Transition to turbulence over convex surfaces

2018 ◽  
Vol 855 ◽  
pp. 1208-1237
Author(s):  
Michael Karp ◽  
M. J. Philipp Hack
Keyword(s):  
Opposite Sign ◽  
Transition To Turbulence ◽  
Transient Growth ◽  
Centrifugal Forces ◽  
Streamwise Vortices ◽  
Boundary Layer Flows ◽  
Convex Surfaces ◽  
Exponentially Stable ◽  
Opposing Effects ◽  
Secondary Instabilities

Although boundary-layer flows over convex surfaces are exponentially stable, non-modal mechanisms may enable significant disturbance growth which can make the flow susceptible to secondary instabilities. A parametric investigation of the transient growth and secondary instabilities in flows over convex surfaces is performed. The optimal disturbance in the steady case corresponds to alternating streaks and streamwise vortices of opposite sign that reinforce one another due to lift-up and centrifugal forces, respectively. The process repeats with a constant (naturally appearing) streamwise wavelength which is proportional to the square root of the radius. Unsteady disturbances achieve a higher optimal gain, compared to the steady case, as a result of the opposing effects of the lift-up and centrifugal mechanisms. Linear analysis shows that the curvature has a negligible effect on secondary instabilities. Direct numerical simulations of transient growth with and without secondary instabilities confirm the predictions obtained by the local stability theory. It is found that the presence of a secondary instability is not sufficient, on its own, to ensure transition to turbulence. Only sufficiently long and energetic streaks trigger the breakdown to turbulence.

scholarly journals Concave Surface Boundary Layer Flows in the Presence of Streamwise Vortices

2011 ◽  
Vol 4 (1) ◽  
pp. 33-46 ◽  
Author(s):  
Sonny H. Winoto ◽  
Tandiono Tandiono ◽  
Dilip A. Shah ◽  
Hatsari Mitsudharmadi
Keyword(s):  
Boundary Layer ◽  
Concave Surface ◽  
Surface Boundary ◽  
Streamwise Vortices ◽  
Boundary Layer Flows ◽  
Surface Boundary Layer

Influence of active control on STG-based generation of streamwise vortices in near-wall turbulence

2012 ◽  
Vol 710 ◽  
pp. 234-259 ◽  
Author(s):  
B.-Q. Deng ◽  
C.-X. Xu
Keyword(s):  
Drag Reduction ◽  
Turbulent Flows ◽  
Active Control ◽  
Phase Control ◽  
Transient Growth ◽  
Vortex Generation ◽  
Streamwise Vortices ◽  
Detection Plane ◽  
Near Wall ◽  
Opposition Control

AbstractNear-wall streamwise vortices are closely related to the generation of high skin friction in wall-bounded turbulent flows. A common feature of controlled, friction-reduced turbulent flows is weakened near-wall streamwise vortices. In the present study, the streak transient growth (STG) mechanism for generating near-wall streamwise vortices by Schoppa & Hussain (J. Fluid Mech., vol. 453, 2002, pp. 57–108) is employed, and the opposition control proposed by Choi, Moin & Kim (J. Fluid Mech., vol. 262, 1994, pp. 75–110) is imposed during the transient growth process of perturbations to determine how active control affects the generation of quasi-streamwise vortices. In the transient growth stage, when the detection plane is located near the wall (${ y}_{d}^{+ } = 15$), the control can suppress the production of streamwise vorticity by weakening the near-wall vertical velocity; when the detection plane moves away from the wall (${ y}_{d}^{+ } = 28$), the control has the opposite effect. In the vortex generation stage, the control cannot change the dominance of the stretching effect. Controls imposed at different stages reveal the importance of the STG stage in vortex generation. Strengthened out-of-phase control and lessened in-phase control are proposed as an extension of the original opposition-control scheme. Application in a fully developed turbulent channel flow shows that strengthened ${ y}_{d}^{+ } = 10$ control can yield an even higher drag reduction rate than the original ${ y}_{d}^{+ } = 15$ control. Moreover, lessened ${ y}_{d}^{+ } = 28$ control can also achieve drag reduction and turbulence suppression.

Flow in a meandering channel

2015 ◽  
Vol 770 ◽  
pp. 52-84 ◽  
Author(s):  
J. M. Floryan
Keyword(s):  
Vortex Formation ◽  
Comprehensive Analysis ◽  
Linear Stability Theory ◽  
Vortex Generation ◽  
Centrifugal Forces ◽  
Streamwise Vortices ◽  
Meandering Channel ◽  
Channel Narrowing ◽  
Effective Channel ◽  
Wall Geometry

A comprehensive analysis of the pressure-gradient driven flow in a meandering channel has been presented. This geometry is of interest as it can be used for the creation of streamwise vortices which magnify the transverse transport of scalar quantities, e.g. heat transfer. The linear stability theory has been used to determine the meandering wavelengths required for the vortex formation. It has been demonstrated that reduction of the wavelength results in the onset of flow separation which, when combined with the wall geometry, results in an effective channel narrowing: the stream ‘lifts up’ above the wall and becomes nearly rectilinear, thus eliminating vortex-generating centrifugal forces. Increase of the wavelength also leads to a nearly rectilinear stream, as the slope of the wall modulations becomes negligible. As shear-driven instability may interfere with the formation of vortices, the conditions leading to the onset of such instability have also been investigated. The attributes of the geometry which lead to the most effective vortex generation without any interference from the shear instabilities and with the smallest drag penalty have been identified.

The effect of spanwise system rotation on Dean vortices

1994 ◽  
Vol 274 ◽  
pp. 243-265 ◽  
Author(s):  
O. John E. Matsson ◽  
P. Henrik Alfredsson
Keyword(s):  
Centrifugal Force ◽  
Coriolis Force ◽  
Travelling Waves ◽  
Streamwise Vortices ◽  
Longitudinal Vortices ◽  
Smoke Visualization ◽  
Rotation Rates ◽  
Dean Vortices ◽  
System Rotation ◽  
Secondary Instabilities

An experimental study is reported of the flow in a high-aspect-ratio curved air channel with spanwise system rotation, utilizing hot-wire measurements and smoke visualization. The experiments were made at two different Dean numbers (De), approximately 2 and 4.5 times the critical De for which the flow becomes unstable and develops streamwise vortices. For the lower De without system rotation the primary Dean instability appeared as steady longitudinal vortices. It was shown that negative spanwise system rotation, i.e. the Coriolis force counteracts the centrifugal force, could cancel the primary Dean instability and that for high rotation rates it could give rise to vortices on the inner convex channel wall. For positive spanwise system rotation, i.e. when the Coriolis force enhanced the centrifugal force, splitting and merging of vortex pairs were observed. At the higher De secondary instabilities occurred in the form of travelling waves. The effect of spanwise system rotation on the secondary instability was studied and was found to reduce the amplitude of the twisting and undulating motions for low negative rotation. For low positive rotation the amplitude of the secondary instabilities was unaffected for most regions in parameter space.

scholarly journals Transient growth in linearly stable Taylor–Couette flows

2014 ◽  
Vol 742 ◽  
pp. 254-290 ◽  
Author(s):  
Simon Maretzke ◽  
Björn Hof ◽  
Marc Avila
Keyword(s):  
Linear Stability ◽  
Reynolds Numbers ◽  
Transition To Turbulence ◽  
Transient Growth ◽  
Energy Growth ◽  
Transient Energy ◽  
Taylor Couette ◽  
Semi Empirical ◽  
Essential Prerequisite ◽  
Cylinder Rotation

AbstractNon-normal transient growth of disturbances is considered as an essential prerequisite for subcritical transition in shear flows, i.e. transition to turbulence despite linear stability of the laminar flow. In this work we present numerical and analytical computations of linear transient growth covering all linearly stable regimes of Taylor–Couette flow. Our numerical experiments reveal comparable energy amplifications in the different regimes. For high shear Reynolds numbers$\mathit{Re}$, the optimal transient energy growth always follows a$\mathit{Re}^{2/3}$scaling, which allows for large amplifications even in regimes where the presence of turbulence remains debated. In co-rotating Rayleigh-stable flows, the optimal perturbations become increasingly columnar in their structure, as the optimal axial wavenumber goes to zero. In this limit of axially invariant perturbations, we show that linear stability and transient growth are independent of the cylinder rotation ratio and we derive a universal$\mathit{Re}^{2/3}$scaling of optimal energy growth using Wentzel–Kramers–Brillouin theory. Based on this, a semi-empirical formula for the estimation of linear transient growth valid in all regimes is obtained.

On the secondary instabilities of transient growth in Couette flow

2017 ◽  
Vol 813 ◽  
pp. 528-557 ◽  
Author(s):  
Michael Karp ◽  
Jacob Cohen
Keyword(s):  
Couette Flow ◽  
Initial Energy ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Transient Growth ◽  
Vortical Structures ◽  
Inflection Points ◽  
Theoretical Predictions ◽  
Secondary Instabilities ◽  
Good Agreement

The secondary instability of linear transient growth (TG) in Couette flow is explored theoretically, utilizing an analytical representation of the TG based on four modes and their nonlinear interactions. The evolution of the secondary disturbance is derived using the multiple time scales method. The theoretical predictions are compared with direct numerical simulations and very good agreement with respect to the growth of the disturbance energy and associated vortical structures is observed, up to the final stage just before the breakdown to turbulence. The theoretical model enables us to perform a full parametric study, including TG symmetry type, various wavenumbers, initial energy, TG nonlinearity and Reynolds number, to find all possible routes to transition and the optimal parameters for each type of the secondary disturbance. It is found that the most dangerous secondary disturbances are associated with spanwise wavenumbers which generate the strongest inflection points, i.e. those having maximal shear, rather than with those maximizing the energy gain during the TG phase.

Direct numerical simulations of roughness-induced transition in supersonic boundary layers

2012 ◽  
Vol 693 ◽  
pp. 28-56 ◽  
Author(s):  
Suman Muppidi ◽  
Krishnan Mahesh
Keyword(s):  
Numerical Simulations ◽  
Shear Layer ◽  
Boundary Layers ◽  
Plate Boundary ◽  
Direct Numerical Simulations ◽  
Transition To Turbulence ◽  
Streamwise Vortices ◽  
Mean Flow ◽  
The Mean ◽  
Near Wall

AbstractDirect numerical simulations are used to study the laminar to turbulent transition of a Mach 2.9 supersonic flat plate boundary layer flow due to distributed surface roughness. Roughness causes the near-wall fluid to slow down and generates a strong shear layer over the roughness elements. Examination of the mean wall pressure indicates that the roughness surface exerts an upward impulse on the fluid, generating counter-rotating pairs of streamwise vortices underneath the shear layer. These vortices transport near-wall low-momentum fluid away from the wall. Along the roughness region, the vortices grow stronger, longer and closer to each other, and result in periodic shedding. The vortices rise towards the shear layer as they advect downstream, and the resulting interaction causes the shear layer to break up, followed quickly by a transition to turbulence. The mean flow in the turbulent region shows a good agreement with available data for fully developed turbulent boundary layers. Simulations under varying conditions show that, where the shear is not as strong and the streamwise vortices are not as coherent, the flow remains laminar.

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