The scope of the thesis is to numerically investigate the aerodynamics of flapping airfoils in hover and forward flight. The flowfields around flapping airfoils are computed by solving the governing equations on moving and/or deforming grids. The effects of Reynolds number, reduced frequency and airfoil geometry on unsteady aerodynamics of flapping airfoils undergoing pure plunge and combined pitch-plunge motions in forward flight are investigated. It is observed that dynamic stall of the airfoil is the main mechanism of lift augmentation for both motions at all Reynolds numbers ranging from 10000 to 60000. However, the strength and duration of the leading edge vortex vary with airfoil geometry and reduced frequency. It is also observed that more favorable force characteristics are achieved at higher reduced frequencies and low plunging amplitudes while keeping the Strouhal number constant. The computed flowfields are compared with the wide range of experimental studies and high fidelity simulations thus it is concluded that the present approach is applicable for investigating the flapping wing aerodynamics in forward flight. The effects of vertical translation amplitude and Reynolds number on flapping airfoils in hover are also studied. As the vertical translation amplitude increases, the vortices become stronger and the formation of leading edge vortex is pushed towards the midstroke of the motion. The instantaneous aerodynamic forces for a given figure-of-eight motion do not alter significantly for Reynolds numbers ranging from 500 to 5500.

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The flapping path of a single airfoil and dual airfoils in a biplane configuration is optimized for maximum thrust and/or propulsive efficiency. Unsteady, low speed viscous flows are computed using a Navier-Stokes solver in a parallel computing environment. A gradient based algorithm and Response Surface Methodology (RSM) are employed for optimization. The evaluation of gradient vector components and the design of experiments for RSM, which require unsteady solutions, are also carried out in parallel. Parallel computations are performed using Parallel Virtual Machine (PVM) library. First, a single airfoil undergoing a combined sinusoidal or non-sinusoidal pitching and plunging motion is studied. The non-sinusoidal flapping motion is described using an elliptic curve or Non-Uniform Rational B-Splines (NURBS). It is shown that the thrust generation may significantly be increased in comparison to the sinusoidal flapping motion. For a high thrust, the airfoil stays at high effective angle of attack values during the upstroke and the downstroke, and the effective pitching occurs at minimum and maximum plunge positions. Secondly, the optimization of sinusoidal and non-sinusoidal flapping paths of dual airfoils is considered. Moving and deforming overset grids are used for computations. The deforming overset grids remove the restrictions on the flapping motion, and improve the optimization results obtained earlier. At low flapping frequencies, an airfoil in a biplane configuration produces more thrust than a single airfoil. Yet, at high frequencies the airfoil in biplane configuration produces less thrust at a significantly lower efficiency than the single airfoil.

Airfoils &deg / apping in pitch and plunge are studied, and the &deg / apping motion parameters are op- timized to maximize thrust generation and the e&plusmn / ciency of the thrust generation. Unsteady viscous &deg / ow&macr / elds over &deg / apping airfoils are computed on overset grids using a Navier-Stokes solver. Computations are performed in parallel using Parallel Virtual Machine library routines in a computer cluster. A single &deg / apping airfoil and dual airfoils &deg / apping in a biplane con- &macr / guration are considered. A gradient based optimization algorithm is employed. The thrust production and the e&plusmn / ciency of the thrust production are optimized with respect to &deg / apping parameters / the plunging and pitching amplitudes, the &deg / apping frequency, and the phase shift between the pitch and plunge motions. It is observed that thrust generation of &deg / apping airfoils strongly depends on the phase shift and high thrust values may be obtained at the expense of reduced e&plusmn / ciency. For a high e&plusmn / ciency in thrust generation, the e&reg / ective angle of attack of the airfoil is reduced and large scale vortex formations at the leading edge are prevented. At a &macr / xed reduced &deg / apping frequency of 1, a single &deg / apping airfoil in pitch and plunge motion produces the maximum average thrust coe&plusmn / cient of 1:41 at the plunge amplitude of 1:60, the pitch amplitude of 23:5o, and the phase shift of 103:4o whereas the maximum e&plusmn / ciency of 67:5% is obtained at the plunge amplitude of 0:83, the pitch amplitude of 35:5o and the phase shift of 86:5o.