【作者】 张钟毓； 吴雪松；

【Author】 Zhongyu Zhang;Xuesong Wu;Department of Mechanics,Tianjin University;Department of Mathematics,Imperial College London;

【机构】 天津大学力学系； Department of Mathematics,Imperial College London；

【摘要】 自由剪切流,如混合层、射流、尾流等流动,因其强烈不稳定性,通常呈湍流流态。目前普遍认为这些完全发展的剪切湍流并不是完全随机的,其间存在一种可以被显示和测量的大尺度涡结构,亦称为"相干结构"或"拟序结构",它们对流体的混合以及动量、能量的输运产生了十分重要的作用,同时也是湍流噪声的主要来源。实验和理论研究表明相干结构与层流中的不稳定模态有许多类似之处,其产生和发展都与平均流场所引起的不稳定波性有关。本文采用这种观点,将流场三项分解,包括平均流,相干结构和小尺度脉动,在流动稳定性和非平衡临界层理论基础上建立强非线性动力学模型,来预测可压缩亚音速自由剪切湍流中相干结构的产生和发展。在模型中,除了粘性和可压缩性,我们考虑了湍流混合层的非平行性及其产生的临界层漂移效应以及小尺度随机脉动对相干结构的影响,利用渐近匹配和多尺度法,我们推导出了一套相互耦合的方程组,包括温度方程、涡量方程和幅值方程,及其定解条件来描述相干结构的动力学特性。数值计算结果清晰地显示了涡的卷起、合并、破碎现象和与之相关的高阶谐波的激发,这是相干结构的最显著的特征。同时给出了在各种流动工况和不同临界层厚度增长率等参数影响下,相干结构幅值的演化,并给出了解释。这套理论包含了亚音速混合层的各种特殊情形,包括不可压缩流体流动、层流流动、无粘流动、平行性假设流动等,与之前相似观点模型的计算结果亦完全符合,这是一个普遍适用的亚音速强非线性动力学理论。更多还原

【Abstract】 The free shear layers,such as mixing layers and jets/wakes,are hydrodynamically unstable and thus often in turbulent motions.It is generally recognised that the fully developed turbulent state is not completely random,because there exist discernable spanwise large-scale vortex structures,known as the "coherent structures".They play a significant role in mixing and heat transport,and are also a main source of turbulent noise.Experimental and theoretical studies showed that there are many similarities between the coherent structures and instability waves in laminar flows in their generation and evolution.This paper adopts this viewpoint and decomposes the flow field into three decompositions,including the mean flow,coherent structures and random small-scale perturbations.A strongly nonlinear dynamical model,based on nonlinear non-equilibrium critical layer theory for hydrodynamic instability,is established to describe the emergence and development of the coherent structures in compressible subsonic turbulent free shear layers.The theory takes into account non-parallelism associated with the fast spread of the turbulent mean flow as well as the effects of small-scale fluctuations.The evolution system is solved numerically for representative parameters to delineate the behaviour of coherent structures.The numerical results clearly show that vortices representing coherent structures roll up,merge and break up,and that the related high-order harmonics are excited,which are the crucial features of coherent structures.更多还原