The effect of compressibility on turbulent shear flow: a rapid-distortion-theory and direct-numerical-simulation study
The effect of compressibility on turbulent shear flow: a rapid-distortion-theory and direct-numerical-simulation study
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DOI：
10.1017/s0022112096003837
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发表时间：
1997-01
影响因子：
3.7
通讯作者：
A. Simone;G. Coleman;C. Cambon
中科院分区：
文献类型：
--
作者：
A. Simone;G. Coleman;C. Cambon
研究了可压缩性对均匀剪切湍流结构的影响。对于剪切速率远大于湍流的非线性相互作用速率的情况，压缩性对平均剪切引起的湍流动能放大的修正主要反映在压力-应变关系中，并与雷诺应力张量的各向异性有关，而不是在明确的解释性条款，如压力膨胀相关性或解释性耗散。证明了“扭曲马赫数”Md = S[lscr ]/a的核心作用，其中S是平均应变或剪切速率，[lscr ]是高能结构的长度尺度，a是音速。这个参数已经出现在以前的快速畸变理论（RDT）和直接数值模拟（DNS）的研究，为了推广以前的分析，准等熵可压缩RDT方程数值求解均匀湍流进行球形（各向同性）压缩，一维（轴向）压缩和纯剪切。对于纯剪切流在有限马赫数，RDT结果显示定性不同的行为在大和小的无量纲时间St：当St 4的逆发生，这是一致的，经常观察到的趋势，可压缩性稳定的湍流剪切流。这种“交叉”行为，这是不存在时，平均失真是无旋的，是由于运动学失真和平均剪切诱导的线性耦合的双曲场和螺线管场。通过与Sarkar（1995）最近的DNS结果以及新的DNS数据的比较，说明了RDT的相关性，这两个结果都是通过求解完全非线性可压缩Navier-Stokes方程获得的。线性准等熵RDT和非线性非等熵DNS解决方案在很宽的参数范围内具有良好的一致性;该协议为可压缩性的稳定和不稳定效应提供了新的见解，并揭示了线性过程负责修改可压缩湍流结构的程度。
The influence of compressibility upon the structure of homogeneous sheared turbulence is investigated. For the case in which the rate of shear is much larger than the rate of nonlinear interactions of the turbulence, the modification caused by compressibility to the amplification of turbulent kinetic energy by the mean shear is found to be primarily reflected in pressure–strain correlations and related to the anisotropy of the Reynolds stress tensor, rather than in explicit dilatational terms such as the pressure–dilatation correlation or the dilatational dissipation. The central role of a ‘distortion Mach number’ Md = S[lscr ]/a, where S is the mean strain or shear rate, [lscr ] a lengthscale of energetic structures, and a the sonic speed, is demonstrated. This parameter has appeared in previous rapid-distortion-theory (RDT) and direct-numerical-simulation (DNS) studies; in order to generalize the previous analyses, the quasi-isentropic compressible RDT equations are numerically solved for homogeneous turbulence subjected to spherical (isotropic) compression, one-dimensional (axial) compression and pure shear. For pure-shear flow at finite Mach number, the RDT results display qualitatively different behaviour at large and small non-dimensional times St: when St 4 the inverse occurs, which is consistent with the frequently observed tendency for compressibility to stabilize a turbulent shear flow. This ‘crossover’ behaviour, which is not present when the mean distortion is irrotational, is due to the kinematic distortion and the mean-shear-induced linear coupling of the dilatational and solenoidal fields. The relevance of the RDT is illustrated by comparison to the recent DNS results of Sarkar (1995), as well as new DNS data, both of which were obtained by solving the fully nonlinear compressible Navier–Stokes equations. The linear quasi-isentropic RDT and nonlinear non-isentropic DNS solutions are in good general agreement over a wide range of parameters; this agreement gives new insight into the stabilizing and destabilizing effects of compressibility, and reveals the extent to which linear processes are responsible for modifying the structure of compressible turbulence.