Numerical simulation of asymmetric flow of coupled heat and mass transfer in a square cavity

doi:10.11949/0438-1157.20200694

Abstract

Abstract:

The heat and mass transfer of fluid in a square cavity with a solutal and thermal source is numerically investigated. For different Rayleigh numbers, buoyancy ratio, Soret and Dufour numbers, the bifurcation characteristics of heat and mass transfer in a symmetrical square cavity are studied systematically. The results show that there is a critical Ra_c for onset of bifurcation that changes the fluid flow pattern. When Ra < Ra_c, the streamline, temperature and concentration are symmetrically distributed; when Ra > Ra_c, the transition from a symmetrical state to a stable asymmetric state is observed. The fluid is more prone to bifurcation with increasing of buoyancy. An increment to the Soret and Dufour effects enhances heat transfer symmetry and increases the critical Rayleigh number for breaking symmetry.

Key words: double diffusion convection, coupling effect, mass and thermal source, symmetric solution, bifurcation

摘要：

对带有质热源的方腔内流体传热传质进行数值研究。针对不同Ra、Nc、Sr和Df，探究对称方腔内流体传热传质的分岔特性。结果表明：存在临界Ra_c使流体流动形态发生转变，当Ra<Ra_c时，流体流线、温度场和浓度场对称分布；当Ra>Ra_c时，流体发生偏斜。增大浮升力，流体更易发生分岔现象。增强Soret和Dufour效应可增强传热对称性并增大流体发生分岔的临界Rayleigh数。

关键词: 双扩散对流, 耦合作用, 质热源, 对称解, 分岔

CLC Number:

TK 124

Yubing LI, Mo YANG, Ruiying DENG, Tingkang LU, Zhenghua DAI. Numerical simulation of asymmetric flow of coupled heat and mass transfer in a square cavity[J]. CIESC Journal, 2020, 71(S2): 127-134.

李钰冰, 杨茉, 邓瑞英, 陆廷康, 戴正华. 方腔内耦合传热传质非对称流动数值模拟[J]. 化工学报, 2020, 71(S2): 127-134.

Figures/Tables 12

Fig.1 Physical model

Fig.2 Streamlines under different RaT

Fig.3 Streamlines under different RaS

Fig.4 Streamlines under different Ra (Nc=1，Df=Sr=0.1)

Fig.5 Temperature and concentration on top wall of square cavity at different Ra

Fig.6 Streamlines under Nc>-1

Fig.7 Temperature and concentration on top wall of the square cavity under Nc>-1

Fig.8 Temperature and concentration on bottom wall of square cavity under Nc<-1

Fig.9 Temperature and concentration on bottom wall of square cavity at different Sr (Df=0.1)

Fig.10 Temperature and concentration on bottom wall of square cavity at different Sr and Df

Fig.11 Critical Rayleigh number varies with Soret and Dufour numbers (Nc=1)

Fig.12 Critical Rayleigh number varies with buoyancy ratio

References 30

1	Yang M, Shen Y Y, Xu H T, et al. Numerical investigation of the nonlinear flow characteristics in an ultra-supercritical utility boiler furnace [J]. Applied Thermal Engineering, 2014, 88: 237-247.
2	刘丽娜, 杨茉, 王治云, 等. 扩缩通道内流动和换热非线性特性的数值模拟[J]. 上海理工大学学报, 2015, 37(5): 440-444.
	Liu L N, Yang M, Wang Z Y, et al. Nonlinear flow and heat transfer phenomena in a channel with sudden expansion followed by sudden contraction [J]. Journal of University of Shanghai for Science and Technology, 2015, 37(5): 440-444.
3	Zhang Z, Yang M, Zhang Y W. Numerical analysis of natural convection in a cylindrical envelope with an internal concentric cylinder with slots [J]. Numerical Heat Transfer, 2011, 59(10): 739-754.
4	Zhang K, Yang M, Zhang Y W. Two-and three-dimensional numerical simulations of natural convection in a cylindrical envelope with an internal concentric cylinder with slots [J]. International Journal of Heat and Mass Transfer, 2014, 70: 434-438.
5	Shen C Y, Yang M, Zhang Y W, et al. Effects of slotted structures on the nonlinear characteristics of natural convection in a cylinder with an internal concentric slotted annulus [J]. Numerical Heat Transfer, 2016, 70(5): 447-459.
6	Li Z, Yang M, Zhang Y W. Double MRT thermal lattice Boltzmann method for simulating natural convection of low Prandtl number fluids [J]. International Journal of Numerical Methods for Heat & Fluid Flow, 2016, 26(6):1889-1909.
7	Turner J S. Double-diffusive phenomena [J]. Annual Review of Fluid Mechanics, 1974, 6(1): 37-54.
8	Kamotani Y, Wang L W, Ostrach S, et al. Experimental study of natural convection in shallow enclosures with horizontal temperature and concentration gradients [J]. International Journal of Heat and Mass Transfer, 1985, 28(1): 165-173.
9	Jiang H D, Ostrach S, Kamotani Y. Unsteady thermosolutal transport phenomena due to opposed buoyancy forces in shallow enclosures [J]. Journal of Heat Transfer, 1991, 113(1): 135-140.
10	Xin S H, Le Quéré P, Tuckerman L S. Bifurcation analysis of double-diffusive convection with opposing horizontal thermal and solutal gradients [J]. Physics of Fluids, 1998, 10(4): 850-858.
11	Li Y R, Zhang H, Zhang L, et al. Three-dimensional numerical simulation of double-diffusive Rayleigh-Bénard convection in a cylindrical enclosure of aspect ratio 2 [J]. International Journal of Heat and Mass Transfer, 2016, 98: 472-483.
12	Altawallbeh A A, Bhadauria B S, Hashim I. Linear and nonlinear double-diffusive convection in a saturated anisotropic porous layer with Soret effect and internal heat source [J]. International Journal of Heat & Mass Transfer, 2013, 59(1):103-111.
13	Chen Z W, Li Y S, Zhan J M. Onset of oscillatory double-diffusive buoyancy instability in an inclined rectangular cavity [J]. International Journal of Heat and Mass Transfer, 2012, 55(13/14): 3633-3640.
14	Bergeon A, Ghorayeb K, Mojtabi A. Double diffusive instability in an inclined cavity [J]. Physics of Fluids, 1999, 11(3): 549-559.
15	Mamou M, Vasseur P, Bilgen E. Multiple solutions for double-diffusive convection in a vertical porous enclosure [J]. International Journal of Heat and Mass Transfer, 1995, 38(10): 1787-1798.
16	Wang J, Yang M, Zhang Y W. Coupling-diffusive effects on thermosolutal buoyancy convection in a horizontal cavity [J]. Numerical Heat Transfer, Part A: Applications, 2015, 68(6): 583-597.
17	Nithyadevi N, Yang R-J. Double diffusive natural convection in a partially heated enclosure with Soret and Dufour effects [J]. International Journal of Heat and Fluid Flow, 2009, 30(5): 902-910.
18	Ghachem K, Kolsi L, Mâatki C, et al. Numerical simulation of three-dimensional double diffusive free convection flow and irreversibility studies in a solar distiller [J]. International Communications in Heat & Mass Transfer, 2012, 39(6): 869-876.
19	Qin Q, Xia Z A, Tian Z F. High accuracy numerical investigation of double-diffusive convection in a rectangular enclosure with horizontal temperature and concentration gradients [J]. International Journal of Heat and Mass Transfer, 2014, 71: 405-423.
20	Xu H T, Wang T T, Qu Z G, et al. Lattice Boltzmann simulation of the double diffusive natural convection and oscillation characteristics in an enclosure filled with porous medium [J]. International Communications in Heat and Mass Transfer, 2017, 81: 104-115.
21	Xu H T, Luo Z, Lou Q, et al. Lattice Boltzmann simulations of the double-diffusive natural convection and oscillation characteristics in an enclosure with Soret and Dufour effects [J]. International Journal of Thermal Sciences, 2019, 136: 159-171.
22	Wang J, Yang M, He Y L, et al. Oscillatory double-diffusive convection in a horizontal cavity with Soret and Dufour effects [J]. International Journal of Thermal Sciences, 2016, 106: 57-69.
23	李钰冰, 杨茉, 陆廷康, 等. 具有质热源的方腔内对流传热传质及其非线性特性[J]. 化工学报, 2019, 70: 130-137.
	Li Y B, Yang M, Lu T K, et al. Study on heat and mass transfer and nonlinear characteristics with heat and mass source in cavity[J]. CIESC Journal, 2019, 70: 130-137.
24	Li Y B, Yang M, Li J, et al. Study on heat and mass transfer with heat and mass and nonlinear characteristics source in cavity [J]. Frontiers in Heat and Mass Transfer, 2019, 13: 11.
25	Gray D D, Giorgini A. The validity of the Boussinesq approximation for liquids and gases [J]. International Journal of Heat & Mass Transfer, 1976, 19(5): 545-551.
26	Barakos G, Mitsoulis E, Assimacopoulos D. Natural convection flow in a square cavity revisited: laminar and turbulent models with wall functions [J]. International Journal for Numerical Methods in Fluids, 1994, 18(7):695-719.
27	Béghein C, Haghighat F, Allard F. Numerical study of double-diffusive natural convection in a square cavity [J]. International Journal of Heat & Mass Transfer, 1992, 35(4):833-846.
28	Neofytou P, Drikakis D. Non-Newtonian flow instability in a channel with a sudden expansion [J]. Journal of Non-Newtonian Fluid Mechanics, 2003, 111(2/3):127-150.
29	蒋燕华, 杨茉, 郭春笋, 等. 文丘里管内非对称流动的数值模拟[J]. 化工学报, 2014, 65: 223-228.
	Jiang Y H, Yang M, Guo C S, et al. Numerical simulation of asymmetric flow in Venturi tube [J]. CIESC Journal, 2014, 65:223-228.
30	申春赟, 陆廷康, 戴正华, 等. 几何结构对圆内开缝圆自然对流的影响[J]. 化工学报, 2016, 67: 84-90.
	Shen C Y, Lu T K, Dai Z H, et al. Natural convection in cylinder with internal slotted annulus under different structures[J]. CIESC Journal, 2016, 67: 84-90.

[1]	JIANG Hao, CHEN Bingzhen. Research progress of chemical process stability analysis [J]. CIESC Journal, 2018, 69(1): 76-87.
[2]	PAN Duotao, SHI Hongyan, YUAN Decheng, XIU Zhilong. Analysis of metabolic oscillation processes in Saccharomyces cerevisiae [J]. CIESC Journal, 2017, 68(3): 964-969.
[3]	YU Minggao, WU Lijie, WAN Shaojie, ZHENG Kai. Inhibition characteristics on methane explosion flame propagation affected by charged water mist containing sodium chloride additive [J]. CIESC Journal, 2017, 68(11): 4445-4452.
[4]	LEI Zhen, WU Yingying, LU Shiqing, YANG Bolun. Mass Transfer Modeling in Pervaporation Based on Multi-fields Synergy Theory [J]. , 2008, 16(1): 79-83.
[5]	SHEN Wenhao, Vincent Van Brunt, XU Xianwen. DYNAMIC ANALYSIS OF GAS STRIPPING DURING ETHANOL FERMENTATION IN CSTR [J]. , 1996, 4(3): 236-245.
[6]	ZHU Jianhua, LIAO Hui, LI Shaofen. STEADY STATE MULTIPLICITY FEATURES OF ETHYLENE OXIDATION ON PLATINUM FOIL [J]. , 1993, 1(1): 1-9.