Transient natural convection in a variable-viscosity fluid between concentric and vertically eccentric spheres

• Main Authors: Wen-Ching Tsai, 蔡文卿
• Other Authors: Horng-Wen Wu
• Format: Others
• Language: zh-TW
• Published: 2002
• Online Access: http://ndltd.ncl.edu.tw/handle/v45x6t

碩士 === 國立成功大學 === 造船及船舶機械工程學系 === 90 === ABSTRACT A numerical simulation has been carried out for the natural convection of high Prandtl number fluids with temperature-dependent viscosity between concentric and vertically eccentric spheres. Furthermore, the results are used to compare with the cases for constant viscosity and the comparison shows that the variable viscosity has the influence on flow field, temperature distribution and heat transfer. Besides, when Rayleigh number is larger than the first critical value, the unicellular convection vortex is broken into a set of unsteady secondary vortices. For Rayleigh number larger than the second critical Rayleigh number, the two secondary vortices re-broken into some smaller counter-rotating tertiary vortices. Temperature gradient increases with variable viscosity, so this can enhance the convection and heat transfer of the flow field, and let the flow become unstable. A four-parameter correlation for the variable viscosity is adopted. When the modified Sorenson's method used to generate the grid line, it can get the grid system with orthogonality along all boundaries and this system can enhance calculation accuracy. The grid system goes along with weighting function scheme (WFS) to discrete the general governing equation. The successive over-relaxation method (SOR) is applied to solve stream function equation and the alternating direction implicit method (ADI) is applied to solve vorticity and energy equations. For giving one confidence to the numerical method in this thesis, the numerical results for constant viscosity are used to compared with the provious experimental results, and have good agreements with the previous. The analysis shows that the convection becomes more obvious and heat transfer increases with increasing Rayleigh number. Moreover, the influence of eccentricity on the flow field is also studied in this thesis. It reveals that the positive eccentricity can improve the average Nusselt number, but the negative eccentricity may not promote the convection effect.