Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-27T05:17:11.544Z Has data issue: false hasContentIssue false
  • English
  • Français

Characterizations of the critical Stokes number for potential and viscous flows

Published online by Cambridge University Press:  26 February 2010

D. Lesnic ,
L. Elliott  and
D. B. Ingham
D. Lesnic
Affiliation:
Department of Applied Mathematical Studies, University of Leeds, Leeds. LS2 9JT.
L. Elliott
Affiliation:
Department of Applied Mathematical Studies, University of Leeds, Leeds. LS2 9JT.
D. B. Ingham
Affiliation:
Department of Applied Mathematical Studies, University of Leeds, Leeds. LS2 9JT.
Get access

Abstract

The impaction on symmetrical obstacles placed in uniform streams of aerosols is investigated. The governing equations of motion are nonlinear differential equations involving a parameter called the Stokes number. The study differentiates between the critical value of the Stokes number on the centre-line, kcr, below which no particles reach the stagnation point in finite time, and the critical value of the Stokes number on the obstacle, Kcr, below which no particles may be deposited on the obstacle in finite time. Based on the properties of the centre-line fluid velocity of the potential and viscous flows past a variety of symmetrically shaped obstacles, upper and lower bounds of Kcr and Kcr are established. Furthermore, using a numerical procedure for solving nonlinear differential equations with unknown parameters the critical values of Kcr and Kcr are obtained.

Type
Research Article
Information
Mathematika , Volume 41 , Issue 2 , December 1994 , pp. 277 - 292
Copyright
Copyright © University College London 1994

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Barbashin, E. A.. Introduction to the Theory of Stability. Trans, ed. Lukes, T., (Wolters-Nordhoff, The Netherlands, 1970).Google Scholar
2.Cesari, L.. Asymptotic Behaviour and Stability Problems in Ordinary Differential Equations, 3rd ed. (Academic Press, New York, 1971).CrossRefGoogle Scholar
3.Chaplygin, S. A.. A new method of approximate integration of differential equations. Collected Works, 1 (1948), 349 (in Russian).Google Scholar
4.Davies, C. N. and Peetz, C. V.. Impingement of particles on a transverse cylinder. Proc. R. Soc., A234 (1956), 269–295.Google Scholar
5.Fernández, J.Mora, de la. Inertial effects on linear and locally linear flows. Aerosol Sci. Tech., 4 (1985), 339–349.CrossRefGoogle Scholar
6.Fuchs, N. A.. The Mechanics of Aerosols (Pergamon Press, London, 1964).Google Scholar
7.Golovin, M. N. and Putnam, A. A.. Inertial impaction on single elements. Ind. Eng. Chem.-Fundam., 1, 1 (1962), 264–273.CrossRefGoogle Scholar
8.Hildyard, M. L.. The fluid mechanics of filters (Ph.D. Thesis, The University of Leeds, 1988).Google Scholar
9.Hirsch, M. W. and Smale, S.. Differential Equations, Dynamical Systems and Linear Algebra (Academic Press, London, 1974).Google Scholar
10.Ingham, D. B., Hildyard, L. T. and Hildyard, M. L.. On the critical Stokes' number for particle transport in potential and viscous flows near bluff bodies. J. Aerosol Sci., 21, 7 (1990), 935–946.CrossRefGoogle Scholar
11.Jordan, D. W. and Smith, P.. Nonlinear Ordinary Differential Equations, 2nd ed. (Clarendon Press, Oxford, 1987).Google Scholar
12.Konstandopoulos, A. G., Labowsky, M. J. and Rosner, D. W.. Inertial deposition of particles from potential flows past cylinder arrays. J. Aerosol Sci., 24, 4 (1993), 471–483.CrossRefGoogle Scholar
13.Langmuir, I.. The production of rain by a chain reaction in cumulus clouds at temperatures above freezing. J. Meteorol, 5 (1948), 175–192.2.0.CO;2>CrossRefGoogle Scholar
14.Langmuir, I. and Blodgett, K.. Mathematical investigation of water droplet trajectories. Collected Work of I. Langmuir, 10 (1946), 348–393.Google Scholar
15.Levin, L. M.. Deposition of particles from a flow of aerosol onto obstacles. Dokl. Akad. Nauk. SSSR, 91, 6 (1953), 1329–1332 (in Russian).Google Scholar
16.Levin, L. M.. Investigations in the Physics of Coarse-dispersed Aerosols (English trans. Foreign Division Document FTD-HT-23-1593-67, 1961).Google Scholar
17.Michael, D. H.. The steady motion of a sphere in a dusty gas. J. Fluid Mech., 31, 1 (1968), 175–192.CrossRefGoogle Scholar
18.Michael, D. H. and Norey, P. W.. Slow motion of a sphere in a two-phase medium. Canadian J. Phys., 48 (1970), 1607–1616.CrossRefGoogle Scholar
19.Milne-Thomson, L. M.. Theoretical Hydrodynamics, 5th ed. (Macmillan Co Ltd, New York, 1968).CrossRefGoogle Scholar
20.Ranz, W. E.. The Impaction of Aerosol Particles on Cylindrical and Spherical Collectors (Univ. Ill., Eng. Expt. Sta. Tech. Rept. 3, 1951).Google Scholar
21.Sell, W.. Dust precipitation on simple bodies and in air filters. Forsch. Geb. Ing. Wes., 2 (1931), 347 (English trans, in Ref. [20]).Google Scholar
22.Taylor, G. I.. Notes on possible equipment and technique for experiments on icing on aircraft. Aeronaut. Res. Comm. R&M, 2024 (1940).Google Scholar