DOI: 10.1017/s0022112074002503. Drag due to the motion of a Newtonian fluid through a sparse random array of small fixed rigid objects

Drag due to the motion of a Newtonian fluid through a sparse random array of small fixed rigid objects

10.1017/s0022112074002503

Crossref journal-article

Cambridge University Press (CUP)

Journal of Fluid Mechanics (56)

Abstract

The averaged equations of slow flow in random arrays of fixed spheres are developed as a hierarchy of integro-differential equations, and an iteration procedure is described for obtaining the mean drag in the case of small volume concentration c. The leading approximation is that given by Brinkman's model of flow past a single fixed sphere, in which the effects of all other spheres are treated as a Darcy resistance. The higher approximations take account of the modification to the mean flow, particularly in the near field, due to the localized nature of the actual resistance. Thus the second approximation finds the change due to a second sphere, and averages over all its possible positions. The result for the mean drag confirms Childress’ terms in clogc and c (apart from an arithmetical correction to the latter), but indicates that for practical values of c numerical evaluation of integrals is needed, rather than expansion in powers of c and log c. The last section of the paper develops the corresponding results for flow through random arrays of fixed parallel circular cylinders.

Bibliography

Howells, I. D. (1974). Drag due to the motion of a Newtonian fluid through a sparse random array of small fixed rigid objects. Journal of Fluid Mechanics, 64(3), 449â476.

Authors 1

I. D. Howells (first)

References 11 Referenced 199

Dates

Type	When
Created	19 years, 5 months ago (March 29, 2006, 8:28 a.m.)
Deposited	6 years, 4 months ago (April 6, 2019, 4 p.m.)
Indexed	3 weeks, 5 days ago (Aug. 6, 2025, 8:34 a.m.)
Issued	51 years, 1 month ago (July 8, 1974)
Published	51 years, 1 month ago (July 8, 1974)
Published Online	19 years, 5 months ago (March 29, 2006)
Published Print	51 years, 1 month ago (July 8, 1974)

Funders 0

None

BibTeX

@article{Howells_1974, title={Drag due to the motion of a Newtonian fluid through a sparse random array of small fixed rigid objects}, volume={64}, ISSN={1469-7645}, url={http://dx.doi.org/10.1017/s0022112074002503}, DOI={10.1017/s0022112074002503}, number={3}, journal={Journal of Fluid Mechanics}, publisher={Cambridge University Press (CUP)}, author={Howells, I. D.}, year={1974}, month=jul, pages={449–476} }

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