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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
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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

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