通过非线性边界区域方程测量可压缩自由剪切层中的离心不稳定性
Gauging Centrifugal Instabilities in Compressible Free-Shear Layers Via Nonlinear Boundary Region Equations
AI总结：
本研究针对弯曲自由剪切层离心不稳定性研究不足的问题，在高雷诺数渐近框架下将可压缩Navier-Stokes方程简化为非线性边界区域方程，探究了多个流动参数对该不稳定性发展的影响。
摘要：
弯曲自由剪切层出现在众多涉及复杂流动几何结构的工程问题中，例如后向台阶绕流、边界层内存在壁面喷注的流动、侧卸式燃烧室内部流动，或是垂直轴风力机产生的尾流等。以往关于离心不稳定性的研究主要聚焦于壁面流动，这类流动中会因离心力与径向压力梯度的不平衡，在两个旋转同心圆柱间产生Taylor不稳定性，或是在边界层中产生Görtler涡。然而，弯曲自由剪切层流动尚未得到足够关注，尤其是在非线性区域。本研究探究了非线性可压缩区域内弯曲自由剪切层流动中离心不稳定性的发展过程。在高雷诺数渐近框架下，假设扰动的流向波长远大于展向和法向波长，我们将可压缩Navier-Stokes方程简化为非线性边界区域方程（BRE）。我们研究了来流马赫数$M_\infty$、剪切层厚度$δ$、入射扰动幅值$A$以及剪切层两侧的相对速度差$ΔV$对这些离心不稳定性发展的影响。
英文摘要：
Curved free shear layers emerge in many engineering problems involving complex flow geometries, such as the flow over a backward facing step, flows with wall injection in a boundary layer, the flow inside side-dump combustors, or wakes generated by vertical axis wind turbines, among others. Previous studies involving centrifugal instabilities have mainly focused on wall-flows where Taylor instabilities between two rotating concentric cylinders or Görtler vortices in boundary layers, resulting from the imbalance between the centrifugal forces and the radial pressure gradients, are generated. Curved free shear layer flows, however, have not received sufficient attention, especially in the nonlinear regime. The present work investigates the development of centrifugal instabilities evolving in a curved free shear layer flow in the nonlinear compressible regime. The compressible Navier-Stokes equations are reduced to the nonlinear boundary region equations (BRE) in a high Reynolds number asymptotic framework wherein the streamwise wavelengths of the disturbances are assumed to be much larger than the spanwise and wall-normal counterparts. We study the effect of the freestream Mach number $\boldsymbol{M_\infty}$, the shear layer thickness $\boldsymbolδ$, the amplitude of the incoming disturbance $\boldsymbol{A}$, and the relative velocity difference across the shear layer $\boldsymbol{ΔV}$ on the development of these centrifugal instabilities.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
