Development of a symbolic regression method for the formulation of wall laws in CFD

IFP Energies nouvelles (IFPEN) est un acteur majeur de la recherche et de la formation dans les domaines de l’énergie, du transport et de l’environnement. De la recherche à l'industrie, l'innovation technologique est au cœur de toutes ses activités.

Dans le cadre de la mission d'intérêt général qui lui a été confiée par les pouvoirs publics, IFP Energies nouvelles (IFPEN) s'attache à :

• Apporter des solutions pour relever les défis de la société en matière d'énergie et de climat, en favorisant l'émergence d'un mix énergétique durable
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Development of a symbolic regression method for the formulation of wall laws in CFD

In fluid dynamics simulations, the effects of wall turbulent boundary layers are generally taken into account through the use of wall laws. However, the latter suffer from a restricted range of validity that limits their predictivity, particularly in the presence of out-of-equilibrium phenomena - pressure gradients, flow separation or high transverse velocities - which are often of crucial importance in many industrial applications. This is one of the key factors limiting the use of simulation for design and optimization.

Recently, a number of research studies have explored the potential of machine learning (ML) techniques to develop approaches for overcoming the limitations of wall laws by learning from high-fidelity data of canonical parietal flows. While these studies have confirmed the potential of these algorithms to improve the prediction of wall friction, they have also revealed limitations linked to their non-interpretability and generalizability.

In this context, the aim of the internship is to implement a GEP (Gene Expression Programming) ML technique, as an alternative to the neural networks (NN) commonly used in the literature, to formulate analytical relationships that can replace wall laws based on training on high-fidelity data from DNS or WR-LES CFD simulations.

The aim is thus to explore whether the expected advantages of GEP in terms of interpretability, regularity and generalizability (Weatheritt and Sandberg 2016; Weatheritt and Sandberg 2017; Akolekar et al. 2018) over NN are indeed proven, and what the prerequisites are in terms of methodology. This will be done by exploiting high-fidelity data available at IFPEN concerning canonical cases for out-of-equilibrium turbulent boundary layers: flow over a hill, abrupt widening and impacting jet. In addition, wall laws based on NNs trained on these data are already available (E. Rondeaux’s PhD thesis) and will be used to critically analyze the advantages and disadvantages of the method developed during the internship.

The main stages of work proposed within the framework of this internship are:

• Identification of existing GEP tools, first application using simple examples;
• Development of a GEP methodology for formulating a wall law based on training on high-fidelity databases available at IFPEN;
• Critical analysis and synthesis of the results obtained, and identification of the pros and cons of GEP.

At the end of the internship, this work could be continued in a PhD thesis between IFPEN and the LISN laboratory at the University of Paris-Saclay, aimed at formulating analytical relationships to improve prediction of parietal heat fluxes during liquid cooling of electric machine components.

Academic background:

University master’s degree or last year engineering school.

• Knowledge (or willingness to learn) of computational fluid dynamics (CFD) and/or artificial intelligence.
• Python programming and fluency in English (spoken and written) are required.

Duration of the internship:  5 months, from February 2024
Location: IFP Energies nouvelles in Rueil-Malmaison (near Paris in France). Possibility of regular teleworking.