Article & Lamination: Magnetic field lines produced by a numerical von Kármán Sodium flow.

Lamination of the Jean Zay supercomputer dedicated to Artificial Intelligence (January 2019) magnetic field lines produced by a numerical von Kármán Sodium flow.

C. Nore, D. Castanon Quiroz, L. Cappanera & J. L. Guermond, Numerical simulation of the Von-Kármán-Sodium dynamo experiment. Journal of Fluid Mechanics, 854, pp. 164–195 (2018). DOI:10.1017/jfm.2018.582 - HAL:01575765

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Context

The figure below shows the magnetic field lines produced numerically by integrating the Magnetohydrodynamics (MHD) equations in the configuration of the von Kármán Sodium (VKS) experiment. It comes from the article published in the Journal of Fluid Mechanics (Nore et al., 2018) which is the result of about 15 years of development of the SFEMaNS code, for Spectral/Finite Element code for Maxwell and Navier-Stokes equations, see website:

https://people.tamu.edu/~guermond//SFEMaNS/html/about.html

The obtained magnetic field reproduces the topology of the experimentally generated one in 2007 in the famous VKS experiment built at CEA Cadarache: 150 liters of liquid sodium are set in turbulent motion by two counter-rotating impellers located at the two extremities of a cylindrical container (Monchaux et al., 2007). Only three experimental setups in the world have been able so far to create a magnetic field from different turbulent flows of liquid sodium through a mechanism called the dynamo effect. There are many anti-dynamo theorems excluding the generation of magnetic fields for fluid flows that are too simple or too symmetrical. No one knows the unfailing recipe for creating magnetic fields from the turbulent motion of a liquid metal or a plasma (mechanism at work in the liquid core of the Earth or in the Sun).

In VKS, the dynamo effect appeared when the impellers, initially made of steel, were changed with impellers made of soft iron. Nobody understood then why the experiment worked. Our team has contributed to finding a credible answer to this puzzle.

Contribution

Our contribution has been to reproduce numerically the VKS experiment. This experiment presents two numerical challenges: first, the Reynolds number, Re=2 pi f R^2/nu, based on the impeller rotation frequency f, the cylinder radius R, and the fluid viscosity nu, exceeds 10^6! Even with today's supercomputers, it is necessary to use a turbulence model adapted to a configuration with walls to reach such high Re. Second, it is necessary to describe numerically the soft iron impellers, which exhibit variations in magnetic permeability.

Using Large-Eddy-Simulation (LES) turbulence modeling based on entropy stabilization concepts and a penalty technique for the impellers, we have performed MHD simulations on various supercomputers (up to 2048 cores on the IDRIS ADA computer) totaling 10^6 hours of computation. The ferromagnetic impellers of the 2007 Cadarache experiment are represented using a pseudo-penalty method. Simulations with high kinetic Reynolds number (10^5) are conducted using a new method of Large Eddy Simulations (LES). The results are in very good accordance with the experiments. The magnetic field is dominated by an axisymmetric axial dipole and azimuthal components located near the impellers in total agreement with the experimental data.

The MHD simulations show the key role played by the ferromagnetic material (with high magnetic permeability) constituting the impellers: increasing the magnetic permeability of the impellers lowers the dynamo threshold, which explains why this effect was achieved when the experimentalists replaced the steel impellers with the same soft-iron-made impellers.

Impact

The reproduction of the experimental velocity and magnetic fields in the VKS experiment is a real achievement since the flow is highly turbulent and the impellers are made of iron that are difficult to model. No other team has been able to conduct such massive numerical computations so far. This has opened the way to study in greater detail the transfers between kinetic and magnetic energies and to identify the terms responsible for the dynamo effect (Creff et al., 2024).

The magnetic field lines are represented in the figure below, which was selected to decorate the new supercomputer acquired by the Ministery de l'Enseignement supérieur, de la Recherche et de l'Innovation through GENCI from Hewlett-Packard Entreprise in January 2019.

References

C. Nore, D. Castanon Quiroz, L. Cappanera , J. L. Guermond, Numerical simulation of the Von-Kármán-Sodium dynamo experiment. Journal of Fluid Mechanics, 854, pp. 164–195 (2018).

R. Monchaux, M. Berhanu, M. Bourgoin, M. Moulin, Ph. Odier, J.-F. Pinton, R. Volk, S. Fauve, N. Mordant, F. Pétrélis, A. Chiffaudel, F. Daviaud, B. Dubrulle, C. Gasquet, L. Marié, and F. Ravelet, Phys. Rev. Lett. 98, 044502 – Published 25 January 2007.

M. Creff, H. Faller, B. Dubrulle, J.-L. Guermond, C. Nore; Tracking dynamo mechanisms from local energy transfers: Application to the von Kármán sodium dynamo. Phys. Plasmas 1 February 2024; 31 (2): 022306. https://doi.org/10.1063/5.0174251

Article: Simple computational strategies for more effective physics-informed neural networks modeling of turbulent natural convection

D. Lucor, A. Agrawal & A. Sergent, Simple computational strategies for more effective physics-informed neural networks modeling of turbulent natural convection. Journal of Computational Physics 456 (2022) 111022. DOI:10.1016/j.jcp.2022.111022 - HAL:hal-03847907

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Context

The high expressivity and agility of physics-informed neural networks (PINNs) make them promising candidates for full fluid flow PDE modeling. An important question is whether this new paradigm, exempt from the traditional notion of discretization of the underlying operators very much connected to the flow scales resolution, is capable of sustaining high levels of turbulence. Another concern is whether it can be used as a numerical substitute to full DNS data retrieval and storage; DNS remains so far the standard tool for validation and inter-comparison with experimental results.

Contribution

We explore the use of PINNs surrogate modeling for turbulent natural convection flows, mainly relying on DNS temperature data from the fluid bulk and velocity data at some fluid boundaries. This technique depends on the minimization of a composite loss function relying on labels and PDE residuals. We demonstrate the large computational requirements under which PINNs are capable of accurately recovering the flow hidden quantities. We then propose new techniques to mitigate the need for large training datasets. First, we propose a padding technique to better distribute some of the scattered coordinates at which PDE residuals are minimized, in particular in zones where no labels are available. We show how it comes into play as a regularization close to the training boundaries and results in a noticeable global accuracy improvement at iso-budget. We then propose a relaxation of the incompressibility condition involved in the loss function contribution related to the PDE residuals. This development drastically benefits the optimization search and results in a much-improved convergence.

Impact

The results obtained for Rayleigh-Bénard flow at Ra = 2E9 are particularly impressive. With training data amounting to only 0.32% of the stored DNS dataset, the predictive accuracy of the surrogate over the entire half a billion DNS coordinates yields errors for all flow variables ranging between [ 0.3% − 4% ] in the relative L 2 norm. This work was the first step towards the ANR project THERMAL (2023-26, with Physics Lab, ENS Lyon).

Article: Suppression of the Kapitza instability in confined falling liquid films

G. Lavalle, L. Yiqin, S. Mergui, N. Grenier, G. Dietze, Suppression of the Kapitza instability in confined falling liquid films. Journal of Fluid Mechanics, 860, 608-639 (2019). DOI:10.1017/jfm.2018.902 - HAL:hal-03322234

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Context

This article is issued from the WavyFILM ANR project in collaboration between FAST, LIMSI/LISN and Air Liquide around wavy films. In the industrial domain of gas processing, cryogenic distillation is the main way to separate different components of air but is also very energy-intensive. A possible route to raise efficiency of the process is to enhance mixing occuring in the distillation columns in which a liquid film flows down on corrugated surfaces and is subject to a counter-current gas flow. Mass transfer between phases is enhanced by increasing gas mass flow but trigger possible flooding of the narrow gap in channels. The objective of this WavyFILM project is to study and improve mass transfer occuring in liquid films surrounded by a gas flow, by understanding mechanisms of instabilities by means of experiments, models and numerical simulations.

Contribution

In this first article published during the project, reduced modelling of the film in a confined channel with a counter-current gas flow and experiments with water film have been used to investigate the aforementionned problem. We have shown that the Kapitza instability at the origin of surface waves is suppressed when the channel is more confined (confinement η (ratio of channel height to film height) decreases, see figure [10(a)]) or when the counter-current gas is increased (measured with the gas Reynolds number Re g, see figure [14(a)]) :

These numerical predictions have been confirmed by our experiments with water, which are quite difficult to conduct to measure instability growth rates in these conditions.

Impact

While this instability suppression was known for turbulent gas flow regime in large channels, this study exhibits this phenomenon for the first time for low gas Reynolds numbers or highly confined channels. This article have been cited 19 times since publication on 2018 (excluding our group citations; source: Google Scholar on 16/05/2023).

After this first step in the linear regime, this work have been extend to solitary waves solitary waves [1] as well as non-linear regime [2], with experimental investigations [3].

References

[1] Solitary waves on superconfined falling liquid films, G Lavalle, N Grenier, S Mergui, GF Dietze - Physical Review Fluids, 2020. URL

[2] Superconfined falling liquid films: linear versus nonlinear dynamics, G Lavalle, S Mergui, N Grenier… - Journal of Fluid Mechanics, 2021. URL

[3] Nonlinear wave attenuation in strongly confined falling liquid films sheared by a laminar counter-current gas flow, S Mergui, G Lavalle, Y Li, N Grenier… - Journal of Fluid Mechanics, 2023. URL