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

The panel vibrations induced by fluctuating wall pressures within wall-bounded jet flow downstream of a high aspect ratio rectangular nozzle are simulated. The wall pressures are calculated using a Hybrid RANS/LES method, where LES models the large-scale turbulence in the shear layers downstream of the nozzle. The convecting turbulence in the shear layers loads the structure 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, generating backward-traveling surface pressure loads that drive the structure at low frequencies. The panel is rectangular with clamped edges along the sides oriented in the flow direction and free edges at the nozzle discharge and downstream edge. The panel modes of vibration are simulated with Finite Element Analysis. The structural vibration time histories are simulated by Fourier transforming the loading to the complex frequency domain, combining with the structural frequency response functions and inverse transforming the response back to the time domain. Simulated wall pressures and structural vibration agree well with measurements at on-design and underexpanded (about 50% higher pressure ratio) nozzle operating conditions. Filtering the negative wavenumber components from the loading and recomputing the structural response shows that the backward-traveling loading is responsible for about 12% of the overall structural vibration at on-design conditions and 25% of the response at underexpanded conditions.