超临界压力流体非绝热边界层中的瞬态增长
Transient growth in diabatic boundary layers with fluids at supercritical pressure
AI总结：
本文研究超临界压力流体边界层中跨越 Widom 线的温度剖面对非模态扰动增长的影响，发现跨临界状态下 Orr 机制导致短距离内强烈次优增长，且非模态 N-factor 与理想气体逆压梯度情形相似，加热跨越 Widom 线时最优增长可促进转捩。
摘要：
在接近热力学临界点以及伪沸腾（Widom）线附近的区域，强烈的物性变化会显著改变模态不稳定性的增长，这一点已在 Ren 等人（J. Fluid Mech., vol. 871, 2019, pp. 831-864）的研究中揭示。本文在局部平行流假设下，利用线性化 Navier-Stokes 方程的特征向量分解，在空间框架中研究非模态扰动。对于流体处于超临界压力的边界层，通过给定壁面和自由来流温度对其进行加热或冷却，使温度剖面完全处于亚临界（类液态）、超临界（类气态）或跨临界（跨越 Widom 线）状态。自由来流 Mach 数设为 $10^{-3}$。在非跨临界状态下，产生的沿流向不变的条纹结构源于 lift-up 效应。壁面冷却会增强亚临界和超临界两种状态下的能量放大。当温度剖面升高并跨越 Widom 线后，由于 Orr 机制，在极短的流向距离上观察到强烈的次优增长。通过 $N$-factor 比较，将非模态增长与模态增长进行了对比分析。在非跨临界状态下，无论壁面温度如何变化，模态稳定性均占主导地位。相反，在跨临界状态下，非模态 $N$-factor 表现出与理想气体状态下施加逆压梯度相似的特征。当冷却跨越 Widom 线时，最优增长显著增强，但强无黏不稳定性仍然占主导。当加热跨越 Widom 线时，最优增长可能足够大，从而有利于转捩的发生，尤其是在自由来流湍流度较高的情况下。
英文摘要：
In the region close to the thermodynamic critical point and in the proximity of the pseudo-boiling (Widom) line, strong property variations substantially alter the growth of modal instabilities, as revealed in Ren et al. (J. Fluid Mech., vol. 871, 2019, pp. 831-864). Here, we study non-modal disturbances in the spatial framework using an eigenvector decomposition of the linearized Navier-Stokes equations under the assumption of locally parallel flow. The boundary layers with the fluid at supercritical pressure are heated or cooled by prescribing the wall and free-stream temperatures so that the temperature profile is either entirely subcritical (liquid-like), supercritical (gas-like), or transcritical (across the Widom line). The free-stream Mach number is set to $10^{-3}$. In the non-transcritical regimes, the resulting streamwise-independent streaks originate from the lift-up effect. Wall cooling enhances the energy amplification for both subcritical and supercritical regimes. When the temperature profile is increased beyond the Widom line, a strong sub-optimal growth is observed over very short streamwise distances due to the Orr mechanism. The non-modal growth is put in perspective with modal growth by means of an $N$-factor comparison. In the non-transcritical regimes, modal stability dominates regardless of a wall-temperature variation. In contrast, in the transcritical regime, non-modal $N$-factors are found to resemble the imposition of an adverse pressure gradient in the ideal-gas regime. When cooling beyond the Widom line, optimal growth is greatly enhanced, yet strong inviscid instability prevails. When heating beyond the Widom line, optimal growth could be sufficiently large to favor transition, particularly with a high free-stream turbulence level.
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