Axial Flow Effects on the Stability of Circular Couette Flow with Viscous Heating
David Cotrell, Geoffrey B. McFadden
We consider flow between concentric circular cylinders driven jointly by a constant axial pressure gradient and rotation of one or both cylinders. In this work we account for viscous heating effects, and have computed critical values for the radius ratio and rotation rate ratio used in the recent experiments of White & Muller. The effects of gravity are neglected, while conductivity, the volumetric coefficient of thermal expansion, density, and constant pressure specific heat are taken to be constant. In this work we allow the viscosity to vary with temperature. The analysis extends previous results with no axial flow, and accounts for arbitrary disturbances of infinitesimal amplitude. Results show that over the entire range of axial flow rates considered, stability boundaries differ significantly from those found for the zero axial flow case. Consistent with the isothermal results of Cotrell, Rani & Pearlstein and the non-isothermal results of Cotrell & McFadden, the critical disturbance is axisymmetric over only a finite range of Reynolds numbers beginning at zero, beyond which the critical disturbance becomes non-axisymmetric.
and McFadden, G.
Axial Flow Effects on the Stability of Circular Couette Flow with Viscous Heating, Physics of Fluids, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=51314
(Accessed September 23, 2023)