Modelling inertial particles in fluid flows. Efficient numerical approaches.

  • Harry B A Stott

Student thesis: Doctoral ThesisDoctor of Philosophy (PhD)


The dynamics of inertial particles have a profound influence in countless contexts in the natural and manmade world. Whether it be droplets of water advected in the atmosphere that cluster and collide to form rain, or volcanic ash clouds carried on the winds that
ground aircraft and block out the sun, inertial particles are prolific in their influence on our lives. An inertial particle is an object with material density different to the fluid in which it resides.
This density difference causes heavy aerosols to be ejected from vortices, and light bubbles to migrate towards vortex centres. These behaviours characterise inertial particles and underpin complex particle processes such as clustering and droplet growth. Due to the breadth of important length scales in many two phase systems, different models are required for different parts of the scale space.
We present a hierarchy of modelling approaches that efficiently capture the inertial properties of particles and can be applied to a wide range of problems. Beginning with comparisons between Lagrangian particle trajectories and experimental results from the literature, we identify, and present solutions to, complications in numerical integration of the Maxey-Riley equation. The numerical model is applied in a paradigmatic vortical flow to help understand the influence of the Basset history force on particle trajectories. For applications with smaller particles, we develop an Eulerian description of the dynamics of particle ensembles. The method is a discretisation of a transfer operator that efficiently captures the important properties of large numbers of particles; its algorithmic complexity is independent of the number of particles, even when collisions are considered between them. Two methods for detecting particle collisions that dramatically improve on algorithmic complexity of pairwise detection schemes are presented and compared. Despite the philosophical difference between the Lagrangian and Eulerian approaches, comparisons between them produce remarkably similar results.
Our methods are then applied in a decaying turbulent flow to investigate sedimentation rates and particle clustering. Throughout, great care is taken to understand the nuances of particle dynamics, allowing parallels to be drawn between behaviours in steady and turbulent flows. From the perspective of the particles, we show that there is very little difference between particle clustering in steady and unsteady flows, provided a range of length scales are present in both.
Work is also conducted that explores the influence of the Basset history force in a range of contexts: vortex ejection, collision rates, and clustering. In decaying turbulence, the Basset force is shown to have a significant effect even for dense aerosols. With reference to these results, we discuss the decay rate of the Basset kernel relative to the decay rate of the turbulence, and question whether its form is appropriate in such contexts.
Date of Award1 Oct 2019
Original languageEnglish
Awarding Institution
  • The University of Bristol
SupervisorAndrew G W Lawrie (Supervisor) & Robert Szalai (Supervisor)

Cite this

Modelling inertial particles in fluid flows. Efficient numerical approaches.
Stott, H. B. A. (Author). 1 Oct 2019

Student thesis: Doctoral ThesisDoctor of Philosophy (PhD)