Similarity solutions of the Navier-Stokes equations for an injection-driven flow between two orthogonally moving porous discs

Abstract

An incompressible fluid is in motion after injection in the space between two parallel porous discs that can move away or come closer along the same axis passing perpendicular to the midpoints of their respective surfaces. The desire of well describing the incompressible fluid flow patterns and the fact that the velocity field of the axisymmetric flow has two components lead to introduce the stream function in the governing equations. A similarity method is applied to transform the vorticity equation satisfied by the stream function into a nonlinear ordinary differential equation. Thus, the analysis is restricted to solving a two-point boundary-value problem containing two control parameters, notably the Reynolds number and a nondimensional parameter representing the measure of the increase or the decrease in volume of the flow domain. Among the main results, it is found that, the high expansion in volume of the flow domain causes flow reversal for low values of the injection Reynolds number, while the contraction in volume of the flow domain creates a linear behavior of the axial velocity for a small injection Reynolds number and a flattening of the radial velocity profile for all the Reynolds numbers.