Obtaining pressure field from particle image velocimetry or Particle Tracking Velocimetry (PIV/PTV) is an attractive technique in fluid dynamics due to its non-invasive nature. This technique generally involves integrating the pressure gradient or solving the pressure Poisson equation using a velocity field measured with PIV/PTV. However, error in the measured velocity field can propagate to and significantly contaminate the reconstructed pressure field. Rather than estimate the error through experiment, we investigate the dynamics of the error propagation by examining the Poisson equation directly. We analytically quantify the error bound in the pressure field, and are able to illustrate the mathematical roots of why and how the pressure calculation propagates error from the velocimetry data, as well as identify the factors that impact the error propagation. Taking advantage of the analogy to the deformation of elastic bodies, we provide analytical insight in why some type of the error in the velocimetry are more amplified and how to tame the error propagation. Based on these results, we introduce a practical method to estimate the error in the pressure field.
Zhao Pan is an assistant professor at the Department of Mechanical and Mechatronics, University of Waterloo, Canada. Before joining Waterloo in late 2019, Zhao worked at Florida Center for Advanced Aero-Propulsion and Utah State University as postdoctoral fellow. Zhao obtained his PhD from Brigham Young University in 2016 and has developed a broad research interest. His interdisciplinary research spans from flow diagnostics (PIV/LPT), uncertainty quantification and data assimilation, soft matter, droplet and bubbles, to bio-mechanics.