Adaptive ensemble PTV

Ensemble particle tracking velocimetry (EPTV) is a method to extract high-resolution statistical information on flow fields from particle image velocimetry (PIV) images. The process is based on tracking particles and extracting the velocity probability distribution functions of the image ensemble in averaging-regions deemed to contain a sufficient number of particle pairs/tracks. The size of the averaging regions depends on the particle density and the number of snapshots. An automatic adaptive variation of the ensemble PTV is presented to further push the spatial resolution of the method. The proposed adaptive-EPTV is based on stretching and orienting the averaging regions along the direction of maximum curvature of the velocity fields. The process requires a predictor calculation with isotropic-window EPTV to compute the second derivatives of the mean velocity components. In a second step, the principal directions of the Hessian tensor are calculated to tune the optimal orientation and stretch of the averaging regions. The stretching and orientation are achieved using a Gaussian windowing with different standard deviation along the local principal direction of the Hessian tensor. The algorithm is first validated using three different synthetic datasets: a sinusoidal displacement field, a channel flow and the flow around a NACA 0012 airfoil. An experimental test case of an impinging jet equipped with a fractal grid at the nozzle outlet is also carried out.