论文标题
通道中高马赫数流的稳定性
Stability of a high Mach number flow in a channel
论文作者
论文摘要
研究了高雷诺的通道流中的模态不稳定性，并研究了三维扰动。除了Tollmien-Schlichting模式外，通道流中还有较高的模式，在不可压缩的极限中没有对应物。通过数值计算获得的这些较高模式的稳定性特征与以前研究过的边界层和couette流相比。与可压缩边界层模式相比，通道流中的主要高模式不稳定性在本质上是粘性的。对于一般可压缩的有界域流，可以获得在Inviscid限制中存在中性模式的必要条件。该标准用于构建一个过程，以确定MACH数的临界值，以下更高模式保持稳定。该标准还描述了波数相对于流动方向的一系列角度，这可能会在指定的马赫数下不稳定。稳定曲线的下部和上部分支在高雷诺数的极限下进行渐近分析。这些指数为上下分支的这些指数确定了一组共同的关系，以延续Tollmien-Schlichting模式和可压缩模式。 Tollmien-Schlichting模式的尺度与不可压缩流相同。有限波数模式的尺度不同。 Wave Speed $ C $缩放为$ \ mbox {Re}^{ - \ frac {1} {3}} $，对于下branch而言，$ \ mbox {re}^{ - \ frac {1} {1} {5}}} $ for the the the the the上blanch，其中$ \ mbox {re} re} $是re y re yynold。渐近分析表明，在高雷诺数下，三维扰动的稳定性边界可以根据应变速率和壁上的基本流量的温度来计算。
Modal instabilities in a flow through a channel at high Reynolds and Mach numbers are studied for three-dimensional perturbations. In addition to the Tollmien-Schlichting modes, there exist higher modes in a channel flow that do not have a counterpart in the incompressible limit. The stability characteristics of these higher modes, obtained through numerical calculations, are compared with boundary layer and Couette flows that have been previously studied. The dominant higher mode instabilities in a channel flow are shown to be viscous in nature, in contrast to compressible boundary layer modes. For general compressible bounded-domain flows, a necessary condition for the existence of neutral modes in the inviscid limit is obtained. This criterion is used to construct a procedure to determine a critical value of Mach number below which the higher modes remain stable. This criterion also delineates a range of angles of inclination of the wave number with respect to the flow direction which could go unstable at a specified Mach number. Asymptotic analysis is carried out for the lower and upper branch of the stability curve in the limit of high Reynolds number. A common set of relations are identified for these exponents for the upper and lower branch for the continuation of the Tollmien-Schlichting modes and the compressible modes. The scalings for the Tollmien-Schlichting modes are identical to those for an incompressible flow. The scalings for the finite wave number modes are different; the wave speed $c$ scales as $\mbox{Re}^{-\frac{1}{3}}$ for the lower branch and $\mbox{Re}^{-\frac{1}{5}}$ for the upper branch, where $\mbox{Re}$ is the Reynolds number. The asymptotic analysis shows that the stability boundaries for three-dimensional perturbations at high Reynolds numbers can be calculated from the strain rate and the temperature of the base flow at the wall.
