Numerical Simulation of Mixing of Effluent through Porous Media: The Effects of Local Inertia on the Flow

The steady-state analytical and numerical solutions are obtained for the mixing of effluent with Newtonian fluid in subsurface. The problem presented in this research work is flow through a channel packed by homogeneous porous media, associated to environmental sciences. Simulations are performed employing a time-marching scheme. Numerical method used in the study is a finite element method, while, the frame of reference is Cartesian coordinate system. Adopted algorithm follow semi-implicit technique through Taylor-Galerkin/Pressure-correction scheme. Analytical solution is Obtained and compared with the numerical predictions. Impact of Darcy's number, influence of change in diffusion coefficient of effluent concentration and time dependent effects of velocity profile is investigated. Numerical predictions are compared against both steady-state and time-dependent analytical solutions obtained in the present study, and observed very good agreement. Various interesting features of the flow are reported. The numerical results exhibit that with increasing fluid inertia, the effluent disperses immediately in flow field when entering from same direction with the flow of fluid. While, increasing dispersion coefficient of effluent at fixed rate of inertia the effluent disperses faster and occupy large area of upstream.