Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-06T07:49:27.873Z Has data issue: false hasContentIssue false

Evaporation from a plane liquid surface into a turbulent boundary layer

Published online by Cambridge University Press:  20 April 2006

P. W. M. Brighton
Affiliation:
UKAEA, Safety and Reliability Directorate, Wigshaw Lane, Culcheth, Warrington WA3 4NE

Abstract

A new analytic solution is presented for predicting evaporation rates from plane liquid surfaces into a neutral turbulent boundary layer. Conditions of passive dispersion are assumed. Molecular diffusivity is incorporated into the boundary conditions. Both smooth and rough surfaces are considered. A comparison with a wide variety of experimental data is made; this tends to reveal inadequacies and inconsistencies in the data, rather than test the theory. The effects of a roughness change at the boundary of the liquid surface and of high vapour pressures can be included for practical purposes by simple formulae. A criterion is derived for the validity of the neglect of buoyancy effects.

Type
Research Article
Copyright
© 1985 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, 8th printing. Dover.
Batchelor, G. K. 1952 Diffusion in a field of homogeneous turbulence. II. The relative motion of particles. Proc. Camb. Phil. Soc. 48, 345362.Google Scholar
Batchelor, G. K. 1964 Diffusion from sources in a turbulent boundary layer. Arch. Mech. Stosowanej 16, 661670.Google Scholar
Brighton, P. W. M., Prince, A. J. & Webber, D. M. 1985 Determination of cloud areas and path from visual and concentration records. Presented at Symp. on Heavy Gas Dispersion Trials at Thorney Island, University of Sheffield, 3–5 April 1984; J. Hazardous Materials (in press).
Browne, L. W. B. & Antonia, R. A. 1979 Calculation of a turbulent boundary layer downstream of a step change in surface temperature. Trans. ASME C: J. Heat Transfer 101, 144150.Google Scholar
Brutsaert, W. 1975 A theory for local evaporation (or heat transfer) from rough and smooth surfaces at ground level. Water Resources Res. 11, 543550.Google Scholar
Brutsaert, W. 1982 Evaporation into the Atmosphere. Reidel.
Calder, K. L. 1949 Eddy diffusion and evaporation in flow over aerodynamically smooth and rough surfaces: a treatment based on laboratory laws of turbulent flow with special reference to conditions in the lower atmosphere. Q. J. Mech. Appl. Maths 2, 153176.Google Scholar
Carslaw, H. S. & Jaeger, J. C. 1963 Operational Methods in Applied Mathematics. Dover.
Chatwin, P. C. 1968 The dispersion of a puff of passive contaminant in the constant stress region. Q. J. R. Met. Soc. 94, 350360.Google Scholar
COVO STEERING COMMITTEE 1982 Risk Analysis of Six Potentially Hazardous Industrial Objects in the Rijnmond Area, A Pilot Study. Reidel.
Elias, F. 1929 Die Wärmeübertragung einer geheizten Platte an strömende Luft. I. Anlage und Ergebnisse der Versuche. Z. angew. Math. Mech. 9, 434453.Google Scholar
Elias, F. 1930 Die Wärmeübertragung einer geheizten Platte an strömende Luft. II. Vergleich der Versuchsergebnisse mit der Theorie. Z. angew. Math. Mech. 10, 114.Google Scholar
Fackrell, J. E. & Robins, A. G. 1982 Concentration fluctuations and fluxes in plumes from point sources in a turbulent boundary layer. J. Fluid Mech. 117, 126.Google Scholar
Gray, D. C. 1974 Solvent evaporation rates. Am. Indust. Hygiene J. Nov. 1974, 695710.Google Scholar
Health And Safety Executive 1978 Canvey: an Investigation of Potential Hazards from Operations in the Canvey Island/Thurrock Area. HMSO.
HEALTH AND SAFETY EXECUTIVE 1981 Canvey: a Second Report. A Review of Potential Hazards from Operations in the Canvey Island/Thurrock Area Three Years after Publication of the Canvey Report. HMSO.
Himus, G. W. 1929 The evaporation of water in open pans. Trans. Inst. Chem. Engrs 7, 166177.Google Scholar
Hinchley, J. W. & Himus, G. W. 1924 Evaporation in currents of air. Trans. Inst. Chem. Engrs 2, 5764.Google Scholar
Hine, T. B. 1924 The rate of evaporation of liquids in a current of air. Phys Rev. 24, 7991.Google Scholar
Hunt, J. C. R. & Simpson, J. E. 1982 Atmospheric boundary layers over non-homogeneous terrain. In Engineering Meteorology (ed. E. J. Plate), chap. 7. Elsevier.
Hunt, J. C. R. & Weber, A. H. 1979 A Lagrangian statistical analysis of diffusion from a ground-level source in a turbulent boundary layer. Q. J. R. Met. Soc. 105, 423443.Google Scholar
Jeulink, J. 1983 Mitigation of the evaporation of liquids by fire-fighting foams. In Proc. 4th Intl Symp. on Loss Prevention and Safety Promotion in the Process Industries, vol. I (Inst. Chem. Engrs Symp. Series no. 80), E12–22.
Jones, C. J. & Mcgugan, P. J. 1978 An investigation of the evaporation of some volatile solvents from domestic waste. J. Hazardous Materials 2, 235251.Google Scholar
Kader, B. A. 1981 Temperature and concentration profiles in fully turbulent boundary layers. Intl J. Heat Mass Transfer 24, 15411544.Google Scholar
Lees, F. P. 1980 Loss Prevention in the Process Industries. Butterworths.
Mackay, D., Paterson, S. & Nadeau, S. 1980 Calculation of the evaporation rate of volatile liquids. In Proc. 1980 Natl Conf. on Control of Hazardous Material Spills, pp. 361368.
Millar, F. G. 1937 Evaporation from free water surfaces. Can. Met. Mem. 1, 4365.Google Scholar
Monin, A. S. & Yaglom, A. M. 1971 Statistical Fluid Mechanics, vol. 1. MIT Press.
O'Brien, L. J. & Stutzman, L. F. 1950 Mass transfer of pure liquids from a plane, free surface. Indust. Engng Chem. 42, 11811187.Google Scholar
Opschoor, G. 1978 Evaporation. In Methods for the Calculation of the Physical Effects of the Escape of Dangerous Material (Liquids and Gases): Report of the Committee for the Prevention of Disasters, chap. 5. Directorate General of Labour, Ministry of Social Affairs, the Netherlands.
Pasquill, F. 1943 Evaporation from a plane, free-liquid surface into a turbulent air stream. Proc. R. Soc. Lond. A 182, 7595.Google Scholar
Reid, R. C., Prausnitz, J. M. & Sherwood, T. K. 1977 The Properties of Gases and Liquids, 3rd edn. McGraw-Hill.
Reijnhart, R., Piepers, J. & Toneman, L. H. 1980 Vapour cloud dispersion and the evaporation of volatile liquids in atmospheric wind fields – I. Theoretical model. Atmos. Environ. 14, 751758.Google Scholar
Reijnhart, R. & Rose, R. 1980 Vapour cloud dispersion and the evaporation of volatile liquids in atmospheric wind fields – II. Wind tunnel experiments. Atmos. Environ. 14, 759762.Google Scholar
Shaw, P. & Briscoe, F. 1978. Vaporization of spills of hazardous liquids on land and water. UKAEA Rep. SRD R100.
Sherwood, T. K., Pigford, R. L. & Wilke, C. R. 1975 Mass Transfer. McGraw-Hill.
Snijders, A. L., Koppius, A. M. & Nieuwvelt, C. 1983 An experimental determination of the turbulent Prandtl number in the inner boundary layer for airflow over a flat plate. Intl J. Heat Mass Transfer 26, 425431.Google Scholar
Sutton, O. G. 1934 Wind structure and evaporation in a turbulent atmosphere. Proc. R. Soc. Lond. A 146, 701722.Google Scholar
Sutton, O. G. 1955 Atmospheric Turbulence. Methuen.
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.
Wade, S. H. 1942 Evaporation of liquids in currents of air. Trans. Inst. Chem. Engrs 20, 113.Google Scholar