Characterizing Lagrangian particle dynamics in decaying homogeneous isotropic turbulence using proper orthogonal decomposition

Abstract

Particle proper orthogonal decomposition (PPOD) is demonstrated as a method for extraction of temporal statistical information on dispersed (discrete) phases of multiphase flows. PPOD is an extension of the classical Eulerian POD, differentiating itself by its Lagrangian formulation and applicability to discrete phases in both stationary and non-stationary flows. The method is demonstrated on a test case of decaying homogeneous isotropic turbulence, where particle data are generated by one-way coupled simulations. Here, particle positions and velocities are integrated forward in time in a Lagrangian manner. The results demonstrate a proof of concept of the PPOD, and its potential for applicability. It is demonstrated that PPOD modes are able to capture both large scale temporal flow features as well as smaller scale variations. Additionally, particle trajectories/velocities are approximated using a subset of the PPOD basis where convergence is demonstrated. In the application of PPOD on multiple particle realizations, an increase in the convergence rate is observed as the initial particle separation is decreased. When decomposing both solid (rigid) and fluid particle velocities, the method provides the possibility of modal analysis of fluid–particle interactions in multiphase flows. For various configurations of rigid particle densities, the modal parallelity between the two phases is mapped, revealing a higher parallelity when the rigid particles are neutrally buoyant.