Mathematical Modelling and Computer Simulation of the Flow in Thin Gap Channel due to Alternating Volumetric Mass Forces

Abstract

The mathematical modelling and computer simulation are presented for the complex flow in thin gap channel due to alternating volumetrically distributed mass forces. The flow equations and obtained analytical solutions for limit cases are considered in the cylindrical coordinate system with the axis directed along the channel, which is rotating around its axis. The channel is placed inside the cylinder on the edge of the circular horizontal disk, which is rotating around vertical axis in its centre. The two rotations around different perpendicular axes create complex unknown features in a flow due to the alternating centrifugal and Coriolis forces, which substantially vary by the angle. The centrifugal force from the disk rotation is directed to its edge, while the centrifugal force due to rotation of the channel is acting by the channel’s radius. As a result, the two different centrifugal forces are directed counter currently in one side of the channel and vary by the angle up to adding of the two of them in the same direction in the opposite side of the channel. The conditions may fit to the strong cavitation regime inside the volume of fluid flow due to a stretching of the liquid in some locations.