Numerical Simulations of High Amplitude Pitching Airfoils at Low Reynolds Numbers

Abstract

Nature is a strong source of inspiration in the development of future technologies. The flapping wing concept has come to the fore in the creation of Micro Air Vehicles (MAVs). For agility, stability and control of MAVs, it is important for force generation from the wings to be periodic. This thesis explores the flow periodicity nature of the force coefficients of a flapping airfoil at high values of reduced frequency, k = 8 - 16, pitching amplitude θo = 10° - 58° and non-dimensional plunge amplitude, h = 1, 2 at low Re = 500 using 2D Navier-Stokes simulations. These larger amplitudes are selected to identify the useful upper range of these kinematic parameters that will be beneficial for MAV flight.

Firstly, the flow periodicity nature of pure pitch and combined pitch and plunge motions has been studied. It is found that a minimum value of pitch motion (kθo) is required to generate thrust from a pitching airfoil and for a given k, generated forces change from periodic to chaotic with increases in θo. For these chaotic cases the thrust coefficient varies significantly from one flapping cycle to the next and the mean thrust drops as the pitch amplitude increases for a given k, in contrast to results from potential flow analysis. The change of pivot location from quarter chord to one-third and half chord has been found to alter the periodic flow nature such that moving the pivot point aft reduces the pitch amplitude at which the flow changes from periodic to chaotic. This is accompanied by an increase in the size of the Leading Edge Vortex (LEV). For combined pitch and plunge motion, the results show the opposite trend from pure pitch motion - for a given k and h, increasing θo causes a change from aperiodic to periodic force generation as the effective angle of attack decreases with increasing θo.

Secondly, the effect of non-sinusoidal pitching motion has been investigated at the same high amplitudes. Within the periodic flow regime, non-sinusoidal pitching is found to give higher mean thrust compared to sinusoidal pitching motion. However, a non-sinusoidal pitching airfoil shows lesser thrust than sinusoidal pitching when the forces change from periodic to chaotic.

Finally the effect on thrust performance has been investigated for a sinusoidal pitching airfoil in close proximity to moving side walls (as close as one chord from the wall to the airfoil pivot point). It is observed that the pitching airfoil can maintain thrust and efficiency while flying through a narrow channel. Narrowing the side wall distance to one chord is found to have a positive effect on mean thrust. The flow periodicity changes from periodic to chaotic at a lower pitch amplitude than sinusoidal pitching without side walls, but the airfoil continues to produce larger positive mean thrust at a large pitch amplitude (at least up to 50°, being the maximum considered) for a given k.