Characterization of the Response of a Curved Elastic Shell to Turbulent Boundary Layer

For the effective operation of sonar system mounted inside the bulbous of a fast ship, it is important to reduce all the possible noise and vibration sources that cause the dome to vibrate thus radiating noise and interfering with sonar sensor response. In particular, pressure fluctuations induced by the turbulent boundary layer on the surface of the sonar dome represent one of the major sources of self-noise for the on board sensors. Calculation of the structural vibrations and of the noise radiated inside the dome requires as a first step the characterization of the frequency spectra of turbulent boundary layer excitation. Most of the literature related to wall pressure fluctuations is devoted to the study of equilibrium turbulent boundary layers on flat plates in zero pressure gradient (ZPG) flow, for which scaling laws for the power spectral densities and empirical models for the cross spectral densities are well established. The turbulent boundary layer on the bulbous can present several differences with respect to the canonical case because of the presence of hull surface curvatures and of the free water surface that produce pressure gradient variation along the bulbous surface. Moreover, hydrodynamic coincidence effects play a markedly different role in the underwater problem than in the aerodynamic problem. Therefore, an experimental campaign was performed in a towing tank to measure wall pressure fluctuations at different locations along a large scale model of a bulbous and to investigate their spectral characteristics in terms of auto and cross spectral densities. Boundary layer mean flow parameters were obtained with a finite volume code solving the Reynolds Averaged Navier Stokes Equations. The auto spectral densities (ASD) of the measured wall pressure fluctuations were scaled using different combinations of inner and outer flow parameters in order to make ASD independent of the tested conditions i.e. of Reynolds number. The modelled load was used as input for a numerical procedure aimed at evaluating the dynamical response of a section of the bulbous under analysis. The validation of this procedure was experimentally obtained through the measurements of the vibrational response of an elastic section inserted into the bulbous model. Moreover, this comparison indirectly provides additional insights on the physics of wall pressure fluctuations for complex flows.