TY - GEN

T1 - Centrifugal instability over a rotating cone

AU - Hussain, Zahir

AU - Garrett, Stephen J.

AU - Stephen, Sharon O.

PY - 2014

Y1 - 2014

N2 - In this study, we provide a mathematical description of the on-set of counter-rotating circular vortices observed for a family of slender rotating cones (of half-angles 15◦, 30◦ and 45◦) in quiescent fluid. In particular, we apply appropriate scalings and apply a change of coordinates, accounting for the effects of streamline curvature. A combined large Reynolds number and large vortex wave number analysis is used to obtain an estimate for the asymptotic right-hand branch of neutral stability for the family of slender rotating cones. Existing experimental and theoretical studies are discussed which lead to the clear hypothesis of a hitherto unidentified convective instability mode that dominates within the boundary-layer flow over slender rotating cones. The mode manifests as G ̈ortler-type counter-rotating spiral vortices, indicative of a centrifugal mechanism. Although a formulation consistent with the classic rotating-disk problem has been successful in predicting the stability characteristics over broad cones, it is unable to identify such a centrifugal mode as the half-angle is reduced. An alternative formulation is developed and the governing equations solved using both short-wavelength asymptotic and numerical approaches to independently identify the centrifugal mode. Our results confirm our earlier predictions pertaining to the existence of the new G ̈ortler mode and capture the effects of the governing centrifugal instability mechanism. Meanwhile, favourable comparisons are drawn between numerical and asymptotic neutral stability curve predictions.

AB - In this study, we provide a mathematical description of the on-set of counter-rotating circular vortices observed for a family of slender rotating cones (of half-angles 15◦, 30◦ and 45◦) in quiescent fluid. In particular, we apply appropriate scalings and apply a change of coordinates, accounting for the effects of streamline curvature. A combined large Reynolds number and large vortex wave number analysis is used to obtain an estimate for the asymptotic right-hand branch of neutral stability for the family of slender rotating cones. Existing experimental and theoretical studies are discussed which lead to the clear hypothesis of a hitherto unidentified convective instability mode that dominates within the boundary-layer flow over slender rotating cones. The mode manifests as G ̈ortler-type counter-rotating spiral vortices, indicative of a centrifugal mechanism. Although a formulation consistent with the classic rotating-disk problem has been successful in predicting the stability characteristics over broad cones, it is unable to identify such a centrifugal mode as the half-angle is reduced. An alternative formulation is developed and the governing equations solved using both short-wavelength asymptotic and numerical approaches to independently identify the centrifugal mode. Our results confirm our earlier predictions pertaining to the existence of the new G ̈ortler mode and capture the effects of the governing centrifugal instability mechanism. Meanwhile, favourable comparisons are drawn between numerical and asymptotic neutral stability curve predictions.

UR - http://www.scopus.com/inward/record.url?scp=84959167475&partnerID=8YFLogxK

M3 - Conference publication

AN - SCOPUS:84959167475

T3 - Proceedings of the 19th Australasian Fluid Mechanics Conference, AFMC 2014

BT - Proceedings of the 19th Australasian Fluid Mechanics Conference, AFMC 2014

T2 - 19th Australasian Fluid Mechanics Conference, AFMC 2014

Y2 - 8 December 2014 through 11 December 2014

ER -