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Communication Dans Un Congrès Année : 2015

STABILITY OF A CIRCULAR COUETTE FLOW UNDER RADIAL THERMAL BODY FORCES

Résumé

A stability analysis of a circular Couette flow of a dielectric fluid subjected to a temperature gradient and an electric field, reveals the generation of internal waves associated with the thermal stratifications of the density and the electric permittivity (Taylor-Couette flow, Electrohydrodynamics). Convective flows and stratified shear flows in a central gravity field are of primary importance in geo-and astrophysics. Realization of laboratory experiments with an artificial radial gravity is regarded as a key to advance the understanding of these flows. Some attempts have been made with an electric effective gravity in annular and spherical geometries [1]. This electric gravity g e originates from the thermal variation of the fluid polarizability: The decrease of the fluid electric permittivity with the temperature yields a thermal Archimedean buoyancy force f e = −αρθg e in an electric field E, where g e = ee ref ∇E 2 /2αρ (α: the coefficient of thermal expansion, ρ: the density, θ: the temperature deviation from a reference one, e: the coefficient of thermal variation of the permittivity, ref : the permittivity at the reference temperature). We perform a theoretical investigation on the stability of a circular Couette flow in the radial electric gravity field under microgravity conditions. The considered system is an annular capacitor of infinite length with the gap filled by a dielectric fluid (Fig.1a). The temperatures of the inner and outer electrodes are maintained constant at T 1 and T 2 , respectively. An electric tension is applied between the electrode, producing a centripetal electric gravity (−g E e r with g E > 0) in the fluid. We model this flow system in the Boussinesq approximation, but with taking into account the centrifugal buoyancy f c = −αρθg c arising from the density stratification in the centrifugal acceleration field (g c = v 2 e r /r). Primary control parameters of the flow are the Taylor number Ta = (R 1 Ωd/ν) d/R 1 and the electric Rayleigh number L = α∆θg E d 3 /νκ, where ν and κ are the kinematic viscosity and thermal diffusivity of the fluid, d = R 2 − R 1 and ∆θ = T 1 − T 2. When the inner cylinder is stationary (Ta = 0), thermal convection develops beyond a critical electric Rayleigh number in outward heating (∆θ > 0) [2]. When the inner cylinder rotates, a classical circular Couette flow is established at small Ta and L. This flow is destabilized at a critical value Ta c of the Taylor number, which depends on L. The linear stability analysis accompanied by detailed examination of critical modes reveals different dynamical regimes (Fig.1b). It is found that, in the regimes where the net effect of the two radial thermal forces, f e and f c , is stabilizing, the critical modes are oscillatory. The frequency of these oscillatory modes is scaled by the buoyancy frequency N based on the radial acceleration field g e + g c. This finding suggests the generation of internal waves through a resonant mechanism inside the Couette flow.
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Dates et versions

hal-01284150 , version 1 (07-03-2016)

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  • HAL Id : hal-01284150 , version 1

Citer

Harunori Yoshikawa, Antoine Mayer, Olivier Crumeyrolle, Innocent Mutabazi. STABILITY OF A CIRCULAR COUETTE FLOW UNDER RADIAL THERMAL BODY FORCES. Sixth International Symposius on Bifurcations and Instabilities in Fluid Dynamics, Laurette Tuckerman; José Eduardo Wesfreid, Jul 2015, Paris, France. ⟨hal-01284150⟩
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