Abstract
In this study, we quantify the accuracy of a simple pressure estimation method from 2D snapshot PIV in attached and separated flows. Particle image velocimetry (PIV) offers the possibility to acquire a field of pressure instead of point measurements. Multiple methods may be used to obtain pressure from PIV measurements, however, the current state-of-the-art requires expensive equipment and data processing. As an alternative, we aim to quantify the efficacy of estimating instantaneous pressure from snapshot (non-time resolved) two-dimensional planar PIV (the simplest type of PIV available). To make up for the loss of temporal information, we rely on Taylor’s hypothesis (TH) to replace temporal information with spatial gradients. Application of our approach to high-resolution 2D velocity data of a turbulent boundary layer flow over ribs shows moderate to good agreement with reference pressure measurements in average and fluctuations. To assess the performance of the 2D TH method beyond average and fluctuation statistics, we acquired a time-resolved measurement of the same flow and determined temporal correlation values of the pressure from our method with reference measurements. Overall, the correlation attains good values for all measured locations. For comparison, we also applied two time-resolved approaches, which attained values of correlation similar to our approach. The performance of the 2D TH method is further assessed on 3D time-resolved velocity data for a turbulent boundary layer and compared with 3D methods. The root-mean-square (RMS) pressure fluctuations of the 2D TH, 3D TH and 3D pseudo-Lagrangian methods closely follow the pressure fluctuation distribution from DNS. These observations on the RMS pressure estimates are further supported by similar analysis on synthetic PIV data (based on DNS) of a turbulent channel flow. The values of spatial correlation between the 2D TH method and the DNS pressure fields in this case, are similar to the temporal correlations achieved in the turbulent flow over the ribs. Finally, we discuss the accuracy of instantaneous pressure estimates and provide a rule of thumb to determine regions where the pressure fluctuation estimate from the 2D TH methods is likely to fail.Graphical abstract
Highlights
The rapid development of particle image velocimetry (PIV) and post-processing techniques has led to a fast increase in temporal and spatial resolution of velocity data (Scarano 2013) that currently allows for full-field pressure estimation
Pressure fields were extracted from multiple methods both in attached, and separated flows to evaluate the performance of Taylor’s hypothesis in estimating pressure from snapshot planar PIV measurements
Estimates of instantaneous pressure can be obtained with a correlation coefficient of about 0.5 with the Taylor’s hypothesis method applied to 2D data
Summary
The rapid development of particle image velocimetry (PIV) and post-processing techniques has led to a fast increase in temporal and spatial resolution of velocity data (Scarano 2013) that currently allows for full-field pressure estimation (van Oudheusden 2013). There is a great interest in techniques estimating pressure from flow velocity information These techniques generally use the Navier–Stokes equations, where all velocity terms can be measured directly through PIV measurements, and solve for the remaining pressure term. Starting with the work of Gurka et al (1999) when timeresolved data were not yet readily accessible, planar PIV velocity snapshots of a pipe and jet flow were used to get time-averaged pressure using a Poisson formulation of the Reynolds-averaged Navier–Stokes (RANS) equations and results were compared with data from previous studies. In a similar line of work, Hosokawa et al (2003), used both planar PIV and particle tracking velocimetry (PTV) data of a laminar liquid flow around bubbles, to estimate timeaveraged pressure using an iterative Poisson solver. Van Oudheusden et al (2007) evaluated time-averaged pressure and forces from planar PIV data in both compressible and incompressible flow cases using a control volume approach and a spatial integration scheme for the pressure gradients
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