A modified log-law of flow velocity distribution in partly obstructed open channels

Flow through rigid and emergent/submerged cylinder arrays are commonly found in several engineering application such as offshore structures, transmission lines, chimneys, array of silos and field array of trees. Various hydrodynamic phenomena may be occurring in the interaction between a flowing fluid and these structures. In this manuscript we focus on the study of flow structures in a channel partially obstructed by an array of equi-spaced, vertical, rigid, emergent, circular steel cylinders. Experimental results show that the presence of the cylinders array strongly affects the flow velocity distribution, forming a transversal sharp transition region at the interface between the obstructed and the unobstructed domains. At the interface, for the current and previous studies, it was observed that the flow distribution always resembles a boundary layer feature. This similarity in feature of the flow distribution as a boundary layer has led to adapting the universal law of the wall to describe the transversal profile of the mean flow velocity, considering, by analogy, the interface separating both domains as a virtual wall. The specific objectives addressed in this study is to propose and validate a new modified log-law predicting the representative transversal profile of the mean flow velocity at the interface between the obstructed and the unobstructed domains. The proposed analytical model is validated by a series of experiments carried out on a very large rectangular channel in the Department of Civil, Environmental, Building Engineering and Chemistry of the Technical University of Bari-Italy. The three-dimensional flow velocity components were measured using a 3D Acoustic Doppler Velocimeter ADV. As a result, it is observed that the measured and the predicted, applying the proposed modified log-law, mean flow velocity data have a perfect matching between them. Moreover, in the second part of the paper, detailed observations on the flow turbulence structure are analyzed and discussed.