Flow in a Circular Pipe Filled with Porous Medium in the Non-Darcian Effects. | ||||
| MEJ- Mansoura Engineering Journal | ||||
| Article 2, Volume 20, Issue 3, September 1995, Page 1-18 PDF (1.28 MB) | ||||
| Document Type: Research Studies | ||||
| DOI: 10.21608/bfemu.2021.161921 | ||||
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| Authors | ||||
| Mohamed Saad Zaghloul El-Kady* 1; M. A. Tolba2; L. H. Rabie2 | ||||
| 1Mechanical Power Engineering Department., Faculty of Engineering.,El-Mansoura University., Mansoura., Egypt. | ||||
| 2Mechanical Power Engineering Department., Faculty of Engineering., El-Mansoura University., Mansoura., Egypt. | ||||
| Abstract | ||||
| Forced flow through a circular pipe filled with saturated porous media has been numerically simulated. The generalized form of the momentum equation including the non-Darcian effects such as the variable porosity, flow inertia, and viscous friction is conssidered. To solve the momentum equation, the finite difference method is used. Different sphere diameters of 3≤ d ≤8mm, and sphere diameter to the pipe radius ratio ''D'' in the range 0.05 ≤ D ≤ 2 are considered. The results are obtained for flow Reynolds number up to 105 , and nondimensional pressure gradient B UP TO 108. The results show that the non-Darcian effects have a significant influence on the velocity profiles. These effects appear clearly in the regions near to the velocity profiles. These effects appear clearly in the regions near to the wall and gives an increase in the magnitude of the velocity and signifies the channeling effect. It has in turns a significant influence on the fluid flow characteristics such as the boundary frictional drag, the frictional drag induced by the solid matrix (designed as Darcy's pressure drop) and the flow inertia drag and in turns in the total drag coefficient. The results show the great influence of sphere diameter d, sphere diameter to the pipe radius ratio D, Darcy number Da and the Reynolds number on the total drag coefficient f1 and also on the behavior of its three components. The predicted results of the total friction as function of Reynolds number exhibit excellent agreement with Ergun equation based on the area mean porosity Em instead of the free porosity Ec. It confirms the fact that Ergun equation is also valid for porous media of identical spherical particles for the laminar, transient and turbulent regimes fm =175/Rem+ 1.75 To verify the numerical results, an experimental investigation was carried out for the flow of water in a circular tube filled with five different steel spheres of diameters 32, 4, 4.7, 5.4 and 6.3 mm respectively. Comparison with predicted results shows a very good agreement, and proves the validity of the model. | ||||
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