A model for roll stall and the inherent stability modes of low aspect ratio wings at low Reynolds numbers.

摘要

The development of Micro Aerial Vehicles has been hindered by the poor understanding of the aerodynamic loading and stability and control properties of the low Reynolds number regime in which the inherent low aspect ratio (LAR) wings operate. This thesis experimentally evaluates the static and damping aerodynamic stability derivatives to provide a complete aerodynamic model for canonical flat plate wings of aspect ratios near unity at Reynolds numbers under 1 x 105. This permits the complete functionality of the aerodynamic forces and moments to be expressed and the equations of motion to solved, thereby identifying the inherent stability properties of the wing. This provides a basis for characterizing the stability of full vehicles.;The influence of the tip vortices during sideslip perturbations is found to induce a loading condition referred to as roll stall, a significant roll moment created by the spanwise induced velocity asymmetry related to the displacement of the vortex cores relative to the wing. Roll stall is manifested by a linearly increasing roll moment with low to moderate angles of attack and a subsequent stall event similar to a lift polar; this behavior is not experienced by conventional (high aspect ratio) wings. The resulting large magnitude of the roll stability derivative, Cl,beta and lack of roll damping, Cl ,rho, create significant modal responses of the lateral state variables; a linear model used to evaluate these modes is shown to accurately reflect the solution obtained by numerically integrating the nonlinear equations. An unstable Dutch roll mode dominates the behavior of the wing for small perturbations from equilibrium, and in the presence of angle of attack oscillations a previously unconsidered coupled mode, referred to as roll resonance, is seen develop and drive the bank angle? away from equilibrium. Roll resonance requires a linear time variant (LTV) model to capture the behavior of the bank angle, which is attributed to the variation in the Cl ,beta derivative. These are purely aerodynamic modes which are demonstrated to be inherently present in LAR wings.;To compare the impact of the roll stability derivative at high and low aspect ratios, a model for roll stall is developed which represents the tip vortices as infinite line vortices and estimates their influence on the surface pressure distribution of the wing; results for the roll moment coefficient are favorably compared with experimental data, and are used to compute Cl ,beta. By estimating the induced spanwise lift acting on a rolling wing, the roll damping derivative may also be computed and, along with the roll stability derivative, used to populate a simplified stability matrix for LAR wings. Solving for the eigenvalues of this system of equations at aspect ratios ranging from the near-unity values applicable to MAVs to high aspect ratio configurations reveals fundamentally different stability regimes. At cruise conditions, aspect ratios below 3.3 do not experience significant roll damping and the large magnitudes of roll stall instigate the divergent Dutch roll mode described by an unstable, complex eigenvalue. At higher aspect ratios above AR = 4.6, the eigenvalues cross into the left side of the complex plane and the lateral mode becomes stable, causing the wing to behave in a conventional, high aspect ratio manner. The disparity in lateral stability regimes between high and low aspect ratios at this Reynolds number suggests a potential explanation for why MAVs are prone to lateral instabilities, as their wings are inherently affected by unique flow physics which are not experienced by more conventional aircraft with a longer span.