Advert for a Master’s internship

Title: CFD-driven Sparse Identification of Algebraic Reynolds-Stress Models: application to curved ducts flows.

Duration: 6 months from March 2021.


Turbulence affects many natural and industrial systems. In particular, in the aeronautical, aerospace and energy industries, accurate prediction of turbulent flows is crucial for system design, analysis and control. Industrial numerical approaches therefore require inexpensive and reliable turbulence models. In practice, the approach commonly used in industry is to solve Reynolds-Averaged Navier-Stokes (RANS) equations using Linear Eddy Viscosity Models (LEVM). This approach allows low simulation costs compared to high-fidelity approaches (LES, DNS). However, this type of turbulence modelling is very unreliable for the simulation of off-stream flows, with strong pressure gradients or with curvature of the flow lines.
In order to overcome these limitations of LEVM models, more sophisticated models have been developed, such as non-linear models with turbulent viscosity. In particular, the Explicit Algebraic Reynolds Stress Models (EARSM).
In recent work, machine learning methods applied to the design of turbulence models have been developed. In particular, data-driven methods have been developed to infer the unknown functions of EARSM models directly from high-fidelity data (LES, DNS) of the quantity to be reconstructed (Reynolds tensor and turbulent kinetic energy). Such models are driven off-line, i.e. without any numerical simulation. These models are then implemented in a CFD solver in order to carry out numerical simulations. Such approaches allow the construction of more accurate EARSM models for the class of flows represented by the high-fidelity data used.
However, as the learning is performed offline, such models may be non-robust and induce numerical singularities in the numerical simulations. Moreover, this approach is not flexible with respect to the data required to train the models. Indeed, this type of method requires high-fidelity Reynolds tensor data. Finally, off-line learning does not guarantee the exact conservation of mechanical energy.
A research work currently in progress between the Institut Jean Le Rond D’Alembert (Sorbonne University) and the Laboratoire DynFluid (CNAM / ENSAM) proposes and develops a “CFD-driven” approach, involving a problem of coefficient optimisation (allowing the construction of the model), in which at each iteration, the quality of the candidate model is evaluated by performing a RANS simulation and comparing the results with high-fidelity data. This approach allows to solve the shortcomings of data-driven approaches. In particular, this “online” approach guarantees the exact conservation of mechanical energy. In addition, any high-fidelity data can be used to drive the model, making the approach more flexible. Finally, non-robust candidate models (leading to simulation discrepancies) are detected and eliminated during the optimisation process. It is thus expected to build a robust model. The already obtained results are very promising.
The subject of the training course is part of a technological transfer approach whose objective will be the implementation of this CFD-driven method in order to build high-performance RANS models for the calculation of flows in curved pipelines of particular interest to the company PHIMECA.


The course will take place in the Parisian premises of PHIMECA Engineering, 18 boulevard de Reuilly, 75012, Paris. PHIMECA Engineering is an engineering company specialised in the evaluation and optimisation of product and system performance. Its vocation is to offer robust and reliable engineering solutions based on a solid scientific base, an entrepreneurial spirit and moral values shared by all its employees. The work will be co-supervised by the research team that develops learning tools at the Institut d’Alembert and the Laboratoire DynFluid.

Candidate profile

The desired candidate is in the second year of a Master’s degree or the last year of an engineering school with a specialisation in fluid mechanics. Good experience and a taste for numerical simulation are essential. Knowledge of machine learning would be appreciated as well as experience with the simulation software OpenFOAM and python programming.

Internship allowances: Legal (~550€ / month depending on the number of working days).

Join Us

The PHIMECA team is composed of engineers and PhDs in mechanics, numerical simulation, structural reliability, statistics and probabilities, computer development. If you too have more or less experience in one of these fields and if you wish to join the PHIMECA Engineering team for a permanent contract, an internship, a thesis or a post-doc, do not hesitate to contact us!

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