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Digital Science and Technology

Power in unity: a new approach to simulate complex flows

Thesis by Mohamed Essadki*

Gas-liquid two-phase flows lie at the heart of numerous industrial applicationsa for which numerical simulation is a dimensioning and optimization support tool. Such simulation must be predictive with reasonable calculation costs.
While monophase flow simulation already meets these requirements, the same cannot be said for the two-phase scenario.
In the injection field, in particular, flow topology is highly complex, with different zonesb with a high level of interactivity. The latter are described by different physical models that cannot be easily combined later, making it difficult to construct predictive models that can be used for industrial-scale simulations.
The research consisted in seeking an original unified approach to describe all these flow topologies.
The method employed focused on:

  • interface statistics to identify new geometric variables valid in all flow regimes(1),
  • advanced numerical analysis making it possible to implement these variables in a Eulerianc flow model(2),
  • algorithmic geometry to calculate these variables in flow DNSd (figure) in order to propose the first closurese for the model.

This new model, incorporated in a parallel 3D simulator, demonstrated its robustness and reasonable cost on a first set of jet simulations.
The thesis’ second contribution resides in a fine-scale gas-liquid interface analysis tool that can be used to characterize the results of DNS-type calculations. Its use will make it possible to improve averaged larger-scale models, proposing new closures.

a- For example: injection process in the automotive and aeronautics sectors, chemical engineering processes.
b- A dense liquid core, droplets and filaments of all forms.
c- A Eulerian model simulates the continuous liquid phase, in contrast to a particle or droplet model.
d- Direct Numerical Simulation.
e- Estimations by physical and numerical experiments of model terms that cannot be calculated directly.


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Published in Science@ifpen n° 35 - December 2018

* Thesis entitled "Contribution to a unified Eulerian modeling of fuel injection: from dense liquid to polydisperse evaporating spray"


  1. (1) M. Essadki, S. de Chaisemartin, M. Massot, F. Laurent, A. Larat & S. Jay. Adaptive Mesh Refinement and High Order Geometrical Moment Method for the Simulation of Polydisperse Evaporating Sprays, OGST, Vol. 71, n°5, Sept.–Oct. 2016
    >> DOI : 10.2516/ogst/2016012.
  2. (2) M. Essadki, S. de Chaisemartin, L. Drui, F. Laurent, M. Massot. SIAM J., High Order Moment Model for Polydisperse Evaporating Sprays towards Interfacial Geometry Description, SIAM J. Appl. Math., 78(4), 2003–2027. (25 pages)
    >> DOI : 10.1137/16M1108364.

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