The superior flight characteristics exhibited by birds and insects can be taken as a prototype of the most perfect form of flying machine ever created. The design of Micro Air Vehicles (MAV) which tries mimic the flight of birds and insects has generated a great deal of interest as the MAVs can be utilized for a number of commercial and military operations which is usually not easily accessible by manned motion. The size and speed of operation of a MAV results in low Reynolds number flight, way below the flying conditions of a conventional aircraft. The insensitivity to wind shear and gust is one of the required factors to be considered in the design of airfoil for MAVs. The stability of flight under wind shear is successfully accomplished in the flight of birds and insects, through the flapping motion of their wings. Numerous studies which attempt to model the flapping motion of the birds and insects have neglected the effect of wind gust on the stability of the motion. Also sudden change in flight conditions makes it important to have the ability to have an instantaneous change of the lift force without disturbing the stability of the MAV.
In the current study, two dimensional rigid airfoil, undergoing flapping motion is studied numerically using a compressible Navier-Stokes solver discretized using high-order finite difference schemes. The high-order schemes in space and in time are needed to keep the numerical solution economic in terms of computer resources and to prevent vortices from smearing. The numerical grid required for the computations are generated using an inverse panel method for the streamfunction and potential function. This grid generating algorithm allows the creation of single-block orthogonal H-grids with ease of clustering anywhere in the domain and the easy resolution of boundary layers. The developed numerical algorithm has been validated successfully against benchmark problems in computational aeroacoustics (CAA), and unsteady viscous flows.
The numerical results for pure-plunge and pure-pitching motion of SD 7003 airfoil are compared with the particle image velocimetry data of Michael Ol by plotting the contours of streamwise velocity and vorticity and also by observing the wake profile of the streamwise velocity. A very good agreement in the location of the vortices was observed between the numerical and experimental results. Also the numerical tracking of streaklines was compared with the dye injection experiments and excellent agreement in the horizontal and vertical locations of the vortex cores was observed. The importance of using the angle of attack to match the wake structures and lift forces of airfoils in pure-pitch and pure-plunge was investigated and it was found that matching the plunging amplitude with the maximum displacement of the leading edge provides a closer match in the observed wake structures and coefficient of lift.
Next, the average coefficient of list of an airfoil in pure-pitch was studied and it was found that the pitching about the leading edge produced the maximum value. Two difference methods of enhancements were considered: (i) axis of rotation, and (ii) moving airfoil, as possible ways to enhance the average coefficient of lift for an airfoil pitching about its leading edge. The first case produced two times increase and the second case produced almost four times increase in the average coefficient of lift respectively. Hence these two kinds of motion can be used for lift enhancement to overcome sudden changes in the flight conditions.
Finally the effect of a sinusoidal gust on an airfoil in pure-pitch and pure-plunge motion was examined. The pitching motion overcomes showed a much lesser drop in the average coefficient of lift compared to the plunging motion, suggesting its effectiveness to overcome disturbances in the freestream. The plunging motion on the other hand can be employed for cases that require the suppression of the oscillation in the lift coefficient.