Pressure-field extraction from Lagrangian flow measurements: first experiences with 4D-PTV data

Abstract

As a follow-up to a previous proof-of-principle study, a novel Lagrangian pressure-extraction technique is analytically evaluated, and experimentally validated using dense 4D-PTV data. The technique is analytically evaluated using the semi-three-dimensional Taylor–Green vortex, and it is found that the Lagrangian technique out-performs the standard Eulerian technique when Dirichlet boundary conditions are enforced. However, the Lagrangian technique produces worse estimates of the pressure field when Neumann boundary conditions are enforced on boundaries with strong pressure gradients. The technique is experimentally validated using flow data obtained for the case of a free-falling, index-matched sphere at \(Re=2100\). The experimental data were collected using a four-camera particle tracking velocimetry measurement system, and processed using 4D-PTV. The pressure field is then extracted using both the Eulerian and Lagrangian techniques, and the resulting pressure fields are compared. Qualitatively, the pressure fields agree; however, quantitative differences are found with respect to the magnitude of the pressure minima on the side of the sphere. Finally, the pressure-drag coefficient is estimated using each technique, and the two techniques are found to be in very close agreement. A comparison to a reference value from literature confirms that the drag coefficient estimates are reasonable, demonstrating the validity of the technique.