【作者】 时晓天；

【导师】 佘振苏；

【作者基本信息】 北京大学 ， 流体力学， 2010， 博士

【摘要】 湍流因为具有多尺度、多自由度的内部复杂性和多样产生环境的外部复杂性两大复杂性而成为尚未解决的世纪难题,其中一个重要的流动类型是自由剪切湍流。可压缩混合层作为自由剪切湍流的一种,在科学研究上具有重要的理论价值而且在工程实际中具有广泛的应用。它是由两股具有不同速度的平行可压缩气流相互作用所形成,也称作可压缩剪切层、超声速混合层和超声速剪切层等。本论文针对可压缩混合层流动,从流动显示和热线测量、数值模拟和结构系综理论三个角度对流场中的结构及其演化形态、不同物理过程以及压缩效应的定量刻画展开研究。对于Mc=0.107和Mc=0.474的可压缩混合层平面激光米氏散射(PLMS)的实验结果,我们基于结构系综的思想,提出了等相位的结构提取方法。根据该方法我们提取了瞬时流场中的斜条纹结构;将斜条纹结构在样本空间进行系综平均得到了斜条纹的空间分布及其斜率沿流向的变化;在两个流动参数下,斜条纹结构的斜率随压缩性变化不明显,因此,我们认为斜条纹结构主要是高速气流在大尺度结构附近受到扰动而形成从混合层核心区域向外传播的马赫波和相干结构曲面效应造成的压缩\膨胀波系组成。基于流动显示的灰度图像,我们计算了混合层的厚度和增长率,得到了与文献相符合结果。流动显示图像的一维灰度信号能谱在对数坐标下存在斜率为- 5/3的惯性区,反映了流动中的被动标量具有多尺度行为。在本文的研究中,我们发展了可压缩流动的间断有限元(DG)计算方法,并首次将DG方法用于可压缩湍流的研究,开展了可压缩混合层流动的二维和三维数值模拟。对于二维时间发展的混合层(Mc=0.2-0.8),我们统计了涡结构的几何特征及涡心轨迹在结构对并中的演化过程,分析了压缩性效应对对并过程的影响;在流场中具有相似的流动结构条件下,我们分析了可压缩耗散和压力胀量项的压缩性效应。对于二维空间发展的混合层(Mc=0.2,0.4.0.6,0.8),数值模拟得到的时序脉动信号具有与热线测量的复合信号具有相似的特征;在充分发展区域,混合层的核心的时序脉动信号的频谱在对数坐标下存在斜率为-4的惯性区。通过采用将涡量、速度散度和压力梯度相结合的流动显示技术,我们观察到了相干结构附近的压缩和膨胀区域,分析了压缩效应对大尺度结构的影响。数值模拟结果表明,在充分发展区域,混合层流动满足很好的自相似特征和线性的混合层厚度增长趋势,这也体现了当前计算的可靠性。利用Favre形式的平均动量方程和湍流雷诺应力方程,我们研究了流场中动量和能量的输运平衡情况,分析了其中不同物理过程的作用,并与文献结果进行了比较。在三维流动中,流动结构及其之间的相互作用更加丰富:在流动初始区域主要是展向涡卷结构,在下游由于展向不稳定性和拉伸机制流场中出现了肋状结构和发卡涡森林结构,这与零压力梯度的空间发展边界层流动相似。与二维结果相比较,三维流动的自相似性更为突出,一些高阶统计量也满足自相似性。动量方程的输运平衡表明,压力梯度项把流向的动量转移到了横向;而在雷诺应力方程中主要是产生项从平均流场中获取能量,与湍流扩散、压力扩散、粘性扩散和粘性耗散作用相平衡。通过流场中的结构来预测平均流场的物理量一直都是流体力学研究的一个努力方向,在混合层流动中存在良好的拟序结构,这为我们建立基于结构的湍流封闭模型提供了可能。在本论文中,我们根据结构系综动力学的理论思想,对二维可压缩混合层的数值模拟结果进行了结构系综分析,通过将平均流场的控制方程分解成状态函数、微分算子和未封闭项三个部分,提出了基于连接状态函数和未封闭项的序函数来实现平均控制方程封闭的湍流模型框架。我们认为序函数的空间变化行为反映了流场中结构的统计信息,它源自传统的流动结构而又升华了传统的流动结构。通过学习数值模拟结果中的经验数据,我们对方程中出现的序函数的空间变化行为和随对流马赫数的变化特征进行了分析,完成了时间发展混合层中序函数的经验规律模拟,为完成可压缩流动在结构系综意义下的封闭,推动和建立新一代可压缩流动的湍流模型奠定了基础。更多还原

【Abstract】 Turbulence is a century-old problem for its internal multi-scale and multi-freedom complexity and various burn environment complexities in daily life and engineering applications, in which one important kind of flow is free shear turbulence. Compressible mixing layers, as one typical kind of free shear turbulence, is resulted by interaction between two parallel compressible free streams with different flow velocities. It not only has theoretical meaning for it contains fundamental physical problems such as instability and vortex interaction, but also has large engineering applications in engine and supersonic combustion.In this thesis, from the view of experiments, numerical simulation and structural ensemble dynamic theory, we try to give a comprehensive study of compressible mixing layers, and obtain the quantitative description of compressibility effect.For the PLMS visualization results for planar compressible mixing layers with Mc=0.107 and Mc=0.474, an“equal phase method”is introduced to pick out the“oblique wave”structures in the instantaneous results of visualization. After an ensemble average for all the oblique wave structures in sample space, the variation of their slope along stream direction is obtained. The oblique wave structures are mainly composed of the Mach waves of high speed free stream that generated near the large scale structures, for their slope change little with compressibility. In addition, the visualization thickness and growth rate that normalized with the counterpart in incompressible cases of mixing layers are calculated, the results agree reference well. An interesting thing in the results of visualization is that a k=-5/3 slope is found in the energy spectrum of one dimensional gray scale signal along the stream direction, which means the multi-scale characteristics of the passive scalar field.Discontinuous Galerkin method is the first time used to do compressible turbulence study for its convenience to handle strong discontinuous in flow field and high accuracy in smooth region, with which compressible mixing layers in two and three dimensions are simulated. With the statistical information of the geometry characteristics of vortexes and their vortex center trajectories in the case of Mc=0.2-0.8, the compressibility effect on vortex merging process in two dimensional temporal mixing layers is analyzed. It is found that the merging process in high Mc cases is different from that of low Mc cases with a vortex center“slip”phenomenon. While for the case of two dimensional spatially developing mixing layers, we obtain the time sequence of velocity fluctuations, which have similar characteristics as the signals obtained in hot-wire experiments. In fully developed region, the energy spectrum of velocity fluctuations in the center of mixing layers has an inertial region with the slope k=-4 in log-log frame. To visualize the compressibility effect on large scale structures in scompressible mixing layers, a hybrid visualization technique that is composed of vorticity, divergence of velocity and pressure gradient is utilized, with which expansion and compressed zones around large scale structures are shown clearly, as Mc increasing the compressed regions shrink till a shocklet is formed. In three dimensions case, Q2 is used instead of vorticity to identify structures. It is found that span-wise roller structures dominate the field in the initial region of mixing layer, rib structures, stream-wise vorticities and the forest of hairpin structures are resulted down-stream for vortex stretch mechanism and complex interaction among structures. The self-similarity in fully developed mixing layers is excellent both in our two and three dimensional numerical results, even some high order statistical variables such as skewness and flatness in three dimensional cases, which verify the credibility of current simulations. To analyze the function of different physical process in the flow, the control equations of momentum and turbulence Reynolds stress in Favre averaged form are used. It is found that, the function of pressure gradient is to transport momentum from stream direction to vertical direction; while for the case of turbulence Reynolds stress equation, the production gains energy from averaged field and feeds the turbulence diffusion, pressure diffusion, viscosity diffusion and viscosity dissipation. There is a long time dream to predict mean flow field with structures in turbulence study, the well organized coherent structures in mixing layers make it is possible here. Recently, structural ensemble dynamic (SED) theory introduced by 2009 She et al. sheds light on the closure problem based on structures in turbulence study. In this theory, the averaged control equations are decomposed into state functions, differential calculator and unknown terms, after introduce order functions, which is the bridge that connect state functions and unknown terms, the control equations is closed. Here the meaning of order functions is to describe the statistical information of structures, which is from traditional flow structures but goes further. In this thesis, the frame of turbulence model based on SED is configured. With the study of numerical results, we analyze the spatial variation of order functions emerged in current control equations, obtain the empirical laws for some order functions in temporal mixing layers, and find the self-similarity of order functions in spatially developing mixing layers, which together makes it is possible to construct the next generate turbulence models based on SED for compressible mixing layers in the near future.更多还原