界面张力梯度驱动对流向湍流转捩的研究

郭子漪; 李凯; 康琦; 段俐; 胡文瑞

doi:10.6052/1000-0992-20-022

界面张力梯度驱动对流向湍流转捩的研究

doi: 10.6052/1000-0992-20-022

中国科学院力学研究所微重力重点实验室, 北京 100190
中国科学院大学工程科学学院, 北京 100049

基金项目:

国家自然科学基金资助项目 (11972353, U1738116).

详细信息

作者简介:

**E-mail: kq@imech.ac.cn
康琦, 研究员、博士生导师. 中国科学院微重力重点实验室主任, 国际宇航联(IAF)微重力专业委员会委员, 空间科学学会理事, 《空间科学学报》副主编. 长期从事微重力流体物理等方面研究, 在SJ-10, TG-2, Taiji-1等任务中完成多项空间实验.
*E-mail: likai@imech.ac.cn
李凯, 研究员、博士生导师. 中国科学院BR计划引进国外杰出人才, 中国科学院微重力重点实验室副主任, 国科大岗位教授. 长期从事微重力流体力学、传热与流动控制、计算流体力学等方面研究, 上述领域发表SCI期刊论文40余篇;

通讯作者:
李凯

康琦

中图分类号: O35
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出版历程
- 收稿日期: 2020-09-14
- 刊出日期: 2021-03-25

Study on bifurcation to chaos of surface tension gradient driven flow

GUO Ziyi,
LI Kai^{*
, ,},
KANG Qi^{**
, ,},
DUAN Li,
HU Wenrui

National Microgravity Laboratory, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China
School of Engineering Science, University of Chinese Academy of Sciences, Beijing 100049, China

More Information

Corresponding author: LI Kai; KANG Qi

摘要

摘要: 作为空间自然对流热质输运的基本形式, 界面张力梯度驱动对流是流动和传热强耦合的复杂非线性过程, 也是一个多控制参数耦合作用的过程, 表现出丰富的流动时空特征. 界面张力梯度驱动对流是微重力流体物理的重要研究内容和学科前沿, 同时在空间燃料输运过程和空间能源或热管利用等空间流体管理问题中均有重要应用. 本文综述了界面张力梯度驱动对流向湍流转捩研究的背景意义、地面实验、空间实验及数值模拟的研究现状, 重点介绍了从非线性动力学角度来研究转捩规律的具体方法, 目前最常见的手段是对观测量的时间序列进行分析, 通过频谱分析及相空间重构等方法计算时间序列的特征量, 从而判断流动模式, 这类方法理论成熟, 计算简单, 但需要对大量数据进行繁琐的处理; 另一种方法是通过数值计算分岔来研究对流在时空中的转捩模式, 这类方法可以直接计算出分岔点, 但是复杂之处在于需要求解大规模的线性或非线性方程组, 本文详细阐述了两种方法的理论背景, 应用状况及局限性, 探讨了将两种方法相互结合, 在研究中互为补充的可能, 并对今后的研究方向提出了建议.
- 界面张力梯度驱动对流 /
- 微重力 /
- 分岔 /
- 混沌
Abstract: As the primary heat and mass transfer mechanism in space through natural convection, surface tension gradient-driven convection is a complex nonlinear process concerning strong coupling between fluid flow and heat transfer. It is also a multiple parameter coupling process that exhibits complex spatial-temporal characteristics. Therefore, the mechanism of the surface tension gradient-driven convection becomes a hotspot in microgravity fluid physics. It also has many important applications, such as in space fluid and energy management. In this paper, recent experimental and numerical results on the transition of surface tension gradient-driven convection are reviewed, especially the nonlinear analysis on the flow bifurcations to chaos. There are several numerical methods to obtain the corresponding bifurcation diagrams. One is to integrate the model forward in time starting from different parameters and initial values, and others are to calculate the asymptotic flow states and bifurcation points directly. The direct numerical simulation method and time series analysis are widely used, but searching for bifurcation points from a large number of data is burdensome. Bifurcation points can be computed directly with the numerical bifurcation method, but such calculations are more difficult to implement than the direct numerical method.
- surface gradient tension-driven convection /
- microgravity /
- bifurcation /
- chaos

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参考文献(105)

[1]	胡文瑞, 唐泽眉, 李凯, 等. 2010. 矩形液池中热毛细对流起振过程的数值模拟. 中国科学: 技术科学, 40(4):370-377.
[2]	胡文瑞, 徐硕昌. 1999. 微重力流体力学 (第一版). 北京: 科学出版社.
[3]	吕金虎, 陆君安, 陈士华. 2002. 混沌时间序列分析及其应用. 武汉: 武汉大学出版社.
[4]	石万元, 李友荣, 彭岚, 等. 2009. 环形浅液池内热流体波的本质特征. 计算力学学报, 26:59-65 (Shi W Y, Li Y R, Peng L, et al. 2009. Natural characteristics of hydrothermal wave in a shallow annular pool. Chinese Journal of Computational Mechanics, 26:59-65).
[5]	唐登斌. 2015. 边界层转捩. 北京: 科学出版社.
[6]	唐泽眉, 胡文瑞. 2007. 液池中大Pr数流体的热流体波. 中国科学: G 辑, 37:250-258.
[7]	Aa Y, Li K, Tang Z M, et al. 2010. Period-doubling bifurcations of the thermocapillary convection in a floating half zone. Science China Physics, Mechanics and Astronomy, 53:1681-1686.
[8]	Abe Y, Iwaski A, Tanaka K. 2005. Thermal management with self-rewetting fluids. Microgravity-Science and Technology, 16:148-152. doi: 10.1007/BF02945966.
[9]	Bandt C, Pompe B. 2002. Permutation entropy: A natural complexity measure for time series. Physical Review Letters, 88:174102. doi: 10.1103/PhysRevLett.88.174102.
[10]	Barna G, Tsuda I. 1993. A new method for computing Lyapunov exponents. Physics Letters A, 175:421-427. doi: 10.1016/0375-9601(93)90994-B.
[11]	Benard H. 1901. Les Tourbillons cellulaires dans une nappe liquide transportant de la chaleur par convection en regime permanent. Annales de Chimie et de Physique, 23:62-144.
[12]	Boro$acute{n}$ska K, Tuckerman L. 2010a. Extreme multiplicity in cylindrical Rayleigh-Benard convection. I. Time dependence and oscillations. Physical review. E, Statistical, nonlinear, and soft matter physics, 81:036320. doi: 10.1103/PhysRevE.81.036320.
[13]	Boro$acute{n}$ska K, Tuckerman L. 2010b. Extreme multiplicity in cylindrical Rayleigh-Benard convection. II. Bifurcation diagram and symmetry classification. Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, 81:036321. doi: 10.1103/PhysRevE.81.036321.
[14]	Braun R, Feudel F, Guzdar P. 1998. Route to chaos for a two-dimensional externally driven flow. Physical Review E, 58:1927.
[15]	Broze G, Hussain F. 1996. Transitions to chaos in a forced jet: intermittency, tangent bifurcations and hysteresis. Journal of Fluid Mechanics, 311:37-71.
[16]	Bucchignani E, Mansutti D. 2004. Horizontal thermocapillary convection of succinonitrile: Steady state, instabilities, and transition to chaos. Physical Review E, 69:056319.
[17]	Chan C L, Chen C. 2010. Effect of gravity on the stability of thermocapillary convection in a horizontal fluid layer. Journal of Fluid Mechanics, 647:91.
[18]	Chen G, Lizee A, Roux B. 1997. Bifurcation analysis of the thermocapillary convection in cylindrical liquid bridges. Journal of Crystal Growth, 180:638-647
[19]	Chen Z W, Li Y S, Zhan J M. 2010. Double-diffusive Marangoni convection in a rectangular cavity: Onset of convection. Physics of Fluids, 22:034106.
[20]	Cliffe K A, Spence A, Tavener S J. 2000. The numerical analysis of bifurcation problems with application to fluid mechanics. Acta Numerica, 9:47. doi: 10.1017/S0962492900000398.
[21]	Cliffe K A, Tavener S J. 1998. Marangoni-Bénard convection with a deformable free surface. Journal of Computational Physics, 145:193-227.
[22]	Cr?ll A, Dold P, Benz K W. 1994. Segregation in Si floating-zone crystals grown under microgravity and in a magnetic field. Journal of Crystal Growth, 137:95-101. doi: 10.1016/0022-0248(94)91254-8.
[23]	Davis S H. 1983. Instabilities of dynamic thermocapillary liquid layers. Part 2. Surface-wave instabilities. Journal of Fluid Mechanics, 132:145-162.
[24]	Derby J, Brown R. 1986. Thermal-capillary analysis of Czochralski and liquid encapsulated Czochralski crystal growth: I. Simulation. Journal of Crystal Growth, 74:605-624.
[25]	Dijkstra H A. 1992. On the structure of cellular solutions in Rayleigh-Bénard-Marangoni flows in small-aspect-ratio containers. Journal of Fluid Mechanics, 243:73-102.
[26]	Dijkstra H A, Wubs F W, Cliffe A K, et al. 2014. Numerical bifurcation methods and their application to fluid dynamics: Analysis beyond simulation. Communications in Computational Physics, 15:1-45. doi: 10.4208/cicp.240912.180613a.
[27]	Feigenbaum M J. 1979. The onset spectrum of turbulence. Physics Letters A, 74:375-378. doi: 10.1016/0375-9601(79)90227-5.
[28]	Frank S, Schwabe D. 1997. Temporal and spatial elements of thermocapillary convection in floating zones. Experiments in Fluids, 23:234-251.
[29]	Fraser A M, Swinney H L. 1986. Independent coordinates for strange attractors from mutual information. Physical Review A, 33:1134.
[30]	Garnier N, Chiffaudel A, Daviaud F. 2003a. Nonlinear dynamics of waves and modulated waves in 1D thermocapillary flows. II. Convective/absolute transitions. Physica D: Nonlinear Phenomena, 174:30-55.
[31]	Garnier N, Chiffaudel A, Daviaud F, et al. 2003b. Nonlinear dynamics of waves and modulated waves in 1D thermocapillary flows. I. General presentation and periodic solutions. Physica D: Nonlinear Phenomena, 174:1-29.
[32]	Garnier N, Normand C. 2001. Effects of curvature on hydrothermal waves instability of radial thermocapillary flows. Comptes Rendus de l'Académie des Sciences-Series IV-Physics, 2:1227-1233.
[33]	Gollub J, Benson S. 1980. Many routes to turbulent convection. Journal of Fluid Mechanics, 100:449-470.
[34]	Grassberger P, Procaccia I. 1983. Characterization of strange attractors. Physical Review Letters, 50:346-349. doi: 10.1103/PhysRevLett.50.346.
[35]	Griewank A, Reddien G. 1983. The calculation of Hopf points by a direct method. IMA Journal of Numerical Analysis, 3:295-303.
[36]	Hu W R, Tang Z M, Li K. 2008. Thermocapillary convection in floating zones. Applied Mechanics Reviews, 61:010803.
[37]	Jepson A D. 1981. Numerical Hopf Bifurcation. California Institute of Technology, Pasadena, California, USA.
[38]	Jiang H, Duan L, Kang Q. 2017a. A peculiar bifurcation transition route of thermocapillary convection in rectangular liquid layers. Experimental Thermal and Fluid Science, 88:8-15.
[39]	Jiang H, Duan L, Kang Q. 2017b. Instabilities of thermocapillary-buoyancy convection in open rectangular liquid layers. Chinese Physics B, 26:114703. doi: 10.1088/1674-1056/26/11/114703.
[40]	Johns L E, Narayanan R. 2002. Interfacial Instability. New York: Springer.
[41]	Kamotani Y, Ostrach S, Masud J. 1999. Oscillatory thermocapillary flows in open cylindrical containers induced by CO$_2$ laser heating. International Journal of Heat and Mass Transfer, 42:555-564.
[42]	Kamotani Y, Ostrach S, Pline A. 1995. A thermocapillary convection experiment in microgravity. Journal of Heat Transfer, 117:611-618
[43]	Kang Q, Jiang H, Duan L, et al. 2019a. The critical condition and oscillation-transition characteristics of thermocapillary convection in the space experiment on SJ-10 satellite. International Journal of Heat and Mass Transfer, 135:479-490.
[44]	Kang Q, Wang J, Duan L, et al. 2019b. The volume ratio effect on flow patterns and transition processes of thermocapillary convection. Journal of Fluid Mechanics, 868:560-583. doi: 10.1017/jfm.2019.108.
[45]	Kang Q, Wu D, Duan L, et al. 2019c. Surface configurations and wave patterns of thermocapillary convection onboard the SJ10 satellite. Physics of Fluids, 31:044105. doi: 10.1063/1.5090466.
[46]	Kang Q, Wu D, Duan L, et al. 2019d. The effects of geometry and heating rate on thermocapillary convection in the liquid bridge. Journal of Fluid Mechanics, 881:951-982. doi: 10.1017/jfm.2019.757.
[47]	Kang Q, Wu D, Duan L, et al. 2020. Space experimental study on wave modes under instability of thermocapillary convection in liquid bridges on Tiangong-2. Physics of Fluids, 32:034107. doi: 10.1063/1.5143219.
[48]	Keller H B. 1987. Lectures on Numerical Methods in Bifurcation Problems. Berlin: Springer.
[49]	Kim H S, Eykholt R, Salas J D. 1999. Nonlinear dynamics, delay times, and embedding windows. Physica D: Nonlinear Phenomena, 127:48-60.
[50]	Lappa M. 2009. Thermal Convection: Patterns, Evolution and Stability. Chichester, UK: John Wiley & Sons, Ltd.
[51]	Laure P, Roux B, Ben Hadid H. 1990. Nonlinear study of the flow in a long rectangular cavity subjected to thermocapillary effect. Physics of Fluids A: Fluid Dynamics, 2:516-524.
[52]	Li K, Tang Z M, Hu W R. 2012. Coupled thermocapillary convection on Marangoni convection in liquid layers with curved free surface. International Journal of Heat and Mass Transfer, 55:2726-2729.
[53]	Li K, Xun B, Hu W R. 2016. Some bifurcation routes to chaos of thermocapillary convection in two-dimensional liquid layers of finite extent. Physics of Fluids, 28:054106.
[54]	Li Y R, Imaishi N, Azami T, et al. 2004. Three-dimensional oscillatory flow in a thin annular pool of silicon melt. Journal of Crystal Growth, 260:28-42.
[55]	Li Y R, Peng L, Akiyama Y, et al. 2003. Three-dimensional numerical simulation of thermocapillary flow of moderate Prandtl number fluid in an annular pool. Journal of Crystal Growth, 259:374-387.
[56]	Li Y R, Wang S C, Wu C M. 2011a. Steady thermocapillary-buoyant convection in a shallow annular pool. Part 1: Single layer fluid. Acta Mechanica Sinica, 27:360.
[57]	Li Y R, Wang S C, Wu C M. 2011b. Steady thermocapillary-buoyant convection in a shallow annular pool. Part 2: Two immiscible fluids. Acta Mechanica Sinica, 27:636.
[58]	Li Y S, Chen Z W, Zhan J M. 2010. Double-diffusive Marangoni convection in a rectangular cavity: Transition to chaos. International Journal of Heat and Mass Transfer, 53:5223-5231.
[59]	Libchaber A, Maurer J. 1978. Local probe in a Rayleigh-Benard experiment in liquid helium. Journal de Physique Lettres, 39:369-372.
[60]	Lorenz E N. 1963. Deterministic nonperiodic flow. Journal of the Atmospheric Sciences, 20:130-141.
[61]	Ma C, Bothe D. 2011. Direct numerical simulation of thermocapillary flow based on the volume of fluid method. International Journal of Multiphase Flow, 37:1045-1058.
[62]	Madruga S, Perez G C, Lebon G. 2003. Convective instabilities in two superposed horizontal liquid layers heated laterally. Physical Review E, 68:041607.
[63]	Madruga S, Pérez-García C, Lebon G. 2004. Instabilities in two-liquid layers subject to a horizontal temperature gradient. Theoretical and Computational Fluid Dynamics, 18:277-284.
[64]	Moore G, Spence A. 1980. The calculation of turning points of nonlinear equations. SIAM Journal on Numerical Analysis, 17:567-576.
[65]	Mukolobwiez N, Chiffaudel A, Daviaud F. 1998. Supercritical Eckhaus instability for surface-tension-driven hydrothermal waves. Physical Review Letters, 80:4661.
[66]	Mukutmoni D, Yang K T. 1993. Rayleigh-Benard convection in a small aspect ratio enclosure: Part I——Bifurcation to oscillatory convection. Journal of Heat Transfer, 115:360-376
[67]	Newhouse S, Ruelle D, Takens F. 1978. Occurrence of strange AxiomA attractors near quasi periodic flows on T m, $mgeq 3$. Communications in Mathematical Physics, 64:35-40.
[68]	Packard N H, Crutchfield J P, Farmer J D, et al. 1980. Geometry from a time series. Physical Review Letters, 45:712.
[69]	Pearson J R A. 1958. On convection cells induced by surface tension. Journal of Fluid Mechanics, 4:489-500. doi: 10.1017/S0022112058000616.
[70]	Pérez-García C, Madruga S, Echebarria B, et al. 2004. Hydrothermal waves and corotating rolls in laterally heated convection in simple liquids. Journal of Non-Equilibrium Thermodynamics, 29:377-388.
[71]	PoincaréH, Magini R. 1899. Les méthodes nouvelles de la mécanique céleste. Il Nuovo Cimento (1895-1900), 10:128-130.
[72]	Pomeau Y, Manneville P. 1980. Intermittent transition to turbulence in dissipative dynamical systems. Communications in Mathematical Physics, 74:189-197. doi: 10.1007/BF01197757.
[73]	Prandtl L. 1904. über Flüssigkeitsbewegung bei sehr kleiner Reibung, Verh 3 int. Math-Kongr, Heidelberg.
[74]	Rahal S, Cerisier P, Abid C. 2007. Transition to chaos via the quasi-periodicity and characterization of attractors in confined Bénard-Marangoni convection. The European Physical Journal B, 59:509-518.
[75]	Riley R, Neitzel G. 1998. Instability of thermocapillary-buoyancy convection in shallow layers. Part 1. Characterization of steady and oscillatory instabilities. Journal of Fluid Mechanics, 359:143-164.
[76]	Rosenstein M T, Collins J J, De Luca C J. 1993. A practical method for calculating largest Lyapunov exponents from small data sets. Physica D: Nonlinear Phenomena, 65:117-134. doi: 10.1016/0167-2789(93)90009-P.
[77]	Ruelle D, Takens F. 1971. On the nature of turbulence. Les rencontres physiciens-mathématiciens de Strasbourg-RC25, 12:1-44.
[78]	Saenz P J, Valluri P, Sefiane K, et al. 2013. Linear and nonlinear stability of hydrothermal waves in planar liquid layers driven by thermocapillarity. Physics of Fluids, 25:094101.
[79]	Saha A K, Muralidhar K, Biswas G. 2000. Transition and chaos in two-dimensional flow past a square cylinder. Journal of Engineering Mechanics, 126:523-532.
[80]	Salinger A G, Burroughs E A, Pawlowski R P, et al. 2005. Bifurcation tracking algorithms and software for large scale applications. International Journal of Bifurcation and Chaos, 15:1015-1032.
[81]	Salinger A G, Lehoucq R B, Pawlowski R P, et al. 2002. Computational bifurcation and stability studies of the $8:1$ thermal cavity problem. International Journal for Numerical Methods in Fluids, 40:1059-1073.
[82]	Schwabe D, Benz S. 2002. Thermocapillary flow instabilities in an annulus under microgravity--results of the experiment magia. Advances in Space Research, 29:629-638.
[83]	Schwabe D, Cramer A, Schneider J, et al. 1999. Experiments on the multi-roll-structure of thermocapillary flow in side-heated thin liquid layers. Advances in Space Research, 24:1367-1373.
[84]	Schwabe D, Frank S. 1999. Experiments on the transition to chaotic thermocapillary flow in floating zones under microgravity. Advances in Space Research, 24:1391-1396.
[85]	Shi W, Ermakov M K, Imaishi N. 2006. Effect of pool rotation on thermocapillary convection in shallow annular pool of silicone oil. Journal of Crystal Growth, 294:474-485.
[86]	Shi W, Li Y R, Ermakov M K, et al. 2010. Stability of thermocapillary convection in rotating shallow annular pool of silicon melt. Microgravity Science and Technology, 22:315-320.
[87]	Sim B C, Zebib A. 2004. Thermocapillary convection in cylindrical liquid bridges and annuli. Comptes Rendus Mecanique, 332:473-486.
[88]	Sim B C, Zebib A, Schwabe D. 2003. Oscillatory thermocapillary convection in open cylindrical annuli. Part 2. Simulations. Journal of Fluid Mechanics, 491:259.
[89]	Smith M K. 1986. Instability mechanisms in dynamic thermocapillary liquid layers. The Physics of Fluids, 29:3182-3186.
[90]	Smith M K, Davis S H. 1983. Instabilities of dynamic thermocapillary liquid layers. Part 1. Convective instabilities. Journal of Fluid Mechanics, 132:119-144.
[91]	Space experimental study on wave modes under instability of thermocapillary convection in liquid bridges on Tiangong-2. 2020. Physics of Fluids, 32:034107. doi: 10.1063/1.5143219.
[92]	Surface configurations and wave patterns of thermocapillary convection onboard the SJ10 satellite. 2019. Physics of Fluids, 31:044105. doi: 10.1063/1.5090466.
[93]	Takens F. 1981. Detecting strange attractors in turbulence//Dynamical Systems and Turbulence, Warwick 1980. Edited by D. Rand and L.S. Young. Berlin Heidelberg, Berlin: Springer.,Heidelberg. pp. 366-381.
[94]	Tang Z M, Hu W R. 2007. The hydrothermal wave of large-Prandtl-number fluid in a shallow cavity. Science in China Series G: Physics, Mechanics and Astronomy, 50:787-796.
[95]	Tang Z M, Hu W R, Xie J C, et al. 1995. Transition from steady to oscillatory convection with chaotic feature in thermocapillary convection. Advances in Space Research, 16:67-70.
[96]	Tuckerman L S. 2020. Computational Challenges of Nonlinear Systems//Emerging Frontiers in Nonlinear Science. Springer. pp. 249-277.
[97]	Walter H U. 1987. Fluid Sciences and Materials Science in Space. Berlin, Heidelberg: Springer.
[98]	Werner B, Janovsky V. 1991. Computation of Hopf branches bifurcating from Takens-Bogdanov points for problems with symmetries//Bifurcation and Chaos: Analysis, Algorithms, Applications. Springer. pp. 377-388.
[99]	Werner B, Spence A. 1984. The computation of symmetry-breaking bifurcation points. SIAM Journal on Numerical Analysis, 21:388-399.
[100]	Wolf A, Swift J B, Swinney H L, et al. 1985. Determining Lyapunov exponents from a time series. Physica D: Nonlinear Phenomena, 16:285-317. doi: 10.1016/0167-2789(85)90011-9.
[101]	Xu J Y, Zebib A. 1998. Oscillatory two-and three-dimensional thermocapillary convection. Journal of Fluid Mechanics, 364:187-209.
[102]	Xu J J, Davis S H. 1984. Convective thermocapillary instabilities in liquid bridges. The Physics of Fluids, 27:1102-1107.
[103]	Yu J J, Ruan D F, Li Y R, et al. 2015. Experimental study on thermocapillary convection of binary mixture in a shallow annular pool with radial temperature gradient. Experimental Thermal and Fluid Science, 61:79-86.
[104]	Zhang L, Li Y R, Wu C M, et al. 2018. Flow bifurcation routes to chaos of thermocapillary convection for low Prandtl number fluid in shallow annular pool with surface heat dissipation. International Journal of Thermal Sciences, 125:23-33.
[105]	Zhu P, Duan L, Kang Q. 2013. Transition to chaos in thermocapillary convection. International Journal of Heat and Mass Transfer, 57:457-464. doi: 10.1016/j.ijheatmasstransfer.2012.10.033.