Mathematical modeling and simulation of biologically inspired hair receptor arrays in laminar unsteady flow separation

Bats possess arrays of distributed flow-sensitive hair-like mechanoreceptors on their dorsal and ventral wing surfaces. Bat wing hair receptors are known to play a significant role in flight maneuverability and are directionally most sensitive to reversed flow over the wing. In this work, we consider the mechanics of flexible hair-like structures for the time accurate detection and visualization of hydrodynamic images associated with unsteady near surface flow phenomena. A nonlinear viscoelastic model of a hair-like structure coupled to an unsteady nonuniform flow is proposed. Writing the hair model in nondimensional form, we identify five dimensionless groups that govern hair behavior. An order of magnitude analysis of the physical forces involved in the fluid–structure hair response is performed. Through the choice of hair material properties, we show how a local measure of near surface flow velocity may be obtained from hair tip displacement and resultant moment. When hair structures are placed into an array, time and space accurate hydrodynamic images may be obtained. We illustrate the imaging of reversed flow that occurs during a laminar unsteady flow separation with an array of hair-like structures.