Modal decomposition method in rectangular ducts in a test-section of a cavitation tunnel with a simultaneous estimate of the effective wall impedance

Highlights

• Acoustic demodulation method in cavitation tunnel.

• Wall-impedance taken into account in the method.

• Effective impedance measurements.

• Assessment of the demodulation method by simulation.

• Performances of the method estimated by corrupted simulated data.

Abstract

The operational requirements for naval and research vessels have seen an increasing demand for quieter ships either to comply with the ship operational requirements or to minimize the influence of shipping noise on marine life. The radiated noise of a ship is estimated during the design stage by measurements with a scale model, generally realized in a tunnel or a depressurized tank. DGA Hydrodynamics owns its cavitation tunnel with low background noise that allows such measurements. Nowadays, a low background noise of the whole facility is not sufficient to perform an accurate acoustic measurement. Improving our knowledge about the acoustic response of the facility is then required to assess the relationship between the measurements and the noise radiated by a propeller for example. The confined geometry of the test-section imposes particular boundary conditions to the acoustic propagation and a reverberation-like behaviour. The acoustic response of the facility is then disturbed compared to a free-field configuration. This particular acoustic behaviour makes the absolute estimate of the underwater radiated noise power very difficult. A possibility to overcome this problem could be the use of an appropriated model coupled with the modal propagation theory. Following this approach, a method to estimate both modal magnitudes and wall impedance is proposed in this paper and confronted to experimental results.

Introduction

Numerous studies have been performed since many years with the aim to improve our understanding of underwater radiated noise induced by a propeller. Military reasons as well as impacts on marine fauna have motivated several institutes to study noise generation by vessels. Even if the help of computational fluid dynamics (CFD) is a way to predict the noise level emitted by a vessel (see Testa et al., 2017), experimental approaches like measurements in cavitation tunnel with a scaled model is nowadays preferred because its reliability (ITTC, 2017). Other experimental facilities deal with the same goals in depressurized tank with others acoustical effects as reverberation and motion of the model inside the facility (see for example Lafeber et al., 2015). The performance of such measurements to predict the underwater noise levels at full-scale is strongly linked to our knowledge of the facility and our capability to take into account its acoustic response during the analysis. From an “acoustical” point of view, the useful section of a cavitation tunnel looks like a duct filled with water. Even if the acoustic propagation in duct is well-known by acousticians, this topic is still subject of research with the aim to develop more applicable models and/or to take into account more details as a particular flow or specific geometries. Actually, since several decades, different experiments have been performed inside ducts in air with or without flow (Abom, 1989, Dalmont, 2001, Schultz et al., 2006, Boucheron, 2017), with the aim to decompose the acoustic field into several modes that propagate. Several methods dedicated to the estimate of complex magnitude of propagative modes have been proposed and used with success in cases without flow and high acoustic levels. The goal is generally to decompose the acoustic field and to estimate the absorption performance of a given liner. Recently, such experiments have been performed with the presence of a mean flow in air in a wind tunnel (Suzuki and Day, 2015). Another application of such approach is described by Xin et al. (2018) to estimate the impedance of a duct termination, or also to combine vibrations of the duct with the acoustic propagation inside (as done for example by Pagneux and Aurégan, 1998).

The problem in our configuration is slightly different. The estimate of the acoustic noise level of an acoustic source in a cavitation tunnel is generally performed with the help of several hydrophones close to the source to be measured (see Section 3 further). The proximity of sensors close to the source is needed to improve the signal-to-noise ratio and also regarding the reverberation of the facility as explained by Briançon-Marjollet et al. (2013) and Tani et al. (2015a). This configuration is classically used with transfer functions to correct the results obtained for different experimental features as directivity of sensors, reverberation or resonance inside the tunnel (see for example Boucheron, 2019a). High deviation of transfer functions could be observed experimentally when the location of the acoustic source is slightly shifted (Tani et al., 2015b): corrections made by the transfer function are then highly sensitive to the accuracy of measurements and location of the source. The reason generally admitted by the community is that the near field imposed by the source is dependent on its location and on the decomposition of the field into propagative/evanescent waves. The closer to an anti-node of a given mode the source, the more important the complex magnitude of this mode (Boucheron, 2017, Hynninen et al., 2017). In consequence, we have to manage both modes that propagate and modes that decay in the vicinity of the source, which generally leads the existing iterative methods to diverge due to their high sensitivity to discrepancies.

In parallel to theoretical studies, acousticians are looking for measuring each mode magnitude (expressed in complex plane, that is including the phase information) to describe the whole acoustic field in the duct. Several methods have been developed in particular cases like hard-wall boundary conditions: this could be done experimentally in rectangular case (see Schultz et al., 2006, Suzuki and Day, 2015) or circular cases (Abom, 1989, Dalmont, 2001 as examples). These techniques could be employed successfully to manage the radiation impedance of a given duct end-stage or to measure absorption of a liner disposed inside the duct as performed by Pagneux et al. (1996) for example. Several numerical methods have also been developed to deduce the liner impedance of a duct with mean flow as done by Jones et al. (2005). The impedance of the duct walls (in air applications) are taken to be so large that the hypothesis of a very small admittance holds. However, in cavitation tunnel, the infinite impedance hypothesis for the duct walls has to be called into question due to the relative impedance ($Z_{\mathrm{mat}}∕Z_{\mathrm{water}}$) between propagation medium (water) and wall material. Indeed, denoting $\varrho$ for density and $c_0$ for celerity in a medium, the impedance ($\varrho c_0$) ratio between water and stainless steel is about 30 which remains a high value, but for Perspex (material used for cavitation tunnel windows), the ratio is around 2. Modifications due to the presence of this finite impedance at wall are important and need to be managed gingerly. This key point in our configuration is taken into account in the proposed method and discussed during the analysis of the results obtained experimentally in our cavitation tunnel. The inverse problem considered here consists of retrieving both modal magnitudes and impedance features.

The paper is structured in five sections. The next one describes the modal acoustic theory whereas the third section presents the proposed demodulation method. The fourth section is dedicated to the results obtained with simulation performed to characterize the main features of the demodulation algorithm and to assess its reliability conditions. The last part presents the facility used to get experimental data. Finally, results are presented and discussed after which the conclusions are given.