的结论可以合理解释现有的物理现象.其次,对于目前研究可压缩自由剪切层广泛应用的对流马赫数进行讨论,认为在建立过程中采用鞍点是压力极大值点假设条件不合理,得出的公式不能反映介质特性,本文采用鞍点是温度极大值点作为假设条件,提出新的求解对流马赫数的公式.根据流动机理分析,提出通过在流场内建立交替出现的鞍点和结点,触发大尺度拟序涡结构,解决超燃冲压发动机混合问题;理论上给出大尺度拟序涡结构频率条件.

Theoretical analyses on compressible free shear layer

In this paper, the analysis is conducted on a converse problem using Navier-Stokes equations and the ordinary difference singular point theory. The problem is: what conditions the fluid parameters should be satisfied when relatively stable, large-scale coherent structures are existed in two dimensional free shear layer? The conditions are: non-equilibrium points of energy are distributed alternatively in the flow filed, and saddle points are the points of maximum temperature value, nodal points are the points of minimum temperature. Analysis is made about the effect of compressibility, the relation within the pressure, temperature and the location of saddle points. Some new conclusions are drawn and agree well with the experimental phenomena. Useful results are gained also, which is helpful on enhancement of the mixture problem about the supersonic scramjet engine.