The statistics of velocity and temperature fluctuations in axisymmetric laminar-to-turbulent transitions
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摘要: 热力学平衡系统连续相变的理论方法，被推广用来讨论圆管内轴对称层流到湍流转捩区间的流动和振荡特性。假设在转捩区间径向脉动速度与充分发展区的湍流在数值上完全相同，在每一个截面上转捩流动可以看成是充分发展区的层流和湍流的合成流动。湍流成分的合成比例作为序参数用来定义合成流动。引入合成比例的振荡后，运用最小熵产生准则得到一个可以描述转捩行为的方程。采用相同的处理方法讨论了加热圆管内转捩区间的对流传热特性。在圆管内的流动和对流传热允许相似和独立的转捩过程，在转捩区间宏观振荡同时具有随机性和确定性。最后与实验进行了对比，包括流动和传热实验得到的测量结果。Abstract: The procedures for studying continuous phase transitions of thermodynamic equilibrium systems are extended to discuss the laminar-to-turbulent transitional flows in circular tubes. The flow in the transition range is treated as a composition of the laminar and turbulent flows assuming that the radial fluctuating velocity has the same value as that of the fully turbulent flow. The composite ratio of the turbulent flow is used as an order parameter to define the composite flow. The fluctuations of the composite ratios are introduced, and the criterion of minimum entropy production is used to derive an equation which can describe the transition behaviors. The convective heat transfer characteristics in the transition range in a heated circular tube are also discussed adopting the same procedures. Similar and separate processes for the transitions of the flow and convective heat transfer types are allowed in the heated circular tube. The macroscopic fluctuations in the transition range show both probabilistic and deterministic characteristics simultaneously. The agreements with measurements are given including those obtained in flow and heat transfer experiments.
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Key words:
- transition range /
- composite flow /
- fluctuations /
- minimum entropy production
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图 3 加热圆管内正十烷的密度、粘性系数和热传导系数以及流动的Re
Figure 3. Density, viscosity, thermal conductivity of the fluid and Re in the heated tube
表 1 二元混合物相变和圆管内流动转捩的对比
Table 1. Analogies between the phase transition of a binary mixture and the flow transition
系统 序参数 热力学函数 处理方法 二元混合物(平衡系统) 浓度x或其线性函数 自由能，混合自由能 混合自由能取极小值来确定x(Landau理论的精神) 一个截面上的流体微元(非平衡系统) 合成比例η或其线性函数 平均熵产生，平均合成熵产生 平均合成熵产生取极小值来确定η(利用了Landau理论的精神) 
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[1] Mullin T. Experimental studies of transition to turbulence in a pipe[J]. Annual Review of Fluid Mechanics, 2011, 43:1-24. doi: 10.1146/annurev-fluid-122109-160652 [2] Durst F, Ünsal B. Forced laminar-to-turbulent transition of pipe flows[J]. J Fluid Mech, 2006, 560:449-464. doi: 10.1017/S0022112006000528 [3] Darbyshire A G, Mullin T. Transition to turbulence in constant-mass-flux pipe flow[J]. J Fluid Mech, 1995, 289:83-114. doi: 10.1017/S0022112095001248 [4] Eckhardt B, Schneider T M, Hof B, et al. Turbulence transition in pipe flow[J]. Annual Review of Fluid Mechanics, 2007, 39:447-468. doi: 10.1146/annurev.fluid.39.050905.110308 [5] Reichl L E. A modern course in statistical physics[M]. New Jersey:John Wiley & Sons Inc, 1998. [6] Landau L D, Lifshitz E M. Statistical physics:part 1[M]. 3rd ed. Oxford:Pergamon Press, 1980. [7] McComb W D. The physics of fluid turbulence[M]. Oxford:Claredon Press, 1992. [8] Nishi M, Ünsal B, Durst F, et al. Laminar-to-turbulent transition of pipe flows through puffs and slugs[J]. J Fluid Mech, 2008, 614:425-446. doi: 10.1017/S0022112008003315 [9] Henkel M, Hinrichsen H, Lübeck S. Non-equilibrium phase tran-sitions, Volume Ⅰ:Absorbing phase transitions[M]. Netherlands:Canopus Academic Publishing Limited, 2008. [10] Cowan B. Topics in statistical mechanics[M]. London:Imperial College Press, 2005. [11] Huang K. Statistical mechanics[M]. New Jersey:John Wiley & Sons Inc, 1987. [12] Landau L D, Lifshitz E M. Fluid mechanics[M]. 2nd ed. Oxford:Pergamon Press, 1987. [13] Eckert E R G, Drake R M Jr. Analysis of heat and mass transfer[M]. Tokyo:McGraw-Hill Kogakusha Ltd, 1972. [14] Koch H, Tataru D. Well-posedness for the Navier-Stokes equations[J]. Adv Math, 2001, 157(1):22-35. http://d.old.wanfangdata.com.cn/OAPaper/oai_arXiv.org_1302.5785 [15] Durmagambetov A A, Fazilova L S. Navier-Stokes equations-millennium prize problems[J]. Natural Science, 2015, 7(2):54262. http://d.old.wanfangdata.com.cn/NSTLHY/NSTL_HYCC0215037970/ [16] Lifshitz E M, Pitaevskii L P. Statistical physics:part 2[M]. Oxford:Pergamon Press, 1980. [17] Glansdorff P, Prigogine I. Structure, stability, and fluctuations[M]. New Jersey:Wiley-Interscience, 1971. [18] Nicolis P, Prigogine I. Self-organization in nonequilibrium systems[M]. New Jersey:Wiley-Interscience, 1977. [19] Prigogine I. Time, structure, and fluctuations[J]. Science, 1978, 201:777-785. doi: 10.1126/science.201.4358.777 [20] Bergman T L, Lavine A S, Incropera F P, et al. Fundamentals of heat and mass transfer[M]. 7th ed. New Jersey:John Wiley & Sons Inc, 2011. [21] Rohsenow W M, Hartnett J P, Cho Y I. Handbook of heat transfer[M]. 3rd ed. New York:McGraw-Hill Book Company, 1998. [22] Zhang R L, Le J L. Natural laminar-to-turbulent transition inside an electrically heated circular tube[C]//Proc of AIP Conference Proceedings 1770: 030035. 2016. [23] 张若凌, 乐嘉陵.电加热圆管内流动的自然转捩过程研究[J].实验流体力学, 2017, 31(2):51-60. http://www.syltlx.com/CN/abstract/abstract11011.shtmlZhang R L, Le J L. Natural laminar-to-turbulent transition inside an electrically heated circular tube[J]. Journal of Experiments in Fluid Mechanics, 2017, 31(2):51-60. http://www.syltlx.com/CN/abstract/abstract11011.shtml [24] Nishi M. Laminar to turbulent transition in pipe flow through puffs and slugs[D]. Der Technischen Fakultät der Friedrich-Alexander-Universität Erlangen-Nürnberg, 2009. [25] Linne D L, Meyer M L, Edwards T, et al. Evaluation of heat transfer and thermal stability of supercritical JP-7 fuel[R]. AIAA-97-3041, 1997. [26] Huang H, Sobel D R, Spadaccini L J. Endothermic heat-sink of hydrocarbon fuels for scramjet cooling[R]. AIAA-2002-3871, 2002. [27] Zhang L, Zhang R L, Xiao S D, et al. Researches on heat transfer correlations of hydrocarbon fuel under supercritical pressure[J]. International Journal of Heat and Mass Transfer, 2013, 64:393-400. doi: 10.1016/j.ijheatmasstransfer.2013.04.058 -
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