湍流射流的大涡模拟及其动力学特性研究
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摘要
射流在工程中应用非常广泛，同时也是当前湍流研究中的热点问题，因此射流的研究具有很重要的理论价值和应用前景。在湍流射流中出现的大尺度拟序结构在湍流形成、卷吸和流体掺混过程中起到主导作用，了解其产生、发展、对并、破裂等动力学演化过程具有重要意义，并对湍流射流控制有重要指导作用。
本文综合运用湍流大涡模拟方法、湍流拟序结构理论和湍流统计理论对湍流射流中的大尺度拟序结构的动力学演化过程进行研究，开展了下列研究工作：
详细综述了湍流自由射流、湍流横向射流和湍流射流控制的研究现状，总结了到目前为止人们对湍流射流大尺度结构的基本认识，在此基础上提出了进一步研究的问题。
对本研究采用的湍流大涡模拟方法、可压缩湍流数值模拟算法、并行机群、POD方法和湍流统计分析方法等进行研究，得到了并行的湍流射流大涡模拟程序。
应用湍流大涡模拟方法得到Re数为15000、网格数为258×125×125、总容量达552GB的三个湍流椭圆射流数据库。通过对自由射流、流向和展向椭圆喷嘴的湍流横向射流大尺度结构的时空演化进行分析，揭示了湍流椭圆射流的基本涡结构。应用Snapshots-POD方法对湍流横向椭圆射流进行研究，对其湍流脉动速度场进行时间序列分析、频谱分析、PDF分析以及时、空截面上的统计平均特性分析。
研究结果表明：湍流椭圆自由射流的最显著特征是椭圆涡环的间歇产生、脱落，这些涡环一旦产生立即脱落。首次发现和提出了湍流横向椭圆射流的三维拉伸涡环模型，指出在其大尺度拟序结构中真正占主导作用的是拉伸、扭曲、沿流向扭动、展向摆动和绕x轴的转动的三维涡环，在众多实验和文献中观察到的反向涡对其实是由三维涡环头部组成。首次应用POD分析方法对上述数据库进行分析，得到湍流横向椭圓射流拟序结构的能量分布规律和各阶POD基的演化规律；应用湍流统计理论对上述数据库进行分析，揭示了湍流横向椭圆射流脉动速度的极为复杂的统计行为；加深了对湍流椭圆射流基本物理过程的非线性动力学机制的理解。
有待进一步研究的问题是：建立基于POD模的湍流射流低维动力系统，并对其进行分析；研究基于湍流射流低维动力系统的湍流射流控制；探讨湍流横向射流中涡环间歇脱落的物理机制。
Turbulent jet is a hightly complex turbulent flow, with application in a vast array of engineering problems. It has been studied both analytically and experimentally for many decades, not only because of their wide application in technology but also because of their fundamental significance as a basic flow to the scientific research community. The large-scale coherent structures in turbulent jets play leading role in the process of turbulence generation, entrainment, and fluid mixing, therefore it is very important to understand the dynamical evolution process, such as the generation, development, collsion and breakup of the large-scale coherent structures, meanwhile it is also important to the control of turbulent jets.In this thesis, the method of large-eddy simulation of turbulence, the coherent structure theory, POD method and the statistical theory of turbulence are applied to analyze the dynamical evolution process of large-scale coherent structures in the turbulent jets. We have done the following research work:The current situation of research of turbulent free jets, turbulent jets in crossflow and control of turbulent jets are investigated in detail, the basic understand of the large-scale coherent structures of turbulent jets are summarized, and based on these understandings the problems needed further study are proposed.The numerical method of large-eddy simulation, the computational method of compressible turbulent flow, parallel cluster, POD method and the statistical analysis method of turbulence are studied, and the parallel program of large-eddy simulation of turbulent jet are obtained.Using the parallel code of large-eddy simulation, three turbulence databases of turbulence elliptic jet are obtained, with Reynolds number is 15000 and grid numbers are 258×125×125 and the total volume size is 552GB. Based on the analysis of the spatio-temporal evolution of large-scale coherent structures of free jet, turbulent jets in crossflow with stream-wise and transverse elliptic nozzles, the basic vortical structures of turbulent elliptic jet are revealed. The method of Snapshots-POD is applied to the turbulent jets
in crossflow, and the analysis of time series, spectrum, PDF and the statistical average properties on the spatio-temporal sections of the fluctuation velocity field are examed in detail.The results show that the most significant feature of turbulent free jet is the intermittently generation, shed of elliptic vortex rings, and once they generate they shed immediately. The model of 3-dimensional stretching vortex ring of turbulent elliptic jet in crossflow are discovered for the first time. It is pointed out that in the evolution of turbulent jet in crossflow the 3D vortex rings, which stretching, distorting, swing in transverse direction and twisting around the stream-wise, play the leading role in the large-scale coherent structures. The counter-rotating vortex pair observed in the literature is in fact the head of the 3-dimensional vortex ring. The POD method is applied for the first time to study the above turbulence database, to obtain the energy distribution of coherent structures of turbulent elliptic jet in crossflow and the evolution process of POD bases. The statistic theory of turbulence is also used to study the turbulence database, and the very complex statistical behavior of the fluctuation velocity field of the turbulent jet in crossflow are revealed. These results are deepening the comprehension of the nonlinear dynamical mechanism of the basic physics process of turbulent elliptic jets.In the future, some issues need to be investigated further, which include: establish and study the low-dimensional dynamical system of turbulent jet, with the POD bases, the control of turbulent jet based on the low-dimensional dynamical system of turbulent jet, investigate the physics mechanism of intermittence shed-off of the vortex ring in turbulent jets in crossflow.
本文综合运用湍流大涡模拟方法、湍流拟序结构理论和湍流统计理论对湍流射流中的大尺度拟序结构的动力学演化过程进行研究，开展了下列研究工作：
详细综述了湍流自由射流、湍流横向射流和湍流射流控制的研究现状，总结了到目前为止人们对湍流射流大尺度结构的基本认识，在此基础上提出了进一步研究的问题。
对本研究采用的湍流大涡模拟方法、可压缩湍流数值模拟算法、并行机群、POD方法和湍流统计分析方法等进行研究，得到了并行的湍流射流大涡模拟程序。
应用湍流大涡模拟方法得到Re数为15000、网格数为258×125×125、总容量达552GB的三个湍流椭圆射流数据库。通过对自由射流、流向和展向椭圆喷嘴的湍流横向射流大尺度结构的时空演化进行分析，揭示了湍流椭圆射流的基本涡结构。应用Snapshots-POD方法对湍流横向椭圆射流进行研究，对其湍流脉动速度场进行时间序列分析、频谱分析、PDF分析以及时、空截面上的统计平均特性分析。
研究结果表明：湍流椭圆自由射流的最显著特征是椭圆涡环的间歇产生、脱落，这些涡环一旦产生立即脱落。首次发现和提出了湍流横向椭圆射流的三维拉伸涡环模型，指出在其大尺度拟序结构中真正占主导作用的是拉伸、扭曲、沿流向扭动、展向摆动和绕x轴的转动的三维涡环，在众多实验和文献中观察到的反向涡对其实是由三维涡环头部组成。首次应用POD分析方法对上述数据库进行分析，得到湍流横向椭圓射流拟序结构的能量分布规律和各阶POD基的演化规律；应用湍流统计理论对上述数据库进行分析，揭示了湍流横向椭圆射流脉动速度的极为复杂的统计行为；加深了对湍流椭圆射流基本物理过程的非线性动力学机制的理解。
有待进一步研究的问题是：建立基于POD模的湍流射流低维动力系统，并对其进行分析；研究基于湍流射流低维动力系统的湍流射流控制；探讨湍流横向射流中涡环间歇脱落的物理机制。
Turbulent jet is a hightly complex turbulent flow, with application in a vast array of engineering problems. It has been studied both analytically and experimentally for many decades, not only because of their wide application in technology but also because of their fundamental significance as a basic flow to the scientific research community. The large-scale coherent structures in turbulent jets play leading role in the process of turbulence generation, entrainment, and fluid mixing, therefore it is very important to understand the dynamical evolution process, such as the generation, development, collsion and breakup of the large-scale coherent structures, meanwhile it is also important to the control of turbulent jets.In this thesis, the method of large-eddy simulation of turbulence, the coherent structure theory, POD method and the statistical theory of turbulence are applied to analyze the dynamical evolution process of large-scale coherent structures in the turbulent jets. We have done the following research work:The current situation of research of turbulent free jets, turbulent jets in crossflow and control of turbulent jets are investigated in detail, the basic understand of the large-scale coherent structures of turbulent jets are summarized, and based on these understandings the problems needed further study are proposed.The numerical method of large-eddy simulation, the computational method of compressible turbulent flow, parallel cluster, POD method and the statistical analysis method of turbulence are studied, and the parallel program of large-eddy simulation of turbulent jet are obtained.Using the parallel code of large-eddy simulation, three turbulence databases of turbulence elliptic jet are obtained, with Reynolds number is 15000 and grid numbers are 258×125×125 and the total volume size is 552GB. Based on the analysis of the spatio-temporal evolution of large-scale coherent structures of free jet, turbulent jets in crossflow with stream-wise and transverse elliptic nozzles, the basic vortical structures of turbulent elliptic jet are revealed. The method of Snapshots-POD is applied to the turbulent jets
in crossflow, and the analysis of time series, spectrum, PDF and the statistical average properties on the spatio-temporal sections of the fluctuation velocity field are examed in detail.The results show that the most significant feature of turbulent free jet is the intermittently generation, shed of elliptic vortex rings, and once they generate they shed immediately. The model of 3-dimensional stretching vortex ring of turbulent elliptic jet in crossflow are discovered for the first time. It is pointed out that in the evolution of turbulent jet in crossflow the 3D vortex rings, which stretching, distorting, swing in transverse direction and twisting around the stream-wise, play the leading role in the large-scale coherent structures. The counter-rotating vortex pair observed in the literature is in fact the head of the 3-dimensional vortex ring. The POD method is applied for the first time to study the above turbulence database, to obtain the energy distribution of coherent structures of turbulent elliptic jet in crossflow and the evolution process of POD bases. The statistic theory of turbulence is also used to study the turbulence database, and the very complex statistical behavior of the fluctuation velocity field of the turbulent jet in crossflow are revealed. These results are deepening the comprehension of the nonlinear dynamical mechanism of the basic physics process of turbulent elliptic jets.In the future, some issues need to be investigated further, which include: establish and study the low-dimensional dynamical system of turbulent jet, with the POD bases, the control of turbulent jet based on the low-dimensional dynamical system of turbulent jet, investigate the physics mechanism of intermittence shed-off of the vortex ring in turbulent jets in crossflow.
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112．吴锤结，湍流研究的低维动力系统方法，《力学-现代工程技术的支柱》(赵光恒主编)，河海大学出版社，2001，385-420．
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114．赵红亮，《尾迹型剪切流中的漩涡位错研究》，中国科学院研究生院博士学位论文，2003年．
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98. Sirovich, L. & Kirby, M., Low-dimensional procedure for the characterization of human faces, J. Opt. Soc. Am., 1987, A 4, 519-524.
99. Sirovich, L., Kirby, M. & Winter, M., An eigenfunction approach to large scale transitional structures in jet flow, Phys. Fluids, 1990, A 2, 127 136.
100. Sirovich, L., Knight, B. W. & Rodriguez, J. D., Optimal low dimensional dynamical approximations, Q. Appl. Math., 1990, 48, 535-548.
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110. Winter, M., Barber, T. J., Everson, R. M. & Sirovich, L., Eigenfunction analysis of turbulent mixing phenomena, AIAA J., 1992, 30, 1681-1688.
111. Wu, C. J., Optimal truncated low-dimensional dynamical systems, Discrete and Continuous Dynamical Systems, 1996, 2(4):559-583.
112．吴锤结，湍流研究的低维动力系统方法，《力学-现代工程技术的支柱》(赵光恒主编)，河海大学出版社，2001，385-420．
113. Yuan, L. L., Street, R. L. & Ferziger, J. H., Large-eddy simulations of a round jet in crossflow, J. Fluid Mech., 1999, 379: 71-104.
114．赵红亮，《尾迹型剪切流中的漩涡位错研究》，中国科学院研究生院博士学位论文，2003年．