The theory and application of Navier-Stokeslets (NSlets)

Chadwick, E ORCID: https://orcid.org/0000-0002-3743-8589 2019, 'The theory and application of Navier-Stokeslets (NSlets)' , Physics of Fluids, 31 (10) , p. 107103.

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Abstract

Consider a closed body moving in an unbounded fluid that decays to rest in the far-field and governed by the incompressible Navier-Stokes equations. By considering a translating reference frame, this is equivalent to a uniform flow past the body. A velocity representation is given as an integral distribution of Green’s functions of the Navier-Stokes equations which we shall call NSlets. The strength of the NSlets is the same as the force distribution over the body boundary. An expansion for the NSlet is given with the leading-order term being the Oseenlet. To test the theory, the following three two-dimensional steady flow benchmark applications are considered. First, consider uniform flow past a circular cylinder for three cases: low Reynolds number; high Reynolds number; and also intermediate Reynolds numbers at values 26 and 36. These values are chosen because the flow is still steady and hasn’t yet become unsteady. For low Reynolds number, approximate the NSlet by the leading order Oseenlet term. For high Reynolds number, approximate the NSlet by the Eulerlet which is the leading order Oseenlet in the high Reynolds number limit. For the intermediate Reynolds numbers, approximate the NSlet by an Eulerlet close to its origin, and an Oseenlet further away. Second, consider uniform flow past a slender body with elliptical cross-section with Reynolds number Re ∼ 10 6 , and approximate the NSlet by the Eulerlet. Finally, consider the Bla- sius problem of uniform flow past a semi-infinite flat plate and consider the first three terms in the NSlet approximation.

Item Type: Article
Additional Information: This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Physics of Fluids and may be found at https://doi.org/10.1063/1.5119331.
Schools: Schools > School of Computing, Science and Engineering
Journal or Publication Title: Physics of Fluids
Publisher: AIP Publishing
ISSN: 1070-6631
Related URLs:
Depositing User: EA Chadwick
Date Deposited: 02 Oct 2019 15:24
Last Modified: 03 Jan 2020 13:21
URI: http://usir.salford.ac.uk/id/eprint/52578

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