Fluid pressure estimations from Particle Image or Tracking Velocimetry (PIV/PTV) measurements offer considerable flow diagnostic capability for fluid mechanics research, allowing measurement of the time-resolved evolution of the pressure fields in up to three spatial dimensions. Our main objective in this area is to develop robust methods for evaluating the time-resolved structural loads and pressure field development experimentally. Using a uniform cylinder as a test case, Video 8 shows the PIV measurements, and their pressure estimates, respectively.

However, like most experimental data, significant random errors can occur in the velocity measurements and the pressure estimations. We developed a mathematical framework which allows the reconstruction of errors in pressure gradient estimation from PIV/PTV data. The technique is benchmarked using velocity data from DNS in the wake of a circular cylinder, with an added correlated random velocity noise (video 9). Research is also being performed to leverage the same mathematical framework in order to predict instantaneous pressure estimation errors. In addition, optimization studies were performed to yield an a priori model of optimal sampling parameters which minimize propagation of random error through the Navier-Stokes equation into the original pressure gradient estimate.

Video 8. PIV velocity magnitude measurements surrounding a uniform cylinder for ReD = 2100 (left), and the pressure estimations from PIV measurements (right).

Video 9. Time sequences of isosurfaces of pressure (Cp = -1.0 and Cp = -1.25) in the wake of a cylinder at ReD = 1575. (top left) DNS solution, (top right) Poisson equation solution using velocity data from the DNS with superimposed correlated error, (bottom left) the same solution when utilizing the Λ pressure gradient correction, and (bottom right) the same solution utilizing the Λ̃ pressure gradient correction, which is a form easily implemented from experimental data.