Study of Oscillatory Flows of a Viscoelastic Fluid in a Flat Channel Based on the Generalized Maxwell Model

Abstract

The problems of the oscillatory flow of a viscoelastic fluid in a flat channel for a given harmonic oscillation of the fluid flow rate are solved on the basis of the generalized Maxwell model. The transfer function of the amplitude-phase frequency characteristics is determined. These functions make it possible to evaluate the hydraulic resistance under a given law, the change in the longitudinal velocity averaged over the channel section, as well as during the flow of a viscoelastic fluid in a nonstationary flow, and allow determining the dissipation of mechanical energy in a nonstationary flow of the medium, which are important in the regulation of hydraulic and pneumatic systems. Its real part allows determining the active hydraulic resistance, and the imaginary part is reactive or inductance of the oscillatory flow.