Repository logo
 

Regularized Stokeslets Lines Suitable for Slender Bodies in Viscous Flow

Published version
Peer-reviewed

Loading...
Thumbnail Image

Type

Article

Change log

Authors

Zhao, Boan 

Abstract

jats:pSlender-body approximations have been successfully used to explain many phenomena in low-Reynolds number fluid mechanics. These approximations typically use a line of singularity solutions to represent flow. These singularities can be difficult to implement numerically because they diverge at their origin. Hence, people have regularized these singularities to overcome this issue. This regularization blurs the force over a small blob and thereby removing divergent behaviour. However, it is unclear how best to regularize the singularities to minimize errors. In this paper, we investigate if a line of regularized Stokeslets can describe the flow around a slender body. This is achieved by comparing the asymptotic behaviour of the flow from the line of regularized Stokeslets with the results from slender-body theory. We find that the flow far from the body can be captured if the regularization parameter is proportional to the radius of the slender body. This is consistent with what is assumed in numerical simulations and provides a choice for the proportionality constant. However, more stringent requirements must be placed on the regularization blob to capture the near field flow outside a slender body. This inability to replicate the local behaviour indicates that many regularizations cannot satisfy the no-slip boundary conditions on the body’s surface to leading order, with one of the most commonly used blobs showing an angular dependency of velocity along any cross section. This problem can be overcome with compactly supported blobs, and we construct one such example blob, which can be effectively used to simulate the flow around a slender body.</jats:p>

Description

Keywords

4012 Fluid Mechanics and Thermal Engineering, 40 Engineering

Journal Title

Fluids

Conference Name

Journal ISSN

2311-5521
2311-5521

Volume Title

6

Publisher

MDPI AG
Sponsorship
Australian Research Council (DE200100168)