4:
TU Deift
DeIft University of TechnologyComputation of hull-pressure fluctuations due to
non-cavitating propellers
By
F.H. Lafeber, E. van Wijngaarden and 3. Bosschers
Report No. 1651-P
2009
Proceedings of the First International Symposium on Marine
Propulsors, SMP'2009, Trondheim, Norway, June 2009, ISBN:
978-82-7174-263-8
Page /of 1/1
Date June 2009
Author Lafeber, F.H., E. van Wijngaarden and 3. Bosschers
Address
Deift University of Technology
Ship Hydromechanics Laboratory Mekelweg 2, 2628 CD Deift
First International Symposium on Marine PropuLsors
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Sessioii 1A1 Numerical I - Scale Effects
MA1-1 Scale Effects on Propellers for Large Container Vessels
Mill/er, Sven-Brian; Abdel-Mak,soud, Motistafa; Hi/bert, Gerd
MAl2 A Viscous/Inviscid Interactive Approach and its Application to Hydrofoils arid Propellers with Non-Zero Trailing Edge Thickness
l'an, Yu/in ;Kinnas, Spyros A.
9
MAi Simulation of the Viscous Flow around a Propeller Using a Dynamic Overlapping Grid Approach
Migscar,, Roberto; Di Mascio, A.
18
MA1-4 CFD Investigation in Scale Effect on Propellers with Different Magnitude of Skew in Turbulent Flow
Krasilnikov, Vladimir; Sun, flaying; Ha/se, Karl Henning
25
Session MA2 Cavitation I
MAE-i Measurements of Controllable Pitch Propeller Blade Loads Under Cavitating Conditions
Jessup, Stiiart D.; Dontie/ly, Martin, McC/iutock, lou; carpenter, Scott
36
MA2-2 Investigation of I-lull Pressure Fluctuations Generated by Cavitating Vortices
/Jossc/iers,Jo/iou
44
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MA2-3 Numerical and Experimental Investigation into Cavitation of' Propellers Having
Blades Designed by Various Load Distributions near the Blade Tips Yamasaki, Shosaburo; 0/aizaki, Akinori; J-iasuike, Nobuh Ira; Kawana,ni, Yasufaka; U/con, Y.
52
Session MA3 Propeller Design
t3J
The High Comfort Class Appendage Design for Cruise Liners, Ferries and Ropax VesselsHfi,nãlüinen, Rainzo
60
MA3-2 Ducted Propeller Design and Verification for Contemporary Offshore Support
Vessels
Minchev, Anton; Ring Nielsen, Jens; Lundgren, Ege
85
MA3-3 Controllable Pitch Propellers for Future Warships and Mega Yachts Zarbock, Oliver
91
Session MBI Powering
Mi.1 Reliability and Accuracy of Ship Powering Performance Extrapolation
Bose, Neil; Mollov, Susan
97
Mi-2 Study on the Powering Perfonnance Evaluation for the Pod Propulsion Ships
Go, Seokcheon; Seo, Heungwon; Choi, Gilliwan
105
MB1-3 A Study on the Characteristics of Self-Propulsion Factors for a Ship Equipped with Contra-Rotating Propeller
Inn/cal, Yasul,i/co; Oclu, Fumitoshi
112
Mir4 50 Years Rational Theory of Propulsion Recent Results and Perspectives
Schmiechen, Michael
117
Session MB2 Dynamic Positioning
MB2-1 Numerical Investigation of the Interaction Between a Stern Tunnel Thruster and
Two Ducted Main Propellers Sileo, Lucia; Steen, Sverre
120
MB2-2 Propulsion Control Strategies for Fixed Pitch Propellers at Low Advance Speed
Sorensen, Asgeir J.; Smo ge/i, Ovvind N.; Ruth, Elvind
139
M Improving Total Efficiency and Safety during DP-Operations Halstensen, Svein; Nordlun, Terje
154
Session MB3 Numerical 2
Ml
Comparison of Hydrodynamics Performances of a Porpoising Foil and aPropeller
Floc '1, F.; Lceurens, J. Iii., Lerou.v; .1.13.
161
M:
Computation of Cavitating Flow through Marine PropulsorsLindazi, J. W.; Moody, William L.; Kinzel, Michael P.; Dreyer, James J.; Kunz, Robert F,; Paterson, EricG.
168
Design of Inflow-Adapted Foil Sections by Using a Multi-Objective Optimization Method
I/wang, Jeng-Lih; 1-Isin, Ching- Ye/i; Cheng, Yu-Hua; Chin, Sliang-Slieng
178
M-4
Unsteady Analysis ofa Horizontal Axis Marine Current Turbine in Yawed Inflow Conditions With a Panel MethodBaltazar, J.; Falcâo de Gampos, l.A.C.
186
Session TA1 Ice
lAin Challenges Related to Propulsor - Ice Interaction iii Arctic Waters
Nor/,amo, Lasse; Bakken, Geir Magne; Deinboll, Oddvar; lseskãr, Jo/ian
Jo/iansson
195
TAl2 Propeller Ice Interaction - Effect of Blockage Proximity Sampson, Rod; At/ar, Mehmet; Sasaki, Nor/vu/cl
205
Session TA2 Pods and Thrusters
Proceedings SMPO9
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i-i
On the Model Tests and Design Method of Hybrid CRP Podded Propulsion System of a Feeder Container ShipSasaki, Noriyu/d; Kuroda, Mariko; Fujisawa, Juiiiclii Imow, Takanori; SaW, Masaharu
213
TA2-2 Viscous/Potential Flow Coupling Study for Podded Propulsors
()zsu, Eren; Takinaci, A/i Can; Odabasi, A. Yücel
221
rA2-3 Hydrodynamic Optima! Design of Ducted Azimuth Thrusters
Funeno, Isao
227
TA2-4 Study on Hydrodynamic Performance of Podded Propulsion in Viscous Flow
Xingrong, S/ien;Xueniei, Feng; Ron gquan, C'ai; }'uejin, Cai
23-I
Session TA3 Numerical 3 - Interaction Effects
Ii
Simulation of Propeller Hub Vortex FlowOchi, Fu,nilos/ii; Fu/isawa, Take/tarti; O/i,uorj, Takuya; Kawainura, Takafurni
239
TA3-2 Comparison of Hexa-Structured and Hybrid-Unstructured Meshing Approaches
for Numerical Prediction of the Flow Around Marine Propellers Morgul, Mit/a; Nobi/e, Enrico
244
TA3-3 Analysis of Unsteady Propeller Blade Forces by RANS
Krasi/nikov, Vladimir; Z/iang, Zhirong; Hong, Fan gn'c'n
25!
Session TA4 Rudders
TA4-1 Rudder - Propeller Hull Interaction: the Results of Some Recent Research,
In-Service Problems and Their Solutions
Car/ton, Jo/in; Radosav/jevic, Dejan; Whitwortli, Stewart
262
TA4-2 Cavitation Research oii a Very Large Semi Spade Rudder
Liicke, J/,o,nas; Streckwall, Ileinrich
27()
TA4-3 Influence of Rudder Location on Propulsive Characteristics of a Single Screw
Container Ship Reic/iel, Maciej
279
Session TB! Green
In1- An Experimental Study into the Effect of Foul Release Coating on the
Efficiency, Noise and Cavitation Characteristics of a Propeller Korkut, E,nin; At/ar, Me/ii;iet
2S5
TB1-2 Simulating Biominietic (Flapping Foil) Flows for Comprehension, Reverse
Engineering and Design
Politis, Gerasinios; TsarsiiaIilis, Vassileios
294
Session TB2 Unconveiitional I
TB2-1 An Experimental and Numerical Study of the l-lydroelastic Behavior of an
Hydrofoil in Transient Pitching Motion
Ducoin, Antoine; AsloIjI, Jacques André; Deniset, Francois; Sigrisl, Jean-Francois
303
TB2-2 Performance Investigation of Ducted Aerodynamic Propulsors
Si, Naipei P.; Kiinmel. Kevin; I-laos, David .J.
311
[2
A Viable Approach to Propeller Safety for Small Crafi; Ringed Propellers C'happ/e, Mark; Reni/son, Martin322
TB2-4 Optimisation of a Linearjet
Steden, Max; Hundemer, Jochen: Abdel-Maksoud, Moustafa
327
Session TB3 Propeller Ventilation
T83-1 Analysis of Different Propeller Ventilation Mechanisms by Means of RANS
Simulations
Califano, Andrea; Stee,,, Sverre
334
TB3-2 Classification of Different Type of Propeller Ventilation and Ventilation
Inception Mechanism
Koz/owska, ,,,ia M.; Steen, Sverre; Koushan, Kourosh
Proceedings SMPO9
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TB-3 Experimental Investigation of the Effect of Waves and Ventilation on Thntster
Loadings
Kouslian, Kourosh; Spence, Silas J. B.; 1-lamsiad, Tora(f
350
Session Tl14 Cavitation 2
TB4-1 Propeller Cavitation Modelling by CFD - Results from the VIRTUE 2008 Rome Workshop
Salvatore, Francesco; Streckwall, Heinricli; van Terwisga, Torn
362
T42 Numerical Analysis of Steady and Unsteady Sheet Cavitation on a Marine Propeller Using a Simple Surface Panel Method "SQCM"
Kaneniaru, Takas/ii; Ando. Jun
372
184-3 A Versatile Partial Sheet Cavitation Model
Phoernsaptha wee Surasak; Leroux, Jean-Baptiste; Laure,zs, Jean-Marc, Deniset, Fran cois
380
Session WAI %Vaterjets
WAI-1 Toward Predicting Performance of An Axial Flow Walerjet Including the Effects of Cavitation aiid Thrust Breakdown
Schroeder, Set/i; Kim, Sung-Eon; Jasak, 1-Irvoje
387
WA1-2 Computation of Viscous Flow for the Joint High Speed Sealift Ship with Axial-Flow Wateijets
R/iee, Bong; Coleman, Roderick
395
WAI-3 Use of RANS for Waterjet Analysis of a High-Speed Sealift Concept Vessel Delaney, Keegan; Donnelly, Martin; Sheet, Michael; Sri', David
408
WAi4 Numerical Simulation of Flow around a Watcrjct Propelled Slip
limo,Takanoii; Ol,as/,i, Kiini/,ide
416
Session WA2 Unconventional 2
WA2i Voith Schneider Propeller (VSP) - Investigations of the Cavitation Behaviour Jürgens, Dirk; Heinke, Hans-Jñrgen
424
WA2-2 Performance Prediction of a Cavitating Rim Driven Tunnel Thruster
Kinnas, Spyros A.; hang, Shu-Hao,'He, Lei; Joliannessen, Ia/in Terje
435
WA2-3 A Novel Power-Saving Device for Full-Form Vessels Mewis, Fri edric/i
443
Session \VA3 Off-Design Hydrodynamics
wi
Exploring the Interfaces among Hydrodynamics, Mechanical Engineering and ControlsVandal, Le?t Røvset, Norvald; Arén, Pep; Aarseth,Leif Vesa, juha-Pekka
449
WA3-2 Analysis of Crashback Forces Compared vitli Experimental Results
Black, Scott; Swit/,enbank, Susan
463
WA3-3 Lateral Propeller Forces and their Effects on Shaft Bearings Vandal, /Jjoi',i Jo/ui,i; Gjestlaiul, Torinod; Antidsen, Terje ingvar
475
Session WA4 Dynamics
WA4-1 Performance Characteristics of Static and Dynamic Aziinuthing Podded
Propulsor
Islam, Mohanined F.; Akintunk, A/ian; Veitc/,, Brian and Liii. Pengfei
482
WM2 Calculation of Propulsion Pod Characteristics in Off-Design Operating Conditions
Yakovlet', Aleksey
493
WA4-3 A Potential Based Panel Method for Prediction of Steady and Unsteady Performances of Contra-rotating Propellers
Xiao-long, Liii
500
W44 Some Unsteady Propulsive Characteristics of a Podded Propeller Unit tinder
Maneuvering Operation
Proceedings SMPO9
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Lit,. Pengfei; is/a,,,, Mohamnied: Veitcl,, Brian
Session WBI Numerical 4
WB1-1 Simulation of Viscous Flow Around a Ducted Propeller With Rudder Using
Different Rans-Based Approaches
Sánchez-C'aja, A.; Sipiki, T.P.; Pylkkãnen, J. V.
517
WB1-2 Comparison of Experimental Measurements and Numerical Calculations for a
Propeller in Axial Cylinder
Gaggero, S.; Savio, L.; flri;zolara, S.; Viviani, M.; Fe,'rando, M.; ('o,tti, F.
525
WB1-3 Coupled Hydrodynamics-Hydroacoustics BEM Modelling of Marine Propellers
Operating in a Wakefield
Salvatore, Francesco; Testa, Claudio; Greco, Luca
537
WB14 Computation of Hull-Pressure Fluctuations due to Non-Cavitating Propellers Lafeber, Fruits Henthik; van lVi/ngaarden, Erik; Bossc/ters, Jo/ui,,
548
Session WB2 Underwater Vehicles
WB2-1 Aspects of Propeller Developments for a Submarine
Andersen, Paul; Kappel, Jeits J.; Spaitgenberg, Eugeit
554
WB2-2 Numerical and Experimental Analysis of the Wake Behavior of a Generic
Submarine Propeller
Di Felice, Fabio; Felli, Mario; Liefi'endal,l, Mattias; Sveiinberg, Urban
562
WB2-3 Experimental Testing of an Autonomous Underwater Vehicle with Tunnel
Thrusters
i'aI,ner, A/is/ui,,' Hear,,, G,'ani F.; Stevenson, Ide/er
569
Session \V83 Propulsion
WB3-1 One Theorem about the Maximum Efficiency System "I-lull and Actuator Disk" in Viscosity Fluid
Achkinadze, Alexander
576
WB3-2 Advanced Design of a Ducted Propeller will, High Bollard Pull Performance
Taketani, Tadashi; Ki,nu,'a, Kovu; ks/ui, Norio,' Matsuura, Masao; Ta,nura,
)'uichi
583
WB3-3 Operating Conditions Aligned Ship Design and Evaluation
G,'eiisch, Lars: F/lard!, Georg; Krueger, Slefan
589
Session WB4 Numerical 5 Cavitation
WB4-1 Numerical Investigation of Cavitation Bubble Collapsing Behavior
S/tin, Byeong Rog
595
WB4-2 Application of Fully Viscous CFD Codes in the Design of Non Cavitating
Propellers for Passenger Vessels
Lavini, Giatipiero; Pedone, Ln,'enzo; Genu:io, Davide i'iarpo
601
WB4-3 Numerical Prediction of Vortex Generated by Hydrofoil
Flasz,'nski, Pa we!; Sza,tlyr, fat,,' Dy,uarski, Panel, Kraskowski, Marek
609
WB4-4 On the Modelling of the Flow in Ducted Propellers With a Panel Method
Ba/lazar, I; Falcão de Cainpos, J,A. C.
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The conference has an international committee consisting of the following individuals Prof. A. S. Achkinadze (RU)
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Dr. Stuart D. Jessup (US) Dr. Ki-Han Kim (US) Prof. Spyros Kinnas (US)
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ABSTRACT
This paper describes a new coupling
procedure of two
boundary element methods aimedat computing propeller-induced hull-pressure fluctuations. The
first method
computes the incompressible
potential flow ofa propeller
Operating in a ship wake field. The second method
computes the
propeller-radiated pressures by replacing the incompressible_flow solution on the
rotating propeller blades by a set ofrings of stationary
sources. This source system is used as input in an acoustic
scattering analysis
of the wetted shiphull and undisturbed
free surface based
on the Kirchhoff-l-lclmlioltz
integral equation.Thus, hull pressures are obtained
iii the frequency domain on he
basis of a time-domain
source description.
Computed hullpressures for non-cavitating
conditions are
presented for a container vessel
that was successively fitted with two
different propellers, one being a six-btaded
propeller designed for
the vessel, the other a two-bladed propeller. Comparisons are made with scale-model
tests
performed in a towing
tank. For the two-bladed propeller,
the computed results are in good agreement with the
experimental results. The six-bladed
propeller shows
somewhat larger variations in correlation.
Keywords
Hull-pressure fluctuations,
non-cavitating propellers, txtundary element
methods, validation experiments. 1 INTRODUCTION
Computation of the
pressure field on the hull due to a propeller operating behind a ship is used to assess the excitation forces on the aftship in an early design stage. This hull-pressure field contains components due to the
passing blades as well
as cavitation and is influenced by the diffraction effectof the wetted ship
hull and the free
surface. For thecomputation of the total
pressure field all
of these contributions
should be taken intd account. Here,
only the computationof the non-cavilating
contribution is
considered using a few validationexperiments.
The advantage
of considering only the non-Cavitatiiig propeller is that its flow is less difficultto compute than that of the
cavitating propeller, andthat the variability in the measurementdata is much smaller. The
prediction of the diffraction effect can thus be
assessed at larger
accuracy than for a cavitating propeller.
Another
important issue is that with thc reduction
mu sheet cavity
First International Symposium on Marine Propulsors smp09, Trondheim, Norway, June 2009
Computation of hull-pressure fluctuations
due to non-cavitating
propellers
Frans Hendrilc Lafeber,
Erik
van Wijngaarden, Johan Bossehers
Maritime Research
Institute Netherlands (MARIN),Wageningen, The Netherlands
extents on modern propellers, the non-cavitating part
becomes of greater practical importance. Often, only the
tip vortex is cavitating andthe hull-pressure amplitude
at the first blade-passage frequency (BPF) is dominated by the contribution from the non-cavitating propeller.
In this paper the hull-pressurefluctuations are computed using a new couplingprocedure between two boundary element methods (BEM). Thecomputational approach is described in Section 2. Sections 3 and 4 discuss the experimental and computational procedures. Results of
the validation study are described in Section 5. 2 THEORY
In this section, the boundary element codes are briefly described. The method of coupling the two codes by replacing the rotating sources representing the propeller
by a set of rings of non-rotating sources is treated in detail, The application of Bernoulli's equation for the
determination of the pressure fluctuations is discussed.
2.1 Propeller flow analysis
For the analysis of the flow past a propeller, use is made
of a time-domain BEM that solves the incompressible
potential flow equations for lifting surfaces, see e.g. Vaz & Bosschers (2006) and Rosschers et at. (2008). The
method, designated PROCAL, has been developed within
MARIN's Cooperative Research Ships (CRS) for the unsteady analysis of cavitating propellers operating in a prescribed ship wake. The code is a low order BEM that
solves for the velocity disturbance potential using the
Morino approach. A sheet cavitation
model was implemented iii which the non-linear kinematic and
dynamic boundary conditions are iteratively solved
assuming that the cavity surface coincides with the body
surface. In the computations presented, the pitch and
contraction of the propellerwake geometry are prescribed using empirical formulations, while the strength of the
wake is computed using an iterative pressure Kutta
condition. The strength of the monopoles and dipoles for each panel on the body and wake is written to file for one revolution.
2.2 Hull-pressure analysis
For the analysis of the diffracted hull pressures induced by the propeller, use is made of a frequency domain BEM that solves the Kirliboff-Helmboltz integral equation
for
compressible fluids (van Wijngaarden,
method, designated EXCALIBIJR, has originally been
developed in MARIN's backgroundresearch program and was recently further developed within CRS. It is a low
order BEM code that solves for the acoustic velocity potential using the Burton & Miller approach. Thus, no main flow is taken into account and the free surface Is modeled through a negative-mirror-imaging procedure.
The diffraction problem is solved for locations on the hull on the basis of a prescribed set of sources. The pressure fluctuations are then obtained by application
of
Bernoulli's equation discussed in Section 2.4.2.3 Combining PROCAL andEXCALIBUR
In the past, hull pressures would have been obtained from
a simple combination ofthe two codes described above.
EXCALIBUR computed a so-called solid boundary factor
(SBF) in the frequency domain. PROCAL would then
compute the pressure in thefree-field at the location ofthe
hull. By multiplying this free field pressure by the SBF,
the pressure on the hull was obtained. However, as
discussed by Bosschers et al. (2008), this method has the
drawback of modeling the hull-diffractioneffect by one monopole only, whereas the source system actually consists of a large set of monopoles and dipoles. A new
method is presented here by which thecomplete solution
from PROCAL is used as input for EXCALIBUR. This
new method is based onreplacing the time domain flow
solution on the propeller by a stationary set of rings of
monopole and dipole sources in the frequency domain as suggested by Brouwer (2005).
The propeller's elemental sources of noise (i.e. monopoles and dipoles) are rotating around the propeller centre line. This can also be said of the heticoidallyshed vorticity; the
propeller wake, which consists of only dipoles. Assuming non-uniform, but stationary propeller inflow, the source
field becomes periodic in time at BPF, , given by
ZQ,
with Z the number of propellerblades and the propeller revolution rate inrad/s. Time,T,
needed forone revolution is 7' = 2.r/c . Likewise,
2ir/Zfl =
2Jr/ denotes the blade-passage period.In the following, a procedure is presented for the Fourier
transformation of the rotating sources to aset of stationary sources pulsating at BPFs in the frequency domain.
To translate the time-domain solution of sourcesmoving with the propeller from PROCAL to a frequency-domain
set of stationary sources for EXCALIBUR. we assume the propeller blades and wakesurfaces to be approximated by Nb +N, panels with panel-collocation points,
,(r) , for
= I.. N5 +
N,.
During one revolution ofperiodT, N,
'snapshots' are made of the propeller at equidistant intervals of At
TIN, . The set of time
samples in a revolution is indexed t. = jAt with j 0.. N, - I. Each ofthe N5 + N, collocation points assumes N, positions,
.
(ti) =
. Also, each of the panels can heassociated
with a point source of monopole type and strength, a, (t,) = o, plus one of surface normal dipole type and
strength, i,.(t,) =p . Note that the trailing vortex sheets
consist of only dipole sources.
For brevity ofnotation, we denote source strengths
1,(t)
or cr,(t) at a fixed point by
f(t). This is the
product of
the instantaneous strength, which we denote f,,
, and a
step function that is one during the time step
when the panel's collocation point
coincides with the source position, and zero at other times. As the
number of time
steps is alwaystaken as a multiple of the blade number,
N,= N,1Z , the step function
actually becomes one at Z
time steps during one propeller revolution. Now,
the
N,,+N,, rotating sourcesare replaced by
(N5+NjN,
stationary ones.
Then, f(t) can
be developedinto a
Fourier series based on an interval covering one blade passage period, T1,
f(t)=Re{(ce" )}
(I)
in which
C,, =
(2)
with &, = n& forthe11I harmonic andn 0. It follows,
c =2-
J e"dt
-5,/2=2f
sin(ai,As/2)a,txi/2
7
(
rn-
z
" N, N, and hence.f(t)=
2f1-,-Re
sinc[r,,
}
(4) (3)with sinc(x) = sin(x)/x. For a certain harmonic order,
the complexamplitude .f,, of source if
is given by
f = 2f
(5)"N,
N,)
The sources with complex amplitudes
given by Eq. (5) form the input for EXCALIBUR. The
scattering effect of
the hull is then computed for harmonicsof the BPF. The resulting pressure fluctuations on the hull are given as a real amplitude andphase lead relative to a sine function.
2.4 Application of Bernoulli's equation
Using the unsteady Bernoulli equation, the pressure
disturbance p is given by
p
=ipcoØ-pU-PVø
Where p is the density of the
fluid, w is
thefrequency, 0 is thedisturbance potential
and U is the free stream velocity in the direction ofthe positive x-axis, which is parallel to the ship center line and positive towards the how. Assuming that the square of
the
disturbance velocities issmall, Eq. (6) is reduced to
During the tests, the pressure on the hull was measured by means of21 sensors, which were mounted flush in the
area above the propeller, see Figure 1 Figure 2.
The results of
the hull pressures are presented as the
amplitude and phase of the pressure at the first four
harmonics of the BPF. Only the results of the nine
pressure sensors close to the propeller are presented:
sensors PO4-P06, P09-Pi I and P14-P16, see Figure 2. The pressure amplitudes at the other sensors were not significant (i.e. smaller than 0.1 kPa full scale equivalent)and have been omitted.
Figure 1: Two-bladed propeller fitted to the ship model equipped wills flush-mounted pressure sensors
S.nior octIons
50 100 ISO
J
350 400 450 500 Figure 2: Locationofpressure sensors with Ihe propeller andrudder location indicated (dimensions on model scale)
4 COMPUTATIONS
PROCAL computations have been performed at the same
propeller rotation rate and thrust coefficient as the model
tests. For the bollard pull tests, steady computations were made using uniform inflow. For the towing-test
conditions, unsteady computations were performed using
the measured ship wake, which was made effective with a force-field method. One propeller revolution is composed
of
120 time steps. In the computations presented, 30
panels have been used between the trailing and leadingedge of the two-bladed propeller and 40 panels in the case
of the six-bladed propeller. In both cases, 20 panels were used between root and tip. Cavitation features have not
been considered for the current investigation.
The PROCAL result was then used as input for the
EXCAUBUR computations, as described in Section 2.3. Only the aft part of the ship was modeled without therudder and the draught was increased by the dynamic trim.
A total of 1300 panels was used to describe the hull
geometry. All computations were performed at modelscale. Figure 3 gives an example of a combined PROCAL and EXCALIBUR solution.
Ill
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Test Z [-] N, [RPM] BPF [Hz] V [mIs] K [-1 D, [mm] A 2 600 20.0 0.00 0.021 340 B 6 579 57.9 2.37 0.204 260 C 6 370 37.0 2,37 -0.010 260
p =ipwØpU
ax (7)When the convective term is neglected as well, we get
pipwØ
(8)Eq. (8) is currently applied in EXCALIBUR to compute the complex amplitude of the pressure fluctuations on the
hull for harmonicsofBPF.
3 EXPERIMENTS
A seriesofexperiments was conducted to provide data to
validate the combination of the computer codes PROCAL
and EXCALIBUR. For the experiments, a model of a
large container vessel was fitted with different propellers, and bollard pull and towing tests were performed. Duringthe bollard pull test, the model was fitted with a large two-bladed stock propeller leading to a tip clearance of 14% of
the propeller diameter. The pitch was reduced such that it
generated a minimal thrust (P07/D = 0.05). This way, only
the thickness contributioii of the propeller plays a role. For the towing tests, the model was fitted with the six-bladed propeller designed for this ship. The tip clearance of this propeller was 33% of the propeller diameter. The model was towed at various speeds and with different propeller rotation rates, see Table 1, where N,,, is the model propeller rotation rate, V, the model speed, K1 the dimensionless thrust coefficient and D, the propeller diameter.
Table I: Model test cotiditions
250 200 150 500 50 C .50 C E 50 5-.150 200 -250
FIgure 3: Example of computational result: propeller with ship wake, propeller wake (one blade) and pressure field on the hull. l)ots on the hull indicate measuring locations.
5 RESULTS
A comparison between the computations and model test results can now be made for all three tests presented in
Table I. The measured and computed pressure amplitudes
are shown for the nine pressure sensors as stated in
Section 3. Of the computed phase, only the error is shown. The error in phase (lead) is given by
=
-
(9)By dividing this error by the harmonic order n and the
number of blades Z, the error relative to the angular blade position in the ship wake is obtained,
e
-
ePh),/
feZ
(tO)Using the phase and amplitude of the first four harmonics,
a time series can be reconstructed of both the computational and experimental data,
p(t)=A,,(sinnt+a,)
(II)
At time i = 0 the propeller's generator line goes through
top dead center.
5.1 Test A
The results of the two-bladed propeller (diameter 340 mm) show a good agreement between computation and
experiment. As can be seen in Figure 4, the amplitude at
the first harmonic is predicted well, especially for the
transducers in the propeller plane. For the higher
harmonics of test A (not shown), the error in amplitude
increases slightly. In Figure 5 it can be seen that the phase of the first harmonic is computed quite accurately as well. The small error is almost constant across the sensors. The relative error remains of the same order of magnitude
(-7°) for all harmonics. The time series of one propeller revolution is shown in Figure 6 for pressure sensor PlO,
which is located straight above the propeller. The shapes
of the time series are very similar from which it can be
concluded that the2nd, .3rdand45harmonics are computed
accurately as well. The small constant offset in phase is also visible. Summarizing, the results for the two-bladed
propeller with almost no inflow and a low thrust are very good. This indicates that the contribution of the propeller thickness to the diffracted hull-pressure field is properly
captured. 450 400 'ii' 350 a-300 a) 250 E 200 l50-a- 100 50 0
56
9101 141516 Sensor numberFigure 4: Computed and measured aniplitudes for 1' harmonic of test A
Pressure phase difference ldegl, test: A lI harmonic, frequency: 20 Hz 150 100 50 C C 0 >_ Measised Conxited r -r 1
Olade position ldegl
Figure 6: Time series reconstructed from the first four harmonics, test A 50 -100 150 F-.- Measured - Computed 400 200 0 a :. -200 90 180! 270 3 0 a, (0 (0 0) .400 -600 -800 -1000 150
.1- -
- - --flt- -
100 4 4 50- .1a - -
- - - 0 50 -100 12 150 100 200 300 400 X [mm]Figure 5: Error iii phase, 10 harnionic, test A Time series of pressure at sensor PlO
5.2 Test B
For the six-bladed propeller (diameter 260 mm) at the design K7, the computed and measured amplitude and phase show a reasonable agreement directly above the
propeller at the first harmonic, see Figure 7 and Figure 8.
30 20 0. E 15 Co 0
456
91011 141516 Sensor numberFigure 7: Computed and measured amplitudes forpt
harmonic or test B _IELI' I'
I
1 40 30 20 10 a, 0 -Jo 40 Measured Computed Measmxed ComputedA
:°.
V
Blade position Ideol
Figure 9: Time series reconstructed from the first four
harmonics, test B
At the higher harmonics, all sensors show insignificant amplitudes. This can also be seen in the reconstructed
time series which is an almost perfect sine (see Figure 9 in
which only two blade passages have been plotted). The error in amplitude and relative phase error remain almost
constant for the higher harmonics. 5.3 Test C
In test C, the thrust coefficient of the six-bladed propeller was reduced to almost zero by reducing the rotation rate of the propeller. Again, the largest errors are seen at the sensors with very low amplitudes, see Figure 10. Directly above the propeller, the amplitude error is small: +3% of the measured value. The distributions of the pressures for the upcoming and downgoing blades are not predicted well.
In I I
4 5 6 9 10 1 14 15 16
Sensor number
Figure 10: Computed and measured amplitudes for 1" harmonic of test C
Pressure phase ditference [deg], test: C
1s1 harmonic, frequency: 37 Hz 150 100-50 E E 0 >--50 -100 1500 Measised Computed -- -T ( I
57-- -59--
-88 - -Hi7
--7 300 150 100 50 0 -50 --100 -150 400 100 200 X[mmlFigure 11: Error in phase, 1" liarnionic, test C
In test C, the error in the phase is larger than in test B (Figure 11). As was seen before, the sensors with a low
pressure amplitude also give the largest errors in the
computed phase. When reconstructing the time series for test C, the errors in amplitude and phase become clearlyvisible, see Figure 12. Especially the pressures at the
higher harmonics are not computed accurately.
Pressure phase difference [deg], test: B harmonic, frequency: 57.9 Hz 150
----.-0- -
-39----
100 - .L .4j-ia
0 -50.__:S
-19
11 -100 -150 -150 0 100 200 300 400 XlmmlFigure 8: Error in phase, 1I harmnoimic, test B Time series of pressure at sensor PlO
Test B, model scale values 150 100 50 E C 0 >--50 -100;
If
IT 9 8'6
E (04 0) (03 U) a 0.210 8 6 4 2 0 -2 -4 -6 -8 -10 -12
Time series ot pressure at sensor PlO
Test C, model scale vakJes
Measured Computed
Blade position [deg]
Figure U:Tiine series reconstructed from the first four harmonics, test C
5.4 Discussion of the results
The fact that the two-bladed propeller showed more
accurate results than the six-bladed might be explained by the omission of the convective term in Bernoulli's
equation; compare Eqs.(7) and (8). A first estimate of this terni revealed that it can influence the computed
amplitude by 10% to 15% and the phase by 5 to 10
degrees. For the case of the two-hladed propeller,
including the convective term will not change the results
since the inflow velocity U is almost zero.
Another possible cause of deviations between the
computations and the measurements is the fact that the
flow vorticity is only coarsely modeled in the BEM.
Leading edge vortices as well as the roll-up of the tip vortex are not properly captured. This may explain the
less accurate prediction of the six-bladed propeller where
in the zero load condition, large pressure peaks at the
leading edge on the face of the propeller were observed in
the computations. These pressure peaks suggest the
presence of a leading edge vortex in the measurements.
6 CONCLUSIONS
A new coupling procedure has been presented of two
boundary element methods aimed at computing propeller-induced hull-pressure fluctuations. The first method computes the incompressible potential flow of a propeller operating in a ship wake field. The second method
computes the propeller-radiated pressures by replacing the
incompressible flow solution on the rotating propeller blades by a set of rings of stationary sources. Thus,
hull-pressures are computed in the frequency doniain on the
basis of a time-domain source description.
The method has been evaluated using experimental data
obtained in a towing basin for a single-screw ship hull equipped with a two-bladed and a six-bladcd propeller, both operating in non-cavitating conditions. For the
two-bladed propeller, the computed hull-pressure fluctuations show good agreement with the experiments. In the case of
the six-bladed propeller at the design loading, the computed results are reasonable to good. However, when
the loading is reduced to a value of almost zero the
differences between computations and experiments increase.
The general conclusion is that the combination of the two
boundary element methods gives a reasonable to good prediction of the pressures on the hull of a ship due to a
non-cavitatitig propeller. Further improvements are expected by including the convective term in Bernoulli's equation. The iniluence of the propeller wake and tip
vortex model used in the boundary element method needs to be further studied, especially for off-design conditions. ACKNOWLEDGEMENTS
The present work was partly funded by the Cooperative
Research Ships (CRS). The graphical user interface (used
for Figure 3) was developed within CRS by DRDC
Atlantic, with Dave Heath as main developer. The authors also like to acknowledge the contributions made by
Herman Beeksma of MARINs software development
department. REFERENCES
Bosschers, J., Vaz, G., Starke, A.R. & Wijngaarden, F. van (2008). 'Computational analysis of propeller sheet cavitation and propeller-ship interaction', Marine CFD 2008, Southampton, United Kingdom
Brouwer, J. (2005). Ship propeller-induced noise and vibrations, M.Sc. Thesis, University of Twente, Enschede, The Netherlands
Vaz, G., Bosschers, J., (2006). 'Modelling three dimensional sheet cavitation on marine propellers using a boundary element method' CAV 2006 Sixth International Symposium on Cavitation, Wageningen, The Netherlands
Wijngaarden, E. van (2006). 'Determination of propeller
source strength from hull-pressure measurements', Proceedings of the 2n,l international ship & noise
