Laboratory investigation of mean drag in a random array of rigid, emergent cylinders

This paper investigates the drag exerted by randomly distributed, rigid, emergent circular cylinders of uniform diameter d. Laboratory measurements are presented for solid volume fraction phi=0.091, 0.15, 0.20, 0.27, and 0.35 and cylinder Reynolds number Re-p U(p)d/nu=25 to 685, where U-p=temporally and cross-sectionally averaged pore velocity and nu=kinematic viscosity. These ranges coincide with conditions in aquatic plant canopies. The temporally and cross-sectionally averaged drag coefficient, C-D, decreased with increasing Re-p and increased with increasing phi under the flow conditions investigated. The dimensionless ratio of the mean drag per unit cylinder length <(f(D)) over bar >(H) to the product of the viscosity, mu, and U-p exhibits a linear Re-p dependence of the form <(f(D)) over bar >(H)/(mu U-p)=alpha(0)+alpha Re-1(p), consistent with Ergun's formulation for packed columns. In the range of experimental conditions, alpha(1), increases monotonically with phi. In contrast, alpha(0) is constant within uncertainty for 0.15 <= phi <= 0.35, which suggests that viscous drag per unit cylinder length is independent of phi in this range.