Efficient time-resolved pressure estimation using sparse sensor optimization and non—time—resolved particle image velocimetry

Abstract Pressure field estimation from particle image velocimetry (PIV) data is a well-established technique. However, the time-resolved pressure estimation strongly depends on the temporal resolution of the PIV measurements. Generally, PIV data have limited time resolution, creating challenges in the understanding of high Reynolds number flows. To overcome this hurdle, sensor data measured at a few optimized locations with higher time resolution is combined with PIV data using data-driven methods to reconstruct time-resolved velocity fields. In this context, if we wish to estimate time-resolved pressure fields from nontime-resolved PIV data, there are two possible approaches. Approach 1: reconstruct the time-resolved velocity field first from the nontime-resolved PIV data using sensor data, and then the time-resolved pressure fields are estimated from the time-resolved pressure fields by applying the pressure Poisson equation (PPE). Approach 2: first estimate nontime-resolved pressure fields from nontime-resolved velocity field measurements using PPE and then reconstruct time-resolved pressure fields directly from nontime-resolved pressure fields. The two approaches are compared in this study. These approaches are demonstrated for the actual PIV data of flow over a cylinder. Time-resolved PIV measurements are downsampled to mimic nontime-resolved velocity data. It is found that Approach 2 is approximately 30 times faster than Approach 1 when the time resolution is improved from 1 Hz to 50 Hz. This is expected because in the second approach, the PPE needs to be solved only with nontime-resolved velocity fields, which reduces the computational load. The use of sufficient optimized sensor data could reconstruct the pressure field with reasonable accuracy even if the PIV data have sampling rates below the vortex shedding frequency.