Velocity Gradient in Filter Backwashing

Abstract

Backwashing of deep bed filters is achieved by fluidizing the filter media. A mathematical model for velocity gradient in two-dimensional turbulent flow that can also be applied to flow in fluidized beds in the transitional state was developed. The theory of fluidization in a circular cross-section column was presented. The existence of a viscous sublayer around each fluidized solid particle and the laminar sublayer thickness at the wall were neglected. To evaluate the theoretical expressions, numerical applications are carried out for filter-bed materials of two different types of sands and anthracite coal. An indirect verification of the existence of an optimum porosity around 0.70–0.75 during filter backwashing was observed in the laboratory experiments. The velocity gradient in backwashing of granular filters was found to be a function of power dissipation in a unit volume and coefficient \IC\N that indicates the effect of turbulence in total power dissipation. It was also found that turbulence intensity decreases with an increase of porosity, and the arithmetic mean shear stress has a maximum value between porosity values of 0.70 and 0.75.