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

The effect of an ice cover on the trimming moment of submarines
Alexandra V. Pogorelova1, Victor M. Kozin2, Vitaly L. Zemlyak1
1Sholom-Aleichem Priamursky State University

Birobidzhan, Khabarovskiy Kray, Russia
2Institute of Machining and Metallurgy FEB RUS

Komsomolsk-na-Amure, Russia

ABSTRACTfew.

The article touches upon an unsteady rectilinear motion of a submarine
in a liquid under an ice sheet. Ice cover is modeled by a viscoelastic iceplate. The viscoelastic properties of ice are described using the KelvinVoigt model. Free surface fluid flow past system of sources and sinks isused to simulate the motion of three submarine hull forms. The authors
analyzed effects of the ice plate thickness, submergence depth, hull form,
the length-to-diameter ratio of submarine, and the speed of uniform
motion (Froude number) on the trimming moment of the submarine.
Trim angle of steady moving submarine model is measured
experimentally in towing tank.

Note that in modern conditions, during the development of the Arctic,submarines are forced to move under an ice cover. The issue of theinfluence of the ice sheet on hydrodynamic loads acting on submarines
is of interest. The wave resistance and lifting force acting on the slenderbody and the spheroid advancing under the elastic plate, wereinvestigated by Pogorelova et al (2020) and Zemlyak et al (2022).
However, the moments acting on submergence bodies under the ice
cover are not yet well studied.
Doctors and Beck (1987), Crook (1994) and Dawson (2014) investigatedtrimming moment acting on submerged bodies of revolution that occur
at steady moving in liquid under free surface. They obtained that “thereis negligible moment acting at low speed (Froude numbers less thanapproximately Fr = 0.20). As the speed increases, the trimming moment
behaves in a oscillatory manner and may alternate between a small bowup and bow down trimming moment. As the speed increases above aFroude number of approximately Fr = 0.35, the trimming moment acts
exclusively to trim the body by the bow (stern-up). This trimming
moment increases to a local maximum at approximately Fr = 0.50.
Beyond this speed the trimming moment slowly decreases andasymptotes at zero. Like the wave resistance and lift force, the magnitudeof the trimming moment decreases with an increase in submergence
depth”.

KEY WORDS: ice cover, viscoelastic plate, submarine hull form,
submergence depth, trimming moment.

INTRODUCTION
Near-surface operation of a submarine is inherently an asymmetricproblem, whereas operation in a deep-water condition is assumed to besymmetric (Dawson, 2014). This is due to the interaction between thesubmerged body and the flexible free-surface boundary which gives rise
to a wave resistance, vertical lift force and trimming moment (Griffin,2002). The wave resistance, lift force and moment occur due to theinteraction effect that exists when the body’s hydrodynamic pressure
field generates free-surface waves, which in turn generate a non-uniform
hydrostatic pressure distribution surrounding the body (Dawson, 2014).

The purpose of this paper is to analyze the effect of ice cover on thetrimming moment generated by a streamlined body travelling in close
proximity to the ice-water interface. The ice sheet is modeled by aviscoelastic homogeneous isotropic plate. Three forms of submarine
geometry are used for theoretical investigation. Trim angle of steadymoving submarine model is measured experimentally in towing tank.

Note that the hydrodynamic loads acting on the body, steady moving
near the free surface, have been studied quite fully. The founders of thesestudies in the framework of the theory of potential motion of an idealincompressible fluid were Havelock (1917, 1931a, 1931b); Kinoshitaand Inui (1953); Wigley (1953); Farell (1973). Further continuation of
the study was obtained in the theoretical and experimental works ofDoctors and Beck (1987), Weinblum et al. (1950), Gertler (1950), Farrelland Güven (1973), Gourlay and Dawson (2015), Crook (1994) to list aTHEORETICAL STUDY
The unsteady moving of a submarine in water under an ice cover is1289