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

Study of wavelength effect on the parametric roll in head waves
Siqi Wu, Liwei Liu*, Xianzhou Wang, Jingyao Chen, Luqun Wang
School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology.
Wuhan, Hubei, Chinaand thereby attracting extensive concerns from many researchers.
According to the previous report proposed by IMO (2017), multitiered
criteria need to be established to assess ship stability, including the level1 vulnerability criterion, level 2 vulnerability criterion, and level 3 direct
stability assessment. If the vulnerability criteria are not met, the direct
stability assessment should be adopted using a numerical simulation tool.
Sakai et al. (2019) conducted the verification study of the level 2 criterionwith the encounter frequency assumption and the results indicated that atleast 24 samples of the operation conditions are required to obtain areliable value for the ship.
It is noted that the correlation between the parametric roll, ship
performance, and wave properties is of great importance for theevaluation of the instability zone of such dynamic stability failure mode.
Many studies have been carried out with different predicting methods,
including the experimental fluid dynamics (EFD) method (Hashimoto etal., 2011; Schumacher et al., 2016; Yu et al., 2018), mathematicalmethod based on the potential theory (Lu et al., 2016; Ghanari et al.,2015; Bu et al., 2019), and computational fluid dynamics (CFD) method(Sadat-Hosseini et al., 2010; Liu et al., 2021; Zhou et al., 2019). SadatHosseini et al. (2010) numerically and experimentally studied theinstability speed zone where the parametric roll occurs for the ONR
Tumblehome model with different transverse metacentric height (GM).
Schumacher et al. (2016) indicated that the quadratic damping moments
lead to more accurate predictions than the linearized damping component.
They also observed that the parametric roll in head seas is more violent
than that in following seas. Ghamari et al. (2015) investigated theparametric roll resonance for a container carrier ship with different wave
amplitudes, heading angles and forward speeds. They concluded that thedangerous zones in head and bow sea are more obvious than those infollowing and beam sea. Lu et al. (2016) and Bu et al. (2019) studied theinfluence of added resistance, radiation and diffraction forces, all ofwhich indicate significant effect on the prediction of parametric roll.
From a massive research carried out in the last decade, it can beconcluded that parametric roll resonance occurs when the encounterwave frequency is approximately twice the natural roll frequency and thewavelength should be of the order of the ship length. As a ship isadvancing in head seas, the encounter wave frequency varies with theABSTRACTThis study presents a numerical investigation for the wavelength effecton the parametric roll in head waves. The computational fluid dynamics(CFD) simulations are carried out for a model-scale ONR Tumblehome
to predict the heave, roll, and pitch motions as the parametric roll occurs.
An in-house unsteady Reynolds-averaged Navier–Stokes (URANS)
solver coupled with a dynamic overset grid approach is applied to thenumerical simulations, along with the systematic verification andvalidation studies based on the experimental data from INSEAN modeltests. The parametric roll of the model is then predicted under the regular
head waves with different wavelengths, aimed at estimating theinstability zone where the parametric roll occurs. The results demonstratethat the parametric roll occurs significantly for the model with Fn = 0.10
as the wavelength is in the range of 0.70–1.20 ship length between
perpendiculars (LPP) but it disappears as the wavelength locates outside
this range. To analyze the occurrence of the wavelength threshold for theparametric roll zone, the variation of the encounter wave frequency as
the ship is advancing in waves is obtained and the relationship between
the encounter wave frequency and the parametric roll angle is assessed,
which indicate that the variation of the encounter wave frequency
induced by different wavelengths is a primary cause leading to the effecton the parametric roll.

KEY WORDS:wavelength.

CFD; parametric roll; ONR Tumblehome;

INTRODUCTION
Parametric roll is a dangerous roll phenomenon which has been includedin the second-generation intact stability criteria proposed byInternational Maritime Organization (IMO). As a typical dynamic
stability failure mode, this phenomenon usually occurs for a shipadvancing in head seas, which is related to the periodic time-varying
restoring moment of the ship. Owing to the large amplitude induced by
the parametric roll, it may cause potential danger for the ship in waves

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