Experiments on the stability and drag of a flexible sheet under in-plane tension in uniform flow

TL;DR

This study investigates how in-plane tension affects the fluid dynamic drag and stability of a flexible sheet in uniform flow, revealing that tension can significantly reduce drag and delay instability onset.

Contribution

It provides experimental insights into the influence of in-plane tension on the fluid-elastic stability and drag characteristics of flexible sheets, a novel aspect not extensively studied before.

Findings

In-plane tension reduces fluid drag below critical flow velocity.

Tension increases the critical velocity for instability onset.

Drag follows turbulent boundary layer law under lateral tension.

Abstract

A flexible sheet in uniform parallel flow is studied in order to quantify its fluid dynamic drag and fluid-elastic stability characteristics. An experimental campaign is undertaken that involves a cantilevered sheet in air flow characterised by Reynolds numbers of order R=10^4-10^6. The properties of the sheet include: constant mass per unit area; small but finite flexural rigidity; varying aspect ratios from within the range 0.43<l/L<1, where L and l denote the length and width respectively; and tension applied at the trailing edge. The unique aspect of the present work is an investigation into the influence of in-plane tension on both the fluid drag and fluid-elastic stability of the sheet. In the absence of tension, the configuration resembles a flag and the drag coefficient is observed to decrease with increasing aspect ratio and Reynolds number. In the presence of tension, the fluid drag is significantly reduced in the region below the critical flow velocity at which convected wave instabilities appear. This critical flow velocity can be increased through the moderate application of in-plane tension. Under lateral tension, the drag of the sheet is given to good approximation by the turbulent boundary layer drag law for a flat plate. Once stability is lost, however, the drag coefficient increases rapidly with Reynolds number due to convected waves travelling over the sheet's surface.