Numerical assessment of underwater noise radiated by a cruise ship

Transcription

1 Ships and Offshore Structures, Numerical assessment of underwater noise radiated by a cruise ship Maria Paola Salio DITEN, University of Genoa, Genoa, Italy (Received 16 December 2011; final version received 19 March 2013) The present paper deals with a methodology for the prediction of propeller-induced acoustic pressures and associated ship response, having considered propellers as the main acoustic source onboard ships. Semi-empirical and numerical approaches have been coupled for the characterisation of the propeller and the determination of the radiated acoustic field, respectively. The boundary element method has been used for numerical analyses, and a commercial solver has been adopted. The procedure has been applied to a cruise ship, and numerical results have been compared to the available experimental measurements. Other two different ships have been taken into account in order to test the methodology. Results show that the influence of the structural finite element mesh of the ship on the computation is comparable to acoustic characterisation of the propeller. Furthermore, it is found that the reliability of semi-empirical methods is not completely satisfactory; nevertheless, they are currently used at an early design stage as common practice. Keywords: underwater acoustics; ship noise; boundary element method (BEM) coupled with finite element method (FEM) Introduction In the frame of subjects concerning naval architecture and marine engineering, acoustics is playing more and more a leading role and becoming a ruling design criterion in all aspects of noise control, both onboard ships and underwater. An effective noise reduction represents a characteristic element of a ship, as well as an important competitiveness factor and at the same time a challenging design aspect. Propellers are the main source of excitation inducing underwater noise and vibration on ship structures, and reliable estimates of generated noise are more and more required. For passenger ships, comfort is a ruling design criterion and noise and vibration reduction is a main concern. In the past few years, new regulations were issued by classification societies for the assignment of additional class notations (i.e. Comfort Class), which set standards for acceptable noise and vibration levels for different types of vessels and vessel compartments and provide different class notations based on the level of performance as measured against these standards. Class notations are mainly based on the international standard for the assessment of ship noise (IMO 1981) and the international guidelines for the evaluation of vibration on merchant ships (ISO 2000). Particularly, IMO standards (1981) establish defined noise limits in different areas of merchant vessels in order to avoid ear damage, noise-induced fatigue and sleep discomfort. ISO standards (2000) assume the frequency-weighted root mean square (RMS) velocity level (or weighted broadband level) as vibration limiting criteria; they replaced the old ISO standards (1984), which adopted a single narrow band frequency response, corresponding to the first two harmonics of the propeller blade rate frequency and performed on a modal basis up to 30 Hz. Furthermore, underwater noise has recently been identified as a harmful form of pollution to marine life and ecosystems and is receiving increasing attention from scientists, policy-makers and the public opinion. Presently, there are no rules of international law that specifically address the transmission of sound through the ocean and this lack has stimulated intense controversy. However, international institutions have begun to recognise the threat that intense ocean noise poses to marine life and have been calling for caution in the generation of anthropogenic ocean noise. Among the existing documents, including noise within the possible threats for the marine fauna, there are the Agreement on the Conservation of Small Cetaceans of the Baltic and North Seas (ASCOBANS 1992) and the Agreement on the Conservation of Cetaceans of the Black Sea, Mediterranean Sea and Contiguous Atlantic Area (ACCOBAMS 1996). However, it is worth pointing out that they only mention ships as a source without directly facing the problem of noise due to ship traffic. Within the IMO, a working group dealing with the impact of ships underwater noise on marine mammals started in 2007 (IMO 2007, 2009a, 2009b, 2010). In the above context, a procedure able to evaluate underwater-radiated noise levels as well as noise and vibration induced on the ship by the propeller pressure field can be a valuable tool for estimating the environmental impact of the ship and the comfort levels onboard, both in the mpsalio@tor.it C 2013 Taylor & Francis

2 2 M.P. Salio design phase and later on to integrate data from onboard measurements. The present study, developed in the frame of a Ph.D. research activity carried out at the Department of Naval Architecture and Electrical Engineering (DINAEL) of the University of Genoa, deals with the implementation of a numerical methodology for the prediction of propeller excitation and associated ship response. The direct boundary element method (BEM) has been used, taking into account the presence of the free surface: both uncoupled BEM and coupled BEM/structural finite element method (FEM) analyses have been carried out and applied to the whole ship. In the second kind of analysis, the dynamic response of the structure is taken into account. A semi-empirical approach has been adopted in order to give the propeller characterisation in terms of elementary equivalent acoustic sources. The commercial code LMS-SYSNOISE R (LMS 2003) has been used for all the numerical simulations. The paper is organised as follows. The first section is devoted to a survey of different methodologies for the prediction of propeller-induced pressure fluctuations, with emphasis on the semi-empirical methods proposed by Holden et al. (1980) and De Bruijn et al. (1986). Then, a presentation of the mathematical formulation of the acoustic problem is given, with a short description of the main numerical solution techniques, focusing on the BEM. A preliminary validation of the proposed procedure for predicting ship underwater-radiated noise is reported and the main results are discussed. The validation consisted of two steps, concerning an ellipsoid, both in submerged and floating conditions, and a cruise ship, respectively. For the cruise ship, particularly, different combinations of elementary acoustic sources have been considered and then a propeller equivalent acoustic source, which has been characterised by means of semi-empirical methods, has been taken into account. Comparisons with results coming from analyses carried out on two different ships, a mega-yacht and a patrol vessel, are finally presented and some conclusions about the finite element mesh building criteria are reported. Lessons learned and future developments are eventually briefly resumed in the last section of the paper. Prediction of the propeller-induced acoustic pressure field The prediction of the fluctuating pressure field is of great importance, especially at an early stage of the design (Besnier et al. 2005), in order to provide the designer with results needed to anticipate problems when freedom to change hull shapes, aft body configuration and propeller design and blade number exist. In the design phase, mostly nothing more is known but the propulsion power, rotation speed, diameter of the propeller, etc.; hence methods presented in the literature have to be taken into account. These methods can be divided into empirical and semi-empirical, numerical and experimental procedures. Empirical and semi-empirical methods represent a cheap and easy tool to describe the induced hull pressures at an early design stage. They are based on the comparison of a great number of experimental data taken from ships of the same type. Afterwards, the most significant parameters for describing the phenomenon are obtained by statistical regression. Typical of these methods are those proposed by Holden et al. (1980) (see the next sections for more details), Choi et al. (2004) and Holtrop (1979). More complete works aiming at better covering double propeller propulsion and broadband were developed by De Bruijn et al. (1986) (see the next sections for more details) and Raestad (1996). Numerical simulations represent a complex method and should be reserved for novel designs where a higher computational effort is justified. For instance, Kinns et al. (2002) adopted a new approach based on the Helmholtz equation to compute the cavitation-induced hull pressures. This methodology appears to be an alternative strategy with respect to the traditional approach based on the solution of the Bernoulli equation for unsteady irrotational flow governed by the Laplace equation. Testa et al. (2008) proposed a comparison between a classical hydro-acoustics formulation based on the Bernoulli equation, with a general hydro-acoustics formulation based on the solution of the Ffowcs-Williams and Hawkings equation. In spite of continuous and important progresses in performances and accuracy of numerical simulation, experimental methods are considered essential in the design process. Accurate predictions are possible by model testing also for non-conventional propeller designs; however, they are quite expensive and it is not easy to carry out tests during an early design stage due to lack of information and very often just minor modifications are possible after the tests due to a tight time schedule. Prediction method proposed by Holden (first two harmonics) The method developed by Holden et al. (1980) permits an evaluation of hull-induced pressures at the two lowest blade rate frequencies, for both non-cavitating and cavitating conditions. A conventional propeller is considered and a complete and precise definition of its geometry and the wake-field distribution is required. For the non-cavitating propeller, it is assumed that the main contribution to the pressure fluctuations on the hull comes from the thickness and the number of blades, whereas the influence of dynamic loading on the blades is neglected. Regarding cavitating conditions, the loading variation expressed by J 1 J M, as the difference between the maximum and mean advance ratios, is considered as the most significant parameter determining the level of pressure amplitudes of blade frequency. The given formulas are for the calculation of pressure amplitudes in kp/m 2.

3 Ships and Offshore Structures 3 A simplified procedure was reported by Carlton (1994), which is valid for the determination of hull-induced pressures at the first blade rate frequency. Two different formulas are reported, relevant to non-cavitating and cavitating pressures, respectively. The total pressure impulse, which combines the two components acting on a local part of the submerged hull, is then found from p z = (p p2 c), (1) where p 0 and p c are the non-cavitating and cavitating components, respectively, expressed in Pa. This methodology has been proven extremely fruitful in the selection of the propeller geometry in the design stage, but, as previously explained, it is only related to the first two harmonics. Hence, the audible noise cannot be predicted by this method, since for the higher harmonics it does not seem accurate any more. It is worth pointing out that methods of this type are particularly useful as a guide to the expected pressures. They should not, however, be regarded as a definitive solution, because differences, sometimes quite substantial, will occur when correlated with full-scale measurements. For example, Equation (1) gives results having a standard deviation of the order of 30% when compared to the base of measurements from which it was derived. Prediction method proposed by De Bruijn (broadband) De Bruijn et al. (1986) presented a method which is very much related to Holden s. It attempts to predict the ship propeller cavitation noise, which is assumed to be one of the most important sources of underwater noise and noise aboard the ship, above the lowest blade rate frequencies, namely between 30 and 500 Hz (broadband). The concept of equivalent monopole is introduced, based on the observation that the noise generated in water appears to be mainly due to cavitation volume variations. On vessels with a sharp wake non-uniformity, this dominant volume variation component of the pressure may be approximated by an oscillating monopole source fixed in a position below the ship s hull, radiating the free field pressure p = ρf U 2r, (2) where ρ is the density of the medium (water), U is the cavitation volume velocity, f is the frequency and r is the distance from the monopole to the observation point. The source strength may also be expressed in terms of a sound pressure at a fictitious distance of 1 m. From the statistical analysis of a large number of hydrodynamical parameters, only two parameters have been selected as the most significant: the logarithm of the dimensionless torque K Q and a parameter depending on the blade geometry F. The first one gives an indication about the quality of the propulsion configuration, being a measure for the propeller load, whereas the second one indicates how far a cavitation criterion exceeds, since the reference blade area which is taken into account appears to be a function of the thrust coefficient, cavitation number, the effective wake field and the pitch. The final formula takes into account several corrections in order to make the volume velocities dimensionless, to eliminate the influence of the blade rate frequency and to obtain a similarity of radiated power. Numerical acoustics The adiabatic propagation of longitudinal waves in a homogeneous, inviscid fluid is governed by the linear acoustic wave equation (Desmet and Sas 2008): 2 p 1 2 p C 2 t = ρ q 2 0 t, (3) where 2 = is the Laplace operator, p is x 2 y 2 z 2 the total acoustic pressure field, c is the phase speed of a longitudinal wave, ρ 0 is the mass density and q is the volume velocity per unit volume induced by the external acoustic source. Most of the acoustic design studies may be confined to the analysis of the steady-state acoustic response to a time-harmonic excitation at a certain circular frequency ω = 2πf. In this case, the acoustic response also has a harmonic time dependence at the same frequency and the wave equation (3) transforms into the linear Helmholtz equation 2 p + k 2 p = jρ 0 ωq, (4) where k = ω/c = 2πf /c is the acoustic wave number at frequency ω; the corresponding wavelength is λ = 2π/k = 2πc/ω = c/f. Exact analytical solutions of the Helmholtz partial differential equation and the associated boundary conditions exist only for a very limited number of acoustic problems, involving radiating structures with simple geometrical shapes. For general, complex configurations, only approximate solutions can be obtained. The most commonly used approach for finding an approximate solution of the Helmholtz equation and the associated boundary conditions is based on the transformation of this mathematical model into a set of approximating (algebraic) equations, which are amenable to numerical solution procedures. Based on their frequency range of application, numerical methods can be classified as follows:

4 4 M.P. Salio low-frequency prediction techniques: Boundary element method (BEM) Finite element method (FEM) high-frequency prediction techniques: Statistical energy analysis (SEA) Geometrical acoustics. In the present study, the involved phenomena are characterised by a low-frequency range. Hence, it is possible to narrow the field down to BEM and FEM techniques. From the analysis of the main properties of the two methods, two important features may be identified regarding the computational loads for solving acoustic problems (Desmet 2008). Since acoustic finite element models are sparsely populated and symmetric and since their matrix coefficients, which are real and frequency independent for the stiffness and mass matrices, result from simple numerical integrations, the construction of these models takes only a minor part of the total computational effort; most of the computational effort is spent on solving the large models for the unknown degrees of freedom. The computational effort for solving acoustic boundary element models for the unknown boundary degrees of freedom benefits from the small model sizes; however, the construction of these models requires a substantial amount of computational effort, since the matrices in acoustic boundary element models are fully populated, complex, frequency dependent and, for the case of direct boundary element models, non-symmetric and since singular integral evaluations are encountered in the calculation of their matrix coefficients. As a result, when comparing the total computational loads of both methods, the BEM can hardly compete with the finite element method (FEM) for solving interior acoustic problems. Therefore, the FEM is usually preferred for studying the acoustic field in complex enclosures. The strength of the BEM becomes mainly apparent for solving acoustic problems in unbounded domains, such as the exterior acoustic radiation or scattering from vibrating structures. Based on the above-mentioned considerations, the ship underwater-radiated noise prediction being an exterior acoustic problem defined in an unbounded fluid domain, the BEM was adopted as the numerical solution technique. Boundary Element Method The BEM is based on the direct or indirect boundary integral formulation of the considered problem, depending on the type of acoustic problem (Desmet 2008). The term direct indicates that the boundary variables, i.e. the pressure and normal velocity distributions on the boundary surface, have a direct physical meaning. Note that, since the direct boundary integral formulation requires that the boundary surface be closed, it can only represent either an interior or an exterior pressure field, but not a combined interior/exterior field. This is the case concerning the analysis of the ship underwater-radiated noise, since the ship hull represents the closed boundary surface and the acoustic problem is solved in an unbounded fluid domain. The term indirect indicates instead that the boundary variables do not represent any direct physical quantities of the pressure field. These formulations relate the distributions of the field variables in the continuum domain to the distribution of some problem-related boundary variables on the boundary surface of the domain. In this way, the BEM follows a two-step procedure. In the first step, the distributions of the boundary variables are determined. In the second step, the field variables in any point in the continuum domain are obtained from the boundary integral formulation, using the boundary surface results of the first step. Similar to the FEM, the BEM is based on two concepts for solving the first-step boundary problem: transformation of the boundary problem into a collocational (direct) or variational (indirect) formulation; approximation of the boundary surface geometry and the boundary variables in terms of a set of shape functions, which are locally defined within small subsurfaces ( boundary elements ) of the boundary surface. The application of the element concept allows the transformation of the original problem of determining field variable distributions on the boundary surface into a problem of determining the boundary surface field variables at some discrete positions within each boundary element, which results in a numerically solvable set of algebraic equations. Coupled vibro-acoustic problems For coupled vibro-acoustic problems, an acoustic and a structural problem must be solved simultaneously to include the mutual coupling interaction between the fluid pressure and the structural deformation (Desmet 2008). The FEM is usually applied for the prediction of the structural response, while the direct or indirect BEM can be applied for the prediction of the acoustic response. In a coupled FE/direct BE model, particularly, for interior or exterior coupled vibro-acoustic systems with a closed boundary surface, an acoustic direct BE model with nodal boundary pressure and boundary normal velocity degrees of freedom is used for the prediction of the steadystate acoustic response on the closed boundary surface of the fluid domain and a structural FE model with nodal translational and rotational displacement degrees of freedom is used for the prediction of the steady-state dynamic displacement of the middle surface of the elastic shell structure.

5 Ships and Offshore Structures 5 Validation of the procedure for assessing the ship underwater-radiated noise Preliminary analyses have been carried out in order to understand the phenomena which come into play, i.e. radiated acoustic pressure fields by different combinations of elementary acoustic sources, the definition of a free-surface condition and the dynamic response of the structure. Capabilities and reliability of the applied commercial code (LMS 2003) have been studied as well and the obtained results are presented here. According to a study proposed by Kinns et al. (2002), a simple geometry of a generic axisymmetric ellipsoid has been considered first. Dimensions, calculation frequencies and source positions have been adopted in agreement with the cited study. Analyses of both submerged and floating half-submerged bodies have been carried out; in this last case, a free-surface condition has been defined by imposing a zero value of pressure on the horizontal plane of symmetry of the body. Unitary monopoles and dipoles have been used as underwater acoustic sources. Ellipsoid has been considered, first, as a rigid body and an uncoupled direct-bem analysis has been carried out: this means that an acoustic analysis is performed. Afterwards, the ellipsoid has been studied as an elastic body, taking into account the effects due to the fluid structure interaction, and a coupled direct-bem/structural FEM analysis has been realised, i.e. a vibro-acoustic analysis. To this aim, a modal analysis has been conducted by means of the commercial FEM code MSC-NASTRAN R (MSC 2007a). Results have been obtained in terms of the solid boundary factor (SBF), i.e. the ratio between the total and the incident pressure field magnitude at a point on the surface. This quantity has been calculated along the line on the top surface of the ellipsoid defined by the intersection with the longitudinal plane. Calculations have been carried out at frequencies equal to f = 187.5, 375, 750, 1500 Hz, which correspond to the following wavelengths: λ = 8d, 4d, 2d, d, where d represents the ellipsoid longitudinal diameter. It is worth pointing out that this choice is consistent with the continuation of the present study represented by the analysis of the ship. If the ship breadth is taken into account, the corresponding wavelengths will be related to frequencies that are similar to the first blade rate frequency harmonics for the considered ship type. With respect to the Kinns et al. (2002) study, good agreement has been found, especially for the half-submerged body. In this paper, only the main results related to the floating body are shown; for more detailed information about the analyses performed, see Annicchiarico et al. (2008) and Salio (2010). As an example, the SBF curves plotted against the longitudinal x-axis are shown in Figure 1 for a floating ellipsoid with a monopole located aft of the body at a distance 0.20d forward of stern waterline and at a depth of 0.10d below the hull surface. Considering uncoupled analysis, at all the considered frequencies, the SBF is equal to zero at the ellipsoid s end points, increases as frequency increases and the presence of a peak near the stern can be noticed. A local minimum near the stern is also noticed at the two highest frequencies, especially at 1500 Hz. As already stated, good agreement can be noticed with the cited study in terms of SBF values (as expected, SBF 2 for locations on the hull near the acoustic source), as well as concerning the presence of the abovementioned local minimum near the stern. Furthermore, a more regular trend of SBF curves has been obtained near the bow, in particular concerning the highest frequency. The results about coupled analysis, which has not been carried out by Kinns et al. (2002), show that all SBF curves have an oscillatory trend, with increasing values as the distance from the source increases and a presence of more pronounced peaks at f = 375 Hz. As previously mentioned, a twin-screw cruise ship with L/B = 6.977, B/T = 4.335, C B = and Fn = has been subsequently considered. The acoustic boundary element model (BEM mesh) has been realised by means of the commercial code I-DEAS R (Siemens PLM Software 2007) from the structural mesh (FEM mesh) created with MSC-PATRAN R (MSC 2007b). The FEM mesh uses 61,034 elements to represent the whole ship model, whereas the BEM mesh, consisting of 2810 elements, describes the submerged hull only, with no stiffeners considered (see Figure 2). As in the case of the ellipsoid, both uncoupled and coupled analyses have been carried out. In the last case, a dry modal basis up to 60 Hz with 7255 dry modes has been calculated, the maximum frequency being limited by the definition of the adopted FEM mesh. As previously explained concerning the half-submerged ellipsoid, a freesurface condition has been defined as well. Several calculations have been carried out in order to characterise the input acoustic sources for the acoustic propagation code in a proper and correct way. Problems with increasing complexity have been studied, considering at each configuration both total and incident acoustic pressure field. At the beginning, uncoupled analyses have only been performed. The first analysis concerned hull-induced acoustic pressure field generated by one monopole located on the port side of the ship. Calculations without a free-surface condition showed a higher value of the acoustic pressure field in comparison with calculations in the presence of a freesurface condition. This is correct from a theoretical point of view, since the free-surface condition makes the monopole act as a vertical dipole. As the second step, a couple of in-phase monopoles have been taken into account and higher acoustic pressure levels have been estimated at midship. This is due to the interaction between the monopoles. Several phase shifts have also been considered.

6 6 M.P. Salio (a) Solid Boundary Factor Monopole at 0.20d, 0.10d -uncoupled analysis- 2 SBF f=187.5 f=375 f=750 f=1500 SBF (b) x Solid Boundary Factor Monopole at 0.20d, 0.10d -coupled analysis x f=187.5 f=375 f=750 f=1500 Figure 1. SBF with respect to the x-axis position for the floating ellipsoid with monopole placed aft of the ellipsoid at 0.20d forward of stern waterline and at a depth of 0.10d below the hull surface. Uncoupled (a) and coupled (b) problems. Finally, coupled analyses have been carried out and the resulting total acoustic pressure field (coupled field) has been compared with the total uncoupled acoustic pressure field (uncoupled field) and the incident acoustic pressure field (incident field). Results showed that the coupled field has a regular trend which is similar to the uncoupled field. Furthermore, as it can be reasonably presumed, the related acoustic pressure values are smaller than the uncoupled field values, but higher than incident field ones. For more details about the above-reported analysis, see Salio (2010). Test case: a cruise ship As a test case for the application of the proposed underwater noise prediction procedure, the same cruise ship considered in the analyses described in the previous section has been adopted. As an acoustic source, the actual propeller has been considered and its main characteristics have been used to define the equivalent elementary source by means of the semi-empirical methodologies reported above (Holden et al. 1980; De Bruijn et al. 1986). In particular, the source strength as a function of the frequency of equivalent monopoles (one for each propeller) has been obtained in order to give a simulation of propeller behaviour. Concerning Holden s procedure, it is worth pointing out that it was not possible to apply the original formulation because of lack of information about propeller geometry and wake field. The simplified procedure reported in Carlton (1994) has been adopted instead. This formulation takes

7 Ships and Offshore Structures 7 Figure 2. Cruise ship: structural FEM mesh (a) and acoustic BEM mesh (b).

8 8 M.P. Salio into account a lesser amount of parameters, which is actually similar to those adopted by De Bruijn s method. In particular, Holden s method has been used for the first harmonic of the blade rate frequency (equal to Hz) and De Bruijn s method for the third harmonic of the blade rate frequency (equal to 34.29, which is comprised in the 1/3 octave band whose centre frequency is equal to 31.5 Hz). As already mentioned, the maximum frequency has been limited by the definition of the adopted FEM mesh, which allowed computing a dry modal basis up to 60 Hz. Equivalent monopoles have been located at the hub, regarding Holden s method, whereas the position of the maximum cavitation volume has been taken into account concerning De Bruijn s method. The last assumption agrees with Kinns et al. (2002). It must be noticed that it was not possible to locate the monopole source with sufficient precision because of lack of information about the wake. According to data related to similar vessels reported by Kinns and Bloor (2004), as a first attempt, the source has been located on the periphery of the propeller disc, 40 inboard of the top dead centre. Other positions of the source have been considered as well. Some examples of results in terms of acoustic pressure fields distribution at the third harmonic of the blade rate frequency on the ship hull and on a transversal plane located at the propeller position, respectively, are reported in Figure 3. Figure 4 shows the comparison between acoustic pressure field distributions at the first and the third harmonic of the blade rate frequency on the ship hull and on the symmetry plane. Both figures refer to vibro-acoustic analysis results. From the analysis of Figures 3 and 4, characteristic radiation lobes generated by propeller and hull vibration can be noticed. In particular, it can be observed that the propellerinduced pressure field is predominant with respect to the hull contribution in the far field, and in the near field, lobes due to hull vibration are well visible instead. Figure 5 reports some results in terms of directivity diagrams, both at the first and at the third harmonic of the blade rate frequency. In particular, horizontal directivity diagrams at radii equal to 500, 1000, 2000 m, respectively, and vertical diagrams relevant to radii equal to 500, 1000 and 3000 m, respectively, are shown. Finally, participation diagrams with the corresponding modal shapes which mostly contribute to the response are shown in Figure 6. These diagrams refer to the modal participation factor (MPF), which is a factor related to the frequencies at which the calculation has been carried out. According to the use of the mode superposition method, this quantity is considered in order to state which natural vibration modes make a significant contribution to the system s response. Results have also been compared to experimental measurements made in depressurised towing tank. In particular, available data regard pressure pulse measurements by means of pressure sensors on the model hull, which are located at different transversal positions. Results concerning three transversal sections are reported here: particularly, one in correspondence to the propeller location, one fore of the propeller location and one aft of the propeller location. From the analysis of Figure 7, which shows the comparison between numerical and experimental results in the case of the first harmonic of the blade rate frequency (application of Holden s method) and in terms of dimensionless RMS acoustic pressure values with respect to the starboard transverse coordinate, it can be noticed that results are not completely satisfactory for all the positions considered. In this case, RMS acoustic pressure has been adimensionalised with respect to the maximum experimental pressure value at each section. In particular, the agreement is better near the propeller and in correspondence to points aft of the propeller location itself, whereas differences increase considerably in the fore parts considered. It has been noticed that a factor 3 exists between numerical and experimental results at the propeller position, and calculations carried out taking into account this correction are also reported in Figure 7. This factor seems to be in agreement with results which have been previously experienced with similar vessels, and it could be explained with the approximation which characterises the simplified Holden method. As mentioned above, in the fore sections the errors seem higher; this may be related to the definition of the FEM mesh rather than an erroneous characterisation of the acoustic source. As previously stated, the FEM mesh definition limited the vibro-acoustic analysis frequency range at 31.5 Hz. Furthermore, the hull seems to amplify the pressure more than expected, and this feature could also be related to a rough definition of the internal reinforced structure. Actually, ordinary stiffeners were not modelled and shell elements of the FEM model were consequently made stiffer in a fictitious way by increasing the ratio between bending stiffness and membrane stiffness homogeneously on the whole model. On the other hand, however, the discrepancies could also be due to a different response of the actual ship structure with respect to the model used during experimental measurements, which presents a more homogeneous structure without stiffeners. Figure 8 shows the comparison between experimental and numerical results at the third harmonic of the blade rate frequency (application of De Bruijn s method), in terms of dimensionless RMS acoustic pressure values with respect to the starboard transverse coordinate. Again, RMS acoustic pressure has been adimensionalised with respect to the maximum experimental pressure value at each section. With respect to the previous results obtained by means of Holden s method, better agreement can be noticed. Numerical results still overestimate experimental measurements, but noticeably less, and it was not necessary to apply a correction factor as in the previous case. At the aft section only, underestimates of the same entity may be noticed.

9 Ships and Offshore Structures 9 Figure 3. Acoustic pressure field distribution on the ship hull (a) and on a transversal plane located at the propeller position (b), respectively, from the vibro-acoustic analysis carried out at the third harmonic of the blade rate frequency. Pressure values expressed in terms of RMS acoustic pressure in Pa.

10 10 M.P. Salio Figure 4. Comparison between acoustic pressure fields on the ship hull and on the symmetry plane from the vibro-acoustic analysis carried out at the first (a) and at the third (b) harmonic of the blade rate frequency, respectively. Acoustic pressure values expressed in db.

11 Ships and Offshore Structures 11 Figure 5. Comparison between horizontal (a and c) and vertical (b and d) directivity diagrams from the vibro-acoustic analysis carried out at the first (a and b) and at the third (c and d) harmonic of the blade rate frequency. Acoustic pressure values expressed in Pa. Comparison with other test cases Other two test cases have been consequently chosen in order to investigate the underwater noise prediction procedure by comparing results relevant to the cruise ship with other numerical evaluations. Available data regarded two ships with different characteristics: a mega yacht and a patrol vessel. Mega yacht main data are L/B = 5.668, B/T = 3.479, C B = and Fn = Its FEM and BEM available models are constituted by 95,110 and 8062 elements, respectively (see Figure 9). Patrol vessel main data are L/B = 6.925, B/T = 3.554, C B = and Fn = 0.459, whereas FEM and BEM models, which are shown in Figure 10, have 10,993 and 1264 elements, respectively. The available experimental measurements were carried out in a depressurised tank for the mega yacht and during sea trials concerning the patrol vessel. For the mega yacht, it must be noticed that difficulties occurred in the FEM model computational management because of the high number of elements. Therefore, as in the case of the cruise ship, but for opposite reasons, again the analysis frequency range was limited. Particularly, it was possible to carry out the modal analysis up to 30 Hz: hence, coupled vibro-acoustic analysis has been carried out at the first harmonic of the blade rate frequency only (21.8 Hz). This modal basis should be considered insufficient anyway, since the maximum uncoupled structural resonance frequency is recommended to be at least times higher than the maximum frequency limit for the coupled analysis. Concerning the patrol vessel, the available FEM mesh was too coarse: for this reason, in this case as well, the modal analysis was limited to a frequency equal to 30 Hz. Consequently, coupled vibro-acoustic analysis was carried out at the first harmonic of the blade rate frequency only ( Hz). At the first assessment, vibro-acoustic analysis results about the mega yacht showed a better numerical experimental correspondence with respect to the cruise ship. A deeper analysis has been carried out and also the incident acoustic pressure field has been taken into account. It has been noticed that this one is higher than the total coupled acoustic pressure field in the whole domain. This is without physical relevance because it means that the calculated acoustic pressure field does not take into account the field which is reflected by the hull structure. Moreover,

12 12 M.P. Salio Figure 6. Participation diagrams relevant to the first (a) and the third (c) harmonic of the blade rate frequency with the corresponding modal shapes which mostly contribute to the response (b and d) (vibration mode No. 187 at Hz and No at Hz). the incident field seems to be attenuated by the hull structure itself, probably because of numerical problems. Results concerning the patrol vessel show the same behaviour with respect to the mega yacht and again the total coupled acoustic pressure field is smaller than the incident one. In this case, however, the reason may be the coarse definition of the FEM mesh: probably, it is not sufficient even to carry out a modal analysis up to 30 Hz and the results coming from the coupled vibro-acoustic analysis are consequently erroneous. It is worth pointing out that, in the latter case, experimental data are referred to the ship scale and no direct comparisons are possible with the other two ships, since the actual dynamic behaviour of the hull structure must be taken into account. A comparison among results concerning the three studied ships is shown in Figure 11 in terms of dimensionless RMS acoustic pressure values with respect to the starboard transverse coordinate, RMS acoustic pressure being adimensionalised with respect to the maximum experimental pressure value. The transversal section in correspondence to the propeller location has been taken into consideration. Results at the first harmonic of the blade rate frequency are reported and refer to both the uncoupled and the coupled analysis. The incident acoustic pressure field has also been taken into account in all the three cases. The uncoupled and the incident acoustic pressure field can be taken as a reference first, since they are not connected with the FEM mesh and the modal basis. Analysing cruise ship and mega yacht plots together, it can be noticed that a factor comprised between 0.5 and 1 exists between the incident and the experimental acoustic pressure field, while the ratio between the uncoupled field and the experimental field is in the range of The ratio of the coupled field to the experimental field is between 2 and 2.5 for the cruise ship, whereas it is about 0.2 for the mega yacht. It is important to say that for the cruise ship only the total coupled acoustic pressure field is correctly higher than the incident one. For the patrol vessel, the factors between the uncoupled and the incident acoustic pressure field with the experimental one are smaller with respect to the other two cases (about 1 2 for the uncoupled one and about 0.5 for the incident one), but it is similar to the mega yacht if the coupled acoustic pressure field is considered instead. Considerations about FEM mesh and modal analysis An analysis of the three test cases revealed another important subject which has been investigated during a

13 Ships and Offshore Structures 13 (a) First harmonic Propeller section 3 pexp max RMS [Pa] 2 1 coupled coupled_corrected experimental y [m] (b) pexp max RMS [Pa] (c) pexp max RMS [Pa] First harmonic Aft section y [m] First harmonic Fore section coupled coupled_corrected experimental coupled coupled_corrected experimental y [m] Figure 7. Cruise ship: comparison between experimental and numerical (coupled analysis) dimensionless pressures, with the direct application of the Holden method and with the application of a dividing factor equal to 3 as well. Results at the first harmonic of the blade rate frequency with respect to the starboard transverse coordinate, transversal section at the propeller position (a), aft of the propeller location and (b) forward of the propeller location (c). subsequent study, i.e. the FEM mesh definition. As already mentioned, this part is necessary to carry out the modal analysis in order to import the dry modal basis into the coupled BEM analysis and, consequently, to take into account the dynamic behaviour of the structure. The study was focused on those aspects which contribute to the mesh definition, that is to say mesh refinement and element stiffness. The influence of the maximum structural resonance frequency on the coupled analysis frequency has been investigated as well. It is worth pointing

14 14 M.P. Salio (a) Third harmonic Propeller section pexp max RMS [Pa] coupled_40deg coupled_20deg coupled_0deg exp y [m] (b) pexp max RMS [Pa] (c) pexp max RMS [Pa] Third harmonic Aft section y [m] Third harmonic Fore section coupled_40deg coupled_20deg coupled_0deg exp coupled_40deg coupled_20deg coupled_0deg exp y [m] Figure 8. Cruise ship: comparison between experimental and numerical (coupled analysis) dimensionless pressures with the application of the De Bruijn method, several source positions considered. Results at the third harmonic of the blade rate frequency with respect to the starboard transverse coordinate, transversal section at the propeller position (a), aft of the propeller location and (b) forward of the propeller location (c). out that the FEM mesh was already existent in all the three cases, but it was built for different purposes. Therefore, the three meshes were realised with different modelling strategies. As a characteristic parameter about refinement, as a first attempt, the ratio between the total number of elements of the mesh and the ship length multiplied by the ship breadth has been considered. The following results have

15 Ships and Offshore Structures 15 Figure 9. Mega yacht: structural FEM mesh (a) and acoustic BEM mesh (b).

16 16 M.P. Salio Figure 10. Patrol vessel: structural FEM mesh (a) and acoustic BEM mesh (b).

17 Ships and Offshore Structures 17 (a) CRUISE SHIP First harmonic f=11,4 Hz pexp max RMS [Pa] Holden_Carlton uncoupl Holden_Carlton coupl Holden_Carlton inc experimental y [m] (b) pexp max RMS [Pa] (c) MEGA YACHT First harmonic f=21,8 Hz y [m] PATROL VESSEL First harmonic f=15.9 Hz Holden_Carlton uncoupl Holden_Carlton coupl Holden_Carlton inc experimental pexp max RMS [Pa] Holden_Carlton uncoupl Holden_Carlton coupl Holden_Carlton inc experimental y [m] Figure 11. Comparison among experimental, uncoupled, coupled and incident acoustic pressure field for the three test cases. Results are represented in terms of dimensionless values with respect to the starboard transverse coordinate and refer to the transversal section at the propeller position. Analyses were carried out at the first harmonic of the blade rate frequency applying the Holden-Carlton method.

18 18 M.P. Salio (a) Modal basis up to 50 Hz FEM meshes with different stiffnesses 2.5 pincident RMS [Pa] uncoupl coupl_e coupl_10e coupl_100e coupl_1000e inc (b) pincident RMS [Pa] y [m] Modal basis up to 60 Hz FEM meshes with different stiffnesses Y [m] uncoupl coupl_e coupl_10e coupl_100e coupl_1000e inc Figure 12. Mega yacht: comparison among uncoupled, coupled and incident acoustic pressure field. Concerning coupled field, the bending to membrane stiffness ratio was multiplied by 10 and several factors (1, 10, 100 and 1000) were applied to the tensile modulus. Results are represented in terms of dimensionless values with respect to the transversal section at the propeller position. Modal basis up to 50 Hz (a) and 60 Hz (b) are considered respectively. been obtained: about 7 for the cruise ship, about 75 for the mega yacht and about 12 for the patrol vessel. As previously explained about the cruise ship, ordinary stiffeners were not modelled and shell elements were consequently made stiffer in a fictitious way by increasing the ratio between bending stiffness and membrane stiffness homogeneously on the whole model. Conversely, for the mega yacht and the patrol vessel, ordinary stiffeners were modelled and no ratio between bending stiffness and membrane stiffness of elements was applied. From this first comparison and considering the results discussed in the previous sections, it seems that very detailed meshes of the whole ship structure are not necessary and even a possible source of error. On the other hand, as in the case of the cruise ship, applying the same ratio between bending stiffness and membrane stiffness of elements on the whole model seems to be a too approximate solution, since modal basis is reduced and information about some local modes is therefore lost. This information appears to be important instead in order to simulate with sufficient accuracy the actual dynamic behaviour of the ship structure, especially the local behaviour of the ship stern, where a comparison with experimental measurements is carried out.

19 Ships and Offshore Structures 19 As the second parameter, the element stiffness has been analysed and several tests have been performed by increasing Young s modulus (E) of each shell element (10, 100, 1000 times, respectively). It must be said that this test does not represent a guideline for the definition of FEM meshes, but it has to be considered for study purposes. As the test case, the mega yacht FEM mesh has been adopted, the patrol vessel one being too coarse and not suitable to obtain a sufficiently wide modal basis. Before increasing Young s modulus, a ratio between bending stiffness and membrane stiffness equal to 10 has been applied in order to act as a filter for unreal local modes. This implies that a wider modal basis can be obtained, so that the first harmonic of the blade rate frequency can be covered. Furthermore, the resulting reduced number of modes is suitable to be imported into the acoustic prediction code. With reference to Figure 12, dimensionless RMS acoustic pressure values (with respect to the maximum incident acoustic pressure value) are shown. It can be noticed that, at both the two maximum resonance frequencies considered (50 Hz and 60 Hz), as Young s modulus increases, the total coupled acoustic pressure trend appears quite irregular at E multiplied by 1 and 10, appears more regular at E multiplied by 100 and becomes similar to the uncoupled total acoustic pressure trend at E multiplied by At the same time, acoustic pressure values increase and become comparable to the uncoupled ones. However, behaviour at the two frequencies seems quite different. Actually, at 60 Hz, acoustic pressure values are higher than at 50 Hz at the two smallest Young s moduli (E multiplied by 1 and 10) and smaller (even smaller than the incident acoustic pressure values) at E multiplied by 100. From these results, it also appears that the maximum resonance frequency (i.e. the modal basis) plays a very important role in the calculation. On the basis of the above considerations, deeper studies and further research developments appear necessary. It would be interesting to focus on the realisation of an FEM mesh with the aim of carrying out the modal analysis and importing the modal basis into the coupled BEM analysis. Therefore, guidelines and recommendations could be consequently defined. Results showed that an FEM model with a sufficient mesh refinement in way of ship stern (both shell and internal structure) and shell elements characterised by equivalent stiffness (as in the case of the cruise ship) in the remaining part of the ship should be used. However, particular attention must be paid in order to verify that numerical problems do not occur. Conclusions In this study, a procedure to assess the ship underwaterradiated noise has been proposed. The ship propeller has been considered as the main acoustic source onboard a ship, and semi-empirical methodologies have been chosen for its acoustic characterisation. A numerical approach based on BEM solution techniques has been adopted for the prediction of the radiated acoustic pressure field, carrying out both uncoupled acoustic (DBEM) and coupled vibro-acoustic (DBEM/FEM) analyses by means of a commercial solver. For propeller acoustic characterisation by means of semi-empirical methods, the obtained results may be considered acceptable, but not completely satisfactory. Nevertheless, these methods are currently used at an early design stage as common practice. It is worth pointing out that the adopted methods are based upon statistical data which are not up-to-date so that they do not probably take into account the latest developments that happened in the marine field in the frame of acoustic emission reduction. As explained in detail in the previous sections, in many cases, overestimated acoustic pressure values are a consequence of it. This result was confirmed by an experimental campaign which was carried out during Ph.D. activities at the cavitation tunnel of the Department of Naval Architecture and Electrical Engineering (DINAEL). In this framework, a hydrophone was used for experimental measurements of propeller underwater noise. For more details about this activity, which had to be omitted here for the sake of shortness, see Salio (2010). On the basis of the above considerations, it appears that a wide and up-to-date experimental database would be a necessary and an invaluable tool in order to deeply investigate the reliability and capability of semi-empirical methods. It would be interesting to create different groups of data based on the kind of measurements (for example, model/ship scale; depressurised tank/cavitation tunnel/sea trials; etc.) and even on result sources, so that possible errors due to different experimental procedures or environmental conditions could be taken into account. Moreover, a refinement of the FEM structural mesh appeared to be very important with regard to its capability to influence the acoustic prediction procedure. A preliminary analysis has been carried out, but the study is still at an early stage and needs further developments. Other test cases would be necessary with a complete set of input data. Furthermore, it would be interesting to continue the analysis carrying out experimental tests on simple models first, in order to define the analysis of phenomena, and subsequently considering a more and more complex object. On the one hand, experimental modal analysis could be carried out for understanding the dynamic behaviour of the structure; on the other hand, defined acoustic sources could be measured first, and then numerical simulation could be performed. Particularly, for the definition of the FEM mesh, it would be useful to subdivide the problem into subsequent more and more complex phases, in order to identify and investigate the different existing contributions. For instance, first, a very simple model with few elements and no stiffeners could be realised; second, several combinations, including increasing the number of elements and introducing ordinary stiffeners and primary members, could be considered;