内圆柱旋转的Taylor-Couette系统中冷水热对流的数值模拟

仝家炜; 曹玉会

doi:10.7523/j.ucas.2022.051

中国科学院大学学报 >

2024 , Vol. 41 >Issue 2: 176 - 187

DOI: https://doi.org/10.7523/j.ucas.2022.051

数学与物理学

内圆柱旋转的Taylor-Couette系统中冷水热对流的数值模拟

仝家炜 ,
曹玉会

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中国科学院大学工程科学学院, 北京 100049

收稿日期: 2022-03-28

修回日期: 2022-05-05

网络出版日期: 2022-05-05

基金资助

国家自然科学基金(52176025)资助

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Numerical simulation for thermal convection of cold water in the Taylor-Couette system with a rotating inner cylinder

TONG Jiawei ,
CAO Yuhui

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School of Engineering Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Received date: 2022-03-28

Revised date: 2022-05-05

Online published: 2022-05-05

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摘要

在内圆柱旋转的具有径向温度梯度的竖直环形腔中对10⁴≤Ra≤10⁶，Re≤150范围内不同密度倒置参数下冷水的热对流开展三维数值模拟研究。环形腔的内外半径比η=0.5，高宽比Γ=8。研究结果表明，在离心力和浮力的共同作用下冷水系统中产生了丰富的三维流态，且与常规Oberbeck-Boussinesq流体的流动特征有明显差异。此外，旋转系统中离心作用导致的流态转变能够显著增强腔体中部的局部传热，进而极大地提高系统整体传热性能。在较高转速条件下，Ra的增加有时会导致系统传热性能呈现非单调变化趋势。

关键词： 密度倒置; Taylor-Couette流动; 数值模拟; 传热

本文引用格式

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

Abstract

The thermal convection of cold water has attracted considerable attention due to its relevance to engineering applications, such as the phase change cool storage device. However, the natural convection of cold water in the vertical annulus inherently has a minimum heat transfer rate due to the density inversion phenomenon of water near 4 ℃. It is feasible to reduce the negative effect of density inversion phenomenon on convective heat transfer by imposing a slow axial rotation on the inner cylinder. In order to better understand the heat transfer enhancement induced by the low-speed rotation of inner cylinder, three-dimensional numerical simulation was carried out to investigate the thermal convection of cold water near its density maximum in a finite vertical annulus with a heated rotating inner cylinder over a wide range of Rayleigh and Reynolds numbers (10⁴≤Ra≤10⁶ and Re≤150) for various density inversion parameters. The radius ratio and aspect ratio of the annulus were 0.5 and 8, respectively. Results indicated that the combination of centrifugal and buoyancy forces led to multiple three-dimensional flow patterns in the cold water, which were distinct from the conventional Taylor-Couette flow under the Oberbeck-Boussinesq approximation. Furthermore, the transition of flow regimes in the rotating system was generally beneficial to heat transfer enhancement. However, at relatively high rotation speeds, the increase of Ra could result in the non-monotonic change of the overall heat transfer rate.

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

参考文献

[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] Viazzo S, Poncet S. Numerical simulation of the flow stability in a high aspect ratio Taylor-Couette system submitted to a radial temperature gradient[J]. Computers & Fluids, 2014, 101: 15-26. DOI:10.1016/j.compfluid.2014.05.025.
[3] Togun H, Abdulrazzaq T, Kazi S N, et al. A review of studies on forced, natural and mixed heat transfer to fluid and nanofluid flow in an annular passage[J]. Renewable and Sustainable Energy Reviews, 2014, 39: 835-856. DOI:10.1016/j.rser.2014.07.008.
[4] Lopez J M, Marques F, Avila M. The Boussinesq approximation in rapidly rotating flows[J]. Journal of Fluid Mechanics, 2013, 737: 56-77. DOI:10.1017/jfm.2013.558.
[5] 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.
[6] Snyder H A, Karlsson S K F. Experiments on the stability of Couette motion with a radial thermal gradient[J]. Physics of Fluids, 1964, 7(10): 1696-1706. DOI:10.1063/1.1711076.
[7] Ali M, Weidman P D. On the stability of circular Couette flow with radial heating[J]. Journal of Fluid Mechanics, 1990, 220: 53-84. DOI:10.1017/S0022112090003184.
[8] Yoshikawa H N, Nagata M, Mutabazi I. Instability of the vertical annular flow with a radial heating and rotating inner cylinder[J]. Physics of Fluids, 2013, 25(11): 114104. DOI:10.1063/1.4829429.
[9] 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.
[10] 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.
[11] 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.
[12] Kuo D C, Ball K S. Taylor-Couette flow with buoyancy: onset of spiral flow[J]. Physics of Fluids, 1997, 9(10): 2872-2884. DOI:10.1063/1.869400.
[13] Lepiller V, Goharzadeh A, Prigent A, et al. Weak temperature gradient effect on the stability of the circular Couette flow[J]. The European Physical Journal B, 2008, 61(4): 445-455. DOI:10.1140/epjb/e2008-00105-2.
[14] 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.
[15] Lopez J M, Marques F, Avila M. Conductive and convective heat transfer in fluid flows between differentially heated and rotating cylinders[J]. International Journal of Heat and Mass Transfer, 2015, 90: 959-967. DOI:10.1016/j.ijheatmasstransfer.2015.07.026.
[16] Kang C, Meyer A, Mutabazi I, et al. Radial buoyancy effects on momentum and heat transfer in a circular Couette flow[J]. Physical Review Fluids, 2017, 2(5): 053901. DOI:10.1103/PhysRevFluids.2.053901.
[17] 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.
[18] Li Y R, Hu Y P, Ouyang Y Q, et al. Flow state multiplicity in Rayleigh-Bénard convection of cold water with density maximum in a cylinder of aspect ratio 2[J]. International Journal of Heat and Mass Transfer, 2015, 86: 244-257. DOI:10.1016/j.ijheatmasstransfer.2015.01.147.
[19] Large E, Andereck C D. Penetrative Rayleigh-Bénard convection in water near its maximum density point[J]. Physics of Fluids, 2014, 26(9): 094101. DOI:10.1063/1.4895063.
[20] 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.
[21] Quintino A, Ricci E, Grignaffini S, et al. Heat transfer correlations for natural convection in inclined enclosures filled with water around its density-inversion point[J]. International Journal of Thermal Sciences, 2017, 116: 310-319. DOI:10.1016/j.ijthermalsci.2017.03.008.
[22] Seki N, Fukusako S, Nakaoka M. Experimental study on natural convection heat transfer with density inversion of water between two horizontal concentric cylinders[J]. Journal of Heat Transfer, 1975, 97(4): 556-561. DOI:10.1115/1.3450430.
[23] Nguyen T H, Vasseur P, Robillard L. Natural convection between horizontal concentric cylinders with density inversion of water for low Rayleigh numbers[J]. International Journal of Heat and Mass Transfer, 1982, 25(10): 1559-1568. DOI:10.1016/0017-9310(82)90034-5.
[24] Raghavarao C V, Sanyasiraju Y V S S. Natural convection heat transfer of cold water between concentric cylinders for high Rayleigh numbers:a numerical study[J]. International Journal of Engineering Science, 1994, 32(9): 1437-1450. DOI:10.1016/0020-7225(94)90122-8.
[25] 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.
[26] Li Y R, Hu Y P, Yuan X F. Three-dimensional numerical simulation of natural convection of water near its density maximum in a horizontal annulus[J]. International Journal of Thermal Sciences, 2013, 71: 274-282. DOI:10.1016/j.ijthermalsci.2013.04.023.
[27] Lin D S, Nansteel M W. Natural convection in a vertical annulus containing water near the density maximum[J]. Journal of Heat Transfer, 1987, 109(4): 899-905. DOI:10.1115/1.3248201.
[28] Ho C J, Lin Y H. Natural convection of cold water in a vertical annulus with constant heat flux on the inner wall[J]. Journal of Heat Transfer, 1990, 112(1): 117-123. DOI:10.1115/1.2910332.
[29] Ho C J, Tu F J. Transition to oscillatory natural convection of cold water in a vertical annulus[J]. International Journal of Heat and Mass Transfer, 1998, 41(11): 1559-1572. DOI:10.1016/S0017-9310(97)00224-X.
[30] Ho C J, Tu F J. Laminar mixed convection of cold water in a vertical annulus with a heated rotating inner cylinder[J]. Journal of Heat Transfer, 1992, 114(2): 418-424. DOI:10.1115/1.2911290.
[31] 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.
[32] 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.
[33] 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.
[34] Zhang Y, Cao Y H. A numerical study on the non-Boussinesq effect in the natural convection in horizontal annulus[J]. Physics of Fluids, 2018, 30(4): 040902. DOI:10.1063/1.5010864.
[35] 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.
[36] Tuliszka-Sznitko E, Kiełczewski K. The numerical simulation of Taylor-Couette flow with radial temperature gradient[C]//Journal of Physics: Conference Series. IOP Publishing, 2016, 760: 012035. DOI:10.1088/1742-6596/760/1/012035.
[37] Lopez J M, Marques F. Impact of centrifugal buoyancy on strato-rotational instability[J]. Journal of Fluid Mechanics, 2020, 890: A9. DOI:10.1017/jfm.2020.135.
[38] Czarny O, Serre E, Bontoux P, et al. Interaction of wavy cylindrical Couette flow with endwalls[J]. Physics of Fluids, 2004, 16(4): 1140-1148. DOI:10.1063/1.1652671.

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