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The goal of this work is to develop low order dynamical systems models for the unsteady lift and drag forces on small wings in various modes of flight, and to better understand the physical characteristics of unsteady laminar separation. Velocity field and body force data for a flat plate at static angle of attack and in sinusoidal pitch and plunge maneuvers are generated by 2D direct numerical simulations using an immersed boundary method at Re = 100. The lift of a sinusoidally plunging plate is found to deviate from the quasi-steady approximation at a reduced frequency of k = 0.5 over a range of Strouhal numbers. Lagrangian coherent structures illustrate formation and convection of a leading-edge vortex in sinusoidal pitch and plunge. A phenomenological ODE model with three states is shown to reproduce the lift on a flat plate at a static angle of attack above the stall angle. DNS for a 3D pitch-up maneuver of a rectangular plate at Re = 300 shows the effect of aspect ratio on vortical wake structure and lift. Wind tunnel experiments of a wing in single pitch-up and sinusoidal pitch maneuvers are compared with a dynamic model incorporating time delays and relaxation times to produce hysteresis.

Unsteady Aerodynamic Forces on Small-Scale Wings: Experiments, Simulations, and Models