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 ϕ=0.091 , 0.15, 0.20, 0.27, and 0.35 and cylinder Reynolds number Rep ≡ Up d∕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 ∕(μ Up )= α0 + α1 Rep , 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...