The Contribution of Added Mass Force to Formation of Propulsive Force of Flapping Airfoil in Viscous Fluid
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ntribution of Added Mass Force to Formation of Propulsive Force of Flapping Airfoil in Viscous Fluid S. V. Guvernyuka*, Ya. A. Dynnikova, G. Ya. Dynnikovaa, and T. V. Malakhovaa a
Moscow State University, Moscow, 119991 Russia *e-mail: [email protected]
Received May 8, 2020; revised May 25, 2020; accepted May 25, 2020
Abstract—This paper investigates the formation mechanism of the propulsive force of a flapping airfoil, which performs harmonic angular oscillations in a continuous medium flow, in the light of the recently proved general theorem on the added mass of bodies in a viscous incompressible fluid. The flow is described by the Navier–Stokes equations. The calculations were performed by the mesh-free numerical method of viscous vortex domains. This work explains the formation mechanism of a reverse vortex street in the wake behind the flapping airfoil in the forward thrust mode. The dominant contribution of the added mass force to the value of the propulsive force is detected. The obtained results reveal to some extent the hydrodynamic action mechanism of the tail fin of underwater animals. Keywords: flapping airfoil, propulsive force, added mass tensor, viscous incompressible fluid. DOI: 10.1134/S1063785020090059
The swimming and flight techniques of living creatures that have been perfected by nature have long attracted the attention of engineers and researchers seeking to use the principle of flapping flight in the design of aircraft, miniature robots, and other such devices that simulate the flight of these creatures. There are a large number of theoretical and experimental works on this topic (for example, review [1] contains more than 300 references). In recent years, thanks to the development of numerical and physical methods of flows visualization, great attention has been paid to the study of vortex structures created by flapping wings and their influence on the formation of propulsive force. In particular, a reverse vortex street was discovered in the hydrodynamic wake behind the flapping profile in the forward thrust (propulsive force) mode, with a rotation direction of the vortices different from the usual Karman vortex street. Such a wake plays the role of a jet stream, causing propulsive force [2]. However, the mechanism of the formation and maintenance of the reverse wake of the waving profile has not been explained. This paper shows that the reason for the formation of a reverse vortex street is the force associated with the airfoil acceleration, the so-called added mass force. Earlier theoretical studies carried out in the framework of the model of continuous flow of ideal fluid past thin flapping plates pointed out that it is necessary to take this force into account [3, 4]. Thanks to the recently proved general theorem on the added mass in a viscous fluid [5], it became possible to justifiably take into account the contribu-
tion of the added mass force to the formation of the flapping airfoil thrust regardless of the flow separation and the accompanying vortex formation processes. We cons
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