Ecoulement d’un fluide visqueux par injection dans l’espace compris entre deux disques poreux en mouvement transversal

Abstract

In this work, a viscous fluid is injected between two porous discs in motion along an axis passing perpendicular to the midpoints of the two circular surfaces. The movement of the discs creates the moving away or bringing together of the boundaries of the flow giving rise respectively to an increase or a decrease in volume of the space containing the fluid. The problem is described by the continuity equation and the Navier-Stokes equations applying the principles of mass and momentum conservations. The flow being that of an incompressible fluid described by a velocity field having two components, the stream function is prescribed in the governing equations of the fluid flow. The stream function verifies the continuity equation on one hand, and is solution of the vorticity equation obtained by taking the curl of the momentum equation on the other hand. The approach for seeking the solutions is the similarity method that enables to transform the partial differential equation verified by the stream function into an ordinary differential equation describing the same problem. The ordinary differential equation and the boundary conditions correspond to a two-point boundary-value problem solved by using the numerical shooting method associated with a fourth-order Runge-Kutta algorithm. The numerical results obtained are presented in terms of velocity profiles, pressure gradients and stream lines under different values of the control parameters of the problem, notably the Reynolds number and the expansion and the contraction ratio which results from the increase or the decrease in volume of the space contained the fluid.