Thermo-hydrodynamic instabilities in a high aspect ratio Couette-Taylor system using Direct Numerical SimulationReport as inadecuate

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1 M2P2 - Laboratoire de Mécanique, Modélisation et Procédés Propres

Abstract : The influence of a radial temperature gradient on the stability of Couette-Taylor flow has been investigated by direct numerical simulation. The cavity is characterized by a narrow gap η=Ri-Ro=0.8 and a high aspect ratio Γ = H-Ro−Ri = 80, Ri and Ro being the radii of the inner and outer cylinders and H their height. The flow depends on two physical parameters: the Taylor number Ta = Ω Ri d-νd-Ri^1-2 and the Rayleigh number Ra = α∆T d 3 -νκ, with d = Ro−Ri and Ω the rotation rate of the inner cylinder. 15 cases have been computed for Ta = 11 − 150 and Ra = 1166 − 13228 to enable comparisons with the experiments of Guillerm. The numerical method is based on the 2D compact fourth-order projection de-composition method of Abide and Viazzo, extended to cylindrical coordinates on non-staggered grids. The time advancement is second-order accurate. The deriva-tives are approximated using fourth-order compact formula in the radial and axial directions and Fourier series in the azimuthal direction. Due to the large aspect ra-tio, the domain is axially decomposed into 8 subdomains using the influence matrix technique. The thermal effects are considered using the Boussinesq approximation. The aim of this work is to characterize all the flow patterns occuring in the system for various Rayleigh and Taylor numbers. At low Ra, the first instability appears in the form of regular spirals Fig.1a. For higher values of Ra, dislocations may occur Fig.1b and when one increases T a, spirals coexist with a wavy vortex flow Fig.1c and finally only the wavy vortex flow subsists at high T a Fig.1d. The spatiotem-poral properties of these patterns have been fully determined and compared to the work of Guillerm.

Keywords : Taylor-Couette Instability Thermal gradient

Author: Sébastien Poncet - Stéphane Viazzo -



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