A frequency domain analysis of compressible linearized Navier-Stokes equations in a hypersonic compression ramp flow

A. Dwivedi, G. Candler, M. Jovanović
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引用次数: 2

Abstract

We utilize the frequency response analysis of the linearized Navier-Stokes equations to quantify amplification of exogenous disturbances in a hypersonic flow over a compression ramp. Using the spatial structure of the dominant response to time-periodic inputs, we explain the origin of steady reattachment streaks. Our analysis of the laminar shock/boundary layer interaction reveals that the streaks arise from a preferential amplification of upstream counter-rotating vortical perturbations with a specific span-wise wavelength. These streaks are associated with heat flux striations at the wall near flow reattachment and they can trigger transition to turbulence. The streak wavelength predicted by our analysis compares favorably with observations from two different hypersonic compression ramp experiments. Furthermore, we utilize the dominant response to analyze the physical effects in the linearized dynamical system responsible for amplification of disturbances. We show that flow compressibility that arises from base flow deceleration contributes to the amplification of streamwise velocity and that the baroclinic effects are responsible for the production of streamwise vorticity. Both these effects contribute to the appearance of temperature streaks observed in experiments and are critically important for the development of control-oriented models for transition to turbulence in hypersonic flows.
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高超声速压缩斜流中可压缩线性化Navier-Stokes方程的频域分析
我们利用线性化的Navier-Stokes方程的频率响应分析来量化压缩坡道上高超声速流动中外源干扰的放大。利用对时间周期输入的主导响应的空间结构,我们解释了稳定再附着条纹的起源。我们对层流激波/边界层相互作用的分析表明,条纹产生于具有特定跨波长的上游反向旋转涡旋扰动的优先放大。这些条纹与流动再附着处壁面的热流密度条纹有关,它们可以触发向湍流的过渡。我们的分析预测的条纹波长与两个不同的高超声速压缩斜坡实验的观测结果比较有利。此外,我们利用主导响应来分析线性化动力系统中引起扰动放大的物理效应。研究表明,由基流减速引起的流动可压缩性有助于增大流向速度,斜压效应是产生流向涡度的原因。这两种效应都有助于在实验中观察到的温度条纹的出现,并且对于在高超声速流动中过渡到湍流的面向控制模型的发展至关重要。
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