Non-Darcian surface tension effects on free surface transport in porous media

The phenomenological analysis of free surface transport through porous media using the Brinkman-Forchheimer-extended Darcy model is presented. A finite difference scheme using the marker and-cell (MAC) method is employed to investigate the momentum and energy transport in a porous channel involving free surface transport phenomena. The interfacial tension effect at the free surface is incorporated in the analysis. The present investigation constitutes one of the first numerical investigations of the free surface momentum and energy transport through porous media using the MAC method. Fully developed velocity and temperature fields for saturated as well as unsaturated porous channels; for cases with different Darcy numbers, are compared and verified against existing analytical solutions. Temporal free surface distributions for cases with different Darcy numbers and Reynolds numbers are presented. Also explored is the effect of the free surface transport in porous media on the energy transfer. It is found that the boundary and inertial effects have a significant influence on the free surface transport through porous media and that the surface tension effects become insignificant for Re-K > 1. The present work constitutes one of the first studies on Non-Darcian effects on free surface transport in porous media.