Analysis of buoyancy driven flow inside a vertical filter chamber

Abstract

Designs based on scientific evidence play an essential role when engineering machinery. The current case study seeks an alternative way of filtering particles using a permeable surface. The filter is designed so that the effects of heat from a permeable bottom wall create a force that drives permeates out of the filter chamber. The model follows the mass conservation, incompressible Navier-Stokes and the energy conservation equations. Effects of parameters arising from flow dynamics and heat distribution are studied to better understand the theory behind the filtrations process. Graphical representations of skin friction and Nusselt number inside the filter chamber are plotted against filtration dynamics parameters. We found that more permeates are produced when the internal energy is low since the system loses internal temperature when less dense fluid, which possesses heat, is withdrawn from the chamber. In addition, the chamber volume increase permeates outflow since it enhances the pulling effects of the buoyancy force. It is found that increasing the Richardson number enhances the buoyancy forces and viscous effects; thus, decreasing permeates outflow velocity and eventually reduces wall drag coefficient. The wall drag coefficients on the left and right vertical walls have extrema towards the bottom of the filter chamber, in the region, 0 <y < 2 % H.