Using uncertainty to improve pressure field reconstruction from PIV/PTV flow measurements

Abstract

A novel uncertainty-based pressure reconstruction method is proposed to evaluate the instantaneous pressure fields from velocity fields measured using particle image velocimetry (PIV) or particle tracking velocimetry (PTV). First, the pressure gradient fields are calculated from velocity fields, while the local and instantaneous pressure gradient uncertainty is estimated from the velocity uncertainty using a linear-transformation based algorithm. The pressure field is then reconstructed by solving an overdetermined linear system which involves the pressure gradients and boundary conditions. This linear system is solved with generalized least-squares (GLS) which incorporates the previously estimated variances and covariances of the pressure gradient errors as inverse weights to optimize the reconstructed pressure field. The method was validated with synthetic velocity fields of a 2D pulsatile flow and the results show significantly improved pressure accuracy with an error reduction of as much as 250% compared to the existing baseline method of solving the pressure Poisson equation (PPE). The GLS was more robust to the velocity errors and provides greater improvement with spatially correlated velocity errors. For experimental validation, the volumetric pressure fields were evaluated from a laminar pipe flow velocity field measured using 3D PTV. The GLS reduced the median absolute pressure errors by as much as 96%.

Flow over an espresso cup: inferring 3-D velocity and pressure fields from tomographic background oriented Schlieren via physics-informed neural networks

“…Moreover, these methods are not able to estimate the pressure from BOS data directly. A pressure reconstruction method, such as solving the Poisson equation, is required for pressure inference, which is used routinely in PIV (Wang et al 2016; Zhang, Bhattacharya & Vlachos 2020). In addition, reconstructing the three-dimensional (3-D) velocity field from tomographic BOS (Tomo-BOS) is still an open area in experimental fluid mechanics.…”

Uncertainty Quantification for PTV/LPT data and Adaptive Track Filtering

“…Nevertheless, by being able to state a reasoned estimate of the involved measurement uncertainties, not only a more complete measurement result can be given, but the knowledge of these uncertainties can also be leveraged to enhance the velocity reconstruction, e.g. by HDR-PIV (Persoons (2015)) or Anisotropic denoising (Wieneke (2017)), or the pressure field reconstruction (Zhang et al (2020)).…”

Machine Learning for Vortex Induced Vibration in Turbulent Flow

“…Meanwhile, scattered velocity or dye trace distribution around the VIV structure in a small region can be obtained experimentally, for example, via the particle image velocimetry [12] or the Schlieren image velocimetry measurements [13,14]. Yet it is also acknowledged that the pressure distribution is difficult to acquire [15,16]. Thus, how to accurately reconstruct the pressure field and thereafter predict the forces according to limited available data in finite time-space coverage is of interest and importance.…”