Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · physics/0511149

Ambivalent effects of added layers on steady kinematic dynamos in cylindrical geometry: application to the VKS experiment

F. Stefani·M. Xu·G. Gerbeth·F. Ravelet·A. Chiffaudel·F. Daviaud·J. Léorat
View original source ↗Read source document ↗Export metadata ↓

Abstract

The intention of the ''von Karman sodium'' (VKS) experiment is to study the hydromagnetic dynamo effect in a highly turbulent and unconstrained flow. Much effort has been devoted to the optimization of the mean flow and the lateral boundary conditions in order to minimize the critical magnetic Reynolds number and hence the necessary motor power. The main focus of this paper lies on the role of ''lid layers'', i.e. layers of liquid sodium between the impellers and the end walls of the cylinder. First, we study an analytical test flow to show that lid layers can have an ambivalent effect on the efficiency of the dynamo. The critical magnetic Reynolds number shows a flat minimum for a small lid layer thickness, but increases for thicker layers. For the actual VKS geometry it is shown that static lid layers yield a moderate increase of the critical magnetic Reynolds number by approximately 12 per cent. A more dramatic increase by 100 until 150 per cent can occur when some rotational flow is taken into account in those layers. Possible solutions of this problem are discussed for the real dynamo facility.

Explore related subjects

physics.flu-dynastro-phphysics.plasm-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

F. Stefani, M. Xu, G. Gerbeth, F. Ravelet, A. Chiffaudel, F. Daviaud, J. Léorat. 2006-02-21. Ambivalent effects of added layers on steady kinematic dynamos in cylindrical geometry: application to the VKS experiment. https://doi.org/10.1016/j.euromechflu.2006.02.002

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Geometry-induced self-excited dynamo in a regular tetrahedron

We present a rotation-free magnetohydrodynamic dynamo driven by laminar thermal convection in a regular tetrahedral cavity. The tetrahedral boundaries organize the convective flow into a robust pattern of helical convection cells without global rotation or turbulence. Direct numerical simulations demonstrate exponential amplification of a weak seed magnetic field followed by nonlinear saturation. In the reference calculation, the saturated magnetic energy exceeds the kinetic energy. The velocity field develops $D_4$ dihedral symmetry, while the self-generated magnetic field exhibits a corresponding signed $D_4$ symmetry, including antisymmetry under $π$ rotations about the two horizontal axes. Analysis of the velocity and magnetic-field structures reveals a closed induction cycle sustained by geometry-induced helical convection. This system provides a conceptually simple setting for isolating and understanding the fundamental physical processes underlying magnetohydrodynamic dynamo action.

physics.flu-dyn↗
arXiv2026

Projection-based segregated, iterative, and multi-stage physics-informed neural network for incompressible Navier-stokes equations

Physics-informed neural networks(PINNs) offer a mesh-free and continuously differentiable approach to fluid simulation. However, standard monolithic PINNs for incompressible Navier-Stokes (NS) equations often suffer from severe constraint coupling and spectral biases, limiting both convergence and accuracy. To address this challenge, we propose a segregated, iterative, and multi-stage PINN (SIM-PINN) inspired by the classical projection method in computational fluid dynamics. In SIM-PINN, the nonlinear NS equations are decoupled into the linearized momentum and pressure Poisson equations. Each is addressed separately using dedicated multi-stage neural networks and coupled through projection-based inner iterations. Each stage of the multi-stage neural networks for the momentum equations corresponds to one iteration of the projection method, in which the velocity fields are progressively refined at targeted frequencies. Upon iteration convergence, solutions to the fully coupled and nonlinear NS equations are recovered. By integrating the segregated and iterative framework with the multi-stage training, SIM-PINN alleviates the optimization difficulties of the incompressible NS equations arising from nonlinearity, constraint coupling, and spectral biases. The improved convergence and accuracy are demonstrated by simulations of steady lid-driven cavity and unsteady Kolmogorov flows.

physics.flu-dyn↗
arXiv2026

Bayesian Kolmogorov-Arnold networks for trustworthy Reynolds-stress closures

Data-driven turbulence closures can improve Reynolds-averaged Navier-Stokes (RANS) predictions, but their use is limited by two issues: learned constitutive relations are often difficult to inspect, and predictions typically lack reliable uncertainty estimates. We develop a Bayesian tensor-basis Kolmogorov-Arnold network (BKAN) for Reynolds-stress anisotropy that addresses both within a single closure. Learnable univariate spline functions on network edges provide an inspectable representation that can, where sufficiently simple, be approximated symbolically. Variational posteriors over spline coefficients yield a predictive distribution separating epistemic uncertainty, due to limited training data, from aleatoric uncertainty, the irreducible scatter of high-fidelity targets at given inputs. Galilean and rotational invariance, symmetry, and tracelessness are enforced through the tensor basis, while physical realisability is treated separately through soft regularisation. A controlled regression benchmark assesses predictive accuracy, calibration, and Bayesian parameterisation. Placing the posterior on spline coefficients gives the best overall balance of accuracy, calibration, parameter cost, and interpretability. Applied to Reynolds-stress anisotropy, the BKAN is accurate in distribution, with calibrated, informative uncertainty that tends to identify larger prediction errors. Under geometric extrapolation, however, the model becomes overconfident: epistemic uncertainty increases but does not fully account for growing prediction errors. Finally, the framework is extended to three-dimensional wind-farm wakes, where the learned correction transfers to unseen layouts and posterior samples are propagated through the RANS solver, with the aleatoric component injected as a spatially correlated field, to obtain uncertainty bounds on the predicted wake flow.

physics.flu-dyn↗