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Computational Thermal Sciences: An International Journal
ESCI SJR: 0.244 SNIP: 0.434 CiteScore™: 0.7

ISSN Print: 1940-2503
ISSN Online: 1940-2554

Computational Thermal Sciences: An International Journal

DOI: 10.1615/ComputThermalScien.2014011446
pages 425-437

OUTFLOW BOUNDARY CONDITION FOR THE UNSTEADY-SATE FLUID FLOW COMPUTATION WITH VARIABLE DENSITY ON A COLLOCATED GRID

Yohsuke Matsushita
Research and Education Center of Carbon Resources, Kyushu University, 6-1 Kasuga-koen, Kasuga, Fukuoka 816-8580, Japan
Sohey Nozawa
Research and Education Center of Carbon Resources, Kyushu University, Fukuoka, Japan
Tomoyuki Katayama
Department of Chemical Engineering, Graduate School of Engineering, Tohoku University, 6- 6-07 Aoba, Aramaki, Aoba-ku, Sendai, Miyagi 980-8579, Japan
Tatsuya Soma
Department of Chemical Engineering, Graduate School of Engineering, Tohoku University, 6- 6-07 Aoba, Aramaki, Aoba-ku, Sendai, Miyagi 980-8579, Japan
Yasuhiro Saito
Department of Chemical Engineering, Graduate School of Engineering, Tohoku University, 6- 6-07 Aoba, Aramaki, Aoba-ku, Sendai, Miyagi 980-8579, Japan
Hideyuki Aoki
Department of Chemical Engineering, Graduate School of Engineering, Tohoku University, Japan

ABSTRACT

This study applies the outflow boundary condition for the unsteady-state variabledensity fluid flow in the staggered grid arrangement to a similar flow in the collocated grid arrangement This application is based on the finite volume method, which successfully satisfies mass conservation. In the staggered grid arrangement, the outflow boundary condition yields the velocities on the outflow boundary using the Neumann condition to relate them to the velocities on the cell face, which are obtained by solving the discretized momentum equations. Here, the Neumann condition instead relates the outflow velocities to those on the cell center. The velocities on the cell face do not always satisfy the discretized continuity equations. Therefore, the velocities on the cell face are corrected using the summation of the discretized continuity equations over the entire computational domain in the staggered arrangement. Moreover, in the staggered grid arrangement, the summation of the discretized continuity equations can be directly obtained since the velocities are defined on the cell face; whereas in the collocated grid arrangement, the summation is evaluated after the Rhie-Chow interpolation since the velocities are on the cell center. As there are different procedures for evaluating the velocities on the outflow boundary in the different grid arrangements, unsteady-state fluid flow computations with variable density in the heating or cooling problems are performed to investigate the applicability of the outflow boundary condition to the collocated grid arrangement. It is found that the outflow boundary condition works well in the collocated grid arrangement and shows excellent mass conservation. Above all, the outflow boundary condition would be applicable to the boundary fitted coordinate system and the unstructured grid, which can treat complex geometries and require the collocated grid arrangement.


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