Oscillating Rectilinear Fluid Flow Generator

Abstract

A Rectilinear Fluid Flow Generator of an oscillating type has been developed for the purpose of studying the rheological properties and flow characteristics of both Newtonian and non-Newtonian liquids [1]. It consists essentially of two long horizontal concentric cylinders, in which the annulus is filled with a liquid. The external tube is mounted on elastic supports, while the internal tube can be harmonically oscillated axially at a predetermined frequency and amplitude. The motion of the external tube and the resultant force (liquid drag) acting on it are readily measurable at any time. The principle of the apparatus depends on the fact that the outside tube motion is dynamically coupled to the inside tube motion by the liquid in the annulus which itself is caused to move by the controlled oscillations of the inside tube. It is assumed, at least in principle, that if the motion of the outside tube is known for a given motion of the inside tube, the constitutive equations for the liquid can be determined. Or conversely, if the constitutive equations are known, the motion of the outside tube can be calculated for a given motion of the inside driving cylinder. It has been shown that the solution of the Navier-Stokes equations can be obtained for the flow of a viscous liquid within the annulus between two infinitely long concentric tubes, for the case where the fluid motion is generated by a rectilinear harmonic motion of the inner tube while the outer tube is assumed to be supported by elastic springs and moving parallel to its longitudinal axis. The velocity and shear stress in the fluid have been obtained, and asymptotic solution for drag force, and tube motions, as well as a method for determining the liquid viscosity coefficient are discussed. It is shown that the theoretical solution is important for the study of the motions of the Rectilinear Fluid Flow Generator.