耦合表面张力的封闭腔体内管外自然对流传热特性

doi:10.16085/j.issn.1000-6613.2020-1055

摘要/Abstract

摘要：

采用格子-玻尔兹曼方法（LBM）构建了考虑表面张力影响下封闭腔体内加热圆柱外自然对流数学模型。在分别对自然对流与表面张力模型模拟验证的基础上，探究了液固表面张力与重力场下浮升力同时作用下加热圆柱外流体自然对流的传热特性。结果表明，在给定Ra数下（10³≤Ra≤10⁶），随着表面张力的增大（Oh数减小），封闭腔体内管外自然对流扰动会加剧，流型会变复杂，壁面换热效率有明显提高。在Ra数为10⁵，长度比（加热圆柱半径和方腔长度之比）为1/10情况下，加入表面张力σ=0.076302N/mm（Oh=0.122），腔体左侧壁面平均努塞尔数和加热圆柱壁面与未加表面张力相比分别提高了93.5%和60.35%。当表面张力大小和自然对流的浮升力相当时，此时的流场波动更加明显剧烈，在一定范围内增大浮升力反而减弱换热。

关键词: 格子Boltzmann方法, 自然对流, 加热腔体, 表面张力, 数值模拟, 传热

Abstract:

A mathematical model of natural convection outside a heated cylinder in a closed cavity under the influence of surface tension is established by using the lattice Boltzmann method (LBM). Firstly, the model of natural convection and surface tension is verified, and then the heat transfer characteristics of natural convection of heated fluid outside the cylinder under the simultaneous action of surface tension of liquid and solid, and buoyancy force of gravity field are studied. Finally, the simulation results show that with the increase of surface tension (Oh number decreases), the disturbance of natural convection inside and outside the closed cavity will be intensified, the flow pattern will become more complicated, and the heat transfer coefficient of the wall will be improved obviously.When the Ra number is 10⁵ and the surface tension σ=0.076302N/mm (Oh=0.122) is added, the averaged Nusselt number on the left wall of the cavity and the heated cylinder wall are 93.5% and 60.35% higher than those without surface tension In addition, when the surface tension is equal to the buoyancy force of natural convection, the flow fluctuation is more obvious and violent, and in this case the increasing the buoyancy force within a certain range may weaken the heat transfer.

Key words: lattice boltzmann method, natural convection, heating chamber, surface tension, numerical simulation, heat transfer

中图分类号:

TK124

苗国民, 雷海燕, 戴传山, 马非. 耦合表面张力的封闭腔体内管外自然对流传热特性[J]. 化工进展, 2020, 39(S2): 26-35.

Guomin MIAO, Haiyan LEI, Chuanshan DAI, Fei MA. Natural convection heat transfer characteristics of coupled surface tension outside the tube in a closed cavity[J]. Chemical Industry and Engineering Progress, 2020, 39(S2): 26-35.

图/表 15

图1 腔体内加热圆柱自然对流模型示意图

图2 两类直接力点的速度插值

图3 偏置圆管自然对流的等温线图对比

图4 偏置圆管自然对流的流函数图对比

图5 偏置圆管自对流的左侧壁面局部Nu数的对比

图6 表面张力的拉普拉斯方程

图7 不同奥内佐格数下的等温线图

图8 不同奥内佐格数下的流函数图

图9 不同Oh数下加热圆柱壁面局部Nu数随角度的变化

图10 不同奥内佐格数下的腔体左侧壁面局部Nu数曲线对比

表1 不同Oh数下圆柱表面和左侧壁面平均Nu数表

Oh数	圆柱表面平均Nu数	左侧壁面平均Nu数
∞	1.014	1.466
0.388	1.073	1.508
0.122	1.625	2.837

图11 不同瑞利数下的等温线图

图12 不同瑞利数下的流函数图

图13 不同瑞利数下腔体左侧壁面局部Nu数的对比

表2 不同Ra数下圆柱表面和左侧壁面平均Nu数表

Ra数	圆柱表面平均Nu数	方腔左侧壁面平均Nu数
10³	1.213	2.124
10⁴	1.193	1.986
10⁵	1.625	2.837
10⁶	2.0478	3.914

参考文献 38

1	NARAHARI M, SURESH Kumar Raju S, PENDYALA R. Unsteady natural convection flow of multi-phase nanofluid past a vertical plate with constant heat flux[J]. Chemical Engineering Science, 2017, 167: 229-241.
2	LU Y W, LI X L, DU W B, et al. Laminar natural convection heat transfer characteristics of molten salt around horizontal cylinder[J]. Energy Procedia, 2015, 69: 681-688.
3	ZHANG T, CHE D. Double MRT thermal lattice Boltzmann simulation for MHD natural convection of nanofluids in an inclined cavity with four square heat sources[J]. International Journal of Heat and Mass Transfer., 2016, 94: 87-100.
4	CHEN W R. A numerical study of laminar free convection heat transfer between inner sphere and outer vertical cylinder[J]. International Journal of Heat and Mass Transfer., 2007, 50(13/14): 2656-2666.
5	IYI D, HASAN R. Natural convection flow and heat transfer in an enclosure containing staggered arrangement of blockages[J]. Procedia Engineering, 2015, 105: 176-183.
6	BAÏRI A, ZARCO-PERNIA E, GARCÍA De María J M. A review on natural convection in enclosures for engineering applications. the particular case of the parallelogrammic diode cavity[J]. Applied Thermal Engineering, 2014, 63(1): 304-322.
7	XU D, HU Y, LI D. A lattice Boltzmann investigation of two-phase natural convection of Cu-water nanofluid in a square cavity[J]. Case Studies in Thermal Engineering, 2019, 13: 100358.
8	LEPORINI M, CORVARO F, MARCHETTI B, et al. Experimental and numerical investigation of natural convection in tilted square cavity filled with air[J]. Experimental Thermal and Fluid Science, 2018, 99: 572-583.
9	CIANFRINI C, CORCIONE M, HABIB E. Free convection heat transfer from a horizontal cylinder affected by a downstream parallel cylinder of different diameter[J]. International Journal of Thermal Sciences, 2006, 45(9): 923-931.
10	VAROL Y, OZTOP H F, KOCA A, et al. Natural convection and fluid flow in inclined enclosure with a corner heater[J]. Applied Thermal Engineering, 2009, 29(2/3): 340-350.
11	EL-GENDI M M. Numerical simulation of unsteady natural convection flow inside a pattern of connected open square cavities[J]. International Journal of Thermal Sciences, 2018, 127: 373-383.
12	Ö ATAYILMAZ S. Experimental and numerical study of natural convection heat transfer from horizontal concentric cylinders[J]. International Journal of Thermal Sciences, 2011, 50(8): 1472-1483.
13	SONDUR S, MESCHER A M. Investigation on the stability of natural convection in an annular cavity with non-isothermal walls[J]. Experimental Thermal and Fluid Science, 2020, 115: 110053.
14	KHATAMIFAR M, LIN W, ARMFIELD S W, et al. Conjugate natural convection heat transfer in a partitioned differentially-heated square cavity[J]. International Communications in Heat and Mass Transfer., 2017, 81: 92-103.
15	SALEH H, ARBIN N, ROSLAN R, et al. Visualization and analysis of surface tension and cooling effects on differentially heated cavity using heatline concept[J]. International Journal of Heat and Mass Transfer., 2012, 55(21/22): 6000-6009.
16	EL-GENDI M M, ALLAH A ALY ABD. Numerical simulation of natural convection using unsteady compressible navier-stokes equations[J]. International Journal of Numerical Methods for Heat & Fluid Flow, 2017, 27(11): 2508-2527.
17	ALSABERY A I, MOHEBBI R, CHAMKHA A J, et al. Effect of local thermal non-equilibrium model on natural convection in a nanofluid-filled wavy-walled porous cavity containing inner solid cylinder[J]. Chemical Engineering Science, 2019, 201: 247-263.
18	YAGHOUBI EMAMI R, SIAVASHI M, SHAHRIARI MOGHADDAM G. The effect of inclination angle and hot wall configuration on Cu-water nanofluid natural convection inside a porous square cavity[J]. Advanced Powder Technology, 2018, 29(3): 519-536.
19	WANG L, SHI B, CHAI Z. Effects of temperature-dependent properties on natural convection of nanofluids in a partially heated cubic enclosure[J]. Applied Thermal Engineering, 2018, 128: 204-213.
20	WANG L, HUANG C, YANG X, et al. Effects of temperature-dependent properties on natural convection of power-law nanofluids in rectangular cavities with sinusoidal temperature distribution[J]. International Journal of Heat and Mass Transfer., 2019, 128: 688-699.
21	HONG C, ASAKO Y, SUZUKI K. Convection heat transfer in concentric micro annular tubes with constant wall temperature[J]. International Journal of Heat and Mass Transfer., 2011, 54(25-26): 5242-5252.
22	LEE T S, HU G S, SHU C. Application of GDQ method for the study of natural convection in horizontal eccentric annuli[J]. Numerical Heat Transfer., 2002, 41: 803-815.
23	SELIMEFENDIGIL F, ÖZTOP H F. Numerical study and identification of cooling of heated blocks in pulsating channel flow with a rotating cylinder[J]. International Journal of Thermal Sciences, 2014, 79: 132-145.
24	HUSAIN S, SIDDIQUI M A. Experimental and numerical analysis of transient natural convection of water in a high aspect ratio narrow vertical annulus[J]. Progress in Nuclear Energy, 2018, 106: 1-10.
25	LEE J M, HA M Y, YOON H S. Natural convection in a square enclosure with a circular cylinder at different horizontal and diagonal locations[J]. International Journal of Heat and Mass Transfer., 2010, 53(25-26): 5905-5919.
26	FATTAHI E, FARHADI M, SEDIGHI K. Lattice Boltzmann simulation of natural convection heat transfer in eccentric annulus[J]. International Journal of Thermal Sciences, 2010, 49(12): 2353-2362.
27	KANG S K, HASSAN Y A. A comparative study of direct-forcing immersed boundary-lattice Boltzmann methods for stationary complex boundaries[J]. International Journal for Numerical Methods in Fluids, 2011, 66(9): 1132-1158.
28	DAI C S, LI M, LEI H Y, et al. Numerical simulation of natural convection between hot and cold microtubes in a cylinder enclosure[J]. International Journal of Thermal Sciences, 2015, 95: 115-122.
29	LI G, YANG S. Thermodynamic analysis of free convection film condensation on an elliptical cylinder[J]. Journal of the Chinese Institute of Engineers, 2006, 29(5): 903-908.
30	JANSSENS S D, CHAURASIA V, FRIED E. Effect of a surface tension imbalance on a partly submerged cylinder[J]. Journal of Fluid Mechanics, 2017, 830: 369-386.
31	KOZHEVNIKOV D A, SHEREMET M A. Natural convection with evaporation in a vertical cylindrical cavity under the effect of temperature-dependent surface tension[J]. Continuum Mechanics and Thermodynamics, 2018, 30(1): 83-94.
32	LU J H, LEI H Y, DAI C S. A unified thermal lattice Boltzmann equation for conjugate heat transfer problem[J]. International Journal of Heat and Mass Transfer., 2018, 126: 1275-1286.
33	LU J H, LEI H Y, DAI C S. A simple difference method for lattice Boltzmann algorithm to simulate conjugate heat transfer[J]. International Journal of Heat and Mass Transfer., 2017, 114: 268-276.
34	KANG S K, HASSAN Y A. A direct-forcing immersed boundary method for the thermal lattice Boltzmann method[J]. Computers & Fluids, 2011, 49(1): 36-45.
35	郭照立, 郑楚光. 格子Boltzmann方法的原理及应用[M]. 北京: 科学出版社, 2008: 72.
	GUO Zhaoli, ZHENG Chuguang. The principle and application of lattice Boltzmann method [M].Beijing: Science Press, 2008: 72.
36	MORRIS J P. Simulating surface tension with smoothed particle hydrodynamics[J]. International Journal for Numerical Methods in Fluids, 2000, 33: 333-353.
37	TARTAKOVSKY A, MEAKIN P. Modeling of surface tension and contact angles with smoothed particle hydrodynamics[J]. Physical Review E, 2005, 72(2): 026301.
38	MARTYS N S, CHEN H, Simulation of multicomponent fluids in complex three-dimensional geometries by the lattice Boltzmann method[J]. Physical Review E, 1996, 53(1): 743-750.

[1]	肖辉, 张显均, 兰治科, 王苏豪, 王盛. 液态金属绕流管束流动传热进展[J]. 化工进展, 2023, 42(S1): 10-20.
[2]	王太, 苏硕, 李晟瑞, 马小龙, 刘春涛. 交流电场中贴壁气泡的动力学行为[J]. 化工进展, 2023, 42(S1): 133-141.
[3]	赵晨, 苗天泽, 张朝阳, 洪芳军, 汪大海. 负压状态窄缝通道乙二醇水溶液传热特性[J]. 化工进展, 2023, 42(S1): 148-157.
[4]	陈匡胤, 李蕊兰, 童杨, 沈建华. 质子交换膜燃料电池气体扩散层结构与设计研究进展[J]. 化工进展, 2023, 42(S1): 246-259.
[5]	郭强, 赵文凯, 肖永厚. 增强流体扰动强化变压吸附甲硫醚/氮气分离的数值模拟[J]. 化工进展, 2023, 42(S1): 64-72.
[6]	邵博识, 谭宏博. 锯齿波纹板对挥发性有机物低温脱除过程强化模拟分析[J]. 化工进展, 2023, 42(S1): 84-93.
[7]	陈林, 徐培渊, 张晓慧, 陈杰, 徐振军, 陈嘉祥, 密晓光, 冯永昌, 梅德清. 液化天然气绕管式换热器壳侧混合工质流动及传热特性[J]. 化工进展, 2023, 42(9): 4496-4503.
[8]	刘炫麟, 王驿凯, 戴苏洲, 殷勇高. 热泵中氨基甲酸铵分解反应特性及反应器结构优化[J]. 化工进展, 2023, 42(9): 4522-4530.
[9]	赵曦, 马浩然, 李平, 黄爱玲. 错位碰撞型微混合器混合性能的模拟分析与优化设计[J]. 化工进展, 2023, 42(9): 4559-4572.
[10]	卜治丞, 焦波, 林海花, 孙洪源. 脉动热管计算流体力学模型与研究进展[J]. 化工进展, 2023, 42(8): 4167-4181.
[11]	汪健生, 张辉鹏, 刘雪玲, 傅煜郭, 朱剑啸. 多孔介质结构对储层内流动和换热特性的影响[J]. 化工进展, 2023, 42(8): 4212-4220.
[12]	王云刚, 焦健, 邓世丰, 赵钦新, 邵怀爽. 冷凝换热与协同脱硫性能实验分析[J]. 化工进展, 2023, 42(8): 4230-4237.
[13]	叶振东, 刘涵, 吕静, 张亚宁, 刘洪芝. 基于钙镁二元盐的热化学储能反应器的性能优化[J]. 化工进展, 2023, 42(8): 4307-4314.
[14]	俞俊楠, 俞建峰, 程洋, 齐一搏, 化春键, 蒋毅. 基于深度学习的变宽度浓度梯度芯片性能预测[J]. 化工进展, 2023, 42(7): 3383-3393.
[15]	单雪影, 张濛, 张家傅, 李玲玉, 宋艳, 李锦春. 阻燃型环氧树脂的燃烧数值模拟[J]. 化工进展, 2023, 42(7): 3413-3419.