The unsteady quasi-vortex-lattice method with applications to animal propulsion

Abstract

In the early theoretical study of aquatic animal propulsion either the two-dimensional theory or the large aspect-ratio theory has been generally used. Only recently has the unsteady lifting-surface theory with the continuous loading approach been applied to the study of this problem by Chopra & Kambe (1977). Since it is well known that the continuous loading approach is difficult to extend to general configurations, a new quasi-continuous loading method, applicable to general configurations and yet accurate enough for practical applications, is developed in this paper. The method is an extension of the steady version of Lan (1974) and is particularly suitable for predicting the unsteady lead-edge suction during harmonic motion.The method is applied to the calculation of the propulsive efficiency and thrust for some swept and rectangular planforms by varying the phase angles between the pitching and heaving motions. It is found that with the pitching axis passing through the trailing edge of the root chord and the reduced frequency k equal to 0·75 the rectangular planform is quite sensitive in performance to the phase angles and may produce drag instead of thrust. These characteristics are not shared by the swept planforms simulating the lunate tails. In addition, when the pitching leads the heaving motion by 90°, the phase angle for nearly maximum efficiency, the planform inclination caused by pitching contributes to the propulsive thrust over a large portion of the swept planform, while, for the rectangular planform, only drag is produced from the planform normal force at k = 0·75. It is also found that the maximum thrust is not produced with maximum efficiency for all planforms considered. The theory is then applied to the study of dragonfly aerodynamics. It is shown that the aerodynamically interacting tandem wings of the dragonfly can produce high thrust with high efficiency if the pitching is in advance of the flapping and the hindwing leads the forewing with some optimum phase angle. The responsible mechanism allows the hindwing to extract wake energy from the forewing.

The fluid dynamics of flight control by kinematic phase lag variation between two robotic insect wings

“…The theoretical work by Lan (1979), who predicted that the optimum kinematics to maximize hindwing lift is a 25% phase shift, supports the finding in our physical dragonfly model but runs counter to lift measurements on a tethered flying dragonfly Aeshna palmatta (Reavis and Luttges, 1988). On the force balance, Aeshna (body weight 0.6·g) produces approximately 1.4·g lift when the 'beta angle' is ~87°.…”

“…Although this finding supports the assumption that parallel stroking might maximize lift production, it has been questioned by analytical modeling in which flight efficiency and mean thrust coefficient was estimated as a function of kinematic phase relationship (Lan, 1979). This study predicts that the hindwing extracts maximum energy from the forewing downwash when the hindwing leads by a quarter stroke cyle (90°), while the thrust coefficient is largest when the phase relationship is 45°.…”

Measurement of hydrodynamic force generation by swimming dolphins using bubble DPIV

“…Numerical calculations of thrust and propulsive efficiency of oscillating rigid flat plates as a three-dimensional lunate-tail model were made by Chopra and Kambe (Chopra and Kambe, 1977) for a series of swept planforms and by Lan (Lan, 1979) and Liu and Bose (Liu and Bose, 1993) using an quasi-vortex lattice method. The latter method was considered superior, because it could be applied to arbitrary planforms and reliably predicted leading-edge suction (Liu and Bose, 1993).…”

“…The latter method was considered superior, because it could be applied to arbitrary planforms and reliably predicted leading-edge suction (Liu and Bose, 1993). Lan (Lan, 1979) found a 20% lower thrust than Chopra and Kambe (Chopra and Kambe, 1977), although the predicted efficiency was in good agreement (Yates, 1983). Unsteady lifting surface models were applied to the kinematics of thunniform swimmers (e.g.…”

Aeroelastic Analysis of Membrane Wings

“…The analytical studies done on the aerodynamics of hover-capable flapping wings have mainly been done on rigid wings [7] [8]. Some of these studies have looked at ornithoptic flapping whereas some have looked at insect flight.…”