Flow Patterns in Three-dimensional Lid-driven Cavities with Curved Boundary: MRT-LBM Study

doi:10.19596/j.cnki.1001-246x.8447

Abstract

Abstract:

D3Q15 model of multi-relaxation time lattice Boltzmann method(MRT-LBM) is applied to simulate flow in three-dimensional lid-drive cavities with different curved boundaries, including rectangular cavity, cylindrical cavity, semi-cylinder cavity, rotating hyperboloid cavity, ellipsoid cavity, hemisphere cavity and two combined cavities. Streamlines, velocity contours and vortex positions of these cavities are analyzed. Flow characteristics of typical cavities with various Reynolds numbers are compared. It shows that under same Reynolds numbers the curved boundary eliminates the second and third vortices caused by the boundary. It leads to the separation of the main vortex in the cavity and increases the vertical reflux velocity of the central profile. Streamlines of the combined cavity with cuboid up semi-cylinder are fit most with the boundary. As the Reynolds number is increasing, the main vortex in the semi-cylindrical cavity separates gradually into two homodromous vortices, and the basic flow characteristics of the cylindrical cavity and the hemispheric cavity are always maintained in the cavity with cylinder up hemisphere; While the main vortex center in the cuboid cavity remains at the same height, the secondary vortex is gradually enhanced, and the flow in the cavity becomes more and more regular in the combined cavity with cuboid up semi-cylinder, the main vortex gradually sinks, and the flow velocity is smaller at the center and is greater near the boundary in the combined cavity with cuboid up semi-cylinder.

Key words: lattice Boltzmann method, multi-relaxation time, lid-drive, cavity with curved boundary

Qiao-ling ZHANG, He-fang JING. Flow Patterns in Three-dimensional Lid-driven Cavities with Curved Boundary: MRT-LBM Study[J]. Chinese Journal of Computational Physics, 2022, 39(4): 427-439.

Figures/Tables 13

References 28

1	CHANG L. Experimental study of the three-dimensional lid-drive cavity flow of the high Reynolds number[D]. Tianjin: Tianjin University, 2014.
2	HAN S L , ZHU P , LIN Z Q . The square cavity top cover drive flow is simulated based on the grid Boltzmann method[J]. China Mechanical Engineering, 2005, 16 (1): 66- 68.
3	CAO X Q , GAO D Y , WEN X T , et al. The Boltzmann method simulates the height-to-width ratio of the cavity top cover to drive the flow[J]. Journal of Nanjing School of Engineering (Natural Science Edition), 2018, 16 (3): 1- 6.
4	YANG F , SHI X M , LIU L G . Two-dimensional top cover drives flow MRT-LBM in semicircle cavity study[J]. Journal of Engineering Thermophysics, 2012, 33 (4): 595- 598.
5	MENDU S S , DAS P K . Fluid flow in a cavity driven by an oscillating lid: A simulation by lattice Boltzmann method[J]. European Journal of Mechanics B: Fluids, 2013, 39 (3): 59- 70.
6	DONG D B , SHI S J , HOU Z X , et al. Numerical simulation of viscous flow in a 3D lid-driven cavity using lattice Boltzmann method[J]. Applied Mechanics and Materials, 2014, 444, 395- 420.
7	SOUAYEH B , ALFANNAKH H A , MUTAIRI M . Natural convection in a square enclosure with a conducting rectangular shape positioned at different horizontal locations[J]. High Temperature, 2019, 57 (4): 539- 546. DOI
8	GONZALEZ L M , FERRER E , DIAZ-OJEDA H R . Onset of three-dimensional flow instabilities in lid-driven circular cavities[J]. Physics of Fluids, 2017, 29 (6): 71- 82.
9	HE Y L , WANG Y , LI Q . Lattice Boltzmann method: Theory and applications[M]. Beijing: Science Press, 2008.
10	LALLEMAND P , LUO L . Theory of the lattice Boltzmann method: Dispersion, dissipation, isotropy, Galilean invariance, and stability[J]. Physical Review E, 2000, 61 (6): 6546- 6562. DOI
11	HOU S , ZOU Q , CHEN S , et al. Simulation of cavity flow by the lattice Boltzmann method[J]. Journal of Computational Physics, 1995, 118, 329- 347. DOI
12	D'HUMIERES D , GINZBURG I , KRAFCZYK M , et al. Multiple-relaxation-time lattice Boltzmann models in three dimensions[J]. Philosophical Transactions: Mathematical, Physical and Engineering Sciences, 2002, 360 (1792): 436- 451.
13	LI W , ZHAO Y S . Mixed finite analysis solution of 3D square cavity flow[J]. Hydrodynamics Research and Progress, 1994, (3): 308- 317.
14	WANG J F , WANG D C . Numerical simulation of 3D lid-driven cubic cavity flow by two kinds of schemes with finite element method[J]. Hydrodynamics Research and Progress, 2014, (5): 511- 523.
15	WU J , SHAO Y . Simulation of lid-driven cavity flows by parallel lattice Boltzmann method using multi-relaxation time scheme[J]. International Journal for Numerical Methods in Fluids, 2004, 46 (9): 921- 937. DOI
16	QIAN Y , D'HUMIERES D , LALLEMAND P . Lattice BGK models for Naver-Stockes equation[J]. Europhysics Letters, 1992, 17 (6): 479- 484. DOI
17	ARUN S , SATHEESH A . Analysis of flow behaviour in a two sided lid driven cavity using lattice Boltzmann technique[J]. Alexandria Engineering Journal, 2015, 54 (4): 795- 806. DOI
18	KEFAYATI GH R , TANG H . MHD mixed convection of viscoplastic fluids in different aspect ratios of a lid-driven cavity using LBM[J]. International Journal of Heat and Mass Transfer, 2018, 124, 344- 367.
19	STHAVISHTHA B R , PERUMAL D A , YADAV A K . Computation of fluid flow in double sided cross-shaped lid-driven cavities using Lattice Boltzmann method[J]. European Journal of Mechanics B: Fluids, 2018, 70 (1): 46- 72.
20	SOROUSH F K , HOJJAT K N , HAMID N . Numerical study of free-fall cylinder water entry using an efficient three-phase lattice Boltzmann method with automatic interface capturing capability[J]. Ocean Engineering, 2021, 235, 309- 328.
21	AIDUN C K , CLAUSEN J R . Lattice-Boltzmann method for complex flows[J]. Annual Review of Fluid Mechanics, 2010, 42, 439- 472.
22	FELDMAN Y , GELFGATA A . Oscillatory instability of a three-dimensional lid-driven flow in a cube[J]. Physics of Fluids, 2010, 22 (9): 293- 298.
23	DE S . Simulation of laminar flow in a three-dimensional lid-driven cavity by lattice Boltzmann method[J]. International Journal of Numerical Methods for Heat & Fluid Flow, 2009, 19 (6): 790- 815.
24	NAZARAFKAN H , MEHMANDOUST B , TOGHRAIE D , et al. Numerical study of natural convection of nanofluid in a semi-circular cavity with lattice Boltzmann method[J]. International Journal of Numerical Methods for Heat & Fluid Flow, 2020, 30 (5): 342- 410.
25	ASLAN E , TAYMAZ I , BENIM A C . Investigation of LBM curved boundary treatments for unsteady flows[J]. European Journal of Mechanics B: Fluids, 2015, 51, 129- 151.
26	NEMATI M A , TOGHRAI D , KARIMIPOUR A . Numerical investigation of the pseudopotential lattice Boltzmann modeling of liquid-vapor for multi-phase flows[J]. Statistical Mechanics and Its Applications, 2018, 489, 65- 77.
27	NEMATI H , FARHAD M , SEDIGHI K , et al. Lattice Boltzmann simulation of nanofluid in lid-driven cavity[J]. International Communications in Heat and Mass Transfer, 2010, 37 (10): 1528- 1534.
28	ZHE F , LIM H . Multi-relaxation time lattice Boltzmann simulations of oscillatory instability in lid-driven flows of 2D semi-elliptical cavity[J]. Journal of Visualization, 2019, 22 (6): 1057- 1070.

模型	c_s/c	c_i/c	ω_i
D3Q15	$ 1 / \sqrt{3} $	(0, 0, 0)	2/9 (i = 0)
		(±1, 0, 0), (0, ±1, 0), (0, 0, ±1)	1/9 (i = 1~6)
		(±1, ±1, ±1)	1/72 (i = 7~14)
D3Q19	$ 1 / \sqrt{3} $	(0, 0, 0)	1/3 (i = 0)
		(±1, 0, 0), (0, ±1, 0), (0, 0, ±1)	1/18 (i = 1~6)
		(±1, ±1, 0), (±1, 0, ±1), (0, ±1, ±1)	1/36 (i = 7~18)
D3Q27	$ 1 / \sqrt{3} $	(0, 0, 0)	8/27 (i = 0)
		(±1, 0, 0), (0, ±1, 0), (0, 0, ±1)	2/27 (i = 1~6)
		(±1, ±1, 0), (±1, 0, ±1), (0, ±1, ±1)	1/54 (i = 7~18)
		(±1, ±1, ±1)	1/216 (i = 19~26)

模型	c_s/c	c_i/c	ω_i
D3Q15	$ 1 / \sqrt{3} $	(0, 0, 0)	2/9 (i = 0)
		(±1, 0, 0), (0, ±1, 0), (0, 0, ±1)	1/9 (i = 1~6)
		(±1, ±1, ±1)	1/72 (i = 7~14)
D3Q19	$ 1 / \sqrt{3} $	(0, 0, 0)	1/3 (i = 0)
		(±1, 0, 0), (0, ±1, 0), (0, 0, ±1)	1/18 (i = 1~6)
		(±1, ±1, 0), (±1, 0, ±1), (0, ±1, ±1)	1/36 (i = 7~18)
D3Q27	$ 1 / \sqrt{3} $	(0, 0, 0)	8/27 (i = 0)
		(±1, 0, 0), (0, ±1, 0), (0, 0, ±1)	2/27 (i = 1~6)
		(±1, ±1, 0), (±1, 0, ±1), (0, ±1, ±1)	1/54 (i = 7~18)
		(±1, ±1, ±1)	1/216 (i = 19~26)

腔体类型	X_max	Y_max	Z_max	SL	腔体特殊参数
长方体腔	56	56	28	2.02
圆柱腔			28	2.02	底面直径=56；高度=28
半圆柱腔			28	1.57	底面直径=56；高度=56
旋转双曲面腔			20	1.18	实半轴=2；虚半轴=3
旋转椭球面腔			20	2.81	长半轴=28；短半轴=20
半球腔			28	1.57	直径=56
“上圆柱+下半球”腔			56	2.57	圆柱高=28；半球高=28
“上长方体+下半圆柱”腔			56	2.57	长方体高=28；半圆柱高=28

腔体类型	X_max	Y_max	Z_max	SL	腔体特殊参数
长方体腔	56	56	28	2.02
圆柱腔			28	2.02	底面直径=56；高度=28
半圆柱腔			28	1.57	底面直径=56；高度=56
旋转双曲面腔			20	1.18	实半轴=2；虚半轴=3
旋转椭球面腔			20	2.81	长半轴=28；短半轴=20
半球腔			28	1.57	直径=56
“上圆柱+下半球”腔			56	2.57	圆柱高=28；半球高=28
“上长方体+下半圆柱”腔			56	2.57	长方体高=28；半圆柱高=28

腔体形状	y/Y_max= 0.15	y/Y_max= 0.3	y/Y_max= 0.38	y/Y_max= 0.5
长方体腔	(0.77, 0.15, 0.55)	(0.68, 0.30, 0.58)	(0.59, 0.38, 0.58)	(0.54, 0.50, 0.58)
圆柱腔	(0.70, 0.15, 0.62)	(0.65, 0.30, 0.45)	(0.33, 0.38, 0.41)	(0.25, 0.50, 0.38)
半圆柱腔	(0.70, 0.15, 0.52)	(0.58, 0.30, 0.66)	(0.50, 0.38, 0.60)	(0.33, 0.50, 0.59)
旋转双曲面腔	(0.49, 0.15, 0.74)	(0.58, 0.30, 0.71)	(0.60, 0.38, 0.78)	(0.65, 0.50, 0.79)
旋转椭球面腔(主涡)		(0.66, 0.30, 0.48)	(0.66, 0.38, 0.86)	(0.93, 0.50, 0.88)
旋转椭球面腔(次涡)		(0.65, 0.30, 0.81)	(0.87, 0.38, 0.79)
半球腔(主涡)	(0.53, 0.15, 0.39)	(0.49, 0.30, 0.53)	(0.49, 0.38, 0.53)	(0.92, 0.50, 0.93)
半球腔(次涡)			(0.59, 0.38, 0.73)
“圆柱+半球”腔(主涡)	(0.67, 0.15, 0.49)	(0.56, 0.30, 0.44)	(0.56, 0.38, 0.42)	(0.30, 0.50, 0.74)
“圆柱+半球”腔(次涡)			(0.36, 0.38, 0.75)	(0.90, 0.50, 0.92)
“长方体+半圆柱”腔	(0.60, 0.15, 0.72)	(0.51, 0.30, 0.54)	(0.51, 0.38, 0.42)	(0.51, 0.50, 0.39)