Numerical Simulation of Magneto Hydrodynamic Natural Convection in a Vertical Cylindrical Crucible (original) (raw)
Related papers
2016
A numerical study of oscillatory magnetohydrodynamic (MHD) natural convection of liquid metal between vertical coaxial cylinders is carried out. The motivation of this study is to determine the value of the critical Rayleigh number, Racr for two orientations of the magnetic field and different values of the Hartmann number (Har and Haz) and aspect ratios A. The inner and outer cylinders are maintained at uniform temperatures, while the horizontal top and bottom walls are thermally insulated. The governing equations are numerically solved using a finite volume method. Comparisons with previous results were performed and found to be in excellent agreement. The numerical results for various governing parameters of the problem are discussed in terms of streamlines, isotherms and Nusselt number in the annuli. The time evolution of velocity, temperature, streamline and Nusselt number with Racr, Har, Haz, and A is quite interesting. We can control the flow stability and heat transfer rate in varying the aspect ratio, intensity and direction of the magnetic field.
Natural Convection of Liquid Metals in an Inclined Enclosure in the Presence of a Magnetic Field
The problem of steady, laminar, natural convective flow of electrically-conducting liquid metals such as gallium and germanium in an inclined rectangular enclosure in the presence of a uniform magnetic field is considered. Transverse gradient of heat is applied on two opposing walls of the inclined enclosure while the other two walls are adiabatic. A magnetic field is applied normal to the non-insulated walls. The problem is formulated in terms of the vorticity – stream function procedure. A numerical solution based on the finite-difference method is obtained. Representative results illustrating the effects of the enclosure inclination angle and the Hartmann number for two different Rayleigh numbers on the contour maps of the streamlines and temperature as well as the profiles of velocity components and temperature at mid-section of the enclosure are reported. In addition, results for the average Nusselt number are presented and discussed for various parametric conditions.
Energies, 2020
Natural convection of liquid metal in an annular enclosure under the influence of azimuthal static magnetic field was numerically studied. The liquid metal in the enclosure whose cross-sectional area is square was heated from an inner vertical wall and cooled from an outer vertical wall both isothermally whereas the other two horizontal walls were assumed to be adiabatic. The static azimuthal magnetic field was imposed by a long straight electric coil that was located at the central axis of the annular enclosure. The computations were carried out for the Prandtl number 0.025, the Rayleigh number 104, 5 × 105 and 107, and the Hartmann number 0–100,000 by using an in-house code. It was found that the contour map of the electric potential was similar to that of the Stokes stream function of the velocity regardless of the Hartmann number. Likewise, the contour map of the pressure was similar to the Stokes stream function of the electric current density in the case of the high Hartmann n...
Magneto-thermal-convection stability in an inclined cylindrical annulus filled with a molten metal
International Journal of Numerical Methods for Heat & Fluid Flow, 2020
Purpose-Metal-cooled reactors generally use molten metals such as sodium, potassium or a combination of sodium and potassium because of their excellent heat transfer properties so that the reactor can operate at much lower pressures and higher temperatures. The purpose of this paper is to investigate the stability of natural convection in an inclined ring filled with molten potassium under the influence of a radial magnetism. Design/methodology/approach-A numerical simulation of electrically conductive fluid natural convection stability is performed on an inclined cylindrical annulus under the influence of a radial magnetism. The upper and lower walls are adiabatic, while the internal and external cylinders are kept at even temperatures. The equations governing this fluid system are solved numerically using finite volume method. The SIMPLER algorithm is used for pressure-speed coupling in the momentum equation. Findings-Numerical results for various effective parameters that solve the problem in the initial oscillatory state are discussed in terms of isobars, isotherms and flow lines in the annulus for a wide range of Hartmann numbers (0 # Ha # 80), inclination angles (0 # g # 90°) and radii ratios l # 6. The dependency stability diagrams between complicated situations with the critical value of the Rayleigh number RaCr and the corresponding frequency FrCr are established on the basis of the numeric data of this investigation. The angle of inclination and the radii ratio of the annulus have a significant effect on the stabilization of the magneto-convective flux and show that the best stabilization of the natural oscillatory convection is obtained by the intensity of the strongest magnetic field, the high radii ratio and inclination of the annulus at g = 30°.
ScienceDirect, 2017
Presets work aims to investigate the natural convection inside a cylindrical annulus mold containing molten gallium under a horizontal magnetic field in three-dimensional coordinates. The modeling system is a vertical cylindrical annulus which is made by two co-axial cylinders of internal and external radii. The internal and external walls are maintained isothermal but in different temperatures. The upper and lower sides of annulus are also considered adiabatic while it is filled by an electrical conducting fluid. Three dimensional cylindrical coordinates as r θ z (, ,) are used to respond the velocity components as u v w (, ,). The governing equations are steady, laminar and Newtonian using the Boussinesq approximation. Equations are nonlinear and they must be corresponded by applying the finite volume approach; so that the hybrid-scheme is applied to discretize equations. The results imply that magnetic field existence leads to generate the Lorentz force in opposite direction of the buoyancy forces. Moreover the Lorentz force and its corresponded electric field are more significant in both Hartmann layer and Roberts layer, respectively. The strong magnetic field is required to achieve better quality products in the casting process of a liquid metal with a higher Prandtl number.
Natural convection in vertical concentric annuli under a radial magnetic field
Heat and Mass Transfer, 1997
Exact solutions for fully developed natural convection in open-ended vertical concentric annuli under a radial magnetic field are presented. Expressions for velocity field, temperature field, mass flow rate and skin-friction are given, under more general thermal boundary conditions. It is observed that both velocity as well as temperature of the fluid is more in case of isothermal condition compared with constant heat flux case when gap between cylinders is less or equal to radius of inner cylinder while reverse phenomena occur when the gap between cylinders is greater than radius of inner cylinder.
Three-dimensional (3D) numerical simulation of natural convection of an electrically conducting fluid under the influence of a magnetic field in an inclined cylindrical annulus has been performed. The inner and outer cylinders are maintained at uniform temperatures and other walls are thermally insulated. The governing equations of this fluid system are solved by a finite volume (FV) code based on SIMPLER solution scheme. Detailed numerical results of heat transfer rate, Lorentz force, temperature and electric fields have been presented for a wide range of Hartmann number (0 ≤ Ha ≤ 60) and inclination angle (0 ≤ γ ≤ 90). The results indicate that a magnetic field can control the magnetic convection of an electrically conducting fluid. Depending on the direction and strength of the magnetic field, the suppression of convective motion was observed. For vertical cylindrical annulus, increasing the strength of the magnetic field causes the loss symmetry, and as the consequence, isotherms lose their circular shape. With increasing the Hartmann number the average Nusselt number approaches a constant value. For vertical annulus, the effect of Hartmann number on the average Nusselt number is not prominent compared to the case of horizontal annulus.
Journal of Thermal Engineering, 2021
In the present numerical study, the effect of an external horizontal magnetic field on the natural convection of an electrically conducting molten metal (gallium) inside a vertical cylindrical crucible has been investigated. The effect of the external magnetic field is evaluated on the flow pattern and also the temperature field of molten gallium in the mold with an aspect ratio of A=1.0 and a radii ratio of λ=3.0. A series of simulations are carried out for Hartmann numbers of 0, 22.5, 112, and 167 and Rayleigh numbers of 104, 105, and 106. The obtained results show that for a given Rayleigh number, increasing the Hartmann number suppresses convection flows in all directions with different intensities. Moreover, it was found that the employed horizontal magnetic field leads to vanishing the axisymmetric pattern of flow structures. This is due to the formation of Roberts and Hartmann layers near the walls parallel (0° and 180°) and normal (90° and 270°) to the magnetic field, respec...
Investigation of Magneto Hydrodynamic Natural Convection Flows in a 3-D Rectangular Enclosure
Journal of Applied Fluid Mechanics, 2016
The article deals with magnetic field of free convective flows in cavities similar to those used in artificial growth of single crystals from melts (horizontal Bridgman configurations) and having aspect ratios an equal to "4". The combined effect of wall electrical conductivity and vertical direction of the magnetic field on the buoyancy induced flow of mercury was investigated numerically. The validation of the numerical method was achieved by comparison with both experimental and analytical data found in the literature. The plotted results for variation of velocity, temperature and Nusselt number in terms of the Hartmann number Ha and Rayleigh number "Ra" showed a considerable decrease in convection intensity as the magnetic field is increased, especially for values of "Gr" situated around 10 7. The calculations also showed that the vertically directed magnetic field (perpendicular to the x-z plane) is the most effective in controlling the flow and hence the speed of growth of the crystal. Also, wall electrical conductivity enhances damping by changing the distribution of the induced electric current to one which augments the magnitude of the Lorentz force.
Applied and Computational Mechanics, 2020
The roll of melting heat transfer on magnetohydrodynamic natural convection in a square enclosure with heating of bottom wall is examined numerically in this article. The dimensionless governing partial differential equations are transformed into vorticity and stream function formulation and then solved using the finite difference method (FDM). The effects of thermal Rayleigh number (Ra), melting parameter (M) and Hartmann number (Ha) are graphically illustrated. As melting parameter and Rayleigh number increase, the rate of fluid flow and temperature gradients also increase. And in the presence of magnetic field, the temperature gradient reduces and hence, the conduction mechanism is dominated for larger Ha. Greater heat transfer rate is observed in the case of uniform heating compared with non-uniform case. The average Nusselt number reduces with increasing magnetic parameter in the both cases of heating of bottom wall.