A revisit of the development of viscoplastic flow in pipes and channels

TL;DR

This paper investigates viscoplastic flow of Bingham plastics in pipes and channels using finite element simulations, focusing on development length, flow patterns, and the effects of regularisation, offering new insights into flow behavior and parameter impacts.

Contribution

It introduces a new definition of development length based on wall shear stress and explores alternative Reynolds number definitions to unify flow development curves.

Findings

Development length correlates with wall shear stress.

Flow patterns of yielded and unyielded regions are characterized.

Regularisation parameter impacts simulation accuracy.

Abstract

This study revisits the development of viscoplastic flow in pipes and channels, focusing on the flow of a Bingham plastic. Using finite element simulations and the Papanastasiou regularisation, results are obtained across a range of Reynolds and Bingham numbers. The novel contributions of this work include: (a) investigating a definition of the development length based on wall shear stress, a critical parameter in numerous applications; (b) considering alternative definitions of the Reynolds number in an effort to collapse the development length curves into a single master curve, independent of the Bingham number; (c) examining the patterns of yielded and unyielded regions within the flow domain; and (d) assessing the impact of the regularisation parameter on the accuracy of the results. The findings enhance the existing literature, providing a more comprehensive understanding of this classic flow problem.