Reorganization of turbulence structure in magnetic Rayleigh–Bénard convection: a T-RANS study

Abstract

Effects of a uniform, vertically oriented, magnetic field on the reorganization of coherent structure in Rayleigh–Bénard convection of electrically conductive fluid were studied using a time-dependent Reynolds-average-Navier-Stokes (T-RANS) approach. This method can be regarded as a very large eddy simulation (VLES) in which the unresolved random motion is modelled using a low-Re-number k–ϵ–θ2 algebraic stress/flux single-point closure model. The large-scale deterministic motion, which is the major mode of heat and momentum transfer in the bulk central region, is fully resolved by the time solution. In contrast to LESs, the contribution of both modes to the turbulent fluctuations are of the same order of magnitude. The approach was first assessed by comparison with the available direct numerical simulations (DNSs) and experimental data for non-magnetic Rayleigh–Bénard convection for Rayleigh (Ra) numbers 6.5 × 105 and 109, as well as with our own LES for Ra = 6.5 × 105, using several criteria: visual observation of the large structure morphology, different structure identification criteria and long-term averaged mean flow and turbulence properties. A visible similarity with large structures in DNSs was observed, confirming the suitability of the T-RANS approach to reproduce the flows dominated by large coherent motions. Application of a uniform magnetic field oriented vertically, which generates the Lorentz force in the horizontal homogeneous direction, was shown to suppress the horizontal motion and its fluctuations, aligning thus the velocity vector with the direction of magnetic field vector. Two cases were considered, both for Ra = 107, corresponding to two values of Hartmann (Ha) number: 20 and 100. For the moderate magnetic field (Ha = 20), the effects are mild. For the strong magnetic field (Ha = 100), the vortical structure shows a strong two-dimensionality in the sense that the variation of all flow properties in the vertical direction are significantly reduced. The total turbulence energy is very much suppressed, although it is still detectable and strongly anisotropic, close to the one-component limit. The wall heat transfer is also strongly reduced as compared with the non-magnetic case for the same Rayleigh number.