Competing roughness effects on the non-stationary crossflow instability of the boundary-layer over a rotating broad cone

Al-Malki, Mushrifah Abdulaziz; Fildes, Matthew; Hussain, Zahir

doi:10.1063/5.0105788

Cited by 8 publications

(2 citation statements)

References 41 publications

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“…Hence, this enabled us to differentiate between the type I (upper) and type II (lower) critical Reynolds numbers boundaries and respective lobes of the neutral curves. The code used here is adapted from Al-Malki et al 43 We computed the neutral stability curves for various parameters combining the mean flow for a rotating disk in axial flow with various suction/injection parameters W * and positive/negative strengths of axial flow T s . Through a neutral curve we can visualise the boundary between decay and exponential growth of any perturbation in the parameter space.…”

Section: Neutral Curvesmentioning

confidence: 99%

Effects of the suction/injection and external free stream on the instability of a boundary layer over a rotating disk

et al. 2023

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In this paper, we investigated the effectiveness of the strength of axial flow and suction/injection for the viscous mode (type II) instability within the boundary layer of a rotating disk. To investigate the lower branch, we scaled the viscous mode by using a familiar triple-deck structure analogous to that which was found for Blasius flow over a flat plate. We also analyzed the linear stability behavior of high-Reynolds laminar-turbulent transition. To describe the stationary type II wavenumber and waveangle, we conducted an asymptotic analysis followed by a comparison with the type I mode. We found that a positive axial flow had a stabilizing effect and vice versa a negative axial flow exhibited a destabilizing effect. The results were consistent with previous studies in the literature for positive axial flow, as disturbances were advected downstream in the radial direction. Regarding the suction/injection study, we found suction to be stabilizing, which aligns with previous results in the literature although, conversely, the injection was found to be destabilizing. For the numerical analysis, we found that parameters which result in an increase or decrease of the critical Reynolds number led to a stabilization or destabilization of the flow, respectively. Finally, we compared the asymptotic and numerical stability results for both types I and II followed by the critical Reynolds numbers comparisons, which were found to be consistent in general with results in the literature.

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Section: Neutral Curvesmentioning

confidence: 99%

Effects of the suction/injection and external free stream on the instability of a boundary layer over a rotating disk

et al. 2023

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“…2016; Song & Dong 2023; Song, Dong & Zhao 2023). The cross-flow instability arises from the inflectional meridional velocity profile – inducing co-rotating vortices, which have been investigated on rotating disks (Smith 1947; Gregory, Stuart & Walker 1955; Lingwood 1995), on smooth rotating broad cones (Kobayashi & Izumi 1983) within still fluid (Garrett, Hussain & Stephen 2009), axial flow (Garrett, Hussain & Stephen 2010) and, more recently, on rough rotating cones (Al-Malki, Fildes & Hussain 2022), as well as on swept wings (Kohama 2000).…”

Section: Introductionmentioning

confidence: 99%

Görtler-number-based scaling of boundary-layer transition on rotating cones in axial inflow

Tambe,

Kato,

Hussain

2024

J. Fluid Mech.

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This paper reports on the efficacy of the Görtler number in scaling the laminar-turbulent boundary-layer transition on rotating cones facing axial inflow. Depending on the half-cone angle $\psi$ and axial flow strength, the competing centrifugal and cross-flow instabilities dominate the transition. Traditionally, the flow is evaluated by using two parameters: the local meridional Reynolds number $Re_l$ comparing the inertial versus viscous effects and the local rotational speed ratio $S$ accounting for the boundary-layer skew. We focus on the centrifugal effects, and evaluate the flow fields and reported transition points using Görtler number based on the azimuthal momentum thickness of the similarity solution and local cone radius. The results show that Görtler number alone dominates the late stages of transition (maximum amplification and turbulence onset phases) for a wide range of investigated $S$ and half-cone angle ( $15^{\circ } \leq \psi \leq 50^{\circ }$ ), although the early stage (critical phase) seems to be not determined by the Görtler number alone on the broader cones ( $\psi =30^{\circ }$ and $50^{\circ }$ ) where the primary cross-flow instability dominates the flow. Overall, this indicates that the centrifugal effects play an important role in the boundary-layer transition on rotating cones in axial inflow.

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An improved asymptotic expansion method for fluid flow and convective heat transfer in cone-and-disk geometries with rotating cone

Shevchuk

2023

Physics of Fluids

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In this paper, an improved asymptotic expansion method has been developed to simulate fluid flow and convective heat transfer in a conical gap at small conicity angles up to 4°. Unlike previous works, the improved asymptotic expansion method was applied to the self-similar system of Navier–Stokes equations for small conicity angles. The characteristic Reynolds number varied in the range from 0.001 to 2.0. A detailed validation of the improved asymptotic expansion method compared to the self-similar solution performed for the case of cone rotation with a fixed disk demonstrated its significant advantages compared to previously known asymptotic expansion methods. For the first time, novel approximate analytical solutions were obtained for the tangential and axial velocity components, the swirling angle of the flow, tangential shear stresses on the surface of a fixed disk, as well as static pressure distribution varying in the gap height, which perfectly coincide with the self-similar solution. The accuracy of the improved asymptotic expansion method in the numerical calculation of the Nusselt number in the range of Prandtl numbers from Pr = 0.71 to Pr = 10 significantly exceeds the accuracy of the previously known asymptotic expansion methods. This enables expanding the range of Reynolds and Prandtl numbers, for which the improved asymptotic expansion method has approximately the same accuracy as the self-similar solution. The fact is confirmed that the account for the radial thermal conductivity in the energy equation in the case of small conicity angles up to 4° leads to insignificant deviations of the Nusselt number (maximum 1.5%).

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Competing roughness effects on the non-stationary crossflow instability of the boundary-layer over a rotating broad cone

Cited by 8 publications

References 41 publications

Effects of the suction/injection and external free stream on the instability of a boundary layer over a rotating disk

Effects of the suction/injection and external free stream on the instability of a boundary layer over a rotating disk

Görtler-number-based scaling of boundary-layer transition on rotating cones in axial inflow

An improved asymptotic expansion method for fluid flow and convective heat transfer in cone-and-disk geometries with rotating cone

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