Mathematical modeling of hydrodynamic resistance in an oscillatory flow of a viscoelastic fluid

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 based on the generalized Maxwell model. The transfer function of the amplitude-phase frequency characteristics is determined. Using this function, the dependence of the hydrodynamic resistance on the dimensionless oscillation frequency is studied for various values of the elastic Deborah number and the concentration of the Newtonian fluid. It is shown that in an oscillatory flow of a viscoelastic fluid, the hydrodynamic resistance decreases depending on the Deborah number. With an increase in this number, the decrease becomes more pronounced than before. This effect allows us to evaluate the hydrodynamic resistance for a given law; the change in the longitudinal velocity averaged over the channel section and for the motion of a viscoelastic fluid in an unsteady flow allows us to determine the dissipation of the mechanical energy of the medium, which is important in the regulation of hydraulic and pneumatic systems.