Laboratory Investigation of Mean Drag in a Random Array of Rigid, Emergent Cylinders

Abstract

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 ϕ=0.091, 0.15, 0.20, 0.27, and 0.35 and cylinder Reynolds number Rep≡Upd∕ν=25 to 685, where Up=temporally and cross-sectionally averaged pore velocity and ν=kinematic viscosity. These ranges coincide with conditions in aquatic plant canopies. The temporally and cross-sectionally averaged drag coefficient, CD, decreased with increasing Rep and increased with increasing ϕ under the flow conditions investigated. The dimensionless ratio of the mean drag per unit cylinder length ⟨fD¯⟩H to the product of the viscosity, μ, and Up exhibits a linear Rep dependence of the form ⟨fD¯⟩H∕(μUp)=α0+α1Rep, consistent with Ergun’s formulation for packed columns. In the range of experimental conditions, α1 increases monotonically with ϕ. In contrast, α0 is constant within uncertainty for 0.15⩽ϕ⩽0.35, which suggests that viscous drag per unit cylinder length is independent of ϕ in this range.