On the turbulent mixing of compressible free shear layers
On the turbulent mixing of compressible free shear layers
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可压缩自由剪切层的湍流混合
DOI：
10.1098/rspa.1990.0128
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发表时间：
1990
期刊：
影响因子：
--
通讯作者：
G. Lilley
中科院分区：
文献类型：
--
作者：
P. Morris;M. Giridharan;G. Lilley
四分之一个多世纪以来，人们已经认识到湍流剪切流是由大尺度结构主导的。然而，大多数湍流混合模型不能显式或隐式地包括结构的性质。与实验观测结果相比，使用这些模型得到的结果似乎是令人满意的，但一般而言，这些模型需要包括经验常数，这使得预测结果仅与用于确定此类常数的经验数据库一样好。除了随机特性外，现有的湍流模型也不能描述湍流剪切流及其发展的随时间变化的特性。本文介绍了一个湍流剪切层中大尺度结构的模型。尽管有一定的保留，该模型适用于大多数湍流剪切流，但我们在这里仅限于考虑两流可压缩剪切层中的湍流混合。建立了描述大尺度运动对湍流混合过程影响的两个模型。第一个模型通过计算与流动中的大尺度结构有关的部分湍流谱的发展来模拟平均行为。第二个模型模拟单个大尺度结构的通过，从而模拟湍流随时间变化的很大一部分特征。在这两种处理中，大尺度结构都是由不稳定波的叠加来描述的。这些波的局部性质是由线性、无粘性、稳定性分析确定的。平均流的流向发展，包括这些不稳定波的振幅分布，由能量积分分析确定。这些模型不包含经验常数。预测了自由流速度和密度比以及自由流马赫数对混合层生长的影响。这些预测与实验观测结果非常吻合。对湍流剪切层随时间变化的运动进行了计算，得到了与观测定性一致的条纹线形式。对于其他一些湍流剪切流，用线性稳定性分析同样可以得到大涡的主导结构，并在附录中给出了这一过程的部分理由。在壁面边界流动中，初步分析表明，线性、粘性、稳定性分析必须推广到二阶，才能得到最不稳定的波动及其后续发展。文中还讨论了将本模型推广到这类情况，以及在模型中考虑化学反应的影响。
For over a quarter of a century it has been recognized that turbulent shear flows are dominated by large-scale structures. Yet the majority of models for turbulent mixing fail to include the properties of the structures either explicitly or implicitly. The results obtained using these models may appear to be satisfactory, when compared with experimental observations, but in general these models require the inclusion of empirical constants, which render the predictions only as good as the empirical database used in the determination of such constants. Existing models of turbulence also fail to provide, apart from its stochastic properties, a description of the time-dependent properties of a turbulent shear flow and its development. In this paper we introduce a model for the large-scale structures in a turbulent shear layer. Although, with certain reservations, the model is applicable to most turbulent shear flows, we restrict ourselves here to the consideration of turbulent mixing in a two-stream compressible shear layer. Two models are developed for this case that describe the influence of the large-scale motions on the turbulent mixing process. The first model simulates the average behaviour by calculating the development of the part of the turbulence spectrum related to the large-scale structures in the flow. The second model simulates the passage of a single train of large-scale structures, thereby modelling a significant part of the time-dependent features of the turbulent flow. In both these treatments the large-scale structures are described by a superposition of instability waves. The local properties of these waves are determined from linear, inviscid, stability analysis. The streamwise development of the mean flow, which includes the amplitude distribution of these instability waves, is determined from an energy integral analysis. The models contain no empirical constants. Predictions are made for the effects of freestream velocity and density ratio as well as freestream Mach number on the growth of the mixing layer. The predictions agree very well with experimental observations. Calculations are also made for the time-dependent motion of the turbulent shear layer in the form of streaklines that agree qualitatively with observation. For some other turbulent shear flows the dominant structure of the large eddies can be obtained similarly using linear stability analysis and a partial justification for this procedure is given in the Appendix. In wall-bounded flows a preliminary analysis indicates that a linear, viscous, stability analysis must be extended to second order to derive the most unstable waves and their subsequent development. The extension of the present model to such cases and the inclusion of the effects of chemical reactions in the models are also discussed.