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Research Papers: Heat and Mass Transfer

Modified Outlet Boundary Condition Schemes for Large Density Ratio Lattice Boltzmann Models

[+] Author and Article Information
Long Li

School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: lilong315@sjtu.edu.cn

Xiaodong Jia

School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: jxd_sjtu@126.com

Yongwen Liu

School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: ywliu@sjtu.edu.cn

1Corresponding author.

Presented at the 2016 ASME 5th Micro/Nanoscale Heat & Mass Transfer International Conference. Paper No. MNHMT2016-6374.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received June 15, 2016; final manuscript received January 29, 2017; published online March 7, 2017. Assoc. Editor: Robert D. Tzou.

J. Heat Transfer 139(5), 052003 (Mar 07, 2017) (8 pages) Paper No: HT-16-1391; doi: 10.1115/1.4036001 History: Received June 15, 2016; Revised January 29, 2017

Outlet boundary conditions (OBCs) and their numerical descriptions are critical to computational fluid dynamics (CFD) since they have significant influence on the numerical accuracy and stability. They present significant challenges to the two-phase lattice Boltzmann (LB) method, especially in the limit of large density ratio. In this study, three commonly used OBCs: convection boundary condition (CBC), Neumann boundary condition (NBC), and extrapolation boundary condition (EBC), are investigated and improved on basis of two LB models for large density ratios (single and double distribution function models). The existing numerical schemes for the OBCs are not directly applicable to the LB models because of the deviation of the momentum balance at the outlet boundary. The deviation becomes substantial at a large density ratio. Thus, in this work, modified OBC schemes are proposed to make the OBCs suitable for the two-phase LB models by adding an independent equation to obtain the outlet velocity. Numerical tests on droplet flowing in a channel are performed to evaluate the performance of the modified OBC schemes. Results indicate that the modified OBC schemes may be extended to tackle large density ratio situations. The modified NBC and EBC schemes are only suitable for the LB model with single distribution function. Three modified CBC schemes exhibit optimum performance for both single and double distribution function LB models which can be implemented for large density ratios.

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Figures

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Fig. 1

Schematic illustration of the nodes around the outlet boundary

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Fig. 2

Schematic illustration of the flow process

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Fig. 3

Droplet shape and velocity fields for different OBC schemes at T∗=5.0,5.5, and 5.75. The contour lines from the exterior to the interior represent ρ=0.1,0.5, and 0.9. Re=24, We=133, and ρr=100.

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Fig. 4

Outlet velocity profiles along the height direction for the modified OBC schemes. Re=24, We=133, and ρr=100.

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Fig. 5

Instantaneous relative error curves for the modified OBC schemes. Re=24, We=133, and ρr=100.

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Fig. 6

Droplet shape and velocity fields for three MCBC schemes at T∗=26.25,  27.5, and 28.75. The contour lines fromexterior to interior represent ρ=0.1,0.5,and 0.9. Re=72, We=133, and ρr=1000.

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Fig. 7

Instantaneous relative error curves for the three MCBC schemes. Re=72, We=133, and ρr=1000.

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Fig. 8

Shape of the droplet for different Weber numbers at T∗=20. (a) We=133, (b) We=400, and (c) We=1333.

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