Role of Skin Friction Drag during Flow-Induced Reconfiguration of a Flexible Thin Plate

Abstract

We investigate drag reduction due to the flow-induced reconfiguration of a flexible thin plate in presence of skin friction drag at low Reynolds Number. The plate is subjected to a uniform free stream and is tethered at one end. We extend existing models in the literature to account for the skin friction drag. The total drag on the plate with respect to a rigid upright plate decreases due to flow-induced reconfiguration and further reconfiguration increases the total drag due to increase in skin friction drag. A critical value of Cauchy number ($Ca$) exists at which the total drag on the plate with respect to a rigid upright plate is minimum at a given Reynolds number. The reconfigured shape of the plate for this condition is unique, beyond which the total drag increases on the plate even with reconfiguration. The ratio of the form drag coefficient for an upright rigid plate and skin drag coefficient for a horizontal rigid plate ($\lambda$) determines the critical Cauchy number ($Ca_{cr}$). We propose modification in the drag scaling with free stream velocity ($F_{x}$ ${\propto}$ $U^{n}$) in presence of the skin friction drag. The following expressions of $n$ are found for $0.01 \leq Re \leq 1$, $n = 4/5 + {\lambda}/5$ for 1 $\leq$ $Ca$ $<$ $Ca_{cr}$ and $n = 1 + {\lambda}/5$ for $Ca_{cr} \leq Ca \leq 300$, where $Re$ is Reynolds number. We briefly discuss the combined effect of the skin friction drag and buoyancy on the drag reduction. An assessment of the feasibility of experiments is presented in order to translate the present model to physical systems.