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Adaptive and model-based control in laminar boundary-layer flows
KTH, School of Engineering Sciences (SCI), Mechanics.ORCID iD: 0000-0003-0010-489X
2014 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

In boundary-layer flows it is possible to reduce the friction drag by breaking the path from laminar to turbulent state. In low turbulence environments, the laminar-to-turbulent transition is dominated by local flow instabilities – Tollmien-Schlichting (TS) waves – that exponentially grows while being con- vected by the flow and, eventually, lead to transition. Hence, by attenuating these disturbances via localised forcing in the flow it is possible to delay farther downstream the onset of turbulence and reduce the friction drag.

Reactive control techniques are widely investigated to this end. The aim of this work is to compare model-based and adaptive control techniques and show how the adaptivity is crucial to control TS-waves in real applications. The control design consists in (i) choosing sensors and actuators and (ii) designing the system responsible to process on-line the measurement signals in order to compute an appropriate forcing by the actuators. This system, called compen- sator, can be static or adaptive, depending on the possibility of self-adjusting its response to unmodelled flow dynamics. A Linear Quadratic Gaussian (LQG) regulator is chosen as representative of static controllers. Direct numerical simulations of the flow are performed to provide a model for the compensator design and test its performance. An adaptive Filtered-X Least-Mean-Squares (FXLMS) compensator is also designed for the same flow case and its per- formance is compared to the model-based compensator via simulations and experiments. Although the LQG regulator behaves better at design conditions, it lacks robustness to small flow variations. On the other hand, the FXLMS compensator proved to be able to adapt its response to overcome the varied conditions and perform an adequate control action.

It is thus found that an adaptive control technique is more suitable to delay the laminar-to-turbulent transition in situations where an accurate model of the flow is not available. 

Abstract [sv]

I det tunna gränsskikt som uppstår en yta, kan friktionen minskas genom att förhindra omslag från ett laminärt till ett turbulent flöde. När turbulensnivån är låg  i omgivningen, domineras till en början omslaget av lokala instabiliteter (Tollmien-Schlichting (TS) v ågor) som växer i en exponentiell takt samtidigt som de propagerar nedströms. Därför, kan man förskjuta omslaget genom att dämpa TS vågors tillväxt i ett gränsskikt och därmed minska friktionen.Med detta mål i sikte, tillämpas och jämförs två reglertekniska metoder, nämligen en adaptiv signalbaserad metod och en statiskt modellbaserad metod. Vi visar att adaptivitet är av avgörande betydelse för att kunna dämpa TS vågor i en verklig miljö. Den reglertekniska konstruktionen består av val av givare och aktuatorer samt att bestämma det system som behandlar mätsignaler (on- line) för beräkning av en lämplig signal till aktuatorer. Detta system, som kallas för en kompensator, kan vara antingen statisk eller adaptiv, beroende på om det har möjlighet till att anpassa sig till omgivningen. En så kallad linjär regulator (LQG), som representerar den statiska kompensator, har tagits fram med hjälp av numeriska simuleringar of strömningsfältet. Denna kompensator jämförs med en adaptiv regulator som kallas för Filtered-X Least-Mean-Squares (FXLMS) både experimentellt och numeriskt. Det visar sig att LQG regulatorn har en bättre prestanda än FXLMS för de parametrar som den var framtagen för, men brister i robusthet. FXLMS å andra sidan, anpassar sig till icke- modellerade störningar och variationer, och kan därmed hålla en god och jämn prestanda.Man kan därmed dra slutsaten att adaptiva regulatorer är mer lämpliga för att förhala omslaget fr ån laminär till turbulent strömning i situationer då en exakt modell av fysiken saknas.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2014. , viii, 25 p.
Series
TRITA-MEK, ISSN 0348-467X ; 24:21
Keyword [en]
Flow control, Control theory, Optimal control, Adaptive control, Boundary-layer flow, Fluid dynamics, Plasma actuator, Surface hot-wire, Transition delay
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-154052ISBN: 978-91-7595-288-8 (print)OAI: oai:DiVA.org:kth-154052DiVA: diva2:754903
Presentation
2014-10-27, D3, Lindstedtsvägen 5, KTH, Stockholm, 10:30 (English)
Opponent
Supervisors
Funder
Swedish Research Council, VR2012-4246
Note

QC 20141020

Available from: 2014-10-20 Created: 2014-10-13 Last updated: 2015-10-29Bibliographically approved
List of papers
1. Adaptive and model-based control theory applied to convectively unstable flows
Open this publication in new window or tab >>Adaptive and model-based control theory applied to convectively unstable flows
2014 (English)In: Applied Mechanics Review, ISSN 0003-6900, E-ISSN 1088-8535, Vol. 66, no 6, 060801- p.Article, review/survey (Refereed) Published
Abstract [en]

Research on active control for the delay of laminar-turbulent transition in boundary layers has made a significant progress in the last two decades, but the employed strategies have been many and dispersed. Using one framework, we review model-based techniques, such as linear-quadratic regulators, and model-free adaptive methods, such as least-mean square filters. The former are supported by a elegant and powerful theoretical basis, whereas the latter may provide a more practical approach in the presence of complex disturbance envi- ronments, that are difficult to model. We compare the methods with a particu- lar focus on efficiency, practicability and robustness to uncertainties. Each step is exemplified on the one-dimensional linearized Kuramoto-Sivashinsky equa- tion, that shows many similarities with the initial linear stages of the transition process of the flow over a flat plate. Also, the source code for the examples are provided. 

Keyword
Flow control, Control theory, Optimal control, Adaptive control, Boundary-layer flow, Fluid dynamics
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-154050 (URN)10.1115/1.4027483 (DOI)000346238700001 ()2-s2.0-84902832513 (Scopus ID)
Funder
Swedish Research Council, 2012- 4246
Note

QC 20141015

MATLAB scrips available at www.mech.kth.se/~nicolo/ks

Available from: 2014-10-13 Created: 2014-10-13 Last updated: 2017-12-05Bibliographically approved
2. On the role of adaptivity for robust laminar flow control
Open this publication in new window or tab >>On the role of adaptivity for robust laminar flow control
Show others...
2015 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 767, R1-R12 p.Article in journal (Refereed) Published
Abstract [en]

In boundary layer flows, one may reduce skin friction drag by delaying the onset of laminar-to-turbulent transition via the attenuation of small-amplitude Tollmien Schlichting (TS) waves In this work, we use numerical simulations and experiments to compare the robustness of adaptive and model-based techniques for reducing the growth of two-dimensional TS disturbances. In numerical simulations, the optimal linear quadratic Gaussian (LQG) regulator shows the best performance under the conditions it was designed for However, it is found that the performance deteriorates linearly with the drift of the Reynolds number from its nominal value. As a result, an order-of-magnitude loss of performance is observed when applying the computation-based I.QG controller in wind-tunnel experiments In contrast, it is shown that the adaptive filtered-X least-mean-squares (FXLMS) algorithm is able to maintain an essentially constant performance for significant deviations of the nominal values of the disturbance amplitude and Reynolds number.

Keyword
boundary layer control, flow control, instability control
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-154351 (URN)10.1017/jfm.2015.45 (DOI)000349688900001 ()2-s2.0-84949117226 (Scopus ID)
Funder
Swedish Research Council Formas, VR-2012-4246, VR-2010-3910
Note

Updated from Manuscript to Article. QC 20150488

Available from: 2014-10-20 Created: 2014-10-20 Last updated: 2017-12-05Bibliographically approved
3. Centralised Versus Decentralised Active Control of Boundary Layer Instabilities
Open this publication in new window or tab >>Centralised Versus Decentralised Active Control of Boundary Layer Instabilities
2014 (English)In: Flow Turbulence and Combustion, ISSN 1386-6184, E-ISSN 1573-1987, Vol. 93, no 4, 537-553 p.Article in journal (Refereed) Published
Abstract [en]

We use linear control theory to construct an output feedback controller for the attenuation of small-amplitude three-dimensional Tollmien-Schlichting (TS) wavepackets in a flat-plate boundary layer. A three-dimensional viscous, incompressible flow developing on a zero-pressure gradient boundary layer in a low Reynolds number environment is analyzed using direct numerical simulations. In this configuration, we distribute evenly in the spanwise direction up to 72 localised objects near the wall (18 disturbances sources, 18 actuators, 18 estimation sensors and 18 objective sensors). In a fully three-dimensional configuration, the interconnection between inputs and outputs becomes quickly unfeasible when the number of actuators and sensors increases in the spanwise direction. The objective of this work is to understand how an efficient controller may be designed by connecting only a subset of the actuators to sensors, thereby reducing the complexity of the controller, without comprising the efficiency. If n and m are the number of sensor-actuator pairs for the whole system and for a single control unit, respectively, then in a decentralised strategy, the number of interconnections deceases mn compared to a centralized strategy, which has n (2) interconnections. We find that using a semi-decentralized approach - where small control units consisting of 3 estimation sensors connected to 3 actuators are replicated 6 times along the spanwise direction - results only in a 11 % reduction of control performance. We explain how "wide" in the spanwise direction a control unit should be for a satisfactory control performance. Moreover, the control unit should be designed to account for the perturbations that are coming from the lateral sides (crosstalk) of the estimation sensors. We have also found that the influence of crosstalk is not as essential as the spreading effect.

Keyword
Flow control, Boundary layer flows, Hydrodynamic stability, Control theory, Model reduction
National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-145661 (URN)10.1007/s10494-014-9552-6 (DOI)000345076500001 ()2-s2.0-84920259408 (Scopus ID)
Note

QC 20141215 Updated from manuscript to article in journal.

Available from: 2014-05-26 Created: 2014-05-26 Last updated: 2017-12-05Bibliographically approved

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