Prediction of channel flow characteristics through square arrays of emergent cylinders

Abstract

This paper describes a theoretical approach of turbulent flow in an infinite square array of emergent cylinders distributed uniformly along a channel bottom. Laboratory experiments were carried out to investigate the flow velocity characteristics in order to confirm this theoretical approach. A model array of vertical, rigid, circular, and threaded steel cylinders, of regular distribution, was mounted on the bed of a recirculating hydraulic channel. Measurements of the three-dimensional flow velocity components were carried out using a 3D acoustic Doppler velocimeter. At a certain distance downstream of a lateral row of cylinders, the transversal profiles of velocities and turbulence parameters are expected to be periodic functions in the lateral position whose period is the centre-to-centre spacing of two side-by-side cylinders. Some empirical expressions for predicting the turbulent flow features have been established. The formulation proposed is consistent with the experimental data over a certain range of the Reynolds number based on the cylinder diameter. In addition, a new formula to estimate the bulk drag coefficient $\overline {C_D }$CD¯ of the array of cylinders is proposed and validated.