A finite difference self‐adaptive mesh solution of flow in a sedimentation tank

Abstract

AbstractA new numerical model has been developed to evaluate the removal efficiency of primary sedimentation clarifiers operating at neutral density condition. The velocity and concentration fields as well as the development in time and space of the settled particle bed thickness are simulated. The main difficulties in simulation of velocity and concentration fields are related to (1) numerical instabilities produced by the prevalence of convective terms in the unknown variable high‐gradient regions and (2) turbulence effects on the suspension of solid particles from the settled bed. The need to overcome the numerical instabilities without the upwind difference approximation, which introduces high numerical viscosity, suggests the use of non‐uniform grids of calculation.The velocity field is obtained by solving the motion equations in the vorticity and streamfunction formulation by means of a new numerical method based upon a dynamically self‐adjusting calculation grid. These grids allow for a finer mesh following the evolution of the unknown quantities. A k–ϵ model is used to simulate turbulence phenomena.The sedimentation field is found by solving the diffusion and transport equation of the solid particle concentration. Boundary conditions on the bottom line are imposed relating the amount of turbulence flux and sedimentation flux to the actual concentration and the reference concentration. Such an approach makes it possible to represent the solid particle suspension from the bottom, taking into account its dependence on (1) the characteristics and the evolution in time of the settled bed, (2) the velocity component parallel to the bottom line and (3) the turbulence structure.