High-frequency flow field reconstruction method based on compressed sensing and its applications

Though particle image velocimetry (PIV) has a high spatial resolution, it is often limited by the temporal resolution, which is typically below 15 Hz and difficult to acquire high-frequency flow information. Compressive sensing (CS) is able to capture the high-frequency information based on sparse sampled data, but if directly employed to all spatial points, the massive data poses a great computational cost. In this study, a high-frequency response flow field reconstruction method via coupling POD and CS is proposed to solve the above difficulty. POD is used first to reduce the dimensionality of the sampled PIV data, and the spatial modes and corresponding time coefficients are calculated at the same time. By taking the time coefficients at the sub-Nyquist sampling points in CS as the observable and selecting an appropriate sparse basis, the high-frequency mode coefficients can be computed via the basic pursuit method. The unsteady flow field with high-frequency temporal information can then be reconstructed via combining the spatial modes and the corresponding resolved time coefficients. Two cases, i.e. the periodic oscillator flow and the non-periodic double-cylinder wake flow, are used to test the adaptivity of the proposed method. The results show that without the aid from contact measurement, the proposed method can accurately reconstruct the original flow field for period flow and the reconstruction error is less than 3%, while for nonperiodic complex flow, the error is significantly increased due to high-frequency noise. Overall, the proposed method can be used for periodic flow to improve the temporal resolution of the measured experimental data.