Reconstruction of surface-pressure fluctuations using deflectometry and the virtual fields method

Abstract

Abstract This study presents an approach for obtaining full-field dynamic surface-pressure reconstructions with low differential amplitudes. The method is demonstrated in a setup where an air jet is impinging on a flat plate. Deformations of the flat plate under dynamic loading of the impinging jet were obtained using a deflectometry setup that allows measurement of surface slopes with high accuracy and sensitivity. The measured slope information was then used as input for the virtual fields method to reconstruct pressure. Pressure fluctuations with amplitudes of down to $${\mathcal {O}}(1)~\text {Pa}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo><mml:mspace/><mml:mtext>Pa</mml:mtext></mml:mrow></mml:math> were extracted from time-resolved deflectometry data using temporal band-pass filters. Pressure transducer measurements allowed comparisons of the results with an established measurement technique. Even though the identified uncertainties in fluctuations were found to be as large as 50%, the spatial distributions of dynamic pressure events were captured well. Dynamic mode decomposition was used to identify relevant spatial information that correspond to specific frequencies. These dynamically important spatio-temporal events could be observed despite their low differential amplitudes. Finally, the limitations of the proposed pressure determination method and strategies for future improvements are discussed. Graphic abstract