Dimensionless Representations of the Interaction Between Turbulent Boundary Layer and Elastic Plates

The study of the interaction between elastic structures and turbulent boundary layer still presents some uncertainties. This is true even assuming a oneway coupling and stationary turbulent boundary layer (TBL) over smooth and flat plates in subsonic flow. The reasons are mainly related to (i) the limitation for the direct numerical simulations of Reynolds number value of the Navier-Stokes equations, (ii) the high frequency structural and acoustic numerical and modelling difficulties and (iii) the lack of experimental data representative of all frequencywavenumber pressure fluctuation regions, needed for the direct validation of the semi-empirical pressure models. In fact, when the pressure convective terms are the dominant sources of vibrations and radiated noise, consolidated and almost case independent formulations exist; on the contrary, when the subconvective terms are of concern, the definition of models seems to be strongly dependent on the flow conditions and the characteristics of the fluid-structure interaction. In order to find a general procedure for the estimation of the response of elastic thin panels to TBL excitation, some scaling laws derived using dimensional analysis and energetic considerations are proposed. These dimensionless relations contain a combination of both flow and structural parameters yielding to simple analytical expressions relating a dimensionless structural response metric and a dimensionless frequency. The found scaling expressions are validated with wall pressure fluctuations and vibrational response data acquired in wind tunnels and towing tank for the case of thin flat plates made of homogeneous isotropic and composite materials.