The Specialist Committee on Cavitation Induced Pressures

Transcription

1 23rd International Proceedings of the 23rd ITTC Volume II 417 The Specialist Committee on Cavitation Induced Pressures Final Report and Recommendations to the 23rd ITTC 1. MEMBERSHIP AND MEETINGS 1.1. Members The membership of the Specialist Committee on Cavitation Induced Pressure Fluctuations includes: Prof. Poul Andersen, Section of Maritime Engineering, Dept. of Mechanical Engineering, Technical University of Denmark, Lyngby, Denmark. Prof. Göran Bark, SSPA Maritime Consulting AB and Chalmers University of Technology, Göteborg, Sweden. Dr. Bong Jun Chang, Hyundai Heavy Industries Co., Ltd., Maritime Research Institute, Ulsan, Korea. Dr. Fabio Di Felice, Italian Ship Model Basin (INSEAN), Circulating Water Channel, Rome, Italy. Mr. Jürgen Friesch (Chairman), Hamburg Ship Model Basin (HSVA), Hamburg, Germany. Dr. Ki-Han Kim (Secretary), Naval Surface Warfare Center, (formerly David Taylor Model Basin), West Bethesda, USA. Dr. Noriyuki Sasaki, Sumitomo Heavy Industries Ltd., Hydrodynamics Group, Ship Design Dept., Yokosuka, Japan Date and Venue of Meetings Four formal meetings of the Committee were held as noted: Hamburg, Germany, February 3-4, 2000 at HSVA, the Hamburg Ship Model Basin, hosted by Mr. J. Friesch. Rome, Italy, November 29-30, 2000 at INSEAN, hosted by Dr. F. Di Felice. Pasadena, USA, June 18-19, 2001, in conjunction with the CAV 2001, hosted by Dr. K.-H. Kim. Tokyo, Japan, October 30 - November 2, 2001 at Sumitomo Heavy Industries, hosted by Dr. N. Sasaki Members Attending the Meetings All members attended the first, second and third meetings. All members except Prof. Bark and Dr. Di Felice attended the fourth meeting. 2. RECOMMENDATIONS OF THE 22ND ITTC The recommendations for the work of this Specialist Committee as given by the 22nd ITTC were as follows. Develop and validate practical experimental and numerical prediction procedures for unsteady hull pressure, including the method

2 418 The Specialist Committee on Cavitation Induced Pressures 23rd International using propeller cavitation volume timevariation. Procedures should use format defined in the Manual of ITTC Recommended Procedures and should be included in the Committee report as separate appendices. Symbols and terminology (SaT) should agree with those in the 1999 ITTC SaT list; if necessary, new symbols should be proposed. 3. INTRODUCTION Cavitation research continues around the world not only in research and development organizations but also to a large extent at educational institutions. Cavitation phenomena consist of a complex combination of fluid dynamics and bubble/cavity mechanics, and are therefore by nature unsteady, unstable and stochastic. The major ITTC-related cavitation interests are analytical prediction, model-scale experimentation and full-scale scaling of developed cavitation patterns and the resulting unsteady hull pressure fluctuations and noise. Much of this work is documented via the many international conferences on cavitation held almost annually (22nd ITTC, 1999). The performance specification for a modern propeller nowadays includes a limitation on maximum levels of hull excitation pressures and/or forces. Those levels should not be exceeded in order to achieve acceptable levels of vibration. In practice, this requirement can vary from a simple statement to a very detailed specification with clearly defined pressure or force levels. Based on experience, several recommended blade-rate single-point pressure amplitude standards have been proposed (15th ITTC, 1978; Wilson, 1991; Friesch, 2000). It is difficult to agree on a widely accepted standard. The main reason is that the peak level of pressure alone cannot be used as a reliable indicator, without taking into account the response properties of the hull. The increasing demand for low-noise ships fast cruise liners, fast ROPAX-ferries and other high-speed vessels with speeds up to 35 knots with propellers makes it necessary to improve the prediction methods further, especially for higher-order pressures and noise. This also holds true for the fast, very large POSTPANMAX containerships. The principal source of forced excitation occurring in modern ships is the partially cavitating propeller, characterized by sheet cavitation in the upper half of the propeller disk and by strong, developed tip vortex cavitation (see Figure 3.1), the latter becoming more and more the dominant noise and vibration source (Friesch, 2000; Kuiper, 2001). Figure 3.1 Full-scale sheet and tip vortex cavitation. In general, the excitation caused by a propeller operating in the nonuniform wake field behind a ship consists of two parts. (i) Forces and moments on the propeller blades are transmitted to the hull structure via the stern-tube bearing and thrust block (referred to as shaft forces or bearing forces). (ii) Forces acting on the hull plating resulting from surface pressures induced by blade loading, blade thickness and pulsating cavitation. In case of a pulsating, bursting tip vortex, these forces act over a large frequency range and are therefore very difficult to handle from the structural side of a ship design.

3 23rd International Proceedings of the 23rd ITTC Volume II 419 Under noncavitating conditions, excitation forces from (i) and (ii) are generally of the same order of magnitude. However, when the propeller cavitates mainly with developed sheet cavitation the contribution from (ii) becomes dominant. The resultant hull excitation force can be many times greater still, due to reductions in phase angle difference between different locations of the excitation. In the past it has been shown that skew can reduce hull fluctuating pressures by more than 50%. The trend of modern propeller design toward high skew and unloaded blade tips has succeeded in reducing the pressure amplitudes in general, but is often considered to cause a rise in pressure pulses of higher order. An explanation can be found in the occurrence of less, but fluctuating, sheet cavitation and sometimes strong and bursting tip vortex cavitation. One of the continuing main topics in cavitation research is unsteady sheet cavitation. In the past, a sheet cavity has been considered to be one vapor volume attached to the propeller blade. But it is now known (Kuiper, 2001) that the inner structure of sheet cavitation is very dynamic, mainly as a result of the reentrant jet which disturbs the edge of the sheet cavity and the tip vortex structure. The pressure fluctuations generated by a fluctuating sheet cavity mainly occur at blade frequency or multiples, sometimes up to three or even five times the blade rate. A heavily cavitating tip vortex tends to produce broadband excitation. But the physical mechanism leading to pressure pulses at higher blade rate, and to broadband noise, are still not fully understood. Phenomena like tip vortex cavitation and especially vortex bursting are very complex since viscosity, compressibility and wake inhomogeneity have a major influence (Friesch, 2000). Unstable, fluctuating and irregular behavior of sheet and tip vortex cavitation lead to a widespread distribution of energy along the frequency band, with higherharmonic pressure levels of amplitude almost the same as or even higher than the first harmonic. These high-harmonic amplitudes, associated with intermediate frequencies not corresponding to blade-frequency multiples, can be extremely dangerous because the wide range of frequency increases the risk of resonance of local parts of the steel structure of the ship. To detect this broadband excitation, a narrowband spectrum of the time signal (registration) is necessary. Figure 3.2 shows a narrowband spectrum of a cavitating propeller with sheet cavitation and a strong and bursting tip vortex. Blade frequencies dominate, but there is a large amount of energy at intermediate frequencies. Amplitude [db -re.1 µpa] Frequency [khz] Figure 3.2 FFT analysis of pressure signals of a cavitating model propeller. Understanding of the tip vortex effect on the pressure signal becomes especially important in cases of twin-screw cruise liners and RoRo-ferries many with podded propulsion where propeller cavitation is reduced to tip vortex cavitation only. In those cases, it often happens that the exciting forces for noncavitating and cavitating propellers are of the same magnitude. Despite significant progress in predicting hull pressure induced by sheet cavitation, it remains difficult to calculate propellerinduced pressure fluctuations related to tip vortex cavitation. Lifting-surface and panel methods are the established tools for predic-

4 420 The Specialist Committee on Cavitation Induced Pressures 23rd International tion of propeller cavitation. Implementation of cavity models in RANS codes for propellers is at an early stage of development and needs further improvement. Therefore, model experiments remain the most-reliable method for estimating full-scale unsteady, pressure excitation. During the first term of this Specialist Committee (22nd ITTC, ), emphasis was placed on: fundamentals of cavitationinduced pressure fluctuations, global descriptions of prediction tools including tests and numerical calculations, and methods of reducing propeller excitation (22nd ITTC report, 1999). The focus of the current term (23rd ITTC, ) has been development of detailed procedures for predicting pressure fluctuations caused by cavitating propellers, both numerically and experimentally. 4. QUESTIONNAIRES As a first step toward accomplishing the assigned task, this committee developed a questionnaire for assessing current practices in use by various organizations, including the ITTC member organizations, for predicting cavitation-induced hull-pressure fluctuation. The questionnaire was sent to 103 organizations comprising most ITTC member organizations, along with industry and academia involved in cavitation research. The questionnaire consisted of two parts: numerical and experimental. The numerical part was divided into three major areas: onset flow and loading conditions, propeller cavitation prediction, and prediction of pressure fluctuations. The experimental part was divided into four major areas: facilities, model and instrumentation set-up, test conditions, and data acquisition, processing and presentation. Appendices 1 and 2 detail the numerical and experimental parts of the questionnaire, respectively, together with the responses Summary of the Responses Of 103 organizations, 38 organizations from 20 countries responded with answers, and 12 organizations from 8 countries responded with no answers primarily because they are not involved in cavitation-related activities. Among 38 that responded with answers, 25 answered both numerical and experimental parts of the questions; 11 answered numerical part only; and 2 answered experimental part only. The 20 countries which responded with answers are as follows, with the number of responding organizations specified in parentheses: Austria (1), Bulgaria (1), Canada (1), People s Republic of China (2), Denmark (2), Finland (2), France (1), Germany (4), Greece (1), Italy (1), Japan (9), South Korea (3), The Netherlands (1), Norway (1), Poland (1), Spain (1), Sweden (1), Turkey (1), UK (1), and USA (3) Analysis of the Responses: Numerical Part The questions were organized in order to gather information on: Onset flow data (from experiments or calculations) and loading conditions, Propeller flow and cavitation prediction including type of cavitation, and Prediction of pressure fluctuations. The 36 numerical responses mostly provided very detailed answers; exceptions were included in the evaluation. Responses are summarized in the following sections, with number of organizations shown in parentheses. Since each organization may use more than one procedure for a particular task, the responses for that task may exceed the total number of answering organizations.

5 23rd International Proceedings of the 23rd ITTC Volume II 421 Onset Flow and Loading Conditions The wake normally used for propeller cavitation prediction by slightly less than half of the organizations is the measured model nominal wake (see Figure 4.1). About onefourth (8) correct this wake to model effective wake. About half (20) indicate that they correct the model wake to full-scale nominal (9), or to full-scale effective wake (11). Computed wakes, model- or full-scale, nominal or effective, not based on measurements, were reported by less than one-fourth of the organizations (8) with no preference for any of the combinations. This means that measured model nominal wake is the basis in the majority of answers, but other methods are used sometimes as an alternative. 45% 40% 35% 30% 25% 20% 15% 10% 5% 0% (a) (b) (c) (d) (e) (f) (g) (h) (a) Measured model nominal wake. (b) Computed model nominal wake. (c) Computed full-scale nominal, based on measured model nominal wake. (d) Computed full-scale nominal, based on other than measured model nominal wake. (e) Computed model effective, based on measured model nominal wake. (f) Computed model effective, based on other than measured model nominal wake. (g) Computed full-scale effective, based on measured model nominal wake. (h) Computed full-scale effective, based on other than measured model nominal wake. Figure 4.1 Wake normally used for propeller cavitation prediction. The loading condition (combinations of J T and/or K T or J Q and/or K Q ) is defined mainly (33) on the basis of model data with few organizations (4) using calculation only for fullscale, sometimes as an alternative. One third (11) use model data without correction whereas two thirds (22) correct their model data to full-scale (correction methods used were not specified). Most organizations that correct model data to full scale use the design propeller (17) as opposed to the stock propeller (2). The general interpretation is that organizations prefer to use the design propeller model and do use it if available. Propeller Cavitation Prediction All organizations deal with sheet cavitation (see Figure 4.2). Many fewer also deal with tip-vortex (12) and bubble cavitation (9) and very few also address cloud (4) and hubvortex cavitation (2). Different methods are used for cavitation prediction, and some organizations have more methods available (see Figure 4.3). 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% (1) (2) (3) (4) (5) (1) Sheet (4) Tip vortex (2) Bubble (5) Hub vortex (3) Cloud Figure 4.2 Types of cavitation accounted for in hull-pressure prediction. In general, propeller lifting-surface methods (23), and to a less extent panel methods (14), are the most commonly used. Those methods are also used as a basis for twodimensional (2-D) profile techniques to address sheet cavitation and as a basis for prediction of other types of cavitation. They are used as routine methods, for customers and for research, the latter for the panel method in particular. Some organizations report that those methods are also in development, indicating refinements and extensions being cur-

6 422 The Specialist Committee on Cavitation Induced Pressures 23rd International rently implemented. RANS methods are only indicated as used for research or being in development, and only one organization uses a RANS method to predict sheet-cavitation. It appears that different methods are used depending on the application. Some purely and semi-empirical methods seem to address several types of cavitation with no specific type being indicated. Cavitation history is accounted for by both quasi-steady (14) as well as fully unsteady (18) procedures, whereas fewer organizations use bubble dynamics (7) (see Figure 4.4). Changes in propeller-blade geometry due to hydroelastic effects are included by very few organizations (3). pressures. A few organizations use empirical or semi-empirical methods for predicting hull surface pressure but use lifting- surface methods for predicting type and extent of cavitation on the propeller. 70% 60% 50% 40% 30% 20% 10% 0% (1) (2) (3) (4) (5) (6) (7) (8) 70% 60% 50% 40% 30% 20% 10% 0% (1) (2) (3) (4) (5) (6) (7) (8) (1) Purely empirical (2) Semi-empirical (3) 2-D (4) 3-D airfoil (5) Propeller liftingsurface (6) Propeller panel (7) RANS equations (8) Other Figure 4.3 Methods used when predicting the types of cavitation shown in Figure 4.2. Prediction of Pressure Fluctuations When predicting hull-pressure fluctuations, only a few organizations (3) use an entire hull representation. About half (16) use partial representation of the hull, whereas the other half (15) use solid boundary factors; a few use both. One-third (11) include freesurface effects, but that approach is not correlated with the method used for calculating hull effect. Hull pressures are predicted mostly on the basis of the unsteady Bernoulli equation (24), but organizations (7) using empirical and semi-empirical methods for cavitation prediction also use such methods for (a) Quasi-steady (b) Fully unsteady (c) Bubble dynamics (d) Other Figure 4.4 Methods used when accounting for cavitation history. One-third of the organizations (12) calculate the hull response to cavitation-induced pressures. Some that do not perform such a calculation indicate that they do not have the necessary information on the ship structure, or that they have no interest in such a result. The results of hull-pressure fluctuation predictions are usually (31) presented at blade-rate frequencies (amplitude and phase), often up to third blade-rate, but sometimes higher. Some organizations (7) also present time series. Summary The onset-flow and loading conditions for propeller cavitation are mainly predicted on the basis of model tests, often with corrections to full scale and effective wake. Only a few organizations use calculations only. Nearly all organizations account for sheet cavitation; many fewer include one or more additional types. Empirical methods are used, but most rely on propeller lifting-surface and slightly fewer on propeller panel methods. Both methods are under further development by the organizations, in particular panel meth-

7 23rd International Proceedings of the 23rd ITTC Volume II 423 ods. RANS methods are in development or used for research. Hull-pressure fluctuation predictions are mainly based on the unsteady Bernoulli equation, but some organizations also use empirical methods. Partial-hull representations or solid-boundary factors are most widely used. exceptions, that smaller facilities implement wake simulation by wire screen. Larger tunnels use more-sophisticated wake simulation methods Dummy models are widely used for medium-size facilities, while full-ship models are adopted for tunnel cross section larger than 1 m 2. One organization uses a combination of full-hull model and flow liners Analysis of the Responses: Experimental Part 1000 OPEN-JET CAVITATION TUNNEL The questions were organized to gather information in the following areas: Test facility involved in pressure fluctuations measurements and wake simulation, FACILITY CROSS SECTION AREA (SQ. M) ITU (1) VWS TU Berlin (KT1) CLOSED-JET CAVITATION TUNNEL FREE-SURFACE CAVITATION TUNNEL DEPRESSURIZED TOWING TANK ITU(2) MIT KRISO Mitsui (1) Mitsui (2) TU Berlin(1) SRI (1) SVA Austria CSSRC MHI CTO DMI TU Berlin(2) HMRI SVA Germany SSPA (1) EL PARDO DTMB_36inch Newcastle BSHC MARINTEK SRI (2) SSPA (3) BECVDR SSPA (2) Samsung CSSRC_LCC HSVA INSEAN DTMB_LCC VWS TU Berlin (UT2) MARIN Propeller and ship models, instrumentation set-up, a. Facility topology versus tunnel size. Adopted test conditions, and Data acquisition, processing, and presentation. Test Facility and Wake Simulation The responses have been analyzed in various ways and presented in graphical form. The types of cavitation tunnels used for cavitation-induced fluctuating pressure measurements vary from open-jet (2), closed-jet (20), free-surface cavitation tunnels (4) to a large depressurized towing tank (1). The responses were sorted by the tunnel test-section area and are presented in Figure 4.5. Facilities having multiple test sections were counted by the number of tunnels. Figure 4.5a shows the topology of the facilities as a function of the tunnel size. The topology of the wake simulation adopted (wire screen, dummy model, and full model) for performing pressure fluctuation tests as a function of the tunnel size is shown in Figure 4.5b. The survey showed, with some FACILITY CROSS SECTION AREA (SQ. M) FULL-HULL MODEL DUMMY MODEL WIRE SCREEN k i l ti FLOW LINERS FULL-HULL MODEL + FLOW LINERS b. Wake simulation versus tunnel size. Figure 4.5 Facility geometric characteristics. Wake simulation is critical when performing pressure-fluctuation tests. Analysis of the responses indicated that tunnel velocity measurements and quality checking of the simulated wake in the facilities are common procedures when performing those tests. Although most facilities are still using pitot tubes, LDV is becoming popular for measuring the time-average velocity field. However, three fourths (16) of the respondents deem their wakes correctly simulated in the cavitation tunnel, and some commercial tanks (10) regard wake measurement as an option to be performed only upon customer request.

8 424 The Specialist Committee on Cavitation Induced Pressures 23rd International The blockage (defined as the ratio of propeller disk area to the test-section area) and the propeller Reynolds number (defined using the propeller diameter as reference length) were analysed as a function of the tunnel size and presented in Figure 4.6. For smaller tunnels, the blockage effect is very important. Some limitations in performing pressurefluctuation measurements could be expected even if one fourth (5) of the respondents stated that they adopt some heuristic corrections. Re (x10 6 ), Blockage (%) Reynolds number Propeller bloc kage (%) Free surface channels Facility Cross Section Area (m 2 ) Figure 4.6 Propeller Reynolds number and blockage versus facility size. Free-surface channels, where the testing speeds are two to three times slower than closed tunnels due to Froude simulation, showed lower Reynolds number than closed tunnels. Similar concerns about possible low Reynolds number apply to some small cavitation tunnels. Despite the fact that the tunnel speed can be higher than 10 m/s, actual test speed could be limited to 3-4 m/s, probably due to screen cavitation and/or deformation that may degrade the quality of the simulated wake. Propeller and Ship Model, Instrumentation A typical propeller diameter used for pressure-fluctuation tests is in the range of mm. Some large facilities use propellers with diameters up to 400 mm. Popular propeller materials are brass and high-strength aluminum alloy. Typical manufacturing accuracy is in the range of mm. About a quarter (6) of the respondents use carborundum turbulence stimulation on propeller blades. Normally for dummy model set-up, brackets and rudder are also mounted. When using full-ship models, wood (12) or fiberglass (6) is used for construction and all the appendages are mounted. Shaft rotational speed is measured using a multiple-pulse encoder (18) mounted on the propeller shaft (6), on the dynamometer (8) or on the motor (11). Particular attention is paid by 70% of the respondents when setting up the mechanical transmission for a full-ship model: shaft alignment is checked in order to reduce the vibration levels induced by the mechanical transmission, especially for twin-screw ship models when only one motor and gear box are used to assure constant propeller rotational speed. For twin-screw ship models, about one quarter (6) of the respondents use a two-motor configuration (one for each shaft). A twomotor arrangement is more reliable and produces reduced vibration and better control of the propeller rotational speed. The number of pressure transducers used, differential or absolute type, varied from 5 to 20. Locations of pressure taps varied widely among the organizations. Most of the respondents placed transducers both upstream and downstream of the propeller plane. Pressure transducer response range varied widely depending on test velocity and static pressure used for pressure fluctuation experiments. The maximum frequency response range of piezoelectric and strain-gauge pressure transducers varied from 1 to 5 khz. In addition to pressure transducers, one to six hydrophones or accelerometers are typically used by about a quarter (6) of the respondents. Test Conditions In general, test conditions are based on towing tank propulsion test results. In some cases, the designer specifies test conditions. In

9 23rd International Proceedings of the 23rd ITTC Volume II 425 both cases, K T identity is widely used (19) compared to K Q (9) or J identity (8). There is no standard definition of the cavitation number σ for pressure fluctuation tests among the organizations. Static pressure is defined variously at the shaft centerline, or at 0.7R or the propeller tip at 12 o clock angular position. The dynamic pressure is calculated with the propeller rotational speed or with the vector sum of the propeller rotational speed and the advance velocity. During the test, water quality is monitored by all of the organizations. Oxygen content (15) or total air content (8) is measured during tests performed below 7 m/s with a propeller rotational speed in the range of rps (16). One organization performs tests at different revolution rates to determine the effect of propeller rotational speed. About half of the organizations observe cavitation using stroboscopic light video or digital still cameras. Data Acquisition, Processing and Presentation Most respondents (18) sample pressure signals and record time histories. Sampling is done at a suitable frequency and time interval to capture from 50 to 1000 propeller revolutions. Most of the respondents (18) record the phase angle of the propeller, but only a few (3) average phase angle to obtain the mean pressure versus shaft angle. Most organizations Fourier-analyze the time series and tabulate up to the 30th bladeharmonic amplitude. One organization also presents the shaft-rate harmonics, because in some cases the shaft-rate harmonic amplitude may not be negligible More than half (14) of the organizations present continuous spectra of the pressure fluctuation. Some (4) also post-process the data to obtain the forces on the hull. A majority of the organizations (16) check the reproducibility of the pressure data, but only a few (4) perform an uncertainty analysis. Summary Questionnaire results indicate that many organizations perform pressure-fluctuation measurements when a cavitation tunnel is available. The wake simulation used varies with the facility type. In some facilities, limitations due to blockage or to low propeller Reynolds number are apparent. Nonetheless, the information obtained even in a poor simulation is valuable data for a ship designer. Larger facilities offer more-advanced testing capabilities and a range of wake simulations (dummy models, full model, shortened model, flow liners, etc.). All the organizations perform data acquisition and analysis in a similar way, but only a few use a phase-sampling technique to analyze pressure time history. Data reproducibility is commonly checked, but uncertainty analysis is not widely performed. 5. DEVELOPMENT OF PROCEDURES This Specialist Committee developed two separate procedures an experimental one and a numerical one for predicting cavitation-induced hull pressures. Both full recommended procedures are included in the ITTC Quality Manual as procedures and The experimental procedure deals with only the measurement of pressure fluctuation generated by a cavitating propeller. Many other aspects are treated elsewhere. Some of the major experimental issues that are not covered in the experimental procedures are presented here. Detailed water-quality effects, including total air content, free air content and nuclei distributions, will be addressed in a separate report of the Specialist Committee on Water Quality and Cavitation (23rd ITTC report, 2002). Details related to cavitation tests

10 426 The Specialist Committee on Cavitation Induced Pressures 23rd International will be reported by the Propulsion Committee. The full-scale measurement procedure has already been reported in a 22nd ITTC Committee report (1999). The numerical procedure is more loosely defined because many existing methods have varying degrees of completeness and computer resource requirements. Most organizations have experience on how to use their particular method with good results. Consequently, the numerical procedure provides guidance to naval architects in shipyards, owners and consultancies on how to use available methods Comments on the Experimental Procedure The committee was assigned to develop a procedure for prediction of cavitation-induced pressure fluctuations on the basis of modelscale experiments. The procedure provides guidelines to ensure the most accurate data possible for the cavitation-induced pressurefluctuation performance of ship propellers. In this part of the report, some physical phenomena are documented which play an important role when performing pressurefluctuation measurements in a cavitation test facility, but which can neither be put in a direct law nor can specific values be given. Influence of Boundary Conditions The engineering problem is to determine the propeller-generated unsteady pressure field at the aft body, expressed so that the force exciting ship vibrations can be determined. Ideally the experiments would be performed so that the measured pressures, after a simple scaling, could be fed directly into an FEM-calculation. In practice other corrections also may be needed to take account of effects not possible to simulate in the model experiment. The group of problems discussed below is related to the influence on the pressure pulses of the boundary conditions at the hull and nearby surfaces. Although parts of the problem are common for numerical and experimental predictions, the discussion is focused on understanding the experimental problem. The influence of the boundary conditions on pressure pulses measured at the hull surface was already known in early work, examples being the discussions by Tsakonas et al. (1962) and Huse (1970). However, intensive discussion did not begin until the mid- and late-1970s and early 1980s when results were collected and analyzed from the new cavitation laboratories employing complete ship models with or without a free water surface. Since then, quite a few papers on the subject have appeared. However, the problems have not been solved in the sense that there exists a standard engineering method that is commonly applied to treat the problems. The flow generating the pressure pulses from the propeller can for most applications be obtained from the velocity potential determined by a Laplace equation which at a large distance from the propeller transforms into a wave equation. The solution for the pressure field p(x,t) in space and time, obtained via the Bernoulli equation, is influenced by the conditions at the boundaries of the domain in which p(x,t) propagates. In potential theory, the boundaries are realized by adding images of the pressure pulse sources such that the boundary conditions are fulfilled on the boundary of the domain, for example at the hull plating and free surface. A direct conclusion from this modeling is that a distant boundary usually has little influence on the field close to the source. However, close to the boundaries, the hull plating and the free water surface for example, the boundary conditions can have a dominating influence on p(x,t). As a result, for example, the 1/r - variation of the pressure from a sim-

11 23rd International Proceedings of the 23rd ITTC Volume II 427 ple source does not hold when approaching boundaries. For a ship at the surface of a deep ocean, the two dominating boundaries affecting p(x,t) close to the propeller are the hull plating, more or less flexible, and the free water surface, completely flexible. Examples of distant boundaries that also can be of interest are the walls in a cavitation tunnel. Sometimes the walls can be close enough to influence the measured hull pressure. If standing waves are excited, measurements rather close to the propeller can also be influenced. In computations, the free-field pressure in an unbounded space is primarily obtained. In a conventional cavitation tunnel, a board with water on both sides usually substitutes for the free water surface. The boundary condition at this board is however not obvious. The general potential theory as applied for pressure pulses from propellers is for example described in Breslin and Andersen (1994), Chapters 21 and 22. Discussions directly related to the present problems are, among others, made by Huse and Guoqiang (1982) and Catley (1984). Physical effects influencing the boundary conditions In an experiment the pressure in the water at the hull surface is more or less influenced by the following: a. The presence of the hull as a body of a specified shape. b. The position of the pressure transducer (in the hull surface) relative to other surfaces (free surface, tunnel walls, etc.). c. The global vibratory motion of the hull. d. The local vibratory motion of the hull. e. The presence of a free water surface. f. The presence of other bounding surfaces as tunnel walls or sea bottom. In the theory these points appear as boundary conditions for the hydrodynamic or possibly acoustic equations describing the behavior of the pressure pulses. Similarity in model testing With regard to the propeller hydrodynamics, including the ship wake and cavitation, an elaborate procedure usually results in adequate simulation of the source of the pressure pulse, i.e. mainly the cavitation dynamics. This is achieved primarily by requiring similarity of the cavitation number and a pressure coefficient reflecting the flow field on the blades (with appropriate ship s wake and advance coefficient). Although important, these similarity conditions are not the only ones; also, they are usually only approximately fulfilled. A corresponding level of accuracy for the boundary conditions influencing the pressure pulses can however be even more difficult to achieve. Also for the factors (a)-(f) above, it happens that one or a few dominate. Different factors can also have opposite influence, meaning that a measured pressure can approach a calculated free-field pressure when it shouldn t. An important problem appears when fullscale measurements have to be compared with model measurements or numerical predictions. Such comparisons are very important for establishing correlation between predictions and true full-scale data. However, as pointed out by Wereldsma (1981), full-scale data can be even more difficult to interpret than model data. This fact is one reason why the effects of boundary conditions have to be taken seriously. The most-complete fulfillment of the boundary conditions is found in a large vacuum tank operating at the correct Froude number. There, not only are the correct hull shape and free surface present, but the channel walls are also reasonably distant from the points at which pressure is measured. Yet ap-

12 428 The Specialist Committee on Cavitation Induced Pressures 23rd International proximations have to be made even in such a facility. For example, the local vibrations of the model and full-scale ship are usually different, and a Mach number similarity needed for a correct pressure-pulse distribution around the hull is also neglected. The Mach number similarity is not very important for low frequencies and close to the propeller, but the local vibrations of the hull can be important. However, things are not always that bad. With a ship model, or an afterbody of realistic shape, tested in a reasonably large cavitation tunnel, and with pressure pulses measured fairly close to the propeller, the boundary conditions can at least for some transducers be approximately fulfilled, yielding measured amplitudes that are a useful estimate of fullscale values. This is particularly true if data are corrected according to an updated fullscale correlation. However, amplitudes from transducers on the ship that are close to the free water surface and/or far from the propeller can require significant corrections. Estimate of boundary condition effects and correction factors Examples If the boundary conditions cannot be fully realized in a test facility, it may be possible to correct the measured data. The corrections can be based on empirical models or on mathematical models that can simulate the conditions at model as well as at full scale. The correction factors used by Huse and Guoqiang (1982) are a suitable basis. They define the combined solid boundary and free surface factor (S tot ) as the product of the solid boundary factor (S b ) and a free surface factor (S f ). Sb is defined as the pressure measured at a rigid fully immersed hull divided by the corresponding pressure in free field, i.e., with the hull removed. S f is defined as the pressure measured at the hull with the free surface present divided by the pressure at the rigid fully immersed hull, i.e., with no free surface present. The pressure field at a rigid stationary body: The simplest formulation occurs when the hull is a rigid stationary body, i.e. not responding to the unsteady pressure by vibrating. That case, with a free water surface, was extensively studied by Huse and Guoqiang (1982). By applying potential theory, they calculated the combined solid-boundary and free-surface factor for four different ships, at five sections for one of the ships and at different conditions for a wedge section. It should be noticed how much smaller the total correction was than the standard flat plate value of 2, even at the deepest point of a section at some distance upstream from the propeller (S tot =0.24 at section position, x/l PP =0.18, their Figure 12). Only when tip clearance relative to propeller tip immersion was quite small (0.07) did S tot approach 2 (their Figure 13). The authors also found the solid-boundary factor (i.e. without the freesurface effect, their p. 90 and Figure 14) to be very close to 2.0 at normal transducer positions for most afterbody forms, a fact of interest for some types of model configuration in cavitation tunnels. The data presented by Huse and Guoqiang provide a point of reference for the combined free-surface and solidboundary effects. With regard to numerical prediction of pressure pulses, Breslin et al. (1982), Kaplan et al. (1982) and later Kehr et al. (1996) also computed the effects of a rigid hull and free surface by similar methods. That type of simulation of the hydromechanics of the pulsating field outside the hull can alternatively be done by a Navier-Stokes or Euler model, as demonstrated by Sunnersjö and Janson (1987). Bloor and Kinns (2000), Kinns and Bloor (2000), Nakatake et al. (2000) and Jensen et al. (2001) also made similar calculations. The pressure field at a vibrating body: The next level of sophistication is to take into account the effect of ship vibration on the hull pressures. The vibration can be global girder vibration as well as local plate vibration. The

13 23rd International Proceedings of the 23rd ITTC Volume II 429 vibration can be generated by a specific propeller cavity, or by sources not correlated with this specific source. Multiple sources make measurement and interpretation more complex, particularly at higher frequencies when wider frequency bands are also used. Wereldsma (1981) discussed the fundamentals of measuring under such conditions. He argued that hull vibration could, even at model scale, contribute significantly to the measured hull pressure. He further claimed that comparisons of pressure amplitude at model and full scale could at worst be meaningless due to different dynamics of model and full-scale hulls. This is possible if particularly strong local plate vibrations are present. However, twenty years of additional experience indicates that the situation is usually not that bad; nonetheless a conservative attitude is still a good idea. Wereldsma also recommended correcting the measured pressures using the recorded acceleration of the pressure transducer. Frivold (1976) studied the influence of hull vibration on measured pressure for a fullscale LNG-carrier. He found that the contribution from the global vibration was less than one-thousandth of the measured pressure, and that the contribution from the local vibration was smaller than the standard deviation. From his Figure 2, however, it can be seen that at distances larger than 1.5 propeller diameters upstream of the propeller the standard deviation was not very small. Catley (1984) presented an extensive review and analysis of the hydroelastics and the computations of solid-boundary factors for a product tanker. He applied potential theory to find the added masses and thus the perturbation pressure generated by global as well as local hull vibration determined by an FEM method. In view of the variation of the calculated solid boundary factors, it is evident that surprises can occur when comparing model and full-scale pressures if a pressure transducer is located on a node. Sunnersjö (1982), Sunnersjö et al. (1984), Sunnersjö and Janson (1987) measured pressure pulses on a fishery research vessel at model and full scale, as well as hull vibration at transducer positions on the ship. With machinery stopped, vibration-induced pressures were measured when the ship was excited by an exciter placed close to the area where the propeller-induced pressure had a maximum. The exciter generated a broadband random force in a 4 40 Hz range. A transfer function was calculated as the measured pressure divided by the acceleration. Assuming that the propeller excited the same modes, this transfer function was used to find the vibrationinduced pressure with the propeller in operation. By applying the transfer function to the transducer vibrations with the propeller in operation, the measured pressure with the propeller in operation could then be corrected. Phase angles, which can influence corrections significantly, were carefully monitored. Added masses for vibration modes were calculated by a CFD-RANS code (run with zero viscosity). It was concluded that for the two first blade-rate harmonics, the corrections to the pressure amplitudes due to vibration were generally modest. An exception occurred for the transducer positioned more than two propeller diameters upstream of the propeller. There the corrections were between 30% and 100%, in opposite directions. Between 4 and 40 Hz (full scale), comparisons of calculated and measured added mass indicated that at the lower frequencies, where global modes dominate, the experimental behaviour tends to the rigid body results, while at the higher frequency more local modes predominate. Nilsson (1980) performed a study at high frequencies, 30 Hz 6 khz. He derived a model for the plate response due to incident pressure by supposing the plates in the afterbody to be simply supported. He verified the model with measurements of pressure pulses and plate vibration in the centers of some product-carrier afterbody plates. All transducers were mounted in plates mm thick

14 430 The Specialist Committee on Cavitation Induced Pressures 23rd International and well below the waterline, i.e. free surface effect was neglected. He concluded that below 40 Hz (blade frequency being around 8 Hz) the velocity of the hull plating was determined by global rather than local vibrations, i.e. the afterbody vibrated mainly as a solid body. The difference between the incident free-field pressure and the measured pressure for this case was predicted to be close to 6 db, i.e. the solidboundary factor equals 2. At frequencies between 125 and 250 Hz, where plate resonances occurred, the measured pressure was predicted to be up to 15 db (a solid-boundary factor close to 5.6) above the incident free-field pressure. Above 6 khz the correction again approached 6 db. The 125 Hz corresponded to the 15th harmonic of blade frequency, i.e. to the region of lowfrequency noise of interest for cruise liners and ferries. The example demonstrates what can happen when pressure transducers are positioned in the middle of plates where the vibration amplitude reaches its maximum. With the pressure transducer in a stiff position close to a frame or on the ship centerline, the correction can be supposed to be significantly lower. What happens to the induced pressure between out-of-phase antinodes as discussed by Sunnersjö et al. (1984) should be further analyzed. Substituting for the free surface with a submerged plate: In some cavitation tunnels a submerged plate substitutes for the free surface. The plate, usually of laminated wood and approximately 15 mm thick, is not intended to be a simulation of the free surface. It is a substitute for the free surface, enabling the tunnel to be operated at higher speeds than follow from Froude number scaling. It is important in this discussion that (non-flowing) water reaches far above the plate. To correct pressure amplitudes measured in such tunnels, some authors calculate a combined solid-boundary and free-surface factor by supposing the plate to be a rigid boundary; for example Huse and Guoqiang (1982) and Kaplan et al. (1982). The correction factor is then obtained as the pressure computed for the presence of a free surface divided by the pressure computed for the measured case, i.e., with a plate substituted for the free surface. In the computations, the plate is supposed to be a rigid solid. As pointed out by Johnsson (1983) in a discussion of Kaplan et al. (1982), that modeling is questionable for a plate of the type mentioned above. The main argument was that the plate is submerged with the water reaching far above the waterline, and that the plate can be assumed to have an impedance not very different from water. Johnsson claimed, supported by acoustical tests, that the configuration with the submerged plate is more equivalent to a ship model with a rigid plate significantly above the water-line, a case that is somewhat closer to a free surface than the one used in the paper. (It is however obvious from the computations by Huse and Guoqiang that the correction close to a free surface is so strong that a submerged condition is also far from adequate there.) The boundary conditions when a plate substitutes for the free surface is also discussed by Breslin and Andersen (1994, pp ). Later Kehr et al. (1996) also made computations based on the numerical model developed by Breslin et al. (1982). They also made the computations for the same ship with a free surface and a rigid surface at the waterline. Although the comments made above are still applicable, it is interesting to look at their Figures 20 and 21 showing the pressure fields over the afterbody for the different boundary conditions. Empirical corrections: The numerical methods mentioned above for correction of less-perfect realizations of boundary conditions can in principle be used for correction of measured pressures. For some reason, such applications have not yet become engineering practice.

15 23rd International Proceedings of the 23rd ITTC Volume II 431 In the original formulations, no automatic account is taken of the wave system of the ship, i.e. of the influence of Froude number. This however can be manually introduced. Particularly for wide and flat afterbodies, as on RO-RO ships, the stern wave can influence the pressure amplitude significantly. In certain ranges the Froude number can be a moreimportant parameter than the immersion at zero speed. Observing this, Johnsson (1983) outlined an empirical procedure; see particularly his Figure 8 (pp. 307) as well as Figure D2 (pp. 896) in the discussion of Kehr et al. (1996). (According to personal communication with Johnsson, later unpublished studies indicate that the curve in Figure D2 cannot be extrapolated to higher Froude numbers. Because of the development of the wave system the curve will have a maximum around the Froude number 0.3 and at 0.35 the correction factor will return to low values.) The advantage of empirical corrections based on full-scale correlation is that all effects are taken into account: solid boundaries, hull vibrations, free surface and not least a number of scale effects related to wake, cavitation and methods of analysis. On the other hand, there is often a need for continuous updating to cover new types of ships, etc., but this can also be true for more theoretically based methods which typically suffer from some approximations. Conclusions on Boundary Condition Effects There is little doubt that the influence of the boundary conditions is significant and has to be considered. The often-used solidboundary factor of 2 can be adequate, although somewhat conservative, for transducers mounted in stiff structures far from the free water surface and close to the propeller. Close to the surface and far from the propeller, however, that value can result in significant overestimation of the pressure amplitude. At higher frequencies, in the range between vibration and low-frequency noise, significant corrections of measured pressure could be necessary if a transducer is influenced by resonant plate vibration. The problems related to the boundary conditions have been extensively discussed for a long time, and methods for treating the problems have been suggested. Proposed methods for calibration of cavitation tunnels and for corrections are cumbersome to apply and possibly not general enough. The needs differ for different cavitation laboratories. No widespread, generally useful and standardized method seems to be in use. The practical problems are typically solved by empirically-based methods supported by physics and brought to quantitative level by full-scale correlation. Such methods often need a high input of engineering skill and are mainly valid for a specific facility only. A need for development of more general procedures seems to remain. Cavitation Instability - Statistical Properties of the Cavitation Process and Scaling Problems The main assumption in scaling of model results is that the model and full-scale processes are exactly similar, and were measured and would be analyzed in ways preserving this similarity. For example, the scaling of pressure amplitudes by the non-dimensional parameter Kp is based on such assumptions. Due to the fact that all similarity requirements cannot all be fulfilled in a model experiment, the cavitation behavior at model and full scale will be more or less different; i.e. scale effects will occur. For example, scale effects in the extent and dynamics of the cavitation will influence the height and shape of the pressure pulse and then also the spectrum. Additionally, the spectrum can also be quite sensitive to the statistical properties of the cavitation process, for example the periodicity of the pulse sequence.

16 432 The Specialist Committee on Cavitation Induced Pressures 23rd International Ideally the pressure signal is periodic, with the blade frequency as the lowest frequency. This corresponds to a line spectrum with spectral lines only at multiples of the blade frequency. If all blades are not identical, there will be a periodic modulation of the signal and spectral lines separated by the shaft frequency will appear as sidebands around all lines at blade frequency multiples. The lowest frequency appearing will be the shaft frequency. If the wake is fluctuating, because of turbulence, separation or ship motion in waves, the cavitation at different blade passages can generate pulses of different shape, amplitudes and phase. The deviations from the ideal signal can be periodic (due to periodic waves for example) or more-or-less random (due to turbulence in the wake, variation of nuclei density etc.). Depending on the statistical character of the disturbances, the modulating mechanisms, the spectrum will be modified in different ways. Random modulations will introduce a continuous spectrum. In fact all continuous parts of the spectrum of a long duration signal can be considered to be a result of modulation. In comparing a typical model test with a full-scale test in sea state zero, the general impression is often that the cavitation at full scale has the more periodic and stable behavior. In other sea conditions the reverse can be true. If the gas content of the water in a model test is on the low side and the cavitation is only of tiny extent, the cavitation becomes intermittent, i.e. some blade passages will generate no or a significantly smaller cavity. This is a type of modulation, usually random and of very low frequency. At model scale, fully developed cavities typically appear more rarely, and therefore fewer significant pressure pulses per propeller revolution are generated, compared to full scale. Since the root-mean-square (rms) value of the pressure depends on the pulse height and on the occurrence frequency, the model rms pressure sometimes leads to underpredicted full-scale fluctuating pressure levels. Friesch and Johannsen (1992) addressed the problem by using a shortened ship model, obtaining a more-stable sheet cavitation and a clearly periodic behavior of the pressure signal. Scale effects due to intermittence and other statistical effects tend to be reduced when tests are done at high water speed, high nuclei content and adequate wake turbulence. The most-extensive discussion of modulation effects in cavitation is found in the paper by Baiter et al. (1982). In computations no modulation will appear, but the effects still have to be accounted for in comparisons with fullscale data. All modulation caused by external processes, manufacturing, operation, etc. affects the statistical properties of the pressure signal. If for example an otherwise constant wake fluctuates from side to side of the ship, the periodicity of the pressure pulse sequence will be distorted. The amplitude and shape of the pulses will not be changed but the interval will fluctuate, i.e. we have a phase-angle modulation. This type does not change the energy content of the signal but it will redistribute energy (amplitude) from bladefrequency multiple lines in the ideal spectrum to sidebands, i.e. to continuous or line spectra at both sides of the ideal spectral lines. This redistribution of energy will decrease the amplitude of the ideal spectral lines. Spreading of energy around the ideal lines by phase modulation is stronger at higher harmonics than lower. This implies particularly that phase modulation of moderate sheet and tip vortex cavitation can be supposed to be involved in generation of spectra showing high continuous levels beyond 5 to 10 blade frequency multiples, i.e. of the types obtained from mainly tip vortex cavitation in the studies by Ingelsten and Johansson (1997) and Johannsen (1998).

17 23rd International Proceedings of the 23rd ITTC Volume II 433 If this modulation does not exist at full scale, at least not during a trial in calm water, a discrepancy will result between the model and full-scale spectra. If on the other hand the wake fraction only fluctuates around a mean value this will (in a simplified model) result in modulation of the cavity volume and thus also of the pulse amplitude, i.e. we have an amplitude modulation. In that case sidebands will also appear in the spectrum, but the total energy of the signal will be higher than for a steady wake. Methods are required to analyze the resulting pressure signal produced by the various forms of cavitation intermittency. If all modulation were of the phase type and existed at model scale only, the energy in the sidebands could be moved back to the ideal spectral lines. In practice this would result in a strong overcorrection, but it points out that it is reasonable to take some account of spectrum levels around the ideal lines at blade-frequency multiples. In practice, different types of modulation will coexist. Some types could be scale effects depending on model conditions, others could be the result of operation or weather at full scale, and still others could be true and exist in both cases. Therefore it can happen that continuous as well as line spectra have to be scaled. It is noted then that the Kp-formula can be different for different spectrum types (Bark, 1992). It is also possible to address intermittency in the pressure amplitude signal itself. Typically, low-amplitude pressure pulses are excluded, and an rms amplitude or harmonic analysis is based on the remaining pulses. This approach was initially based on the assumption that excessive intermittency tends to occur at model scale, primarily due to lack of nuclei. In one demonstration, Johnsson et al. (1976) excluded from analysis insignificant pulses generated mainly by noncavitating blade passages at model scale. Pulse exclusion can be stated as: An rms value of the X% highest amplitudes is calculated. At X=100, the standard rms value is obtained. With X<100, a higher rms value is obtained. A problem is that no general principle can be derived to determine the amplitude below which pulses should be disregarded. A low value of X at both model and full scale can sometimes be adequate, comparing typical large pulses in both cases. When the standard rms amplitude is used, with no record of the intermittency, the uncertainty is out of control and may be large. If X<100 is used for an intermittent signal, the uncertainty can still be out of control, albeit usually smaller, and the prediction will be more conservative. For this reason, it is very important to document cavity intermittency. A simple video recording yields valuable information. However, more-advanced techniques have been developed. Weitendorf and Tanger (1992) used a video recording system coupled with post-processing software that produced a representation of cavity fluctuation. Johannsen (1998 and 2000) further developed video techniques by simultaneously recording hullpressure pulses and high-speed video. Pressure-pulse levels were superimposed on the video image to show temporal effects of cavity development and related hull-pressure variation. A reasonable analysis might use the usual rms (X=100) as the standard measurement, with an X<100 value as a supplement to provide information about the intermittency effect. Results for several X<100 values could also be useful in comparisons among different test facilities and full-scale conditions. Selecting X-values for standard reporting should be based on extensive experience and correlation of the procedure with full-scale results. Such values might vary according to different conditions, ships, etc. It is highly advisable to include the usual X=100 value. In the end, use of either standard rms values and/or rms of

18 434 The Specialist Committee on Cavitation Induced Pressures 23rd International the X% highest values is a matter of judgment. Both can, if supported by full-scale correlation, result in relevant predictions. Water Quality The effect of water quality has been a subject of continuous discussion in ITTC. The cavitation nuclei concentration in the water has a significant influence on the tensile strength of the water, and therefore on propeller cavitation characteristics, especially inception and intermittence. However, the detailed effects of cavitation nuclei are not yet completely clear in spite of much effort. The ultimate solution will not involve reproducing the seawater nuclei full-scale spectra in model tests. Minimizing the liquid tension and maximizing the number of nuclei is one method to reduce scale effects; however, in many facilities, this is not always practical. The natural nuclei spectrum of any cavitation facility depends on the history of the fluid through the facility. This means that the nuclei spectrum will depend on conditions such as dissolved air content, pressure level, velocity, and the transit time through the different parts of the circuit, i.e. the main pump, vanes, resorber, etc. Consequently, the natural spectrum is different in each cavitation test facility. Each facility has its own unique relationship between air content and nuclei distribution for a given operating condition. It must, therefore, be observed that too high a level of nuclei (air bubbles) could introduce a damping effect on the measured unsteady pressure amplitudes. It is certain that operating at high Reynolds numbers will reduce water-quality scale effects on model blade cavitation. To minimize these scale effects, the experiments should be run at high Reynolds number and high flow velocity with high nuclei content, which is often reached by increasing the dissolved air content. Previously measured liquid tension/nuclei distributions/oxygen content can be used to establish a reference during testing and a correlation to air content level. More details should be taken from the report of the Specialist Committee on Water Quality and Cavitation (23rd ITTC, 2002). Small Tunnels and Blockage Effects In comparison with large cavitation tunnels, small or medium-sized cavitation tunnels have inherent drawbacks in performing hull-pressure measurements. It is nearly impossible to simulate transverse velocity components in acceptable agreement with those components of full-ship model wake, even if a dummy model is used in conjunction with wire screens. Also, wire screens upstream of a propeller may have a major influence on the cavitation behavior of the propeller blades. The turbulence characteristics of propeller inflow are influenced by the mesh size. Furthermore, in a relatively low-pressure condition, small-sized bubble cavities generated on the wire mesh may flow downstream and initiate cavitation on the blade. Low air-content ratio is helpful in avoiding this phenomenon, but is unfavorable for other types of cavitation, biasing the characteristics of the cavitation and the level of the fluctuating pressure. When a flat plate or the tunnel wall is used for pressure measurements, additional attention must be paid to the vibration level of the plate and flow pattern around the plate. Pressure pulse levels have been measured on a flat plate positioned at a varying distance above the propeller. Such a plate may be good for research but usually is not ideal for commercial projects. The plate vibrations can influence the results. Locally the pressure field at such a vibrating plate is not very different from that at a vibrating tunnel wall or a window or hull plating, but it has greater dipole character (Kimball et al., 1997). The differences vary with size and frequency. In any

19 23rd International Proceedings of the 23rd ITTC Volume II 435 case, the vibration has to be considered and measured. It is important to keep in mind that the plate vibrations are natural, corresponding to hull vibrations, while tunnel-wall vibrations are an artifact caused by the tunnel, and are therefore a background noise. The flow on the plate is simply a boundary layer, but the inflow to the plate may not be parallel to the plate due to the nonuniformity of the simulated wake. As a result, a large cavity may form, attached to the plate. It is necessary to check if such a cavity occurs or not. It is recommended that special attention be paid to the flow around a plate, especially for tests with unconventional wakes. If a cavity, stationary or not, occurs close to a pressure transducer, the pressure amplitudes can be significantly influenced and the setup must be modified. The blockage effect is one of the major constraints for hull-pressure measurements. As mentioned in several ITTC reports (ITTC 1990, 1993, 1996, 1999), large scatter existed in hull-pressure measurements among different facilities. One of the sources of the scatter in hull-pressure fluctuations was considered to be the blockage effect, and the previous ITTC comparative tests showed that different levels of pressure fluctuation are measured in differently sized test sections (ITTC 1999). The effect of blockage on pressure measurement has not been clarified quantitatively. Systematic study of this effect is needed. Wake Simulation Correct simulation of the full-scale ship wake is an essential requirement for pressurefluctuation measurements. For a twin-screw ship, a full-ship model will correctly simulate the three-dimensional full-scale propeller inflow provided that the propellers are operating outside the hull boundary layer. In the case of a single-screw hull, where the propeller is working in the hull boundary layer, the large difference of the model and ship Reynolds numbers will produce a wider wake in model scale. A shortened full-ship model can be adopted to reduce model and ship boundary layer differences, but particular attention shall be applied when shortening the model to avoid possible flow separation on the model forebody that will worsen propeller inflow simulation. Prior testing with oil paint or tuft visualization is recommended for verification. Wire screens are widely used in smaller tunnels to simulate primarily the axial velocity distribution. It is very difficult to produce the tangential and the radial velocity distribution. A dummy afterbody model can be used to simulate the full scale propeller inflow, but it requires a time-consuming iterative process of model modifications and wake measurements to achieve the target propeller inflow. Full Scale Correlation/Measurements Correlations between model- and fullscale data serve a variety of purposes and are considered to be very important by both the testing community and customers. Those uses depend critically upon the full-scale measurements having been professionally made and analyzed. Obtaining and analyzing full-scale data properly is itself a major challenge, substantially different from model-scale testing. For guidance in that endeavor, a systematic and thorough discussion of full-scale measurement methodology was presented in the 22nd ITTC report Comments on the Numerical Procedure Calculations of cavitation-induced hull pressure generally fall into two categories: one based on empiricism, relying heavily on

20 436 The Specialist Committee on Cavitation Induced Pressures 23rd International model-test results; and one based on solving the flow problem by first principles. For the latter category, calculation of hull pressures is the last part of a series of calculations: first, the ship wake field is calculated; second, the fully wetted flow; third, the cavitating propeller flow field; and fourth, hull pressure. The wake field is most often obtained from model tests and scaled to full-scale effective-wake field. However, direct CFD calculations are becoming more common. In the procedure, these points are addressed briefly, with more emphasis on the cavitation calculation, which is considered to be the most difficult part. Cavitation volume time variation is the most-important single parameter for accurate hull pressure prediction. Cavity geometry and its development over time on the rotating propeller blade are also important, for evaluation of propeller performance with respect to erosion, vibration and noise by propeller designers and naval architects. Among the various types of cavitation, geometry can be predicted accurately mainly for sheet cavitation The problem of computing the ship wake field will be treated in detail by the Resistance Committee (23rd ITTC, 2002). A brief overview of numerical capability for predicting ship wake flow is presented in the following section. 6. RECENT DEVELOPMENTS: REVIEW OF LITERATURE 6.1. Numerical Work Current efforts in CFD will no doubt eventually lead to accurate computation of the complete flow field around a ship at full scale. Such flow includes the nominal and effective wake field of a ship traveling at constant speed in calm water, i.e. the onset flow necessary for calculation of the flow over a cavitating propeller and subsequently the hull pressure. At present, however, propeller designers and analysts tend to rely on model-scale nominal wake surveys, possibly with a correction to full-scale effective wake. One way of performing such a correction is to use an Euler solver coupled with a propeller vortex lattice or boundary element method. Further investigation and validation will show whether such methods will become established procedure. Calculation of propeller performance in a spatially nonuniform inflow is usually done with vortex-lattice or boundary-element methods, the latter being state-of-the-art. Effects of hub, wake alignment, etc. are generally included. Incorporating cavitation into the propeller flow-field calculation is a main research area. Sheet cavitation has been included with varying degrees of sophistication. Tip vortex cavitation is being addressed. Much of the published work concentrates on 2-D and 3-D hydrofoils to avoid the extra complication of rotating blades. Most work uses potential flow, but substantial effort is being devoted to theoretical study of cavitation via CFD. The CFD work is too immature for application to hull pressure calculations. Once the unsteady flow field of a cavitating propeller has been obtained, it appears fairly straightforward to compute the pressures on the hull. Yet few publications on this problem have been found. One of those addressed application of simple, solid boundary factors and concluded that the method was inadequate. Many papers report applications of methods for designing and analyzing propellers. Such applications include optimization of propellers with respect to efficiency and performance, i.e. low-pressure pulses, including innovative propulsors. More details about the various developments are given in the following sections.

21 23rd International Proceedings of the 23rd ITTC Volume II 437 Calculation of Wake Calculation of the wake of a ship as input in the form of onset flow to propeller calculations can be considered as a part of the task of predicting the viscous flow over the entire ship hull. Significant progress has been made over the past two decades in the capability of CFD, especially RANS methods, in such predictions. State-of-the-art CFD computations were presented by 20 organizations at the Göteborg 2000 workshop, known as the G2K workshop (Larsson et al., 2000). The workshop dealt with three modern hull forms: a tanker (VLCC), a container ship, and a naval combatant. Detailed discussions were also presented on numerics, physical modeling, and verification/validation. The presentations at that workshop indicated an increased use of sophisticated turbulence models, including two-equation and Reynolds-stress models, compared to previous similar workshops, and a clear correlation between model complexity and accuracy in the predicted stern-flow results. Overall, there was significant progress in predicting the viscous ship flow. However, prediction accuracy showed considerable sensitivity to numerics, gridding, and turbulence models. Further research is required to establish greater consistency and a well-defined degree of accuracy in the computations of hull wake. Despite concerns about potential deterioration of the solution close to the hull using a wall-function approach, Kim (2001) presented a quite-realistic nominal wake of a tanker model using a commercial code (FLUENT) employing Reynolds-stress turbulence model in conjunction with a wall function. The grid size (maximum cells used) and computational cost are considered to be moderate. Hoekstra et al. (2001) reported a singlescrew hopper-dredger design for which the usual model tests were not carried out. Instead, the RANS code, PARNASSOS (MARIN) was used for a preliminary and modified hullform. The propeller designer was provided with the nominal wake fields for both model and full-scale hulls, as well as the flow field with propeller. Once the nominal wake field has been obtained, the transformation to effective wake can be obtained, for instance, by the method of Kinnas, Choi, Kosal, Young and Lee (1999), a 3-D steady Euler procedure using a finite-volume method coupled with a vortexlattice method. It is believed that viscosity plays a major role in developing the nominal wake, but contributes very little to the interaction between the rotational inflow and the propeller action. Choi (2000) (see also Choi and Kinnas, 2000a, 2000b and 2001) developed a fully 3- D unsteady Euler solver using a finite-volume scheme and the pressure correction method. The propeller was analyzed by the vortexlattice method and then modeled via unsteady body-force terms in the Euler equations. Predicted cavity shapes and unsteady velocity fields were compared with data measured in a cavitating propeller experiment, with good agreement. They suggested an improved body-force model including blade thickness for future research. That approach would also allow for a consistent representation of unsteady cavity shapes within the Euler-equation solver. Jensen et al. (2001) also used a similar procedure for calculation of effective wake. Calculation of Propeller Flow and Cavitation With the onset flow given, the flow over the propeller, whether fully wetted or cavitating, is usually computed with vortex-lattice or boundary-element methods. At present, published RANS methods are limited to steady, fully wetted (noncavitating) propeller analysis.

22 438 The Specialist Committee on Cavitation Induced Pressures 23rd International Kinnas, Choi, Kosal Young and Lee (1999) compared a vortex-lattice and a panel method, both state-of-the-art (MPUF-3A and PROPCAV). The methods include among other things hub effect, sheet cavitation, and wake alignment. It was shown that the two methods agreed well with each other and with experiments. The authors suggested, however, that the faster vortex-lattice method be used for predicting overall forces and cavity characteristics with acceptable accuracy, and the panel method for more-accurate local-flow and pressure computations. In general, tunnel wall effects are neglected when computing the cavitation extent and volume on a propeller operating in the water tunnel. Those effects are, however, important, comprising blockage that may need to be corrected for when applying model results to full-scale conditions and when validating computer programs using model test results. It was shown by Choi and Kinnas (1997) that the tunnel wall effects were significant in their computations and that the predicted cavity extent was in better agreement with the measurements when the tunnel wall boundary conditions and a downstream flux boundary condition were included. Further investigation of tunnel wall effects on cavity-induced pressure was made by Kimball et al. (1997). They extended the numerical method of Choi and Kinnas (1997) by including tunnel upstream and downstream conditions based on a continuity argument relating to the cavity volume flux. The computed tunnel wall pressure using that method was unrealistically high. To circumvent the difficulty, they developed some ad hoc boundary conditions for the upstream and downstream lids. They also tried a boundary condition on the tunnel windows by assuming that the pulsating cavity flux was uniformly absorbed by the vibrating Plexiglas window of the MIT tunnel test section. Although those new boundary conditions appear to be physically sound, the predicted tunnel wall pressure was significantly different from the measured values. They recommended that effects of tunnel vibration and acoustic impedance be studied more thoroughly to better understand the discrepancy between the numerical predictions and experimental measurements. They also suggested that the compressibility effect might need to be accounted for. Szantyr (2000) reviewed the state-of-theart of analytical methods for predicting propeller cavitation and its consequences. The methods comprised lifting-surface and boundary-element methods, with RANS briefly mentioned. Cavitation models included inception, sheet, bubble and cloud, and vortex cavitation. For the latter type, the double-layer lifting-surface model was mentioned as a moresophisticated approach to tip vortex cavitation that should be well suited for incorporation into a boundary-element model. Comparisons between numerical and experimental results were shown for cavitation inception, cavitation extent and induced pressures, obtained by vortex-lattice and boundary-element methods. Kinnas and Pyo (1999) carried out theoretical analyses of a cavitating propeller to examine the effects of blade wake-alignment modeling. The wake model without alignment gave propeller forces that were underpredicted, whereas the cavity extent and volume were not affected appreciably. The predicted wake shape with full wake alignment compared well with the measured shape. All methods predicted the forces with acceptable accuracy, especially in the range of design advance ratio. Those calculations were done for uniform inflow. The examination also included the propeller in inclined inflow. Wake alignment was shown to influence the blade forces as well as the cavity volume history. Pyo and Suh (2000) used a low-order potential-based boundary-element method to predict the flow around a cavitating propeller in steady or unsteady inflow. Hyperboloidal panel geometry and a modified split-panel method were used to improve the solution behavior near the tip. They applied the method

23 23rd International Proceedings of the 23rd ITTC Volume II 439 to a number of cavitating hydrofoils and propellers in uniform and nonuniform inflow; results agreed with those from other numerical methods and published experiments. Kinnas et al. (2001) presented a vortexlattice method to predict the performance of two-blade-row propulsors, including the effects of sheet cavitation. The effective wake for each component was determined via an unsteady Euler solver (Choi, 2000) in which both components were represented by body forces. An axisymmetric solver was used to predict the mean performance of a contrarotating propulsor and of a pre-swirl stator/rotor combination. A non-axisymmetric method was used for flow behind the preswirl stator. A sample unsteady sheet cavity was computed on the rotor blades operating in the pre-swirl wake. More validations, especially for unsteady cavitating performance, are required to validate the method for each blade row of a two-stage propulsor. Cavitating Foils Many models for cavitating propeller flow are first developed and tested on 2-D or 3-D hydrofoils, to avoid the complication of propeller geometry and of rotating flows. Current published efforts have focused on improvement of cavitation models on lifting surfaces. These efforts concentrate mainly on profiles, either 2-D or 3-D. These activities can be subdivided into two classes, of which one uses potential-flow methods, typically boundary-element techniques. Only sheet cavitation can be treated in this way since, according to Kuiper (2001), for a long time the (sheet) cavity has been considered as a single valued volume of vapour attached to the surface which can be calculated by potential flow methods. This requires an artificial closure condition at the trailing edge of the cavity. Extensions with effects of viscosity included via boundary layer and with cavitating tip vortex have also been reported. Esposito and Salvatore (2000) considered optimization of propeller blade sections by genetic algorithms. The aim of the optimization was to reduce cavity extent, optionally combined with drag reduction. The hydrodynamic model was validated with other numerical results and with experiments. Comparisons between cavity shapes and pressure distributions for initial and optimized configurations were shown. Salvatore and Esposito (2001a) used a boundary-element model to analyze partial sheet cavitation on a 3-D hydrofoil, using a closed-cavity nonlinear model. Viscous effects via boundary layer were included, as well as wake alignment. Results for extent of cavitation as well as tip vortex location compared well with results from other experiments and calculations. Salvatore and Esposito (2001b) used a viscous/inviscid technique to take into account viscosity effects in sheet cavitation on propellers. First the inviscid cavitating flow was modeled by a boundary-element approach including a sheet cavitation model. Comparisons with experiments for a propeller in uniform inflow showed that the radial extent of the cavity was predicted accurately, whereas the chordwise extent was overestimated. Subsequently a viscous-flow correction was made by 2-D boundary layer theory over strips of the propeller blade. Calculations were carried out for a 3-D hydrofoil. The results were in good agreement with experimental observations, demonstrating that viscosity effects are fundamental for determining the exact location of the cavity detachment position. A validation was reported underway for the case of propellers. Krisnaswamy et al. (2001) addressed partial sheet cavitation on a two-dimensional hydrofoil with special attention to the re-entrant jet. A boundary-element method (BEM) was used. Calculated jet, cavity thickness and cavity shapes were compared with other numerically obtained results from the literature. Pres-

24 440 The Specialist Committee on Cavitation Induced Pressures 23rd International sure distributions, calculated including effects of viscosity, were in good agreement with published experimental data. Achkinadze and Krasilnikov (2001) used a velocity-based boundary-element method to compute partial cavities on hydrofoils and propeller blades. The method used iterative cavity alignment with free cavity length and miscellaneous (closed/open) cavity closure models. The results obtained were in agreement with experiments and with results of o- ther authors. Ando and Nakatake (2001) used the simple surface-panel method SQCM (Source and Quasi-Continuous vortex-lattice Method) for unsteady sheet cavitation on a hydrofoil of finite span. The cases examined included a partially cavitating hydrofoil in heave motion, as well as partially cavitating and supercavitating hydrofoils in a sinusoidal gust. Results were compared mainly with calculations of other authors, confirming the accuracy of the method. Kinnas, Lee and Mueller (1999) considered cavitation on a non-rotating propeller blade. They used a BEM and examined the influence of walls as in a cavitation tunnel. The cavitation model was fully 3-D sheet, and included face in addition to back cavitation. A model for a developed tip vortex cavity was also presented. Lee and Kinnas (2001) used a BEM for modeling unsteady blade sheet and developed tip vortex cavitation. The fully wetted problem was solved and the wake surface aligned, including the trajectory of the tip vortex cavity core. The shapes of the blade sheet and tip vortex cavities were determined. Applications comprise simplified 2-D vortex, 3-D elliptic wing and propeller blades in inclined and nonaxisymmetric inflows. For the hydrofoil, the computed trajectory of the tip vortex core agreed well with experiments. For one propeller, good agreement was found between observed and predicted cavity shapes near the tip, and with clear convergence in the prediction, unlike prediction without modeling the tip vortex cavity. For a second propeller, the BEM with full wake alignment gave more accurate unsteady blade forces than a vortexlattice method, based on experiments. This method would potentially be able to predict the unsteady tip vortex cavitation and the resulting hull pressure. CFD techniques are used to study cavity flows in greater detail than can be treated with potential methods. In reported work, the Navier-Stokes equations were coupled with a cavity model, most often on the volumefraction or volume-of-fluid basis. The majority of papers reviewed addressed 2-D problems. This way of computing cavity flows is an extension of calculations with viscosity (RANS). Such calculations for propellers are mainly limited to the steady case. Further development in computer technology and software will no doubt be required before an unsteady calculation is possible. An intermediate step toward fully unsteady calculations may be coupling of panel and RANS methods. Chahine and Hsiao (2000) coupled an unsteady RANS code and a potential code (BEM) to model unsteady sheet cavities in three dimensions. The RANS code was used to describe the turbulent viscous flow around the blade, while the BEM code was used to describe the unsteady and nonlinear cavity free surface. The method was used to study sheet cavitation dynamics on a straight and a twisted elliptical hydrofoil. Hosangadi et al. (2001) presented a multiphase model for gas-liquid mixtures where cavitation was modeled via a finite-rate source term that initiated phase change. Results included a cavitating NACA 66 hydrofoil. Good comparison was obtained with experimental data. In particular, the details of the cavity closure and the re-entrant jet were captured well.

25 23rd International Proceedings of the 23rd ITTC Volume II 441 Tamura et al. (2001) modeled cavitation using the dynamics of bubbles, representing the gas phase as groups of many small and locally uniform cavitation bubbles. They applied their procedure to 2-D and 3-D profiles, obtaining qualitative agreement with experiments. Lohrberg et al. (2001) considered the unsteady cavitating flow in a cascade of three hydrofoils. They modeled the liquid-vapor mixture as a homogenous medium, and described it as a single fluid with varying specific mass and with a simple description of the vaporization and condensation. The RANS equations were then solved for this single fluid. Experiments were also conducted, and comparisons between numerical and experimental results were given. Iga et al. (2001) calculated 2-D unsteady cavity flow in a cascade, with particular attention to instability phenomena of the sheet cavity in transient cavitation and to the mechanism of the break-off phenomenon. The gasliquid mixture of finite bubbles was approximated as an infinite number of infinitesimal bubbles with the same void fraction. The local mixture condition of the cavity was specified in each computational cell. The governing 2- D compressible Navier-Stokes equations were then solved. Comparisons with experiment confirmed that the method was fairly effective in predicting the time-averaged characteristics of single and cascade hydrofoils in noncavitating and cavitating conditions. The method also simulated strong unsteady cavity flows well. Song and Qin (2001) applied a compressible Navier-Stokes code and a virtual singlephase equation of state to cavitating flows a- bout a 2-D hydrofoil. They addressed bubble cavitation, bubble/cloud cavitation, sheet/cloud cavitation and supercavitation. No comparisons with experiments were presented. Arndt et al. (2000) carried out an integrated numerical/experimental investigation of sheet cavitation and its transition to cloud cavitation. The simulation methodology was based on large-eddy simulation using a barotropic phase model to couple the continuity and momentum equations. Excellent agreement with experiments was found. Berntsen et al. (2001) used a commercial CFD code, Fluent 5, to investigate flows over a 2-D hydrofoil from inception to supercavitation. They also performed calculations for a 3- D hydrofoil with elliptical planform. Special focus was placed on tip vortex strength and lift variation with cavitation number. Both were well predicted based on experimental data. Senocak and Shyy (2001) developed a pressure-based algorithm to compute turbulent sheet cavitating flows. Their model used single-fluid Navier-Stokes equations with a volume fraction transport equation. Applications included cavitation over a 2-D hydrofoil. The overall behavior, including the pressure distribution and cavity shape, was consistent with experimental results. Hull Pressure Calculations With the flow field from the propeller known in terms of potential and velocity, it is straightforward to compute the pressure at any point in an unbounded fluid by the unsteady Bernoulli equation. This is the basis for the application of solid-boundary factors representing the mirror effects of the hull and free surface. Alternatively, acoustic modeling can be applied. Also, a more-accurate calculation of the hull surface pressure will require the solution of the diffraction problem. Bloor and Kinns (2000) used acoustic boundary-element modeling techniques to examine cavitation-induced hull excitation. They considered a simplified, rigid ship hull and modeled the cavitating propeller as a stationary, fluctuating monopole source whose

26 442 The Specialist Committee on Cavitation Induced Pressures 23rd International strength was related to the varying cavity volume. This technique was also used to examine the effect of shaft rotation direction (inward/outward) in twin-screw ships (Kinns and Bloor, 2000). The simplifications in the model (hull and propeller) were made to aid understanding of how hull excitation is influenced by cavitation location and oscillation frequency, and to illustrate application of boundary-element techniques. The authors plan to use the same techniques for realistic hull designs. Nakatake et al. (2000) considered the pressure induced on a flat plate above a wing in a sinusoidal gust. The wing was represented by source distributions on the surface and discrete vortex distributions on the camber surface. The pressure on the flat plate was calculated by four different methods: mirror image, solid boundary factor, source distribution (on the plate) and quasi-continuous vortex, where the plate is treated as a thin wing. They considered both 2-D and 3-D cases for the foil in a gust with and without varying thickness, modeling the effects of a timevarying cavity. No model test results were given. They concluded that the solidboundary-factor and mirror-image methods are less applicable. Empirical Methods Few empirical methods for calculation of hull pressures have recently been reported. Koushan et al. (2000) gave results of their empirical method for predicting pressure pulses due to a noncavitating and a cavitating propeller. They used an artificial neural networks method for analyzing a database that consists of 359 measurements for the singlescrew case and 155 for twin-screw. Applications of Numerical Methods There were also found in the recent literature notable applications of numerical methods, often supplemented by experiments. These applications dealt with practical problems for naval architects and propeller hydrodynamicists, including designing an optimum propeller for a given ship with respect to efficiency and pressure signature, providing data for a structural vibration analysis, and evaluating unconventional propulsors. The methods used were not necessarily new, although generally state-of-the-art, and had been previously evaluated with respect to accuracy. Meyne et al. (2000) described the design procedure for the propellers for a series of large reefer container ships. They detailed the specifications, design considerations, and test results including powering, cavitation performance, and vibration excitation with three different model propellers. The pressure pulses were predicted by an empirical method as well as by lifting-surface theory. Results from measurements in the large cavitation tunnel HYKAT were also presented. The numerical method used did not predict the same details observed during the experiments. However, the cavitation behavior of the three propellers, the differences in cavitation behavior, and the hull pressures were generally well predicted. Kawakita and Hoshino (1999) described a design system for marine propellers with new blade sections. The propeller flow was analyzed with a lifting-surface method (Quasi- Continuous Method) coupled with a procedure for minimizing cavitation. For instance, the pressure distributions on the back side of the propeller were prescribed as flatter and higher at the section leading edge than those of NACA blade sections. Results of cavitation tests show generally lower pressure peaks for the cases presented. Jensen et al. (2001) presented a survey of propeller cavitation performance measured at model and full scale, supplemented with calculations. The calculations were made with a panel method and a simple model of the sheet cavitation extent. The effective wake was calculated with a procedure similar to that of Choi and Kinnas (2000b). The hull-pressure

27 23rd International Proceedings of the 23rd ITTC Volume II 443 pulses and integrated forces were calculated by including the combined hull-propeller image diffraction problem. Cavitating as well as noncavitating contributions to the pressure distributions were shown. Two different propeller designs were evaluated, turning both inward and outward. Maximum calculated pressure pulses were found to be considerably higher than the contribution from cavitation, but the spatial extension was greater for the cavitation contribution. Only sheet cavitation was dealt with. Furthermore, structural considerations were outlined in the paper. Andersen et al. (2000) showed results of measured and calculated pressure amplitudes on a ship hull due to Kappel (tip fin) and conventional propellers. The calculations were made by a BEM for the noncavitating propeller coupled with 2-D calculations for the cavitating blade sections. Comparisons with experiments were shown but were less satisfactory in some cases. Takinaci and Atlar (2002) assessed the performance of a thrust-balanced propeller, where the pair of blades can rotate together about the spindle axis. They use a liftingsurface model for a conventional fixed-pitch propeller with cavitation, coupled with a simplified model of the pitching blades. Results included cavitation extent and hull pressures. The concept needs to be proved through physical model tests, which are planned to be done in a cavitation tunnel. Onofrei et al. (2000) described a method for predicting unsteady pressures and surface forces on wide flat-afterbody ships, especially in cavitating conditions, in early stages of a ship project. The theory relied on a number of simplifications including lifting-line modeling with lifting-surface correction factors, 2-D profile theory for cavitating sections and solid-boundary factors. Good correlation with experiment at the first and the second bladerate frequency was found Experimental Work Kimball et al. (1997) presented measurements of the fluctuating pressure on the tunnel wall above a cavitating propeller operating in a screen-generated wake. They reported that the tunnel-wall vibration could have a significant influence on the fluctuating pressure measured on the tunnel wall. It was suggested that the effect of tunnel vibration be subtracted from the measured pressure to isolate the pure cavitation effect. Korkut et al. (2000) explored the effect of free-stream turbulence on tip vortex cavitation inception and noise generation. Free-stream turbulence was controlled in a cavitation tunnel using different wire mesh screens. Results pointed out that free-stream turbulence is an important parameter influencing cavitation inception. The effect on cavitation inception was found to be similar to that of leading edge roughness. Ingenito et al. (2000) performed LDV measurement in the wake of an installed propeller. The velocity field during the propeller revolution was resolved and was correlated with the pressure measured on the hull. The correlation function between the velocity at a point and the pressure on the hull showed the importance of the tip vortex in the generation of pressure fluctuations, including for noncavitating conditions. Johannsen (2000) showed the importance of simulating the 3-D inflow to the propeller when measuring pressure fluctuation. Such simulation enables determining the effect of propeller rotational direction on cavitationinduced pressure, and the effect of adoption of a vortex-generation fin for pressure-pulse reduction. Such studies were cited as examples of studies that can be performed only in a large cavitation facility using a full-ship model. Friesch (2000) reviewed the capability for pressure pulse tests in the HYKAT cavitation

28 444 The Specialist Committee on Cavitation Induced Pressures 23rd International tunnel, based on model-full scale correlation during the past ten years of operation. Atlar et al. (2001) presented the noise measurement on a fisheries research vessel propeller. The results were extrapolated to full scale using the scaling law recommended by 18th ITTC and compared with full-scale measurements. Kuiper (2001) reviewed the broadband excitation due to a bursting tip vortex. He mentioned that the broadband excitation can only be captured by narrow-band analysis of time series. Kimball et al. (2001) presented detailed flow measurements on a stationary 3-D hydrofoil, representing a typical modern naval propeller blade, in the MIT water tunnel. The detailed structure of the tip vortex flow was measured using LDV and documented for cavitating and non-cavitating conditions. The information will be useful for the validation of numerical modeling of tip vortex flow and cavitation. 7. GENERAL TECHNICAL CONCLUSIONS Propeller-excited hull pressure fluctuations are strongly influenced by intermittence of sheet cavitation, the dynamics of tip vortex cavitation, and the statistical properties of the cavitation. On modern propellers, tip vortex cavitation may be even more important than sheet cavitation for hull pressure fluctuation. The influence of turbulence and blade surface roughness on cavitation-induced pressure fluctuations is still not quantifiable. Both experimental and numerical procedures for predicting propeller excitation need to be validated using results of sophisticated full-scale investigations. In model-scale testing, the levels of unsteady pressure amplitudes can be seriously affected by the size of the facility test section (blockage effects), the method of wake simulation, and operation at very low Reynolds number. Model-scale measurements should also consider the influence of experimental boundary conditions: solid-boundary factors, hull vibration, and free-surface effects, before comparison with full-scale pressure levels. High-frequency excitation due to tip vortex cavitation must be considered during testing. Measurement of unsteady hull pressures at full and model scale should be accompanied by propeller cavitation viewing and hullsurface vibration measurements. Calculations are done mostly with vortexlattice or panel methods, and in most cases only sheet cavitation is included. With the propeller and cavity flows obtained, hullpressure fluctuation predictions are made generally based on the unsteady Bernoulli equation. The influence of the unsteady effective wake on the pressure fluctuations is not considered realistically in the present calculation methods. RANS simulations are still not able to predict unsteady cavitation correctly. But the trend of CFD applications toward 2-D and 3- D cavitating hydrofoils shows the great potential of those codes for propeller applications as well. For all numerical predictions, potential methods as well as RANS, it is important that the cavitation simulation is fully unsteady, particularly if higher harmonics are aimed at. Propeller design procedures should be capable of handling problems with higherharmonic frequency excitation in addition to minimizing blade-rate pressure fluctuations.

29 23rd International Proceedings of the 23rd ITTC Volume II RECOMMENDATIONS TO THE CONFERENCE Cavitation, Pasadena, CA, USA. Web Site: Adopt the Procedure, Propulsion; Cavitation-Induced Pressure Fluctuations, Numerical Prediction Methods Adopt the Procedure, Propulsion; Cavitation-Induced Pressure Fluctuations, Model Scale Experiments REFERENCES Achkinadze, A.S., and Krasilnikov, V.I., 2001, A velocity based boundary element method with modified trailing edge for prediction of the partial cavities on the wings and propeller blades, Proc. CAV2001, 4th Int. Symp. on Cavitation, Pasadena, CA, USA. Web Site: Andersen, P., Andersen, S.V., Bodger, L., Friesch, J., and Kappel, J.J., 2000, Cavitation considerations in the design of Kappel propellers, Proc. NCT 50 Int. Conf. on Propeller Cavitation, Newcastle upontyne, United Kingdom. Ando J., and Nakatake, K., 2001, Calculation of three-dimensional unsteady sheet cavitation by a simple surface panel method SQCM, Proc. CAV2001, 4th Int. Symp. on Cavitation, Pasadena, CA, USA. Web Site: Arndt, R., Song, C., Kjeldsen, M., He, J., and Keller, A., 2000, Instability of partial cavitation: a numerical/experimental approach, Proc. 23rd Symp. on Naval Hydrodynamics, Val de Reuil, France. Atlar M., Takinaci, A.C., Korkut, E., Sasaki, N., and Aono, T., 2001, Cavitation Tunnel Test for Propeller Noise of a FRV and Comparison with Full Scale Measurement, Proc. CAV2001, 4th Int. Symp. on Baiter, H.-J., Grüneis, F., and Tilmann, P., 1982, An extended base for the statistical description of cavitation noise, Proc. Int. Symp. on Cavitation Noise, ASME, Phoenix, AZ, USA, pp Bark, G., 1992, On the scaling of propeller cavitation noise with account of scale effects in the cavitation, Proc. Int. Symp on Propulsors and Cavitation, Hamburg, Germany, STG-Nr Berntsen, G.S., Kjeldsen, M., and Arndt, R.E.A., 2001, Numerical modeling of sheet and tip vortex cavitation with Fluent 5, Proc. CAV2001, 4th Int. Symp. on Cavitation, Pasadena, CA, USA. Web Site: Bloor, C., and Kinns, R., 2000, Development of acoustic boundary element models for the prediction of fluctuating hull forces due to propeller, Proc. NCT 50 Int. Conf. on Propeller Cavitation, Newcastle upon- Tyne, United Kingdom. Breslin, J.P., and Andersen, P., 1994, Hydrodynamics of Ship Propellers, Cambridge University Press, Cambridge, United Kingdom. Breslin, J.P., Van Houten, R.J., Kerwin, J.E., and Johnsson, C.-A., 1982, Theoretical and experimental propeller-induced hull pressures arising from intermittent blade cavitation, loading and thickness, Trans. SNAME, vol. 90, pp , USA. Catley, D., 1984, The mathematical modelling of ship hydroelastics, Proc. Int. Symp. on Ship Vibrations, Genoa, Italy. Chahine, G., and Hsiao, C.-T., 2000, Modeling 3D unsteady sheet cavities using a coupled UnRANS-BEM code, Proc. 23rd Symp. on Naval Hydrodynamics, Val de

30 446 The Specialist Committee on Cavitation Induced Pressures 23rd International Reuil, France, pp Choi, J.K., 2000, Vortical Inflow - Propeller Interaction Using an Unsteady Three- Dimensional Euler Solver, Ph.D. Thesis, Department of Civil Engineering, The University of Texas at Austin, Austin, TX, USA. Choi, J.K., and Kinnas, S., 1997, Numerical Propeller Tunnel, Proc. SNAME Propellers/Shafting 97 Symposium, Virginia Beach, VA, USA. Choi, J.K. and Kinnas, S. (2000a), Nonaxisymmetric Effective Wake Prediction by Using an Unsteady Three Dimensional Euler Solver, Proc. Propellers/Shafting 2000 Symposium, Virginia Beach, USA. Choi, J.K., and Kinnas, S., 2000b, An unsteady 3-D Euler solver coupled with a cavitating propeller analysis method, Proc. 23rd Symp. on Naval Hydrodynamics, Val de Reuil, France. Choi, J.K., and Kinnas, S., 2001, Prediction of non-axisymmetric effective wake by a three-dimensional Euler solver, J. of Ship Research, Vol. 45, No. 1, pp Esposito, P.G., and Salvatore, F., 2000, Optimal design of cavitating blade sections by genetic algorithms, Proc. NCT 50 Int. Conf. on Propeller Cavitation, Newcastle upontyne, United Kingdom. Friesch J., 2000, Ten Years of Research in the Hydrodynamics and Cavitation Tunnel HYKAT of HSVA, Proc. NCT 50 Int. Conf. on Propeller Cavitation, Newcastle upontyne, United Kingdom. Friesch, J., and Johannsen, C., 1992, Correlation Investigations in the New Hydrodynamics and Cavitation Tunnel (HYKAT), STG/HSVA International Symposium on Propulsors and Cavitation, Hamburg, Germany. Frivold, H., 1976, Solid boundary factors for the after-body of an LNG carrier, Norwegian Maritime Research, no. 1, pp Hoekstra, M., de Jager, A., and Valkhof, H.H., 2001, Viscous flow calculations used for dredger design, Proc. 8th Int. Symp. on Practical Design of Ships and Mobile Units (PRADS 2001), pp Hosangadi, A., Ahuja, V., and Arunajatesan, S., 2001, A generalized compressible cavitation model, Proc. CAV2001, 4th Int. Symp. on Cavitation, Pasadena, CA, USA. Web Site: Huse, E., 1970, Hull vibrations and measurements of propeller induced pressure fluctuations, Int. Shipbuilding Progress, vol. 17, no. 187, pp Huse, E., and Guoqiang, G., 1982, Cavitation-induced excitation forces on the hull, Transactions, SNAME, vol. 90, pp Iga, Y., Nohmi, M., Goto, A., Shin, B.R., and Ikohagi, T., 2001, Numerical study of sheet cavitation break-off phenomenon on a cascade hydrofoils, Proc. CAV2001, 4th Int. Symp. on Cavitation, Pasadena, CA, USA. Web Site: Ingelsten, C., and Johansson, M., 1997, Cavitation mechanisms and noise for a propeller series, (Report in Swedish), Chalmers Univ. of Tech. Dept. of Naval Arch. and Ocean Eng. Göteborg, Sweden. Ingenito G., Costanzo, M., and Di Felice, F., 2000, A Phase Sampling Technique for Pressure Fluctuation Analysis, IX Cong. of the Int. Maritime Assoc. of Mediterranean, Ischia Italy. Jensen, J.S., Sørensen, A.R., and Rasmussen, U.M., 2001, Recent experience in cavitation performance and structural vibrations for fast ferries, Proc. 2nd Int. Euro Conf.

31 23rd International Proceedings of the 23rd ITTC Volume II 447 on High-Performance Marine Vehicles (HIPER 01), Hamburg, Germany. Johannsen, C., 1998, Investigation of propeller induced pressure pulses by means of high speed video recording in the threedimensional wake of a complete ship model, Proc. 22nd Symp. on Naval Hydrodynamics, Washington, DC, USA. Johannsen, C., 2000, Recent Consideration on Dealing with Propeller Induced Hull Pressure Pulse, NAV2000, Venice, Italy. Johnsson, C.-A., Rutgersson, O., Olsson, S., and Björheden, O., 1976, Vibration Excitation Forces from a Cavitating Propeller, Model and Full Scale Tests on a High Speed Container Ship, Proc. 11th Symposium on Naval Hydrodynamics, London, United Kingdom. Johnsson, C.-A., 1983, Simple methods for first estimate of propeller induced pressure fluctuations and vibration, Proc. PRADS 83, Tokyo, Japan, and Seoul, Korea, pp Kaplan, K., Bentson, J., and Benatar, M., 1982, Analytical prediction of pressures and forces on a ship hull due to cavitating propellers, Proc. 14th Symp. on Naval Hydrodynamics, Ann Arbor, MI, USA. Kawakita, C., and Hoshino, T., 1999, Design System of Marine Propellers with New Blade Sections, Proc. 22nd Symp. on Naval Hydrodynamics, Washington, DC, USA, pp Kehr, Y.-Z., Hsin, C.-Y., and Sun, Y.-C., 1996, Calculations of pressure fluctuations on the ship hull induced by intermittently cavitating propellers, Proc. 21st Symp. on Naval Hydrodynamics, Trondheim, Norway, pp Kim, S.E., 2001, A Numerical Investigation of Three-Dimensional Turbulent Shear Flow Around a Ship Hull at Straight Maneuver, Proc. ASME FEDSM 01. Kimball, R.W., Choi, J.K., and Kinnas, S., 1997, Experimental and Numerical Study of Propeller Induced Tunnel Pressures, Proc. ASME Symp. on Marine Hydrodynamics and Ocean Eng., Vol.14, pp , Dallas, TX, USA. Kimball, R.W., Sura, D., and Harness, M., 2001, Velocity Measurements around a Cavitating Tip Vortex on a 3-D Hydrofoil using Laser Doppler Velocimetry, Proc. 26th American, Webb Institute, Glen Cove, NY, USA. Kinnas. S.A., Choi, J.K., Kakar, K., and Gu, H., 2001, A General Computational Technique for the Prediction of Cavitation on Two-Stage Propulsors, Proc. 26th American, Webb Institute, Glen Cove, NY, USA. Kinnas, S.A, Choi, J.K., Kosal, E.M, Young, J., and Lee, H., 1999, An integrated computational technique for the design of propellers with specified constraints on cavitation extent and hull pressure fluctuations, Proc. Int. CFD Conf. (CFD 99), Ulsteinvik, Norway. Kinnas, S., Lee, H., and Mueller, A., 1999, Prediction of Propeller Blade Sheet and Developed Tip Vortex Cavitation, Proc. 22nd Symp. on Naval Hydrodynamics, Washington, DC, USA. Kinnas, S. A., and Pyo, S., 1999, Cavitating propeller analysis including the effects of wake alignment, Journal of Ship Research, Vol. 43, No. 1, pp Kinns, R., and Bloor, C., 2000, The effect of shaft rotation direction on cavitationinduced vibration in twin-screw ships, Proc. NCT 50 Int. Conf. on Propeller Cavitation, Newcastle upontyne, United Kingdom.

32 448 The Specialist Committee on Cavitation Induced Pressures 23rd International Korkut, E., Atlar, M., and Odabasi, A.Y., 2000, Effect of the Viscous Scale on the Inception of Cavitation and Noise of Marine Propeller, Proc. NCT 50 Int. Conf. on Propeller Cavitation, Newcastle upon- Tyne, United Kingdom, pp Koushan, K., Halstensen, S.O., and Sandtorv, L.G., 2000, Systematic investigation of blade design influence on cavitation performance and on induced pressure pulses, Proc. NCT 50 Int. Conf. on Propeller Cavitation, Newcastle upontyne, United Kingdom, pp Krisnaswamy, P., Andersen, P., and Kinnas, S.A., 2001, Re-entrant jet modelling for partially cavitating two dimensional hydrofoils, Proc. CAV2001, 4th Int. Symp. on Cavitation, Pasadena, CA, USA. Web Site: Kuiper, G., 2001, New developments around sheet and tip vortex cavitation on ships propellers, Proc. CAV2001, 4th Int. Symp. on Cavitation, Pasadena, CA, USA. Web Site: Larsson, L., Stern, F., and Bertram, V. (eds), 2000, Göteborg 2000 Workshop on Numerical Ship Hydrodynamics, Göteborg, Sweden. Lee H., and Kinnas, S.A., 2001, Modeling of unsteady blade sheet and developed tip vortex cavitation, Proc. CAV2001, 4th Int. Symp. on Cavitation, Pasadena, CA, USA. Web Site: Lohrberg, H., Stoffel, B., Fortes-Patella, R., and Reboud, J.L., 2001, Numerical and experimental investigations on the cavitating flow in a cascade of hydrofoils, Proc. CAV2001, 4th Int. Symp. on Cavitation, Pasadena, CA, USA. Web Site: Meyne, K., Praefke, E., and Koop, K.H., 2000, The development of the propeller design for the world s largest reefer container ships, Proc. Propellers/Shafting 2000 Symposium, SNAME, pp Nakatake, K., Ohashi, K., and Ando, J., 2000, Pressure fluctuation on finite flat plate above wing in sinusoidal gust, Proc. 23rd Symp. on Naval Hydrodynamics, Val de Reuil, France, pp Nilsson, A.C., 1980, Propeller induced hull plate vibrations, J. of Sound and Vibration, vol. 69, part 4, pp Onofrei, G., Iorga, G., and Ceanga, V., 2000, Study on fluctuating pressure field induced by the propeller on the hull structure, Proc. NCT 50 Int. Conf. on Propeller Cavitation, Newcastle upontyne, United Kingdom. Pyo, S.W., and Suh, J.C., 2000, Modified split panel method applied to the analysis of cavitation propellers, Journal of Ship and Ocean Technology, The Society of Naval Architects of Korea, Vol. 4, No. 2. Salvatore, F., and Esposito, P.G., 2001a, An improved boundary element analysis of cavitating three-dimensional hydrofoils, Proc. CAV2001, 4th Int. Symp. on Cavitation, Pasadena, CA, USA. Web Site: Salvatore, F., and Esposito, P.G., 2001b, Numerical analysis of cavitating propellers including viscous flow effects, Proc. 8th Int. Symp. on Practical Design of Ships and Mobile Units (PRADS 2001). Senocak, I., and Shyy, W., 2001, Numerical simulation of turbulent flows with sheet cavitation, Proc. CAV2001, 4th Int. Symp. on Cavitation, Pasadena, CA, USA. Web Site: Song, C.C.S., and Qin, Q., 2001, Numerical simulation of unsteady cavitating flows,

33 23rd International Proceedings of the 23rd ITTC Volume II 449 Proc. CAV2001, 4th Int. Symp. on Cavitation, Pasadena, CA, USA. Web Site: Sunnersjö, C.S., 1982, Propeller induced pressure fluctuations and vibrations Model and full scale measurements on F/R Argos, SSPA Report No , Göteborg, Sweden. Sunnersjö, C.S., Brännström, K.G., and Janson, C.-E., 1984, Modal hull properties for a small ship A comparison of Vlassov-Timoshenko beam theory and two-dimensional FEM modelling with full scale measurements, Proc. Int. Symp. on Ship Vibrations, CETENA, Genoa, Italy. Sunnersjö, C.S., and Janson, C.-E., 1987, Hydrodynamic inertia and damping of ship hull vibrations, Trans. Royal Inst. of Naval Architects, vol. 130, pp Szantyr, J.A., 2000, Analytical methods for prediction of propeller cavitation and its consequences, Proc. NCT 50 Int. Conf. on Propeller Cavitation, Newcastle upon- Tyne, United Kingdom, pp Takinaci, A.C., and Atlar, M., 2002, Performance assessment of a concept propulsor: the thrust-balanced propeller, Ocean Engineering, Vol. 29, No 2, pp Tamura, T., Sugiyama, K., and Matsumoto, Y., 2001, Cavitating flow simulations based on the bubble dynamics, Proc. CAV2001, 4th Int. Symp. on Cavitation, Pasadena, CA, USA. Web Site: Tsakonas, S., Breslin, J.P., and Jacobs, W.R., 1962, The vibratory force and moment produced by a marine propeller on a long rigid strip, J. Ship Research, March Weitendorf, E.A., and Tanger, H., 1992, Cavitation correlation and nuclei investigations in two water tunnels Comparisons in the HYKAT and the medium size tunnel, Cavitation, Proc. of the Institution of Mechanical Engineers, ImechE , Cambridge, United Kingdom. Wereldsma, R., 1981, Experiments and interpretation of propeller vibratory hull pressures on an elastic structure of a ship model, Int. Shipbuilding Progress, Vol. 28, No Wilson, M., 1991, Selected Elementary Criteria for Evaluating Propeller Induced Surface Force Excitation, Phil. Trans. Royal Soc., Vol. 334, London, UK, pp

34 450 The Specialist Committee on Cavitation Induced Pressures 23rd International APPENDIX A. RESPONSES TO THE QUESTIONNAIRE ON NUMERICAL METHODS

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38 454 The Specialist Committee on Cavitation Induced Pressures 23rd International APPENDIX B. RESPONSES TO THE QUESTIONNAIRE ON EXPERIMENTAL METHODS

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