Hostname: page-component-848d4c4894-2pzkn Total loading time: 0 Render date: 2024-05-22T08:55:27.923Z Has data issue: false hasContentIssue false
  • English
  • Français

Mathematical modelling of three-dimensional heated surface jets

Published online by Cambridge University Press:  19 April 2006

J. J. McGuirk  and
W. Rodi
J. J. McGuirk
Affiliation:
Sonderforschungsbereich 80, University of Karlsruhe, Germany Present address: Department of Chemical Engineering, Imperial College, London.
W. Rodi
Affiliation:
Sonderforschungsbereich 80, University of Karlsruhe, Germany
Get access Rights & Permissions [Opens in a new window]

Abstract

A new economical finite-difference method is described for the calculation of three-dimensional heated surface jets discharging into stagnant water. The equations solved are for continuity, lateral and longitudinal momentum, and thermal energy. The turbulent shear stresses and heat fluxes in these equations are determined with a turbulence model involving simplified forms of the transport equations for these stresses and fluxes and the solution of differential transport equations for the turbulent kinetic energy κ and the rate of its dissipation ε. The experimentally observed entrainment reduction due to buoyancy is reproduced by this model. The predictions are compared in detail with the recent measurements of Pande & Rajaratnam, which are judged to be superior to those of other investigators. The agreement is generally satisfactory.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 95 , Issue 4 , 27 December 1979 , pp. 609 - 633
Copyright
© 1979 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

Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Chu, V. H. & Vanvari, M. R. 1976 Experimental study of turbulent stratified shearing flow. J. Hydraul. Div. A.S.C.E. 102, (HY6), 691–706.Google Scholar
Demuren, A. D. & Spalding, D. B. 1977 Mathematical modelling of steady two-dimensional surface flows. Dept. Mech. Engng, Imp. Coll. Rep. HTS/77/23.Google Scholar
Dunn, W. E., Policastro, A. J. & Paddock, R. A. 1975 Surface thermal plumes; evaluation of mathematical models for the near and complete field. Argonne National Laboratory Rep. ANL/WR-75-3.Google Scholar
Ellison, T. H. & Turner, J. S. 1959 Turbulent entrainment in stratified flows. J. Fluid Mech. 15, 413–448.Google Scholar
Engelund, F. 1976 Hydraulics of surface buoyant jet. J. Hydraul. Div. A.S.C.E. 102 (HY9), 1315–1325.Google Scholar
Gibson, M. M. & Launder, B. E. 1976 On the calculation of horizontal, turbulent free shear flow under gravitational influence. Trans. A.S.M.E., J. Heat Transfer, C 98, 81–87.Google Scholar
Hayashi, T. & Shuto, N. 1967 Diffusion of warm water jets discharged horizontally at the water surface. 12th Cong. IAHR, Fort Collins, Colorado, U.S.A.
Hossain, M. S. 1979 Mathematische Modellierung von turbulenten Auftriebsströmungen. Ph.D. thesis, University of Karlsruhe.
Hossain, M. S. & Rodi, W. 1977 Influence of buoyancy on the turbulence intensities in horizontal and vertical jets. In Heat Transfer and Turbulent Buoyant Convection: Studies and Applications for Natural Environment, Buildings, Engineering Systems, vol. 1 (ed. D. B. Spalding & N. Afgan). Washington, D.C.: Hemisphere Publishing Corp.
Jirka, G. H., Abraham, G. & Harleman, D. R. F. 1975 An assessment of techniques for hydrothermal prediction. Ralph M. Parsons Laboratory for Water Resources and Hydromechanics, MIT Rep. no. 203.
Launder, B. E. 1975 On the effect of a gravitational field on the turbulent transport of heat and momentum. J. Fluid Mech. 67, 569–587.Google Scholar
Launder, B. E. 1976 Progress in the modelling of turbulent transport. Lecture Series 76. von Kármán Institute.
Launder, B. E. & Spalding, D. B. 1974 The numerical computation of turbulent flows. Comp. Meth. in Appl. Mech. & Eng. 3, 269–289.Google Scholar
Launder, B. E., Reece, G. J. & Rodi, W. 1975 Progress in the development of a Reynolds stress turbulence closure. J. Fluid Mech. 68, 537–566.Google Scholar
Mcguirk, J. J. & Rodi, W. 1977 Calculation of three-dimensional heated surface jets. In Heat Transfer and Turbulent Buoyant Convection: Studies and Applications for Natural Environment, Buildings, Engineering Systems, vol. 1 (ed. D. B. Spalding & N. Afgan). Washington, D.C.: Hemisphere Publishing Corp.
Mcguirk, J. J. & Rodi, W. 1979 The calculation of three-dimensional turbulent free jets. In Turbulent Shear Flows I (ed. F. Durst, B. E. Launder, F. W. Schmidt & J. H. Whitelaw). Springer.
Pande, B. B. LAL & Rajaratnam, N. 1975 An experimental study of heated surface discharges into quiescent ambients. Tech. Rep. Dept. of Civil Engng, The University of Alberta, Edmonton, Canada. 1977 partly published in J. Hydraul. Res. 15, 261–275.Google Scholar
Patankar, S. V. & Spalding, D. B. 1972 A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows. Int. J. Heat Mass Transfer 15, 1787–1806.Google Scholar
Paul, J. 1973 A numerical model for a three-dimensional, variable-density jet, doctoral dissertation. Dept. Fluid, Thermal and Aerospace Science, Case Western Reserve University.Google Scholar
Rodi, W. 1978 Turbulence models and their application in hydraulics - a state of the art review. University of Karlsruhe Rep. SFB 80/T/127.Google Scholar
Sharma, D. 1974 Turbulent convective phenomena in straight, rectangular-sectional diffusers. Ph.D. thesis, University of London.
Shirazi, M. 1973 Pacific Northwest Environmental Research Laboratory Working Paper No. 4, U.S.E.P.A., Corvallis, Oregon, U.S.A.
Shirazi, M. & Davis, L. E. 1976 Analysis of buoyant surface jets. Trans. A.S.M.E., J. Heat Transfer 367–372.Google Scholar
Stefan, H. & Schiebe, F. R. 1970 Heated discharge from flume into tank. J. Sanitary Engng. Div. A.S.C.E. 96 (SA6), 1415–1433.Google Scholar
Stefan, H. & Vaidyaraman, P. 1972 Jet-type model for the three-dimensional thermal plume in a cross current underwind. Water Resources Res. 8, 4.Google Scholar
Stolzenbach, K. D. & Harleman, D. R. F. 1971 An analytical and experimental investigation of surface discharges of heated water. Ralph M. Parsons Laboratory for Water Resources and Hydrodynamics, MIT Rep. no. 135.
Waldrop, W. & Farmer, R. 1974 Three-dimensional computation of buoyant plumes. J. Geophys. Res. 79, 9.Google Scholar
Wiuff, R. 1978 Experiments on surface buoyant jet. J. Hydraul. Div. A.S.C.E. 104 (HY5), 667–679.Google Scholar