Perturbation methods in hydrodynamics of porous media

The applicability of the perturbation techniques in hydrodynamics of a fluid saturated porous medium bounded by a 2-D channel or a tube is investigated.The flow field is modeled using the full Brinkman- Forchheimer-extended Darcy equation. The nonlinear momentum equations (for both channel flow and tube flow) are solved using the straight forward and matched asymptotic expansion methods. The accuracy of results is also investigated via a numerical simulation performed based on the finite difference method. Results reveal that the perturbationtechniques can be applied to solve these nonlinear momentum equations in both Cartesian and polar frames with a good accuracy. Also, the obtained results (the velocity profiles) have very simple forms. Moreover, a general criterion for t he depen dency of the velocity profile on the Forchheimer term is proposed. It is shown that the Forchheimer term (F) is important when F ~ O (s3) in both channel flow and tube flow filled with saturated porous media.

کلیدواژه ها:

Perturbation ، Porous medium ، Brinkman- Forchheimer-extended Darcy model ، Channel flow ، Tube flow