Two-dimensional turbulent convection in a toroidal duct of a liquid metal blanket of a fusion reactor

Abstract

Convection in a horizontal duct aligned with a uniform magnetic field is analysed computationally. The motivation of the study is the concept of a liquid metal blanket for a tokamak fusion reactor, in which ducts are oriented toroidally, i.e. parallel to the main component of the magnetic field. Computations of two-dimensional (streamwiseuniform) flows appearing at very strong magnetic fields and of three-dimensional flows in long domains are conducted. Non-uniform volumetric internal heating is applied, while the walls are maintained at a constant temperature. Two-dimensional or nearly two-dimensional turbulent convection is found at high Grashof and Hartmann numbers typical for fusion reactor conditions. The turbulence results in stronger mixing and more uniform distribution of wall heat flux, indicating promising potential of this concept of the blanket.

Computational modeling of magnetoconvection: Effects of discretization method, grid refinement and grid stretching

“…The method uses the discretization scheme first introduced as scheme B in [22]. The scheme was expanded to include the effects of heat transfer and thermal convection and implicit treatment of temperature diffusion and viscous terms in [7,8,10]. The method was validated in comparison…”

“…It has been recently understood that the suppression of turbulence by the magnetic field does not necessarily mean that the flow acquires a simple laminar steady-state form. On the contrary, growth of the MHD-specific convection instability modes that have weak or zero variations along the magnetic field lines and, thus, are not suppressed, may lead to unsteady, essentially nonlinear and complex flow dynamics [7][8][9][10][11][12][13][14][15][16].…”

Instabilities in Extreme Magnetoconvection

“…This means that full three-dimensional unsteady nonlinear equations have to be solved. Simplified models, such as the quasi-two-dimensional model [33] or the model of a purely two-dimensional flow in the absence of wall crossing the field lines [40,41,42,43], can only be used rarely, when their accuracy is verified via three-dimensional simulations or experiments. Also, since conventional three-dimensional turbulence is suppressed, no models are available for small-scale behavior, which has to be resolved.…”

“…In principle, they should be considered as approximations, since in an infinite domain and for an arbitrarily strong magnetic field one can introduce perturbations of the wavelength sufficiently large to survive the magnetic damping (see [36] for a discussion). Practically, however, the analysis of [40] shows that at the typical parameters of a fusion reactor, the axially non-uniform component of the velocity is very weak, and the flow can be approximated as two-dimensional with good accuracy.…”

“…Further studies have shown that the two-dimensional turbulence regime is highly sensitive to the features of the blanket system not taken into account in the simple model of [40]. One such feature is the vertical (poloidal) component of the magnetic field inevitably present in the blanket.…”