Strip Integral Method Applied to Settling Tanks

Abstract

The nonstratified steady flow hydrodynamics of rectangular sedimentation tanks is simulated using a combination of the strip integral and finite element methods. The strip integral method is generally a forward marching scheme in which the partial differential equations of continuity and momentum are reduced to a set of ordinary differential equations in terms of certain preselected parameters. These parameters, along with a set of shape functions, describe the velocity distribution. In this study three shape functions are chosen, corresponding to the boundary layer, the potential core, and the free mixing and recirculation zone. The shape functions were: (1) Power law in the boundary layer; (2) uniform velocity in the potential core; and (3) Gaussian distribution in the free mixing zone. The shape functions are chosen to allow recirculation above the mixing zone. A modified mixing length approach is used to introduce the effect of recirculation into the solution. A Runge‐Kutta method is used to integrate the set of ordinary differential equations; a finite element solution is used in the withdrawal zone. The numerical results compare favorably with experimental velocity distributions obtained by laser anemometry and with available field data. The convective and mixing characteristics of the flow can be obtained from this model and used with a transport model to determine the removal efficiency of the tank.