The Ffowcs-Williams and Hawkings acoustic analogy is utilized to analyze the signature of a system consisting of a propeller and a downstream hydrofoil, mimicking a rudder at incidence. This study is carried out exploiting the database generated by Large-Eddy Simulations on a cylindrical mesh consisting of almost 2 × 109 grid points. Three rotational speeds of the propeller are considered. The analysis reveals that the major sources of sound are located at the leading edge of the hydrofoil, due to the impingement by the propeller wake. With the exception of small radial coordinates around the propeller wake, between two and four diameters from the propeller axis, where the non-linear sources of sound have the lead, most noise comes from the linear, loading sources on the surface of the hydrofoil, due to fluctuations of the hydrodynamic pressure. As a result, the azimuthal directivity of the sound pressure levels develops a dipole-like distribution, elongated in the direction of the span of the hydrofoil. The attenuation of the acoustic pressure along the radial direction is initially cubic, then quadratic, and eventually, within less than ten diameters away from the system, linear.
References
1.
C.
Erbe
, S.
Marley
, R.
Schoeman
, J.
Smith
, L.
Trigg
, and C.
Embling
, “The effects of ship noise on marine mammals—A review
,” Front. Mar. Sci.
6
, 606
(2019
).2.
E. D.
Franco
, P.
Pierson
, L. D.
Iorio
, A.
Calò
, J.
Cottalorda
, B.
Derijard
, A. D.
Franco
, A.
Galvé
, M.
Guibbolini
, J.
Lebrun
, F.
Micheli
, F.
Priouzeau
, C.
Risso-de Faverney
, F.
Rossi
, C.
Sabourault
, G.
Spennato
, P.
Verrando
, and P.
Guidetti
, “Effects of marine noise pollution on Mediterranean fishes and invertebrates: A review
,” Mar. Pollut. Bull.
159
, 111450
(2020
).3.
A.
Popper
, A.
Hawkins
, and F.
Thomsen
, “Taking the animals' perspective regarding anthropogenic underwater sound
,” Trends Ecol. Evol.
35
, 787
–794
(2020
).4.
S.
Ianniello
, “The Ffowcs Williams-Hawkings equation for hydroacoustic analysis of rotating blades. Part 1. The rotpole
,” J. Fluid Mech.
797
, 345
–388
(2016
).5.
M.
Felli
, M.
Falchi
, and G.
Dubbioso
, “Tomographic-PIV survey of the near-field hydrodynamic and hydroacoustic characteristics of a marine propeller
,” J. Ship Res.
59
, 201
–208
(2015
).6.
M.
Felli
, M.
Falchi
, and G.
Dubbioso
, “Experimental approaches for the diagnostics of hydroacoustic problems in naval propulsion
,” Ocean Eng.
106
, 1
–19
(2015
).7.
G.
Tani
, B.
Aktas
, M.
Viviani
, and M.
Atlar
, “Two medium size cavitation tunnel hydro-acoustic benchmark experiment comparisons as part of a round robin test campaign
,” Ocean Eng.
138
, 179
–207
(2017
).8.
G.
Tani
, D.
Villa
, S.
Gaggero
, M.
Viviani
, P.
Ausonio
, P.
Travi
, G.
Bizzarri
, and F.
Serra
, “Experimental investigation of pressure pulses and radiated noise for two alternative designs of the propeller of a high-speed craft
,” Ocean Eng.
132
, 45
–69
(2017
).9.
G.
Tani
, B.
Aktas
, M.
Viviani
, N.
Yilmaz
, F.
Miglianti
, M.
Ferrando
, and M.
Atlar
, “Cavitation tunnel tests for ‘The Princess Royal’ model propeller behind a 2-dimensional wake screen
,” Ocean Eng.
172
, 829
–843
(2019
).10.
M.
Witte
, M.
Hieke
, and F.-H.
Wurm
, “Identification of coherent flow structures and experimental analysis of the hydroacoustic emission of a hubless propeller
,” Ocean Eng.
188
, 106248
(2019
).11.
S.
Ianniello
, R.
Muscari
, and A.
Di Mascio
, “Ship underwater noise assessment by the acoustic analogy. Part I: Nonlinear analysis of a marine propeller in a uniform flow
,” J. Mar. Sci. Technol.
18
, 547
–570
(2013
).12.
S.
Ianniello
, R.
Muscari
, and A.
Di Mascio
, “Ship underwater noise assessment by the acoustic analogy. Part II: Hydroacoustic analysis of a ship scaled model
,” J. Mar. Sci. Technol.
19
, 52
–74
(2014
).13.
S.
Ianniello
, R.
Muscari
, and A.
Di Mascio
, “Ship underwater noise assessment by the acoustic analogy, Part III: Measurements versus numerical predictions on a full-scale ship
,” J. Mar. Sci. Technol.
19
, 125
–142
(2014
).14.
S.
Ianniello
and C.
Testa
, “An overview on the use of the Ffowcs Williams-Hawkings equation for the hydroacoustic analysis of marine propellers
,” in VIII International Conference on Computational Methods in Marine Engineering (MARINE 2019)
, Göteborg, Sweden, 13–15 May 2019
.15.
S.
Sezen
and O.
Kinaci
, “Incompressible flow assumption in hydroacoustic predictions of marine propellers
,” Ocean Eng.
186
, 106138
(2019
).16.
A.
Lidtke
, S.
Turnock
, and V.
Humphrey
, “Use of acoustic analogy for marine propeller noise characterisation
,” in Fourth International Symposium on Marine Propulsors (SMP15)
, Austin, TX, 2015.17.
A.
Lidtke
, V.
Humphrey
, and S.
Turnock
, “Feasibility study into a computational approach for marine propeller noise and cavitation modelling
,” Ocean Eng.
120
, 152
–159
(2016
).18.
V.
Viitanen
, A.
Hynninen
, L.
Lübke
, R.
Klose
, J.
Tanttari
, T.
Sipilä
, and T.
Siikonen
, “CFD and CHA simulation of underwater noise induced by a marine propeller in two-phase flows
,” in Fifth International Symposium on Marine Propulsors (SMP17)
, Espoo, Finland, 2017
.19.
Q.
Wu
, B.
Huang
, G.
Wang
, S.
Cao
, and M.
Zhu
, “Numerical modelling of unsteady cavitation and induced noise around a marine propeller
,” Ocean Eng.
160
, 143
–155
(2018
).20.
S.
Sezen
, M.
Atlar
, P.
Fitzsimmons
, N.
Sasaki
, G.
Tani
, N.
Yilmaz
, and B.
Aktas
, “Numerical cavitation noise prediction of a benchmark research vessel propeller
,” Ocean Eng.
211
, 107549
(2020
).21.
S.
Sezen
, T.
Cosgun
, A.
Yurtseven
, and M.
Atlar
, “Numerical investigation of marine propeller underwater radiated noise using acoustic analogy Part 1: The influence of grid resolution
,” Ocean Eng.
220
, 108448
(2021
).22.
S.
Sezen
, T.
Cosgun
, A.
Yurtseven
, and M.
Atlar
, “Numerical investigation of marine propeller underwater radiated noise using acoustic analogy Part 2: The influence of eddy viscosity turbulence models
,” Ocean Eng.
220
, 108353
(2021
).23.
R.
Bensow
and M.
Liefvendahl
, “An acoustic analogy and scale-resolving flow simulation methodology for the prediction of propeller radiated noise
,” in The Thirty-First Symposium on Naval Hydrodynamics
, Monterey, CA, 11–16 September 2016.24.
P.
Di Francescantonio
, “A new boundary integral formulation for the prediction of sound radiation
,” J. Sound Vib.
202
, 491
–509
(1997
).25.
Z.
Zhou
, H.
Wang
, and S.
Wang
, “Simplified permeable surface correction for frequency-domain Ffowcs Williams and Hawkings integrals
,” Theor. Appl. Mech. Lett.
11
, 100259
(2021
).26.
Z.
Zhou
, H.
Wang
, S.
Wang
, and G.
He
, “Lighthill stress flux model for Ffowcs Williams-Hawkings integrals in frequency domain
,” AIAA J.
59
, 4809
–4814
(2021
).27.
Z.
Zhou
, Z.
Zang
, H.
Wang
, and S.
Wang
, “Far-field approximations to the derivatives of Green's function for the Ffowcs Williams and Hawkings equation
,” Adv. Aerodyn.
4
, 12
(2022
).28.
G.
Ku
, J.
Cho
, C.
Cheong
, and H.
Seol
, “Numerical investigation of tip-vortex cavitation noise of submarine propellers using hybrid computational hydro-acoustic approach
,” Ocean Eng.
238
, 109693
(2021
).29.
J.
Kimmerl
, P.
Mertes
, and M.
Abdel-Maksoud
, “Application of large eddy simulation to predict underwater noise of marine propulsors. Part 2: Noise generation
,” J. Mar. Sci. Eng.
9
, 778
(2021
).30.
C.
Testa
, F.
Porcacchia
, S.
Zaghi
, and M.
Gennaretti
, “Study of a FWH-based permeable-surface formulation for propeller hydroacoustics
,” Ocean Eng.
240
, 109828
(2021
).31.
R.
Muscari
, A.
Di Mascio
, and R.
Verzicco
, “Modeling of vortex dynamics in the wake of a marine propeller
,” Comput. Fluids
73
, 65
–79
(2013
).32.
S.
Sezen
, M.
Atlar
, and P.
Fitzsimmons
, “Prediction of cavitating propeller underwater radiated noise using RANS & DES-based hybrid method
,” Ships Offshore Struct.
16
, 93
–105
(2021
).33.
M.
Cianferra
, A.
Petronio
, and V.
Armenio
, “Non-linear noise from a ship propeller in open sea condition
,” Ocean Eng.
191
, 106474
(2019
).34.
M.
Cianferra
and V.
Armenio
, “Scaling properties of the Ffowcs-Williams and Hawkings equation for complex acoustic source close to a free surface
,” J. Fluid Mech.
927
, 927
(2021
).35.
V.
Viitanen
, A.
Hynninen
, T.
Sipilä
, and T.
Siikonen
, “DDES of wetted and cavitating marine propeller for CHA underwater noise assessment
,” J. Mar. Sci. Eng.
6
, 56
(2018
).36.
J.
Hu
, X.
Ning
, W.
Zhao
, F.
Li
, J.
Ma
, W.
Zhang
, S.
Sun
, M.
Zou
, and C.
Lin
, “Numerical simulation of the cavitating noise of contra-rotating propellers based on detached eddy simulation and the Ffowcs Williams-Hawkings acoustics equation
,” Phys. Fluids
33
, 115117
(2021
).37.
J.
Keller
, P.
Kumar
, and K.
Mahesh
, “Examination of propeller sound production using large eddy simulation
,” Phys. Rev. Fluids
3
, 064601
(2018
).38.
A.
Posa
, M.
Felli
, and R.
Broglia
, “Influence of an upstream hydrofoil on the acoustic signature of a propeller
,” Phys. Fluids
34
, 045112
(2022
).39.
A.
Posa
, R.
Broglia
, and E.
Balaras
, “Flow over a hydrofoil in the wake of a propeller
,” Comput. Fluids
213
, 104714
(2020
).40.
A.
Posa
, R.
Broglia
, and E.
Balaras
, “The wake structure of a propeller operating upstream of a hydrofoil
,” J. Fluid Mech.
904
, A12
(2020
).41.
A.
Posa
, R.
Broglia
, and E.
Balaras
, “The wake flow downstream of a propeller-rudder system
,” Int. J. Heat Fluid Flow
87
, 108765
(2021
).42.
J.
Yang
and E.
Balaras
, “An embedded-boundary formulation for large-eddy simulation of turbulent flows interacting with moving boundaries
,” J. Comput. Phys.
215
, 12
–40
(2006
).43.
F.
Nicoud
and F.
Ducros
, “Subgrid-scale stress modelling based on the square of the velocity gradient tensor
,” Flow, Turbul. Combust.
62
, 183
–200
(1999
).44.
A.
Posa
, R.
Broglia
, M.
Felli
, M.
Falchi
, and E.
Balaras
, “Characterization of the wake of a submarine propeller via large-eddy simulation
,” Comput. Fluids
184
, 138
–152
(2019
).45.
A.
Posa
, R.
Broglia
, and E.
Balaras
, “The dynamics of the tip and hub vortices shed by a propeller: Eulerian and Lagrangian approaches
,” Comput. Fluids
236
, 105313
(2022
).46.
A.
Gilmanov
, F.
Sotiropoulos
, and E.
Balaras
, “A general reconstruction algorithm for simulating flows with complex 3D immersed boundaries on Cartesian grids
,” J. Comput. Phys.
191
, 660
–669
(2003
).47.
E.
Balaras
, “Modeling complex boundaries using an external force field on fixed Cartesian grids in large-eddy simulations
,” Comput. Fluids
33
, 375
–404
(2004
).48.
K.
Fukagata
and N.
Kasagi
, “Highly energy-conservative finite difference method for the cylindrical coordinate system
,” J. Comput. Phys.
181
, 478
–498
(2002
).49.
J. J. I. M.
Van Kan
, “A second-order accurate pressure-correction scheme for viscous incompressible flow
,” SIAM J. Sci. Stat. Comput.
7
, 870
–891
(1986
).50.
T.
Rossi
and J.
Toivanen
, “A parallel fast direct solver for block tridiagonal systems with separable matrices of arbitrary dimension
,” SIAM J. Sci. Comput.
20
, 1778
–1793
(1999
).51.
E.
Balaras
, S.
Schroeder
, and A.
Posa
, “Large-eddy simulations of submarine propellers
,” J. Ship Res.
59
, 227
–237
(2015
).52.
A.
Posa
, R.
Broglia
, and E.
Balaras
, “LES study of the wake features of a propeller in presence of an upstream rudder
,” Comput. Fluids
192
, 104247
(2019
).53.
A.
Posa
and R.
Broglia
, “Flow over a hydrofoil at incidence immersed within the wake of a propeller
,” Phys. Fluids
33
, 125108
(2021
).54.
A.
Posa
and R.
Broglia
, “Development of the wake shed by a system composed of a propeller and a rudder at incidence
,” Int. J. Heat Fluid Flow
94
, 108919
(2022
).55.
M.
Lighthill
, “On sound generated aerodynamically I. General theory
,” Proc. R. Soc. London, Ser. A
211
, 564
–587
(1952
).56.
J. E.
Ffowcs-Williams
and D. L.
Hawkings
, “Sound generation by turbulence and surfaces in arbitrary motion
,” Philos. Trans. R. Soc. London, Ser. A
264
, 321
–342
(1969
).57.
M.
Felli
and M.
Falchi
, “A parametric survey of propeller wake instability mechanisms by detailed flow measurement and time resolved visualizations
,” in 32nd Symposium on Naval Hydrodynamics
, Hamburg, Germany, 5–10 August 2018.58.
M.
Felli
, S.
Grizzi
, and M.
Falchi
, “A novel approach for the isolation of the sound and pseudo-sound contributions from near-field pressure fluctuation measurements: Analysis of the hydroacoustic and hydrodynamic perturbation in a propeller-rudder system
,” Exp. Fluids
55
, 1651
(2014
).59.
G.
Tani
, M.
Viviani
, M.
Felli
, F.
Lafeber
, T.
Lloyd
, B.
Aktas
, M.
Atlar
, S.
Turkmen
, H.
Seol
, J.
Hallander
, and N.
Sakamoto
, “Noise measurements of a cavitating propeller in different facilities: Results of the round robin test programme
,” Ocean Eng.
213
, 107599
(2020
).60.
A.
Powell
, “Theory of vortex sound
,” J. Acoust. Soc. Am.
36
, 177
–195
(1964
).61.
M.
Felli
, M.
Falchi
, and G.
Dubbioso
, “Hydrodynamic and hydroacoustic analysis of a marine propeller wake by TOMO-PIV
,” in The Fourth International Symposium on Marine Propulsors
, Austin, TX, 2015.© 2022 Author(s). Published under an exclusive license by AIP Publishing.
2022
Author(s)
You do not currently have access to this content.
