# Contribution to the study of nonstationary aerodynamic forces in problems of interest for micro-air vehicles

- Enrique Sanmiguel Rojas Director
- Ramón Fernández Feria Director

Defence university: Universidad de Málaga

Fecha de defensa: 20 May 2016

- Joaquín Ortega Casanova Chair
- Manuel García Villalba Navaridas Secretary
- David Fabre Committee member

Type: Thesis

## Abstract

The main aim of this dissertation is the quantitative characterization of the contributions of individual fluid elements (vortices) to aerodynamic forces, explaining and quantifying the mechanisms by which both drag and lift are generated. For this purpose, a vorticity forces formulation was used to the two problems addressed in this thesis. Thus, a novel physical point of view of the flow dynamics is provided which is expected to be useful for the Micro-Air Vehicles (MAVs) design. Firstly, the well-known Magnus effect problem is studied. In this problem, the two-dimensional flow past a spinning cylinder is investigated numerically using a vorticity forces formulation with the aim of analyzing quantitatively the flow structures, and their evolutions, that contribute to the lift and drag forces on the cylinder. The Reynolds number considered, based on the cylinder diameter and steady free stream speed, is Re = 200, while the non-dimensional rotation rate (ratio of the surface speed and free stream speed) selected was α = 1 and 3. For α = 1 the wake behind the cylinder for the fully developed flow is oscillatory due to vortex shedding, and so are the lift and drag forces. For α = 3 the fully developed flow is steady with constant (high) lift and (low) drag. Each of these cases is considered in two different transient problems, one with angular acceleration of the cylinder and constant speed, and the other one with translating acceleration of the cylinder and constant rotation. We characterize quantitatively the contributions of individual fluid elements (vortices) to aerodynamic forces, explaining and quantifying the mechanisms by which the lift is generated in each case. In particular, for high rotation (when α = 3), we explain the relation between the mechanisms of vortex shedding suppression and those by which the lift is enhanced and the drag is almost suppressed when the fully developed flow is reached. On the other hand, the thrust efficiency of a two-dimensional flapping airfoil is studied computationally for a low Reynolds number via the same vortex force decomposition as the one cited previously. The auxiliary potentials that separate the total vortex force into lift and drag (or thrust) are obtained analytically by using an elliptic airfoil. With these auxiliary potentials, the added-mass components of the lift and drag (or thrust) coefficients are also obtained analytically for any heaving motion of the airfoil and for any value of the mean angle of attack α. The contributions of the leading- and trailing-edge vortices to the thrust during their down- and up-stroke evolutions, are computed quantitatively with this formulation for different dimensionless frequencies and heave amplitudes (St c and St a ) and for several values of α. Very different types of flows, periodic, quasi-periodic, and chaotic, described as St c , St a , and α, are varied. The optimum values of these parameters for maximum thrust efficiency are obtained and explained in terms of the interactions between the vortices and the forces exerted by them on the airfoil. As in previous numerical and experimental studies on flapping flight at low Reynolds numbers, the optimum thrust efficiency is reached for intermediate frequencies (St c slightly smaller than one) and a heave amplitude corresponding to an advance ratio close to unity. The optimal mean angle of attack found is zero. The corresponding flow is periodic, but it becomes chaotic and with smaller average thrust efficiency as |α| becomes slightly different from zero. Finally, some conclusions and some future work related to the MAVs design based on the vortex force decomposition to study some other interesting flight mechanisms are outlined.