Wavenumber Analyses of Panel Vibrations Induced by Supersonic Wall-Bounded Jet Flow from an Upstream High Aspect Ratio Rectangular Nozzle

The structural vibrations of a flat plate induced by fluctuating wall pressures within wallbounded jet flow downstream of a high-aspect ratio rectangular nozzle are simulated. The wall pressures are calculated using Hybrid RANS/LES, where LES models the large-scale turbulence in the shear layers downstream of the nozzle. The structural vibrations are computed using modes from a finite element model and a time-domain forced response calculation. At low speeds, the convecting turbulence in the shear layers loads the plate in a manner similar to that of turbulent boundary layer flow. However, at supersonic discharge conditions the shear layer turbulence also scatters from shock cells near the nozzle, generating backward traveling low frequency surface pressure loads that also drive the plate. The structural mode shapes and subsonic and supersonic surface pressure fields are transformed to wavenumber space to better understand the nature of the loading distributions and individual modal responses. Modes with wavenumber distributions which align well with those of the pressure field respond strongly. Negative wavenumber loading components are clearly visible in the transforms of the supersonic flow wall pressures, showing backward propagating pressure fields. In those cases the modal joint acceptances include significant contributions from negative wavenumber terms.