Pressure from PIV for oscillating internal flow

Most PIV-based pressure field reconstructions pertain to steady, external flows. For such cases, the measurement domain is extended to include well-behaved boundary conditions. This approach is not applicable to internal flows of practical interest, where the choice of measuring or prescribing boundary conditions is limited by experimental constraints. In this work, the pressure field for an impinging synthetic jet is computed from time-resolved tomo-PIV data. The pressure field is reconstructed by 4D, 3D, and 2D Poisson solvers and the results are compared to a dynamic pressure transducer. The pressure field computed by the 3D solver shows random temporal fluctuations that can be attributed to PIV measurement noise and limitations in the boundary condition implementation. The 4D solver uses information from the temporal gradient of the pressure to mitigate these fluctuations; however, this yields a non-physical temporal drift. With mostly computed boundary conditions, the 2D solver also produces random fluctuations. Significant improvement of the reconstructed pressure field is possible by adjusting the type and implementation of the boundary conditions. Eliminating the squared source terms in the governing equation of the 2D Poisson solver further improves the pressure field.