Calculation of secondary flow in a straight open channel with RANS and LES

Abstract

In depth-averaged water quality model, dispersion-like terms will appear when the three dimensional shallow water equations are averaged over the water column. In the present paper, the effect of dispersion terms in the transport equation is examined with numerical method. The depth-averaged transport equation is solved over a rectangular domain with constant velocity field and constant water depth. The dispersion terms are modeled following Preston’s way in which the longitudinal dispersion coefficient and the transversal diffusion coefficient are calculated with Elder’s method. The mass discharges from a vertical line source with three types of rate which are instantaneous, constant and periodical and the movement of the mass cloud are observed. The dispersion terms have a great effect upon the results of instantaneous discharges while exert little influence on steady result of constant discharge. With respect to periodical discharge, the effect has a good correlation with the dispersion Peclet number, which is a dimensionless number defined by velocity, discharge period and dispersion coefficient. The effect reaches a peak value at a middle-value of Peclet number and vanishes when the Peclet number increases to larger enough.