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Research Papers: Evaporation, Boiling, and Condensation

Coupled Lattice Boltzmann and Meshless Simulation of Natural Convection in the Presence of Volumetric Radiation

[+] Author and Article Information
Kang Luo, Qing Ai

School of Energy Science and Engineering,
Harbin Institute of Technology,
Harbin 150001, China

Hong-Liang Yi

School of Energy Science and Engineering,
Harbin Institute of Technology,
Harbin 150001, China
e-mail: yihongliang@hit.edu.cn

He-Ping Tan

School of Energy Science and Engineering,
Harbin Institute of Technology,
Harbin 150001, China
e-mail: tanheping@hit.edu.cn

1Corresponding authors.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received September 6, 2014; final manuscript received May 7, 2015; published online July 21, 2015. Assoc. Editor: Zhuomin Zhang.

J. Heat Transfer 137(11), 111504 (Jul 21, 2015) (12 pages) Paper No: HT-14-1589; doi: 10.1115/1.4030904 History: Received September 06, 2014

In this work, the coupled lattice Boltzmann and direct collocation meshless (LB–DCM) method is introduced to solve the natural convection in the presence of volumetric radiation in irregular geometries. LB–DCM is a hybrid approach based on a common multiscale Boltzmann-type model. Separate particle distribution functions with multirelaxation time (MRT) and lattice Bhatnagar–Gross–Krook (LBGK) models are used to calculate the flow field and the thermal field, respectively. The radiation transfer equation is computed using the meshless method with moving least-squares (MLS) approximation. The LB–DCM code is first validated by the case of coupled convection–radiation flows in a square cavity. Comparisons show that this combined method is accurate and efficient. Then, the coupled convective and radiative heat transfer in two complex geometries are simulated at various parameters, such as eccentricity, Rayleigh number, and convection–radiation parameter. Numerical results show that the LB–DCM combination is a potential technique for the multifield coupling models, especially with the curved boundary.

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Figures

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Fig. 1

Schematic of the LB–DCM system: (a) D2Q9 LB model for convection with the lattice cells as the basic computational units in which the fluid particles undergo collision and streaming steps, (b) the arrangement of lattices and collocation points, and (c) DCM method with MLS approximation for radiation where the lattice nodes are taken as collocation points for MLS approximation

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Fig. 2

Layout of the regularly spaced lattices and curved wall boundary: lattice and boundary nodes are taken as collocation points

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Fig. 3

General flow chart of LB–DCM method

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Fig. 4

Geometries of (a) a square cavity, (b) eccentric annulus, and (c) a square cavity with an internal cylinder

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Fig. 5

Total Nusselt number along inner cylinder for Rc = 1 and τ = 10 at different Ra: comparison of LB–DCM and FVM–DOM

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Fig. 6

Isotherms (top) and streamlines (bottom) in eccentric annulus at different eccentricities for Ra=104, Rc=1, and τ=10: (a) ɛ=(0.5,0), (b) ɛ=(0.5,π/2), (c) ɛ=(0.5,π), and (d) ɛ=(0.5,3π/2)

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Fig. 7

Isotherms (top) and streamlines (bottom) in eccentric annulus at different Rayleigh numbers for ɛ=(0.5,0), Rc=1, and τ=10: (a) Ra=103, (b) Ra=104, (c) Ra=3×104, and (d) Ra=105

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Fig. 8

Isotherms (top) and streamlines (bottom) in eccentric annulus at different convection–radiation parameters for ɛ=(0.5,0), Ra=104, and τ=10: (a) Rc=0.1, (b) Rc=0.5, (c) Rc=1, and (d) Rc=5

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Fig. 9

The distributions of total Nusselt number along the inner cylinder of eccentric annulus at different parameters: (a) effect of ε, (b) effect of Ra, (c) effect of Rc, and (d) effect of τ

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Fig. 10

Nondimensional temperature (left) and incident radiation (right) in a square cavity with an internal cylinder at different Rayleigh numbers for Rc=1 and τ=10: (a) Ra=103, (b) Ra=104, (c) Ra=3×104, and (d) Ra=105

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Fig. 11

The distributions of Nusselt number along the inner cylinder immersed in a square cavity at different Rayleigh numbers for Rc=1 and τ=10: (a) convective, (b) radiative, and (c) total Nusselt number

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