Analysis of collisions between droplets in homogeneous isotropic turbulence

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Analysis of collisions between droplets in homogeneous isotropic turbulence

An increasing number of applications related to IFPEN activities, such as water treatment or biomass production, include flows laden with a dispersed phase which must be studied at the process scale. These studies can rely on experimental data which are limited by the technique and cost. It is then crucial to supplement these experimental approaches with numerical simulations to design processes and understand their underlying hydrodynamics aspects.

In liquid-liquid emulsions, an important quantity is the size distribution of droplets which drive the mass transfer in the process. This distribution depends on the frequency at which droplets collide and coalesce.

The modelling of coalescence frequency is then of prior importance in the prediction of droplet size distribution in the formalism of population balance equations (PBE).

A predictive model for the coalescence frequency requires to account for interactions between droplets and eddies but also on more local effects of film rupture at the interface.

While the former phenomenon allows to predict the collision frequency, the latter determines coalescence efficiency i.e., the probability that a collision leads to coalescence of the droplets.

Objective

This internship proposes to improve the modelling of PBE by analyzing data from direct numerical simulations of droplets in homogeneous isotropic turbulence. This work aims to exploit data generated from the Basilisk solver during a prior postdoctoral project and extend the study from collision frequency to coalescence efficiency.

First, the student will expose the state of the art on the modelling of coalescence efficiency of droplets in turbulence. Then, the identified theoretical models will be compared to the simulation results with a thorough analysis of the data.

Finally, interactions with an ongoing PhD on the film rupture by a multi-layer approach are also considered. In this context, the hydrodynamic forces computed from the direct simulation data can be injected as boundary conditions in the multi-layer approach.

Figure 1. Example of 3D simulation of an emulsion with 160 droplets in homogeneous isotropic turbulence.

Profile:

Student in Master 1 or 2 (or equivalent) with a major in fluid mechanics.

• Interest in theoretical physics and knowledge of a programming language (ideally python and C)

Supervisors : Victor Boniou and Jean-Lou Pierson
Duration: 5 months
Period: from January/March 2025
Internship in prevision of a PhD: no

Location: IFPEN – Rueil-Malmaison (92) or Solaize (69)
Sites are accessible by public transportation.

Internship compensation : yes