Resumen de On the steady and unsteady aerodynamics of wing models at low reynolds numbers for micro air vehicle applications
In this thesis we have studied the stationary and non-stationary aerodynamic characteristics of wings at low Reynolds numbers commonly achieved in MAVS vehicles. The lift coefficient for a flat plate at low angles of attack is obtained experimentally for various aspect ratios (AR=1,2,4,8) and moderate Reynolds numbers (Re=40x10^3 to Re=200x10^3). The variation of the lift coefficient with the angle of attack in the pre-stall region is consistent with a linear slope approximation. We consider this slope to be a function of both the aspect ratio and Reynolds number. In this research, we provide a correlation that can predict the lift slope value with an average error of less than 5%.
Further extending this idea, we study experimentally the lift coefficient on NACA0012 wing model at different Reynolds numbers from 40x10^3 to 200x10^4. A non-linearity around the zero angle of attack leading to a shift of sign in the lift was observed for a sufficiently large aspect ratio at Re=40×10^3. The existence of the negative lift for wing models with the largest aspect ratio suggests that the three-dimensional effects are negligible. Therefore, two-dimensional simulations were performed to understand the cause of the negative lift. For the cases with the negative lift, the flow displays an interesting feature of pre-alignment with the chord upstream of the airfoil. Furthermore, it was found that the negative lift is directly related to the positive net circulation (anti-clockwise) around the airfoil.
The following chapters of this thesis focus on the non-intrusive measurement of forces that will eventually be applied to a flapping wing. We introduce a new Particle Image Velocimetry (PIV) software coded in Python that is based on the already existing DPIVSoft program which is a double pass with a window deformation algorithm. We present a code for GPU computing using the open-source language Open Computing Language (OpenCL). We obtain almost the same accuracy as with DPIVSoft, but having a dramatic increase in performance.
Two methods of obtaining the forces from velocity fields, the Momentum balance (MB) and the Impulse formulation (IF), have been also studied. We make use of the velocity fields obtained from the numerical simulation of the flow around a square cylinder at Re=100 to investigate the influence of both, grid refinement and window size to perform the calculations in the prediction of the forces. The forces obtained from CFD calculations are compared with those obtained from velocity fields. The prediction given by MB is more accurate than IF. However, the following common features appear in both methods, MB and IF. The grid refinement seems sufficiently precise even when using a coarse grid of 10 boxes in a chord, but the influence of domain size becomes very important, with better results being found for smaller domains, as expected. IF is very sensitive to the window domain and can produce wrong estimations if the vortices are diffused at domain limits or if there are large differences in the order of magnitude between the different terms appearing in the formulations.
In the last study performed, we applied IF to a physical experiment to calculate the forces on an oscillating flat plate. We analyze both forward flight and hovering configurations with a null angle of attack. For this purpose, we perform 2D-PIV measurements in a towing tank to calculate the instantaneous velocity field during several flapping cycles. IF is slightly in better agreement with the forward flight configuration since the vortex patterns, captured using a 2D-PIV in the wake behind the moving plate, are well defined. Conversely, in the hovering configuration, chaotic patterns and strong diffusion are in play. The spatial domain size has a stronger influence in the hovering case than in the forward flight configuration. Finally, the main drawback is that IF does not provide a reasonable estimate of the drag coefficient.
