TY - JOUR
T1 - The centrifugal instability of the boundary-layer flow over a slender rotating cone in an enforced axial free-stream
AU - Hussain, Z.
AU - Garrett, Stephen
AU - Stephen, S. O.
AU - Griffiths, Paul
N1 - © 2016 Cambridge University Press. The final publication is available via Cambridge Journals Online at http://dx.doi.org/10.1017/jfm.2015.671
PY - 2016/2/10
Y1 - 2016/2/10
N2 - In this study, a new centrifugal instability mode, which dominates within the boundary-layer flow over a slender rotating cone in still fluid, is used for the first time to model the problem within an enforced oncoming axial flow. The resulting problem necessitates an updated similarity solution to represent the basic flow more accurately than previous studies in the literature. The new mean flow field is subsequently perturbed, leading to disturbance equations that are solved via numerical and short-wavelength asymptotic approaches, yielding favourable comparisons with existing experiments. Essentially, the boundary-layer flow undergoes competition between the streamwise flow component, due to the oncoming flow, and the rotational flow component, due to effect of the spinning cone surface, which can be described mathematically in terms of a control parameter, namely the ratio of streamwise to axial flow. For a slender cone rotating in a sufficiently strong axial flow, the instability mode breaks down into Görtler-type counter-rotating spiral vortices, governed by an underlying centrifugal mechanism, which is consistent with experimental and theoretical studies for a slender rotating cone in otherwise still fluid.
AB - In this study, a new centrifugal instability mode, which dominates within the boundary-layer flow over a slender rotating cone in still fluid, is used for the first time to model the problem within an enforced oncoming axial flow. The resulting problem necessitates an updated similarity solution to represent the basic flow more accurately than previous studies in the literature. The new mean flow field is subsequently perturbed, leading to disturbance equations that are solved via numerical and short-wavelength asymptotic approaches, yielding favourable comparisons with existing experiments. Essentially, the boundary-layer flow undergoes competition between the streamwise flow component, due to the oncoming flow, and the rotational flow component, due to effect of the spinning cone surface, which can be described mathematically in terms of a control parameter, namely the ratio of streamwise to axial flow. For a slender cone rotating in a sufficiently strong axial flow, the instability mode breaks down into Görtler-type counter-rotating spiral vortices, governed by an underlying centrifugal mechanism, which is consistent with experimental and theoretical studies for a slender rotating cone in otherwise still fluid.
KW - Boundary layer stability
KW - Rotating flows
KW - Transition to turbulence
UR - https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/abs/centrifugal-instability-of-the-boundarylayer-flow-over-a-slender-rotating-cone-in-an-enforced-axial-free-stream/1CA04360ADA50023DF942894E38B2802
U2 - 10.1017/jfm.2015.671
DO - 10.1017/jfm.2015.671
M3 - Article
SN - 0022-1120
VL - 788
SP - 70
EP - 94
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
ER -