Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-05T13:36:23.210Z Has data issue: false hasContentIssue false
  • English
  • Français

A depth-averaged mathematical model for the near field of side discharges into open-channel flow

Published online by Cambridge University Press:  12 April 2006

J. J. Mcguirk  and
W. Rodi
J. J. Mcguirk
Affiliation:
Sonderforschungsbereich 80, University of Karlsruhe, Germany
W. Rodi
Affiliation:
Sonderforschungsbereich 80, University of Karlsruhe, Germany
Get access Rights & Permissions [Opens in a new window]

Abstract

A two-dimensional mathematical model is described for the calculation of the depth-averaged velocity and temperature or concentration distribution in open-channel flows, an essential feature of the model being its ability to handle recirculation zones. The model employs the depth-averaged continuity, momentum and temperature/concentration equations, which are solved by an efficient finite-difference procedure. The ‘rigid lid’ approximation is used to treat the free surface. The turbulent stresses and heat or concentration fluxes are determined from a depth-averaged version of the so-called k, ε turbulence model which characterizes the local state of turbulence by the turbulence kinetic energy k and the rate of its dissipation ε. Differential transport equations are solved for k and ε to determine these two quantities. The bottom shear stress and turbulence production are accounted for by source/sink terms in the relevant equations. The model is applied to the problem of a side discharge into open-channel flow, where a recirculation zone develops downstream of the discharge. Predicted size of the recirculation zone, jet trajectories, dilution, and isotherms are compared with experiments for a wide range of discharge to channel velocity ratios; the agreement is generally good. An assessment of the numerical accuracy shows that the predictions are not influenced significantly by numerical diffusion.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 86 , Issue 4 , 28 June 1978 , pp. 761 - 781
Copyright
© 1978 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

Carter, H. H. 1969 A preliminary report on the characteristics of a heated jet discharged horizontally into a transverse current. Part 1 – constant depth. Chesapeake Bay Inst., Johns Hopkins Univ. Tech. Rep. no. 61.Google Scholar
De Vahl Davis, G. & Mallinson, G. D. 1972 False diffusion in numerical fluid mechanics. School Mech. Indust. Engng, Univ. New South Wales Rep. no. 1972/FMT/1.Google Scholar
Fink, L. 1977 Abschätzung der Rezirkulationsgefahr bei Brauchwasser-Entnahme- und Rückgabesystemen in FliesZgewässern. Wasserwirtschaft 67 (3), 65–70.Google Scholar
Fischer, H. 1973 Longitudinal dispersion and transverse mixing in open-channel flow. Ann. Rev. Fluid Mech. 5, 59–78.Google Scholar
Flokstra, C. 1976 Generation of two-dimensional horizontal secondary currents. Delft Hydraul. Lab. Res. Rep. S 163, part II.Google Scholar
Gosman, A. D. & Pun, W. M. 1973 Lecture notes for course entitled – Calculation of recirculating flows. Heat Transfer Section, Dept. Mech. Engng, Imp. Coll. Rep. HTS/74/2.Google Scholar
Jirka, G. H., Abraham, G. & Harleman, D. R. F. 1975 An assessment of techniques for hydrothermal prediction. Final Rep. to U.S. Atomic Energy Comm., R. M. Parsons Lab. Water Resources Hydrodyn., Dept. Civil Engng, MIT Rep. no. 203.Google Scholar
Kuipers, J. & Vreugdenhil, C. B. 1973 Calculations of two-dimensional horizontal flow. Delft Hydraul. Lab. Rep. S 163, part 1.Google Scholar
Laufer, J. 1951 Investigation of turbulent flow in a two-dimensional channel. N.A.C.A. Rep. no. 1053.Google Scholar
Launder, B. E., Morse, A., Rodi, W. & Spalding, D. B. 1972 Prediction of free shear flows – a comparison of the performance of six turbulence models. Proc. Conf. Free Turbulent Shear Flows, N.A.S.A. Langley Research Center, vol. 1, pp. 361–422.Google Scholar
Launder, B. E. & Spalding, D. B. 1974 The numerical computation of turbulent flows. Comp. Meth. in Appl. Mech. Engng 3, 269–289.Google Scholar
Leendertse, J. J. 1967 Aspects of a computational model for long period water wave propagation. Rand Corp. Mem. RM-5294-PR.Google Scholar
Loziuk, L. A., Anderson, J. C. & Belytschko, E. 1972 Hydrothermal analysis by finite-element method. J. Hydraul. Div., Proc. A.S.C.E. 98 (HY3), 1983–1997.Google Scholar
Mikhail, R., Chu, V. H. & Savage, S. B. 1975 The reattachment of a two-dimensional turbulent jet in a confined cross flow. Proc. 16th IAHR Cong., São Paulo, Brazil, vol. 3, pp. 414–419.Google Scholar
Nakagawa, H., Nezu, I. & Ueda, H. 1975 Turbulence of open-channel flow over smooth and rough beds. Proc. Japan Soc. Mech. Engrs 241, 155–168.Google Scholar
Patankar, S. V. & Spalding, D. B. 1970 Heat and Mass Transfer in Boundary Layers, 2nd edn. London: Intertext Books.
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
Policastro, A. J. & Tokar, J. V. 1972 Heated effluent dispersion in large lakes – state of the art of analytical modelling. Part I: critique of model formulations. Argonne Nat. Lab. Centre for Environmental Studies Rep. ANL/ES-11.Google Scholar
Pope, S. B. & Whitelaw, J. H. W. 1976 The calculation of near-wake flows. J. Fluid Mech. 73, 9–32.Google Scholar
Raithby, G. 1976 Skew upstream differencing schemes for problems involving fluid flow. Comp. Meth. in Appl. Mech. Engng 9, 151–162.Google Scholar
Rastogi, A. K. & Rodi, W. 1978 Two- and three-dimensional calculations of heat and mass transfer in open channel flows. J. Hydraul. Div., Proc. A.S.C.E. (in press).Google Scholar
Roache, P. J. 1976 Computational Fluid Mechanics. Hermosa Publishers.
Rouse, H. 1957 Diffusion in the lee of a two-dimensional jet. Proc. 9th Cong. Int. Méc. Appl., Univ. Bruxelles.Google Scholar
Spalding, D. B. 1975 THIRBLE – Transfer of heat in rivers, bays, lakes and estuaries. Heat Transfer Section, Dept. Mech. Engng, Imp. Coll. Rep. HTS/75/4.Google Scholar
Strazisar, A. & Prahl, J. 1973 The effects of bottom friction on river entrance flow with crossflow. Proc. 16th Conf. Great Lakes Res. pp. 615–625.Google Scholar