湍流局部结构分析和涡旋识别
|
摘要
湍流脉动信号的数理统计可分为大样本统计和局部时频分析。本文借助小波分析：工具等对边界层与尾迹相互作用这一复杂流动做了一些时频分析，得到了一些结论。在该流动实验中，尾迹形成的涡旋脱落机制比边界层形成的涡量向外扩散形成涡旋的机制能够形成更多的、更强的、凝聚性更好的涡旋结构。尾迹强剪切处最容易产生涡旋。壁面处可发现猝发结构，但该处的标度指数表明，流动状态以层流占主导。负产生区缺乏涡旋形成机制，不能形成结构良好的涡旋(无论是数量、强度、凝聚性还是标度性)。但有一个显著特点，小尺度上的脉动强度远大于其它测点，线性标度律在小尺度上不成立，且法向速度分量形成的耗散大于流向速度分量形成的耗散。流动条件简单(或者说涡形成机制单一)的位置处，具有很好的各向同性和均匀性，以及紧支的涡旋结构；反之，各向异性、非均匀性愈加明显，涡旋结构也较松散。
本文同时介绍了小波分析的理论背景及其在湍流中的几个应用，如强间歇性是如何使K41理论偏离线性标度律的。特别地，定义了相干结构，指出它是具有一定脉动强度的大尺度结构，并提出了能量比最小准则识别相干结构，相比于能量最大准则，更能反映流动的物理内涵且判断结果更加客观。
最后介绍了新设计的一个涡旋识别方法。通过分析瞬时流线结构，包括单条流线的特性和相邻流线之间的关系，并以相邻流线之间的缠绕关系来定义涡旋(核)区，依此提出新的涡旋识别算法，最后通过例子验证其有效性。
The statistical analysis of turbulent fluctuation signals can be divided into two categories, large amount sample analysis and local time-frequency analysis respectively. With the tool of wavelet analysis, the author did some time-frequency analyses on the basement of an experimental flow interacted between boundary-layer and wake. The conclusions are as follows, the vortexes formed by the wake's falling off mechanism are more than those by the boundary-layer in quantity, stronger in power and compacter in structure; the place of the wake's strongest shear produce well vortexes both in quantity and quality, but bust structures can be found in the boundary-layer occasionally; vortexes in the inverse energy cascade region are weak and incompact due to lack of vortex forming mechanism, and the linear scaling does not exist at small spatial scale because of strong fluctuation in the small scale. Meanwhile, the flow approach to locally isotropic and uniform turbulence if the flow condition is simple, and vortexes here are compacter than other place, vice versa.
The wavelet theory is introduced in brief, then several applications in turbulence are referred including how strong intermittency makes the scaling exponent of velocity structure deviates from the K41 theory's linear scaling law when order-number is relatively large. The coherent structure is defined, we consider it's a large structure with a certain powerful fluctuation; then, a new method for coherent structure detection is put forward, i.e. the minimum of energy ratio criterion, which is more objective and meaningful than the previous methods.
The last chapter introduces a new method of vortex detection, which is based on the streamline and streamline- cluster's topological characteristics, then several examples are used to verify the effectiveness of this method.
本文同时介绍了小波分析的理论背景及其在湍流中的几个应用，如强间歇性是如何使K41理论偏离线性标度律的。特别地，定义了相干结构，指出它是具有一定脉动强度的大尺度结构，并提出了能量比最小准则识别相干结构，相比于能量最大准则，更能反映流动的物理内涵且判断结果更加客观。
最后介绍了新设计的一个涡旋识别方法。通过分析瞬时流线结构，包括单条流线的特性和相邻流线之间的关系，并以相邻流线之间的缠绕关系来定义涡旋(核)区，依此提出新的涡旋识别算法，最后通过例子验证其有效性。
The statistical analysis of turbulent fluctuation signals can be divided into two categories, large amount sample analysis and local time-frequency analysis respectively. With the tool of wavelet analysis, the author did some time-frequency analyses on the basement of an experimental flow interacted between boundary-layer and wake. The conclusions are as follows, the vortexes formed by the wake's falling off mechanism are more than those by the boundary-layer in quantity, stronger in power and compacter in structure; the place of the wake's strongest shear produce well vortexes both in quantity and quality, but bust structures can be found in the boundary-layer occasionally; vortexes in the inverse energy cascade region are weak and incompact due to lack of vortex forming mechanism, and the linear scaling does not exist at small spatial scale because of strong fluctuation in the small scale. Meanwhile, the flow approach to locally isotropic and uniform turbulence if the flow condition is simple, and vortexes here are compacter than other place, vice versa.
The wavelet theory is introduced in brief, then several applications in turbulence are referred including how strong intermittency makes the scaling exponent of velocity structure deviates from the K41 theory's linear scaling law when order-number is relatively large. The coherent structure is defined, we consider it's a large structure with a certain powerful fluctuation; then, a new method for coherent structure detection is put forward, i.e. the minimum of energy ratio criterion, which is more objective and meaningful than the previous methods.
The last chapter introduces a new method of vortex detection, which is based on the streamline and streamline- cluster's topological characteristics, then several examples are used to verify the effectiveness of this method.
引文
[1] 邹正平，湍流层次结构理论的试验研究．北京大学湍流实验室博士后出站报告．2001．
[2] Hinze, J. O. Turbulence. 2nd. McGraw-Hill, New York. 1975.
[3] 邹文楠，湍流思问录，北京大学湍流实验室博士后出站报告，2002．
[4] Richardson L. F. Weather Prediction by Numerical Process. Cambridge University Press, 1992.
[5] Kolmogorov A N. Dissipation of energy in locally isotropic turbulence. Dokl. Akad. Nauk USSR. 1941, 32: 16-18 (reprint in Proc. R. Soc. Lond. A. 1991, 434: 15-17).
[6] Landau, L. D. , Lifshitz, E. M. Fluid Mechanics. 2nd ed. Pergamon Press. 1987.
[7] Benzi, R. et al. Extended self-similarity in turbulent flows. Phys. Rev. E. 1993, 48: 29-32.
[8] She Z S & Levesque E. Universal scaling laws in fully developed turbulence. Phys. Rev. Lett. 72, 336-339.
[9] She Z. S. , Ren K. , Lewis G. S. , Swinney H. L. Scaling and structures in turbulent Couette-Taylor flow. Phys. Rev. E, 2001.
[10] 刘海峰等．应用小波分析研究湍流相干结构．化工学报．2000，51(6)：762-770．
[11] 科恩，L．(白居宪译)．时频分析：理论与应用．西安交通大学出版，Prentice Hall．1998．3．
[12] Daubenchies, I. Ten Lectures on Wavelets. Capital City Press. 1992.
[13] Chui, C. K. An Introduction to Wavelets. Academic Press, Ltd. 1992.
[14] Resnikoff, H. L. , Wells, Jr. R. O. Wavelet Analysis. Springer-Verlag. 1998.
[15] 是勋刚编，湍流，天津大学出版社，1994年．
[16] 卢志明，刘宇陆，湍流结构的统计及动力模型及其对传热影响研究，应用数学和力学，VOL．19，NO．8，Aug，1998年．
[17] 姜楠，壁湍流相干结构的实验系列，力学与实践，Vol21，1999年．
[18] Tennekes, H. , Lumley, J. L. A First Course in Turbulence. The MIT Press, 1972.
[19] 张贤达，保铮．非平稳信号分析与处理．国防工业出版社．1998．
[20] Boggess, A. , Narcowich F. J. 著，康健等译．小波分析与傅立叶分析基础．电子工业出版社，2004．
[21] 徐长发、李国宽．实用小波方法．华中科技大学出版社，2001．
[22] 傅强、夏克青，用子波方法提取Rayleigh-Benard对流温度信号的相干结构，解放军理工大学学报，2001，Vol．2(3)，23-28．
[23] Farge, M. Wavelet transforms and their applications to turbulence. Annul. Rev. Fluid Mech. 1992. 24: 395-457.
[24] Katul, G. G. , Parlange, M. B. , Chu, C. R. Intermittency, local isotropy, and non-Gaussian??statistics in atmospheric surface layer turbulence. Phys. Fluids 6 (7), July 1994.
[25] Meneveau, C. , Sreenivasan, K. R. Simple multifractal cascade model for fully developed turbulence. Phys. Rev. Lett. 59, 1427 (1987).
[26] 子波分析辨识壁湍流猝发事件的能量最大准则姜楠、王振东、舒玮，力学学报，Vol．29，No．4．1997．
[27] 小波分析辨识相干结构的能量最大准则，刘海峰等，化工学报，Vol．51．No．6．
[28] Liandrat, J. , Perrier, V. , Tchamitchian, P. The wavelet transform: some applications to fluid dynamics and turbulence. Eur J. Mech. B/Fluid, 1990, 9 (1) : 1-19.
[29] 邹文楠．湍流脉动信号的时频结构研究，自然科学基金面上项目总结报告，2005．
[30] 吴介之，马晖扬，周明德．涡动力学引论．高等教育出版社，1993．
[31] Johnson C. R, Hansen C. D. The Visualization Handbook Elsevier Butterworth-Heinemann, 2005
[32] Roth M. , Peikert P. Flow Visualization for Turbomachinery Design, 2004.
[33] Wu J. Z. , Xiong A. K. , Yang Y. T. Axial stretching and vortex definition. Phys. Fluid. 17, 038108(2005).
[34] Hailer, G. An objective definition of a vortex, to appear in J. Fliuid Mech.
[2] Hinze, J. O. Turbulence. 2nd. McGraw-Hill, New York. 1975.
[3] 邹文楠，湍流思问录，北京大学湍流实验室博士后出站报告，2002．
[4] Richardson L. F. Weather Prediction by Numerical Process. Cambridge University Press, 1992.
[5] Kolmogorov A N. Dissipation of energy in locally isotropic turbulence. Dokl. Akad. Nauk USSR. 1941, 32: 16-18 (reprint in Proc. R. Soc. Lond. A. 1991, 434: 15-17).
[6] Landau, L. D. , Lifshitz, E. M. Fluid Mechanics. 2nd ed. Pergamon Press. 1987.
[7] Benzi, R. et al. Extended self-similarity in turbulent flows. Phys. Rev. E. 1993, 48: 29-32.
[8] She Z S & Levesque E. Universal scaling laws in fully developed turbulence. Phys. Rev. Lett. 72, 336-339.
[9] She Z. S. , Ren K. , Lewis G. S. , Swinney H. L. Scaling and structures in turbulent Couette-Taylor flow. Phys. Rev. E, 2001.
[10] 刘海峰等．应用小波分析研究湍流相干结构．化工学报．2000，51(6)：762-770．
[11] 科恩，L．(白居宪译)．时频分析：理论与应用．西安交通大学出版，Prentice Hall．1998．3．
[12] Daubenchies, I. Ten Lectures on Wavelets. Capital City Press. 1992.
[13] Chui, C. K. An Introduction to Wavelets. Academic Press, Ltd. 1992.
[14] Resnikoff, H. L. , Wells, Jr. R. O. Wavelet Analysis. Springer-Verlag. 1998.
[15] 是勋刚编，湍流，天津大学出版社，1994年．
[16] 卢志明，刘宇陆，湍流结构的统计及动力模型及其对传热影响研究，应用数学和力学，VOL．19，NO．8，Aug，1998年．
[17] 姜楠，壁湍流相干结构的实验系列，力学与实践，Vol21，1999年．
[18] Tennekes, H. , Lumley, J. L. A First Course in Turbulence. The MIT Press, 1972.
[19] 张贤达，保铮．非平稳信号分析与处理．国防工业出版社．1998．
[20] Boggess, A. , Narcowich F. J. 著，康健等译．小波分析与傅立叶分析基础．电子工业出版社，2004．
[21] 徐长发、李国宽．实用小波方法．华中科技大学出版社，2001．
[22] 傅强、夏克青，用子波方法提取Rayleigh-Benard对流温度信号的相干结构，解放军理工大学学报，2001，Vol．2(3)，23-28．
[23] Farge, M. Wavelet transforms and their applications to turbulence. Annul. Rev. Fluid Mech. 1992. 24: 395-457.
[24] Katul, G. G. , Parlange, M. B. , Chu, C. R. Intermittency, local isotropy, and non-Gaussian??statistics in atmospheric surface layer turbulence. Phys. Fluids 6 (7), July 1994.
[25] Meneveau, C. , Sreenivasan, K. R. Simple multifractal cascade model for fully developed turbulence. Phys. Rev. Lett. 59, 1427 (1987).
[26] 子波分析辨识壁湍流猝发事件的能量最大准则姜楠、王振东、舒玮，力学学报，Vol．29，No．4．1997．
[27] 小波分析辨识相干结构的能量最大准则，刘海峰等，化工学报，Vol．51．No．6．
[28] Liandrat, J. , Perrier, V. , Tchamitchian, P. The wavelet transform: some applications to fluid dynamics and turbulence. Eur J. Mech. B/Fluid, 1990, 9 (1) : 1-19.
[29] 邹文楠．湍流脉动信号的时频结构研究，自然科学基金面上项目总结报告，2005．
[30] 吴介之，马晖扬，周明德．涡动力学引论．高等教育出版社，1993．
[31] Johnson C. R, Hansen C. D. The Visualization Handbook Elsevier Butterworth-Heinemann, 2005
[32] Roth M. , Peikert P. Flow Visualization for Turbomachinery Design, 2004.
[33] Wu J. Z. , Xiong A. K. , Yang Y. T. Axial stretching and vortex definition. Phys. Fluid. 17, 038108(2005).
[34] Hailer, G. An objective definition of a vortex, to appear in J. Fliuid Mech.