Hydraulics of fluidized cavities in porous matrices: cavity heights and stability for upward water jets

Abstract

Theoretical and experimental results for the evolution of cavities generated by upward vertical leakage jets in porous media are presented. The formulation is based on the conservation principles of mass, momentum, and energy. Two conditions were considered: two-dimensional isotropic medium and three-dimensional isotropic medium. The results of the cavity height are given in nondimensional form and related to the Froude number that considers the inlet flow characteristics (width of the slot or diameter of the orifice, and inlet velocity). Both the two-dimensional and the three-dimensional cases provided theoretical results for the length of the cavity limited by a maximum Froude number. This characteristic implies that the cavity destabilizes for Froude numbers higher than this maximum critical value. It was observed that parameters of the porous medium (soil parameters) not present in the conservation formulation must be added a posteriori to cover a larger spectrum of soil possibilities. The experimental results show that the theoretical proposition follows the main characteristics of the observations.