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

Effect of Tip to Hub Ratio on the Hydrodynamic Characteristics ofa Finite-Span Wing with Leading-edge Tubercles
Peng Yan*,1,2, Ning Li1,2, Yi Li1,2, Churui Wan1,2, Yan Zhang*,1,2,3
1 Science and Technology on Water Jet Propulsion Laboratory, Shanghai, China
2 Marine Design & Research Institute of China, Shanghai, China3 School of Naval Architecture, Ocean & Civil Engineering, Shanghai Jiao Tong University, Shanghai, China

have sinusoidal leading-edge with the same amplitude and different
wavelength were investigated by detached eddy simulation. The opposite
effect of different wavelengths on the lift was well captured by thenumerical simulations. The interaction between the corner separationand the streamwise vortex induced by leading-edge tubercles is the main
reason for variation in hydrodynamic characteristics of the finite-spanwings with different wavelengths.

ABSTRACTThe leading-edge tubercles, which were inspired by the morphology of
the Humpback whale flipper, are known to improve the post-stall
performance and produce a smoother stall characteristic. To gain adeeper insight into the three-dimensional effect of finite-span wing withleading edge tubercles, the effects of tip to hub ratio on thehydrodynamic characteristics of a finite-span wing with leading edge
tubercles were investigated by numerical simulation. The finite-spanwings investigated have an underlying foil profile NACA 634-021. The
finite span wings have an aspect ratio of 2.15, the leading-edge tubercles
are represented by sinusoidal leading-edge geometries with an amplitude
0.005 times the local hydrofoil chord length. Three wing geometries with
tip to hub ratio of 0.33, 0.6 and 1 were designed and built. Each wing canbe attached with straight leading edge and leading-edge tubercles. The
numerical simulations were performed at Re=450000. The detachededdy simulations were performed to study the unsteady characteristics offinite-span wings at different angle of attack. The performancecoefficients of wing and pressure fluctuations downstream the wing werecompared and analyzed. The flow field was presented to explain thevariation in its flow characteristics.

Miklosovic et al. (2007) indicated that leading-edge tubercles had largelya three dimensional benefit that is a function of the planform shape.
Hansen et al. (2010) suggests that the wavy leading edge could increase
the performance in wings with sweep and/or taper due to the fact thatthese geometries carry significantly more spanwise flow. Thiago et al.
(2017) investigated the wing three-dimensional effects on wavy leadingedge performance through experiments. Although the works mentioned
above contribute to the understanding of the finite wing effects on
tubercle performance, there are lack of works related to numericalinvestigation of three-dimensional effects on leading-edge tubercles.
Dropkin et al. (2012) numerically computed the flow field and theaerodynamic forces on a two-dimensional airfoil with leading-edge
tubercles by RANS with Spalart–Allmaras models, the results show thatthe predicted lift and drag coefficients are in relatively good agreementwith the experiments, and smoother stall characteristics caused byleading-edge tubercles are also captured. Skillen et al. (2015) and PérezTorróet al. (2017) carried out large-eddy simulations on two-dimensional
airfoils with straight leading edge and leading-edge tubercles at deep stall
operating condition, the leading-edge tubercles induced lift improvement
is predicted by the numerical simulation, while there are still
discrepancies between the numerical and experimental results, indicating
the intricacy in capture the deeply stalled flow. Pérez-Torró found outthat the simulation results display a clear convergence towards
experimental data with the increasing aspect ratio. Weber et al. (2011) used
STAR-CCM+ and SolidWorks Flow Simulation to perform computational
simulations of flippers with smooth leading edge and leading-edge
tubercles, Numeric lift predictions in the nonstall region were reasonablyaccurate, while lift predictions in the poststall region were problematic.
Numeric drag predictions in the early nonstall region were within
experimental error for STAR-CCM+ using the Spalart–Allmaras

KEY WORDS: Leading-edge tubercles; Finite-span wing; Tip to hub
ratio; Detached eddy simulation; Pressure fluctuations.

INTRODUCTION
The Humpback whale shows high maneuverability while hunting. Many
researchers attribute this capability to the leading-edge tubercles on its
flippers (Fish et al., 1995; Miklosovic et al., 2004; Miklosovic et al.,2007). The leading-edge tubercles are able to improve the post-stall
performance of airfoils and produce smoother stall characteristics (Johariet al., 2007; Pedro et al., 2008), the flow mechanism for the performance
improvements is believed to be the streamwise vortex which can
improve the momentum exchange in the boundary layer.
In previous study (Yan et al., 2020), the flow characteristics of a finitespan wing with straight leading-edge and two finite-span wings which2175