Assessment of models for velocity distribution in turbulent smooth-wall open channel flows

ABSTRACT

This study attempts to provide a more precise and comprehensive model for stream-wise velocities in turbulent smooth-wall open channel flows. Velocity profiles are obtained from the resolution of two ordinary differential equations. The first is derived from the Reynolds-averaged Navier-Stokes (RANS) equation while the second is from the equilibrium between turbulent kinetic energy (TKE) production and dissipation. We assessed different analytical models for eddy viscosity, TKE and mixing length. Computation results for velocity profiles were assessed and compared to experimental data for different flow conditions and the well-known linear, log and log-wake laws. Our results show that the model based on the RANS equation provides more accurate velocity profiles. In the viscous sublayer and buffer layer, the method based on Prandtl’s eddy viscosity model and Van Driest mixing length gives more precise results. For the log layer and outer region, a mixing length equation derived from Von Karman’s similarity hypothesis, provides the best agreement with measured data except near the free surface where we used an additional correction based on a damping function for eddy viscosity. This method allows more accurate velocity profiles with the same value of the damping coefficient that is valid under different flow conditions.

KEYWORDS:

• Open channel flow
• velocity distribution
• momentum equation
• eddy viscosity
• improved accuracy

Acknowledgments

This study is part of the PhD thesis of the first author which is funded by Ethio-France sandwich program, co-financed by the Ethiopian Ministry of Education and the French Embassy in Addis Ababa, Ethiopia.

Disclosure statement

No potential conflict of interest was reported by the authors.