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 Δ x 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 Δ x values but very good agreement for the smallest Δ x. 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 Δ x to be 20% or less of the flowfield characteristic length in terms of density gradient.

Combined Experimental and Numerical Investigation of a Hypersonic Turbulent Boundary Layer by Means of FLDI and Large-Eddy Simulations

“…This algorithm is based on the ray-tracing model presented in [44], with further improvements detailed in [48]. A detailed description of the cFLDI algorithm used in the present work is presented in [49]. That work also validates the implemented cFLDI, using measurements on the flowfield generated by a weak blast wave.…”

“…This is especially the case for the free stream spectra in the present work. The conical flowfield contributions to the FLDI signal are expected to be approximately equal throughout the probing volume, or at least within the boundaries of the conical shock (notwithstanding, the circular symmetry of the flowfield surrounding the conical model must be properly considered when probing along a straightline FLDI, as seen in [49]). With such an extensive probing volume, the influence of the varying sensitive length is expected to cause significant amplitude differences across the frequency spectrum.…”

“…In these works, computational FLDI was confirmed to be able to extract information from the numerical flowfield directly comparable with experiments. This ability was applied in [49], where cFLDI was used to check the validity of simplifying hypotheses adopted in a postprocessing approach for FLDI measurements in circular flowfields. Computational FLDI has also been used to perform parametric studies on the FLDI response to single-frequency disturbances [50].…”