Underwater flow noise measurements with a towed body

J. Abshagen1, D. Küter and V. NejedlWTD 71 Bundeswehr Technical Centre for Ships and Naval Weapons, Maritime Technology and Research

Division for Underwater Detection and Communication, Germany

ABSTRACTThe transmission behaviour of a thin plate excited by turbulent wall pressure fluctuations is investigated inan underwater experiment. The flat plate made of fibre-reinforced plastic is mounted laterally flush to atowed body and a turbulent boundary layer develops along the flat plate region for towing speeds between U= 2.4 m/s, . . ., 6.2 m/s (4.6 kn to 12.0 kn). A reduction index is determined from the ratio of the (Corcoscorrected) power spectral density (PSD) of wall pressure fluctuations and the (spatially incoherent part of the)PSD of interior hydroacoustic noise. A comparison with results from a previous study [1] on the transmissionbehaviour of a thick sandwich plate (fibre-reinforced plastic plate with outer polyurethane layer) is performed.The measurements were conducted with RV ELISABETH MANN BORGESE in Sognefjord, Norway, in2014.

Keywords: Underwater noise, Movement of solid body through fluid, Flow noise produced by turbulence

1. INTRODUCTION

Wall pressure fluctuations can induce noise in the interior of a moving body from a surrounding turbulentboundary layer [2–4]. At sufficient speed flow-induced interior noise can dominate, for instance, the cabinnoise of a vehicle, such as a car [5] or an aircraft [6], but it can also limit the hydroacoustic performance ofan underwater sonar system [7]. The level of flow-induced interior noise does not only depend on the wallpressure fluctuations as the noise source [8–11], it depends in particular also on the mechanical properties ofthe hull structure [12–15].

Hydrophones in a sonar system are typically immersed in water and shielded by a hull structure fromflow-induced noise generated by the turbulent boundary layer [16]. Since sonar systems are hydroacousticreceivers specific requirements with respect to hydroacoustic performance and vibroacoustic properties needto be fulfilled for a suitable hull material. Ideally such materials should be transparent to underwater soundbut fully shield the flow-induced self-noise. Suitable hull materials are therefore not only designed to reduceself-noise, but to ensure an optimal signal-to-noise ratio.

Underwater experiments on flow-induced noise have been performed, for instance, with a towed body[17, 18], a lifting body [19], and a towed array [20]. In those experiments the hydrophones were integratedinto the mechanical hull structure. Recently, an underwater experiment with a towed body on the transmis-sion behaviour of a flat plate excited by a turbulent boundary layer have been conducted [1]. The interiorhydrophones in this experiment were immersed in water beneath the hull structure, which was composed ofa thin layer of fibre-reinforced plastic on the inside and an thick outer layer made of polyurethane.

In this work the transmission behaviour of a thin plate excited by wall pressure fluctuations is studiedwith a towed body in an underwater experiment. The surface layer of the plate is identical to the fibre-reinforced plastic layer of the sandwich plate studied in [1]. A reduction index defined as the ratio of (exterior)hydrodynamic wall pressure fluctuations and (interior) hydroacoustic pressure fluctuations is determined andthe transmission loss is compared to that of the thick sandwich plate. Both experiments were performedduring the same research cruise.

1email: janabshagen@bundeswehr.org

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2. TOWING EXPERIMENTS

The research cruise was conducted with RV ELISABETH MANN BORGESE in Sognefjord, Norway, inSeptember 2014. The so-called FLAME (Flow Noise Analysis and Measurement Equipment) towed bodyprovides a platform for the study of flow-induced self noise under open-sea conditions. It has a length of5.26 m, a width of 1.353 m (0.935 m without fins), and a total height of 1.715 m. The weight in air is about2800 kg and the total mass of the body flooded with water amounts roughly 3500 kg. A picture of the towedbody during launching from the research vessel is shown in Fig.1.

Figure 1: Picture of towed body with fibre-reinforced plastic plate during launching from RVELISABETH MANN BORGESE in Sognefjord, Norway, in September 2014. The joints at theedges of the plate are smoothed with filling material.

The shape of the towed body is symmetric, but on the starboard side replaceable flat plates can be mountedlaterally flush. The fibre-reinforced plastic studied in this work can be seen in Fig.1. The size of the plateis 2000 mm×550 mm in streamwise and spanwise direction, respectively, and it has a thickness of 2 mm.Within the flat plate region there exists a rectangular measurement area of size 300 mm×575 mm in verticaland horizontal direction, respectively. In this area interior hydroacoustic noise is measured with a hydrophonearray on the reverse side of the plate in the interior of the towed body. The array is surrounded by a cavity inorder to reduce external disturbances. The contours of the white cavity shines through the thin plate in Fig.1.The principle measurement setup is depicted in Fig.2.

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Figure 2: Sketch of measurement setup in side view: The thin fibre-reinforced plastic layer(2 mm) is baffled outside of the measurement area by a thick layer made of steel and damp-ing material. The array consists of 16 hydrophones (hdy1 . . . hyd16) and is positioned 5 mmbeneath the plate. Wall pressure fluctuations are measured with a flush-mounted hydrophone(fmh) 64.5 mm downstream of the measurement area. At sufficient wall-normal distance theflow speed corresponds to the towing speed U.

The hydrophone array is aligned in streamwise direction and positioned 5 mm beneath the plate insideof the towed body on the horizontal centre line of the measurement area. It consists of 16 hydrophones of

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type RESON 4013 which have an equidistant spacing of 11.5 mm. Since the towed body is flooded the plateand the hydrophones are surrounded by water. Wall pressure fluctuations are measured with a flush-mountedhydrophone of type RESON 4050, which is located 64.5 mm downstream of the measurement area. Outsideof the measurement area the thin plate is baffled by a steel layer supported by a thick layer of dampingmaterial.

The measurement were performed for towing speeds between U = 2.4 m/s and 6.2 m/s (4.6 kn to 12.0kn) at depths of more than 100 m. At such depths below the local thermocline the sound speed profile wasalmost constant. During a measurement the towed body went on a straight track without active control. Thetowing speed U is estimated from the average of the speed over ground (SOG) of RV ELISABETH MANNBORGESE during a measurement run. A single run typically requires 360 s of data recording time. Powerspectral densities (PSD) shown in this work are calculated with a bandwidth of ∆f = 1 Hz from an averageover 360 short-time (Hamming windowed) Fast Fourier transforms.

3. WALL PRESSURE FLUCTUATIONS AND INTERIOR NOISE

PSD of turbulent wall pressure fluctuations and interior noise are depicted in Fig.3 (a) for three differenttowing speeds. It can be seen that (except for very low frequencies) the spectral level of wall pressurefluctuations is significantly higher than that of interior noise for each speed.

(a) (b)

Figure 3: (a) Power spectral densities (PSD) of wall pressure fluctuations (dashed line) andinterior flow-induced noise (solid line) for three towing speeds U, (b) PSD scaled by wall shearstress τ and time scale δ/uτ for the potential flow velocities U∞ corresponding to the towingspeeds in (a). Scaled PSD obtained at two intermediate flow speeds are added.

Instead of the towing speed U the potential flow velocity U∞ at the surface of the towed body displays theouter flow velocity of the boundary layer in the measurement area. The potential flow is calculated from vonKarman’s singularity method for a two-dimensional body having a similar contour than the towed body at thevertical position of the hydrophones. From the potential flow the laminar momentum thickness is determinedby Thwaites’ method and further estimates of turbulent boundary layer parameters are derived from flat platerelations [2]. Details of the method can be found in [18]. The potential flow velocity U∞ and estimatedboundary layer quantities evaluated at the position of the flush-mounded hydrophone are given in Tab.1.

PSD scaled by boundary layer parameters are depicted in Fig.3 (b). Here, pressure is scaled with wallshear stress τ and time with δ/uτ . The scaled PSD collapse onto each other in a mid-frequency regimeand this collapse implies that the increase of spectral level with speed, as depicted in Fig.3 (a), is fullydetermined by the hydrodynamic quantities. Therefore scaling by hydrodynamic quantities is appropriate forwall pressure fluctuations. The collapse of PSD of interior noise, on the other hand, is not as good, because

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Table 1: Estimated values of flow and boundary layer parameters at the measurement positionfor five towing speeds.

Towing speed u (kn) 4.6 6.2 8.3 10.0 12.0Towing speed U (m/s) 2.4 3.2 4.3 5.1 6.2Potential flow velocity U∞ (m/s) 2.7 3.7 4.9 5.9 7.1Friction velocity uτ (m/s) 0.099 0.130 0.171 0.202 0.239Boundary layer thickness δ (m) 0.043 0.040 0.038 0.036 0.035Wall shear stress τ (N/m) 10.1 17.3 30.0 42.0 58.8

Figure 4: Scaled PSD of the wall pressure fluctuations without (Φo) and with (Φo,corr) Cor-cos correction. Typical spectral decay laws of wall pressure fluctuations in the mid- and highfrequency regime are plotted for comparison (see [10]).

plate properties not related to the flow influence hydroacoustic noise generation [14]. It can be seen fromFig.3 (b), however, that spectral decay of interior noise follows roughly a f−4 decay law.

While hydrophones are well suited for the measurement of hydroacoustic noise in the frequency regimeconsidered in the work, spectral corrections are necessary for wall pressure fluctuations due to the finitetransducer size [21, 22]. A Corcos-correction [21] with an assumed convective speed Uc = 0.66 U∞, aneffective transducer radius of r = 4 mm, and Corcos parameters of a1 = 0.7 and a3 = 0.11 is applied to thePSD of wall pressure fluctuations. The Corcos-corrected PSD (Φo,corr) are shown in Fig.4 in comparisonto the measured PSD (Φo). PSD of the (outer) wall pressure fluctuations are marked with an index (o) incontrast to those of (interior) hydroacoustic noise marked with the index (i) in the following. The correctedand scaled PSD of turbulent wall pressure fluctuations display a spectral decay similar to a f−1 decay law ina mid-frequency regime and approach a steeper f−5 decay law at higher frequencies. Similar spectral decaysin the different frequency regimes have been found in previous studies (see [10]).

4. TRANSMISSION BEHAVIOUR OF THIN PLATE

In analogy to the transmission loss of sound waves through a panel, a reduction index R=10log10(1/τ ) forwall pressure fluctuations can be defined with transmission coefficient τ . Transmission loss of an incidentsound wave through a panel is described by τsound = |pT / pI|2, where pI and pT is the pressure of incident

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(a) (b)

Figure 5: (a) Reduction index of wall pressure fluctuations for three different flow speeds. Forcomparison the mass law of sound waves is plotted, (b) spatial coherence function γ2(x, f) withx = |pos(hydn) - pos(hyd1)|, n = 2, . . ., 16, for U∞ = 4.9 m/s. The white horizontal line indicatesthe position of hyd9.

and transmitted sound wave, respectively. The reduction index for turbulent wall pressure fluctuations canappropriately be defined as the ratio of PSD, i.e. τ = (Φi/Φo,corr). In this definition the outer pressure isnot separated into an incident and a reflected part, as this is done for sound waves. The reduction index ofwall pressure fluctuations is depicted in Fig.5 (a) for three different flow speeds. It can be seen that at verylow frequencies almost no reduction occurs, i.e. the panel is almost transparent. Here, the curves followrather the mass law of sound waves, that is defined as τsound = 1 / | 1+i ( ω m / 2 ρ0c )2 | (for normalincident), with density of sea water ρ0 = 1026 kg/m3, speed of sound c = 1484 m/s, mass of the panel(per unit area) m, and angular frequency ω. Here, an idealised value of the density of fibre-reinforced plastic(ρ=2ρ0) is assumed. For larger frequencies the reduction index of wall pressure fluctuations substantiallyincreases but this increase is interrupted by collapses for some frequencies.

In Fig.5 (b) the spatial coherence γ2(x, f) for U∞ = 4.9 m/s, i.e. for a towing speed of U = 4.3 m/s, isdepicted. The variable x refers to the distance from the reference hydrophone hyd1 (by definition γ2(x =

0, f)=1). In the very low frequency regime pronounced peaks with a large coherence length exists. This is atypical property of underwater sound in this frequency regime, so these peaks very likely origin from externalsound sources [7, 23], such as the towing vessel, and disturb the measurement. Therefore it is appropriate toremove contributions having a large spatial coherence length from the PSD. This can be done by separatingthe spatially incoherent part according to Φi,inc = Φi (1 - γ2(|pos(hydj) - pos(hydi)|,f) ). In this work we havechosen i = 1 and j=9. The position of hyd9 is indicated by a horizontal line in Fig.5 (b). It should be noted,that the pattern of spatial coherence differ qualitatively beneath the thin and the thick plate [1].

For the modified reduction index of wall pressure fluctuations the spatially incoherent part of the PSD,i.e. Φi,inc, is used instead of Φi and therefore the transmission coefficient is defined as τinc = (Φi,inc/Φo,corr).In Fig.6 the modified reduction index is shown for the same speeds as in Fig.5 (a). It can be seen that theexperimental curves are smoother than those depicted in Fig.5 (a), because the coherent peaks have beenremoved from the PSD of interior noise.

In [1] a general form of a transmission coefficient τ = 1/ | 1+ ( Z / ρ0 c)2 |, with plate impedance Z =p/v (p pressure, v panel velocity) has been considered. Assuming this dependence for the reduction index ofwall pressure fluctuations, than the plate impedance Z would be three orders of magnitude larger for R thanfor Rsound. In Fig.6 two different theoretical curves for R are depicted. The reduction index RPU reflects thebehaviour of the thick sandwich plated studied in [1] with ZPU = 2500 ω m. For comparison a curve of Rwith Z = 15000 ω m′ is added for the thin plate. Note, that the mass of the thin plate m′ is smaller than thatof the tick plate m (m′ < m). This curve would reflect an even higher reduction index for the thin than for the

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Figure 6: Modified reduction index R=10log10(1/τinc) of wall pressure fluctuations for threedifferent flow speeds. For comparison the mass law of sound waves and two theoretical curves,R and RPU , are plotted. RPU reflects the transmission behaviour of the thick sandwich plate [1],while R is adapted to the behaviour of the thin plate.

thick plate despite of the additional layer of polyuerthan [1]. Though it must be stressed that the experimentalcurves do not support this conclusion with absolute certainty, it can be stated, however, that the reductionindex of wall pressure fluctuations is in the same order of magnitude for both the thin and the thick plate.

5. CONCLUSIONS

In this work the transmission behaviour of a thin plate excited by turbulent wall pressure fluctuations isinvestigated in an underwater experiment. The transmission loss of wall pressure fluctuations through theplate is some order of magnitude larger than that of sound waves in the considered frequency regime, becauseno coincidence between plate vibrations and wall pressure fluctuations occur due to the high wavenumber ofthe fluctuations. In order to quantify the transmission behaviour of the plate a reduction index is defined asthe ratio between the (Corcos-corrected) PSD of wall pressure fluctuations and the (spatially incoherent partof the) PSD of interior hydroacoustic noise. The experimental curves follow a reduction index with an f2

asymptotic for large frequencies. In particular the order of magnitude of transmission loss is the same for thethin and the thick [1] plate for all flow speeds. The reduction of flow noise induced from a turbulent boundarylayer by a mechanical structure is crucial in underwater applications.

ACKNOWLEDGEMENT

The excellent support from the technical division of WTD71-FWG as well as from captain and crew of RVELISABTH MANN BORGESE is gratefully acknowledged.

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