An advection-based model to increase the temporal resolution of PIV time series

A numerical implementation of the advection equation is proposed to increase the temporal resolution of PIV time series. The method is based on the principle that velocity fluctuations are transported passively, similar to Taylor's hypothesis of frozen turbulence. In the present work, the advection model is extended to unsteady three-dimensional flows. The main objective of the method is that of lowering the requirement on the PIV repetition rate from the Eulerian frequency toward the Lagrangian one. The local trajectory of the fluid parcel is obtained by forward projection of the instantaneous velocity at the preceding time instant and backward projection from the subsequent time step. The trajectories are approximated by the instantaneous streamlines, which yields accurate results when the amplitude of velocity fluctuations is small with respect to the convective motion. The verification is performed with two experiments conducted at temporal resolutions significantly higher than that dictated by Nyquist criterion. The flow past the trailing edge of a NACA0012 airfoil closely approximates frozen turbulence, where the largest ratio between the Lagrangian and Eulerian temporal scales is expected. An order of magnitude reduction of the needed acquisition frequency is demonstrated by the velocity spectra of super-sampled series. The application to three-dimensional data is made with time-resolved tomographic PIV measurements of a transitional jet. Here, the 3D advection equation is implemented to estimate the fluid trajectories. The reduction in the minimum sampling rate by the use of super-sampling in this case is less, due to the fact that vortices occurring in the jet shear layer are not well approximated by sole advection at large time separation. Both cases reveal that the current requirements for time-resolved PIV experiments can be revised when information is poured from space to time. An additional favorable effect is observed by the analysis in the frequency domain whereby the spectrum becomes significantly less prone to aliasing error for the super-sampled data series.