Mathematical model for power consumption at mixing of industrial and domestic wastewater sludge

Physical investigations have been carried out to characterize the power consumption in a laboratory autoclave vessel equipped with an anchor impeller (diameter d = 0.068 mm), without baffles, at 8 speed ratio, from 100 to 800 rpm. The laminar flow regime was investigated using sludge proceeding from the treatment of mixed industrial and domestic wastewater, with a view to its subsequent processing: mixing, filtration, dewatering. The mathematical modeling focused on finding an accurate equation linking the Power number (N_p) and the Reynolds number (R_e) at different levels (H) of sludge in the vessel.

The rheological curves indicate that the sludge have non-Newtonian behaviors which are better described by the Herschel-Buckley model. The models resulted from the N_p variation versus Re are power function type N_p = a ×Re^b , where the coefficient a is a linear functions of H/d ratio and b = -1.016 have a constant value.