Error propagation dynamics of PIV-based pressure field calculation (3): What is the minimum resolvable pressure in a reconstructed field?

Abstract

An analytical framework for the propagation of velocity errors into PIV-based pressure calculation is established. Based on this framework, the optimal spatial resolution and the corresponding minimum field-wide error level in the calculated pressure field are estimated. This minimum error is viewed as the smallest resolvable pressure. We find that the optimal spatial resolution is a function of the flow features, geometry of the flow domain, and the type of the boundary conditions, in addition to the error in the PIV experiments, making a general statement about pressure sensitivity is difficult. The minimum resolvable pressure is affected by competing effects from the experimental error due to PIV and the truncation error from the numerical solver. This means that PIV experiments motivated by pressure measurements must be carefully designed so that the optimal resolution (or close to the optimal resolution) is used. Flows (Re=1.27 × 10⁴ and 5×10⁴) with exact solutions are used as examples to validate the theoretical predictions of the optimal spatial resolutions and pressure sensitivity. The numerical experimental results agree well with the analytical predictions.