Pressure from PIV for an Oscillating Internal Flow

Reconstruction of the pressure field from experimental velocity data is challenging, and no single method performs well for all experimental conditions. The challenge primarily comes from the noise in the experimental velocity data that propagates into the reconstructed pressure field. In internal flows, pressure reconstruction is especially challenging as there is often a lack of quiescent or friction-less boundaries. As a result, Bernoulli’s principle cannot be applied for Dirichlet boundary conditions. Furthermore, the noise in the velocimetry data are particularly high near the boundaries of the measurement domain. These errors contaminate the reconstructed pressure field through the Neumann boundary conditions. In this dissertation, the pressure field of an oscillating internal flow is computed from time-resolved, three-dimensional, three-component Particle Image Velocimetry (PIV) velocity data. The experiment for this study is an impinging synthetic jet confined in a hexagonal water tank. This flow was chosen to enable a systematic investigation of the effects of both the boundary conditions and the spatial resolution on the computed pressure field. The instantaneous pressure fields are reconstructed through the mid-plane of the synthetic jet using a 2D formulation of the pressure Poisson equation. The reconstruction of the pressure field from experimental velocity field is performed for both PIV and PTV velocity data using different pressure reconstruction techniques. We demonstrate that the reconstructed pressure fields show sensitivity to the type and implementation of the boundary conditions. The pressure fields exhibit large random fluctuations when the majority of the boundary conditions are the Neumann type directly calculated from the PIV data. Increasing the length of Dirichlet boundary conditions and replacing the calculated Neumann boundary conditions with prescribed values reduces these fluctuations in the reconstructed pressure fields. A new approach to calculate the error in the pressure field for experiments, where a ground truth is not available, is used based on a recent analytical work leveraging the incompressibility and periodic nature of the flow. Phase-averages of the reconstructed pressure field of the synthetic jet is used as experiment-based ground truth. The optimal spatial resolution and the error level in the reconstructed pressure fields show strong dependence to the formulation of the pressure Poisson equation and the length scale of the flow relative to the spatial resolution