Abstract
There is a continuous need for an updated series of numerical benchmarks dealing with various aspects of the magnetohydrodynamics (MHD) phenomena (i.e. interactions of the flow of an electrically conducting fluid and an externally imposed magnetic field). The focus of the present study is numerical magnetohydrodynamics (MHD) where we have performed an extensive series of simulations for generic configurations, including: (i) a laminar conjugate MHD flow in a duct with varied electrical conductivity of the walls, (ii) a back-step flow, (iii) a multiphase cavity flow, (iv) a rising bubble in liquid metal and (v) a turbulent conjugate MHD flow in a duct with varied electrical conductivity of surrounding walls. All considered benchmark situations are for the one-way coupled MHD approach, where the induced magnetic field is negligible. The governing equations describing the one-way coupled MHD phenomena are numerically implemented in the open-source code OpenFOAM. The novel elements of the numerical algorithm include fully-conservative forms of the discretized Lorentz force in the momentum equation and divergence-free current density, the conjugate MHD (coupling of the wall/fluid domains), the multi-phase MHD, and, finally, the MHD turbulence. The multi-phase phenomena are simulated with the Volume of Fluid (VOF) approach, whereas the MHD turbulence is simulated with the dynamic Large-Eddy Simulation (LES) method. For all considered benchmark cases, a very good agreement is obtained with available analytical solutions and other numerical results in the literature. The presented extensive numerical benchmarks are expected to be potentially useful for developers of the numerical codes used to simulate various types of the complex MHD phenomena.
Highlights
One of the pre-requisites to be able to deal with advanced physical transport phenomena involving the magnetohydrodynamics (MHD) in teractions is to have a well-validated and numerically efficient computer code
We have presented a comprehensive numerical benchmark study addressing a range of single- and multi-phase one-way coupled MHD flows
The single-phase cases included the conjugate MHD flows in ducts with varied electric conductivity of the wall – in both laminar and tur bulent flow regimes, and the laminar back-step flow subjected to a transverse magnetic field
Summary
One of the pre-requisites to be able to deal with advanced physical transport phenomena involving the magnetohydrodynamics (MHD) in teractions is to have a well-validated and numerically efficient computer code. One of the simplest numerical MHD benchmarks is a fully developed laminar channel, duct, or pipe flow subjected to a uniform magnetic field of different orientations, for which an exact analytical solution exists, Hartmann and Lazarus (1937), Shercliff (1953). The commercial multi-physics finite-element code COMSOL was successfully applied to simulate transient natural convection phenomena under influence of the imposed uniform magnetic field, Sahu and Bhattacharyay (2018). The main goal of the present study is to obtain and validate results from our newly developed OpenFOAM solver over a range of various magnetohydrodynamic flows, and based on these findings, to propose an extensive numerical MHD benchmark, which can be potentially useful for developers of the computer codes for simulations of the MHD phe nomena. For all mentioned cases we performed a detailed comparative assessment against available analytical solutions or/and numerical results presented in the literature
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