Pietro Carlo Boldini, Benjamin Bugeat, Jurriaan W. R. Peeters, Markus Kloker, Rene Pecnik
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引用次数: 0
Abstract
In the region close to the thermodynamic critical point and in the proximity of the pseudoboiling (Widom) line, strong property variations substantially alter the growth of modal instabilities, as revealed in Ren et al. [J. Fluid Mech.871, 831 (2019)]. Here, we study nonmodal disturbances in the spatial framework using an eigenvector decomposition of the linearized Navier-Stokes equations under the assumption of locally parallel flow. To account for nonideality, a new energy norm is derived. Several heat transfer scenarios at supercritical pressure are investigated, which are of practical relevance in technical applications. 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 (liquidlike), supercritical (gaslike), or transcritical (across the Widom line). The free-stream Mach number is set to . In the nontranscritical 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 suboptimal growth is observed over very short streamwise distances due to the Orr mechanism. Due to the additional presence of transcritical Mode II, the optimal energy growth at large distances is found to arise from an interplay between lift-up and Orr mechanism. As a result, optimal disturbances are streamwise-modulated streaks with strong thermal components and with a propagation angle inversely proportional to the local Reynolds number. The nonmodal growth is put in perspective with modal growth by means of an -factor comparison. In the nontranscritical regimes, modal stability dominates regardless of a wall-temperature variation. In contrast, in the transcritical regime, nonmodal 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.
正如 Ren 等人[J. Fluid Mech. 871, 831 (2019)]所揭示的那样,在接近热力学临界点的区域和伪沸(Widom)线附近,强烈的性质变化会大大改变模态不稳定性的增长。在此,我们在局部平行流假设下,使用线性化纳维-斯托克斯方程的特征向量分解来研究空间框架中的非模态扰动。为了考虑非理想性,我们导出了一种新的能量规范。研究了超临界压力下的几种传热情况,这些情况在技术应用中具有实际意义。通过预设壁面温度和自由流温度,对超临界压力下的流体边界层进行加热或冷却,使温度曲线完全为亚临界(液态)、超临界(气态)或跨临界(跨越维多姆线)。自由流马赫数设定为 10-3。在非跨临界状态下,产生的与流无关的条纹源于抬升效应。壁面冷却增强了亚临界和超临界状态下的能量放大。当温度曲线上升到超过维多姆线时,由于奥尔机制的作用,在很短的流向距离上观察到强烈的次优增长。由于跨临界模式 II 的额外存在,发现大距离的最佳能量增长来自于升力和奥尔机制之间的相互作用。因此,最佳扰动是具有强热成分的流调制条纹,其传播角度与局部雷诺数成反比。通过 N 因子比较,我们将非模态增长与模态增长进行了比较。在非跨临界状态下,无论壁面温度如何变化,模态稳定性都占主导地位。相反,在跨临界状态下,非模态 N 因子与理想气体状态下施加的不利压力梯度相似。当冷却超过维多姆线时,最佳增长会大大增强,但会出现强烈的不粘性不稳定性。当加热超过维多姆线时,最佳增长可能大到有利于过渡,特别是在自由流湍流水平较高的情况下。
期刊介绍:
Physical Review Fluids is APS’s newest online-only journal dedicated to publishing innovative research that will significantly advance the fundamental understanding of fluid dynamics. Physical Review Fluids expands the scope of the APS journals to include additional areas of fluid dynamics research, complements the existing Physical Review collection, and maintains the same quality and reputation that authors and subscribers expect from APS. The journal is published with the endorsement of the APS Division of Fluid Dynamics.