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 Study of Cavitation Noise around 2-D Hydrofoil with Direct Volume Integration
Lianjie Yu1, Qingjie Meng2, Decheng Wan1*
1

Computational Marine Hydrodynamics Lab (CMHL), School of Naval Architecture, Ocean and Civil Engineering,
Shanghai Jiao Tong University, Shanghai, China
2Wuhan Second Ship Design and Research Institute, Wuhan, China*Corresponding author

prediction of the flow-induced noise needs to directly solve thecompressible N-S equation, but the solution strategy in aerodynamics
cannot be applied to the water medium, and this method iscomputationally expensive (Cianferra, 2019). In recent years, acoustic
analogy has been adopted in most researches (Epikhin, 2015; Schmalz,2015; Choi, 2016). Within this framework, the flow field is regarded as
the sound source, and the free space Green's function is used to describe
the sound pressure propagation in the far field. The acoustic analogy wasfirst proposed by Lighthill (1952) and developed by Curle (1955),Ffowcs Williams (1969) and others. By now, it has achieved greatdevelopment. The commonly-used formulation is called FW-H equation,
which regards the various motion of solid objects as sound sources.
The FW-H equation was first proposed in the aerodynamics. Theequation contains 3 kinds of sound sources: monopole, dipole andquadrupole. The monopole sound source is caused by the movement ofthe object. The dipole is caused by the pressure fluctuation near theobject. And the quadrupole sound source is caused by the turbulentbehavior of the flow itself (such as vortex, shock wave, etc.). The
quadrupole term (nonlinear sound source) has little effect on noise in theair, and it requires expensive volume integrations, so this term is often
ignored. However, the results of hydrodynamic noise in recent years
showed that the influence of the quadrupole is important, even dominates
the acoustic far field (Choi, 2016; Cianferra, 2018). Therefore, thequadrupole term must be considered for the prediction of underwater
noise.
An alternative choice is the penetrable FW-H formulation, whichmoves the integral surface from the object to the flow field. Suchintegration is believed to consider the nonlinear terms enclosed by theporous surface. However, this approach is greatly affected by theselection of the penetrable surface (Cianferra, 2019). The direct volume
integration is the most accurate way to calculate the quadrupole. Somescholars carried out the volume integration successfully (Cianferra, 2018;Cianferra, 2019). It is found that the computation cost is within an
acceptable range, if the time delay is ignored (compact source
hypothesis). And the requirements of compact sound sources are met formost of the underwater flows (low Mach number).

ABSTRACT
Underwater noise (URN) is the focus of academic research, andcavitation is an important source of underwater noise. This paper takes
NACA66 (mod) two-dimensional hydrofoil as the research object, anduses the open source software OpenFOAM to simulate the sheet
cavitation and sound field. The turbulence model is DDES, and thecavitation model is the Schnerr-Sauer model. The sound field is predictedby the FW-H formulation. Unlike the traditional method, this paper
solves the quadrupole term (non-linear term) by direct volume
integration, so the nonlinear term can be predicted more accurately. At
the same time, a new method of changing sound wave velocity isproposed considering the two-phase medium problem caused bycavitation. Four methods are compared including two-phase volume
integration, direct volume fraction, object surface integration andpenetrable formulation. It was found that the influence of two-phase flow
is greater near the closure area of the cavity, which needs to beconsidered separately. The closer to the cavity closure zone, the greater
the nonlinear effect.

KEY WORDS: cavitation noise, NACA66 (mod), FW-H formulation,
direct volume integration.

INTRODUCTION
The underwater noise not only causes harm to marine life, but also
affects the stealth of military equipment. The International Maritime
Organization (IMO) issued non-mandatory noise standards forcommercial ships (IMO, 2014). More and more attention is paid to theacoustic environment. At this stage, the prediction of such noise becomesa hot topic (Deane, 2010; Ianniello, 2013; Bensow, 2016).
The underwater noise can be divided into three parts: structurevibration noise, propeller noise and flow-induced noise. Flow-induced
noise is caused by pressure fluctuations. As the speed of structures
increases, the impact of flow-induced noise also increases. Theoretically,

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