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Optimisation and control of shear flows
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control.
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 [en]
shear flows, flow control, optimal disturbances, Lagrange method, transition to turbulence, non-linear dynamics
National Category
Mechanical Engineering
Identifiers
URN: urn:nbn:se:kth:diva-33771ISBN: 978-91-7415-987-5OAI: oai:DiVA.org:kth-33771DiVA: diva2:417450
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
List of papers
1. Global three-dimensional optimal disturbances in the Blasius boundary-layer flow using time-steppers
Open this publication in new window or tab >>Global three-dimensional optimal disturbances in the Blasius boundary-layer flow using time-steppers
2010 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 650, 181-214 p.Article in journal (Refereed) Published
Abstract [en]

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.

Keyword
Asymptotic response, Blasius, Computational domains, Disturbance growth, Eigen modes, Energy amplification, Flat plate, Flow perturbations, Geometrical configurations, High Reynolds number, Initial conditions, Lateral directions, Lift-up mechanism, Linear Stability, Linearized navier-stokes equations, matrix, Objective functions, Oblique wave, Optimal disturbances, Optimal time, Optimization problems, Optimization techniques, Periodic forcing, Propagation speed, Spatial structure, Streaky structure, Streamwise vortices, Tollmien-Schlichting waves, Unstable flows, Zero frequency, Amplification, Boundary layer flow, Boundary layers, Frequency response, Lagrange multipliers, Navier Stokes equations, Reynolds number, Three dimensional, Wave packets, Waves
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-10648 (URN)10.1017/S0022112009993703 (DOI)000278212500007 ()2-s2.0-77952398610 (ScopusID)
Note
QC 20100924. Uppdaterad från submitted till published (20100924).Available from: 2009-06-09 Created: 2009-06-09 Last updated: 2011-05-18Bibliographically approved
2. Optimal disturbances above and upstream a flat plate with an elliptic leading edge
Open this publication in new window or tab >>Optimal disturbances above and upstream a flat plate with an elliptic leading edge
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:nbn:se:kth:diva-33798 (URN)
Note
QC 20110518Available from: 2011-05-18 Created: 2011-05-18 Last updated: 2011-05-18Bibliographically approved
3. Nonequilibrium Thermodynamics and the Optimal Path to Turbulence in Shear Flows
Open this publication in new window or tab >>Nonequilibrium Thermodynamics and the Optimal Path to Turbulence in Shear Flows
Show others...
2011 (English)In: Physical Review Letters, ISSN 0031-9007, Vol. 106, no 13, 134502- p.Article in journal (Refereed) Published
Abstract [en]

We determine the initial condition on the laminar-turbulent boundary closest to the laminar state using nonlinear optimization for plane Couette flow. Resorting to the general evolution criterion of nonequilibrium systems we optimize the route to the statistically steady turbulent state, i.e., the state characterized by the largest entropy production. This is the first time information from the fully turbulent state is included in the optimization procedure. We demonstrate that the optimal initial condition is localized in space for realistic flow domains.

Keyword
maximum-entropy production, pipe-flow, transition, dissipation, growth, waves
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-33795 (URN)10.1103/PhysRevLett.106.134502 (DOI)000288901200012 ()2-s2.0-79960631982 (ScopusID)
Funder
Swedish e‐Science Research Center
Available from: 2011-05-18 Created: 2011-05-18 Last updated: 2012-05-23Bibliographically approved
4. DNS and LES of estimation and control of transition in boundary layers subject to free-stream turbulence
Open this publication in new window or tab >>DNS and LES of estimation and control of transition in boundary layers subject to free-stream turbulence
2008 (English)In: International Journal of Heat and Fluid Flow, ISSN 0142-727X, E-ISSN 1879-2278, Vol. 29, no 3, 841-855 p.Article in journal (Refereed) Published
Abstract [en]

Transition to turbulence occurring in a flat-plate boundary-layer flow subjected to high levels of free-stream turbulence is considered. This scenario, denoted bypass transition, is characterised by the non-modal growth of streamwise elongated disturbances. These so-called streaks are regions of positive and negative streamwise velocity alternating in the spanwise direction inside the boundary layer. When they reach large enough amplitudes, breakdown into turbulent spots occurs via their secondary instability. In this work, the bypass-transition process is simulated using direct numerical simulations (DNS) and large-eddy simulations (LES). The ADM-RT subgrid-scale model turned out to be particularly suited for transitional flows after a thorough validation. Linear feedback control is applied in order to reduce the perturbation energy and consequently delay transition. This case represents therefore an extension of the linear approach (Chevalier, M., Hoepffner, J., Åkervik, E., Henningson, D.S., 2007a. Linear feedback control and estimation applied to instabilities in spatially developing boundary layers. J. Fluid Mech. 588, 163-187, 167-187.) to flows characterised by strong nonlinearities. Control is applied by blowing and suction at the wall and it is both based on the full knowledge of the instantaneous velocity field (i.e. full information control) and on the velocity field estimated from wall measurements. The results show that the control is able to delay the growth of the streaks in the region where it is active, which implies a delay of the whole transition process. The flow field can be estimated from wall measurements alone: The structures occurring in the "real" flow are reproduced correctly in the region where the measurements are taken. Downstream of this region the estimated field gradually diverges from the "real" flow, revealing the importance of the continuous excitation of the boundary layer by the external free-stream turbulence. Control based on estimation, termed compensator, is therefore less effective than full information control.

Keyword
Boundary layer, Bypass transition, Direct numerical simulation (DNS), Large-eddy simulation (LES), Optimal control, State estimation
National Category
Engineering and Technology
Identifiers
urn:nbn:se:kth:diva-10645 (URN)10.1016/j.ijheatfluidflow.2008.03.009 (DOI)000257133300026 ()2-s2.0-43949103375 (ScopusID)
Conference
The Fifth International Symposium on Turbulence and Shear Flow Phenomena (TSFP5). München, Germany. 27-29 August 2007
Note
QC 20101020Available from: 2009-06-09 Created: 2009-06-09 Last updated: 2012-05-16Bibliographically approved
5. Feedback Control of Boundary-Layer Bypass Transition: Comparison of Simulations with Experiments
Open this publication in new window or tab >>Feedback Control of Boundary-Layer Bypass Transition: Comparison of Simulations with Experiments
2010 (English)In: AIAA Journal, ISSN 0001-1452, E-ISSN 1533-385X, Vol. 48, no 8, 1848-1851 p.Article in journal (Refereed) Published
National Category
Vehicle Engineering Aerospace Engineering
Identifiers
urn:nbn:se:kth:diva-29621 (URN)10.2514/1.J050150 (DOI)000280721300024 ()2-s2.0-77956356874 (ScopusID)
Funder
Swedish e‐Science Research Center
Note
QC 20110405Available from: 2011-04-05 Created: 2011-02-11 Last updated: 2012-05-22Bibliographically approved
6. Control of a separating boundary layer with travelling waves on the wall
Open this publication in new window or tab >>Control of a separating boundary layer with travelling waves on the wall
2011 (English)Report (Other academic)
Abstract [en]

We perform numerical simulations of control of a separating laminar boundary layer by means of blowing and suction at the wall in the form of traveling waves. Separation is imposed by prescribing accelerating and decelerating free-stream velocity for the flow over a flat plate. We find that downstream traveling waves already at very low amplitudes are able to eliminate the separation and induce a turbulent but attached boundary layer flow. Upstream traveling waves of relatively higher amplitudes only slightly reduce separation while keeping the flow laminar. The amplitude of the blowing/suction needed to achieve such significant effects are considerably smaller than those previously considered for drag reduction and transition delay in plane geometries.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2011. 14 p.
National Category
Other Materials Engineering
Identifiers
urn:nbn:se:kth:diva-33797 (URN)
Note
QC 20110518Available from: 2011-05-18 Created: 2011-05-18 Last updated: 2011-05-18Bibliographically approved

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