A Voronoi-based smooth particle hydrodynamics approach for estimating instantaneous pressure from PTV measurements

Estimating local pressure from experimental optical measurement techniques like particle tracking velocimetry (PTV) remains challenging. Traditional methods project the Lagrangian data onto an Eulerian grid, using memory intensive techniques that introduce averaging errors. In this work, a novel approach is proposed to compute the instantaneous pressure from PTV data using a Voronoi-based smooth particle hydrodynamics (SPH) method. Voronoi tessellation is performed on the particle field to obtain local volumes, and efficiently identify nearest neighbours. Velocity gradients at each particle are computed via a smoothing kernel, and the pressure is obtained by enforcing the full Navier-Stokes equations. One of the major benefits of the approach is that it does not require special treatment at measurement boundaries. The proposed approach is validated using a model problem of a Taylor-Green vortex, and application of the methodology to high-speed time-resolved PTV measurements in the wake of a bluff-body (Re ~ 110000) is discussed. Furthermore, a detailed comparison on the computational errors and the associated costs with different smoothing kernels is presented.