Effect of Prandtl number on the linear stability of compressible Couette flow

湍流普朗特数 普朗特数 雷诺数 马赫数 机械 磁普朗特数 物理 湍流 泰勒-库特流 线性稳定性 滞止焓 热力学 不稳定性 经典力学 努塞尔数 传热
作者
Ashwin Ramachandran,Bijaylakshmi Saikia,Krishnendu Sinha,Rama Govindarajan
出处
期刊:International Journal of Heat and Fluid Flow [Elsevier BV]
卷期号:61: 553-561 被引量:13
标识
DOI:10.1016/j.ijheatfluidflow.2016.06.014
摘要

Accurate prediction of laminar to turbulent transition in high-speed flows is a challenging task. Compressibility, and the resultant large variations in the transport properties can affect the transition process significantly. In this paper, we study the influence of Prandtl number, the ratio of momentum to heat diffusivity, in Couette flows at high Mach numbers. It is a part of an ongoing research programme to isolate and understand the transport property effects on the stability of high-speed flows. As a first step, we neglect the high-temperature effects and vary the Prandtl number in the range 0.9 to 0.2, by changing the relative magnitudes of viscosity and conductivity. A temporal linear stability analysis shows that the variation of phase speed with Prandtl number leads to synchronization between two acoustic modes, with peaks in growth rate at the synchronization points. Two types of branching patterns are observed depending on the Prandtl number, and the branch type determines which of the two modes is destabilized and which one is stabilized due to synchronization. Further, the mode shapes are either retained as earlier or interchanged between the two acoustic modes depending on the branching pattern. The stability diagrams for varying Mach and Reynolds numbers show a destabilizing role of decreasing the Prandtl number, both in terms of increased disturbance growth rates, and of larger regions of instability in the parameter space. It also results in a significant reduction in the critical Reynolds number of the flow, especially at high Mach numbers with wall cooling.
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