Numerical Study of the Influence of Geometry on the Primary Fluid Instability in the Couette-Taylor

Abstract

This work concerns the numerical study which aims at the influence of geometry on the primary instability of water (Pr=0.802),with physical properties are temperature dependent confined between two concentric cylinders horizontal and closed at the ends by two walls and which are adiabatic, a temperature gradient is imposed (Δ T=100°), the hot inner cylinder (T<inf>1</inf>=100°) is rotated with an angular velocity (Ω<inf>1</inf>≠0), while the colder outer cylinder (T<inf>2</inf>=100°) is fixed (Ω<inf>2</inf>=0). Three radii ratios and three aspect ratio are used (η<inf>1</inf>=0.827, η<inf>2</inf>=0.727, η<inf>3</inf>=0.627), (Γ<inf>1</inf>=37.36, Γ<inf>2</inf>=18.86, Γ<inf>3</inf>=4.67) respectively. The control parameters are the Grashof number which is fixed (Gr=10³), and varies Taylor number (2022.4<Ta<2851.9). The problem is solved by the finite volume method with numerical schemes of second-order spatiotemporal precision. The results show the first instability of the fluid (completely spiral), characterized by a variety of critical Taylor numbers, whose evolution is studied according to the ratio of radius and aspect, these two parameters accelerate or delay the attenuation of the critical Taylor number, thus the number of cells (n) occupying the entire in gap and a function of the aspect ratio.