Surface pressure measurements of an impinging jet with deflectometry*

Optical measurements were used to reconstruct low amplitude surface pressure fluctuations in high resolution on a thin plate with the Virtual Fields Method (VFM). Surface slopes induced by an impinging synthetic jet were measured contactless using a highly sensitive deflectometry setup. The periodic slope signals, which were below instantaneous noise level, were recovered using phase averaging. Time filter techniques were used with equal success, obtaining slope maps with amplitudes well below 10 mm km^-1. Based on the Principle of Virtual Work, the VFM allowed reconstructions of surface pressure from full-field data. It requires knowledge of the plate material parameters, surface curvatures and accelerations as well as a set of virtual fields to be chosen. Curvatures were calculated from the measured surface slopes. Accelerations were found to be negligible here based on LDV measurements. Virtual fields were defined piecewise using Hermite 16 shape functions. Sensitivity analysis allowed assessing the systematic error. Results were validated using pressure transducer measurements. The outcome is remarkable with reconstructed pressure amplitudes of down to only several Pa of flow structures of the size of few mm in high resolution.