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.

On a class of unsteady, non-parallel, three-dimensional disturbances to boundary-layer flows

2001 ◽  
Vol 441 ◽  
pp. 31-65 ◽  
Author(s):  
PETER W. DUCK ◽  
SONIA L. DRY
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Natural Extension ◽  
Three Dimensional ◽  
Bypass Transition ◽  
Boundary Layer Flows ◽  
Unstable Flow ◽  
Similarity Type ◽  
Hypersonic Boundary Layers ◽  
Flow Disturbances

Steady, spatial, algebraically growing eigenfunctions are now known to occur in several important classes of boundary-layer flow, including two-dimensional hypersonic boundary layers and more recently in Blasius boundary layers subject to three-dimensional linearized disturbances, and in more general three-dimensional boundary layers. These spatial eigensolutions are particularly important and intriguing, given that they exist within the broad limits of the classical steady boundary-layer approximation, and as such are independent of Reynolds number.In this paper we make the natural extension to these previous (stability) analyses by incorporating the effects of unsteadiness into the model for treating disturbances to a quite general class of similarity-type boundary-layer flows. The flow disturbances are inherently non-parallel, but this effect is properly incorporated into the analysis.A further motivation for this paper is that Duck et al. (1999, 2000) have shown that by permitting a spanwise component of flow within a boundary layer of the appropriate form (in particular, growing linearly with the spanwise coordinate), it is found that new families of solutions exist – even the Blasius boundary layer has a three-dimensional ‘cousin’. Therefore a further aim of this paper is to assess the stability of the different solution branches, using the ideas introduced in this paper, to give some clues as to which of the solutions may be encountered experimentally.Several numerical methods are presented for tackling various aspects of the problem. It is shown that when algebraically growing, steady eigensolutions exist, their effect remains important in the unsteady context. We show how even infinitesimal, unsteady flow perturbations can provoke extremely large-amplitude flow responses, including in some cases truly unstable flow disturbances which grow algebraically downstream without bound in the linear context. There are some interesting parallels suggested therefore regarding mechanisms perhaps linked to bypass transition in an important class of boundary-layer flows.

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.

Global three-dimensional optimal disturbances in the Blasius boundary-layer flow using time-steppers

2010 ◽  
Vol 650 ◽  
pp. 181-214 ◽  
Author(s):  
ANTONIOS MONOKROUSOS ◽  
ESPEN ÅKERVIK ◽  
LUCA BRANDT ◽  
DAN S. HENNINGSON
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Wave Packets ◽  
Three Dimensional ◽  
Computational Domain ◽  
Initial Condition ◽  
Oblique Wave ◽  
Layer Flow ◽  
Optimal Disturbances ◽  
Matrix Free

The global linear stability of the flat-plate boundary-layer flow to three-dimensional disturbances is studied by means of an optimization technique. We consider both the optimal initial condition leading to the largest growth at finite times and the optimal time-periodic forcing leading to the largest asymptotic response. Both optimization problems are solved using a Lagrange multiplier technique, where the objective function is the kinetic energy of the flow perturbations and the constraints involve the linearized Navier–Stokes equations. The approach proposed here is particularly suited to examine convectively unstable flows, where single global eigenmodes of the system do not capture the downstream growth of the disturbances. In addition, the use of matrix-free methods enables us to extend the present framework to any geometrical configuration. The optimal initial condition for spanwise wavelengths of the order of the boundary-layer thickness are finite-length streamwise vortices exploiting the lift-up mechanism to create streaks. For long spanwise wavelengths, it is the Orr mechanism combined with the amplification of oblique wave packets that is responsible for the disturbance growth. This mechanism is dominant for the long computational domain and thus for the relatively high Reynolds number considered here. Three-dimensional localized optimal initial conditions are also computed and the corresponding wave packets examined. For short optimization times, the optimal disturbances consist of streaky structures propagating and elongating in the downstream direction without significant spreading in the lateral direction. For long optimization times, we find the optimal disturbances with the largest energy amplification. These are wave packets of Tollmien–Schlichting waves with low streamwise propagation speed and faster spreading in the spanwise direction. The pseudo-spectrum of the system for real frequencies is also computed with matrix-free methods. The spatial structure of the optimal forcing is similar to that of the optimal initial condition, and the largest response to forcing is also associated with the Orr/oblique wave mechanism, however less so than in the case of the optimal initial condition. The lift-up mechanism is most efficient at zero frequency and degrades slowly for increasing frequencies. The response to localized upstream forcing is also discussed.

An Assessment of Three-Dimensional Turbulent Boundary Layer Prediction Methods

1973 ◽  
Vol 95 (3) ◽  
pp. 415-421 ◽  
Author(s):  
A. J. Wheeler ◽  
J. P. Johnston
Keyword(s):  
Boundary Layer ◽  
Eddy Viscosity ◽  
Three Dimensional ◽  
High Sensitivity ◽  
Boundary Layer Flows ◽  
Mean Velocity ◽  
Eddy Viscosity Model ◽  
Separating Flow ◽  
Dimensional Boundary ◽  
Stress Models

Predictions have been made for a variety of experimental three-dimensional boundary layer flows with a single finite difference method which was used with three different turbulent stress models: (i) an eddy viscosity model, (ii) the “Nash” model, and (iii) the “Bradshaw” model. For many purposes, even the simplest stress model (eddy viscosity) was adequate to predict the mean velocity field. On the other hand, the profile of shear stress direction was not correctly predicted in one case by any model tested. The high sensitivity of the predicted results to free stream pressure gradient in separating flow cases is demonstrated.

Secondary instability and subcritical transition of the leading-edge boundary layer

2016 ◽  
Vol 792 ◽  
pp. 682-711 ◽  
Author(s):  
Michael O. John ◽  
Dominik Obrist ◽  
Leonhard Kleiser
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
High Speed ◽  
Three Dimensional ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Secondary Instability ◽  
Bypass Transition ◽  
Wall Suction ◽  
Transition Mechanism

The leading-edge boundary layer (LEBL) in the front part of swept airplane wings is prone to three-dimensional subcritical instability, which may lead to bypass transition. The resulting increase of airplane drag and fuel consumption implies a negative environmental impact. In the present paper, we present a temporal biglobal secondary stability analysis (SSA) and direct numerical simulations (DNS) of this flow to investigate a subcritical transition mechanism. The LEBL is modelled by the swept Hiemenz boundary layer (SHBL), with and without wall suction. We introduce a pair of steady, counter-rotating, streamwise vortices next to the attachment line as a generic primary disturbance. This generates a high-speed streak, which evolves slowly in the streamwise direction. The SSA predicts that this flow is unstable to secondary, time-dependent perturbations. We report the upper branch of the secondary neutral curve and describe numerous eigenmodes located inside the shear layers surrounding the primary high-speed streak and the vortices. We find secondary flow instability at Reynolds numbers as low as$Re\approx 175$, i.e. far below the linear critical Reynolds number$Re_{crit}\approx 583$of the SHBL. This secondary modal instability is confirmed by our three-dimensional DNS. Furthermore, these simulations show that the modes may grow until nonlinear processes lead to breakdown to turbulent flow for Reynolds numbers above$Re_{tr}\approx 250$. The three-dimensional mode shapes, growth rates, and the frequency dependence of the secondary eigenmodes found by SSA and the DNS results are in close agreement with each other. The transition Reynolds number$Re_{tr}\approx 250$at zero suction and its increase with wall suction closely coincide with experimental and numerical results from the literature. We conclude that the secondary instability and the transition scenario presented in this paper may serve as a possible explanation for the well-known subcritical transition observed in the leading-edge boundary layer.

Large Eddy Simulation of Boundary Layer Transition Mechanisms in a Gas-Turbine Compressor Cascade

2018 ◽  
Author(s):  
Ashley D. Scillitoe ◽  
Paul G. Tucker ◽  
Paolo Adami
Keyword(s):  
Boundary Layer ◽  
Large Eddy Simulation ◽  
Boundary Layer Transition ◽  
Bypass Transition ◽  
Suction Surface ◽  
Layer Transition ◽  
Turbulent Spots ◽  
Pressure Surface ◽  
Eddy Simulation ◽  
Large Eddy

Large Eddy Simulation (LES) is used to explore the boundary layer transition mechanisms in two rectilinear compressor cascades. To reduce numerical dissipation, a novel locally adaptive smoothing scheme is added to an unstructured finite-volume solver. The performance of a number of Sub-Grid Scale (SGS) models is explored. With the first cascade, numerical results at two different freestream turbulence intensities (Ti’s), 3.25% and 10%, are compared. At both Ti’s, time-averaged skin-friction and pressure coefficient distributions agree well with previous Direct Numerical Simulations (DNS). At Ti = 3.25%, separation induced transition occurs on the suction surface, whilst it is bypassed on the pressure surface. The pressure surface transition is dominated by modes originating from the convection of Tollmien-Schlichting waves by Klebanoff streaks. However, they do not resembled a classical bypass transition. Instead, they display characteristics of the “overlap” and “inner” transition modes observed in the previous DNS. At Ti = 10%, classical bypass transition occurs, with Klebanoff streaks incepting turbulent spots. With the second cascade, the influence of unsteady wakes on transition is examined. Wake-amplified Klebanoff streaks were found to instigate turbulent spots, which periodically shorten the suction surface separation bubble. The celerity line corresponding to 70% of the free-stream velocity, which is associated with the convection speed of the amplified Klebanoff streaks, was found to be important.

Three-Dimensional Calculation of Wall Boundary Layer Flows in Turbomachines

1987 ◽  
Author(s):  
W. L. Lindsay ◽  
H. B. Carrick ◽  
J. H. Horlock
Keyword(s):  
Boundary Layer ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Cross Flow ◽  
Flow Profile ◽  
Boundary Layer Flows ◽  
Wall Boundary Layer ◽  
Boundary Layer Development ◽  
Flow Through ◽  
The Cross

An integral method of calculating the three-dimensional turbulent boundary layer development through the blade rows of turbomachines is described. It is based on the solution of simultaneous equations for (i) & (ii) the growth of streamwise and cross-flow momentum thicknesses; (iii) entrainment; (iv) the wall shear stress; (v) the position of maximum cross-flow. The velocity profile of the streamwise boundary layer is assumed to be that described by Coles. The cross-flow profile is assumed to be the simple form suggested by Johnston, but modified by the effect of bounding blade surfaces, which restrict the cross-flow. The momentum equations include expressions for “force-defect” terms which are also based on secondary flow analysis. Calculations of the flow through a set of guide vanes of low deflection show good agreement with experimental results; however, attempts to calculate flows of higher deflection are found to be less successful.

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