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Analytical inviscid stability analysis of the hypersonic boundary layer.

机译：高超声速边界层的无形分析稳定性分析。

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The neutral stability of a zero-pressure gradient hypersonic boundary layer flow over a flat plate is considered. The derivation of the linear stability equations from the Navier-Stokes equations is reviewed, and a formulation of the governing second order linear differential equation for the pressure disturbance is developed that lends itself to application of the WKB method over the entire boundary layer. This formulation provides a high order approximate analytical eigenfunction and eigenvalue relations for the pressure disturbance, and is applicable to several types of flows at moderate and high Mach numbers as well. The solution in this type of formulation is shown to be dependent only on the relative Mach number profile in the boundary layer, with the relative Mach number referring to the Mach number of the disturbance (with wavespeed c) relative to the mean-flow speed of sound. Pressure perturbation solutions and eigenvalues are determined for the non-inflectional cases of the wave speed c = 0 and c = 1 flow over an adiabatic surface, and show good qualitative agreement with numerical computations as well as results in the asymptotic limit of freestream Mach number {dollar}Msb{lcub}infty{rcub}toinfty{dollar}.; The case for a mean flow profile which possess a generalized inflection point and a wavespeed equal to the mean velocity at the generalized inflection point ({dollar}c = csb{lcub}s{rcub}{dollar}) is examined for the cases with and without heat transfer to the surface. These results also show a good qualitative comparison with the numerical results. The eigenvalue relations for these cases are examined in detail and the "near-linking" of the high-Mach number inviscid vorticity and multiple acoustic modes at moderate Mach numbers are investigated. These regions of the finite Mach number eigenvalue relation is shown to be described as a region of eigenvalue loci veering. This characteristic of the eigenvalue relation which, has only been observed previously in numerical computations, is shown to be approximated locally in the region near the interaction of these inviscid modes by a local hyperbolic approximation which qualitatively models the key aspects of this interaction.
机译：考虑平板上零压力梯度高超声速边界层流动的中性稳定性。回顾了从Navier-Stokes方程式推导线性稳定性方程式的过程，并开发了用于压力扰动的控制性二阶线性微分方程式的公式，使其适合在整个边界层上应用WKB方法。该公式为压力扰动提供了高阶近似分析特征函数和特征值关系，并且适用于中等和高马赫数的几种类型的流动。示出了这种形式的解仅依赖于边界层中的相对马赫数分布，相对马赫数指的是相对于流体平均流速的扰动马赫数（波速为c）。声音。确定了波速c = 0和c = 1在绝热面上流动的非拐点情况下的压力摄动解和特征值，它们与数值计算显示出良好的定性一致性，并导致自由流马赫数的渐近极限{dollar} Msb {lcub} infty {rcub} toinfty {dollar}。对于具有以下条件的情形，研究了具有广义拐点和等于广义拐点处的平均速度的波速的平均流量分布的情况（{dollar} c = csb {lcub} s {rcub} {dollar}）并且没有热量传递到表面。这些结果也显示出与数值结果良好的定性比较。详细研究了这些情况下的特征值关系，并研究了高马赫数无粘性涡旋和中等马赫数下的多种声学模式的“近链接”。马赫数有限特征值关系的这些区域显示为被描述为特征值基因座转向的区域。特征值关系的这种特性，以前仅在数值计算中观察到，通过局部双曲线逼近，定性地模拟了这种相互作用的关键方面，显示出在这些无粘性模式的相互作用附近的区域中是局部近似的。

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