Flow in a cylindrical channel of a nonlinear viscoplastic fluid

DOI: 10.34759/trd-2022-125-09

Аuthors

Kolodezhnov V. N.^*, Veretennikov A. S.^**

Air force academy named after professor N.E. Zhukovskii and Y.A. Gagarin, Voronezh, Russia

*e-mail: bars4558@mail.ru
**e-mail: vas3141@gmail.com

Abstract

A combined rheological model has been proposed for viscoplastic working media that exhibit a non-monotonic dependence of viscosity on shear rate. This model assumes three typical behaviors in three adjacent ranges of shear rate variation. In the first range, the dependence of the shear stress on the shear rate is described by a linear function and characterized by a constant viscosity value. In the second and third shear rate ranges, this dependence is approximated by nonlinear functions describing dilatant and pseudoplastic behavior. On the basis of such a model, the solution to the steady flow of fluid in a cylindrical channel has been obtained. It is shown that three different flow patterns can be implemented depending on the level of pressure drop along the channel length. For each of the schemes inside the channel, characteristic zones of flow should be identified. In the case of the most complex third flow pattern inside the channel, four zones with different mechanical behavior of the fluid should be distinguished. In such a situation, the zone of plastic flow is formed in the central part of the channel in the vicinity of its fore-and-aft axis of symmetry. The next zone is characterized by shear flow with a constant viscosity value. Two more zones of nonlinear-viscous flow, in which the fluid exhibits dilatant and pseudoplastic behavior, are formed in the vicinity of the channel wall. Expressions for determining the boundaries of flow zones, and expressions for calculating the liquid velocity profile and the dependence of the volume flow on the pressure drop were obtained. The influence of the main parameters of the system under consideration on the velocity distribution characteristics and the dependence of the volumetric flow rate on the pressure drop over the channel length has been analyzed.

Keywords:

rheological model, viscoplastic fluid, shear rate, shear stress, viscosity

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