OPEN CHANNEL FLOW COMPUTED USING A LOW-REYNOLDS-NUMBER k-ε TURBULENCE MODEL

摘要

The present contribution is concerned with the application of the two-equation k-ε turbulence model of Launder and Sharma (1974) to open channel flow (k is the turbulent kinetic energy and ε the rate of viscous dissipation of k). The model is of the 'low-Reynolds-number' type in which departures from the standard (high-Reynolds-number) approach take the form of functions based upon a local Reynolds number of turbulence, Re_t = k~2/vε, where ε is a modified dissipation rate variable. It is found that the turbulence model tends to under-predict turbulence levels in comparison against Direct Numerical Simulation and experimental data for open channel flows at low or moderate bulk Reynolds number. Particular attention is paid to the prescription of the free surface boundary condition on the ε-equation and a new boundary condition is derived from the limiting form of the k-equation in the vicinity of a shear-free surface. The 'limiting form' boundary condition leads to profiles of eddy viscosity, v_t that are significantly different over the upper half of a channel from those obtained if a zero gradient boundary condition is applied to the ε -equation. It is anticipated that this finding will have implications for the calculation of the distribution of suspended sediment in free surface flows.