Abstract
We report on hybrid numerical simulations of a turbulent magnetic dynamo. The simulated set-up mimics the Riga dynamo experiment characterized by Re ≈ 3.5 × 106 and (Gailitis et al 2000 Phys. Rev. Lett. 84 4365–8). The simulations were performed by a simultaneous fully coupled solution of the transient Reynolds-averaged Navier–Stokes (T-RANS) equations for the fluid velocity and turbulence field, and the direct numerical solution (DNS) of the magnetic induction equations. This fully integrated hybrid T-RANS/DNS approach, applied in the finite-volume numerical framework with a multi-block-structured nonorthogonal geometry-fitted computational mesh, reproduced the mechanism of self-generation of a magnetic field in close accordance with the experimental records. In addition to the numerical confirmation of the Riga findings, the numerical simulations provided detailed insights into the temporal and spatial dynamics of flow, turbulence and electromagnetic fields and their reorganization due to mutual interactions, revealing the full four-dimensional picture of a dynamo action in the turbulent regime under realistic working conditions.
Highlights
DEUTSCHE PHYSIKALISCHE GESELLSCHAFT dynamo in a laboratory took place in 1999 when experimentalists in Riga (Gailitis et al [9]–[15]) and in Karlsruhe (Stieglitz and Müller [16], Müller and Stieglitz [17], Müller et al [18, 19]) independently detected the self-generation of a magnetic field
We focused on mimicking the Riga dynamo experimental set-up which provided the first ever experimental proof of the dynamo action in a turbulent regime, but the approach can be applied to any other configuration
For the fluid flow variables we introduce the transient Reynolds-averaged Navier–Stokes (RANS) (T-RANS) method, whereas a fully resolving (DNS) approach was used for the electromagnetic variables
Summary
Kenjereset al [27] we presented the first attempt to simulate the Riga dynamo experimental set-up under realistic working conditions. With an increase in the hyper-viscosity and/or hyper-diffusivity, the dissipative subrange of flow scales is significantly reduced (and so is, the numerical grid resolution), Biskamp and Müller [34] Such a simple approach does not account for the local turbulence effects, which strongly influence the velocity field and its interactions with the electromagnetic field. In contrast to the previous segregated numerical simulations, this iterative procedure involves the simultaneous solution of both the momentum and magnetic induction equations with implicitly updated (the most recent) fields This procedure is advanced in time reproducing the growth of a self-generated magnetic field. The generated magnetic field creates the Lorentz force, which feeds back into the momentum equation and, the saturation magnetic regime is achieved As it will be shown below, the T-RANS approach applied proved to be capable of capturing large-scale instabilities and the consequent dynamo action manifested in magnetic and velocity field oscillatory growth and saturation. Its effect on the fluid flow and dynamo is fully accounted for by subscale models of the ensemble-averaged turbulence quantities
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