Linear growth rates of types I and II convective modes within the rotating-cone boundary layer

Garrett, S. D.

doi:10.1088/0169-5983/42/2/025504

Cited by 17 publications

(26 citation statements)

References 30 publications

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“…Meanwhile, the second formulation is in the inertial (stationary) frame of reference and considers disturbances traveling at fixed phase speeds with respect to the disk surface. This is related to Garrett's recent numerical studies of the rotating disk, cone, and sphere boundary layers [26][27][28] where disturbances traveling at around 75% of each body's surface are found to be most amplified. This is consistent with Kobayashi and Arai's 29 experimental observation of slow vortices over rotating spheres under particular conditions.…”

Section: Introductionmentioning

confidence: 64%

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The instability of the boundary layer over a disk rotating in an enforced axial flow

2011

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A study of similarity solutions for laminar swirling axisymmetric flows with both buoyancy and initial momentum flux Phys. Fluids 23, 113601 (2011) On particle spin in two-way coupled turbulent channel flow simulations Phys. Fluids 23, 093302 (2011) First-order virial expansion of short-time diffusion and sedimentation coefficients of permeable particles suspensions Phys. Fluids 23, 083303 (2011) The stochastic Burgers equation with vorticity: Semiclassical asymptotic series solutions with applications J. Math. Phys. 52, 083512 (2011) Roles of particle-wall and particle-particle interactions in highly confined suspensions of spherical particles being sheared at low Reynolds numbers Phys. We consider the convective instability of stationary and traveling modes within the boundary layer over a disk rotating in a uniform axial flow. Complementary numerical and high Reynolds number asymptotic analyses are presented. Stationary and traveling modes of type I (crossflow) and type II (streamline curvature) are found to exist within the boundary layer at all axial flow rates considered. For low to moderate axial flows, slowly traveling type I modes are found to be the most amplified, and quickly traveling type II modes are found to have the lower critical Reynolds numbers. However, near-stationary type I modes are expected to be selected due to a balance being struck between onset and amplification. Axial flow is seen to stabilize the boundary layer by increasing the critical Reynolds numbers and reducing amplification rates of both modes. However, the relative importance of type II modes increases with axial flow and they are, therefore, expected to dominate for sufficiently high rates. The application to chemical vapour deposition (CVD) reactors is considered.

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Section: Introductionmentioning

confidence: 64%

“…26 that considers linear growth rates within the rotating-disk boundary layer for T s ¼ 0. That work has since been extended to the boundary-layer flows over the family of rotating cones and spheres by Garrett 27,28 with a view to understanding the vortex-speed selection process over smooth bodies (see Sec. V).…”

Section: Linear Amplification Ratesmentioning

confidence: 99%

The instability of the boundary layer over a disk rotating in an enforced axial flow

2011

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“…However, results were unchanged for those boundary layers with a zero axial flow. Further investigations on the family of rotating-cone boundary layers were undertaken by the Garrett group [37][38][39][40], who studied the type of convective instabilities that develop for variable cone half-angles. For broad rotating-cones, the crossflow instability that forms the corotating vortices on the rotating-disk was found to dominate the boundary layer stability process (at least until the conditions required…”

Section: Introductionmentioning

confidence: 99%

Global linear instability of rotating-cone boundary layers in a quiescent medium

Thomas

Davies

2019

Phys. Rev. Fluids

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The global linear stability of the family of infinite rotating-cone boundary layers in an otherwise still fluid is investigated using a velocity-vorticity form of the linearized Navier-Stokes equations. The formulation is separable with respect to the azimuthal direction. Thus, disturbance development is simulated for a single azimuthal mode number. Numerical simulations are conducted for an extensive range of cone half-angles (ψ ∈ [20 • : 80 • ]) and stability parameters (Reynolds number, azimuthal mode number), where conditions are taken to be near those specifications necessary for the onset of absolute instability. A localized impulsive wall forcing is implemented that excites disturbances that form wave packets. This allows the disturbance evolution to be traced in the spatial-temporal plane. When a homogeneous flow approximation is utilised that neglects the spatial variation of the basic state, linear perturbations display characteristics consistent with local stability theory. For disturbances to the genuine spatially dependent inhomogeneous flow, global linear instability characterized by a faster than exponential temporal growth arises for azimuthal mode numbers greater than the conditions for critical absolute instability. Furthermore, a reasonable prediction for the azimuthal mode number needed to bring about a change in global behavior is achieved by coupling solutions of the Ginzburg-Landau equation with local stability properties. Thus, the local-global stability behavior is qualitatively similar to that found in the infinite rotating-disk boundary layer and many other globally unstable flows.

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“…Although the rotating system clearly represents a fundamentally different system to the stationary, swept cylinder, the parallels drawn between high-level experimental observations of the two systems mean that the ongoing analysis of the rotating-cone system by Garrett, Hussain and Stephen [37][38][39] could provide useful insights into the swept-cylinder problem. To date, Garrett et al have been able to correctly predict observable quantities for vortices in the crossflow-dominated transitional flow over broad cones, using a combination of numerical and asymptotic approaches.…”

Section: Connection To Rotating Conesmentioning

confidence: 99%

The Influence of Streamwise Vorticity on Transition in the Presence of Sweep

Gostelow

Garrett

Jean

2011

41st AIAA Fluid Dynamics Conference and Exhibit

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Experimental observations and theoretical predictions of streamwise vorticity on circular cylinders in crossflow and on turbine blades are considered. The observations on cylinders confirm earlier predictions and this forms a firm basis for referencing other measurements and predictions of vortical behavior. It also results directly in a correlation for predicting the spanwise wavelength of streamwise vortices on the convex surfaces of turbomachine blades. Highly resolved Large Eddy Simulation has shown that fine scale organized streamwise vorticity may exist on the convex surfaces of turbine and compressor blading and is predictable. For a turbine blade with a blunt leading edge the streamwise vorticity may persist on a time-average basis to influence the entire suction surface at suitably low Reynolds numbers typical of aircraft cruise conditions. The results emphasize the enormous computing resource required to resolve the flow on a routine basis for design purposes. It is demonstrated computationally that streamwise vorticity interacts with spanwise vorticity in leading edge bubbles to promote early transition and bubble closure. Time resolution is required to capture the flow complexity that is fundamental for an understanding of the physical behavior of the laminar boundary layer and its separation and transition. A narrow spanwise strip does not allow the streamwise vorticity to settle into the organized pattern. For streamwise vorticity to become organized, an adequate spanwise domain and run duration for time averaging are also essential. Any accurate treatment of laminar boundary layers at low Reynolds numbers needs to be performed three dimensionally and with a sufficiently fine spanwise spacing and duration of run to resolve streamwise vortical structures. Sweep of the body, wing or blade poses special problems. Not least is a serious lack of information on even the most basic cases. An attempt is made to relate the streamwise vorticity studied by Kestin and Wood to the more aggressive crossflow instability studied by Poll. More research is needed if designers are to be confident about the flow regimes they might expect to prevail for a given sweep angle. Nomenclature D Cylinder diameter n Amplification factor in inception prediction Re Reynolds number Tu Free-stream turbulence level u Velocity component in x direction x, y, z Coordinate directions    Angle between normal to the inflow and axis of the body    Spanwise spacing between vortex pairs  ___________________________________________________________________________________

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Linear growth rates of types I and II convective modes within the rotating-cone boundary layer

Cited by 17 publications

References 30 publications

The instability of the boundary layer over a disk rotating in an enforced axial flow

The instability of the boundary layer over a disk rotating in an enforced axial flow

Global linear instability of rotating-cone boundary layers in a quiescent medium

The Influence of Streamwise Vorticity on Transition in the Presence of Sweep

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