Boundary layer instability over a rotating slender cone under non-axial inflow

Tambe, Sumit; Schrijer, F.F.J.; Rao, Arvind Gangoli; Veldhuis, L.L.M.

doi:10.1017/jfm.2020.990

Cited by 6 publications

(17 citation statements)

References 24 publications

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“…For a still cone with almost zero background noise, the stationary is usually observed experimentally; see for example (Gregory et al 1955;Kobayashi & Izumi 1983). However, when the axial stream is introduced, the background noise may enhance the excitation of the travelling modes, as observed by Tambe 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: 67%

“…However, when the axial stream is introduced, the background noise may enhance the excitation of the travelling modes, as observed by Tambe 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 subsequent experiment (Tambe et al. 2021) confirmed its accuracy on the prediction of critical Reynolds number, and the effect of the incident angle was also studied. According to the previous investigations, the different instability regimes in the – plane are sketched in figure 1.…”

Section: Introductionmentioning

confidence: 89%

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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: 67%

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

confidence: 90%

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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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“…For a broad cone, the cross-flow instability at the upper-branch neutral point is driven by an inviscid regime, associated with the inflectional point of the base flow, whereas that at the lower-branch neutral point is driven by the balance of the viscosity, pressure gradient and Coriolis force in the near-wall region, which is a viscous mode (Hall 1986;Malik 1986;Garrett, Hussain & Stephen 2009). For a slender cone inserted into an axial flow, increase of the axial velocity leads to a suppression of the centrifugal instability (Kobayashi, Kohama & Kurosawa 1983;Hussain et al 2016;Tambe et al 2021) but an enhancement of the travelling Tollmien-Schlichting wave (Schubauer & Skramstad 1943). The compressible effect on the linear instability of rotating discs or cones was considered by Turkyilmazoglu, Cole & Gajjar (2000), Turkyilmazoglu (2005), Towers & Garrett (2012 and Towers (2013).…”

Section: Introductionmentioning

confidence: 99%

“…2016; Tambe et al. 2021) but an enhancement of the travelling Tollmien–Schlichting wave (Schubauer & Skramstad 1943). The compressible effect on the linear instability of rotating discs or cones was considered by Turkyilmazoglu, Cole & Gajjar (2000), Turkyilmazoglu (2005), Towers & Garrett (2012, 2016) and Towers (2013).…”

Section: Introductionmentioning

confidence: 99%

Effect of cone rotation on the nonlinear evolution of Mack modes in supersonic boundary layers

Song,

Dong,

Zhao

2023

J. Fluid Mech.

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In this paper, we present a systematic study of the nonlinear evolution of the travelling Mack modes in a Mach 3 supersonic boundary layer over a rotating cone with a $7^{\circ }$ half-apex angle using the nonlinear parabolic stability equation (NPSE). To quantify the effect of cone rotation, six cases with different rotation rates are considered, and from the same streamwise position, a pair of oblique Mack modes with the same frequency but opposite circumferential wavenumbers are introduced as the initial perturbations for NPSE calculations. As the angular rotation rate $\varOmega$ increases such that $\bar \varOmega$ (defined as the ratio of the rotation speed of the cone to the streamwise velocity at the boundary-layer edge) varies from 0 to $O(1)$ , three distinguished nonlinear regimes appear, namely the oblique-mode breakdown, the generalised fundamental resonance and the centrifugal-instability-induced transition. For each regime, the mechanisms for the amplifications of the streak mode and the harmonic travelling waves are explained in detail, and the dominant role of the streak mode in triggering the breakdown of the laminar flow is particularly highlighted. Additionally, from the linear stability theory, the dominant travelling mode undergoes the greatest amplification for a moderate $\varOmega$ , which, according to the $e^N$ transition-prediction method, indicates premature transition to turbulence. However, this is in contrast to the NPSE results, in which a delay of the transition onset is observed for a moderate $\varOmega$ . Such a disagreement is attributed to the different nonlinear regimes appearing for different rotation rates. Therefore, the traditional transition-prediction method based on the linear instability should be carefully employed if multiple nonlinear regimes may appear.

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