Fluid Dynamic Forces on Plunging Spanwise-Flexible Elliptical Flat Plates at Low Reynolds Numbers

Abstract

We consider the aerodynamic performance of flexible isotropic elliptical wings undergoing periodic plunge motions. Experiments were conducted in the Low Turbulence Water Channel at the University of Michigan using a pitch-plunge apparatus. Experimental results include dye flow visualization, laser Doppler vibrometer (LDV) wing deformation measurements, particle image velocimetry (PIV) flowfield quantification, and direct force measurements establishing a novel experimental framework for investigating pitchingplunging and flapping flexible wings. This investigation focuses on the effect of wing stiffness parameter, , defined as the ratio of elastic to fluid dynamic forces. A parameter sweep is performed that spans four orders of magnitude from order 10 1 to 10 4. The-parameter is varied by changing the plate thickness and material properties. The effects of structural density to fluid density, �, and the thickness to chord ratio, � , are shown to be small. The wings have elliptical planform with aspect ratio 6.1. Sinusoidal plunging kinematics are used in forward fight at a low Reynolds number (5,300) with a neutral mean effective angle of attack. The plunging motion has large reduced frequency (1.82) and modest chordnormalized plunge amplitude (0.175). Deformation measurements show that for the present conditions the wings bend without twisting. PIV measurements at the 50%-and 75%spanwise locations show that large deflections at the wing tip result in a stronger outboard leading edge vortex due to the increased effective angle of attack for increased flexibility. The force measurements proved that the prescribed parametric configuration is not thrust producing due to small wing cross-sectional thickness, motion kinematics, and lack of aerodynamic-twist. The lift (normal) force coefficient for moderate wing stiffness parameter (Π 1 of order 10 2 I. Nomenclature) is larger compared to the rigid wing results. The most flexible wing produced a lift coefficient history below the rigid wing and lags the rigid wing phase. For the rigid cases the force measurements show good agreement with quasi-steady two-dimensional potential flow theory, suggesting that for the present conditions tip vortex effects are small.

Flow Around Flapping Flexible Flat Plate Wings

“…This study builds on past work performed in a water tunnel facility using the same planform wing and the same scaling parameters 3,21 . The PIV measurements reported here are performed on models that were fully supported along the wings root with a Π of 55 (LDPE) and a Π of 1702 (HDPE).…”

“…The flexibility is varied by changing the effective stiffness (Π ) over three orders of magnitude. The relevant scaling parameters for the study of plunging flexible wings are provided by Baik 20 , and are obtained through performing a dimensional analysis using the fluid density, flow velocity, and the chord as the basis variables 14,21 . These were also derived by evaluating the kinematics and governing equations for the structure (flat plate) and fluid 1,22 .…”