Numerical Model for Discrete Settling

A numerical method of solution is given for the differential equation describing the discrete settling in two-dimensional uniform and turbulent open-channel flow. Stability condition of the finite difference equations is derived by applying linear stability analysis. By neglecting the effect of longitudinal turbulent diffusion, settling efficiency is generally expressed in terms of two independent variables. Further, it is assumed that turbulence is isotropic and solid particles behave like a fluid mass. Three sets of solutions are obtained for uniform, logarithmic, and parabolic velocity distributions in vertical direction. However, the results of the last two are graphically given herein. In the case of uniform velocity distribution, results of numerical solution is compared with Camp’s solutions and high accuracy is obtained. The effect of turbulence and velocity distribution is shown. Solutions obtained for the logarithmic velocity distribution which was experimentally verified are suggested for practical applications.