Flow reconstruction and particle characterization from inertial Lagrangian tracks

This text describes a method to simultaneously reconstruct flow states and determine particle properties from Lagrangian particle tracking (LPT) data. LPT is a popular measurement strategy for fluids in which particles in a flow are illuminated, imaged (typically with multiple cameras), localized in 3D, and then tracked across a series of frames. The resultant "tracks" are spatially sparse, and a reconstruction algorithm is commonly employed to determine dense Eulerian velocity and pressure fields that are consistent with the data as well as the equations governing fluid dynamics. Existing LPT reconstruction algorithms presume that the particles perfectly follow the flow, but this assumption breaks down for inertial particles, which can exhibit lag or ballistic motion and may impart significant momentum to the surrounding fluid. We report an LPT reconstruction strategy that incorporates the transport physics of both the carrier fluid and particle phases, which may be parameterized to account for unknown particle properties like size and density. Our method enables the reconstruction of unsteady flow states and determination of particle properties from LPT data and the coupled governing equations for both phases. We use a neural solver to represent flow states and data-constrained polynomials to represent the tracks (though we note that our technique is compatible with a variety of solvers). Numerical tests are performed to demonstrate the reconstruction of forced isotropic turbulence and a cone-cylinder shock structure from inertial tracks that exhibit significant lag, streamline crossing, and preferential sampling.