Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-19T22:59:21.224Z Has data issue: false hasContentIssue false
  • English
  • Français

Linear pressure waves in fogs

Published online by Cambridge University Press:  26 April 2006

R. Duraiswami  and
A. Prosperetti
R. Duraiswami
Affiliation:
Dynaflow Inc., 7210 Pindell School Road, Fulton, MD 20759, USA
A. Prosperetti
Affiliation:
Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The modelling of small-amplitude pressure waves in dilute single- or multi-component fogs by means of averaged equations is considered. The problem is cast in a singular-perturbation framework in which the suspended droplets are the singularities. This point of view simplifies the local problem in the vicinity of the droplets. Matching in the overlap region provides the coupling with the averaged fields. Among the advantages of the method is the fact that the leading-order effects are clearly identified. In particular it is shown that, for low-amplitude waves and far below the fluid's critical point, phase change effects only start to be important when the vapour mean free path becomes comparable with the drop radius and dominate for yet smaller drops.

This present method for the derivation of effective equations appears to be of general applicability to a variety of multi-phase situations and is illustrated in detail.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 299 , 25 September 1995 , pp. 187 - 215
Copyright
© 1995 Cambridge University Press

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

Aoki, K. & Cercignani, C. 1983 Evaporation and condensation on two parallel plates at finite Reynolds numbers. Phys. Fluids 26, 1163–1164.Google Scholar
Aoki, K., Sone, Y. & Yamada, T. 1990 Numerical analysis of gas flows condensing on its plane condensed phase on the basis of kinetic theory. Phys. Fluids A 2, 1867–1878.Google Scholar
Caflisch, R. E., Miksis, M. J., Papanicolaou, G. C. & Ting, L. 1985 Effective equations for wave propagation in bubbly liquids. J. Fluid Mech. 153, 259–273.Google Scholar
Caflisch, R. E. & Rubinstein, J. 1986 Lectures on the Mathematical Theory of Multi-Phase Flow. Lecture Notes, New York University, Courant Institute of Mathematical Sciences.
Cercignani, C. 1988 Kinetic Theory and Gas Dynamics. Springer.
Cercignani, C., Fiszdon, W. & Frezzotti, A. 1985 The paradox of the inverted temperature profiles between an evaporating and a condensing surface. Phys. Fluids 28, 3327–3240.Google Scholar
Duraiswami, R. 1990 I. Effective equations for sound propagation in fogs. II. Orthogonal mapping in two dimensions. PhD Dissertation, Department of Mechanical Engineering, The Johns Hopkins University (available from University Microfilms, Ann Arbor, Michigan).
Foldy, L. L. 1945 The multiple scattering of waves. Phys. Rev. 67, 107–119.Google Scholar
Fukuta, N. & Walter, L. A. 1970 Kinetics of hydrometer growth from a vapor spherical model. J. Atmos. Sci. 27, 1160–1172.Google Scholar
Guha, A. 1992 Structure of partly dispersed normal shock waves in vapor-droplet flows. Phys. Fluids. A 4, 1566–1578.Google Scholar
Guha, A. 1994 A unified theory of aerodynamic and condensation shock waves in vapor-droplet flows with or without a carrier gas. Phys. Fluids 6, 1893–1913.Google Scholar
Gumerov, N. A., Ivandaev, A. I. & Nigmatulin, R. I. 1988 Sound waves in monodisperse gasparticle or vapour-droplet mixtures. J. Fluid Mech. 193, 53–74.Google Scholar
Gyarmathy, G. 1982 The spherical droplet in gaseous carrier streams: Review and synthesis. In Multiphase Science and Technology (ed. G. F. Hewitt, J. M. Delhaye & N. Zuber), Vol. 1, pp. 99–279. Hemisphere.
Hermans, L. J. F. & Beenakker, J. J. M. 1986 The temperature paradox in the kinetic theory of evaporation. Phys. Fluids 29, 4231–4232.Google Scholar
Jaeschke, M., Heller, W. J. & Meier, G.E.A. 1975 Acoustic damping in a gas mixture with suspended submicroscopic droplets. J. Sound Vib. 43, 467–481.Google Scholar
Koffman, L. D., Plesset, M. S. & Lees, L. 1984 Theory of evaporation and condensation. Phys. Fluids 27, 876–880.Google Scholar
Kogan, M. N. 1973 Molecular gas dynamics. Ann. Rev. Fluid Mech. 5, 383–404.Google Scholar
Labuntsov, D. A. & Kryukov, A. P. 1976 Analysis of intensive evaporation and condensation. Intl J. Heat Mass Transfer 22, 989–1002.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics. Pergamon.
Landau, L. D. & Lifshitz, E. M. 1981 Physical Kinetics. Pergamon.
Marble, F. E. 1969 Some gasdynamic problems in the flow of condensing vapors. Astronautica Acta 14, 585–614.Google Scholar
Marble, F. E. & Wooten, D. C. 1970 Sound attenuation in a condensing vapor. Phys. Fluids 13, 2657–2664.Google Scholar
Millikan, R. A. 1923 The general law of fall of a small spherical body through a gas, and its bearing upon the nature of molecular reflection from surfaces. Phys. Rev. 22, 1–23.Google Scholar
Onishi, Y. 1986 The spherical-droplet problem of evaporation and condensation in a vapour-gas mixture. J. Fluid Mech. 163, 171–194.Google Scholar
Pao, Y. P. 1971a Application of kinetic theory to the problem of evaporation and condensation. Phys. Fluids 14, 306–312.Google Scholar
Pao, Y. P. 1971b Temperature and density jumps in the kinetic theory of gases and vapors. Phys. Fluids 14, 1340–1346.Google Scholar
Rubinstein, J. 1986 Effective equations for flow in random porous media with a large number of scales. J. Fluid Mech. 170, 379–383.Google Scholar
Schaaf, S. A. & Chambré, P. L. 1961 Flow of Rarefied Gases, p. 39. Princeton University Press.
Shankar, P. N. & Deshpande, M. D. 1990 On the temperature distribution in liquid-vapor phase change between plane liquid surfaces. Phys. Fluid A 2, 1030–1038.Google Scholar
Sone, Y., Takata, S. & Wakabayashi, M. 1994 Numerical analysis of a rarefied gas flow past a volatile particle using the Boltzmann equation for hard-sphere molecules. Phys. Fluids 6, 1914–1928.Google Scholar
Sugimoto, H. & Sone, Y. 1992 Numerical analysis of steady flows of a gas evaporating from its cylindrical condensed phase on the basis of kinetic theory. Phys. Fluids A 4, 419–440.Google Scholar
Wei, R., Tian, Y. & Lu, Q. 1987 Absorption of sound in water fog composed of submicron droplets. J. Acoust. Soc. Am 81, 1350–1354.Google Scholar
Wei, R. & Wu, J. 1981 Absorption of sound in water fog. J. Acoust. Soc. Am. 70, 1213–1219.Google Scholar
Young, J. B. 1982 The spontaneous condensation of steam in supersonic nozzles. PhysicoChem. Hydrodyn. 3, 57–82.Google Scholar
Young, J. B. 1984 Semi-analytical techniques for investigating thermal non-equilibrium effects in wet steam turbines. Intl J. Heat Fluid Flow 5, 81–91.Google Scholar
Young, J. B. & Guha, A. 1991 Normal shock wave structure in two-phase vapour-droplet flows. J. Fluid Mech. 228, 243–274.Google Scholar
Ytrehus, T. 1983 Asymmetries in evaporation and condensation Knudsen layer problems. Phys. Fluids 26, 939–952.Google Scholar