Injection driven flow in a dilating or contracting filter chamber with parabolic left inlet velocity

摘要

Filter design is an essential aspect of the development of industrial machines. This study investigates and analyses an injection-driven flow in a dilating or contracting filter chamber with weak permeable walls. The design is such that an opening allows influx into the filter channel with parabolic velocity and another opening that serves as an outlet for the filtrates. The model follows the mass conservation, incompressible Navier- Stokes and the energy conservation equations. The study seeks steady-state operation to understand a stable filtration process. The solutions of the dependent variables are then approximated using the spectral-based paired quasilinearization technique. We found, among other results, that in the region where the flow is developing due to the inflow velocity, the axial flow when the chamber compresses is greater than the velocity when the filter chamber expands. Further, there is more average wall friction in the current design than the filter chamber design with two outlets because more fluid is present in the current filter design due to injection through the semi-permeable walls and the inflow through the left inlet. This high average wall friction causes a delay in the transition of the flow and consequently retard the outflow of the filtrates.