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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as MARINE PROPULSOR NOISE INVESTIGATIONS IN THE HYDROACOUSTIC WATER TUNNEL “G.T.H.” 262 MARINE PROPULSOR NOISE INVESTIGATIONS IN THE HYDROACOUSTIC WATER TUNNEL “G.T.H.” D.Fréchou, C.Dugué, L.Briançon-Marjollet, P.Fournier, M.Darquier, L Descotte, L.Merle (Bassin d'Essais des Carènes, Chaussée du Vexin, 27100 Val de Reuil, France) 1. ABSTRACT Since its first use in 1988, the Grand Tunnel Hydrodynamique (G.T.H.) has proved that it is a rather unique experimental facility to conduct innovative experiments to improve the design of ship propulsors specially with regard to cavitation and hydroacoustic performances. This paper presents a review of the experimental capabilities of the tunnel and of the measuring techniques used, with emphasis on the significant advance in propulsor noise investigations obtained from the model tests performed in this facility. 2. INTRODUCTION For several years now, the noise reduction has been a major goal for the hydrodynamic/hydroacoustic studies not only on Navy ships, but also on ships like oceanographic or seismic research vessels and cruise liners. From a general standpoint, three domains of interest [Aucher, 1996] can be distinguished: • the flow noise which is the wall pressure fluctuations induced either by turbulence or travelling bubbles or breaking of waves, which decreases the performance of a sonar system. • the radiated noise in the far field (≈100m) of a ship which is related to the fluctuating hydrodynamic forces on the rotating blades of the propeller and on the hull, as well as to the fluctuating forces on hull induced by the propeller. These fluctuating forces lead to different types of noise as shown in Figure 1: – a discrete frequency lines noise type at low frequencies range which correspond to noise radiation from the propeller and the hull excited by the propeller either directly through the blade passage closed to the hull or through the shaft bearings. The discrete frequency lines correspond to the blade revolution rate harmonic (k n Z) and their amplitudes are directly dependent on the hull wake in-homogeneity and propeller geometry (number of blades, skew angle…), – a discrete frequency lines noise at shaft rate harmonics might also occurs if the shaft line presents a mechanical problem (shaft alignment or torsion, gearing mal-performance…) and if there are differences between blades geometry or blades pitch setting or blades elasticity, – a discrete frequency lines noise type at medium frequencies range which results from the hull radiation excited by all the internal machinery of the ship (motor, reduction gear assembly…), – a discrete frequency lines noise type, at medium frequencies ranges, known as “propeller singing” which results from the fluid-structure interaction at the trailing edgs of the propeller blades [Blake, 1977], – a broad band noise at low, medium and high frequencies range which results from the fluctuating hydrodynamic forces on hull induced by the hull boundary layer the authoritative version for attribution.

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as MARINE PROPULSOR NOISE INVESTIGATIONS IN THE HYDROACOUSTIC WATER TUNNEL “G.T.H.” 263 turbulence and from the fluctuating forces on blades induced by the inflow turbulence of the wake ([Jonson, 1995], [Kirshner & al, 1993], [Manoha, 1998]). The broad band noise is highly increased as soon as the cavitation is appearing (high loading on blade at maximum ship speed or under trawling operations). As cavitation is developing, the medium frequencies range then the low frequencies range are concerned and the blade rate frequency lines amplitude level are also increased because the hull excitation is increased [Baiter, 1992]. • the radiated noise inside the ship which more concerns the passengers cabins of cruise liners ([Holland & Wong, 1995], [Raestad, 1996]). The generation of this noise is related to the propeller induced hull excitation and the response of the hull to this excitation (transfer function of the hull). Figure 1: Sound pressure level radiated by ship with cavitating and non cavitating propeller With regard to the ship radiated noise in the far field, it is necessary not only to investigate the propeller radiated noise but also the hull radiated noise. The investigation of the later one is generally difficult to make using experiments on model of the ship (hull & propeller) at reduced scale. The main reason is that the hull model and shaft arrangement are often difficult to manufacture with the same mechanical structure as at full scale. Nevertheless, if the model hull is stiff enough, it is possible to investigate the propeller induced hull excitation, by measuring the fluctuating forces induced on hull by the propeller either directly or through the shaft bearing. These hull fluctuating forces can be then introduced as inlet data of computational vibro-acoustics codes, for hull vibration and radiated noise prediction. This means that from model scale experiments in tunnel, we can only investigate differences in radiated noise from different propellers and that it is not possible to really forecast the ship radiated noise. Indeed, the radiated noise inside the ship cannot be predicted from model tests alone. For propeller radiated noise investigations, the similarity conditions summarized in Table 1 compel to make propeller tests at model scale: • with the right wake field as at full scale. This means to have a facility with large test section in which the complete or modified (dummy) hull model can be used, and with high flow speed to overcome the viscous scale effect between model scale and full scale on the hull boundary layer development, the authoritative version for attribution. • with the same material (same mechanical structure) as full scale for the propeller and with a flow speed equal to the full scale ship speed, • with the same local pressure on blade (the flow velocity is equal to the ship speed) and with nuclei control for cavitation similarity, • with a facility that allows a very low “minimum measurable noise source level”. We should keep in mind that these similarity laws are only for a ship in calm water. Additional similarity laws are needed for ship in waves.

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as MARINE PROPULSOR NOISE INVESTIGATIONS IN THE HYDROACOUSTIC WATER TUNNEL “G.T.H.” 264 Table 1: Summary of the similarity laws for hydroacoustic tests on ship model Similarity Non dimensional parameter Implications Geometrical similarity geometry, P/D for controllable pitch the accuracy of the propeller geometry is propeller specially important for the blade profile (leading edge, trailing edge and blade tip). A minimum model scale ratio is then required. Wake similarity (effective wake) impossible to keep equal but necessary to be higher than 5 107 . (i.e. advance ratio similarity) Vx/V, Vt/ V, Vr/V the complete hull model (at least the scaled after body of the hull) is needed for a good simulation of the effective wake. Viscous flow on the propeller blades Reynolds number has to be as high as similarity possible because it is impossible to keep equal to full scale. Similarity of propeller loading It ensures same average blade loading even if there are slight differences between model and full scale pitches and hull wakes. Cavitation similarity The pressure p is taken in the vertical plane of the propeller at 0.7R above the shaft axis, in order to take into account the scale effect on the hydrostatic pressure in the propeller plane if the Froude similarity is not kept. Froude similarity This similarity is not compatible with the Reynolds number similarity. Model test at higher flow speed than the Froude speed generally prevails. Acoustic & Structural similarity To have similar elastic bending and modal (structural vibration and induced vibrations: acoustic radiation) same material and same mechanical structure same fluid (water) same flow speed at model scale and full scale This is possible for the propeller but it is very difficult to extend to the hull and shaft line. Additional requirements – no hydrodynamic blockage effect This mainly concerns the characteristics of – free field like acoustic propagation the facility. – free surface the authoritative version for attribution.

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as MARINE PROPULSOR NOISE INVESTIGATIONS IN THE HYDROACOUSTIC WATER TUNNEL “G.T.H.” 265 3. PRINCIPAL CHARACTERISTICS OF THE G.T.H. The GTH is a closed circuit tunnel of demineralised and decarbonated water fully comparable to wind tunnel. We recall hereby the principal characteristics of the GTH which have been already largely detailed ([Lecoffre & al, 1987]). Figure 2: Overview of the test sections of the GTH Figure 3: C ross section of the large test section and the small test section • Two test sections are available with large Plexiglas windows (33 in the large tests section and 21 in the small test section) that give a high visibility on model. While one test section is in use, model preparation can be done on the second test section, as each test section can be isolated using closing doors located upstream and downstream the test sections. The small test section (dimensions: 1.14m x 1.14m x 6m) is more dedicated to studies at very high speed and the large test section (dimensions: 2m x 1.35m x 10m) is more dedicated to propeller with complete hull tests. the authoritative version for attribution.

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as MARINE PROPULSOR NOISE INVESTIGATIONS IN THE HYDROACOUSTIC WATER TUNNEL “G.T.H.” 266 • The water velocity and pressure are continuously variable: [0 OCR for page 262
About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as MARINE PROPULSOR NOISE INVESTIGATIONS IN THE HYDROACOUSTIC WATER TUNNEL “G.T.H.” 267 tunnel is uncoupled from the building itself by means of vibration absorbers. Finally, the vibration level of the tunnel is less than 1mm/s2. – noise from the main pump: The 10 blades rotor axial pump has been designed to be free of cavitation and to have a low shaft revolution rate even at high speeds and low ambient pressure conditions for both test sections. The water lubricated bearing has also been designed to ensure laminar flow in the chambers. – noise from machinery: Piping and auxiliary pumps have been structurally isolated from the tunnel. They are gathered with the motor and reduction gear of the pump, in the engine room with concrete walls and ceiling that isolated the main building of 40dB from airborne noise. – noise from nuclei production: the nuclei production is generating noise at high frequencies (f>1kHz). This noise is not critical for radiated noise measurements of a cavitating propeller. However, this noise is troublesome for radiated noise measurements of a non cavitating propeller. In order to get rid of this problem, the propeller noise testing procedure includes at first a determination of the cavitating domain (σn, Kt, P/D) of the propeller using the nuclei injection, then a noise measurement with nuclei injection for propeller operating conditions with cavitation, and finally a noise measurement without nuclei injection for propeller operating conditions without cavitation. 4. MODEL EQUIPMENTS AND INSTRUMENTATION FOR THE G.T.H. 4.1 Model equipme nt The table in Appendix I summarizes the different model test configurations in both test sections. We should emphasize some of this arrangements: • The models are as much as possible supported by the top cover of the test sections, so that the mounting and the preliminary tests of the instrumentation is done outside the test section. Specific top covers are available for surface ship and underwater vehicle (submarine, torpedo, AUV…). Any of the Plexiglas windows can be replaced by acoustic windows (sound absorbing lining window or hydrophone array window) or a 6 components force balance for foils window. • The shaft driving system for propulsors tested with the ship hull (propeller diameter of 200mm–300mm and hull overall length of 4m–9m) is done by an immersed AC electric motor (10kW-3200rpm) for the non acoustic tests and by hydraulic turbines (Type I: 45kW-5000rpm; Type II: 50kW-2000rpm) for acoustic tests. As a matter of fact, it is important not to lower the hydroacoustic quality of the tunnel by using noisy shaft driving system. The use of hydraulic axial and multi-stage turbines provides several advantages compared to mechanical and electrical motor. The frequency line type noise (gearing noise, ball bearing noise, electromagnetic noise) is significantly reduced by the high number of stages and blades on rotor and stator, and the use of water lubricated bearing. The broad band noise is largely lower than the one of the propulsor mounted because the flow speed is low in the turbine and the pressurization and the deaeration of the hydraulic circuit make the turbine free of cavitation. Finally, due to the small size of the turbine, sound absorbing linings around the turbine contribute to lower down the broad band radiated noise. • Tests of large scale propellers and contra-rotating propeller (D>400mm) in open water or behind dummy hull model are done using a 2 coaxial shafts driving system with an external electrical motor (250kW-5000rpm-2x500daN-2x25m.daN) that can be inclined of ±10°. • For acoustic studies of large scale propellers and pump-jet, a silent shaft driving system is used with a high power hydraulic turbine (530kW-1500rpm-4000daN). 4.2 Instrume ntation • Data acquisition systems Every type of measurements has its own data acquisition system: forces measurement on shaft (including the angular position of the shaft and the revolution rate measurements), forces measurement on appendages (including the angular position of the appendage), static pressures measurement on model, Laser velocimetry measurement, acoustic-vibration- fluctuating forces measurement. Each data acquisition system acquires the flow conditions in the test section (speed, pressure, temperature, air the authoritative version for attribution.

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as MARINE PROPULSOR NOISE INVESTIGATIONS IN THE HYDROACOUSTIC WATER TUNNEL “G.T.H.” 268 content level, nuclei injection settings). In addition, an Ethernet network makes the communication between data acquisition systems very easy. • Cavitation images re cording Cavitation images on models are recorded with standard video cameras and with stroboscopic lights. Figure 5: Visualization and video recording arrangement for cavitation on rotating propeller The strobe lights are triggered with a shaft encoder signal that allows selecting a given blade angular position. The operating flow conditions (speed, pressure, shaft revolution, blade angular position) are directly fitted into the video images. Two views are at least recorded: either two cameras looking at the suction side of the blade from both side of the test section, or one camera looking at the suction side of the blade from one side of the test section and a second camera looking at the pressure side of the blade from the same side of the test section. The radiated noise is recorded on the audio channel of the video tape. The cavitation images can be digitized and analyzed through numerical image processing algorithms [Godefroy & al, 1998] in order to obtain statistical information on the 2D dimensions of the cavitation and location on the blade surface at different angular positions. • Fluctuating forces on shaft measurement - Mean thrust and torque measurements: In house designed dynamometers are mounted on propeller shaft for mean thrust and torque measurements. These dynamometers use strain gauges technology sensors and special design to minimize cross-talk between torque and thrust measurements sections. They are also able to work at low pressure level (5kPa) and high shaft revolution rate (n=5000rpm). However, this type of dynamometer is not able to measure time-dependent thrust and torque. - Fluctuating thrust measurements: For the fluctuating thrust measurement, an unsteady thrust dynamometer (Figure 6) is integrated in the shaft closed to the propeller hub. This dynamometer is similar to the one developed at ARL Penn State [Jonson, 1995]. Figure 6: Thrust fluctuation measurements The sensor is a piezoelectric crystal that provides a high stiffness mounted on the shaft centerline with steel hemisphere to be insensitive to side forces and bending. The crystal is pre-loaded so that thrust fluctuation in both axial directions can be measured. Because of the high stiffness of the crystal, this technique is able to measure very low thrust fluctuations (∆T/T≪1%). The shaft mass is at least 10 times higher than the propeller mass in order to obtain an impedance break. A pre-amplification of the piezoelectric signal is included in the shaft before the slip ring transmission to increase the signal to noise ratio. Within the frequency bandwidth obtained that goes up to 1kHz, there are inevitably resonant frequencies of the whole shaft (between propeller and drive motor) that can be considered as a multiple lumped-mass- spring system. This is the reason why a force calibration is made using a dynamic force shaker at zero rpm of the shaft. From the acquisition of the thrust triggered by the shaft encoder signal, a synchronous analysis is made to sort the frequency lines related to the shaft revolution rate and its harmonics, and the propeller inflow spatial periodicity. It is then the authoritative version for attribution. possible to compare the effect of different propellers geometry or different wakes fields on the same propeller. This fluctuating thrust measurements are the first step to investigate the differences that one could expect on sound pressure level at the blade rate frequency and its harmonics, and further more on broad band noise related to wake turbulence interaction with the propeller blades.

OCR for page 262
About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as MARINE PROPULSOR NOISE INVESTIGATIONS IN THE HYDROACOUSTIC WATER TUNNEL “G.T.H.” 269 • Fluctuating forces on hull measureme nt Fluctuating forces on the hull induced by the blade passage closed to the hull are measured by a pressure transducers array. About 20 transducers are flush mounted on the hull surface just above the propeller plane. The afterbody of ship model is stiffened using glass reinforced plastic in order to measure only the hull excitation and not the excitation with the response of the hull. Figure 7: Hull pressure transducers arrangement on stiffened hull with a cavitating propeller of an oceanographic vessel The pressure signals acquisition are triggered by a 2048 pulses shaft encoder. A spectrum analysis is then process on the pressure signal in order to get the pressure amplitude at the blade rate frequency and its harmonics. As for the fluctuating thrust measurements, the hull pressure transducers are of piezoelectric type (equivalent to hydrophone transducers). These transducers measure only the unsteady part of the pressure but with a high signal to noise ratio (>80dB) compared to classical pressure transducers such as strain gauge type. This is necessary when we want to look at the high harmonics pressure amplitude without any cavitation on the propeller or to compare the hull excitation of two propellers geometry. From the spatial integration of the pressure amplitude, the resulting fluctuating forces and moments on the hull are calculated with reference to a given co-ordinate system. • Acoustic measurement For radiated noise measurements in closed-jet type hydrodynamic tunnel, three major effects have to be taken into consideration: hydrophone support vibration isolation, turbulent flow noise isolation and acoustic impedance between the noise source (propeller) and the hydrophone. Figure 8: Radiated sound measurements (hydrophone plug and streamlined hydrophone fairing) The principal acoustical techniques (Figure 8) used in the GTH were designed to overcome these problems: – hydrophone plugs for the radiated noise in the cross section of the main flow. These hydrophone plugs are flush mounted and are made up of a standard hydrophone in a box filled with polyurethane coating. The polyurethane elastomer, the box dimensions and the location of the hydrophone relative to the internal wall of the tunnel were chosen in order to provide both vibration isolation from wall structure accelerations and attenuation of turbulence near field wall pressures. Concerning flow induced pressure fluctuations, the hydrodynamic wave lengths are so short that the hydrophone plug dimensions is doing a spatial filtering of the turbulent boundary layer pressure fluctuations. As a matter of fact, the effective wave length of these pressure, i.e. (l≈0.7V/f with V≤20m/s), are at the authoritative version for attribution. least 100 time shorter than the acoustic wave length from the source (l≈c/f with c=l450m/s). – one streamlined hydrophone for measuring noise from downstream the model. This hydrophone is made up of a piezoelectric sensing element inside a shell head

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as MARINE PROPULSOR NOISE INVESTIGATIONS IN THE HYDROACOUSTIC WATER TUNNEL “G.T.H.” 270 manufactured in polyurethane coating. The nose geometry of the head shell, in some way similar to sonar dome, is designed to develop a stable laminar boundary layer which is not sensitive to changes in turbulence level or direction of the upstream flow. Using different measurement techniques, we should keep in mind that closed-jet test sections are not free-field environment. The large difference of acoustic impedance between water and the ensemble air-Plexiglas-stainless steel of the tunnel structure make different sound power propagation depending on the frequency we want to look at. In a short cut, we can say that for a noise source located on the test section axis, the propagation is of plane wave type at low frequencies (wave length higher than the characteristic length scale of the test section, which are propagating in the test section axis direction) and of spherical wave type at high frequencies (wave length lower than the characteristic length scale of the test section). In order to reduce the reverberation at high frequencies, two sound absorbing lining windows have been built. In order to assess these acoustic “blockage” effects, acoustic calibration are made using a known sound source located on the test section axis, and with water tunnel velocity equal to zero. The complex transfer function to apply to the received acoustic signal at the measurement system is then identified provided that the coherence between the received signal and the source signal is close to one. The acoustic data acquisition system is able to process 32 analog input signals at a sampling rate of 2 MHz, and with a 14-bit words analog to digital converters and anti-aliasing filters. Standard and specific data processing tools are available such as: auto-spectrum and cross-spectrum analysis, joint time-frequency analysis, harmonic analysis, frequency demodulation, frequency line detection algorithm, coherence analysis… • Vibration measurement For noise investigations related to flow induced structural vibrations, coherence analysis is performed from noise signals and vibration signals. For specific tests with model manufactured (foil, ducted propeller) and tested according to the hydroelastic similarity (i.e. same flow speed as full scale and same mechanical structure between model and full scale), the model response to the flow excitation is measured using standard accelerometers. The main drawback using standard accelerometers is that the volume needed for the accelerometer location in the model can locally change the structure response of the model. The use of Laser vibrometer (Polytec) enables to get rid of this problem on small scale models [Serander & al, 1994]. Furthermore vibration measurements on the hull model and on the shaft line elements can warn the test operator about any troublesome noise resulting from unexpected performances of those parts of the test arrangement. 5. HYDROACOUSTIC PERFORMANCES OF THE GTH 5.1 Kine tic performances of the flow: • Owing to the contraction ratio of the convergent, and the honeycomb and flow straighteners of the test sections, the boundary layer are of 40mm at the inlet of the test sections and of 100mm at the outlet of the test sections. The turbulence level (ratio of RMS velocity and mean velocity) is of 0.3% over the flow speed range (0–20 m/s). This turbulence level is measured in the frequency range of 1 Hz–1kHz with a 2D Laser Doppler Velocimeter enhanced in order to get a signal to noise ratio less than 0.2% (forward scattering mode used without the Bragg cell for frequency shift). • The spatial distribution of the local mean velocity in the cross section of the test sections except the boundary layer area is not very large for the maximum discrepancy is less than 0.2%. 5.2 Deaeration and cavitation nuclei control performances: • Deaeration process from an air content of 100% of the saturation at atmospheric pressure (⇔24mg/liter) to an air content of 30% of the saturation at atmospheric pressure (⇔7mg/liter) is done within 2 hours. It is then possible to carry out the deaeration process as soon as it is necessary, which is not the case of most of the hydrodynamic tunnels. As a matter of fact, degassing a tunnel like the GTH without microbubbles injection and without a bubbles separating tank, can take more than 12 hours. Standard air content for cavitation and acoustics tests is 7mg/liter. the authoritative version for attribution.

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as MARINE PROPULSOR NOISE INVESTIGATIONS IN THE HYDROACOUSTIC WATER TUNNEL “G.T.H.” 271 • The nuclei content control is compulsory in hydrodynamic tunnel dedicated to cavitation studies [Cavitation Committee Report of 20th ITTC, 1993]. The injection process (flow rate, water gassing pressure, number of injectors in use over the 121 available ones) is able to control the nuclei content from 0.1 nuclei/cm3 up to few tens nuclei/cm3 with an average diameter of 50µm. Several studies (for instance [Gindroz & Billet, 1993]) have confirmed the merit of the nuclei control of the GTH for cavitation tests. 5.3 Hydroacoustic performance s: • Minimum measurable sound source level The minimum measurable sound source level in a tunnel is defined [Abbot & al, 1993] as the minimum level of an equivalent sound source to the propulsor, which can be measured by the acoustic receiver, in the same flow operating conditions as with propulsor (i.e. noise source located at the same location as the propulsor, same flow speed and pressure and same air content and nuclei content). The minimum measurable sound source level is then related on one hand to the background noise of the tunnel and/or to the background noise of the acoustic receiver, and on the other hand to the transfer function G between the source and the receiver. For frequencies range in which the propagation is a free field type (f>1kHz), the transfer function gain was found to be close to a spherical spreading loss. This leads to a minimum measurable sound source level defined as: The background noise of the GTH (See Appendix II and Figures 9 & 10) is mainly dependent on the flow speed, provided that the air content is low enough. The background noise measured with the streamlined hydrophone is lower in the low frequencies range because of the laminar boundary layer developed on the head form of the hydrophone but it is also lower in the high frequencies range because of the low background noise of the hydrophone sensing element. Figure 10: Background noise of the large test section measured with the streamlined hydrophone Figure 9: Background noise of the large test section measured with the hydrophone plug Even if the sound pressure level of a propeller measured at model scale and extrapolated to full scale do not account for the hull amplification because the model hull is not in mechanical similarity to full scale, we can still compare after extrapolation (given a model scale 1/20 and a test flow speed Vmodel) a propeller radiated sound pressure level measured in the GTH that would be equivalent to the minimum measurable sound level (background noise), with a target sound pressure the authoritative version for attribution.

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as MARINE PROPULSOR NOISE INVESTIGATIONS IN THE HYDROACOUSTIC WATER TUNNEL “G.T.H.” 272 level of the full scale ship noise. We took the example of a target sound level of an oceanographic research vessel at a speed of 12 knots. The graph of figure 11 clearly points out the capabilities of the GTH for the hydroacoustic studies of propulsors. The limitation at frequency below 3Hz is not critical because the propeller blade rate frequency line is always higher and the propeller broad band signature is in the frequency range where the margin is more than 30 dB. Figure 11: Extrapolated minimum equivalent free field sound power density spectrum for a ship with a full scale speed of 12 knots, a model scale of 1/20 and a model test at flow speed of 6m/s The extrapolation law applied on the minimum measurable sound pressure level is using the assumption that the measured sound power density level is only dependent on speed (flow speed at model scale and ship speed at full scale), on the distance in between the source and the receiver, on the scale ratio: - for a cavitating propeller - and for a non cavitating propeller • Shaft driving motor noise The minimum measurable sound level of the tunnel should also take into account the background noise of the shaft driving motor. Using hydraulic turbine as shaft driving motor avoids degradation of the hydroacoustic performances of the GTH. Figure 12 shows that the background noise of a shaft driving motor using hydraulic turbine is lower than the background noise of the tunnel for a given flow speed in the small test section. It then becomes possible to measure the propeller sound radiated without any cavitation, which is impossible with standard electrical motors. Figure 12: Sound power density level using hydraulic turbine in the small test section of the GTH 6. SOME RESULTS OF HYDROACOUSTIC SURVEYS IN GTH Several studies have been carried out in the GTH that emphasize the hydroacoustic performances of the GTH. We present hereafter some examples of these studies: study on the flow noise of transient and turbulent boundary layer, study the authoritative version for attribution. on propeller induced fluctuating forces on shaft, study of cavitation effect on propeller induced fluctuating pressure on hull, noise radiated on propeller.

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as MARINE PROPULSOR NOISE INVESTIGATIONS IN THE HYDROACOUSTIC WATER TUNNEL “G.T.H.” 273 • Flow noise of transient and turbulent boundary layer In order to investigate the instability of laminar boundary layer on a sonar dome, an experiment was carried out on a laminar boundary with a pressure distribution with negative gradient. The boundary layer development was made on a flat plate on which flush mounted transducers were installed and a second plate with an appropriate geometry was used to force a negative pressure gradient along the flow axis (Figure 13) on the first plate. In total, 17 fluctuating pressure transducers flush mounted with a pinhole of 0.1mm diameter, 3 hot film sensors for wall shear stress measurements were used and velocity profile was measured using Laser Doppler velocimeter in forward scattering mode. Thanks to the very low turbulence level and the very low background noise of the tunnel, a laminar boundary layer of 1.8m at flow speed of 10m/s (i.e. to Reynolds number of 18 106), was achieved in this experiment and the sensitivity of different roughness heights on the boundary layer stability has been studied [Perraud & al, 1995]. Figure 13: Test set-up for boundary layer development with an adverse pressure gradient • Propelle r ope rating condition with and without cavitation Before investigating the radiated noise of a propeller, it is important to know the domain of operating conditions of the propeller with and without cavitation. As a matter of fact, the presence of cavitation even at the inception point induces large increases of the radiated noise and the fluctuating forces on hull and on the shaft. Model tests are therefore performed to explore different operating conditions of the propeller (i.e. to different Kt, σn, P/D). The nuclei content has then a major effect on the determination of the cavitating and non cavitating domains of the propeller operating conditions [Gindroz & Billet, 1993]. The figure 14 shows a comparison between model scale and full scale of inception point of tip vortex cavitation on a marine propeller. Figure 14: Comparison between full scale and model scale of cavitation inception points This comparison can only be done if the similarity of the loading of the propeller blades are the same. This means that not only the global loading should be equivalent (Ktm=KtFS) but also the radial distribution of blades loading should be equivalent. The later requirement imposes to have a hull wake field similarity between model and full scale. Cordier & al [1995] showed that the similarity of the wake field is rather well predicted if model tests are run at flow speed equal to ship speed rather than if model tests are run at Froude speed. • Fluctuating forces on shaft: fluctuating thrust on a submarine propeller The wake field is largely modified when a ship is maneuvering and so it is for the radiated noise at blade rate harmonics frequencies. The fluctuating thrust modification, when changing of course, gives a good approximation of radiated noise modification at blade rate harmonics frequencies. Figure 15 presents the results of fluctuating thrust the authoritative version for attribution. measurements at first and second blade rate harmonics frequencies for a propeller of submarine tested at two drift angle 0° & 10°, in the large test section of the GTH. The measurements were done using the set-up described in the instrumentation paragraph. The drift angle largely increases the fluctuating thrust and the residual fluctuating thrust with a bare hub instead of the propeller is far lower. Therefore, it is possible to predict that the radiated noise at these frequencies will increase of the same level.

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as MARINE PROPULSOR NOISE INVESTIGATIONS IN THE HYDROACOUSTIC WATER TUNNEL “G.T.H.” 274 Figure 15: Fluctuating thrust on propeller shaft for 2 drift angles of a submarine • Propelle r induced fluctuating pressure on hull: cavitation effect Hull pressure fluctuations is not only used to determine the force excitation of the hull but also as a criterion for an acceptable propeller at the design stage for civilian shipyards. Current practice [Carlton & Bantham 1997] gives the following acceptable hull pressure amplitude at the first blade rate frequency: General ship type Typical blade rate hull surface pressure range (freq.=n.Z) Cruise liner 1–2 kPa Ro/Ro Ferry 2–4 kPa Container and fast Cargo ships 3–6 kPa Slow bulk trade ships 4–7 kPa A comparison between model and full scale results is shown in figure 16, for a fixed pitch propeller of a tanker. The instantaneous measured pressure signal is averaged for every fraction of shaft revolution, over 250 shaft revolutions for both full scale and model scale measurements. The results at model scale have been obtained at two flow speeds, the lower one corresponding to Froude speed and the higher one corresponding to the highest flow speed that was possible to achieve. Figure 16: Time trace over 1 shaft revolution of the hull pressure signal of a 5 blades propeller of a tanker The results show that the cavitation at low flow speed, is very unstable, which is not the case at high speed. This clearly demonstrates that keeping the similarity of the classical dimensionless numbers (σn, Kt, P/D) is not enough for a good representation of the full scale signature and that the test should be performed at maximum flow speed, i.e. to flow speed as close as possible to full scale ship speed, in order to simulate the right wake and to get a more stable cavitation pattern [Cordier & al, 1995]. Full scale hull excitation at blade rate harmonics has now become so low, specially on twin screw ships with highly skewed propellers, that vibration induced by the broadband background energy of the hull excitation become questionable ([Carlton & Holland, 1998–1999]). This broadband energy is related to cavitation collapses in the tip region of the blades. As shown by the Figure 17 for a four blades propeller of a cruise liner, as the cavitation is developing (i.e. Cavitation number σn decreasing), the broadband level induced by the collapse of cavities tends to merge towards the low frequencies range and this increases significantly the high harmonic levels although the 1st blade rate harmonic amplitude is not the authoritative version for attribution. modified. Typical cavitation pattern related to this phenomena and to highly

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as MARINE PROPULSOR NOISE INVESTIGATIONS IN THE HYDROACOUSTIC WATER TUNNEL “G.T.H.” 275 skewed propeller is a combined sheet and tip vortex cavitation. Figure 17: Spectrum analysis on hull pressure fluctuations on a 4 blades propeller with and without cavitation of a twin screw ship As already mentioned, it should be recall that the hull structure response to the hull excitation is an important issue not to forget. As matter of fact, results of measurements at full scale of pressure fluctuations and vibration level at a same location on the hull above the port side propeller of a twin screw navy ship (Figures 18 & 19) clearly point out the amplification of the hull in a broadband frequency range. Figure 18: Full scale hull pressure fluctuation for Figure 19: Full scale hull velocity fluctuation for different RPM of the port side propeller (fixed pitch) of different RPM of the port side propeller (fixed pitch) of a twin screw navy ship a twin screw navy ship Another point to clear up in the analysis of the correlation between full scale and model scale for highly skewed propellers, is the effect of the differences between blades geometry and pitch setting on the hull excitation signature. Differences between blades hull pressure signature are largely increased due to the non linear effect of the cavitation. This is shown by Figure 20 which presents the pressure signature with and without cavitation (σn=1.7 & σn=8.0) for a same loading of the blade (same Kt) and with maximum differences of pitch setting between blades of 0.5°. This also rises the necessity to make the harmonic analysis of the hull pressure signals rather on the shaft rate component basis than on the blade rate component basis. With no blades differences, the shaft rate component should not exist. the authoritative version for attribution.

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as MARINE PROPULSOR NOISE INVESTIGATIONS IN THE HYDROACOUSTIC WATER TUNNEL “G.T.H.” 276 Figure 20: Effect of blades differences on pressure signature of non cavitating and cavitating 4 blades propeller These remarks point out the importance of the accuracy of the pitch setting of the blades of controllable pitch propellers: typically an accuracy of less than 0.2° at model scale as well as at full scale is needed. In the case of highly skewed propeller with either fixed or controllable pitch, the accuracy of the tip region geometry of the blades is also of much concern. In this respect, the propeller manufacturing tolerances, specially at model scale, have to be better than the ISO class S tolerances. Finally, it should be recall, that the full scale ship trials and propeller operating conditions must be known with a great confidence in order to improve the prediction of the higher harmonic pressure amplitude from model scale [Cavitation Induced Pressure Fluctuations Committee Report of the 22nd ITTC, 1999]. • Propelle r radiated noise: Concerning the radiated noise at blade rate frequency and its harmonics, similar conclusions as the one presented on the hull pressure excitation can be made, specially on the cavitation effect on the level increase of these frequency lines and on the hull amplification effect. The propeller broad band noise level is very sensitive to cavitation. Figure 21 shows the broad band signature of a navy ship type propeller measured in GTH operating at the same shaft revolution rate, same flow speed but at two different flow pressures such that one case is with cavitation (σV=1.5) and the other one is without cavitation (σV=2). A reference curve of noise radiated in the same operating conditions but with a bare hub instead of the propeller is superimposed. The results show an increase of 20 dB of the broad band radiated noise once the propeller is cavitating (σV=1.5). Figure 21: Sound Power density spectrum of a propeller of a twin screw navy ship with and without cavitation at model scale The frequencies lines at medium frequencies range that appear on the spectrum and which do not depend on the propeller rpm, result from the so called “propeller singing” induced by the trailing edge geometry. If this frequencies lines do appear at model scale, they will or will not appear at full scale. On the contrary, if they do not appear at model scale, they will not appear at full scale. This is due to the fact that the trailing edge vortices activity is reduced as the Reynolds number increases. Figure 22 presents a comparison between radiated noise of propeller extrapolated from model test and radiated noise measured at full scale on a submarine propeller at operating conditions without cavitation. The model test was made at flow speed equivalent to full scale ship speed. The sound power density the authoritative version for attribution.

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as MARINE PROPULSOR NOISE INVESTIGATIONS IN THE HYDROACOUSTIC WATER TUNNEL “G.T.H.” 277 spectrum at model scale is extrapolated using the following formula: which is based on the dimensionless formulas of paragraph 5.3 where the reference length scale is taken equal to the propeller diameter and VFS is equal to Vm.. Figure 23: Radiated noise of propeller extrapolated Figure 22: Extrapolated model scale and full scale from model test and ship radiated (twin screw navy sound power density spectra of a submarine propeller surface ship) (without cavitation) The full scale measurement was done by an hydrophone towed by the submarine and located not far away and downstream the propeller plane. The results in Figure 21 show a very good agreement as difference are less than 5dB at medium and high frequency ranges. Furthermore, we have here a nice case of propeller radiated noise comparison between model scale and full scale because the radiated noise measured at full scale is predominantly the propeller noise and not the radiated noise due to the hull and internal machinery. We can then conclude that, from model test in GTH, we can predict with a good confidence the full scale propeller noise specially without cavitation. Figure 22 presents a comparison between radiated noise of propeller extrapolated from model test and radiated noise measured at full scale of a twin screw navy surface ship. In this case, the full scale trials involve an array of hydrophones hung vertically in deep water at fixed location [Urick, 1975]. The vessel is arranged to run at constant speed and course so to pass at the measurement hydrophones at a known distance. Two ship speeds were performed with no cavitation on the controllable pitch propellers. The same laws as described before is used for the extrapolation of the propellers noise. The results show that the contribution of the propeller on the ship noise is not predominant at low speed. From this example, we can conclude that the propeller noise is one noise source of the ship but it is not the only one that matters. 7. CONCLUSIONS From model test performed in accordance with the hydro-acoustics similarities laws requirements, it is possible to predict - the cavitating and non cavitating operating conditions of a propeller - the radiated noise of a propeller: broadband and tonal noise - the propeller induced hull and shaft excitation - then to evaluate the contribution of the propeller on the ship noise. This has become possible because of the hydroacoustic performances of the GTH, its equipment and instrumentation, and specially: - the large test sections of the facility - the control of both nuclei content and air content - the low background noise of the facility the authoritative version for attribution. - the low background noise of the hydraulic motor - the high dynamical sensitivity of the transducers - and model test performed at flow speed equal to ship speed.

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as MARINE PROPULSOR NOISE INVESTIGATIONS IN THE HYDROACOUSTIC WATER TUNNEL “G.T.H.” 279 NOMENCLATURE ρ (kg/m3) water density ρs (kg/m3) hull/propeller material density λ scale ratio (ship dimension divided by model dimension) c sound speed (m/s) (m/s2) g gravity acceleration f frequency (Hz) kr roughness coefficient of the solid material (propeller/hull) (m) Es elastic modulus of the solid material (propeller /hull) (Mpa) µs Poisson ratio ηs damping constant of the material kth shaft rate harmonic BRk kth blade rate harmonic (µPa 2/ Hz) Φ pp Power Density Spectrum of the sound pressure r distance between source (propeller/ship) and receiver (m) (hydrophone) (/m3) n Nuclei concentration p reference hydrostatic pressure (propeller shaft axis or propeller (Pa) shaft axis+0.7R) pcrit Nuclei critical pressure (Pa) pV vapor pressure (Pa) p, p(t) fluctuating pressure amplitude on the hull, hull pressure signal (Pa) V flow speed in the test section or ship full scale speed (m/s) w wake deficit L reference length (m) (sound pressure level =10 log(Φpp) (Power density spectrum L (dB re. 1µPa & 1Hz) level) D(R) diameter (radius) of the propeller (m) P/D pitch (ratio of pitch at 0.7R and propeller diameter) Z number of blades n shaft revolution rate (rev/s) T propeller thrust (N) Q propeller torque (N.m) Reynolds number propeller Reynolds number propeller Froude number propeller thrust coefficient propeller torque coefficient propeller cavitation number based on shaft revolution speed where P is the hydrostatic pressure at +0.7R of the shaft axis propeller cavitation number based on flow speed where P is the hydrostatic pressure at shaft axis hull fluctuating pressure amplitude coefficient Si propeller cavitation number at inception point Subscripts full scale the authoritative version for attribution. FS model scale m

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as APPENDIX I: TESTS & EQUIPMENT IN THE GTH 280 APPENDIX I: Tests & equipment in the GTH Application Test section Measurements Equipment configuration - cavitation (σn , Kt) Submarine, torpedo - closed test section - silent motorisation - complete hull - self propulsion with - boundary layer D≤250mm and without cavitation blowing V≤10m/s Kt, Kq, η - dynamometry - with ou without - nominal—effective - hydrophone plug drift angle wake and/or streamlined - acoustics hydrophone and - hull fluctuating anechoïcal window pressure - 3D LDV - fluctuating thrust - velocity down and upstream the propulsor - cavitation (σn , Kt) Single propeller and contra-rotating propeller survey at - closed test section - contra-rotating large scale - complete hull - self propulsion with carter. D≥250mm and without cavitation - electric motorisation V≥7m/s Kt, Kq, η - dynamometer - velocity down and - specific operating - 3D LDV conditions upstream the (deceleration, propulsor maneuvering & astern perf…) - shaft inclination 0° et 10° - cavitation (σn , Kt) Single propeller and pump-jet survey at large scale - closed test section - silent motorisation - complete hull - self propulsion with - dynamometers on D≥250mm and without cavitation duct and rotor V≥7m/s Kt, Kq, η - 3D LDV - velocity down and - hydrophone plug upstream the and/or streamlined propulsor hydrophone and - acoustic meas. anechoïcal window - cavitation (σn , Kt) Surface ship - single screw and - specific top cover twin screw - self propulsion with - silent motorisation - closed test section and without cavitation - boundary layer Kt, Kq, η - complete hull blowing D≤250mm - nominal/effective - dynamometer V≤10m/s wake - hydrophone plug - acoustics - wake generator of - 3D LDV - hull fluctuating shaft and brackets pressure - fluctuating thrust - blade forces - velocity down and upstream the propulsor - cavitation (σn , Kt) Specific Propulsors survey (Pods) - closed test section - silent motorisation - Vmax - self propulsion with - dynamometer - specific operating and without cavitation - 6 components force Kt, Kq, η conditions transducer the authoritative version for attribution. - acoustics (deceleration, - 3D LDV - velocity down and manoeuvring & - hydrophone plug upstream the astern perf…) - shaft inclination and propulsor drift angle 0°<α ° <180°

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as APPENDIX I: TESTS & EQUIPMENT IN THE GTH 281 APPENDIX II: BACKGROUND NOISE OF THE GTH • Background noise of the small test section at high pressure and at different flow speeds. The levels presented on the graphs hereafter are lower in the high frequencies than the one presented in the ASME paper [Boissinot & al, 1990], because the bearing of the rotor of the pump has been slightly modified. • Background noise of the large test section at high pressure and at different flow speeds. The levels on the graphs hereafter are lower than the one presented in the ASME paper [Boissinot & al, 1990], because the skimmer downstream the large test section ([Lecoffre & al, 1987]) has been removed. • Background noise of the large test section with and without nucle i injection the authoritative version for attribution.

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as APPENDIX I: TESTS & EQUIPMENT IN THE GTH 282 DISCUSSION R.Arndt, University of Minesota, USA How do you scale nuclei content between a model propeller and a full scale propeller operating in a ship's wake? AUTHOR'S REPLY The measurement of nuclei is done using a centre-body venturi. This means that the results is not a size distribution but a critical pressure distribution. This nuclei measurement technique has been used at sea in the Atlantic Ocean not far away of the French Brittany coast. The measurements were done from a ship at rest, therefore not in a ship's wake. The results show discrepancies according to the sea state, depth and certainly temperature. For sea state 0, we have the critical pressure distribution given on the following figure. Nuclei measurement at sea (French Brittany west coast) A similar measurement in the large test section of GTH for different tuning of the nuclei injection gives the result presented on the following figure. Nuclei measurement in the large test section of GTH Theoretically, we should have the following scale effect between the critical pressure distribution: The concentration ratio is kept between full scale and model scale (scale≈1/20), for critical pressure close to the vapor pressure, but not for the lowest critical pressure (pcrit.< −500mbar). The first reason is that, up to now, there is no other nuclei generation process than the one on the GTH that can produce such an amount of nuclei with a stable concentration and distribution of sizes in large cavitation facility. The second reason is that we do not really need such a scaling amount for the lowest critical pressure because we already get a cavitation nuclei saturation from the nuclei with critical pressure closed to vapor pressure. DISCUSSION G.Chahine, Dynaflow Inc., USA Since you control the nuclei distribution in the GTH, do you find a correlation between nuclei size distribution and cavitation inception? Do you measure that distribution of nuclei as a function of time? Is the number of nuclei the only important parameter as you said in your talk? When you showed the cavitation noise scaling between the full scale and the model you used a correction of 30 dS. What does this correspond to in terms of power of the ratio Dfull scale/Dmodel? the authoritative version for attribution. AUTHOR'S REPLY Yes we do find a correlation between nuclei distribution and cavitation inception. This correlation has largely been discussed in the paragraph 8 of the Cavitation Committee Final Report of the 21st ITTC. We do not measure the distribution of nuclei as a function of time. Because the deaeration process is very fast, we can adjust precisely the air content every 4 hours, so that the air content do not change within 10% of the value set for the test. Moreover, because of the downstream tank, there is no recirculation of the nuclei in the tunnel. Also, the nuclei generation process is monitored as a function of flow speed and pressure in the tunnel in order to keep the same nuclei distribution. Those are the reasons why the nuclei content is stable during the tests. This has been checked few times and that is the reason why we do not have a continuous measurement of the nuclei. The scaling of is related to power of 3 of the ratio Dfull scale/Dmodel. This comes from the

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About this PDF file: This new digital representation of the original work has been recomposed from XML files created from the original paper book, not from the original typesetting files. Page breaks are true to the original; line lengths, word breaks, heading styles, and other typesetting-specific formatting, however, cannot be retained, and some typographic errors may have been accidentally inserted. Please use the print version of this publication as the authoritative version for attribution. Power Spectrum, the scaling would be APPENDIX I: TESTS & EQUIPMENT IN THE GTH related to a power of 2 of Dfull scale/Dmodel. 283 fact that we are comparing noise spectrum in terms of Power Density Spectrum. If we do the noise scaling in terms of