Propulsive Performance and Optimum Configuration of Tandem Flapping Foils

Abstract

The application of tandem flapping foil propulsors to conventional aerial and underwater vehicles plays the 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 toward the development of tandem flapping wing robots is 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 consume less power compared to the single flapping foil. In this study, the thrust of two flapping foils arranged in the tandem mode subjected to pitching motion with different pitching amplitudes ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A_D</i> ), Strouhal numbers ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">St_D</i> ), streamwise distance ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> / <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</i> ), and phase lag <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ ({\rm{\varphi)\ }}$</tex-math></inline-formula> of foils is studied numerically using the reynolds-averaged navier-stokes equation (RANSE)-based computational fluid dynamics 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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">St_D</i> = 0.2. At this condition, the effects of streamwise distance and phase lag of tandem foils are also investigated. When <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\rm{\varphi \ }}$</tex-math></inline-formula> is constant and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> / <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</i> changes from 0.109 to 1, the efficiency of the upstream foil decreases and the efficiency of downstream foil increases. When <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> / <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</i> is constant and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\rm{\ \varphi \ }}$</tex-math></inline-formula> changes from 0° to 180°, the efficiency of the upstream foil increases and the efficiency of the downstream foil decreases with an increase in phase lag. When <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\rm{\ \varphi }}$</tex-math></inline-formula> is 90°, the total efficiency of the two foils gets the maximum value. In general, when <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> / <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</i> is 1 and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\rm{\varphi }}$</tex-math></inline-formula> 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 play a signif