Three dimensional oscillating foil propulsion

Liu, Pengfei (1991) Three dimensional oscillating foil propulsion. Masters thesis, Memorial University of Newfoundland.

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Abstract

An unsteady numerical method, called the quasi-vortex-lattice method (QVLM), to calculate aerodynamic forces on oscillating wings is investigated and applied to the problem of oscillating foil propulsion. It is based on the vortex-lattice-method (VLM). The method was formulated for prediction of aerodynamical characteristics of a non-planar wing with arbitrary shape in unsteady harmonic motion. Based on three dimensional (3 — D) unsteady lifting surface theory, the method has been designed to handle irregular wing shapes of both planar and non-planar wings and to work with low aspect ratio foils. A computer program was written for the prediction of propulsion features of a harmonically oscillating hydrofoil. This computer program was checked by comparing present results with existing published results for some given planforms. The computer program is capable of solving unsteady three dimensional, non-planar rigid foil propulsion problems. -- Convergence of the QVLM implemented computer program and CPU time are discussed. The advantages and disadvantages of the unsteady QVLM method, and the improvement of the numerical approximation in the integration of the unsteady kernel function were investigated. -- Propulsive features of three fast swimming animals were investigated. Three cetacean's flukes were studied by use of calculations of the propulsive efficiency and mean total thrust coefficient. These three fast swimmers were: fin whale (Balaenoptera physalus); white-sided dolphin (Lagenorhynchus acutus); and white whale (Delphinapterus leucas). Fin whale's flukes have the highest aspect ratio (6.1) and moderate sweep angle (31°); white-sided dolphin's flukes have the highest leading edge sweep angle (47°) and lowest aspect ratio (2.72); and white whale's flukes have moderate aspect ratio (3.25) and the lowest sweep angle (28.3°). -- Calculation and comparisons were made for three cases: predictions of propulsive efficiency and thrust coefficient of the planforms of three cetaceans versus an advance ratio, J; the effects of changes in pitching axis positions and in phase angle (pitch leading heave) on those predictions; relations between the leading edge thrust coefficient and mean total thrust coefficient of the flukes. -- It was found that fin whale's flukes had the highest propulsive efficiency in all cases, when the heave amplitude h was taken as the corresponding to these flukes' root chord length. The propulsive efficiency from white-sided dolphin's flukes was higher than that from white whale's, though the planform of the white-sided dolphin had a lower aspect ratio. Over the complete range of the phase angle from 0° to 360°, only the fin whale's flukes predicted positive thrust. The flukes of white-sided dolphin and white whale produced negative thrust for phase angle between 190° ~ 270° and 140° ~ 340° at the reduced frequency k = 0.75 respectively; and 175° ~ 340° at the reduced frequency k = 0.15 only for the flukes of white-side dolphin. When the root chord length was to be taken as reference length and the reduced frequency k was small, it was found that the variations of the efficiency and thrust were small. It was also found that the best propulsive efficiency and smallest thrust coefficient occurred at about same phase angle position, and vice versa. The best propulsive efficiency was found when the pitching axis was placed at 0.6, 0.7, 0.8 root chord position for the flukes of white whale, fin whale and white-sided dolphin respectively. -- The recommended shape of man-made oscillating propeller in marine engineering applications was also discussed.

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