Discussion About Different Methods for Introducing the Turbulent Boundary Layer Excitation in Vibroacoustic Models

Abstract

For controlling the noise radiated from vibrating structures excited by turbulent boundary layer (TBL) it is relevant to develop numerical tools for understanding how the structure reacts to TBL excitation. Usually, the wall pressure fluctuations of the TBL are described through statistical quantities (i.e. space-frequency or wavenumber-frequency spectra) which depend on the TBL parameters. On the other hand, the vibro-acoustic models (i.e. Finite Elements, Boundary Elements, Transfer Matrix Methods, Analytical models, etc) evaluate deterministic transfer functions which characterise the response of the considered structures. The first part of this paper focuses on the coupling between the stochastic TBL and the deterministic vibro-acoustic models. Five techniques are presented. Numerical applications on an academic marine test case are proposed in order to discuss the calculation parameters and the interests / drawbacks of each technique. In the second part of the paper, the high frequency modelling with the Statistical Energy Analysis (SEA) method is considered. The focus is placed on the estimation of an important input of this method: the injected power by the TBL into the structure for each third octave band.

Modeling vibrating panels excited by a non-homogeneous turbulent boundary layer

“…When ω increases, the convective wavenumber k c moves in the high-wavenumber region, further away from k f , and the main contributing part becomes the low-wavenumber region of the spectrum. Well above The calculation processes described in the literature generally assume that the TBL is spatially homogeneous (Maury et al, 2002;Hambric et al, 2004;Ciappi et al, 2009;Maxit et al, 2015). For practical applications, this assumption is rarely met.…”

“…Several authors have studied different ways to achieve this coupling for spatially homogeneous TBL. Maxit et al (2015) summarized five techniques for coupling stochastic TBL and deterministic vibro-acoustic structure models:…”

“…The spatial method is based on a regular discretization of the excited surface. The discretization step must be substantially smaller than the convective wavelength λ c = 2π/k c (Maxit et al, 2015), which gives a dense mesh, especially when the frequency increases, and therefore significant computing time. Franco et al (2013) present three time saving approaches applied with FEM model.…”

Estimation of turbulent boundary layer induced noise using energy flow analysis for ship hull designs

“…4,5 Studies to adopt relative methods developed in the aeroacoustic fields for naval ships are being performed in a limited manner on the local elements of the structure such as square plates; however, numerical methods have limitations due to lower convective speed of turbulent flows having relatively low frequency range excitation and involving higher speed of sound propagation. 6,7 The lack of usable acoustic performance assessment methods is a cause of concern in the context of the acquirement programs of future naval ships in gaining a competitive edge at the “Noise War” considering a typical 10-year-period of the design stage and 20 years of operation.…”

“…However, the SEA method is limited to the high-frequency range where the frequency range is broad and modal density is high; thus, its limitations are more emphasized for underwater environments wherein the input force wavenumber is low and sound propagation speed is high. 6,7 In addition, it is limited to applications of local damping and input power owing to a lack of information concerning the spatial energy distributions for subsystems. 14 To overcome these limitations, among various approximating methods being developed, Belov et al 15 suggested the energy flow analysis (EFA) methods.…”