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Linear Stability of Spiral Poiseuille Flow with a Radial Temperature Gradient: Centrifugal Buoyancy Effects

Published

Author(s)

David Cotrell, Geoffrey B. McFadden

Abstract

Instability of steady circular Couette flow with radial heating across a vertically oriented annulus with inner cylinder rotating and outer cylinder stationary is investigated using linear stability analysis. The convection regime base flow is developed for infinite aspect ratio and constant fluid properties where buoyancy is included through the Boussinesq approximation. Critical stability boundaries are calculated for this presumed base flow. Stability of mixed convection is tested with respect to both toroidal and helical disturbances of uniform wavenumber. The numerical investigation is primarily restricted to radius ratio (? = r1/r2) = 0.6 at Prandtl number 100. Critical stability boundaries in Taylor-Grashof number space are presented for two values of the stratification parameter ? (4 and 13). The results follow the development of critical stability from Taylor cells at small Grashof number up to a maximum Grashof number used in this calculation of 80000 and 20000 for g = 13 and 4, respectively. Results show that increasing the stratification parameter stabilize the isothermal Taylor vortices followed by a destabilization effect at higher azimuthal mode number (n > 0). The results also show that for ? = 4 (close to conduction regime), two modes are obtained: one is axisymmetric, and the other is non-axisymmetric. However, for the completely convection regime (boundary-layer type) six asymmetric modes are obtained. Finally, disturbance wavelength, phase speed, and spiral inclination angle are presented as a function of the critical Grashof number for the stratification parameters mentioned earlier.
Citation
Physics of Fluids
Volume
17

Keywords

centrifugal buoyancy effects, linear stability, radial temperature gradient, spiral Poiseuille flow, Taylor Couette flow

Citation

Cotrell, D. and McFadden, G. (2005), Linear Stability of Spiral Poiseuille Flow with a Radial Temperature Gradient: Centrifugal Buoyancy Effects, Physics of Fluids (Accessed July 12, 2024)

Issues

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Created December 1, 2005, Updated February 19, 2017