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Optimisation and control of boundary layer flows
KTH, School of Engineering Sciences (SCI), Mechanics.
2009 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Both optimal disturbances and optimal control are studied by means of numerical simulations for the case of the flat-plate boundary-layer flow. The optimisation method is the Lagrange multiplier technique where the objective function is the kinetic energy of the flow perturbations and the constraints involve the linearised Navier–Stokes equations. 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. 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. Control is applied to the bypass-transition scenario with high levels of free-stream turbulence. In this scenario low frequency perturbations enter the boundary layer and streamwise elongated disturbances emerge due to the non-modal growth. These so-called streaks are growing in amplitude until they reach high enough energy levels and breakdown into turbulent spots via their secondary instability. When control is applied in the form of wall blowing and suction, within the region that it is active, 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.

 

 

Place, publisher, year, edition, pages
Stockholm: KTH , 2009. , iii, 23 p.
Series
Trita-MEK, ISSN 0348-467X ; 2009:09
Keyword [en]
boundary layer, control, estimation, optimal disturbances, Lagrange method
National Category
Mechanical Engineering
Identifiers
URN: urn:nbn:se:kth:diva-10652ISBN: 978-91-7415-368-2 (print)OAI: oai:DiVA.org:kth-10652DiVA: diva2:222648
Presentation
2009-06-15, Sal D42, KTH, Lindstedtsvägen 5, Stockholm, 10:00 (English)
Opponent
Supervisors
Available from: 2009-06-09 Created: 2009-06-09 Last updated: 2010-10-20Bibliographically approved
List of papers
1. 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 (Scopus ID)
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: 2017-12-13Bibliographically approved
2. Feedback control of boundary layer bypass transition: experimental and numerical progress
Open this publication in new window or tab >>Feedback control of boundary layer bypass transition: experimental and numerical progress
2009 (English)In: 47th AIAA Aerospace Sciences Meeting, Orlando, FL, American Institute of Aeronautics and Astronautics , 2009Conference paper, Published paper (Refereed)
Abstract [en]

Experimental and numerical work at the Linné FLOW Centre on active control of transition induced by free-stream turbulence is reviewed and two extensions to previous work are reported. Previously, an experimental setup with upstream sensors and downstream actuators has been built. It has been demonstrated that an 

ad-hoc  control algorithm is able to give a considerable attenuation of the disturbance amplitude downstream of the ac- tuators. Furthermore, large-eddy simulations (LES) of optimal feedback control have been performed for a similar flow configuration and disturbance attenuation as well as transition delay have been obtained. Two extensions are made. First, an effort is made to match the disturbance behavior in the experimental flow case and in the LES. Control is applied in simulations of the matched system aiming at approaching the type of actuation used in the experiments (localized suction). The control law is still computed as optimal feedback of the linear system. As the actuation ability approaches the experiments (where much simpler controllers were used), so does the control effect. Second, system identification (SI) is applied to the experimental data and a more efficient controller is designed. It is made plausible that controllers designed by SI can give considerable improvements in the disturbance attenuation. Implications for future work in the area of active control are discussed.

Place, publisher, year, edition, pages
American Institute of Aeronautics and Astronautics, 2009
National Category
Engineering and Technology
Identifiers
urn:nbn:se:kth:diva-10647 (URN)2-s2.0-78549262075 (Scopus ID)
Conference
47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition, 5 - 8 January 2009, Orlando, Florida
Note
QC 20101020Available from: 2009-06-09 Created: 2009-06-09 Last updated: 2010-10-20Bibliographically approved
3. 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 (Scopus ID)
Note
QC 20100924. Uppdaterad från submitted till published (20100924).Available from: 2009-06-09 Created: 2009-06-09 Last updated: 2017-12-13Bibliographically approved

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