Unsteady Force Generation and Vortex Dynamics of Pitching and Plunging Flat Plates at Low Reynolds Number

Abstract

An experimental investigation of pitching and plunging flat plate at a prescribed effective angle of attack in the St range of 0.16 to 0.32 and k range of 0.5 to 1.0 is presented. Force measurements and PIV technique were used to analyze and quantify the unsteady flow field created by the wing kinematics. A momentumbalance based non-intrusive force measurement technique and a systematic vortex detection algorithm were successfully implemented as a post-processing for PIV data to gain insight on the interplay between the unsteady force generation and vortex dynamics. It was determined that the inertial effects, which are proportional to the St, dominate the unsteady force generation while the differences in the force generation for the same St kinematics are contributed by the circulatory effects such as the size and location of the leading edge vortex. The normal force with respect the flat plate was the primary contributor to the lift and drag production, and the projection of the normal force due to high pitch amplitude at higher St prompted higher thrust generation. Nomenclature Geometric angle of attack [rad or °] 0 Mean angle of attack [rad or °] eff () t Effective angle of attack [rad or °] plmax Maximum plunge angle of attack [rad or °]

Wing/Wall Aerodynamic Interactions in Free Flying, Maneuvering MAVs

“…The vortex boundary for |Γ 2 | of about 2 can be visualized as an inflection point for Γ 2 in the curve in In summary, the Γ 1 and Γ 2 vortex identification method results can clearly be seen in a paper by Baik et al [33]. In this research, Γ 1 and Γ 2 are used to identify the center of the vortex as well as the vortex bounds for the wake of a pitching and plunging flat plate at low Reynolds numbers.…”

“…Baik et al [33] produce a plot in Figure 3.5 that compares the results for the two circulation calculation methods applied to PIV experiments. The calculated values are essentially the same.…”

Flow Around Flapping Flexible Flat Plate Wings

“…It was also shown that the development of a larger leading edge vortex was the result of an increase in plunge induced angle of attack. The formation and evolution of these vortical structures and their effects on the force production has been documented in previous studies 1,[4][5][6] . This study will focus on wing flexibility and the resulting fluid-structure interactions.…”

“…The method is derived from the incompressible, momentum equation for a Newtonian fluid with the assumption of constant density and dynamic viscosity . The equation governing this can be defined as (5) where is the pressure, is the force per unit volume, is the velocity tensor, and is the Cartesian coordinate tensor. Reynolds decomposition is performed on the component, assuming that the flow is periodic.…”

Evaluation of Lift Formulas Applied to Low-Reynolds-Number Unsteady Flows

“…(5), the force is mainly determined by the quantities on the surface of the control volume. Using the flux equation, Baik et al [28] evaluated the terms in Eq. (5) to identify the contributions from vortical structures and acceleration.…”