Date Author
Address
June 2009
Francesco Salvatore, Heinrich Streckwall & Tom van Terwisga
Delft University of Technology
Ship Hydromechanics Laboratory
Mekelweg 2, 2628 CD Deift
TUDeift
Deift University of Technology
Propeller Cavitation Modelling by CFD- Results
from the VIRTUE 2008 Rome Workshop
By
Francesco Salvatore, Heinrch Streckwall and
Tom van Terwisga
Report No. 1653-P
2009
Proceedings of the International Symposium on Marine Propulsors, smp'09, Trondhein, Norway, Edited by
K. Koushan & S. Steen, ISBN: 978-82-7174-263-8
First International Symposium on Marine Propulsors
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Proceedings of smp'09
Proceedings of the First International Symposium on Marine Propulsors - smp'09 22 24 June 2009, Trond helm, Norway
Edited by: Kourosh Koushan and Sverre Steen www.niarinepropulsors.com secretariat(tmarinepropuIsorscom ISBN (electronic proceedings): 978-82-7174-264-5 ISBN (printed proceedings): 978-82-7174-263-8
Copy right: smp-chair committee (Kourosh Koushan and Sverre Steen) Publisher: MARINTEK (Norwegian Marine Technology Research Institute) www.marintek.sintefno
Organised by: MARINTEK and NTNU www.rnarinteksintef.no www.ntnu.no
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Committees I formaton Sponsors Contact
Session MAI INumerical I Scale Effects
MA1-1 Scale Effects on Propellers for Large Container Vessels Muller, Sven-Brjan; Abde/-Maksoud, Moustafa; Hi/bert, Gerd
1
MA1-2 A Viscous/Inviscid Interactive Approach and its Application to Hydrofoils and Propellers with Non-Zero Trailing Edge Thickness
Pan, Yu/in , Kinnas, Spyros A.
9
ui-
Simulation of the Viscous Flow around a Propeller Using a Dynamic Overlapping Grid ApproachMuscari, Roberto; Di Mascio, A.
18
MA1-4 CFD Investigation in Scale Effect on Propellers with Different Magnitude of Skew in Turbulent Flow
Krasi/nikov, Vladimir; Sun. Jiaving; Ha/se, Karl Henning
25
Session MA2 Cavitation I
M1
Measurements of Controllable Pitch Propeller Blade Loads Under Cavitating ConditionsJessup, Stuart D.; Donnelly, Martin; McC!intock, bit; Carpenter, Scott
36
MA2-2 Investigation of Hull Pressure Fluctuations Generated by Cavitating Vortices
Bosschers, 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
Yanjasaki, Shosaburo; Okazaki, Akinori; Hasuike, Nobuhiro; Kawana,ni,
Yasutaka; Ukon, Y
52
Session MA3 Propeller Design
MA3-1 The High Comfort Class Appendage Design for Cruise Liners, Ferries and Ropax Vessels
Hdmäläinen, Rai,no
60
MA32 Ducted Propeller Design and Verification for Contemporary Offshore Support
Vessels
Minchev, Anton, Ring Nielsen, Jens; Lundgren, Ege
85
MA-3 Controllable Pitch Propellers for Future Warships and Mega Yachts Zarbock, Oliver
91
Session MBI Powering
MB1-1 Reliability and AccuracyofShip Powering Performance Extrapolation Bose, Neil; Mo/by, Susan
97
M12 Study on the Powering Performance Evaluation for the Pod Propulsion Ships Go, Seokcheon; Seo, Heungii'on; Choi, Gilhuwi
105
MB1-3 A Study on the CharacteristicsofSelf-Propulsion Factors for a Ship Equipped with Contra-Rotating Propeller
Inukai, Yasuhiko; Ochi, Fuinitos hi
112
Mi
50 Years Rational TheoryofPropulsion Recent Results and Perspectives Schmiechen, Michael117
Session MB2 Dynamic Positioning
MB2:1 umerical Investigation of the Interaction Between a Stern Tunnel Thruster and Two Ducted Main Propellers
Sileo, Lucia; Steen, Sverre
129
un Propulsion Control Strategies for Fixed Pitch Propellers at Low Advance Speed Sorensen, Asgeir J.; Smogeli, øyvind N.,' Ruth, Eivind
139
MB2-3 Improving Total Efficiency and Safety during DP-Operations Ilaistensen, Svein; Nordtien, Terje
154
Session MB3 Numerical 2
MB3-1 Comparison of Hydrodynamics Performances of a Porpoising Foil and a Propeller
Fboc'/i, F.; Laurens, f.M.; LerolLv;
IS.
161
M32 Computation of Cavitating Flow through Marine Propulsors
Lindau, J. W.; Moody, William L.; Kinzel, Michael P.; Dreyer, James I.; K,,,,:, Robert F.; Paterson, Eric G.
168
Design of Inflow-Adapted Foil Sections by Using a Multi-Objective Optimization Method
liwang, Jeng-Lih; I/si,,, Ching- Yeh; Cheng, Yu-Ilua; Chin, Shang-Sheng
178
Unsteady Analysis of a Horizontal Axis Marine Current Turbine in Yawed Inflow Conditions With a Panel Method
Baltazar, I; Falcão de Campos, JA.C.
186
Session TAI Ice
JAM Challenges Related to Propulsor - Ice Interaction in Arctic Waters Norhamo, Lasse; Bakken, Geir Magne; Dein boll, Oddvar; iseskár, Johan Johansson
195
TA1-2 Propeller Ice Interaction - Effect of Blockage Proximity Sampson, Rod; At/ar, Itlelimet; Sasaki, Norii'uki
205
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TA2-1 On the Model Tests and Design Method of Hybrid CRP Podded Propulsion System of a Feeder Container Ship
Sasaki, Norivuki; Kuroda, Mariko; Fujisawa, Junichi; Iniofo, Takanori; Sato,
Pvlasaharu
213
1A2-2 Viscous/Potential Flow Coupling Study for Podded Propulsors Ozsu, Eren; Takinaci, A/i can; Odabasi, A. Ylicel
22!
TA2-3 Hydrodynamic Optimal Design of Ducted Azimuth Thrusters Funeno, Isao
227
TA2-4 Study on Hydrodynamic Performance of Podded Propulsion in Viscous Flow Xingrong, S/ten; Xuemei, Feng; Rongquan, Cai; Yuejin, Cai
234
Session TA3 Nunierical 3 - Interaction Effects TA3-1 Simulation of Propeller Hub Vortex Flow
Ochi, Fu,nitoshi; Fujisawa, Takeharu; Ohmori, Takuva; Kawa,nura, Takafwni
239
TA3-2 Comparison of Hexa-Structured and Hybrid-Unstructured Meshing Approaches for Numerical Prediction of the Flow Around Marine Propellers
Morgut, AIitja; Nobile, Enrico
244
TA3-3 Analysis of Unsteady Propeller Blade Forces by RANS Krasi/nikov, Vladimir; Zhang, Zhirong; Hong, Fan given
2Sl
Session TA4 Rudders
TA4-1 Rudder - Propeller - Hull Interaction: the Results of Some Recent Research, In-Service Problems and Their Solutions
Car/ton, John; Radosavijevic, Dejan; Whitivorth, Slewarl
262
TA4-2 Cavitation Research on a Very Large Semi Spade Rudder
Li/eke, Thomas; Strec/cwall, Hem rich
270
TA4-3 Influence of Rudder Location on Propulsive Characteristics of a Single Screw Container Ship
Reichel, Maciej
279
Session TBI Green
TB1-1 An Experimental Study into the Effect of Foul Release Coating on the Efficiency, Noise and Cavitation Characteristics of a Propeller Korkut, Emin; At/ar, Mehinet
285
T1-2 Simulating Biomimetic (Flapping Foil) Flows for Comprehension, Reverse Engineering and Design
Politis, Gerasimos; Tsarsita!idis, Vassileios
294
Session TB2 Unconventional I
TB2-1 An Experimental and Numerical Study of the Hydroelastic Behavior of an Hydrofoil in Transient Pitching Motion
Ducoin, Antoine; Astolfi, Jacques André; Deniset, Francois; Signs!, Jean-Francois
303
TB2-2 Performance Investigation of Ducted Aerodynamic Propulsors Bi, Naipei P.; Ki,n,nel, Kevin; Haas, David J.
311
A Viable Approach to Propeller Safety for Small Craft; Ringed Propellers ('happle, Mark; Renilson, Martin
322
T2-4 Optimisation of a Linearjet
Steden, Max; Hunde,ner, Jochen; Abdel-Maksoud, Moustafa
327
Session TB3 Propeller Ventilation
I-i
Analysis of Different Propeller Ventilation Mechanisms by Means of RANS SimulationsC'alifano, Andrea; Steen, Sverre
334
TB3-2 Classification of Different Type of Propeller Ventilation and Ventilation Inception Mechanism
Kozlowska, Anna M.; Stee,,, Sverre; Koushan, Kourosh
342
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TB3-3 Experimental Investigation of the Effect of Waves and Ventilation on Thruster
Loadings
Koushan, Kourosh; Spence, Silas I. B.; Hamsiad, Toraif
350
Session T84 Cavitation 2
TB4-1 Propeller Cavitation Modelling by CFD - Results from the VIRTUE 2008 Rome
Workshop
Salvatore, Francesco; Streckwall, Heinrich; van Terwisga, Tom
362
rB4-2 Numerical Analysis of Steady and Unsteady Sheet Cavitation on a Marine Propeller Using a Simple Surface Panel Method "SQCM
Kaneinan,, Takashi; Ando. Jun
372
TB4-3 A Versatile Partial Sheet Cavitation Model
Phoeinsaptha wee, Surasak; Lero:&v, Jean-Baptiste; Laurens, Jean-Marc;
Deniset, Fran cois
380
Session WAI Waterjets
Wti
Toward Predicting Performance of An Axial Flow Waterjet including the Effects of Cavitation and Thrust BreakdownSchroeder, Seth; Kim, Sung-Eun; Jasak, Hrvoje
387
WA1-2 Computation of Viscous Flow for the Joint High Speed Sealift Ship with
Axial-Flow Waterjets
Rhee, Bong; Coleman, Roderick
395
WA1-3 Use of RANS for Waterjet Analysis of a High-Speed Sealift Concept Vessel
Delaney, Keegan; Don nd/v. Mail/n; Ebert, Michael; Fry, David
408
WA1-4 Numerical Simulation of Flow around a Waterjet Propelled Ship
Hino, Takanori; Ohashi, Kuni/mide
416
Session WA2 Unconventional 2
WA2i Voith Schneider Propeller (VSP) - Investigations of the Cavitation Behaviour .Jürgens, Dirk; Heinke, Hans-Jurgen
424 WA2-2 i'crformance Prediction of a Cavitating Rim Driven Tunnel Thruster
Kinnas, Spvros A.; C/tang, Shu-Hao;He, Lei; Johannessen, Jo liii Terje
435
WA2 A Novel Power-Saving Device for Full-Fomt Vessels Mewis, Friedrich
443
Session %VA3 Off-Design Hydrodnamics
WA3-1 Exploring the Interfaces among Hydrodynamics, Mechanical Engineering and
Controls
Vmidal, Leif, Rayset, Norvald; Arén, Per; Aarseth,Lef Vesa, Juha-Pekka
449
WA3-2 Analysis of Crashback Forces Compared with Experimental Results Black, Scott; Swithenbank, Susan
463
WA3-3 Lateral Propeller Forces and their Effects on Shaft Bearings Vandal, Bjørn Johan; Gjestland, Tonmnod; Arvidsen, Terje Ingvar
475
Session WA4 Dynamics
WA41 Performance Characteristics of Static and Dynamic Azimuthing Podded
Propulsor
[slain, Mohammed F.; Akinturk.Avhan; Veitch, Brian and Lin, Pengfei
482
WA4-2 Calculation of Propulsion Pod Characteristics in Off-Design Operating
Conditions Yakovlev, Aleksey
493
WA4-3 A Potential Based Panel Method for Prediction of Steady and Unsteady
Perfomiances of Contra-rotating Propellers
Xiao-long. Liii
500
WA4-4 Some Unsteady Propulsive Characteristics of a Podded Propeller Unit under
Maneuvering Operation
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Lii,, Pen gfei; Islam, Mohammed; Veitch. Brian
Session WBI Numerical 4
WB1-1 Simulation of Viscous Flow Around a Ducted Propeller With Rudder Using Different Rans-Based Approaches
Srinche:-Ca/a, A.; Sipilli, T.P.; Pvlkkänen, J. V.
517
W1-2 Comparison of Experimental Measurements and Numerical Calculations for a Propeller in Axial Cylinder
Gaggero, S.; Savio, L.; Brizzolara, S.; Viviani, M.; Ferrando, M.; Conti, F.
525
Wi
Coupled HydrodynamicsHydroacoustics BEM Modelling of Marine Propellers Operating in a WakefieldSalvatore, Francesco; Testa, Claudio; Greco, Luca
537
WB1-4 Computation of Hull-Pressure Fluctuations due to Non-Cavitating Propellers Lafeber, Frans Hendrik; van Wzjngaarden, Erik; Bosschers, Jo/ian
548
Session WB2 Underwater Vehicles
WB2-1 Aspects of Propeller Developments for a Submarine .4 ndersen, Paul; Kappel, Jens J.; Span genberg, Eugen
554
W02.2 Numerical and Experimental Analysis of the Wake Behavior of a Generic Submarine Propeller
Di Felice, Fabjo; Felli, Mario; Liefvendahl, Mattias; Svennberg, Urban
562
W2 Experimental Testing of an Autonomous Underwater Vehicle with Tunnel Thrusters
Palniei A list air; Hewn. Grant S.: Stevenson, Peter
569
Session VB3 Propulsion
WB3-1 One Theorem about the Maximum Efficiency System "Hull and Actuator Disk" in Viscosity Fluid
A chkinadze, Alexander
576
W2
Advanced Design of a Ducted Propeller with I-ugh Bollard Pull Performance Taketani, Tadashi; Kimura, Kayo; Ishii, Norio; Matsuura, Masao; Taniura,Yuichi
583
WB3-3 Operating Conditions Aligned Ship Design and Evaluation Greiisch, Lars; El/ardi, Georg; Krueger, Stcfan
589
Session WB4 Numerical 5 Cavitation
WB4- Numerical Investigation of Cavitation Bubble Collapsing Behavior Shin, Bveong Rag
595
WB4-2 Application of Fully Viscous CFD Codes in the Design of Non Cavitatiiig
Propellers for Passenger Vessels
Lavini, Gianpiero; Pedone, Lorenzo; Genuzio, Davide Harpo
601
W4 Numerical Prediction of Vortex Generated by Hydrofoil
Flaszvnski, Pastel; Szantvr, Jan, Dv,narski, Pawel; Kraskowski, Marek
609
WB4-4 On the Modelling of the Flow in Ducted Propellers With a Panel Method Baltazar, J.; Fa/câo de Campos, J.A.C.
First International Symposium on Marine Propulsors
Ho meCommittees
Chair Committee
The conference is the first in a series, so a chair committee has been established to supervise the first conference and organise future events. Dr. Kourosh Koushan (NO)
Prof. Sverre Steen (NO)
International Committee
The conference has an international committee consisting of the following individuals Prof. A. 5. Achkinadze (RU)
Prof. Mehmet Atlar (UK) Prof. Goran Bark (SE) Prof. Neil Bose (AU) Prof. John Canton (UK) Prof. Odd M. Faltinsen (NO) Kjell Holden (NO) Dr. Stuart D. Jessup (US) Dr. Ki-Han Kim (US) Prof. Spyros Kinnas (US)
Prof. Moustafa Abdel-Maksoud (DE) Prof. Gerasimos Politic (GR) Dr. Francesco Salvatore (IT) Dr. Noriyuki Sasaki (JP) Dr. Antonio Sanchez Caja (F!) Dr. Brian Veitch (CA)
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First International Symposium on Marine Propulsors smp'09, Trondheim, Norway, June 2009
Propeller Cavitation Modelling by CFD
-Results from the VIRTUE 2008 Rome Workshop
Francesco Salvatore', Ileinrich Streckwall2, Tom van Terwisga3
'Italian Ship Model Basin (INSEAN), Rome, Italy 2Hamburg Ship Model Basin (HSVA), Hamburg, Germany
3Maritime Research Institute of Netherlands (MARIN), Wageningen, / Del ft University of Technology, The Netherlands
ABSTRACT
Results from the Rome 2008 Workshop on cavitating propeller modelling are presented. Seven computational
models by RANS, LES and BEM are benchmarked
against a common test case addressing the INSEAN
E779A propeller in uniform flow and in a wakefield.
Submitted results provide a wide picture about capabilities of solvers based on different discretization techniques, turbulence and two-phase flow models. The comparative analysis of numerical results highlights a
good agreement
for the non-cavitating steady flow predictions, whereas for the cavitating flow, discrepancies in cavity extent are observed. In the case of a propeller operating in a non-unifonii flow, difficulties to correctlymodel the inflow to the propeller are reflected in the
differences in non-cavitating pressure distributions on the blade and hence in the transient cavity patterns.
Keywords
Marine Propellers, Cavitation, Multi-phase Models, RANS, LES, BEM, CFD Validation.
1 INTRODUCTION
During recent years Computational Fluid-Dynamics
(CFD) models have demonstrated to rapidly become
effective tools to analyse marine propeller single-phase flows. In contrast to this, cavitation presents complex two-and multi-phase
flow phenomena that
are stilldifficult to accurately simulate. In particular, cavitation nuisance like erosion, pressure fluctuations and noise are hardly captured by CFD-based solvers.
In
this framework, the primary aim of the EU-FP6
Research Project 'VIRTUE, The Virtual Tank Utility in Europe' (www.virtual-basin.org) is to develop and assess multi-phase flow models for the analysis and design of marine propulsors. One of the five work packages of the VIRTUE Project, 'The Virtual Cavitation Laboratory,' is devoted to this topic.
In October 2007, project partners involved into this Work Package organized a workshop to review the progress achieved in cavitation modeling by CFD. Results from
this Workshop, held at Wageningen, The Netherlands, are summarized by Streckwall and Salvatore (2008).
The present
paper offers a reviewof the
second workshop, held in October 2008, in Rome, Italy. As in theWageningen 2007 Workshop, aim of the Rome 2008
Workshop is to analyse the performance of computational models to describe cavitating propeller flows. To compare results from different models, common test cases were proposed, and experimental results were made available
to Workshop participants beforehand. Relevant flow
features to be described by the CFD models were known a priori and computational set-ups could thus be adjusted to achieve the best performance with the computational models used. Thus, the numerical
results from the
workshop yield a clear picture of capabilities of different
solvers, allowing for an analysis of weaknesses and
strengths of computational models and identifying areas where further developments are required.
A cavitating propeller in "behind" conditions (that
isoperating in a non-uniform wakefield) was to be
simiulated. The Rome 2008 Workshop also proposed preceding test cases with a limited amount of geometrical/onset flow complexity: (i,) a two-dimensional
NACA 0015
foil, (ii) a three-dimensional twisted hydrofoil, that are not addressed here. Scope of this paper is to review test cases describing a propeller in a uniform inflow (Case A) and in a non-homogeneous wakefield (CaseB). Common case definition
reflects existing experimental data describing the INSEAN E779A model propeller tested at the Italian Navy Cavitation Tunnel (CEIMM, Rome, Italy), see Pereira et al (2004a, 2004b). Propeller flow studies submitted by seven organizations(five from VIRTUE partners and two external to the
project) allowed for a comparison of five solvers based on Reynolds-averaged Navier-Stokes (RANS) equations, one Large-Eddy Simulation (LES) model and one inviscid-flow Boundary Element Method (BEM). In the following sections, the proposed test cases are described and a brief overview of the computational models is given. Subsequently, the corresponding numerical results
submitted by workshop participants are compared and discussed.
2 THE PROPELLER FLOW TEST CASE
The [NSEAN E779A propeller is chosen as reference case for the CFD benchmark exercise. A comprehensive series of experimental data addressing the propeller in a unifonn as well as in a non-homogeneous flow is available for this propeller from an experimental programme performed at
INSEAN over the
last decade. Descriptionof the
INSEAN E779A experimental dataset may be found, e.g, in Pereira et al. (2004a) and Pereira Ct at (2004b). 2.1 Propeller geometry and test case definition The INSEAN E779A is a four-bladed, fixed pitch,right-handed propeller, originally designed in 1959. Blade skew
and rake are small, and pitch ratio is almost constant
along radius (P/D=l.l). A bronze model of diameter
D227.27 mm is used for experimental work, Fig.
1.Geometry details are given in Salvatore et al (2006a).
S
Figure 1. The INSEAN E779A model propeller (D=227.27
mm) and mathematical description of one blade (IGES).
In spite of a rather obsolete geometry typical of a 1950 design, the E779A propeller represents a challenging test
case for validation of propeller codes and in particular, of cavitation
models. For the Workshop purposes,
thefollowing operating conditions are considered:
uniform flow at speed V = 5.808 ni/s and
propeller rotational speed n = 36.0 rps (advance coefficientJ = V/nD = 0.71); non-cavitating
and cavitating flow at a,, =
(p-p)/ '/2 (nD)2 =1.763;
non-homogeneous flow at at speed V = 6.22 ni/s
and propeller rotational speed n 30.5 rps (J = 0.90); non-cavitating flow and cavitating flow at a,, = 4.455.
To achieve consistency among different numerical studies presented at the Workshop, a common description of
propeller geometry in IGES format is provided to all
participants. Similarly,
a common definition
of the
computational domain is proposed. Experimental conditions reflect measurements performed at the Italian Navy Cavitation Tunnel (CEIMM, Rome, Italy). This
tunnel has a squared test section of width 0.6 in and
length 2.6m. To simplify the computational modelling of propeller in uniform flow, an idealized tunnel having a circular cross section and identical sectional area as the
actual tunnel was proposed at the Wageningen 2007
Workshop. This solution is kept for test case specifications at the 2008 Workshop, as illustrated in Fig. 2, where also dimensions of the prescribed computational
domain upstream and downstream propeller disc
are given.A common definition
of
boundary conditions is also
proposed: prescribed velocity at inlet section, zero pressure at outlet section, and slip at tunnel walls. No-slip conditions are enforced on propeller and shaft surfaces. Kinematic viscosity is v = 1.01 e-6 m2/s and onset flow turbulence level is 2%.
Figure 2. Idealized tunnel test section and dimensions (R, = 1.471 Dr).
2.2 Non-homogeneous inflow modelling
Workshop Case B is inspired to the INSEAN E779A
dataset (Salvatore et at, 2006a),
in which
anon-homogeneous inflow is established through
a wake
generator placed upstream the propeller plane, Fig. 3. This physical set-up is used to approximately simulate a propeller operating behind a single-screw hull. To ensure a common definition of the non-homogeneous inflow to
the
propeller, no computational modelling of wake
generator in the computational domain is requested, whereas suitable velocity boundary conditions at inlet
section are imposed. This choice is motivated by the
geometrical complexity of the wake generator. Numerical modelling of such a complex assembly might raise large discrepancies of wake generator wakefields resulting from different calculations, with uncontrolled consequences in propeller flow predictions.
Figure 3. Propeller in non-homogeneous flow: tunnel set-up
(left) and axial velocity distribution measured by LDV at section = -0.26 Dp) used to prescribe velocity inlet conditions (right).
To overcome these problems, a common propeller inflow
is defined through wakefield measurements by
Laser-Doppler Velocimetry (LDV) at a transversal plane at
distance
d =
0.26 D
upstream propeller disc.Measurements without propeller (nominal wake) and with propeller
(total wake) are available
in the INSEAN E779A dataset, see Salvatore et al (2006a).Axial velocity describing the LDV nominal wake is used to specify velocity conditions at inlet boundary (x = -1.25 Dp) for Workshop test case B, and no physical model of the wake generator is accounted for in the computational domain. Zero transversal velocity components along the inlet boundary are enforced.
3 SURVEY OF COMPUTATIONAL MODELS
Results submitted by seven organizations participating to
the
2008 Workshop provide
a wide spectrumof
capabilities applied to marine propeller flow and
cavitation modelling. Numerical solution of the Navier-Stokes equation is addressed by RANS (six participants), and by LES (one participant). As a term of comparison, numerical results
by an
inviscid-flow BEM solver including a sheet cavitation model are also considered. 3.1 Mathematical models and computational schemes Computational models are briefly recalled here, whereas cavitation models are summarized in the next subsection. Hamburg Ship Model Basin (HSVA, Germany) presents numerical studies by FreSCo, an incompressible unsteady RANS finite volume solver under development as a joint initiative between HSVA, the Maritime Research Institute of the Netherlands (MARIN), and the Technical University Hamburg-Harburg (TUHH). Transport equations are discretized with a cell-centred scheme and solved with a pressure-velocity coupling based onSIMPLE. The fully-implicit algorithm is second-order accurate in space and time. A standard K-w turbulence
model is used for present calculations. The solver is
applied to unstructured grids using arbitrary poyhedral
cells. Computational grids are obtained by using HEXPRESS, an automated grid generator. Details in Vaz & Hoekstra (2006) and Vorhölter et al (2006).
NUMECA mt. s.a, Belgium, presents
results by its
Commercial package FineTM/Turbo, a structured, density-based finite volume solver. Centered space discretization is employed with Jameson artificial dissipation. A
four-stage explicit Runge-Kutta scheme is used for time
discretization. Preconditioning is used to solve incompressible non-cavitating and cavitating flows.
Present results are obtained by using a one-equation
Spalart-Alimaras turbulence model, and compi.itational grids are built by automated grid generators AUTOGRID 5 and IGO by NIJMECA.
The Swedish Ship Model Basin (SSPA, Sweden) presents
results by the commercial software FLUENT6.3, an
unstructured cell-centred finite volume solver. Present calculations adopt its incompressible RANS formulation
and SIMPLE scheme, with a second-order QUICK
scheme for convection terms and a second-order central difference for diffusion terms. The standard RNG k-turbulence model is used for the non-cavitating flows, whereas a modified RNG k- c model is adopted for the prediction of cavitating flows. Further detail of using the latter approach can be found in Li and Grekula (2008).
VII Technical Research Center of Finland presents
numerical studies by FINFLO code, a finite volume
solver based on
the pseudo-compressibility method. Second order central-differencing is used for diffusion terms, whereas different upwind schemes are used for convection terms in steady, unsteady or cavitating flows. Time-integration is performed via approximate factorization and local time stepping. Present calculations adopt Chien's low-Re K-r turbulence modelling, fordetails see Sánchez-Caja et al (1999).
The Applied Research Laboratory (ARL) from Pennstate University, Pennsilvania, USA, proposes a numerical study by the in-house code M-UNCLE, a cell-centered, finite volume solver based on a pseudo-compressibility formulation. Preconditioning is based on a second-order accurate dual-time scheme. Present calculations are
performed through an incompressible flow assumption, and K-r, K-w or DES turbulence models are employed.
The computational domain is discretized by an
overlapping structured grid approach (Kunz et al, 2000). Chalmers University, Sweden, presents results by a cell-centered finite volume incompressible LES solver
developed from OpenFOAM, the open source CFD
library. The code adopts a velocity-pressure coupling by a
PISO algorithm. The so-called mixed formulation
isapplied and dissipative subgrid modelling is accomplished via an implicit approach. Wall modelling is based on LES boundary layer equations and viscosity adaptation. Computational grids are unstructured, with tetrahedral cells away from walls and prisms in the boundary layer. See Bensow et al (2008) for details.
In addition to the above mentioned viscous-flow solvers, the Italian Ship Model Basin (INSEAN, Italy) contributes with results from an inviscid-flow model implemented through a Boundary Element Methodology (BEM) into the PFC-BEM code. An outline of this model is given in Pereira et at (2004a) and in Salvatore et al (2006b). 3.2 Cavitation models
Different cavitating flow models are implemented in
RANS, LES and BEM solvers presented at the Workshop.
A single-fluid, single-phase barotropic model by
Delannoy and Kueny (1990)
is implemented in the FineTM/Turbo code. Density is constant in the pure liquid and pure vapor regions whereas it varies according to an equation of state p=f(p) in the mixture region. Continuity and momentum equation for a single compressible fluid having density p are solved. A standard sine function lawAll the other Navier-Stokes solvers adopt multi-phase models based on a transport equation describing generation and evolution of vapor content in the fluid. Vaporization and condensation of vapor in respectively, cavity growth and collapse phases, are described through finite rate mass transfer models implemented via suitable source terms. This transport equation is solved in addition to mass and momentum equations for the mixture fluid. Alternative vaporization and condensation models characterize different multi-phase models addressed in the Workshop.
Chalmers' OpenFOAM and FINFLO codes adopt mass transfer models derived
from an
original approach proposed by Merkle et al (1998) and Kunz et al (2000)and implemented into
the M-UNCLE code.
Semi-empirical constants are used in the expressions of vapor production and destruction terms.
Cavitation models derived from isolated bubble dynamics
via the Rayleigh equation are implemented in codes
FreSCo and FLUENT 6.3. Tn particular, the formulation
by Sauer (2000) is implemented in the FreSCo code,
whereas the 'Full Cavitation Model' by Singhal et al
(2002) is implemented in FLUENT 6.3,
Finally, an unsteady-flow
sheet cavitation model
is implemented into the PFC-BEM code. The approach isbased on a cavity surface tracking model using the
condition that flow pressure equals vapor pressure in the cavity. The methodology is valid only to address cavities attached to the blade surface.
3.3 Computational details
A summary
of computational frameworks used
toevaluate propeller flow by the Navier-Stokes solvers
above is given in Table 1. Common to all RANS and LES models, propeller in uniform flow is studied in a rotating frame of reference fixed to propeller blades. Only one blade is explicitely considered and periodicity conditions are enforced. In most cases non-homogeneous inflow conditions are described by using a rotating grid block surrounding the
propeller and fixed blocks
for theremaining part of the computational domain. A sliding mesh technique is used at the interface between fixed and rotating blocks and governing equations are solved in the inertial frame. Numerical studies by Chalmers' OpenFOAM and FreSCo are performed by rotating the whole computational domain. This approach requires that inlet velocity distribution is interpolated at rotating grid cells at each time step.
As mentioned above, both structured and unstructured computational grids are used. The M-UNCLE code adopts an overlapping block technique. Propeller flow test cases A and B represent challenging grid generation exercises in that grid refinement at blade tip and along wake tip-vortex are necessary. The correct description of the non-homogeneous wakefield implies adequate modelling of the inlet region to avoid excessive numerical dissipation upstream the propeller. Furthermore, cavitation studies require that suitable grid cell clustering is made in flow
regions where vapor generation/destruction is expected to
occur. Representative examples
of
structured and unstructured computational grids are given in Fig. 4. Although trivial as compared to Navier-Stokes solvers,the computational set-up
for BEM calculations
isdescribed for completeness. Inviscid-flow calculations by PFC-BEM are performed by assuming the propeller in an
unbounded flow (no tunnel wall confinement effect
described). Unsteady non-cavitating flow calculations proceed until periodic solution is achieved and then the cavitation model is switched on. Propeller surface discretization is
chosen to minimize grid refinement
effects and time discretization corresponding to angular step of 2.5 deg is used.Table I. Summary of computational details.
Figure 4. Examples of computational grid details. Structured
grids (top) and unstructured grids (bottom).
4 NUMERICAL RESULTS: UNIFORM FLOW
The E779A propeller in uniform flow repeats a test case originally proposed at the Wageningen 2007 VIRTUE Workshop. In view of open issues left by the analysis of results submitted to the 2007 Workshop, this test case is proposed again for the 2008 Workshop, as a preliminary
Code (organization) Grid size wet 'cai'
Time. step
angular step CPU effort OpenFoani (Chalmers) 4.6 M 1.1 E-6 s 10.012 deg
FreSCO (HSVA) 2.4 1 3.1 M 4.55E-5 s / 0.5 deg 3 days ta-proct Fine-Turbo (NUMECA) 3.0/11.4 M 2.28E-4 6/2.5 deg 3 days(2lproct Fluent 6.3 (SSPA) 0.8 / 2.3 M 4.55E-4 if 5 deg
FINJFLO )VTT) 1.7 /5.9 M 4.55E5 s / 0.5 deg (16.pcoc)4 days M-Unde (ARL-PtJ) 3.7 / 7.3M 2.28E.5 S 0.25 dog 0.6 days 192 proc./ BEM-PFC (INSEAN) surface 2.5 deg 9 hours
step towards unsteady propeller flow calculations. Streckwall and Salvatore (2008) provide a detailed review of results presented at the 2007 Workshop.
4.1 Non-cavitating flow
First, non-cavitating conditions at the design point J
= 0.71
are considered. Numerical predictions of propeller thrust and torque coefficients by allcomputational models are shown in Fig. 5. Experimental data from open water tests in towing tank are also shown for comparison. Evaluated thrust and torque coefficients are generally in fair agreement with experimental data over the considered range of advance coefficients J. Few cases present a rather constant offset from the average of computational results. As expected, inviscid-flow results by PFC-BEM correctly predict thrust, whereas torque is overestimated at high J and underestimated at low J.
Results for J = 0.7l are analysed in Table 2. Most of
numerical model predict KT and KQ in close agreement with open water measurements. In fact, averaging the five best results out of seven, differences between measured and predicted thrust is 1.2% whereas the difference for torque is about 1%.
04
Aó.*C,*4j J
Figure 5. Uniform non-cavitating flow. Predicted propeller thrust and torque coefficients compared to OW.
data.
Table 2. Uniform flow, J = 0.71. summary of predicted thrust and torque coefficients and experimental data.
The comparison with
open water measurements isqualitative in that flow confinement effects are taken into
account in numerical calculations, with the only exception of BEM results. In the present case, confinement effects
are estimated as 2% of both thrust and torque. For
completeness, Table 2, gives also thrust and torque from cavitation tunnel measurements. Loads measured in the tunnel are about 8% higher than in open water, due to a particular calibration technique used. The comparison between numerical results and measurements from tunnel tests is presented in Fig. 6.
Figure 7. Uniform non-cavitating flow. Pressure isosurfaces on blade suction side.
To get a first impression of the cavity extent without
invoking a cavitation model, it is interesting to analyse the flow domain where the pressure in wetted flow conditions
LI a 'Sn Unifoni flow J=0.71 Non-cavitating Cao'italing KT IO8KQ l( I08K Measured(tunnel) 0.256 0.464 0.255 0.460 Measured (OW.) 0.238 0.429 -FreSCo 0.237 0.438 - -F1neTM/Turbo 0.250 0.428 0.260 0.447 Fluent 6.3 0.240 0.426 - -FINFLO 0.234 0.418 0.249 0.459 M-UNCLE 0.276 0.498 0.256 0.476 Ch's OpenFOAM 0.256 0.453 0.252 0.450 PFC-BEM 0.244 0.4 19 0.247 0.449
Figure 6. Difference in computed and measured thrust and torque coefficient for uniform flow conditions in tunnel @ J=0.71
The limited scatter among thrust and torque predictions is reflected by the comparison of pressure distributions on the blade surface. Figure 7 depicts pressure coefficient isosurfaces on blade suction side. All calculations detect a strong negative pressure peak in the leading edge region that is typical for this type of propellers with constant pitch distribution along radius. It should be noted that comparisons of results from different contour maps can be only qualitative in that slightly different color maps and levels are used. This comment holds for Fig. 7 below as well as for all contour plots shown hereafter.
too 8.0 60 7 40 20 00 1) 20 S 40 a -SM -80 .000 12.0
drops to values close to the vapor pressure. To this end, Fig. 8 illustrates isopressure contours at C=-J.O in a flow region surrounding the blade suction side. It is noted this pressure criterion is supposed to show a larger volume (corresponding to a,, = 1.0) than the cavitation number of a,, = 1.76, which is discused later. This type of result in
terms of volume regions
istypically not given by
inviscid-flow BEM calculations where in first instance only flow quantities on the propeller surface are evaluated. Comparing the results of different codes, a region extending from mid-span leading edge to blade tip is clearly observed in all solutions. It is expected that vaporization mostly occurs in this area. Differences between the results from different codes become especially apparent in the tip region and the blade root region.Figure 8. Uniform non-cavitating flow. Constant pressure
contour for Cp = -1.0 on blade suction side predicted by
viscous-flow solvers.
4.2 Cavitating flow
Cavitating flow conditions at the design point J = 0.71
and cavitation number a = 1.76 are considered in the
following. Pressure isosurfaces on blade suction side are
shown in Fig. 9, whereas Fig. 10 compares predicted
extensions of cavitating regions. Dealing with inviscid-flow BEM-PFC results, the cavity shape determined
through a surface tracking technique
is plotted. The irregular shapeof
the cavity trailing edge is aconsequence of the comparatively coarse discretization of the blade surface. In viscous-flow calculations, cavity
extension is assumed to be limited by vapor fraction
contours with a = 0.5
. Although the correspondancebetween cavity and flow regions tagged by a = 0.5 is
open to discussion, the results from plots in Fig. 10 may
be used to compare the extension of cavitating flow
regions predicted by CFD codes with the results from experiments.
The comparison from Fig. 10 highlights that all computational models are qualitatively able to describe the basic features of the cavitating flow observed during
the experiments. There
is a fair correspondence inspanwise sheet cavity extent. All codes predict that the
cavity length increases rapidly from the inner to the outer radial stations and at the blade tip the cavity merges into a strongly cavitating tip-vortex. The cavity is attached to blade surface and stable, with very limited formation of clouds. This is confirmed by experimental data indicating an standard deviation of the measured cavity extension of only 2.5% of its mean extent (projected cavitating area). It is noted that all numerical predictions overestimate the cavity extension. This is true in particular for results by FINFLO and Chalmers' OPENFOAM where excessive vapor at blade mid-chord is detected. Tip-vortex cavitation is observed in results by M-LTNCLE, Chalmers' OPENFOAM, and to a very limited extent by FRESCO. Reasons for these discrepancies are cavitation modelling,
and the computational grid density in
the tip-vortex region.MUNCLE
Figure 9. Uniform cavitating flow. Pressure isosurfaces on blade Suction side.
Fig. 10. Unifonu cavitating flow. Vapor fraction contour for
= 0.5 on blade suction side by RANS and LES solvers. Predicted cavity surface by BEM code and observed cavity
5 NUMERICAL RESULTS: UNSTEADY FLOW
The test case addressing the E779A propeller in non-homogeneous inflow is complicated by the necessity to ensure a correct description of the prescribed velocity distribution at the
inlet section of the computational
domain. As for the CFD models, the
results fromFLUENT, FINFLO and M-UNCLE are obtained by
interpolating the prescribed velocity distribution from LDV measurements in the cavitation tunnel, see Fig. 11.
A different approach
is used in the calculations by Chalmers' OPENFOAM and FreSCo where an idealized velocity distribution approximating the LDV-based inflow in Fig. 3 is considered. Boundary conditions forinviscid-flow calculations by the BEM-PFC code are
obtained by imposing a velocity distribution at propeller plane obtained through interpolation of LDV data. To quantif' the effect of different numerical descriptions of the incoming velocity field, a comparison of the axial
velocity component on a transverse plane located
atdistance d = 0.52 R upstream of the propeller disc is
depicted in Fig. 11. Numerical results from RANS and LES solvers are compared here with experimental data by
LDV. Although color maps are different between the
various plots, large discrepancies in numerical results are apparent.
Chalm.rs
I FINFLO
Figure 11. Axial velocity distributions at transversal plane at distance d = 0.52 R upstream the propeller disc. Numerical
results and experimental data by LDV.
5.1 Non-cavitating flow
Non-cavitating flow conditions at J = 0.90 are considered.
The non-homogeneous wakefield incoming to the
propeller an(l illustrated in Fig.
II induces a periodic
variation of the pressure on the blade surface, with high loadings occurring when the blade crosses the narrow
wake peak where most of the
velocity defect isconcentrated (see Fig. 3).
Figure 12 shows pressure isosurfaces, on blade suction
side for three blade angular positions: 0
-30, 0, +30 deg, with 0 = 0 corresponding to the reference blade inthe twelve oclock position. Similarly, Fig.
13 shows isopressure contours for Cp = -3.0 on blade suction side for the same angular positions. Available results fromFreSCo, FENFLO, FINE-TURBO and BEM-PFC codes present a qualitative agreement in Fig. 12.
Figure 13. Unsteady, non cavitating flow. Constant pressure contour for Cp -3.0 on blade suction side predicted by
viscous-flow solvers. Blade angles -30, 0, +30 deg.
5.2 Cavitating flow
Cavitating flow conditions at J
0.90, o = 4.455 are
considered. As a result of the periodic variation of blade loading, a transient cavitation is observed on the propeller blades. A sequence of snapshots describing the cavity pattern variation as observed from experimental visualizations is shown in Fig. 14. Frames are taken for
Figure 12. Unsteady, non cavitating flow. Pressure isosurfaces on blade suction side at blade angular positions -30, 0, +30 deg.
blade angular positions between -35 and +20 degrees,
with angular steps of 5 degrees. Figure 15 illustrates
predicted cavity extensions for three angular positions. Similarly to cavitating flow results shown in Section 4,
viscotis-flow results from the RANS and LES codes
presented correspond to vapor fraction contours with a = 0.5, whereas the actual cavity surface determined by the surface tracking technique coupled to the BEM method is used to describe results by the inviscid-flow code PFC.
Figure 14.
Sequence of snapshots describing cavity
pattern variation as observed from tunnel visualizations. Blade angular positions between -35 and +20 degrees,
step S degrees.
Figure 15. Unsteady, cavitating flow. Vapor fraction contour for
a
0.5 on blade suction side by RANS and LES solvers.Predicted cavity surface by BEM code. Angular positions -30, 0, ±30 deg.
6. COMPARATIVE ANALYSIS OF CAVITATING FLOW
PREDICTIONS
Let us first have a closer look at the cavitating propeller in a uniform flow. Combining results for the present test
case from the VIRTUE 2007 Workshop with those
submitted to
the 2008 Workshop, a total of eleven
different models can be compared.
Predicted cavity patterns from RANS and LES code (isosurface a = 0.5) and by BEM (evaluated cavity surface) are in Fig. 16. Come,Figure 16. Uniform cavitating flow. Synopsis of predicted cavity patterns from VIRTUE 2007 and 2008 Workshops.
Numerical predictions show a qualitative agreement with experimental observations. In particular, the shape of the cavity is captured
in most cases, whereas a common
trend to overestimate the extent of vapor regions on the blade surface is noted. Larger values of the ct threshold used would improve the agreement with experimental
data. Related to this, the analysis of predicted cavity
volume defined as the integral of vapor fraction values over the whole computational domain is more rigorous. For the case addressed in Fig. 16, cavity volume values of 3.75e-6 and 3.86e-5 m3 are reported by two participants (no experimental data available). Similarly, predicted cavity area defined as the integral of vapor fraction values over blade surface grid cells are in the range 3.84e-5 to
I .33e-3 m2 (four results
submitted, compared to
ameasured value of 7.l3e-4 m2, see Pereira eta! (2004). Let us now consider the differences between the various codes for the unsteady flow conditions when the propeller operates in a non-homogeneous wakefield. The differences in modelling the inflow to the propeller are
recognized here as a major source for these different
results.
In some calculations, too strong a numerical
dissipation weakens the wakefield in the propeller region (see Fig. 11). As a result, the propeller blade does not
reach the maximum loading and
the corresponding calculated cavity patterns tend to be underestimated compared to the experimental observations, as shown in Figs. 14 and 15. In this case, predicted blade cavity areas are in a relatively narrow range, I .80e-4 to 9.84e-4 m2 (maximum value during propeller revolution) compared to a measured value of 8.21 e-4 m2. To the contrary, the scatter of predicted cavity volume values is even largerthan in uniform flow, with estimates between 2.8e-7 and l.41e-5. This aspect raises a question on the reliability of current CFD models to predict dynamic cavitation effects like pressure fluctuations, noise and erosion.
In the case of a propeller operating in
a wakefield, numerical results are furthermore affected by the different meshing techniques used to impose the prescribed axial wake. Models based on a sliding mesh approach where the measured axial wake is imposed as inlet condition arecompared to models where the whole computational
domain is rotating with the propeller, and an idealized analytical definition of the wakefield is used.
A grid refinement study was beyond the scope of the
propeller test case. Nevertheless, results presented by some organizations comparing solutions obtained using different grids reveal a large variation in the predicted cavity patterns. In particular, the correct modelling of cavitation requires that flow regions
where vapor
generation, transport and destruction occur are discretized with a much higher grid density than typically needed for the non-cavitating flow outside the inner boundary layer. LES simulations resolve (not surprisingly) more
stnictures in time and space than RANS calculations.
Transient cavitation results show that two-phase flow details like the process of leading-edge detachment are in this case accurately described by LES. Moreover, results comply with the non-periodic nature of cavitation usually observed on model scale propellers. From the workshop results it appears that LES-based models are promising tools to investigate the risk of cavitation erosion. It should however be noted that the computational time needed for the propeller computations with Chalmers'OPENFOAM is of the order of CPU months.
For a further analysis of the differences in computed
results, reference is made to the NACAOO15 2D test case, that
served as one of the three
test casesfor the
Workshop. Results on this 2D foil in a uniform inflow showed a similar scatter in results for the cavity extent
and dynamics as found on the propeller. Some of the
findings from the 2D foil are summarized here:
It was shown that turbulence models can change the character of the cavity. Computations with STAR-CD for instance showed that the character of the sheet cavity could change from a non-shedding oscillating cavity with a frequency of approx. 4Hz to an unstable shedding cavity with a dominant frequency of 14 Hz.
This difference was obtained by using a K-E
turbulence model for the first, and an RNG
model for
the second case. Computations with COMET showed that using the RNG K - e modelshowed stronger dynamics than the K - w model. The choice of the cavitation model (Sauer's versus Kunz model) was shown to cause a clear difference in the thickness of the re-entrant jet.
The grid density was shown to have an important effect on the extent and volume of sheet cavitation
from a systematic
study with FreSCo.
It wasconcluded that the grid should not only be refined in the wetted boundary layer flow, but also at the cavity interface. Too much numerical dissipation seems to result from too coarse a grid. It is believed that the grid density is likely to be the most important source for differences between properly verified codes. Based on the workshop results, it is hypothesized that differences between results
are to a large extent
caused by grid density and numerical dissipation and to a lesser extent by the different turbulence models (and probably by different cavitation models as well). This hypothesis is supported by the results obtained with the non-viscous Euler solver CATUM in e.g. Schmidt et al. (2008). In this paper, the authors show that the cavitating vortices in the wake of a triangular prism are predicted qualitatively well and that thelocation of the impact pressures caused by the
breaking up of the cavitating vortex corresponds to the experimentally determined locus
of erosive
damage. These authors conclude that the mechanism governing the cavity dynamics is "strongly inertia controlled".
7. CONCLUSIONS AND RECOMMENDATIONS
Results of computational studies submitted to the
VIRTUE 2008 Workshop provide a broad view on state-of-the-art propeller cavitation models by RANS, LES and BEM. Performances of computational models have been benchmarked against a common test-case addressing the INSEAN E779A propeller in uniform flow and in a given wakefield.
Considering the open water performance, it is concluded that the uncertainty in predicting thmst and torque is
lower than 5%, this latter value being the standard
deviation of the differences between measurement and computed value. It is also noted that the trend of the open water performance with J is properly predicted.
The predicted cavity extents for both steady and unsteady inflow do qualitatively agree with experimental observations, whereas important quantitative differences
are observed. These differences in cavity extent and
volume render computations not sufficiently suitable for a prediction of radiated pressure fluctuations nor predictions of cavitation erosion. It is concluded that predictions of pressure fluctuations from a potential flow BEM code (in this case the INSEAN PFC code) give, so far, the most reliable results.
The differences in results of the various CFD codes are likely to be caused primarily by a lack of grid density and/or too much numerical dissipation in the vicinity of
the cavity-fluid interface. In addition to these effects,
turbulence and cavitation models were also demonstrated to affect the cavity extents and dynamics.
Related to the issue of grid resolution, is the finding that predictions by LES solve time and space scales better than RANS. The capability of an LES code to describe
important two-phase flow structures has been
demonstrated. This resolution in predicting flow
phenomena appears useful for the assessment of erosion
risks.
The modelling of a non-homogeneous inflow was shown to represent a critical issue. The correct interpolation of
velocity between fixed and rotating grid blocks when a
sliding mesh technique
isused and
the numericaldiffusion in the wakefield are
of primary importancewhen modelling a propeller operating in a hull wake by
CFD.
The issue of grid resolution in the cavitating flow region and numerical dissipation were demonstrated to be of great importance for the prediction of cavity extent and dynamics. The VIRTUE 2008 Rome Workshop demonstrated that this issue is generally not yet under control. Numerical uncertainty studies are required before firm conclusions about the adequacy of turbulence and cavitation models can be drawn. The 2D NACAOOI5 foil test case can be regarded as a starting point.
ACKNOWLEDGEMENTS
The authors wish to thank workshop participants who made possible this paper providing detailed reports of their computational studies: Rickard Bensow, Alexandre Capron, Dieke Hafermann, Robert Kunz, Da-Qing Li, Jay Lindau, Jussi Martio, Benoit Tartinville, Thomas Sipila. Part of work described in this paper has been performed in the Framework ofthe Eu-FP6 VIRTUE Project, grant
TIP5-CT-2005-5 16201.
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