Simulation of the pressure field beneath a turbulent boundary layer using realizations of uncorrelated wall plane waves

Abstract

This paper investigates the modelling of a vibrating structure excited by a turbulent boundary 15 layer (TBL). Although the wall pressure field (WPF) of the TBL constitute a random excitation, the element-based methods generally used for describing complex mechanical structures consider deterministic loads. The response of the structure to a random excitation like TBL is generally deduced from calculations of numerous Frequency Response Functions. The result is that the process requires costly computational resources. To tackle this issue, an efficient 20 process is proposed for generating realizations of the WPF corresponding to the TBL. This process is based on a formulation of the problem in the wave-number space and the interpretation of the wall pressure field as uncorrelated wall plane waves. Once the WPF have been synthesized, the local vibroacoustic responses are calculated for the different realizations and averaged together in the last step. A numerical application of this process to a plate beneath 25 a TBL is used to verify its efficiency and ability to reproduce the partial space correlation of the excitation. Finally an application on a stiffened panel modelled with the finite element method is proposed to illustrate the interest of the proposed process.Running title: Numerical synthesis of random pressure field 30

Numerical prediction of turbulent boundary layer noise from a sharp‐edged flat plate

“…Figure 18 shows the Graham's parameter in the wavenumber domain. Hence, the criteria defined in Equation (23) can be updated as follows: Equation (29) implies that, for a given k x , k y is varying between upper and lower bounds governed by two lines as depicted in Figure 18. 46 Although a finite-span plate is considered in this work, the contribution of the subcritical gusts to the far-field scattered pressure is negligible as the Hann window has been applied to the incident pressure at the two sides of the contraction outlet, which forces the pressure gust magnitudes to zero at the plate spanwise ends.…”

“…The two lines with the slope of ± M∕Λ are supercritical gusts and are expected to dominate the scattered pressure. This is due to the fact that, using the criteria in Equation (29), only a small part of the wavenumber space domain was considered to numerically evaluate the Fourier integral in Equation (4), as shown in Figure 18. This is due to neglecting larger wavenumbers in the spanwise direction, which have shorter wavelength.…”

“…This is due to neglecting larger wavenumbers in the spanwise direction, which have shorter wavelength. This study was performed on 10% of the full span of the plate, and the cutoff wavenumbers in Equation (29) were used. Figure 19 shows two realizations of the wall pressure field at the same frequencies as those used in Figure 12.…”

“…At all frequencies, it can be observed that there is no radiation in directions corresponding to 0 • and 180 • , attributed to the finiteness of the chord. The UWPW-BEM results were obtained by ensemble averaging the scattered pressure over 30 realizations using the criteria in Equation (29). They travel along the surface of the airfoil until they arrive at the leading edge where they are diffracted.…”

“…The UWPW approach is summarized in what follows. The space-frequency cross-spectrum of the wall pressure fluctuations is given by 29,36…”