Lagrangian Strain- and Rotation-Rate Tensor Evaluation Based on Multi-pulse Particle Tracking Velocimetry (MPTV) and Radial Basis Functions(RBFs)

Physical conservation laws are inherently Lagrangian. However, analyses in fluid mechanics using the Lagrangian framework are often forgone in favor of those using the Eulerian framework. This is perhaps due to a lack of experimental techniques with high temporal and spatial resolution that track the movement of fluid tracers in a flow domain. The development of time-resolved Particle Tracking Velocimetry/Accelerometry (TR-PTV/A) that measures flows with high seeding density has made the use of the Lagrangian framework more accessible. A challenge facing PTV/A is the need for robust mesh-free numerical schemes that handle random particle locations. Such a scheme can be created with high-order accuracy using Radial Basis Functions (RBFs). RBFs allow direct evaluation of derivatives of vector and scalar fields at random locations with infinite-order smoothness. The current work uses RBF-based differential schemes to develop a post-processing tool for PTV/A data, which can accurately evaluate spatial derivatives directly from Lagrangian particle tracks. This RBF-based strain/rotation-rate tensor evaluation tool is validated with two and three-dimensional flows from analytical solutions and is then tested with experimental data measured by a multi-pulse PTV/A system.