Mathematical Modeling of Flow in a Granular Permeable Bed Channel

In this research, a two-dimensional mathematical model using  turbulence model was developed in a rectangular channel with granular permeable bed. Finite volume method was used for numerical solution of governing equations. The equations considered are discretized using Hybrid difference scheme while applying SIMPLE algorithm to correct velocity components in the continuity equation. In the developed turbulence method, wall function was considered for simulation of the boundary conditions. The results show that the proposed model yields better values than the earlier laboratory experiments by the researchers. Gravity component is a negative source in V momentum equation. This negative source is integrated into pressure content via a tricky manner to converge the numerical solution. By various repetitions, appropriate range of "under relaxation factor" is obtained in order to make a better and faster convergence in resolving the equations. Results of the mathematical model as well as earlier laboratory results show that changing of the permeable bed conditions will affect the turbulence parameters especially in the area near the permeable boundary. Comparison of the velocity components, kinetic energy and dissipation rate of the kinetic energy which is derived from the earlier laboratory simulations as well as mathematical results indicates the precision of the proposed mathematical model.