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Pressure-driven flows in helical pipes: bounds on flow rate and friction factor

Published online by Cambridge University Press:  06 October 2020

Anuj Kumar Open the ORCID record for Anuj Kumar [Opens in a new window]
Anuj Kumar*
Affiliation:
Department of Applied Mathematics, Baskin School of Engineering, University of California, Santa Cruz, CA95064, USA
*
†Email address for correspondence: [email protected]
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Abstract

In this paper, we use the well-known background method to obtain a rigorous lower bound on the volume flow rate through a helical pipe driven by a pressure differential in the limit of large Reynolds number. As a consequence, we also obtain an equivalent upper bound on the friction factor. These bounds are also valid for toroidal and straight pipes as limiting cases. By considering a two-dimensional background flow with varying boundary layer thickness along the circumference of the pipe, we obtain these bounds as a function of the curvature and torsion of the pipe and therefore capture the geometrical aspects of the problem. In this paper, we also present a sufficient criterion for determining which pressure-driven flow and surface-velocity-driven flow problems can be tackled using the background method.

JFM classification

Mathematical Foundations: Variational methods Boundary Layers: Pipe flow boundary layer
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 904 , 10 December 2020 , A5
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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References

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