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Transport in Porous Media

, Volume 98, Issue 1, pp 147–172 | Cite as

Flow of Particulate-Fluid Suspension in a Channel with Porous Walls

  • Jun YaoEmail author
  • Ke Tao
  • Zhaoqin Huang
Article

Abstract

The problem of the dispersed particulate-fluid two-phase flow in a channel with permeable walls under the effect of the Beavers and Joseph slip boundary condition is concerned in this paper. The analytical solution has been derived for the longitude pressure difference, stream functions, and the velocity distribution with the perturbation method based on a small width to length ratio of the channel. The graphical results for pressure, velocity, and stream function are presented and the effects of geometrical coefficients, the slip parameter and the volume fraction density on the pressure variation, the streamline structure and the velocity distribution are evaluated numerically and discussed. It is shown that the sinusoidal channel, accompanied by a higher friction factor, has higher pressure drop than that of the parallel-plate channel under fully developed flow conditions due to the wall-induced curvature effect. The increment of the channel’s width to the length ratio will remarkably increase the flow rate because of the enlargement of the flow area in the channel. At low Reynolds number ranging from 0 to 65, the fluids move forward smoothly following the shape of the channel. Moreover, the slip boundary condition will notably increase the fluid velocity and the decrease of the slip parameter leads to the increment of the velocity magnitude across the channel. The fluid-phase axial velocity decreases with the increment of the volume fraction density.

Keywords

Two-phase flow Particulate-fluid suspension  Permeable boundary  Beavers and Joseph slip condition Perturbation method 

Notes

Acknowledgments

This study was supported by the National Basic Research Program of China (”973” Program) (Grant No. 2011CB201004), the National Natural Science Foundation of China (Grant No. 51234007), and the Fundamental Research Funds for the Central Universities (Grant No. 11CX06026A).

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of Reservoir EngineeringSchool of Petroleum Engineering, China University of Petroleum (Huadong)QingdaoChina

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