T w e n t y - T h i r d S y m p o s i u m o n
NAVAL
HYDRODYNAMICS
C o n t e n t s
Wave-induced Motions and Loads
Hydrodynamics in Siiip Design
Propulsor Hydrodynamics and Hydroacoustics
CFD Validation
Viscous Siiip Hydrodynamics
Cavitation and Bubbly Flow
Wave Hydrodynamics
Wake Dynamics
Shiallow Water Hydrodynamics
Fluid Dynamics in the Naval Context
Sponsored Jointly by
Office of Naval Research
Bassin d'Essais des Carènes
Naval Studies Board
National Research Council
NATIONAL A C A D E M Y P R E S S
Washington, D.C.
Instability of Partial Cavitation:
A Numerical/Experimental Approach
R.E.A.. Arndt', C C S . Song', M. Kjeldsenl, J. He' , A. Kellei-^
('Saint Antliony Falls Laboratory, University of Minnesota, ^Norwegian University of
Science and Technology, ^Technical University of Munich)
ABSTRACT
Sheet cavitation and tlie transition to cloud cavitation on hydrofoils and marine propellers results in a highly unstable flow that can induce significant fluctuations in lift, thrust and torque. In order to gain a better understanding of the complex physics involved, an integrated numerical/experimental investigation was carried out. A 2D NACA 0015 hydrofoil was selected for study, because of its previous use by several investigators around the world. The simulation method-ology is based on large eddy simulation (LES), using a barotropic phase model to couple the continuity and momentum equations. The complementary experiments were carried at two different scales in two different water tunnels. Tests at the Saint Anthony Falls Lab-oratory (SAFL) were carried out in a 19 cm square water tunnel and a geometrically scaled up series of tests were carried out in the 30 cm square water tunnel at the Versuchsanstalt flir Wasserbau (VAO) in Obernach, Germany. The tests were designed to complement each other and to capitalize on the special features of each facility.
INTRODUCTION
Marine propellers and hydrofoils must often operate in the cavitating regime. Various types of cavi-tation can be found in practice, including bubble cavitation, sheet cavitation, cloud cavitation, vortex tube cavitation and vortex sheet cavitation, depending upon how the low pressure regions are generated. In spite of considerable research, there are still many features of the problem that have not been properly explored. For example, inception studies are based on fiiUy wetted flow properties, i.e. pressure distribution, turbulence level etc. in the absence of cavitation. On the other hand, classical models of developed cavitation consider only cavitation number as the primary variable. What has not been given adequate attention is a class of partially
cavitating flows in which there is an interaction
between fluid turbulence and cavitation. For example,
vortex generation at the trailing edge of sheet cavitation is a manifestation of the cavitation itself (Ye et al, 1997). This is an important finding since turbulence is normally attributed to being a factor in the inception process, but cavitation as a mechanism for turbulence generation has been given scant attention.
Cavitation is also known to produce air bubbles due to incondensible gas coming out of solution in low pressure (supersaturated) regions of the flow. The production of bubbly flows in hydraulic equipment can have insidious effects on the stability of operation and on vibration. There are a variety of references in the literature to the interrelation between cavitation per-formance and dissolved air dating back as early as 50 years ago. However, a quantitative understanding of the interrelation between dissolved gas and cavitation phenomena is still beyond our grasp.
A particularly important form of cavitation from a technical point of view is attached cavitation on the surface of lifting surfaces. At typical angles of attack, this takes the form of a sheet, often terminated at the trailing edge by a highly dynamic form of cloud cavitation. Vortex cavitation is often observed in the cloud which is caused by vorticity shed into the flow field. These cavitating micro-structures are highly energetic and are responsible for significant levels of noise and erosion. Laboratory experimentation indicates that a variety of cavitating flow patterns are possible within the sigma-angle of attack (• -•) plane (Kjeldsen, et al, 1999).
In spite of many excellent studies, the details concerning the transition of sheet cavitation to cloud cavitation is still not understood. From a design point of view, cavitating flows must be modeled over a given performance envelope in the • -• plane in order to
An Experimental Investigation of Cavitation Inception and
Development of Partial Sheet Cavities on Two
-Dimensional Hydrofoils.
J. Astolfi, P. Dorange, J.-B. Leroux, J.-Y. Billard
(Ecole Navale, France)
ABSTRACT
The main results of an experimental study concerning the inception and the development of partial sheet cavities on four two-dimensional hydrofoils are presented. The conditions of cavitation inception are measured together with the minimum pressure coefficient in some cases. The effect of the Reynolds number is studied. Concerning cavitation development, depending on the cavitation number or the angle of incidence various types of cavitation are observed as partial sheet cavities, bubble, fingers, patches or siipercavitation patterns.
For partial sheet cavities, the cavity lengths were measured on the foils for various conditions of cavitation number and angle of incidence. An attempt to correlate the cavity length data is studied at the end of the paper.
INTRODUCTION
The physical process associated with the inception and the development of cavitation is complex and basic experiments on two-dimensional hydrofoils remain an effective way to study the fundamentals of cavitation and to understand cavitation in more complex situations as on marine propellers for instance. Partial sheet cavity is one of the cavitation patterns that occurs on a two-dimensional hydrofoil typically near the leading edge. It corresponds to the situation for which a cavity of vapor extends over a fraction of the hydrofoil's surface.
For inception of partial cavities, the two questions which arise are where and when do cavitation occur ? It is generally accepted that cavitation occurs on a full-scale lifting surface at the position of the minimum pressure and when the local minimum pressure falls to or below the vapor pressure of the flowing liquid. But in many cases, particularly on scale models, the incipient cavitation number 0; is found to be different (often smaller) from the opposite of the minimum pressure coefficient, - Cp„,i„ generally obtained theoretically by computation for an inviscid flow (Arndt 1981). The main reason is that on scale models such as hydrofoils or headforms, long or short separation
bubbles, occurring at the leading edge, influence the inception conditions, Arakeri (1975), Arakeri et al (1981). When at full scale, the flow separafion bubbles are expected to disappear and transition will occur near the leading edge. This phenomenon is known to complicate the correlation of model and fiiU-scale cavitation scaling, (Huang and Peterson 1976, Billet et al. 1981). Arakeri (1975), Katz (1984) and Franc and Michel (1985) indicated that attached sheet cavity development on hydrofoils requires the presence of a laminar separation. In that case, according to Katz (1984) the scenario is that "band type cavitation occurred as bubbles were entrained through the reattachment region, where they were pushed upstream by the reverse flow". In this quiescent region, the bubbles increase progressively as the cavitation number decreases and form a vapor cavity attached near the leading edge. However, Gopalan and Katz (2000) argued that sheet cavitation can occur also on attached flow. In that case, other parameters can induce favorable conditions, for instance local pressure distribution, local surface imperfections, surface nucleus,...
Concerning parfial sheet cavity development, the following points need to be studied :
• the mean characteristics ofthe vapor cavity, • the inspection of the flow near the detachment
point and the surface of the cavity,
• the examination of the closure region of the cavity together with the unsteadiness of the cavity, i f any.
Many authors have addressed these points in the past. Measurements or computations have been performed to determine the mean characteristics of sheet cavities, for example length, height or volume (Le et al 1993, Deshpande et al 1994, Kinnas et al 1994, Farhat 1994, Dang and Kuiper 1998, Dorange et al 1998). But it seems that little has been done to compare experiment and computation results intensively.
Arakeri (1975) and Tassin Leger and Ceccio (1998) have studied the cavity detachment region. The latter carefully examined the separated flow over a series of bodies (including hydrofoils) near the front of the mid-chord attached cavity (occurring at a position of 37-42% of the foil chord
Modern Seakeeping Computations for Ships
R. Beck (University of Michigan)
A. Reed (David Taylor Model Basin, Carderock Division, Naval Surface Warfare Center)
ABSTRACT
Current computational methods for solving seakeeping problems of ships with forward speed are reviewed. A brief historical perspective is given to show the interde-pendency and development of the different ship motion theories that are presently being used. These are placed in context by a discussion of the taxonomy of seakeep-ing computations relative to the fully-nonlinear incom-pressible free-surface viscous flow problem. The state-of-the-art in computational seakeeping of ships is dis-cussed. In general, the accuracy of the solution must be balanced against the computational effort. The ad-vanced codes give more detailed and better solutions, but they require super computers or the equivalent. Fully and partially nonlinear inviscid computations for wave diffraction, and added mass and damping are described and a few examples are provided to illustrate the impact of the various levels of complexity of the calculations on the accuracy of results compared to experimental re-sults. FinaUy, a series of state-of-the-art issues are raised: computationally efficient numerical methods, large am-plitude motions and capsizing, horizontal plane motions (coupling between seakeeping and maneuvering), finite depth in the littorals, and validation and verification of codes for extreme motions.
1 INTRODUCTION
Modern seakeeping computations are used in all aspects of engineering for the marine environment. They have become a standard design tool; they are used in sim-ulators; and they are used operationally to predict the motions of a vessel in real time. Modem seakeep-ing computations are perfomed usseakeep-ing a wide variety of techniques—from simple strip theory to extremely com-plex fully nonlinear unsteady RANS computations. To cover aU aspects would require a book, not a short pa-per. Consequently, we are going to limit the discus-sion to ships at forward speed. This largely eliminates any discussion of the computational techniques devel-oped by the offshore oil industry in order to compute wave loads and motions of offshore structures. We do not want to minimize the contributions of the offshore
industry which have been substantial (some might even argue that modern computational techniques have been driven by the needs of the offshore industi y), but the fo-cus of this symposium is naval hydrodynamics with its emphasis on ships at forward speed.
Modem seakeeping computations are far from a ma-ture engineering science. There are several aspects to ship seakeeping that make it one of the most challeng-ing problems in the marine hydrodynamics field. It has all the complexities of wave resistance or maneuvering problems with the addition of unsteadiness due to inci-dent waves. The ultimate goal, of course, is a unified the-ory of resistance, maneuvering, and seakeeping. Histori-caUy and for a variety of reasons, each of the fields have developed independentiy. At present, they are still sepa-rated and it will probably be twenty years before compu-tations are truly unified. Unfortunately, design problems wUl not wait and designers are constantly pushing for better computations. In this paper, we want to summa-rize the present state-of-the-art in seakeeping computa-tions and then point out major research issues that need to be addressed.
The major difficulties in seakeeping computations are the nonlinearities. There are nonhnearities associ-ated with the fluid in the form of viscosity and the ve-locity squared terms in the pressure equation. The free surface causes nonUnear behavior due to the nature of the free-surface boundary conditions and the nonUnear behavior of the incident waves. Finally, the body geom-etry often causes nonlinear hydrostatic restoring forces and nonlinear behavior at the body/free-surface intersec-tion line. The only good news is that because of forward speed ships tend to be long and slender with smooth vari-ations along their length. This geometric feature of typ-ical ships is the basis of many approximations that have allowed a significant amount of progress to date.
Recently, seakeeping computations for ships oper-ating in the Uttoral region have become of interest. Off-shore computations are often done in finite depth, but it is unusual for ships. Most theories and computations have been for infinitely deep water. Many theories could be extended to finite depth in a relatively straightforward manner. For example, replacing the deep water Green function with a finite depth Green function can extend
Computation of Nonlinear Turbulent Free
Surface Flows Using the Parallel Uncle Code
M . Beddhu, R. Panlcajakshan, M.-Y. Jiang, M . Remotigue, C. Sheng,
L. Taylor, W. Briley, D. Whitfield (Mississippi State University, U S A )
ABSTRACT
A numerical approach is presented in this work suitable for the computation of nonlinear fi-ee surface flows over complex geometries such as ship hulls in a fast, reliable and robust manner. The governing equa-tions solved are the incompressible Reynolds Averaged Navier-Stokes (RANS) equations coupled with the free surface kinematic condition and a two equation turbu-lence model. Simple no normal-gradient dynamic boundary conditions are used at the free surface. The governing equations are cast with respect to an unsteady (non-ineitial) general curvilinear coordinate system. The numerical approach uses the modified ailificial compressibility formulation. The governing equations are discretized using a finite volume approach where the numerical fluxes at cell interfaces are obtained using Roe's inviscid flux averages coupled with van Leer's MUSCL formulation for higher order flux extrapola-tion. Viscous fluxes are averaged using central differ-encing. Time is discretized implicitly using the first or-der Euler backward differencing. The resulting non-linear algebraic equations are solved using the dis-cretized Newton-relaxation (DNR) approach with sym-metrical Gauss-Seidel sweeps. To speed up the solution process a parallel implementation of the numerical al-gorithm that uses MPI for message passing is used. In or-der to accelerate the solution convergence process a multilevel approach coupled with the traditional multi-grid approach is taken. The resulting algorithm has been applied to various ship geometries and comparisons with the sequential code solutions and experimental re-sults are presented. The rere-sults show that the parallel version of the free surface UNCLE code accurately re-produces these earlier results.
INTRODUCTION
Nonlinear, turbulent free surface flows repre-sent an important class of problems with immediate na-val applications especially when such flows occur in the vicinity of a body. These problems are very challenging from a Computational Fluid Dynamical point of view in that they demand a very robust numerical algorithm, veiy large computational resources and very large amounts of computing time. More importantly, in
addi-tion to robustness, the CFD algorithm must model the correct physics. The original UNCLE ( for UNsteady Computation of fieLd Equations ) code (Taylor (1991), Whitfield and Taylor (1991)) was developed based on first principles to solve the unsteady Reynolds averaged Navier-Stokes (unRANS) equations without any fur-ther simplifying assumptions. This sequential version was further extended in (Beddhu et al (1994), (1999)) to include the effects of a free surface. In Beddhu et al (1999) the free surface governing equation was formu-lated in terms of surface cui-vilinear coordinates introduced on the actual evolving free surface for the first time. Previous efforts have introduced the surface cuivilinear coordinates on a flat surface. The formula-tion introduced in Beddhu et al (1999) allows for the computation of steep and breaking waves. The sequen-tial version of the free surface UNCLE code has been applied to various geometries with a good degree of suc-cess (see Beddhu et al (1999) and the references there-in). However, these computations took enormous com-puting time.
With the motivation of reducing the run-time of the sequential UNCLE code when applied for com-plex configurations, a parallel version of the UNCLE code without the free surface capability was developed by Pankajakshan and Briley (1996). It is designed to op-erate at coarse/medium grain parallelism levels for opti-mum performance and is based on Single Program Mul-tiple Data (SPMD) model. It uses MPI for message passing. This version represents one of the first parallel CFD codes that has been used for solving practical prob-lems in a routine manner. Numerous test cases were used to test the robustness and accuracy of the code (Pankajakshan (1997)). The effort presented in the pres-ent paper incorporates the free surface capability into the parallel version of the UNCLE code. This involved a complete re-write of the free surface code using FOR-TRAN-90 which is now included as a separate module in the parallel code.
The approach adopted to compute free surface flows is to cast the governing equations with respect to a non-inertial frame so that the free surface can always be made to coincide with a coordinate surface. Thus, Navier-Stokes equations are cast with respect to a set of general unsteady cuivilinear coordinates and are solved
Submarine manoeuvrability assessment using
Computational Fluid Dynamic tools
D. Bellevre, A . Diaz de Tuesta, P. Perdon
(Bassin d' Essais des Carènes, France)
A B S T R A C T
Thanks to the constant increase in computing power, it is now becoming possible to aim at more and more ambitious results in using Computational Fluid Dynamic. The object of this paper is the description of the implementation of a calculation tool, which should eventually contribute to the setting up of a quasi-exhaustive data bank of hydrodynamic coefficients of any submarine, for any maneuvers likely to be studied.
A mesh generation tool developed in order to facilitate the pre-processing stage of CFD calculation is presented. Then different cases of calculation performed are described, the results are compared to those obtained with towing tank model tests. The validity of each type of calculation is discussed, with an overview on the actual progress. A mathematical maneuverability model has been identified from the results obtained through calculation. Simulations performed with this model are compared to results obtained at sea.
I N T R O D U C T I O N
It is now possible to expect rapid results for a wide range of calculations. CFD (Computational Fluid Mechanic) is considered here as a "numerical towing tank", which allows to compare the results with model test data.
Although the direct simulations of maneuvers using an unsteady RANSE code is possible, it is very time consuming and the use of a mathematical model based on coefficients in a quasi steady approach is practically instantaneous and allows a very wide range of simulations in a short time.
In order to facilitate the pre-processing stage of CFD calculation, a mesh generation tool has been developed at Bassin d'essais des carènes. This tool automatically provides a 3D mesh when cinematic parameters (drift angle, angle of attack, rate of turn in horizontal/vertical plane) are given or when changes in the geometry of the submarine (L/D ratio, number, size or location of the appendages, shape of deck, . . . ) are proposed. This avoids the
long and laborious task which consists in re-mesh the submersible for any minor change in its geometry. Furthermore, using this tool the grid topology is identical from one case to another so that the numerical results are more reliable, at least for comparison purposes.
This study has been performed on an existing submarine for which model test results were available, and calculations have been done on the basis of usual captive model test: rudder effectiveness tests, oblique towing tests, and rotating arm test in both vertical and horizontal planes. The solver used was a commercially available Reynolds Average Navier-Stokes code (Newtonian homogeneous and incompressible fluid).
M E S H G E N E R A T I O N
The philosophy of the numeric tool used to conduct this study is based on a "modular" conception of the submarine, so that the shape, position, or even a detail in the mesh of each part of the ship can easily be changed, and re-incorporated into the mesh of the whole ship. The following paragraphs describe briefly the chronology of manipulations carried out to obtain this adaptable mesh.
Body and deck
The shapes of the deck and of the body of the submarine are obtained from a CAD file. At this stage, the number, size and repartition of the cells corresponding to those two parts of the submarine are set up.
Appendages
We mean by "appendages" the direction and dive rudders, and the sail. The geometric data necessary are, on the one hand, the general characteristics of the appendage (wingspread, chord, relative thickness), and on the other hand the files of Bezier poles defining the thickness laws at the base and in head of the appendage.
Ship Wake Detectability
in the Ocean Turbulent Environment
A. Benilov, G. Bang (Stevens Institute of Technology, USA)
A. Salray, I . Tkachenko (Institute of Oceanology, Russian Academy of Sciences, Russia)
ABSTRACT
The turbulent structure of ship wake and ocean upper layer is presented in this study. We discuss results of: 1) theory on the turbulent ship-wake and the ocean upper layer turbulence under surface waves effects including wave breaking - an analytical study; 2) based on k-e turbulent closure a couple 3-D non-steady numerical model (wake -i- upper layer) which includes the wave breaking; 3) experimental investigation (preliminary results) in the Davidson Laboratory towing tank on ship-wake detection by measuring turbulence in-situ.
The theoretical analysis of the ship-wake turbulence uses the shear-free model, self-modeling and Kolmogorov's hypothesis for the purpose of closure. The environmental turbulence in the ocean upper layer has been formulated by the assumption of horizontally uniform hydrodynamic field and k — £ group model under the existence of surface waves and its breaking. Based on k-e turbulent closure a couple 3-D non-steady numerical model (wake + upper layer) which includes the wave breaking, has been used, in the shear-free approach, to cany out numerically the ship-wake detectability in the ocean turbulent environment. Both of the analytical and numerical results show the 3-D structure of the ship wake for different wind conditions and ship speeds, and the detection range on the ocean surface and the detectability in depth of the ship wake in terms of ship parameters and the wind speed.
The experimental study is destined to verify the theoretical and numerical prediction on detectability of turbulent ship wake under different experimental conditions. The wake turbulence significantly exceeds the natural level of fluctuations in the tank and the vibration noise produced by the towing system. The wake turbulent spectrums have well expressed Kolomogov's range. The ship-wake turbulence is well detectable and Kolmogorov's range can be identified even for the most remote
location of the probe (~ 10 L^ , L j is the ship length) as well under the random surface wave condition.
1. INTRODUCTION
1.1. Ship Wake. The physical mechanism of ship
wake in the ocean is a result of the turbulence generated by moving ship. The turbulent diffusion defines the region of the turbulent wake that is spreading in time. Naudascher (1965) studied the wake of self-propelled bodies. He found that the wake width has a power law behavior. Field measurements for ship wakes have been made by Milgram et al. (1993) and they found the wake width has a power law of A'"^ behavior where X is a distance from the ship. Hoekstra & Ligtelijn (1991) measured the maximum value of turbulence intensity in each cross-section of the wake of a 5m long ship model. The result shows that the turbulent kinetic
—4/5
energy has a X asymptotic behavior. The result of measurements done by Milgram et al.(1993). Hoekstra & Ligtelijn (1991) agree with the text books written by Birkhoff & Zarantonello (1957, chapter 14), and Tennekes & Lumley (1990, chapter 4). Dommermuth et al (1996) performed numerical large-eddy simulations on turbulent fi-ee-surface flows. They obtained probability distributions of velocity field in the wake and compared the results with experimental measurements.
Another aspect of ship wake detection is the surface nonuniformity of surfactants. The physical mechanism allowing the detection of ship-wake on the ocean surface is a result of the diffusion of the surface-active substance in the turbulent region of the wake (Peltzer et al. 1991, Benilov 1994, 1997, Zilman and Miloh 1996). The turbulent diffusion forms the surface nonuniformities ofthis substance as well as the associated nonuniformities of the surface tension, which effectively suppress the centimeter band of surface waves that is responsible for the radar
Investigation of Global and Local Flow Details
by a Fully Three-dimensional Seakeeping M e t h o d
V . Bertram (HSVA, Germany)
H . Yasukawa (Mitsubishi Heavy Industries, Japan)
A b s t r a c t
A fully-three-dimensional Rankine panel method in the frequency domain is validated for local pressures, motions, and added resistance. Previous formulae for added resistance contained errors result-ing in large differences to experiments. This has now been remedied. The method is linearized with respect to wave height. The steady flow contribution is cap-tured completely by solving the fully nonlinear wave-resistance problem first and linearizing the seakeep-ing problem around this solution. The same grids on the hull are taken for both steady and seakeeping computation. On the free surface different grids are used, either following quasi-streamlined grids or rect-angular grids with cut-outs for the hull. The results from the steady solution are interpolated on the new free-surface grid. The method is applied to various test cases. Motions are in good agreement with ex-periments, but this is also the case for strip method results. Local pressures, especially for shorter waves, are much better predicted tlian by strip method. The added resistance is sensitive to higher derivatives of the potential and a numerical differentiation of these terms may be preferable to using higher-order panels. 1. I n t r o d u c t i o n
The most commonly used tools to determine seakeeping properties are based on strip theory. The strip method approach is cheap, fast, and for most cases also quite accurate. However, strip methods do not perform so well for high-speed ships, full hull-forms (tankers), ships with strong ffare, and generally for low encounter frequencies which typically occur in following seas. They are also questionable with regard to local pressures which are needed as input for finite-element analyses.
Approaches to improve predictions of sea-keeping properties should capture:
- 3-D effects of the flow
3-D efi'ects are important for low encounter frequencies and full hull forms. 3-D diffraction at the bow region of tankers contributes con-siderably to added resistance, [1].
- Forward-speed effects
Strip methods include forward speed by the change in encounter frequency. But forward speed enters the ship motion problem in ad-ditional ways: the local steady flow field, the steady wave pattern of the ship, and the change of the hull form and wetted surface due to scjuat (dynamic sinkage and trim).
We will present here a 3-d Rankine singularity method (RSM) which captures all forward-speed ef-fects. The method is 'fully three-dimensional', i.e. both steady and unsteady flow contributions are cap-tured three-dimensionally. For a recent survey of Rankine singularity methods for forward-speed sea-keeping, we refer to [1], [2].
2. T h e o r y
2 . 1 . P h y s i c a l m o d e l
We consider a ship moving with mean speed
U in a harmonic wave of small amplitude h. We
assume an ideal flow. Then the fundamental field equation is Laplace's equation. I n addition, bound-ary conditions are postulated:
1. No water flows through the ship's surface. 2. A t the trailing edge of the ship, the pressures
are equal on both sides. (Kutta condition) 3. No water flows through the free surface.
Hydrofoil Turbulent Boundary Layer Separation
at High Reynolds Numbers
D. Bourgoyne, S. Ceccio, D. Dowling (University of Michigan, USA)
W. Brewer, S. Jessup, J. Park (Naval Surface Warfare Center, Carderock Division, USA)
R. Pankajakshan (Mississippi State University, USA)
A B S T R A C T
One ofthe main hydroacoustic noise sources fi'om fully submerged lifting surfaces is the unsteady separated turbulent flow near the surface's trailing edge that produces pressure fluctuations on the surface and unsteady oscillatory flow in the near wake. However, the turbulent flow characteristics near boundary layer separation are largely undocumented at the high Reynolds numbers typical of many hydrodynamic applications. This paper describes results from the first phase of an experimental effort to identify and measure the dominant flow features near the trailing edge of a hydrofoil at chord-based Reynolds numbers approaching l O l The experiments are conducted at the US Navy's Large Cavitation Channel with a two-dimensional test-section-spanning hydrofoil (2.1 m chord, 3.0 m span) at flow speeds from 0.5 to 18 m/s. The foil section is a modified NACA 16 with a flat pressure side and an anti-singing trailing edge. The results presented here cover the first phase of experiments and emphasize LDV-measured mean flow velocities and turbulence statistics from the separating boundaiy layer flows near the hydrofoil's trailing edge at Reynolds numbers from 6 to 60 million.
I N T R O D U C T I O N
The flow at the trailing edge of lifting surfaces has received considerable attention and has been investigated by many researchers. Designers of ship propulsors and control surfaces have examined flows over two-dimensional hydrofoils and airfoils in order to understand how modiflcation of the trailing edge geometiy influences the production of lift and drag as well as the creation of flow generated noise. (Blake 1986). Similarly, researchers have attempted to compute both the flow field and the noise it generates (Wang et al. 1996, Arabshahi et al. 1999).
' Currently at Mississippi State University
Unfortunately highly controlled test data at operational scales is essentially non-existent. Thus, sea trials of actual hardware have been the only means of validating scaling laws or computational models of propeller performance. Many important flow phenomena are Reynolds number dependent between model and flill scale. Controlled tests over a wide range of Reynolds numbers can result in improved scaling rules.
An example of a Reynolds number dependant flow is that over the trailing edge of a hydrofoil. Interestingly, relatively small modifications to the trailing edge geometiy can lead to substantial changes in the hydrodynamic and hydroacoustic performance of a hydrofoil (Blake 1986). The application of a chamfer or knuckle to the trailing edge of the hydrofoil can increase the transverse thickness of the wake and consequently modify the shedding of large-scale vorticity from the trailing edge. This, in turn, can substantially change the magnitude and spectrum of the acoustic energy generated near the trailing edge. The trailing edge flow near the hydrofoil is strongly related to the wall-bounded shear flows on the suction and pressure sides. These boundaiy layer flows separate and ultimately combine together to form the wake. The complexity of turbulent boundary layer separation -on either flat or curved surfaces - is substantial (Simpson 1989). Thus, signiflcant changes in Reynolds number may lead to flindamental modification of the trailing-edge boundaiy layers (especially on the suction side of the foil) and near-wake flow.
Typical wind and water tunnel tests of hydrofoils can achieve chord-based Reynolds numbers of up to lO'' or so. However, fiiU scale Reynolds numbers achieved on the lifting surfaces associated with naval vessels easily exceed lO'. Consequently, examination of these flows is desirable at the highest Reynolds number that can be achieved
Modeling 3D unsteady sheet cavities using
a coupled UnRANS-BEM code
by
Georges L. Chahine and Chao-Tsung Hsiao D Y N A F L O W , I N C .
7210 Pindell School Road Fulton, MD 20759 e-mail: info@dynaflow-inc.com
http://ww\v.dynaflow-inc.com
ABSTRACT
The flow field of a propeller blade subjected to sheet and cloud cavitation includes several complex and strongly interacting features: flow separation, turbulence, presence of vortical structures, deforming and moving free surfaces, free surface instability, and cavity break-up. To best describe this flow field we are developing a numerical scheme combining a viscous Navier Stokes code (UnRANS) and a potential code (BEM) combining the capabilities of each model to address portions of the problem and to achieve a description level that is not possible with each of the methods alone. The UnRANS code is used to describe the turbulent viscous flow around the blade, while the BEM code is used to describe the non-linear cavity fi-ee surface deformations.
In this paper we apply the developed method to study sheet cavitation dynamics on a straight and a twisted elliptical hydrofoil. We show the results obtained and discuss issues and future development efforts. Cases presented consider the influence of the cavitation number, the incidence angle, the oscillation of the foil, and the Reynolds number on the results. Also the influence on the cavity dynamics of a perturbation in the inflow field, such as in a wake is considered.
INTRODUCTION
The periodic shedding fi-om a sheet cavity of a bubble cloud and its subsequent convection downstream followed by collapse leads to deleterious effects such as noise, erosion and vibrations which can strongly affect the expected performance of marine propellers (Bark & van Berlekom, 1978, Shen & Peterson, 1978, Brennen, 1994). Even though, this phenomenon have been observed and documented for many years, the processes by which cloud cavitation inception occurs have not been elucidated. Numerical modeling of the phenomenon remains one of the fi'ontier problems. The flow involves several complex
features — transition zones, turbulence, presence of vortical structures; deforming and moving fi-ee surfaces; fi-ee surface instability and break-up; detachment and fiow of a bubbly medium. The lack of fundamental knowledge of the basic physics at play in the problem has made simulations using conventional assumptions questionable until these assumptions have been confronted.
At this time several numerical methods have been developed. The more recent involve non-linear three-dimensional modeling of partially cavitation (Kinnas et al 1993, 1999, Pellone et al 1998, Dan and Kuiper 1999 a,b. Lange, 1996). Other approaches such as by Kubota et al. (1989) and Reboud & Delannoy (1994) consider a two-phase flow or a level set model to describe the periodic cloud shedding. Some experimental studies were also conducted to understand the mechanism of unsteady attached cavitation (Franc & Michel 1988, Tassin Leger et al 1998 a,b, Katz et al 1999). The dynamics of bubble clouds was studied among others by Brennen et al (1994), Wang and Brennen (1999), Chahine et al (1983,1992). We considered a potential flow and computed by a three-dimensional boundary element method (BEM), which efficiently and accurately describes moving boundary flows (Brebbia et al 1989, Becker 1992) the bubble dynamics. The advantages of the BEM lie in the economy of unknowns only sought on the discretized liquid domain boundaries, and in its accuracy in handling boundary deformation. Moreover the movement of the boundary is easily followed in a Lagrangian fashion using the local velocity.
In order to study sheet cavitation instability and cloud inception, we couple the BEM and the UnRANS to use the best features of each of these approaches. More particularly we modified and coupled the UnRANS code, UNCLE, developed by Mississippi State University (MSU) with
DYNAFLOW'S Boundary Element Method code, 3DYNAFS. UNCLE is used to accurately describe the basic physics ofthe viscous flow around the propeller
New Green-Function M e t h o d
to Predict Wave-Induced Ship Motions and Loads
X-B Chen, L. Diebold (Bureau Veritas - D T A , France)
Y . Doutreleau (Bassin d'Essais des Carènes, France)
A B S T R A C T
A three-dimensional numerical method based on the new Green function given in Chen (1999) and the higher-order description of ship hull by bi-quadratic patches has been developed in order to predict wave-induced ship motions and loads. The development of this new method and its validations through a com-prehensive comparison with semi-analytical solutions and results of experimental measm-ements, are de-scribed in the paper.
Recent work on the ship-motion Green function in both analytical and numerical aspects provides an acctrrate and efficient way to evaluate the influence coefRcieiits involved in integral equations. Tlie use of bi-ciuadratic patches gives a precise representation of the ship geometry and a continuous representation of the velocity potential over the ship hull. Furthermore, application of the Galerkin procedure yields a square-matrix system and improves the accuracy of solutions. The excellent level of agreement with known semi-analytical solutions and experimental measurements shows that the present numerical method is reliable and practical in a number of applications.
I N T R O D U C T I O N
Very important in practice, notably for design, several 3D panel methods making use of the Green function, which satisfies the linearized free-surface boundary condition corresponding to time-harmonic flows ob-served from a translating system of coordinates, have been developed in recent decades for computing wave-induced ship motions and loads. However, the fairly small number of panels used in these methods and the large discrepancies observed among numerical predic-tions indicate the formidable numerical burdens. In fact, the substantial difficulties associated with the numerical evaluation of the Green function and its gradient, and their subsequent integrations over ship-hull panels and waterline-segments, have been a
ma-jor stumbling block hindering the development of re-liable and practical methods. These difficulties have been addressed in various ways in the numerical solu-tion procedures developed by Chang (1977), Inglis &
Price (1981), Guével & Bougis (1982), Wu & Eatock Taylor (1989) and Iwashita & Ohkusu (1992), and in
the development of methods for computing the ship-motion Green function by Hoff (1990), Jankowski (1990), Bougis & Coudray (1991) and Ba & Guilbaud (1995), and very recently confirmed by the work in
Chen (2000). I t is shown formally in this work by an
asymptotic analysis that the source potential is singu-lar and highly-oscillatory for a field point approaching the track of the som-ce at the free surface.
To circumvent the above-mentioned difficiflties encountered i n previous studies, a new numerical method, based on the recent results in both theo-retical and numerical aspects of ship-motion Green functions and the higher-order description of ship-hull geometry and fluid kinematics, has been devel-oped. The newly-obtained important results for ship-motion Green functions given by Chen (1999) include several imiovative featiues. First, new formulations of the fi-ee-surface component are developed based on the basic decomposition of the double Fourier inte-gral obtained by Noblesse & Chen (1995) and new expressions of the wavenumber integrals. The resul-tant wave and local components are both expressed by simple integrals. The asymptotic analysis of the wave component gives analytical expressions of far-field ship waves and reveals their direct relationship with the dispersion relation. The singular and highly-oscillatory properties of potential flows generated by a source located at the free surface are analyzed and expressed in a closed form. Analysis of the line in-tegrals on the free surface shows that they can be evaluated in an analytical way. Furthermore, efficient numerical developments have been realized to evalu-ate ship-motion Green functions in all configurations accurately including the most critical case for which
Prediction of Nonlinear Motions of High-speed Vessels
in Oblique Waves
F-C Chiu,' Y - H Lin,' C-C Fang,^ S-K Chou^
('National Taiwan University, ^United Ship Design and
Development Center, Taiwan)
A B S T R A C T
A practical method, based on a nonlinear strip synthesis scheme, to calculate the nonlinear motions of a high-speed vessel in oblique waves is presented in this paper. In this method, the equations of motions are described by the body-fixed coordinate, rather than the conventionally used ship-carried vertical coordinate. Moreover, the time-vaiying submerged hull surface and the coupling effect between transverse and vertical motions are considered. By using the momentum theory, the flare impact and dynamic lift are also taken into account. In the time domain simulation, to prevent the numerical divergence due to the drift of sway and/or yaw motions, artificial springs in sway and yaw modes are introduced.
In order to clarify the validity of the proposed predicrion method, a series of seakeeping tests in oblique waves have been carried out in SSPA with a model of 90-meter patrol vessel, which is designed by USDDC (United Ship Design & Development Center, Taiwan). The experimental results are compared with the calculation by the present method and some of the selected results of comparison study are shown in this paper. As a practical tool for predicting the nonlinear motions of high-speed vessels in oblique waves, the validity of the present method is verified.
I N T R O D U C T I O N
In this two decades, the expanding demand of large-sized high-speed ocean-going vessels urged the necessity of developing analytic tools to evaluate their nonlinear behavior in rough sea. Up to the present, several more sophisticated methods have been proposed to predict nonlinear motions and wave loads of a ship at foiward speed in head sea. For example, a three-dimensional Rankine Panel Method (Kring et al 1996) and a three-dimensional transient free-surface Green function source distribution method (Lin & Yue
1990) have proven to be sufficiently useful. On the other hand, a practical technique basing on a nonlinear strip synthesis (Chiu & Fujino 1989; Chou, Chiu & Lee 1990) has also proven to be accurate enough for practical use.
Several years ago, one of the authors Chiu and Liaw (1993), following the same nonlinear strip synthesis scheme, developed a practical method for predicting the nonlinear motions of a high-speed vessel in oblique waves. Based on the numerical investigation, an existing 60-feet planing boat had been shown its fundamental characteristics of vertical and transverse motions in bow/beam sea. In this method, the equations of motions are described by the body-fixed coordinate, rather than the conventionally used ship-carried vertical frame. Moreover, the time-vaiying submerged hull surface and the coupling effect between transverse and vertical motions are considered. Besides, using the momentum theory, the flare impact and dynamic lift are also taken into account. However, in the time domain simulation, artificial springs in sway and yaw modes are introduced to prevent the numerical divergence due to the drift of sway and/or yaw motions.
In this paper, the dynamic responses of a 90-meter high-speed patrol vessel RD-200, which is designed by USDDC, travelling in oblique waves are predicted by the present method and compared with the result of experiments earned out by Lundgi-en (1997) at SSPA, in order to confirm the validity of the present method. The detailed formulation of the present method was fully described in Chiu & Liaw (1993). For convenience sake, however, the basic concept of the method will be described briefly.
T H E O R E T I C A L F O R M U L A T I O N
Coordinate System
The right hand Cartesian coordinate systems and sign convention used for following theoretical formulation are shown in Figure 1.
A n Unsteady Three-Dimensional Euler Solver Coupled
w i t h a Cavitating Propeller Analysis M e t h o d
J.-K. Choi, S. Kinnas (The University of Texas at Austin, U.S.A.)
A B S T R A C T
A fully three-dimensional unsteady Euler solver, based on a finite volume scheme and the pressure correction method, is developed and applied to the prediction of the effective wake for propellers sub-ject to non-axisymmetric inflows. The propeller is modeled via unsteady body force terms in the Euler eciuations. First, the Euler solver is validated against the analytical solution of actuator disk theory, and the solution in the case of uniform inflow. Then, the unsteady effective wake is predicted for a three-cycle axial inflow wake, and it is found that the unsteadi-ness in the effective wake is small in this case. Finally, the predicted cavity shape and the unsteady velocity field arc compared with the experimental data mea-sured in cavitating propeller experiments which have been performed at the M I T water tunnel.
1 I N T R O D U C T I O N
The effective wake is a very crucial issue during the design and assessment of propeller performance, es-pecialty in the presence of blade cavitation, because it is well known that the predicted cavity extent and volume, as well as the magnitude of the predicted pressure pulses depend strongly on the estimated ef-fective wake inflow.
There has been experimental (Huang et al 1976, Huang & Cox 1977) and theoretical work (Huang & Groves 1980, Shih 1988) for the prediction of the ef-fective wake by employing steadj^ axisymmetric Eu-ler ecpiations. Later, effective wake prediction meth-ods using Reynolds Averaged Navier-Stokes(RANS) equations were developed (Stern et al 1988b, Stern et al 1988a, Kerwin et al 1994, Kerwin et al 1997) for axisymmetric flow applications and (Stern et al 1994) for non-axisymmetric applications. In the above methods, the propeller is represented bj' the body force term in RANS equations. The method using the body force to represent the blades was also used in turbomachinery applications (Damle et al 1997), where the body force was determined by iteratively adjusting it until the velocity tangency condition on the rotor and stator blades was satisfied. A different
approach which does not need the propeller poten-tial solution is to solve the RANS equations directly with the no-slip boundary condition on the propeller blade surface. (Chen et al 1994, Stanier 1998)
In a first effort toward the better prediction of the effective wake harmonics, the authors have al-ready developed a steady three-dimensional Euler solver and successfully applied it to predict the steady non-axisymmetric effective wake for given propeller geometry and inflow nominal wake (Choi & Kinnas 1998a, Kinnas et al 1999). I n that method, the pro-peller effect, which appears through the body force terms in the Euler equations, is averaged with time. Nevertheless, the propeller loading is allowed to vary in space with strength which depends on the loading at each blade angle.
In the present work, a fully three-dimensional unsteady Euler solver, based on a finite volume ap-proach and the pressure correction method, is de-veloped and applied to the prediction of the un-steady effective wake for propellers subject to non-axisymmetric inflows. The proposed unsteady anal-ysis, which is the unstead)^ extension of our previous work (Choi & Kinnas 1998a), captures the truly un-steady behavior ofthe interaction between the vortic-ity in the inflow and the propeller action by adopting the body force distribution which varies in both space and time.
2 P R E S E N T M E T H O D
The unsteady flow field around a propeller can be de-composed into two parts; one rotational and one ir-rotational field. In the present method, the propeller
induced velocity field, qp, is the irrotational velocity
field. The propeller induced velocity, qp, can be ex-pressed in terms ofthe perturbation potential, 4>p, by the following relation.
ilp{x,t)^VMS,t) (1)
The propeller vortex lattice method (VLM), named MPUF-3A, is used to solve for the perturbation po-tential on the propeller as shown on the left side of Figure 1 (Kinnas et al 1998, Kinnas et al 1999).
Analysis of Turbulence Free-Surface Flow around Hulls
in Shallow Water Channel by a Level-set Method
H. H . Chun, I . R. Park, S. K. Lee (Pusan National University, Korea)
ABSTRACT
In the present study on turbulence free surface problems in shallow water channel, two fluids Reynods averaged Navier-Stokes equations are solved by using a Finite Volume Method, where SIMPLEC algorithm is used for velocity and pressure coupling, and standard
k-e turbulence model is introduced for modeling
Reynolds stresses. A Level-set method is used for capturing the free-surface movement and the influence of the turbulence layer of the free surface is implicitly considered. For the validation of the present numerical scheme, the numerical results for Wigley and Series 60 Cj=0.6 ships in deep water are compared with the experimental results. Computations are made for various depth Froude numbers for the calculations of the shallow water channel flow. In the numerical results, the present solutions show good agreements with the experimental results for the deep water case, and for the case of the shallow water solutions with the viscous effect, present numerical results show reasonable physical phenomena. In addition, it is demonstrated that the level-set method can treat the free surface flows around hulls with a reasonable accuracy together with a simple numerical procedure.
INTRODUCTION
Shallow-water channel flow near the critical depth Froude number i^;, (= ?7 / . ^ g ^ ) = 1 is an unsteady, nonlinear phenomenon and has peculiar flow characteristics, where h is water depth, U is the ship speed and g is the gravitational acceleration. At this critical speed, a ship generates two-dimensional waves propagating in front of the ship, which are faster than the ship speed and show the unsteady flow pattems. These waves are named solitons or solitai-y waves. The influences of the channel wall and shallow water cause the increase of the resistance and sinkage of the ship at near the critical speed.
In the experimental investigations. Thews and Landweber (1935), Helm (1940), Graff et al (1964) and Ertekin (1984) observed these unsteady and nonlinear waves in shallow water towing tanks. Especially,
Ertekin (1984) carried out a series of experiments in which certain parameters such as water depth, ship draft and channel width were changed.
For the inviscid flow problems, Bai and Kim (1989) used a Finite Element Method for solving a nonlinear free-surface flow for a ship moving in restricted shallow water tank. In case of the numerical works, Choi and Mel (1989) used Kadomtsev-Petviashivili equations and Ertekin & Qian (1989) and Jiang (1998) used Boussinesq equations for solving the nonlinear shallow water waves. Kim and Lee (1996) investigated these phenomena based on Euler equations.
For the viscous solutions in shallow water channel, Bertram and Ishikawa (1997) used the hybrid approach computing first squat and potential flow with fi-ee-surface calculation and then the viscous flow without free-surface effect at the subcritical depth Froude number. In their numerical results, the pressure on the channel bottom and hull surface are compared with experimental results, where it is explained that the discrepancies are caused by disregard of the defoi-mation of the free-surface.
In the present work, the viscous and free-surface effects are considered in the calculation of the shallow water channel flow at the critical and super-critical depth Froude number speeds. For the analysis of turbulence flow, two fluids Reynols averaged Navier-Stokes equations are solved by using a Finite Volume Method, where standard k—E turbulence model is used for modeling Reynolds stresses.
For the free surface treatment, two main approaches (front tracking & front capturing methods) have been used. In front capturing methods, the level-set scheme has been only recently used in free surface problems (Vogt 1998, Dommermuth et al. 1998, Bet et al. 1998 and Park & Chun 1999 (a), (b)). The level-set method is a numerical technique which can follow the evolution of interfaces. These interfaces can develop shaip corners, break apart, and merge together. The level-set method has a wide range of applications, including problems in fluid mechanics, combustion, manufacturing of computer chips, computer animation, image processing, structure of snowflakes, and the shape of soap bubbles. Especially for many complex free surface problems (e.g. breaking wave, spray
Control of the Turbulent Wake of an
Appended Streamlined Body
S. Cordier, L. Descotte (Bassin d'Essais des Carènes, France)
A B S T R A C T
Propulsor tests at model scale behind a ship model are faced with the problem that Reynolds number similarity cannot be met, even i f large test facilities are used.
In the work presented we are specifically concerned with the fiow similarity over the after pai1 of the hull with and without appendages. This issue concerns the mean flow into the propulsor (wake fi-action) and the powering characteristics such as shaft speed, thmst and power. When cavitation or hydroacoustic studies are concerned, it also becomes important to simulate the three dimensional distribution of velocities, and perhaps the turbulent flow properties in the propeller plane. Several means of altering the flow over the hull in order to simulate Reynolds number similarity have been studied and tested in different laboratories. Boundaiy layer blowing has been selected and implemented on a model tested in the GTH.
The design of this set up is briefly described. Results of LDV measurements are presented which show how the blowing system modifies the distribution of velocities in a veiy effective manner. The characteristics of the wakes generated are analyzed (wake fraction, haimonic content) in particular with respect to the effect of appendages. A method for analyzing LDV measurements in order to estimate the turbulence in the flow is outlined and applied to the measurements performed on the after-body. Finally, the effect of the changes in wake on the steady and unsteady performances of a propeller are presented.
I N T R O D U C T I O N
Tests conducted at model scale in naval hydrodynamics are confi-onted with the problem of Reynolds number similarity which cannot be met, even i f large test facilities are used. This similarity problem requires the use of extrapolation methods adapted to the diflferent flows : ship resistance and propulsion, flows on lifting surfaces and propellers, separated flows, sheet or bubble cavitation, vortex cavitation, etc... The variety of difficulties which arise fi-om the differences in Re is veiy challenging to the experimental hydrodynamicist. These issues are not easily solved by CFD either because of the large Re involved (10^ to 10') which create numerical problems and the infiuence of transition which is not modeled by RANSE codes. Finally, although one can imagine that flill scale measurements are the answer to these issues, the economical cost and technical complexity of performing scientific quality full scale velocity measurements on a ship have so far reduced these instances to a very limited number with vaiying degrees of success (extent, number of components, accuracy).
We focus our attention in this paper on the flow around the hull and more precisely in the propeller disk. Indeed, the velocity field in this plane determines the volumetric flow rate in the propulsor disk (wake fi-action) and the powering characteristics such as rate of turn of the propulsor, thiust, and power. When cavitation or noise is the purpose of the tests, then it is important to simulate the 3D dimensional mean flow field and in some instances the turbulence levels in the wake.
Unsteady Flow Quantities on Two-Dimensional Foils :
Experimental and Numerical Results
p. Creismeas, L. Ivlerle, O. Perelman, L. Brian9on-Marjollet
(Bassin d' Essais des Carènes, France)
ABSTRACT
This paper presents the validation of a new numerical tool, based on LES method and applied by Bassin d'essais des carènes. This tool is applied to calculate flows on two-dimensional foils at several angles of attack. It provides the knowledge of non-stationaiy quantities for non cavitating flow. The validation is conducted by comparison with experimental results obtained at high Reynolds number in the G.T.H. for non-cavitating and cavitating flows.
NOMENCLATURE Cp : pressure coefficient; Cp a : cavitation parameter; (7
P-?ref
1pVref
Vref-Pv
1pVref^
Pref: reference value for pressure Pv : vapor pressureVref: reference value for flow velocity p : volumic mass of water
a : flow angle of attack
INTRODUCTION
The prediction of noise radiated by a propeller is still vei-y complicated at the design stage. It requires advanced numerical tools which need to be validated. Bassin d'essais des carènes has been active in the development and validation of new tools which can provide the knowledge of flow fluctuating quantities and more particularly of structures which generate pressure fluctuations on the blades. The next step will be the calculation of the noise radiated by the blades when turbulent excitations act on it.
This paper presents the numerical method which relies on Large Eddy Simulation (LES). For validation purpose, we also describe briefly the experimental set-up which allows us to measure non-stationary quantities. The comparison between
experimental and numerical results takes a large place in this paper. As a conclusion illustrations of Reynolds number effects on cavitation pattern will be presented in order to emphasise their importance and the necessity to have a very precise description of the flow and of its turbulent structures.
NUMERICAL SIMULATION
To our knowledge, veiy little work had been published with comparisons between experiments and numerical results in hydrodynamic field (showing pressure fluctuations spectra calculated by LES method). Jordan (Jordan 1996) did calculation for laminar flow with Reynolds number equal to 25000. Moreover, empirical models for parietal pressure fluctuations in an accelerated or decelerated flow do not give accurate results. So, up to now, we do not have numerical tool capable to optimise the blade sections with respect to hydrodynamic excitation.
LES is a method which calculates flow scales selected by mean of a filter , G. This one is convoluted to the flow variables which scales are filtered or are
macroscopic. Let f(x,t) be the generic name of flow
variables (velocity, pressure, etc..) we can write:
f ( x , t ) = nx,t) + f'{x,t) (1)
^ J *• /
compulation mod elisatiou def
f { x , t ) = r f { y , t ) G { x - y ) d y (2)
f(x,t) is the fijfl and correct solution. f(x,t) contains the information which is lost through filtering and is called residual or subgrid scale. By using eq(2 ), it is possible to perfomi a global filtering of the incompressible Navier-Stokes equations,
dill
dx'du'
= 0 ( 3 )dt
du[
dx'
1dp
d'u'
p dx' dx'dx'
(4)Propulsor Design Using Clebsch Formulation
C. Dai, R. Miller (Naval Surface Warfare Center, Carderock Division, USA),
M . Zengeneh, C. Yiu (University College London, United Kingdom)
A B S T R A C TA three dimensional inverse design method is presented for the design of marine propulsors. This method makes use of the Clebsch representation of the rotational part of the velocity field for modeling both the bound vorticity of blade surfaces and the free stream vorticity. The blade shape is determined by imposing the flow tangency condition for a given loading specification. This technique is demonstrated here for the design of a ducted pod propulsor operating in a uniform stream and a ducted propulsor mounted on the tail of an axisymmetric body operating in a shear onset flow. For the case of ducted propulsor design, both mixed and axial flow configurations are presented to demonstrate the use of mixed flow concept for cavitation performance improvement.
I N T R O D U C T I O N
The problem of propulsor design has aroused considerable theoretical interest for over half a century. For example, the lifting line [1] and lifting surface theories [2], [3] have advanced to a stage that they are routinely used in propulsor design in the last three decades. Particularly, in the area of open screw propeller design, the classical approach of lifting line and lifting surface in conjunction with the notions of thrust deduction and wake fraction has been proven to be a very reliable approach to the propulsor design problem. Recently, there has been a strong interest in the internal or ducted types of propulsor. The internal type of propulsor is mainly referred to as a waterjet propulsor. Both waterjet and ducted types of propulsors were conceived and developed in the latter part of 19"^ century. The resurgence of interest in the internal and ducted propulsors is mainly due to the fact that there is better understanding of both physical phenomena and design issues related to those types of propulsors. For example, the hull and propulsor interaction can contribute positively to the waterjet
hydrodynamic performance [4]. The ducted propulsor has long been recognized for its ability to improve cavitation performance and sustain higher loading near the tip region. Historically, the ducted propulsor design is based on the principle of potential flow [5]. In the last decade, efforts have been made to couple Euler or Navier-Stokes solver with a lifting surface code for the ducted propulsor designs [6], [7] and [8]. The procedure has been used very successfully in the situation, which involves simple throughflow geometry, or the onset shear Is weak. Another approach that has been taken In the last 3 decades in the design of internal or ducted propulsors is the use of streamline curvature methods for throughflow analysis and a semi-empirical method of meanline design for blades [9]. Despite the fact that the streamline curvature method can handle the throughflow with the blading effect more efficiently than the Euler/lifting surface approach, the blading design is relatively weak and it has to rely on experience and the experimental database.
With increased demand for high performance propulsor, a design method, based on a high order physical model, which can account for multiple stages, shear flow and fully three-dimensional effect, is needed. An inverse design method based on the idea of Clebsch
decomposition ofthe velocity field has been successfully developed in [10] for uniform flow and vortex free loading conditions. Subsequently, the method has been applied successfully to
turbomachinery designs [11]. It has also been used to demonstrate its potential for ducted propulsor design [12], [13]. The work to further develop the inverse design method as part of code enhancement and verification processes is described in this paper. Several improvements and new design capabilities were incorporated in the existing code so it can be more effectively used for propulsor design. The new features include addition of three dimensional boundary layer calculations, arbitrary blade planform layout for accommodation of rake and skew, and a new
A Design Tool for High Speed Ferries Washes
D. Aelbrecht' J.-C. Dem ^'^ Y . Doutreleau*
(^EDF - Laboratoire National d'Hydraulique et Environnement, ^Consultant,
Océa^ide BGO/FIRST, "DGA-Bassin d'Essais des Carènes, France)
A B S T R A C T
The high waves generated by fast ferries may have detrimental effects when approaching the coast.
The aim of this study is to determine the characteristics of ship wash or groups of high-speed ship waves in coastal and shallow water regions. The purpose of the method developed herein is to provide a tool for authorities as regards speed limits and routes for fast ferries approaching the coasts.
The waves generated by high-speed ships are represented by their free wave spectrum. This spectrum is determined digitally using a wave resistance program (POTFLO) based on the Neumann Kelvin model.
It is assumed that the free waves propagate in the same manner as a short crested sea, defmed by a directional energy spectrum. This energy spectrum is expressed explicitly in terms of the free wave spectrum.
Spatial wave propagation is then modeled over time using a third-generation spectral wave model named TOMAWAC, based on a fmite element technique. Evolution over time is depicted at certain critical positions along the shore. Resuhs are given in terms of significant wave heights and mean wave periods for different ship routes and speeds.
INTRODUCTION
In recent years, numerous papers have been published on fast ship wash (Danish M.A. 1997, Henrik Kofoed et al 1996, Kirkegaard et al 1998, Stumbo et al 1999). The term "ship wash" (or "wake wash") refers to the arrival on the coast of waves created by fast ships travelling offshore.
I f the ship is travelling at high speed, the amplitude of the waves arriving on the coast may be high.
These high waves are potentially dangerous in that they provoke unacceptable motions and reduced stability for small vessels and ships in coastal waters, plus unacceptable wave agitation and risks for swimmers and other users along the coast and on beaches.
This paper describes a simulation method developed as a tool for maritime safety authorities and
shipyards involved in the design and building of high-speed ships.
Recent simulation results are presented for the case of a standard high-speed ferry referred to as " N r f (navire rapide type), approaching the Port of Nice from Corsica.
The characteristics of the Nrt are as follows: length at wateriine = 87 metres displaced volume V = 1200 m ' length / width ratio equal to 5.7 length / draft ratio equal to 36
max. speed ii^ = 37 noeiids i.e. a Froude
number F = //Q ƒ ^ g L p p = 0.65 corresponding to a hydrodynamically fast ship
the Froude number based on the displaced
. . Vl = Unl^gy"is equal to 1.865, 1/3 . V = " 0 /
hence categorizing this ship as a fast ship according to IMO regulations (safety code -chapter 10 of SOLAS). According to this rule, adopted by Bureau Veritas in the framework of its regulations concerning high-speed ships, a ship is considered to be fast i f Fy > 1.181.
SHIP WAVE F I E L D AND AMPLITUDE S P E C T R U M
Ships travelling at a constant speed in calm waters generate a complex wave system (referred to as "ship wave field") moving at the same speed as the ship itself and therefore appearing as immobile to observers on board the ship.
Using a fixed point, the wash can be modeled in the form of superimposed plane waves (Newman
1977):
f(nO=I \A{li,e)e ~i [kXcose+k.Y.s\ne-ca l] kdkde (1)
within a Cartesian coordinate system QXYZ whereby: Z = 0 signifies undisturbed water,
