# Pressure–velocity coupling algorithm-based pressure reconstruction from PIV for laminar flows

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### Abstract

In this study, we propose a method to reconstruct pressure fields from planar particle image velocimetry measurements for laminar flows by employing semi-implicit method for pressure-linked equations algorithm to solve governing equations where measured velocities are inherently used as boundary conditions. The method starts with interpolating the measured velocity field on a staggered computational grid. The continuity equation, in the form of pressure equation for incompressible flows, is solved with this velocity data to reach an initial pressure field. Momentum equations are solved with calculated pressure field and then pressure correction equation is solved for calculating the mass imbalance in continuity equation. Using this mass imbalance, the current velocity field is corrected. Repeating this procedure until convergence provides not only the pressure field that satisfies governing equations, but also error reduction on the measured velocity. The method is validated with theoretical flows and its sensitivity to the velocity field error is assessed. This method reconstructs the pressure fields exactly for error-free velocity fields and can correct the flow-fields to accurate values even with extremely high experimental errors. Application on a flapping airfoil experiment showed that the method can successfully reconstruct pressure field by slightly altering the measured velocity field. The proposed method offers a non-intrusive, global pressure measurement for laminar flows with minimum end user input.

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## References

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