Pressure-Field Extraction from Lagrangian Flow Measurements

Abstract

As a follow-up to a previous proof-of-principle study, a novel Lagrangian pressure-extraction technique is analytically evaluated and experimentally validated. This technique employs a Poisson solver to extract the instantaneous pressure field on a network connecting scattered Lagrangian data. The technique is analytically evaluated using the semi-three-dimensional Taylor-Green vortex, and experimentally validated using flow data obtained for the case of a free-falling, index-matched sphere at Re = 2100. The experimental data was collected using a four-camera particle tracking velocimetry measurement system, and processed using the recently-developed Shake-The-Box algorithm. In the analytical evaluation, it is found that the Lagrangian technique out-performs the standard Eulerian technique when Dirichlet boundary conditions are enforced. However, the Lagrangian technique suffers when Neumann boundary conditions are enforced. In order to validate the experimental results, the surface pressure on the sphere is compared to results from literature, and is found to be in agreement. Based on the extracted pressure fields, the pressure-drag coefficient of the sphere is calculated, and the resulting estimate compares favourably with the expected value from literature. It is concluded that there is a clear advantage in using the proposed Lagrangian technique compared to interpolating Lagrangian flow data to a grid, and that further investigation into Lagrangian analysis techniques is merited.