Abstract
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.
Highlights
This paper advances the study of boundary-layer transition over rotating cones
The results show that an increase in s leads to a reduction in the critical Reynolds number, which suggests that a stronger rotational flow promotes the centrifugal instability mode, destabilising the flow
We have presented a physical extension to the problem of boundarylayer flow over a rotating cone
Summary
This paper advances the study of boundary-layer transition over rotating cones. we consider the convective instability of a slender rotating cone of half-angle 15◦ placed in oncoming uniform axial flows of various strengths. While travelling modes, which move along the surface in the axial direction, have been shown to play an important role in the rotating-disk case (see Corke & Knasiak (1998), Hussain et al (2011)), the slender rotating-cone boundary layer is dominated by a different underlying centrifugal instability. Such travelling modes are neglected in the present study, but their effect on the flow maybe be considered in future investigations.
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