Abstract
In the analysis of Lagrangian particle tracking data, ensemble averaging with spatial bins is used to generate Eulerian flow statistics. Due to the scattered nature of the particles over independent snapshots, the possible spatial resolution is directly dependent on the measured particle position accuracy and the amount of available data. This requires a balance between convergence of the underlying statistic and the bin resolution. Current binning approaches use the velocity information of the particle positions at single time steps directly and do not exploit the additional information available from the temporal filtering of the tracking process. We present a novel functional approach to the binning procedure that extracts all available information from the particle tracks and improves convergence speed. For a given experiment this allows for higher resolution of flow statistics than classical approaches or alternatively to reduce the necessary amount of data required for a given resolution. Furthermore, uncertainty measures from the particles position, velocity and acceleration can be propagated directly by weighting coefficients.
Highlights
For a given experiment this allows for higher resolution of flow statistics than classical approaches or alternatively to reduce the necessary amount of data required for a given resolution
Ensemble averaging of flow fields measured for a time series of snapshots is a key component in the calculation of flow statistics
While particle image velocimetry (PIV) can be used to determine the flow fields for snapshots, it is limited by the use of correlation windows which inherently introduces a low pass filtering effect on resolvable flow structures and velocity fluctuations respective gradients
Summary
Ensemble averaging of flow fields measured for a time series of snapshots is a key component in the calculation of flow statistics. The fitted polynomial is evaluated at the bin center to give the mean velocity value for that bin All these approaches have in common that they consider flow information at individual particle positions. A different way, which is currently in use for MPSTB, considers only the midpoint of a fitted track to provide a single virtual particle with low error at the cost of less particles that are available for binning It is not just individual particles that are available, but a track in form of a parametric function over time, e.g. 2nd/3rd order B-spline or polynomial fits along pulses One way this could be improved upon would be to sample additional points along the track, for example at the points closest to each bin center.
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