3D Particle Position Determination And Correction At High Particle Densities
D. Schanz, T. Jahn, A. Schröder
German Aerospace Center (DLR), Inst. of Aerodynamics and Flow Technology, Göttingen, Germany
The method of Iterative Particle Reconstruction (IPR), introduced by Wieneke in 2013, constitutes a major step towards high-density 3D Lagrangian Particle Tracking. It reconstructs 3D particle positions from their projections onto several cameras. In the first part of this work, we present several approaches to enhance the original IPR working principle which, in combination, nearly triple the processable particle image densities, allowing complete and ghost-free reconstructions on a single snapshot from a four-camera system at up to 0.14 particles-per pixel (ppp). The updated method is proven to be fast, accurate and robust against image noise and other imaging artifacts. A central piece of the IPR functionality is a position optimization algorithm, using the difference of the local re-projected and original images (the residual images) as a cost function and displacing particles along its steepest gradient ('shaking' of the particles). The same approach is used within the Shake-The-Box (STB) Lagrangian Particle Tracking (LPT) scheme to correct predicted particle positions. The positional errors to be corrected during IPR-processing are typically in the sub-pixel range, however larger errors can occur at the prediction stage of STB. The second part of this manuscript quantifies the ability of the position optimization to successfully correct misplaced particles and proposes a method to further increase this range. Cost-function-gradient based methods require a certain overlap of the re-projected image with the original image for any given particle. Still, a misplacement of 2-3 pixels - depending on its direction relative to the camera positions - is shown to be reliably correctable. As seen by statistics from a DNS of a turbulent cylinder flow, such high accelerations (and therefore mispredictions) are rare at typical sampling rates. Therefore, most particle predictions can be successfully optimized to the correct position. In order to additionally handle rare events of large acceleration and misplacement, an iterative grid-search is applied specifically to particles not being optimally placed yet ('Variable Space step', VS). Such particles are identified using the local shape of the cost-function gradient. Using synthetic data, it is demonstrated that this method is able to correct even large prediction errors with high reliability. Applying a low temporal sampling on the test case of turbulent cylinder flow results in 20.8 px average particle shift. In this case, using noisy image data at a particle image density of 0.1 ppp, approx. 95.3% of the particle predictions can be corrected by pure position optimization, while around 99.5 % are achieved by additionally applying VS. Transferring this approach to experimental data could further improve tracking fidelity and would allow relaxing on the temporal resolution demands.