Instability and transition in the boundary layer driven by a rotating slender cone

Kato, Ken; Segalini, Antonio; Alfredsson, P. Henrik; Lingwood, R. J.

doi:10.1017/jfm.2021.216

Cited by 12 publications

(15 citation statements)

References 16 publications

(38 reference statements)

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“…If distributed roughness elements are imposed on the surface for a rotating cone, the stationary mode is usually observed experimentally; see for example Corke & Knastak (1998) and Kato et al (2019a). However, if the surface is rather smooth, the background noise may enhance the excitation of the travelling modes, as observed by Corke & Knastak (1998) and Kato et al (2021). This argument is also true for the analysis of the centrifugal mode to be illustrated in the next subsection.…”

Section: Cross-flow Modementioning

confidence: 87%

“…However, if the surface is rather smooth, the background noise may enhance the excitation of the travelling modes, as observed by Corke & Knastak (1998) and Kato et al. (2021). This argument is also true for the analysis of the centrifugal mode to be illustrated in the next subsection.…”

Section: The Linear Instability Of a Rotating-cone Boundary Layermentioning

confidence: 90%

“…A short-wavelength asymptotic analysis was performed and the numerical results did provide a better prediction for small θ values. A series of recent experiments confirmed that the CF instability dominates the transition process in rotating broad cones (Kato, Alfredsson & Lingwood 2019a;Kato et al 2019b), whereas the centrifugal instability dominates that in rotating slender cones (Kato et al 2021).…”

Section: Introductionmentioning

confidence: 98%

“…2019 b ), whereas the centrifugal instability dominates that in rotating slender cones (Kato et al. 2021).…”

Section: Introductionmentioning

confidence: 99%

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Linear instability of a supersonic boundary layer over a rotating cone

Song

Dong

2023

J. Fluid Mech.

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In this paper, we conduct a systematic study of the instability of a boundary layer over a rotating cone that is inserting into a supersonic stream with zero angle of attack. The base flow is obtained by solving the compressible boundary-layer equations using a marching scheme, whose accuracy is confirmed by comparing with the full Navier–Stokes solution. Setting the oncoming Mach number and the semi-apex angle to be 3 and 7 $^\circ$ , respectively, the instability characteristics for different rotating rates ( $\bar \varOmega$ , defined as the ratio of the rotating speed of the cone to the axial velocity) and Reynolds numbers ( $R$ ) are revealed. For a rather weak rotation, $\bar \varOmega \ll 1$ , only the modified Mack mode (MMM) exists, which is an extension of the supersonic Mack mode in a quasi-two-dimensional boundary layer to a rotation configuration. Further increase of $\bar \varOmega$ leads to the appearance of a cross-flow mode (CFM), coexisting with the MMM but in the quasi-zero frequency band. The unstable zones of the MMM and CFM merge together, and so they are referred to as the type-I instability. When $\bar \varOmega$ is increased to an $O(1)$ level, an additional unstable zone emerges, which is referred to as the type-II instability to be distinguished from the aforementioned type-I instability. The type-II instability appears as a centrifugal mode (CM) when $R$ is less than a certain value, but appears as a new CFM for higher Reynolds numbers. The unstable zone of the type-II CM enlarges as $\bar \varOmega$ increases. The vortex structures of these types of instability modes are compared, and their large- $R$ behaviours are also discussed.

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Section: Cross-flow Modementioning

confidence: 87%

Section: The Linear Instability Of a Rotating-cone Boundary Layermentioning

confidence: 90%

Section: Introductionmentioning

confidence: 98%

“…2019 b ), whereas the centrifugal instability dominates that in rotating slender cones (Kato et al. 2021).…”

Section: Introductionmentioning

confidence: 99%

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Linear instability of a supersonic boundary layer over a rotating cone

Song

Dong

2023

J. Fluid Mech.

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“…However, an alternative instability mechanism may be at work when the half-apex angle is smaller than about 40 • , meaning that the two categories, broad and slender (or sharp) cones, have distinctly different stability characteristics. Such a difference has also been observed in several experiments (Tien and Campbell, 1963;Kobayashi and Izumi, 1983;Kato et al, 2021aKato et al, , 2021b and also studied through linear stability analysis (Garrett et al, 2009;Hussain et al, 2014). The difference between broad and slender cones has been suggested to be that below some cone angle (ψ ≲ 40 • ) centrifugal effects dominate the flow in the boundary layer setting up a centrifugal instability similar to a Görtler instability.…”

Section: Introductionmentioning

confidence: 59%

Rotating disks and cones a centennial of von Kármán’s 1921 paper

KATO

Lingwood

Alfredsson

2023

JFST

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It is now more than 100 years since the work of von Kármán (1921) on the boundary-layer flow over a rotating disk was published in the first volume of Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM, Vol. 1(4), pp 233-252). Recently, there has been a large amount of work undertaken addressing the instability and transition of the boundary-layer flows over rotating disks and cones using theoretical, numerical and experimental techniques. Here we will discuss some different methods to analyze experimental data that can give insight into the instability and transition to turbulence of boundary-layer flows over rotating slender and broad cones (including the disk). At first, we discuss the pdf-method (probability density function) that allows a simple way to determine regions of instability growth, transition and fully developed turbulence. Secondly, we look at various ways to use spectral information to investigate the boundary layers giving a deeper understanding of the transition process. Finally, a method to determine the most probable flow structure leading up to fully developed turbulence is discussed. We envisage that some of these methods can be useful in analyzing instability and transition also in other flow cases.

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