Water-Entry Slamming Characteristics of Porous Plates with Varying Porosity and Entry Velocity

In this paper, steady flow of the fourth-grade fluid as a one of the most complicated fluid inside porous flat channel with monotonous injection and suction rates has been analyzed with two flat porous plates at y = b and y = −b intervals through two analytical methods, and the effect of changes in each parameter on velocity profile has been shown. We assumed that the velocity of suction and injection is inconsiderable compare with the entrance velocity. The velocity profile and boundary layer thickness change due to an increase in cross-flow Reynolds R and fourth-grade fluid parameter γ is investigated.

The author has found a class of entry velocity profiles that develop into the Raithby fully developed second solution for flow in a parallel porous plate channel with strong suction. The entry profiles of interest are characterized by a velocity defect at the channel centerline. Two numerical solution techniques are employed. The faster first technique involving solution of the boundary layer equations is used to predict overall trends of profile development. The boundary layer solutions are compared to exact solutions of the Navier-Stokes equations. A detailed examination was made of the double Poiseuille entry condition which was found to develop into Raithby’s profile.