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 $\varphi =0.091$ , 0.15, 0.20, 0.27, and 0.35 and cylinder Reynolds number ${\mathit{Re}}_p\equiv U_{p}d∕\nu =25$ 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 ${\mathit{Re}}_p$ and increased with increasing $\varphi$ under the flow conditions investigated. The dimensionless ratio of the mean drag per unit cylinder length $⟨\overline{f_D}{⟩}_H$ to the product of the viscosity, $\mu$ , and $U_p$ exhibits a linear ${\mathit{Re}}_p$ dependence of the form $⟨\overline{f_D}{⟩}_H∕\left(\mu U_p\right)={\alpha }_0+{\alpha }_1{\mathit{Re}}_p$ , consistent with Ergun’s formulation for packed columns. In the range of experimental conditions, ${\alpha }_1$ increases monotonically with $\varphi$ . In contrast, ${\alpha }_0$ is constant within uncertainty for $0.15⩽\varphi ⩽0.35$ , which suggests that viscous drag per unit cylinder length is independent of $\varphi$ in this range.