Paper Submission
01. Experimental/Computational Fluid Dynamics
Linear stability analysis of three-dimensional natural convection at various low Prandtl number in an annular enclosure using a non-uniform grid
Thermal convection in liquid metals undergoes a transition from two-dimensional to three-dimensional steady flows as the Rayleigh number increases in annular containers. Analyzing the critical transition from two-dimensional to three-dimensional states is crucial for further improving the precision and efficiency of semiconductor single crystal manufacturing, ultimately achieving a homogeneous single crystal. Natural convection within annular containers varies not only with temperature differences but also with aspect ratio and radius ratio. This study aims to analyze the linear stability at low Prandtl numbers in annular containers, varying the Rayleigh number with uneven grids and changing the radius ratio defined as the ratio of the inner to outer radii. We conducted linear stability analysis of liquid metal-filled annular containers where the inner perimeter is heated and the outer perimeter is cooled, inducing natural convection inside. The working fluid is an incompressible Newtonian fluid approximated using the Boussinesq approximation. The methodology involves solving the base state and subsequently the linear disturbance equations using the derived base state. Parameters such as Rayleigh numbers and wavenumbers are treated as constants, yielding complex amplitudes and eigenvalues. The considered Prandtl numbers range from 0.01 to 0.035, and the radius ratios are 0.5 and 0.75. For a radius ratio of 0.5 and Prandtl number of 0.035, the critical wave number is 20 with a critical Rayleigh number of 8028.23. For a radius ratio of 0.75 and Prandtl number of 0.025, the critical wave number is 40 with a critical Rayleigh number of 2213.60.
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Author Information
Mr.
Tougo Imai
Presenting author
Dr.
Takuya Masuda
Dr.
Toshio Tagawa
Corresponding author