非等温Taylor-Couette系统内冷水的对流传热特性

doi:10.7523/j.ucas.2024.037

摘要/Abstract

摘要：

对内圆筒高温且旋转的Taylor-Couette系统内冷水的对流传热进行直接数值模拟，旨在探究密度倒置特性的影响。选用多个密度倒置参数，研究从自然对流到湍流的流态演化。结果表明，随着雷诺数的增大，流动经历了2次流态转变：第1次是从浮升力主导的大尺度环流转变为螺旋涡流，密度倒置效应越显著，轴向流动对径向热传输的抑制作用越强，在 $Θ m = 0.5$ 附近存在传热极小值；第2次流态转变发生在离心力主导的区域，流动由波状涡流发展为湍流波状涡，产生Görtler涡，有效增强了传热。从密度倒置效应、离心效应和浮力效应联合作用的角度探讨流态转变的物理机理。结果表明，密度倒置效应越强，浮力效应越弱，流动越易在较低雷诺数下提前进入离心力主导的流态。

关键词: 密度倒置, Taylor-Couette流动, 数值模拟, 对流传热

Abstract:

This paper conducts a direct numerical simulation of the convective heat transfer of cold water in a Taylor-Couette system with a high-temperature and rotating inner cylinder， aiming to elucidate the flow features and heat transfer characteristics under different density inversion parameters. For this purpose， multiple density inversion parameters were selected to study the evolution of flow states from natural convection to turbulence. By examining the hydrodynamic and thermal behaviors of cold water across various parameter variations， this paper reveals the diversity of flow regimes and the tight association between heat transfer characteristics and flow features. With the increase in Reynolds number， the flow undergoes two transitions. The initial transition is from a buoyancy-dominated regime to a spiral vortex flow. Pronounced density inversion effects intensify the axial flow’s suppression of radial heat transfer， manifesting a minimal value of heat transfer near $Θ m = 0.5$ . The subsequent transition occurs within the rotation-dominated regime， where the flow progresses from wavy vortex flow to wavy turbulent vortex， accompanied by the emergence of Görtler vortices and an increase in smaller-scale structures at elevated Reynolds numbers， thus enhancing heat transfer capability. The mechanisms behind flow regime transitions are explored from the perspective of the combined effects of density inversion， centrifugal force， and buoyancy. The results suggest that a marked density inversion effect weakens the buoyancy effect and strengthens the sensitivity to the centrifugal force， leading to an earlier onset of centrifugal-dominated flow at a lower Reynolds number.

Key words: density inversion, Taylor-Couette flow, numerical simulation, heat transfer

中图分类号:

TK124

李天昱, 曹玉会. 非等温Taylor-Couette系统内冷水的对流传热特性[J]. 中国科学院大学学报, 2026, 43(3): 326-335.

Tianyu LI, Yuhui CAO. Convection heat transfer of cold water in a non-isothermal Taylor-Couette system[J]. Journal of University of Chinese Academy of Sciences, 2026, 43(3): 326-335.

图/表 9

表 1 网格检验情况

Table 1 Grid independent test

$Θ m$	$R a$	$R e$	Mesh $N r × N θ × N z$	$κ e q i ¯ t$
0.5	$106$	1 500	M1: 96×160×160	14.021
			M2: 96×192×320	13.893
			M3: 96×240×480	13.842

表 1 网格检验情况

Table 1 Grid independent test

$Θ m$	$R a$	$R e$	Mesh $N r × N θ × N z$	$κ e q i ¯ t$
0.5	$106$	1 500	M1: 96×160×160	14.021
			M2: 96×192×320	13.893
			M3: 96×240×480	13.842

图1 r-z截面上的瞬时温度场和速度矢量注：上方数字对应Θm取值，黑色虚线表示密度极值线。

Fig.1 Instantaneous temperature field and velocity vector on a vertical cross-section

图2 瞬时周向速度等值面uθ=80

Fig.2 Instantaneous isosurface of azimuthal velocity uθ=80

图3 准周期振荡流动特征

Fig.3 Quasi-periodic oscillatory behaviors

图4 高Re下r=1.5处θ-z展开面上的瞬时uθ分布

Fig.4 Distribution of uθ under high Re values on the unwrapped θ-z plane at r=1.5

图5 高Re下的uθ在r-z截面上的分布

Fig.5 Distributions of uθ on r-z plane under relatively high Re values

图6 不同Re和Θm下的平均剖面图

Fig.6 Average profile obtained for various Re and Θm

图7 Re=2 500的温度脉动场

Fig.7 Temperature fluctuation field for Re=2 500

图8 传热性能随参数的变化

Fig.8 Variation in heat transfer performance with parameters

参考文献 32

[1]	Lappa M. Rotating thermal flows in natural and industrial processes［M］. Chichester， Sussex： John Wiley & Sons， 2012： 413-422. DOI：10.1002/9781118342411 .
[2]	Lian W L， Chang W M， Xuan Y M. Numerical investigation on flow and thermal features of a rotating heat pipe［J］. Applied Thermal Engineering， 2016， 101： 92-100. DOI： 10.1016/j.applthermaleng.2016.02.110 .
[3]	Donnelly R J. Taylor-Couette flow： the early days［J］. Physics Today， 1991， 44（11）： 32-39. DOI： 10.1063/1.881296 .
[4]	Lee Y N， Minkowycz W J. Heat transfer characteristics of the annulus of two coaxial cylinders with one cylinder rotating［J］. International Journal of Heat and Mass Transfer， 1989， 32（4）： 711-722. DOI： 10.1016/0017-9310（89）90218-4 .
[5]	Fénot M， Bertin Y， Dorignac E， et al. A review of heat transfer between concentric rotating cylinders with or without axial flow［J］. International Journal of Thermal Sciences， 2011， 50（7）： 1138-1155. DOI： 10.1016/j.ijthermalsci.2011.02.013 .
[6]	Vivès C. Effects of a forced Couette flow during the controlled solidification of a pure metal［J］. International Journal of Heat and Mass Transfer， 1988， 31（10）： 2047-2062. DOI： 10.1016/0017-9310（88）90116-0 .
[7]	Shi L， Hof B， Rampp M， et al. Hydrodynamic turbulence in quasi-Keplerian rotating flows［J］. Physics of Fluids， 2017， 29（4）： 044107. DOI： 10.1063/1.4981525 .
[8]	Rüdiger G， Seelig T， Schultz M， et al. The stratorotational instability of Taylor-Couette flows with moderate Reynolds numbers［J］. Geophysical & Astrophysical Fluid Dynamics， 2017， 111（6）： 429-447. DOI： 10.1080/03091929.2017.1382487 .
[9]	Andereck C D， Liu S S， Swinney H L. Flow regimes in a circular Couette system with independently rotating cylinders［J］. Journal of Fluid Mechanics， 1986， 164： 155-183. DOI： 10.1017/S0022112086002513 .
[10]	Lei Y， Farouk B. Three-dimensional mixed convection flows in a horizontal annulus with a heated rotating inner circular cylinder［J］. International Journal of Heat and Mass Transfer， 1992， 35（8）： 1947-1956. DOI： 10.1016/0017-9310（92）90197-Z .
[11]	Kang C， Yang K S， Mutabazi I. Thermal effect on large-aspect-ratio Couette-Taylor system： numerical simulations［J］. Journal of Fluid Mechanics， 2015， 771： 57-78. DOI： 10.1017/jfm.2015.151 .
[12]	Bilson M， Bremhorst K. Direct numerical simulation of turbulent Taylor-Couette flow［J］. Journal of Fluid Mechanics， 2007， 579： 227-270. DOI： 10.1017/S0022112007004971 .
[13]	Dong S. Direct numerical simulation of turbulent Taylor-Couette flow［J］. Journal of Fluid Mechanics， 2007， 587： 373-393. DOI： 10.1017/S0022112007007367 .
[14]	Ostilla-Mónico R， van der Poel E P， Verzicco R， et al. Boundary layer dynamics at the transition between the classical and the ultimate regime of Taylor-Couette flow［J］. Physics of Fluids， 2014， 26（1）： 015114. DOI： 10.1063/1.4863312 .
[15]	Snyder H A， Karlsson S K F. Experiments on the stability of Couette motion with a radial thermal gradient［J］. The Physics of Fluids， 1964， 7（10）： 1696-1706. DOI： 10.1063/1.1711076 .
[16]	Ball K S， Farouk B. On the development of Taylor vortices in a vertical annulus with a heated rotating inner cylinder［J］. International Journal for Numerical Methods in Fluids， 1987， 7（8）： 857-867. DOI： 10.1002/fld.1650070806 .
[17]	Ball K S， Farouk B， Dixit V C. An experimental study of heat transfer in a vertical annulus with a rotating inner cylinder［J］. International Journal of Heat and Mass Transfer， 1989， 32（8）： 1517-1527. DOI： 10.1016/0017-9310（89）90073-2 .
[18]	Ball K S， Farouk B. A flow visualization study of the effects of buoyancy on Taylor vortices［J］. Physics of Fluids A： Fluid Dynamics， 1989， 1（9）： 1502-1507. DOI： 10.1063/1.857328 .
[19]	Ball K S， Farouk B. Bifurcation phenomena in Taylor-Couette flow with buoyancy effects［J］. Journal of Fluid Mechanics， 1988， 197： 479-501. DOI： 10.1017/S0022112088003337 .
[20]	Teng H， Liu N S， Lu X Y， et al. Direct numerical simulation of Taylor-Couette flow subjected to a radial temperature gradient［J］. Physics of Fluids， 2015， 27（12）：125101. DOI： 10.1063/1.4935700 .
[21]	Khawar O， Baig M F， Sanghi S. Taylor-Couette flows undergoing orthogonal rotation subject to thermal stratification［J］. Physics of Fluids， 2021， 33（3）： 035107. DOI： 10.1063/5.0035546 .
[22]	Leng X Y， Zhong J Q. Mutual coherent structures for heat and angular momentum transport in turbulent Taylor-Couette flows［J］. Physical Review Fluids， 2022， 7（4）： 043501. DOI： 10.1103/PhysRevFluids.7.043501 .
[23]	Ho C J， Tu F J. An investigation of transient mixed convection heat transfer of cold water in a tall vertical annulus with a heated rotating inner cylinder［J］. International Journal of Heat and Mass Transfer， 1993， 36（11）： 2847-2859. DOI： 10.1016/0017-9310（93）90104-E .
[24]	Cao Y H， Tong J W. Rotating thermal flow of water near its density inversion point in a vertical annulus： flow regime transition and heat transfer enhancement［J］. International Journal of Heat and Mass Transfer， 2022， 199：123470.DOI： 10.1016/j.ijheatmasstransfer.2022.123470 .
[25]	仝家炜，曹玉会. 内圆柱旋转的Taylor-Couette系统中冷水热对流的数值模拟［J］. 中国科学院大学学报， 2024， 41（2）： 176-187. DOI： 10.7523/j.ucas.2022.051 .
[26]	Gebhart B， Mollendorf J C. A new density relation for pure and saline water［J］. Deep Sea Research， 1977， 24（9）： 831-848. DOI：10.1016/0146-6291（77）90475-1 .
[27]	Huang X J， Li Y R， Zhang L， et al. Turbulent Rayleigh-Bénard convection of cold water near its maximum density in a vertical cylindrical container［J］. International Journal of Heat and Mass Transfer， 2018， 116： 185-193. DOI： 10.1016/j.ijheatmasstransfer.2017.09.021 .
[28]	Li Y R， Yuan X F， Wu C M， et al. Natural convection of water near its density maximum between horizontal cylinders［J］. International Journal of Heat and Mass Transfer， 2011， 54（11/12）： 2550-2559. DOI： 10.1016/j.ijheatmasstransfer.2011.02.006 .
[29]	Wei T， Koster J N. Density inversion effect on transient natural convection in a rectangular enclosure［J］. International Journal of Heat and Mass Transfer， 1994， 37（6）： 927-938. DOI： 10.1016/0017-9310（94）90218-6 .
[30]	Shishkina O， Stevens R J A M， Grossmann S， et al. Boundary layer structure in turbulent thermal convection and its consequences for the required numerical resolution［J］. New Journal of Physics， 2010， 12（7）： 075022. DOI： 10.1088/1367-2630/12/7/075022 .
[31]	Usman M， Son J H， Park I S. A low-Rayleigh transition into chaos for natural convection inside a horizontal annulus at Prandtl number 0.1［J］. International Journal of Heat and Mass Transfer， 2021， 179： 121658. DOI： 10.1016/j.ijheatmasstransfer.2021.121658 .
[32]	Kedia R， Hunt M L， Colonius T. Numerical simulations of heat transfer in Taylor-Couette flow［J］. Journal of Heat Transfer， 1998， 120（1）： 65-71. DOI： 10.1115/1.2830066 .