Super-temporal global reconstruction of convective disturbances from images of two-dimensional flows

Abstract

A method for converting spatial data from high-speed schlieren visualizations into upsampled temporal data, previously limited to applications involving fluid flows with uniform-velocity disturbances, is extended to flows with variable-velocity disturbances. Schlieren-based velocimetry is first employed to derive disturbance propagation speeds and directions throughout the schlieren field of view. The velocity field is then integrated to determine disturbance streamlines through discrete pixel locations, permitting reconstructions of the temporal signal at times between schlieren images. The resulting temporal signals have an effective sampling rate governed by the spatial resolution of the images, rather than the camera frame rate, with the local propagation speeds providing the necessary conversion to temporal units. The efficacy of the method is demonstrated by applying it to a schlieren dataset capturing Mach 6 flow over a cone–flare model with a frame rate of 824 kHz. The frame rate is sufficient to resolve the relevant second-mode disturbances from the raw pixel times series, allowing for quantitative comparisons between the raw and reconstructed signals. The reconstruction process enhances the information extractable from the temporal signals by eliminating aliased content previously constrained by the camera’s Nyquist frequency and enabling the analysis of additional high-frequency content. The accuracy and robustness of the reconstruction are validated by introducing known errors into the signals. Increased camera frame rates correlate with improved robustness, with errors in propagation speed of up to \(\pm 10\%\) having minimal impact on the spectral characteristics of the signal for frame rates as low as approximately half the primary disturbance frequency.