Propulsive Performance of Tandem Flapping Wings for Autonomous Underwater Vehicles (Auvs) and Surface Ships

Abstract

The application of tandem flapping foils propulsors to conventional aerial and underwater vehicles plays a most important role in the exploration of aerial and marine environments. The hydrodynamic study of fish schooling or birds flock when swimming/flying in fluid media and the application towards development of tandem flapping wing robots gaining more importance in the field of bioinspired vehicles. The advantages of tandem flapping wing configuration are improved thrust performance; maneuvering and less energy input as the downstream foils consumes less power compared to the single flapping foils. In thist study, the thrust of two flapping foils arranged in tandem mode subjected to pitching motion with different pitching amplitudes(A <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</inf> ), Strouhal numbers (St <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">D</inf> ), stream wise distance (S/c) and phase-lag ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\varphi$</tex> ) of foils are studied numerically using RANSE based CFD solver. This novel study mainly investigates the effects of Strouhal number and the dimensionless pitching amplitude on the thrust and efficiency of tandem foils. It is observed that the tandem foils generate higher efficiency at <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\text{St}_{\mathrm{D}}=0.2$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathrm{A}_{\mathrm{D}}= 0.7$</tex> . At this condition, the effects of stream wise distance and phase-lag of tandem foils are also investigated. When <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\varphi$</tex> is constant and S/c changes from 0.109 to 1, the efficiency of the upstream foil decreases and the efficiency of downstream foil increases. When S/c is constant and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\varphi$</tex> changes from 0° to 180°, upstream foil efficiency increases and downstream foil efficiency decreases with increase in phase-lag. When <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\varphi$</tex> is 90°, total efficiency of the two foils gets the maximum value. In general, when S/c is 1 and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\varphi$</tex> is 90°, the tandem flapping foils get the maximum propulsive efficiency. For achieving this condition, pitching amplitude, frequency and increased phase lag between the two foils plays a significant role compared to the stream wise distance(S/c) between the tandem foils.