Investigation and prediction of the bending of single and tandem pillars in a laminar cross flow

Cantilever beams are increasingly applied as sensory structures for force and flow measurements. In nature, such hair-like mechanoreceptors often occur not as single hairs but in larger numbers distributed around the body-surface and with different mechanical properties. In addition, reconfiguration of such structures with the flow changes their response and mutual interaction. This raises the question how it affects the signal conditioning on each individual sensor. Simple configurations involving single and tandem pairs of flexible cylinders (of aspect ratio 10) are studied as elementary units of such sensor arrays at Reynolds numbers of order Red=O(1-10). Experimental reference studies were carried out with a tandem pair of up-scaled models using flexible cylinders mounted on a flat plate and towed in a viscous liquid environment. Direct numerical simulations (DNS) are used to determine the local drag along the rigid cylinders (pillars) for different orientations of the tandem relative to the main flow direction at steady flow conditions. The bending is then computed via beam bending theory. A prediction model based on the cross-flow velocity and an empirical relation for the drag coefficient is proposed and tested. The results show good agreement of the bending lines with the experiments and the direct numerical simulations for single and tandem configurations. It is then used to illustrate the expected sensor response at any point in a given complex flow field. This study contributes to the understanding of pre-conditioning effects in a sensor array measuring near-wall flow.