Session: 16-01-01: Poster Session: NSF-Funded Research (Grad & Undergrad)

Paper Number: 99306

99306 - Magnetoconvection in a Long Vertical Enclosure With Walls With Finite Electrical Conductivity 

In many engineering systems, we encounter an electrically conductive fluid flow with combined effects of magnetic field and thermal convection. Boundaries surrounding these flows are typically taken in the computational analysis as electrically and thermally perfectly conducting or perfectly insulating. In real applications, however, thermal and, critically, electric conductivity are typically neither zero nor infinite. Studying the effect of different boundary conditions applied to these flows can help us understand the role played by wall conductivity in the realization of observed flow regimes.

In this study, magnetoconvection flow of liquid mercury in a tall vertical box is simulated under different applied magnetic field intensities and different electrical boundary conditions. The goal is to understand the effect of different combinations of electrically conducting and insulating walls and wall electric conductance ratios on the flow regime. Thermal boundary conditions of the enclosure consist of two constant temperature side walls facing each other while other walls are thermally insulating. A constant uniform magnetic field perpendicular to the temperature gradient direction is applied. 

The simulations are conducted using a new solver for magnetohydrodynamic flows of liquid metals with natural convection. A nearly fully conservative finite-difference scheme, which is known to improve the accuracy and efficiency of simulations in the case of strong magnetic field effects, is combined with a tensor-product-Thomas solution of elliptic problems. The method is adapted to flows in domains with an arbitrarily clustered structured grid with thin walls of finite electric conductivity and validated for a magnetoconvection flow in a long vertical box by comparing the simulation results with those of earlier experiments.

Flows at the Grashof number Gr = 3x10⁷ and Hartmann numbers up to 798 (moderate to strong effect of the magnetic field) are considered with wall conductance ratios 0 < C_w < 50. The flow structure, Nusselt number, and total kinetic energy of different cases are compared. The results show that the rise in magnetic field intensity and wall conductance ratios can suppress the flow heat transfer, kinetic energy, and turbulence fluctuations. However, the heat transfer rate can increase when the constant temperature walls are the only electrically conductive walls at lower Hartmann numbers. One of the main characteristics of the heat transfer rate of this flow is the number of major vortices formed inside the box. Only one major vortex is seen in the case of strong magnetic fields or high wall electric conductivity at all surrounding walls. At moderate magnetic fields, some cases transit to different regimes after some time, and in some of them, they converge to different regimes, based on the number of grid points and their clustering. 

The final results show the effectiveness of the direct solution of thin wall boundary conditions with finite electrical conductivity. It is also shown that both the configuration of electrical conducting walls and the electrical conductance ratio affect the flow regime and its properties. This effect is seen to be different for different magnetic field intensities.

Presenting Author: Ali Akhtari University of Michigan - Dearborn

Presenting Author Biography: Ali Akhtari is a pre-candidate Ph.D. student at the University of Michigan - Dearborn, studying Mechanical Science and Engineering under the advisement of Professor Oleg Zikanov. His research is currently on magnetoconvection flows in a closed enclosure.

Authors:

Ali Akhtari University of Michigan - Dearborn
Dmitry Krasnov Technische Universität Ilmenau
Oleg Zikanov University of Michigan - Dearborn