Relevance of the Basset history term for Lagrangian particle dynamics

2024-07-01

arXiv.org

AI Summary

The role of the Basset history term (BHT) in the Maxey–Riley equation remains poorly quantified for finite-size particle Lagrangian dynamics, particularly regarding spatial clustering and chaotic transport in turbulent and isotropic shear flows. Method: High-accuracy numerical integration and parallel particle trajectory simulations are employed to systematically compare particle behavior with and without BHT under varying Stokes numbers. Contribution/Results: This study reveals that, at moderate-to-high Stokes numbers, BHT dominates the formation of particle clustering structures. Even for small particles, omitting BHT induces over 20% deviation in finite-time Lyapunov exponent (FTLE) fields, severely distorting chaotic fronts and mixing characteristics. These findings demonstrate that BHT is not a negligible correction but a pivotal physical mechanism governing Lagrangian statistical behavior of inertial particles. The work establishes rigorous theoretical foundations and quantitative criteria for high-fidelity modeling of particle-laden flows.

Technology Category

• Multiagent Systems: Agent-Based Simulation and Emergent Behavior
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Studies of user behavior, including longitudinal effects of personalized systems

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.

Problem

• Investigates impact of Basset history term on particle dynamics
• Compares clustering patterns with and without history term
• Analyzes differences in Lyapunov exponents due to term neglect

Innovation

• Numerically compares trajectories with and without history term
• Investigates history term impact on large-scale dynamics
• Computes finite-time Lyapunov exponents for validation