Localized edge states in the asymptotic suction boundary layer

2013 ◽  
Vol 717 ◽  
Author(s):  
T. Khapko ◽  
T. Kreilos ◽  
P. Schlatter ◽  
Y. Duguet ◽  
B. Eckhardt ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Coherent Structures ◽  
Spanwise Direction ◽  
Edge States ◽  
Streamwise Vortices ◽  
Boundary Layer Flows ◽  
Edge Tracking ◽  
Subcritical Regime ◽  
Asymptotic Dynamics ◽  
Asymptotic Suction

AbstractThe dynamics on the laminar–turbulent separatrix is investigated numerically for boundary-layer flows in the subcritical regime. Constant homogeneous suction is applied at the wall, resulting in a parallel asymptotic suction boundary layer (ASBL). When the numerical domain is sufficiently extended in the spanwise direction, the coherent structures found by edge tracking are invariably localized and their dynamics shows bursts that drive a remarkable regular or irregular spanwise dynamics. Depending on the parameters, the asymptotic dynamics on the edge can be either periodic in time or chaotic. A clear mechanism for the regeneration of streaks and streamwise vortices emerges in all cases and is investigated in detail.

scholarly journals Edge states as mediators of bypass transition in boundary-layer flows

2016 ◽  
Vol 801 ◽  
Author(s):  
T. Khapko ◽  
T. Kreilos ◽  
P. Schlatter ◽  
Y. Duguet ◽  
B. Eckhardt ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Discrete Symmetry ◽  
Edge State ◽  
Bypass Transition ◽  
Computational Domain ◽  
Edge States ◽  
Boundary Layer Flows ◽  
Turbulent Spots ◽  
Edge Tracking

The concept of edge states is investigated in the asymptotic suction boundary layer in relation to the receptivity process to noisy perturbations and the nucleation of turbulent spots. Edge tracking is first performed numerically, without imposing any discrete symmetry, in a large computational domain allowing for full spatial localisation of the perturbation velocity. The edge state is a three-dimensional localised structure recurrently characterised by a single low-speed streak that experiences erratic bursts and planar shifts. This recurrent streaky structure is then compared with predecessors of individual spot nucleation events, triggered by non-localised initial noise. The present results suggest a nonlinear picture, rooted in dynamical systems theory, of the nucleation process of turbulent spots in boundary-layer flows, in which the localised edge state plays the role of state-space mediator.

scholarly journals On the formation of streamwise vortices by plasma vortex generators

2013 ◽  
Vol 733 ◽  
pp. 370-393 ◽  
Author(s):  
Timothy N. Jukes ◽  
Kwing-So Choi
Keyword(s):  
Boundary Layer ◽  
Flow Direction ◽  
Vortex Formation ◽  
Vortex Generator ◽  
Streamwise Vortex ◽  
Spanwise Direction ◽  
Formation Mechanisms ◽  
Wall Jet ◽  
Streamwise Vortices ◽  
Barrier Discharge Plasma

AbstractThe streamwise vortices generated by dielectric-barrier-discharge plasma actuators in the laminar boundary layer were investigated using particle image velocimetry to understand the vortex-formation mechanisms. The plasma vortex generator was oriented along the primary flow direction to produce a body force in the spanwise direction. This created a spanwise-directed wall jet which interacted with the oncoming boundary layer to form a coherent streamwise vortex. It was found that the streamwise vortices were formed by the twisting and folding of the spanwise vorticity in the oncoming boundary layer into the outer shear layer of the spanwise wall jet, which added its own vorticity to increase the circulation along the actuator length. This is similar to the delta-shaped, vane-type vortex generator, except that the circulation was enhanced by the addition of the vorticity in the plasma jet. It was also observed that the plasma vortex was formed close to the wall with an enhanced wall-ward entrainment, which created strong downwash above the actuator.

Free-stream coherent structures in parallel boundary-layer flows

2014 ◽  
Vol 752 ◽  
pp. 602-625 ◽  
Author(s):  
Kengo Deguchi ◽  
Philip Hall
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Coherent Structures ◽  
Free Stream ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Homotopy Continuation ◽  
Boundary Layer Flows ◽  
Navier Stokes Equations ◽  
High Reynolds

AbstractOur concern in this paper is with high-Reynolds-number nonlinear equilibrium solutions of the Navier–Stokes equations for boundary-layer flows. Here we consider the asymptotic suction boundary layer (ASBL) which we take as a prototype parallel boundary layer. Solutions of the equations of motion are obtained using a homotopy continuation from two known types of solutions for plane Couette flow. At high Reynolds numbers, it is shown that the first type of solution takes the form of a vortex–wave interaction (VWI) state, see Hall & Smith (J. Fluid Mech., vol. 227, 1991, pp. 641–666), and is located in the main part of the boundary layer. On the other hand, here the second type is found to support an equilibrium solution of the unit-Reynolds-number Navier–Stokes equations in a layer located a distance of $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}O(\ln \mathit{Re})$ from the wall. Here $\mathit{Re}$ is the Reynolds number based on the free-stream speed and the unperturbed boundary-layer thickness. The streaky field produced by the interaction grows exponentially below the layer and takes its maximum size within the unperturbed boundary layer. The results suggest the possibility of two distinct types of streaky coherent structures existing, possibly simultaneously, in disturbed boundary layers.

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

The effect of stable thermal stratification on the stability of viscous parallel flows

1971 ◽  
Vol 47 (1) ◽  
pp. 1-20 ◽  
Author(s):  
K. S. Gage
Keyword(s):  
Boundary Layer ◽  
Richardson Number ◽  
Thermal Stratification ◽  
Neutral Stability ◽  
Plane Poiseuille Flow ◽  
Boundary Layer Flows ◽  
A Value ◽  
Parallel Flows ◽  
The Stability ◽  
Asymptotic Suction

A unified linear viscous stability theory is developed for a certain class of stratified parallel channel and boundary-layer flows with Prandtl number equal to unity. Results are presented for plane Poiseuille flow and the asymptotic suction boundary-layer profile, which show that the asymptotic behaviour of both branches of the curve of neutral stability has a universal character. For velocity profiles without inflexion points it is found that a mode of instability disappears as η, the local Richardson number evaluated at the critical point, approaches 0.0554 from below. Calculations for Grohne's inflexion-point profile show both major and minor curves of neutral stability for 0 < η [les ] 0.0554; for\[ 0.0554 < \eta < 0.0773 \]there is only a single curve of neutral stability; and, for η > 0.0773, the curves of neutral stability become closed, with complete stabilization being achieved for a value of η of about 0·107.

scholarly journals Localised streak solutions for a Blasius boundary layer

2018 ◽  
Vol 849 ◽  
pp. 885-901 ◽  
Author(s):  
Richard E. Hewitt ◽  
Peter W. Duck
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Theoretical Work ◽  
Spanwise Direction ◽  
Growth Mechanisms ◽  
Boundary Layer Flows ◽  
Periodic Disturbances ◽  
Blasius Boundary Layer ◽  
Global Nature ◽  
Field Decay

Streaks are a common feature of disturbed boundary-layer flows. They play a central role in transient growth mechanisms and are a building block of self-sustained structures. Most theoretical work has focused on streaks that are periodic in the spanwise direction, but in this work we consider a single spatially localised streak embedded into a Blasius boundary layer. For small streak amplitudes, we show the perturbation can be described in terms of a set of eigenmodes that correspond to an isolated streak/roll structure. These modes are new, and arise from a bi-global eigenvalue calculation; they decay algebraically downstream and may be viewed as the natural three-dimensional extension of the classical two-dimensional Libby & Fox (J. Fluid Mech., vol. 17 (3), 1963, pp. 433–449) solutions. Despite their bi-global nature, we show that a subset of these eigenmodes (including the slowest decaying) is fundamentally related to the solutions first presented by Luchini (J. Fluid Mech., vol. 327, 1996, pp. 101–116), as derived for spanwise-periodic disturbances (at small spanwise wavenumber). This surprising connection is made by an analysis of the far-field decay of the bi-global state. We also address the fully non-parallel downstream development of nonlinear streaks, confirming that the aforementioned eigenmodes are recovered as the streak/roll decays downstream. Encouraging comparisons are made with available experimental data.

scholarly journals Canonical exact coherent structures embedded in high Reynolds number flows

2014 ◽  
Vol 372 (2020) ◽  
pp. 20130352 ◽  
Author(s):  
K. Deguchi ◽  
P. Hall
Keyword(s):  
Boundary Layer ◽  
Coherent Structures ◽  
Shear Flows ◽  
Wave Interaction ◽  
Vortex Sheet ◽  
Boundary Layer Flows ◽  
Burgers Vortex ◽  
Infinite Region ◽  
High Reynolds ◽  
First Time

The applications and implications of two recently addressed asymptotic descriptions of exact coherent structures in shear flows are discussed. The first type of asymptotic framework to be discussed was introduced in a series of papers by Hall & Smith in the 1990s and was referred to as vortex–wave interaction theory (VWI). New results are given here for the canonical VWI problem in an infinite region; the results confirm and extend the results for the infinite problem inferred the recent VWI computation of plane Couette flow. The results given define for the first time exact coherent structures in unbounded flows. The second type of canonical structure described here is that recently found for asymptomatic suction boundary layer and corresponds to freestream coherent structures (FCS), in boundary layer flows. Here, it is shown that the FCS can also occur in flows such as Burgers vortex sheet. It is concluded that both canonical problems can be locally embedded in general shear flows and thus have widespread applicability.

Three-Dimensional Structure of a Nominally Planar Turbulent Boundary Layer

1979 ◽  
Vol 101 (3) ◽  
pp. 326-330 ◽  
Author(s):  
Y. Furuya ◽  
I. Nakamura ◽  
H. Osaka
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Three Dimensional ◽  
Leading Edge ◽  
Turbulent Boundary Layers ◽  
Main Flow ◽  
The Other ◽  
Dimensional Structure ◽  
Spanwise Direction ◽  
Streamwise Vortices

This research is concerned with detailed experiments on spanwise nonuniformity of nominally planar turbulent boundary layers. Two procedures for eliminating spanwise nonuniformity are studied. One method is to remove the original, natural vortices by introducing additional ones arising from protuberances attached to the leading edge of a flat plate, and the other technique is by making the main flow entirely uniform. Effects of artificially controlled streamwise vortices on spanwise nonuniformity are examined. From these experiments, the process by which induced vortices cause nonuniformity of turbulent boundary layer characteristics in the spanwise direction is discussed.

Experimental investigation of coherent structures of a three-dimensional separated turbulent boundary layer

2018 ◽  
Vol 859 ◽  
pp. 1-32 ◽  
Author(s):  
Mohammad Elyasi ◽  
Sina Ghaemi
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Turbulent Boundary Layer ◽  
Saddle Point ◽  
Turbulent Kinetic Energy ◽  
Coherent Structures ◽  
Three Dimensional ◽  
Spanwise Direction ◽  
Mean Flow ◽  
Elliptical Cross

Coherent structures of a three-dimensional (3D) separation due to an adverse pressure gradient are investigated experimentally. The flow set-up consists of a flat plate to develop a turbulent boundary layer upstream of an asymmetric two-dimensional diffuser with one diverging surface. The diffuser surface has an initial mild curvature followed by a flat section where flow separation occurs. The top and the two sidewalls of the diffuser are not equipped with any flow control mechanism to form a 3D separation. Planar particle image velocimetry (PIV) using four side-by-side cameras is applied to characterize the flow with high spatial resolution over a large streamwise-wall-normal field of view (FOV). Tomographic PIV (tomo-PIV) is also applied for volumetric measurement in a domain flush with the flat surface of the diffuser. The mean flow obtained from averaging instantaneous velocity fields of this intermittent unsteady flow appears as a vortex with an elliptical cross-section. The major axis of the ellipse is tilted with respect to the streamwise direction. As a result, the average velocity in the mid-span of the diffuser has an upstream forward flow and a downstream backward flow, separated by a point of zero wall shear stress. Sweep motions mainly carry out transport of turbulent kinetic energy upstream of this point, while ejections dominate at the downstream region. In the instantaneous flow fields, forward and backward flows have equivalent strength, and the separation front is extended in the spanwise direction. The conditional average of the separation instants forms a saddle-point structure with streamlines converging in the spanwise direction. Proper orthogonal decomposition (POD) of the tomo-PIV data demonstrates that about 42 % of the turbulent kinetic energy is present in the first pair of modes, with a strong spanwise component. The spatial modes of POD also show focus, node and saddle-point structures. The average of the coefficients of the dominant POD modes during the separation events is used to develop a reduced-order model (ROM). Based on the ROM, the instantaneous 3D separation over the diffuser is a saddle-point structure interacting with focus-type structures.

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