Experimental and computational results are presented on an aerofoil undergoing pitch oscillations in ground effect, that is, close to a solid boundary. The time-averaged thrust is found to increase monotonically as the mean position of the aerofoil approaches the boundary while the propulsive efficiency stays relatively constant, showing that ground effect can enhance thrust at little extra cost for a pitching aerofoil. Vortices shed into the wake form pairs rather than vortex streets, so that in the mean a momentum jet is formed that angles away from the boundary. The time-averaged lift production is found to have two distinct regimes. When the pitching aerofoil is between 0.4 and 1 chord lengths from the ground, the lift force pulls the aerofoil towards the ground. In contrast, for wall proximities between 0.25 and 0.4 chord lengths, the lift force pushes the aerofoil away from the ground. Between these two regimes there is a stable equilibrium point where the time-averaged lift is zero and thrust is enhanced by approximately 40 %.

Unsteady propulsion near a solid boundary

We study experimentally the effect of adding an in-line oscillatory motion to the oscillatory heaving and pitching motion of flapping foils that use a power downstroke. We show that far from being a limitation imposed by the muscular structure of certain animals, in-line motion can be a powerful means to either substantially augment the mean lift, or reduce oscillatory lift and increase thrust; propulsive efficiency can also be increased. We also show that a model-based optimization scheme that is used to drive an iterative sequence of experimental runs provides exceptional ability for flapping foils to tightly vector and keep the force in a desired direction, hence improving performance in locomotion and manoeuvring. Flow visualization results, using particle image velocimetry, establish the connection of distinct wake patterns with flapping modes associated with high lift forces, or modes of high thrust and low lift forces.

Adding in-line motion and model-based optimization offers exceptional force control authority in flapping foils

Inviscid computational results are presented on a self-propelled virtual body combined with an airfoil undergoing pitch oscillations about its leading edge. The scaling trends of the time-averaged ...

Inviscid Scaling Laws of a Self-Propelled Pitching Airfoil

Unsteady inviscid flow models of wings and airfoils have been developed to study the aerodynamics of natural and man-made flyers. Vortex methods have been extensively applied to reduce the dimensionality of these aerodynamic models, based on the proper estimation of the strength and distribution of the vortices in the wake. In such modelling approaches, one of the most fundamental questions is how the vortex sheets are generated and released from sharp edges. To determine the formation of the trailing-edge vortex sheet, the classical steady Kutta condition can be extended to unsteady situations by realizing that a flow cannot turn abruptly around a sharp edge. This condition can be readily applied to a flat plate or an airfoil with cusped trailing edge since the direction of the forming vortex sheet is known to be tangential to the trailing edge. However, for a finite-angle trailing edge, or in the case of flow separation away from a sharp corner, the direction of the forming vortex sheet is ambiguous. To remove any ad hoc implementation, the unsteady Kutta condition, the conservation of circulation as well as the conservation laws of mass and momentum are coupled to analytically solve for the angle, strength and relative velocity of the trailing-edge vortex sheet. The two-dimensional aerodynamic model together with the proposed vortex-sheet formation condition is verified by comparing flow structures and force calculations with experimental results for several airfoil motions in steady and unsteady background flows.

Unsteady aerodynamics and vortex-sheet formation of a two-dimensional airfoil

Aerodynamic dissipation effects on the rotating blades of floating wind turbines

A numerical model based on a boundary-element method is developed to predict the performance of flapping foils for the general cases where vorticities are shed near the leading edge as well as from the trailing edge. The shed vorticities are modelled as desingularized thin shear layers which propagate with the local flow velocity. Special treatments are developed to model the unsteady and alternating leading-edge separation (LES), which is a main element of difficulty for theoretical and numerical analyses of general flapping foils. The present method is compared with existing experiments where it is shown that the inclusion of LES significantly improves the prediction of thrust and efficiency, obtaining excellent agreement with measurements over a broad range of flapping frequencies (Strouhal number) and motion amplitudes (maximum angle of attack). It is found that the neglect of LES leads to substantial over-prediction of the thrust (and efficiency). The effects of LES on thrust generation in terms of the circulation around the foil, the steady and unsteady thrust components, and the vortex-induced pressure on the foil are elucidated. The efficiency and robustness of the method render it suitable for design optimization which generally requires large numbers of performance evaluations. To illustrate this, we present a sample problem of designing the flapping motion, with the inclusion of higher harmonic components, to maximize the efficiency under specified thrust. When optimal higher harmonic motions are included, the performance of the flapping foil is appreciably improved, mitigating the adverse effects of LES vortex on the performance.

Boundary-element method for the prediction of performance of flapping foils with leading-edge separation

The understanding and prediction of the coupled dynamics of atmosphere-ocean-wave interactions are of vital importance to environmental applications such as global warming and pollutant transport as well as Navy operations. Due to the complex nature of the air-water interactions, our current understanding of the mechanisms for the transport of mass, momentum and heat within the atmosphere-ocean wave boundary layer (WBL) is quite limited. There is a critical need for a detailed investigation of the small-scale physics, which is essential for the understanding of the air-sea coupling dynamics and is the foundation for the development of parameterization tools.

Xiaoxia Dong

Papers

Boundary-element method for the prediction of performance of flapping foils with leading-edge separation

Numerical investigation of Coupled Boundary Layers Air-Sea Transfer (CBLAST) at small scales