Purely accelerating and decelerating flows within two flat disks

Abstract

This paper deals with the power series solutions of the steady, laminar, radial flows either purely accelerating, or purely decelerating, that develop in the gap formed by two flat disks. The results include velocity profiles and static pressure distributions. These are compared with previously reported approximate solutions or the experimental data for the pressure obtained by others. The development of the two types of flows is shown to be entirely different except for λ (parameter that combines the non-dimensional radial distance and Reynolds number) close to zero where both behave as Poiseuille's flows between two infinite plates. For the inflow, the radial velocity flattens near the mid-plane diffusing towards the walls as the parameter λ increases. In contrast to the inflow, the magnitude of the maximum velocity of the outflow is shown to increase with λ, indicating that most of the fluid motion is taking place near the central channel region. For the outflow, two critical values of λ are used to indicate notable flow field transformations. The first marks the point where the pressure difference changes sign, while the second denotes when the derivative of the velocity (in the axial direction) on the wall becomes zero. Beyond the second value, purely decelerating flow cannot exist. The sign change of the pressure is attributed to the interaction between the inertia, viscous, and pressure forces.