Pressure reconstruction of a planar turbulent flow field within a multiply connected domain with arbitrary boundary shapes

Abstract

This paper reports for the first time the implementation procedures and validation results for pressure reconstruction of a planar turbulent flow field within a multiply connected domain that has arbitrary inner and outer boundary shapes. The pressure reconstruction algorithm used in this study is the rotating parallel-ray omni-directional integration algorithm that offers high-level of accuracy in the reconstructed pressure. While preserving the nature and advantage of the parallel ray omni-directional pressure reconstruction at places with flow data, the new implementation of the algorithm is capable of processing an arbitrary number of inner void areas with arbitrary boundary shapes. Validation of the multiply connected domain pressure reconstruction code is conducted using the Johns Hopkins DNS (Direct Numerical Simulation) isotropic turbulence databases [J. Graham et al., J. Turbul. 17(2), 181 (2016)], with 1000 statistically independent pressure gradient field realizations embedded with random noise used to gauge the code performance. For further validation, the code is also applied for pressure reconstruction from the DNS data [E. Johnsen and T. Colonius, J. Fluid Mech., 629, 231 (2009)] about a shock-induced non-spherical bubble collapse in water. It is demonstrated that the parallel-ray omni-directional integration algorithm outperforms the Poisson equation approach in terms of the accuracy for the pressure reconstruction from error embedded pressure gradients in both simply connected and multiply connected domains.