Flows of Liquids with a Yield Strength in Pipes under a Pulsating Pressure Drop

Abstract

Laminar flows of fluids with a yield strength in pipes under the action of a periodically changing pressure drop are considered. The Herschel–Bulkley model is adopted to describe the rheological properties of moving fluids. The effect of pressure drop fluctuations on velocity profiles, as well as on the mean flow rates, friction on the pipe walls, and the thickness of the “quasi-solid” core, is studied numerically, depending on the amplitude and frequency of pressure drop fluctuations, the generalized Bingham number, and the fluid power index. It is shown that in flows of viscoplastic fluids with a power index greater than one, the effect of pressure drop fluctuations is qualitatively different in different ranges of shear rates. Additionally, flows are investigated in which the relative amplitudes of pressure drop oscillations are large. At large amplitudes and low frequencies of pressure drop oscillations, counter-flows periodically arise in the flow and two (rather than one) zones of “quasi-solid” flow are formed; moreover, finite time intervals periodically appear in which the flow rate is zero.