On MHD turbulence models for simulation of magnetic brakes in continuous steel casting processes

摘要

A novel approach is discussed for extending Reynolds stress transport (RST) turbulence modelling to include magnetic Joule dissipation. A scalar dimensionality anisotropy parameter is introduced to carry information about the distribution of energy in spectral space. This information is vital in modelling MHD turbulence, as it determines both magnitude and anisotropy of the Joule dissipation tensor. The Joule dissipation tensor is modelled by a tensor function in the Reynolds stress anisotropy tensor, the unit direction vector of the magnetic field and the scalar dimensionality parameter. A phenomenological transport equation for the dimensionality parameter is proposed for the case of homogeneous turbulence. The model is closed using the pressure-strain model of Sarkar, Speziale and Gatski, and a magnetic destruction term in the standard dissipation equation. Model predictions for the case of decaying turbulence show very good agreement with direct numerical simulations.