In this paper, force and particle-image-velocimetry vorticity measurements of biologically inspired hover kinematics are compared to corresponding results of an unsteady aerodynamic vortex model and a Navier-Stokes (NS) solver. The Reynolds number and the reduced frequency are 4.8 × 10 3 and 0.38, respectively. Three kinematics derived from the measured hovering kinematics of an Agrius convolvuli are considered: 1) without elevation angle, 2) elevation angle accounted in the pitch angle, and 3) pure sinusoidal pitch-plunge neglecting higher harmonics. The Navier-Stokes computations show good qualitative agreement with experiments with consistent underprediction. The time-averaged thrust coefficients obtained using Navier-Stokes computations are 82 to 87% of the corresponding force measurements. The standard deviation of time history of thrust coefficients, also normalized by the measured time-averaged values, is 13 to 20%. The underprediction is possibly due to blockage effects in the experiments, also reflected in lower values of the vorticity compared to particle-image-velocimetry measurements. The unsteady aerodynamic vortex model captures some of the peaks in a qualitative manner. The relative difference in the timeaveraged forces and standard deviation are 8 to 18% and 66 to 93%, respectively. The differences in prediction of time histories are not reflected in the estimation of time-averaged forces due to cancellation effects, wherein the forces are underpredicted in the first half of the stroke and overpredicted in the second half. The discrepancies are attributed to the simplifying assumptions in the unsteady aerodynamic vortex model, which overpredicts the vorticity in the leading-edge vortex and results in significant differences in the wing-wake interaction process.
This paper presents the results of an experimental study of the aerodynamics of an elliptical flap plate wing in pitch-plunge motion. Several wing motion kinematics are derived from the kinematics of the Agrius Convolvuli (hawk moth) in hover. The experiments are conducted at a Reynolds number of 4, 800 and reduced frequency of 0.38, which are typical of the hawk moth flight. Three cases are reported: the hawk moth kinematics in which the elevation angle is ignored, the hawk moth kinematics with a correction to account for elevation angle effects, and a harmonic pitch-plunge kinematic of the same frequency and amplitude as the hawk moth kinematics. In all cases the wing pivots about the leading edge. The experiments are performed in The University of Michigan water channel. The wing model used has a Zimmerman planform shape with aspect ratio 3.87. Phase averaged force measurements are reported. Average thrust coefficients of 2.79, 2.64 and 2.39, respectively, are measured for the three cases. The measured peak thrust coefficients are 5.0, 4.8 and 6.1, respectively. The propulsion figure of merit in hover was also measured and found to be 0.47, 0.48 and 0.49 for the three cases. The flow evolution was measured using PIV. The results show formation of Leading Edge Vortices (LEV) and Trailing Edge Vortices (TEV) at different phases of the motion which depend on the particular kinematics. The relation between LEV and TEV vortex evolution and force generation is discussed.
An experimental investigation of the parameter space of biologically inspired hover kinematics for flapping wings is conducted. The present research continues earlier work conducted at a Reynolds number of 4.8 × 103 and with a reduced frequency of 0.38. The kinematics considered are pitch and plunge motions based on the kinematics of the Agrius Convolvuli, which include a hover kinematic ignoring elevation angle, a hover kinematic incorporating a correction for elevation angle, and a harmonic pitch/plunge motion of the same amplitude. A parameter space exploration of these baseline motions is performed. First, the reduced frequency is increased to a value of 0.7. Second, a phase lag of 10 %T and −10 %T are introduced to study the effects of advanced and delayed rotation. Force measurements are reported and the results compared to the baseline motions. An increase in reduced frequency increases the average thrust coefficient substantially for all motions. The efficiency decreases slightly for all but the pure sinusoidal motion. Introducing a phase lag of 10 % of the period changes the forces significantly. For delayed rotation thrust production and efficiency decrease by a large amount. Increases in thrust occur in the advanced rotation cases, although there is a penalty in efficiency.
This paper presents preliminary results of an experimental investigation of the aerodynamics of rigid and flexible flapping wings with bio-inspired kinematics. We consider rigid and isotropic flexible wings undergoing two degrees of freedom periodic motions of the flapping angle and the pitch angle. The wing models are thin flat plates with Zimmerman elliptical planform of aspect ratio 7.2. We present comparisons of two bio-inspired kinematics derived from the hawkmoth kinematics along with a purely sinusoidal motion. The experiments are conducted at conditions relevant to biological flight, properly scaled for water tests, which are Reynolds number of 7100 and a reduced frequency of 0.21 based on flow properties at the 75% span location. The performance of the flapping motions is compared between the differing motions and between flexible and rigid wings. Time resolved phase-averaged force measurements show the development of two force peaks during the flapping cycle for the bio-inspired kinematics and a single peak for the sinusoidal kinematic. These features are not strongly influenced by wing flexibility. Propulsion efficiency is characterized by the measured figure of merit for each case and it is found that flexibility improves performance in terms of both thrust and efficiency compared to rigid wings. Nomenclature = swept areaflat plate bending stiffness /12 1 [N·m] E = Young's Modulus [Pa] f = frequency [Hz] k = reduced frequency ref ⁄ = lift [N] ref = reference length = figure of merit ideal ⁄ = power [W] = dynamic pressure ½ = half span [cm] % = 75% of the half span = Reynolds number = wing planform area = thrust [N] ⁄ = phase of motion = thickness = reference velocity = pitch angle = pitch amplitude = kinematic viscosity = Poisson's ratio Π = effective stiffness = fluid density Φ = stroke amplitude (peak to peak)
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