Proceedings of the Thirty-second (2022) International Ocean and Polar Engineering Conference
Shanghai, China, June 5–10, 2022
Copyright © 2022 by the International Society of Offshore and Polar Engineers (ISOPE)
ISBN 978-1-880653-81-4; ISSN 1098-6189

www.isope.org

Numerical simulations of the propulsive performance of dual flapping foils
in a tunnel and the vortex motions
Haopeng Cai1,2, Dechao Yang2, Guodong Xu2, He Zhang3
1. Institute of Acoustics, Chinese Academy of Sciences, Beijing, China
2. College of Shipbuilding Engineering, Harbin Engineering University, Harbin, China
3. China Ship Research and Development Academy, Beijing, China

flapping plate; the leading edge of vortex can be reduced or eliminatedwhen the Strouhal number increases. For flapping foil without leadingedge vortex shedding, Xu and Wu (2013) proposed an unsteady vortex
method based on boundary element; the effects of the motion
parameters on the thrust and propulsive efficiency have beeninvestigated.
The performance of dual flapping foil configuration would beaffected by the multi-body configuration. Liu et al (2010) and Wang etal (2009) studied propulsion of Wing In Ground (WIG) effects and thepropulsion of dual wings; they showed that symmetrical dual wings canimprove propulsion performance. The maximum thrust and propulsive
efficiency appear when the dynamic angle of attack between 6°~9°. Xuet al (2015) studied the propulsion of dual flapping foils; the thrustcoefficient and propulsive efficiency can be improved when D/C issmall. Lin et al (2017) investigated the wake flow induced by dual
flapping foils, the flow profiles of the downstream flow were analysed.
Apart from dual foils, Xu et al (2017) studied the propulsion
performance of flapping foils in tandem; three typical vortex interaction
modes are described using global phase shift, the highest thrust mode,
highest efficiency mode and the lowest thrust/efficiency mode are
discussed. Moreira et al (2020) studied the oscillating dual foils inwaves with unaligned configurations, the propulsion efficiency inwaves have been studied numerically.
When a ship or underwater vehicle is amounted with dual foil
propulsor, the side wall tunnel becomes necessary. The side wall of atunnel can protect the flapping foil propulsor from the creatures likefish and seaweed. The effects of side wall tunnel would change thethrust and efficiency. The hydrodynamic performance of dual flapping
foils in a tunnel has been studied in this paper. The effects of sidewall
effects are investigated. The interactions of the flapping foils and fluid
flow are simulated using commercial software STAR-CCM+ (Version12.04). The effects of sidewall effects are investigated. Various pitch
motion and flapping frequency are considered. Comparing with those inopen water, the thrust coefficients are close while the efficiencydecreases slightly. The highest efficiency decreases as pitch amplitude
increases. However, the peak efficiency is achieved at higher flapping
frequency when the pitch amplitude increases. The results will help thedesign of new flapping foil propulsion devices.

ABSTRACTThe propulsive performance of dual flapping foils in a tunnel and theirvortex motions have been studied through numerical simulations. The
dual flapping foils can be high efficient. They can be used for thepropulsor of surface vessels or underwater vehicles. Computational
fluid dynamics (CFD) techniques has been adopted to simulate the dual
flapping foils in a tunnel; the thrust, propulsive efficiency at various
flapping frequency have been investigated. The mean thrust of the dual
foils has not changed significantly, while the efficiency decreases
slightly, due to the tunnel block effects. Given pitch motion amplitude(θ0), the thrust coefficient of flapping foil increases as the increase ofStrouhal number St. The thrust coefficient decreases as the increase of
θ0, and the maximum propulsion efficiency is achieved at higher St.

KEY WORDS: dual flapping foil; propulsive performance; Strouhalnumber; vortex motion.

INTRODUCTION
The propulsion of flapping foil origins from biomimetics. Theflapping foil is of efficiency, which could help the reduction ofgreenhouse gas emission. The noisy can be reduced significantly as thecavitation can be generally avoided. This environment friendly
propulsion technology is promising. However, a single-flapping-foil
propulsor will generate periodical lateral force as it swings. The lateralforce will cause yaw motion of a vehicle. When two foils are arranged
with symmetry, and they perform counter flapping motion, the lateralforces of these two foils will cancel each other. Several researches(Jones,2000; Alben,2005; Lin,2015) indicated that the dual flapping
foil may improve the propulsion performance due to the counter motion.
The propulsion performance of the flapping foil depends on theReynolds numbers, flapping frequency, heave and pitch motion
amplitudes, phase difference between the heave and pitch motions. The
hydrodynamic problem can be solved through inviscid method or thecomputational fluid dynamic method. Anderson et al (1998)
investigated the high propulsive efficiency of flapping foils; thedominant parameters for high efficiency and the vortex structure
induced by the flapping foil have been revealed. Ashraf et al (2011)
investigated the effects of Reynolds number through numericalsimulation; they found that the thicker foil can reduce the leading edge
vortex shedding. Ellington et al (1996) performed experiments on a1059