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Optimal disturbances above and upstream a flat plate with an elliptic leading edge
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0002-4346-4732
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.ORCID iD: 0000-0001-7864-3071
2011 (English)Report (Other academic)
Abstract [en]

Adjoint-based iterative methods are employed in order to compute linear optimal disturbances in a spatially growing boundary layer around an elliptic leading edge. The Lagrangian approach is used where an objective function is chosen and constraints are assigned. The optimisation problem is solved using power iterations combined with a matrix-free formulation, where the state is marched forward in time with a standard DNS solver and backward with the adjoint solver until a chosen convergence criterion is fulfilled. We consider the global and the upstream localised optimal initial condition leading to the largest possible energy amplification at time T. We found that the twodimensional initial condition with the largest potential for growth is a Tolmien-Schlichting-like wave packet that includes the Orr mechanism and is located inside the boundary layer, downstream of the leading edge. Three-dimensional disturbances induce streaks by the lift-up mechanism. Localised optimal initial condition enables us to better study the effects of the leading edge; with this approach we propose a new method to study receptivity. Two-dimensional upstream disturbances, are inefficient at triggering an unstable eigenmode. The three-dimensional disturbances instead induce elongated streamwise streaks; both the global and upstream localised disturbances give significant growth. This advocates for high receptivity to three-dimensional disturbances.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology , 2011. , 16 p.
National Category
Other Materials Engineering
Identifiers
URN: urn:nbn:se:kth:diva-33798OAI: oai:DiVA.org:kth-33798DiVA: diva2:417779
Note
QC 20110518Available from: 2011-05-18 Created: 2011-05-18 Last updated: 2011-05-18Bibliographically approved
In thesis
1. Optimisation and control of shear flows
Open this publication in new window or tab >>Optimisation and control of shear flows
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Transition to turbulence and flow control are studied by means of numerical simulations for different simple shear flows. Linear and non-linear optimisation methods using the Lagrange multiplier technique are employed.

In the linear framework as objective function the standard disturbance kinetic energy is chosen and the constraints involve the linearised Navier–Stokes equations. We consider both the optimal initial condition leading to the largest disturbance energy growth at finite times and the optimal time-periodic forcing leading to the largest asymptotic response for the case of the flat plate boundary layer excluding the leading edge. The optimal disturbances for spanwise wavelengths of the order of the boundary layer thickness are 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. Also linear optimal disturbances are computed around a leading edge and the effect of the geometry is considered. It is found that two-dimentional disturbances originating upstream, relative to the leading edge of the plate are inefficient at generating a viable disturbance, while three dimentional disturbances are more amplified.

In the non-linear framework a new approach using ideas from non-equilibrium thermodynamics is developed. We determine the initial condition on the laminar/turbulent boundary closest to the laminar state. Starting from the general evolution criterion of non-equilibrium systems we propose a method to optimise the route to the statistically steady turbulent state, i.e. the state characterised by the largest entropy production. This is the first time information from the fully turbulent state is included in the optimisation procedure. The method is applied to plane Couette flow. We show that the optimal initial condition is localised in space for realistic flow domains, while the disturbance visits bent streaks before breakdown.

Feedback control is applied to the bypass-transition scenario with high levels of free-stream turbulence. The flow is the flat-plate boundary layer. In this scenario low frequency perturbations enter the boundary layer and streamwise elongated disturbances emerge due to non-modal growth. The so-called streaky structures are growing in amplitude until they reach high enough energy levels and break down into turbulent spots via their secondary instability. When control is applied in the form of wall blowing and suction, the growth of the streaks is delayed, which implies a delay of the whole transition process. Additionally, a comparison with experimental work is performed demonstrating a remarkable agreement in the disturbance attenuation once the differences between the numerical and experimental setup are reduced.

Open-loop control with wall travelling waves by means of blowing and suction is applied to a separating boundary layer. For downstream travelling waves we obtain a mitigation of the separation of the boundary layer while for upstream travelling waves a significant delay in the transition location accompanied by a modest reduction of the separated region.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2011. ix, 37 p.
Series
Trita-MEK, ISSN 0348-467X ; 2011:04
Keyword
shear flows, flow control, optimal disturbances, Lagrange method, transition to turbulence, non-linear dynamics
National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-33771 (URN)978-91-7415-987-5 (ISBN)
Public defence
2011-05-27, D3, Lindstedtsvägen 5, KTH, Stockholm, 10:00 (English)
Opponent
Supervisors
Funder
Swedish Research CouncilSwedish e‐Science Research Center
Note
QC 20110518Available from: 2011-05-18 Created: 2011-05-17 Last updated: 2012-05-24Bibliographically approved

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