Focused laser differential interferometry post-processing methodology for flowfields with circular symmetry

Abstract

An analytic methodology is presented to reconstruct the pressure waveform of flowfields with circular symmetry from the phase shift detected with Focused Laser Differential Interferometry (FLDI). A weak blast wave generated by an electric spark in ambient air is investigated with the proposed approach. Values of separation distance between the differentiating foci of the FLDI Δx of 76, 120, 175, and 252 μm are employed to probe the flowfield at locations between 3 and 50 mm from the spark source. In a subset of these distances, reference measurements of peak pressure obtained with a surface pressure sensor indicate good agreement with the reconstructed data when small separation distances are used. Further analysis of FLDI reconstructed data is conducted using theoretical correlations for N-waves in terms of the distribution of pressure peak amplitude and compression phase as the wave front propagates. Agreement with theory is verified for all differentiation separation distances except the largest, for which peak pressure comparison shows a 10% loss of measured vs predicted value. A computational FLDI is employed to scrutinize the simplifying hypotheses supporting the waveform reconstruction approach. The direct comparison between experimental and computational FLDI output reveals additional discrepancies for intermediate Δx values but very good agreement for the smallest Δx. The proposed methodology is thus verified to be reasonable, upon appropriate minimization of the FLDI differentiation distance. A parametric analysis using computational FLDI indicates the adequate value of FLDI Δx to be 20% or less of the flowfield characteristic length in terms of density gradient.