Boundary-Layer Transition on Broad Cones rotating in an Imposed Axial Flow

Garrett, S. D.; Hussain, Zahir; Stephen, Sharon

doi:10.2514/1.j050021

Cited by 36 publications

(33 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…From the study by Kobayashi et al (1983), it is found that the number of vortices around the circumference at an axial location is always greater than or equal to 8. Similar results have also been reported in the theoretical study by Garrett et al (2010), where they performed linear stability analyses on the range of broad cones (half angles • < < 90 • ). They observe that n decreases with increasing S but stays n ≥ 8 even at S → ∞ .…”

Section: Physical Admissibility Of Pod Modessupporting

confidence: 86%

An experimental method to investigate coherent spiral vortices in the boundary layer over rotating bodies of revolution

et al. 2019

View full text Add to dashboard Cite

Infrared thermography is applied to measure the spiral vortices in the boundary layer over a rotating cone under axial inflow. The data sets are analysed using proper orthogonal decomposition (POD). A criterion based on the signal-to-noise ratio is defined for the selection of relevant POD modes, such that a low-order reconstruction with reduced measurement noise is obtained without affecting the thermal footprint of the spiral vortices. The resulting reconstruction still includes the largescale modulations in the local vortex strength, relating to low-frequency phenomena like amplification, changing vortex states, disturbances in outer flow, etc. The effect of coherent vortical structures is further separated from such phenomena by selective reconstruction of the POD modes based on the number of observed vortices (n) along the circumference. The counter-rotating nature of these vortices is confirmed by PIV measurements. The number of spiral vortices shows good agreement with previously reported methods in the literature. The spiral vortex angle is in good agreement with the previous methods at low rotation ratio (S) , but deviates towards the direction of the local wall shear for high values of S.

show abstract

Section: Physical Admissibility Of Pod Modessupporting

confidence: 86%

An experimental method to investigate coherent spiral vortices in the boundary layer over rotating bodies of revolution

et al. 2019

View full text Add to dashboard Cite

show abstract

“…This crucial difference motivates separate publication of the two cases and a preliminary Orr-Sommerfeld analysis of the rotating-cone boundary layer is presented in Ref. 4.…”

Section: Discussionmentioning

confidence: 99%

“…18 and all following laminar-flow investigations, the incompressible study presented in this paper can be considered as a preliminary investigation into how relevant instability analyses are to the design of CVD processes. This paper is related to the theoretical investigations of Garrett and Peake, 21 recently revisited by the current authors, 4 which consider the absolute instability of the boundary-layer flows over a family of cones rotating within imposed axial flows. There the rotating disk is considered as a special case of cone with half-angle 90…”

Section: Introductionmentioning

confidence: 97%

See 1 more Smart Citation

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

2011

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…Theoretical studies on the convective instabilities associated with the spiral vortices were undertaken by Kobayashi and co-workers [32,35]. Using a new base flow model, Garrett et al [36] improved upon the earlier linear stability calculations presented by Garrett and Peake [8] for rotating-cones in a uniform axial flow. However, results were unchanged for those boundary layers with a zero axial flow.…”

Section: Introductionmentioning

confidence: 99%

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

Thomas

Davies

2019

Phys. Rev. Fluids

View full text Add to dashboard Cite

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.

show abstract

Boundary-Layer Transition on Broad Cones rotating in an Imposed Axial Flow

Cited by 36 publications

References 29 publications

An experimental method to investigate coherent spiral vortices in the boundary layer over rotating bodies of revolution

An experimental method to investigate coherent spiral vortices in the boundary layer over rotating bodies of revolution

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

Contact Info

Product

Resources

About