Abstract
Processing techniques for particle-based optical flow measurement data such as 3D particle tracking velocimetry (PTV) or the novel dense Lagrangian particle tracking method ‘Shake-the-Box’ (STB) can provide time-series of velocity and acceleration information scattered in space. The following post-processing is key to the quality of space-filling velocity and pressure field reconstruction from the scattered particle data. In this work we describe a straight-forward extension of the recently developed data assimilation scheme FlowFit, which applies physical constraints from the Navier–Stokes equations in order to simultaneously determine velocity and pressure fields as solutions to an inverse problem. We propose the use of additional artificial Lagrangian tracers (virtual particles), which are advected between the flow fields at single time instants to achieve meaningful temporal coupling. This is the most natural way of a temporal constraint in the Lagrangian data framework. FlowFit’s core method is not altered in the current work, but rather its input in the form of Lagrangian tracks. This work shows that the introduction of such particle memory to the reconstruction process significantly improves the resulting flow fields. The method is validated in virtual experiments with two independent DNS test cases. Several contributions are revised to explain the improvements, including correlations of velocity and acceleration errors in the reconstructions and the flow field regularization within the inverse problem.
Highlights
Processing techniques for particle-based optical flow measurement data such as 3D particle tracking velocimetry (PTV) or the novel dense Lagrangian particle tracking method ‘Shake-the-Box’ (STB) can provide time-series of velocity and acceleration information scattered in space
We propose the use of additional artificial Lagrangian tracers, which are advected between the flow fields at single time instants to achieve meaningful temporal coupling
This paper addresses the questions of both uncertainty quantification and temporal consistency in FlowFit’s flow field reconstructions, as an understanding of either one of these topics may greatly contribute to the other
Summary
In applications of particle based optical flow measurement techniques images, in the form of subsequently illuminated tracer particle pictures, are captured from which velocity information can be estimated by PIV evaluation methods [10] or particle tracks can be inferred by tracking techniques such. The found particle trajectories and related velocity and acceleration information is well-defined regarding their individual positions in space, their scattered appearance and (mean) interparticle distances does not enable a simple and global spatial filling calculation of the desired (time-resolved) 3D velocity gradient tensor [14] and pressure fields For this purpose, different spatial interpolation algorithms were proposed, such as FlowFit [7, 15] and VIC+ [8, 16], which take instantaneous Lagrangian particle-track data (position, velocity and acceleration) as input and exploit known physical properties such as vanishing divergence and the Navier–Stokes equations for incompressible and uniform-density flows to reconstruct accurate and space-filling velocity, acceleration and/or pressure fields [17,18,19]. The inverse nonlinear optimization problem is addressed by minimization of a cost function that is composed of the deviations from the incompressible Navier–Stokes equations; see the appendix for a brief recapitulation of the applied method or [7] and [15]
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