Effect Of Magnetic Field On Plane-parallel Rayleigh-Bénard Convection

With the development of renewable energy such as solar energy and wind energy,the liquid metal batteries is considered as one promising option for large-scale,high-efficiency energy storage.However,the thermal convection might imply a risk of short-circuiting the battery and an external magnetic field is imposed to suppress the flow.In this paper,The Rayleigh-Bernard thermal convection system under the external magnetic field is numerically simulated within a two-dimensional horizontally periodic computational domain between parallel plates.A direct numerical simulation code based on incompressible Navier-Stokes equations is developed,with the high-order finite-difference method in the vertical direction,the Fourier-Galerkin spectral method in the horizontal direction,and the second-order Adams-Bashforth method for time terms.The accuracy of the algorithm and code is proved by comparing with the results in the literature.Considering a uniform vertical magnetic field,the horizontal flow and convection heat transfer intensity are drastically suppressed.For the same Rayleigh number,as the magnetic intensity increases,the horizontal velocity first decreases rapidly and then slowly.The flow pattern can be divided into three stages: quasi-turbulent regime,transitional regime,and the laminar regime.In laminar regime,the number of convective cells increases with magnetic intensity,and the aspect ratio of convective cells has a positive correlation with the ratio of horizontal velocity and vertical velocity.Corresponding to the flow pattern,the convection heat transfer intensity shows three stages: decreases in quasi-turbulent regime,increases slowly in transitional regime,and decreases in laminar regime.The heat transfer intensity is suppressed in most cases,while it was increased slightly when near the critical parameter of the transitional regime transition to the laminar regime.Considering a uniform horizontal magnetic field,the vertical flow and convection heat transfer intensity are drastically suppressed.With the increase of magnetic intensity,the vertical velocity decreases rapidly and then slowly.The change of flow pattern is similar to the vertical magnetic field,but the aspect ratio of convective cells increases and then the number of convective cells decreases as the ratio of the horizontal velocity to the vertical velocity decreases in laminar regime.Convective heat transfer intensity continuously decreases,and the slopes of the three stages are significantly different.Result is that the velocity component perpendicular to the direction of the magnetic field is suppressed and convective cells are stretched along the magnetic field direction.The flow pattern is more turbulent at small magnetic intensity and eventually completely inhibits flow at almost the same magnetic intensity in both vertical and horizontal magnetic fields.Differently,the horizontal magnetic field suppresses the flow velocity and convective heat transfer intensity more drastically,and requires a stronger magnetic intensity than the vertical magnetic field to make flow steady,indicating that the vertical magnetic field performs better in stabilizing flow.