Hostname: page-component-7479d7b7d-c9gpj Total loading time: 0 Render date: 2024-07-12T10:49:33.695Z Has data issue: false hasContentIssue false
  • English
  • Français

A model of interfacial stress and spray generation by gas flowing over a deep, wavy pool

Published online by Cambridge University Press:  21 April 2006

Y. L. Sinai
Y. L. Sinai
Affiliation:
Research and Development, National Nuclear Corporation Limited, Warrington Road, Risley, Warrington, Cheshire, WA3 6BZ, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

A wave Reynolds number is the controlling parameter in Wang & Street's (1978) correlation for spray generation in developing air flow over a pool. A novel feature of the present theory is the prediction of the time-mean interfacial stress which, together with a wave-height correlation, is proposed and tested as a tool for quantifying that Reynolds number. The validation exercise shows that the results are generally acceptable, although the technique tends to underestimate the interfacial stress and droplet flux at high gas speeds. The analysis of experimental data has revealed some differences in the correlations which should be resolved.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 179 , June 1987 , pp. 327 - 344
Copyright
© 1987 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

Abramowitz, M. & Stegun, I. A. 1972 Handbook of Mathematical Functions. Dover.
Antonia, R. A. & Luxton, R. E. 1971 The response of a turbulent boundary layer to a step change in surface roughness. Part 1. Smooth to rough. J. Fluid Mech. 48, 721–761.Google Scholar
Boyadjiev, C., Mitev, P. & Bechkov, V. 1976 Laminar boundary layers at a moving interface generated by a counter-current gas-liquid stratified flow. Intl J. Multiphase Flow 3, 61–66.Google Scholar
Brighton, P. W. M. 1985 Evaporation from a plane liquid surface into a turbulent boundary layer. J. Fluid Mech. 159, 323–345.Google Scholar
Brodkey, R. S. 1967 The Phenomena of Fluid Motion. Addison-Wesley.
Brutsaert, W. & Jirka, G. H. (ed.) 1984 Gas Transfer at Water Surfaces. Reidel.
Cantwell, B. J. 1981 Organised motion in turbulent flow. Ann. Rev. Fluid Mech. 13, 457–515.Google Scholar
Charnock, H. 1955 Wind stress on water surface. Q. J. R. Met. Soc. 81, 639.Google Scholar
Clarke, D. 1985 Problems in triple-deck boundary layer theory. Ph.D. thesis, Department of Mathematics, University of Manchester.
Coantic, M. 1980 Mass transfer across the ocean-air interface: Small scale hydrodynamic and aerodynamic mechanisms. Physico-Chemical Hydrodyn. 1, 249–279.Google Scholar
Cousins, L. B. & Hewitt, G. F. 1968 Liquid phase mass transfer in annular two-phase flow: Droplet deposition and liquid entrainment. AERE-R5657.
Deaves, D. M. 1981 Computations of wind flow over changes in surface roughness. J. Wind Engng & Ind. Aerodyn. 7, 65–94.Google Scholar
Dukler, A. E. 1972 Characterisation effects and modelling of the wavy gas-liquid interface. Proc. Intl Symp. on Two-phase Systems, Haifa (1971). Prog. Heat Mass Transfer 6, 207–234.Google Scholar
Elliott, W. P. 1958 The growth of the atmospheric boundary layer. Trans. Am. Geophys. Union 39, 1048–1058.Google Scholar
Ewing, J. A. 1983 Wind waves: A review of research during the last twenty-five years. Geophys. J. R. Astr. Soc. 74, 313–329.Google Scholar
Favre, A. & Hasselmann, K. 1978 Turbulent Fluxes Through the Sea Surface. Wave Dynamics and Prediction. Plenum.
Garner, F. H., Ellis, S. R. M. & Lacey, J. A. 1954 The size distribution and entrainment of droplets. Trans. Instn Chem. Engrs 32, 222–235.Google Scholar
Goldstein, S. 1965 Modern Developments in Fluid Dynamics. Dover.
Hanratty, T. J. & Engen, J. M. 1957 Interaction between a turbulent air stream and a moving water surface. AIChE J. 3, 299–304.Google Scholar
Hanratty, T. J. & Woodmansee, D. E. 1965 Stability of the interface for a horizontal air-liquid flow. Symp. on Two-Phase Flow, Exeter, June 1965, Paper A1.
Hewitt, G. F. & Hall-Taylor, N. S. 1970 Annular Two-phase Flow. Pergamon.
Hidy, G. M. & Plate, E. J. 1966 Wind action on water standing in a laboratory channel. J. Fluid Mech. 26, 651–687.Google Scholar
Hsu, C.-T., Wu, H.-Y. & Street, R. L. 1982 Momentum and energy transfer in wind generation of waves. J. Phys. Oceanogr. 12, 929–951.Google Scholar
Hsu, S. A. 1974 A dynamic roughness equation and its application to wind stress determination at the air-sea interface. J. Phys. Oceanogr. 4, 116–120.Google Scholar
Hunt, J. C. R. & Simpson, J. E. 1982 Atmospheric boundary layers over non-homogeneous terrain. In Engineering Meteorology (ed. E. J. Plate). Elsevier.
Ishii, M. & Grolmes, M. A. 1975 Inception criteria for droplet entrainment in two-phase concurrent film flow. AIChE J. 21, 308–318.Google Scholar
Jensen, R. J. & Yuen, M. C. 1982 Interphase transport in horizontal stratified co-current flow. NUREG/CR-2334, US Nuclear Regulatory Commission, Washington.
Kataoka, I. & Ishii, M. 1984 Mechanistic modelling of pool entrainment phenomenon. Intl J. Heat Mass Transfer 27, 1999–2014.Google Scholar
Kataoka, I., Ishii, M. & Mishima, K. 1983 Generation and size distribution of droplets in annular two-phase flow. Trans. ASME 1: J. Fluids Engng 105, 230–238.Google Scholar
Kinsman, B. 1965 Wind Waves. Prentice-Hall.
Kitaigorodskii, S. A. 1973 Physics of Air-Sea Interaction. Israel Program of Scientific Translations, Jerusalem.
Kotake, S. 1974 Gas-liquid laminar boundary-layer flows with a wavy phase-changing interface. Intl J. Heat Mass Transfer 17, 885–897.Google Scholar
Lai, R. J. & Shemdin, O. H. 1974 Laboratory study of the generation of spray over water. J. Geophys. Res. 79, 3055–3063.Google Scholar
Longuet-Higgins, M. S. 1982 Parametric solutions for breaking waves. J. Fluid Mech. 121, 403–424.Google Scholar
Longuet-Higgins, M. S. 1983 Bubbles, breaking waves and hyperbolic jets at a free surface. J. Fluid Mech. 127, 103–121.Google Scholar
Macha, J. M. 1981 Modelling the marine ABL including the effects of sea spray. In Designing with the Wind Symposium, Nantes, June 15–19, 1981, vol. 1. CSTB.
Monahan, E. C. 1968 Sea spray as a function of low elevation wind speed. J. Geophys. Res. 73, 1127–1137.Google Scholar
Nakagawa, T. 1983 On characteristics of the water-particle velocity in a plunging breaker. J. Fluid Mech. 126, 251–268.Google Scholar
Newitt, D. M., Dombrowski, N. & Knelman, F. H. 1965 Liquid entrainment: 1. The mechanism of drop formation from gas or vapour bubbles. Trans. Instn Chem. Engrs 32, 244–261.Google Scholar
Nikitin, I. K. 1972 Approximate calculation of thermally stratified turbulent boundary layer in a region downstream of a sharp change in the roughness of the surface at which flow takesplace. Fluid Mech. Sov. Res. 1, 177–184.Google Scholar
Pai, S.-I. 1957 Viscous Flow Theory, vol. 2. Van Nostrand.
Phillips, O. M. 1977 The Dynamics of the Upper Ocean, 2nd edn. Cambridge University Press.
Pinchak, A. C. 1966 Correlation of some laboratory experiments in two-phase flow with phenomena at the air-sea interface. USAF Office of Aerospace Res. ARL-66–0159.
Plate, E. J. 1978 Wind-generated surface waves: The laboratory evidence. In Turbulent Fluxes Through the Sea Surface, Wave Dynamics and Prediction (ed. A. Favre & K. Hasselmann). Plenum.
Schlichting, H. 1960 Boundary Layer Theory. McGraw-Hill.
Shaw, C. Y. & Lee, Y. 1976 Wind-induced turbulent heat and mass transfer over large bodies of water. J. Fluid Mech. 77, 645–664.Google Scholar
Sinai, Y. L. 1982 A gross momentum-integral estimate of boundary-layer development over rough water. 24th Brit. Theoret. Mech. Colloquium, City University, London, March 1982.
Sinai, Y. L. 1983a A Charnock-based estimate of interfacial resistance and roughness for internal, fully-developed stratified, two-phase horizontal flow. Intl J. Multiphase Flow 9, 13–19.Google Scholar
Sinai, Y. L. 1983b The application of a Charnock-based estimate of interfacial stress to some near-horizontal, stratified two-phase flows. Thermal-Hydraulics of Nuclear Reactors (ed. M. Merilo), vol. 1, pp. 226–234. ANS, Lagrange Park.
Sinai, Y. L. 1986a An extended Charnock estimate of interfacial stress in stratified two-phase flows. Intl J. Multiphase Flow 12, 839–844.Google Scholar
Sinai, Y. L. 1986b Interfacial phenomena of fully-developed, stratified, two-phase flows. Encyclopedia of Fluid Mechanics, vol. 3. (ed. N. P. Cheremisinoff), pp. 475–491. Gulf.
Sinai, Y. L. 1986c An asymptotic estimate of boundary-layer development over rough water. Proc. 4th Miami Intl Symp. on Multi-Phase Transport and Particulate Phenomena, 15–17 December 1986, Miami, USA. Hemisphere.
Street, R. L. 1979 Turbulent heat and mass transfer across a rough, air-water interface: A simple theory. Intl J. Heat Mass Transfer 22, 885–899.Google Scholar
Street, R. L., Wang, C. S., McIntosh, D. A. & Miller, A. W. 1978 Fluxes through the boundary layers at an air-water interface; Laboratory studies. In Turbulent Fluxes Through the Sea Surface, Wave Dynamics and Prediction (ed. A. Favre & K. Hasselmann). Plenum.
Streeter, V. L. & Wylie, E. B. 1979 Fluid Mechanics. McGraw-Hill Kogakusha, Tokyo.
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.
Townsend, A. A. 1965 Self-preserving flow inside a turbulent boundary layer. J. Fluid Mech. 22, 773–797.Google Scholar
Ursell, F. 1956 Wave generation by wind. In Surveys in Mechanics. (ed. G. K. Batchelor & R. M. Davies). Cambridge University Press.
Wang, C. S. & Street, R. L. 1978 Measurements of spray at an air-water interface. Dyn. Atmos. Oceans 2, 141–152.Google Scholar
Wengefeld, P. 1978 Impuls, Warme, und Wasserdampf transport an der Oberflache ines offenen Gerinnes Unter dam Einflub des Windes. Commun. Inst. Hydraul. Engng, University of Karlsruhe vol. 12.
Wood, D. H. 1982 Internal boundary layer growth following a step change in surface roughness. Boundary-Layer Met. 22, 241–244.Google Scholar
Wit, J. 1968 Laboratory studies of wind-wave interactions. J. Fluid Mech. 34, 91–111.Google Scholar
Wu, J. 1973 Spray in the atmospheric surface layer: Laboratory study. J. Geophys. Res. 78, 511–519.Google Scholar
Wu, J. 1979 Spray in the atmospheric surface layer: Review and analysis of laboratory and oceanic results. J. Geophys. Res. 84, 1693–1704.Google Scholar
Wu, J. 1980 Wind-stress coefficients over sea surface near neutral conditions - a revisit. J. Phys. Oceanogr. 10, 727–740.Google Scholar
Wu, J. 1982 Sea spray: A further look. J. Geophys. Res. 87, 8905–8912.Google Scholar
Zanelli, S. & Hanratty, T. J. 1971 Relationship of entrainment to wave structure on a liquid film. Proc. Intl Symp. on Two-Phase Systems, Haifa, Israel, 1971.