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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Research-Article
Modified Outlet Boundary Condition Schemes for Large Density Ratio Lattice Boltzmann Models
Long Li,
Long Li
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: lilong315@sjtu.edu.cn
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: lilong315@sjtu.edu.cn
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Xiaodong Jia,
Xiaodong Jia
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: jxd_sjtu@126.com
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: jxd_sjtu@126.com
Search for other works by this author on:
Yongwen Liu
Yongwen Liu
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: ywliu@sjtu.edu.cn
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: ywliu@sjtu.edu.cn
Search for other works by this author on:
Long Li
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: lilong315@sjtu.edu.cn
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
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
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. May 2017, 139(5): 052003 (8 pages)
Published Online: March 7, 2017
Article history
Received:
June 15, 2016
Revised:
January 29, 2017
Citation
Li, L., Jia, X., and Liu, Y. (March 7, 2017). "Modified Outlet Boundary Condition Schemes for Large Density Ratio Lattice Boltzmann Models." ASME. J. Heat Transfer. May 2017; 139(5): 052003. https://doi.org/10.1115/1.4036001
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