Relevance of the Basset history term for Lagrangian particle dynamics

TL;DR

This paper investigates the importance of the Basset history term in the Maxey-Riley equation for accurately modeling the movement of particles in fluid flows, showing that neglecting it can lead to significant errors in particle clustering and flow analysis.

Contribution

It provides a comprehensive numerical analysis of the Basset history term's impact on particle dynamics across different flow regimes, highlighting its significance especially in turbulent flows.

Findings

Ignoring the history term affects clustering patterns at moderate to large Stokes numbers.

Neglecting the Basset history term can cause significant differences in scalar fields in turbulent flows.

The history term influences finite-time Lyapunov exponents and particle trajectory accuracy.

Abstract

The movement of small but finite spherical particles in a fluid can be described by the Maxey-Riley equation (MRE) if they are too large to be considered passive tracers. The MRE contains an integral "history term" modeling wake effects, which causes the force acting on a particle at some given time to depend on its full past trajectory. The history term causes complications in the numerical solution of the MRE and is therefore often neglected, despite both numerical and experimental evidence that its effects are generally not negligible. By numerically computing trajectories with and without the history term of a large number of particles in different flow fields, we investigate its impact on the large-scale Lagrangian dynamics of simulated particles. We show that for moderate to large Stokes numbers, ignoring the history term leads to significant differences in clustering patterns. Furthermore, we compute finite-time Lyapunov exponents and show that, even for small particles, the differences in the resulting scalar field from ignoring the BHT can be significant, in particular if the underlying flow is turbulent.