Acceleration motion of geometric and spherical particles in two dimensions and implications in design of continuous sedimentation rectangular tanks

摘要

The design procedure outlined by Camp (1946) for design of continuous gravity sedimentation tank was revisited. The viscous effects of flowing fluid were included in the model by development of the velocity profile of the fluid in the horizontal direction. The transient motion of the spherical and geometric particles unhindered prior to reaching terminal settling velocity, was simulated using a desktop computer. The governing equations in two dimensions, vertical and horizontal were written in terms of velocity of the particle and the drag coefficient in transient motion was assumed to be of the same functional form as that obtained from empirical observations at steady state. The five constant expressions of Turton and Levenspiel (1989) was used and the trajectory of the particle was obtained relative to the motion of the fluid by use of fifth order Runge-Kutta method of numerical integration. As the density of the particle and size of the particle increases, the acceleration zone of the particles increased in size. Deeper tanks have to be constructed for such systems. The geometric particles reached their terminal settling velocities sooner compared with the spherical particles. The pressure drop, throughput and separation efficiency trade-offs are discussed.