Pressure-field extraction on unstructured flow data using a Voronoi tessellation-based networking algorithm: a proof-of-principle study

Abstract

A novel technique is described for pressure extraction from Lagrangian particle-tracking data. The technique uses a Poisson solver to extract the pressure field on a network of data nodes, which is constructed using the Voronoi tessellation and the Delaunay triangulation. The technique is demonstrated on two cases: synthetic Lagrangian data generated for the analytical case of Hill’s spherical vortex, and the flow in the wake behind a NACA 0012 which was impulsively accelerated to $Re = 7{,}500$. The experimental data were collected using four-camera, three-dimensional particle-tracking velocimetry. For both the analytical case and the experimental case, the dependence of pressure-field error or sensitivity on the normalized spatial particle density was found to follow similar power-law relationships. It was shown that in order to resolve the salient flow structures from experimental data, the required particle density was an order of magnitude greater than for the analytical case. Furthermore, additional sub-structures continued to be identified in the experimental data as the particle density was increased. The increased density requirements of the experimental data were assumed to be due to a combination of phase-averaging error and the presence of turbulent coherent structures in the flow. Additionally, the computational requirements of the technique were assessed. It was found that in the current implementation, the computational requirements are slightly nonlinear with respect to the number of particles. However, the technique will remain feasible even as advancements in particle-tracking techniques in the future increase the density of Lagrangian data.