Calculation of Drag Coefficient for Arrays of Emergent Circular Cylinders with Pseudofluid Model

The emergent vegetation in open-channel flows is usually simulated using arrays of circular cylinders in laboratory experiments. Analysis of recent experimental data reveals that for a given Reynolds number, the drag coefficient of a cylinder in a dense array is larger than that of an isolated cylinder. A new approach is applied to parameterize the drag coefficient and Reynolds number for flows through arrays of emergent cylinders. The approach is developed based on the concept of pseudofluid, for which an analogy is made between the cylinder-induced drag in an open-channel flow and that induced by the cylinder settling in a stationary fluid. With the proposed parameterization, the experimental database is successfully reorganized in such a way that a generalized drag coefficient is related to a generalized Reynolds number by one single curve, which is valid for a wide range of solid fractions and Reynolds numbers. However, it should be mentioned that only rigid circular stems are considered in this study and their induced drag is assumed to be dominant in comparison with the channel bed resistance.