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Modelling and control of turbulent and transitional flows
KTH, School of Engineering Sciences (SCI), Engineering Mechanics.ORCID iD: 0000-0001-6343-7507
2020 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The dynamics of fluid motion can accurately be described by the Navier– Stokes equations. Manipulating these equations to reduce their complexity but preserving their main characteristics has always been a key research activity in the field of fluid mechanics. Effort has been made to provide high-fidelity models for wall-bounded turbulent flows or reduced-order models for applications such as drag reduction, lift enhancement, or noise suppression. Model order reduction has also been employed for studying the dynamics of the Navier-Stokes equations. In this PhD thesis, the emphasis is on providing computationally inexpensive methods for industrial applications.

Numerical simulations are performed to tackle model order reduction for flow control of transitional boundary-layer flows for drag reduction. It is assumed that localized wall sensors and actuators are available, and that only the time signals accessible in experiments are provided. Thus, a method to include unknown high-dimensional input disturbances in a reduced-order model of a transitional boundary-layer flow is presented. The method is applied for the design of an optimal controller for drag reduction through delay of transition. Moreover, the role of the actuator is discussed and a comparison between realistic actuators and actuators computed using optimization methods is presented. Here, the emphasis is on the effectiveness of the actuators for the studied flow control cases.

Numerical simulations are also performed to tackle high-fidelity modeling in wall-bounded turbulent flows. The accuracy of the resolvent analysis in predicting the most energetic flow structures in a wall-bounded turbulent flow is quantified for different temporal frequencies. A direct comparison between the predictions from the resolvent analysis and the flow structures identified in DNS data is presented. Moreover, the beneficial effects attained with the inclusion of the Reynolds-stresses via an eddy-viscosity model are clarified for flows with friction Reynolds number up to 1007.

Abstract [sv]

Dynamiken av fluiders rörelse kan väl beskrivas med hjälp av Navier-Stokes ekva- tioner. Att manipulera dessa ekvationer för att minska deras komplexitet utan att förlora väsentliga egenskaper har alltid varit ett viktigt forskningsomr ̊ade inom strömningsmekanik. Mycket forskning har utförts för att utveckla högkvalitativa modeller t.ex. för beskrivning av väggbundna turbulenta flöden samt styrlagar baserad på lågordnings modeller för applikationer som motståndsminskning, förhöjning av lyftkraft eller bullerreducering. Modellreduktion har också använts för att studera strömningsdynamiken som beskrivs av Navier-Stokes ekvationer.

Tonvikten av arbetet presenterat i denna doktorsavhandling ligger på utveckling av beräkningsmässigt snabba och effektiva metoder för industriella tillämpningar. Vi har utfört numeriska simuleringar för att framta reducerade modeller för strömningsstyrning i syfte att minska motst ̊andet i gränsskiktsflöde genom att fördröja laminär-turbulent omslag. I dessa beräkningar har vi antagit att lokaliserad väggmätning och styrning är möjlig och att endast inputdata i form av tidssignaler fr ̊an dessa mättningar är tillgängliga. Vi har tagit fram en metod för att ta hänsyn till det högdimensionella bruset i mätdata i utvecklingen av lågordnings modeller för gränsskiktsflöden under inverkan av hög friströmsturbulens. Metoden har använts för att utforma en optimal styrlag för motst ̊andsminskning i gränsskiktsflöden. Dessutom har vi undersökt aktuatorns roll och jämfört realistiska aktuatorer med de beräknade med hjälp av optimeringsmetoder. Jämförelsen har gjorts med betoning på aktuators effektivitet i de studerade fallen.

Vi har också utfört numeriska simuleringar av väggbundna turbulenta flöden för att utveckla modeller med hög fidelitet av dessa flöden. Genom resultaten av dessa simuleringar har vi undersökt noggrannheten av den så kallade “resolvent” analysen för prediktering av de mest energiska strukturerna i väggbundna turbulenta flöden. En direkt jämförelse mellan strukturer identifierade i simuleringsdata och de predikterade genom resolvent analysen har presenterats. Dessutom har vi visat fördelarna med användning av en “eddy-viscosity” modell för Reynolds-spänningar i resolvent analysen för strömningsfall med friktion Reynoldstal upp till 1007.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2020. , p. 56
Series
TRITA-SCI-FOU ; 2020:08
Keywords [en]
reduced order modeling, flow control, resolvent analysis, transi- tional boundary layer, turbulent boundary layer, drag reduction, high-fidelity wall-turbulence modelling
Keywords [sv]
modellreduktion, strömningskontroll, resolvent analys, laminär- turbulent omslag, turbulent gränsskikt, motståndsminskning, väggturbulens modellering
National Category
Fluid Mechanics and Acoustics
Research subject
Engineering Mechanics
Identifiers
URN: urn:nbn:se:kth:diva-273165ISBN: 978-91-7873-489-4 (print)OAI: oai:DiVA.org:kth-273165DiVA, id: diva2:1429228
Public defence
2020-06-04, Live-streaming: https://kth-se.zoom.us/j/62627066334 If you lack computer or computer skills, contact Luca Brandt, brandtl@kth.se, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

QC 20200512

Available from: 2020-05-12 Created: 2020-05-08 Last updated: 2020-05-26Bibliographically approved
List of papers
1. On the wave-cancelling nature of boundary layer flow control
Open this publication in new window or tab >>On the wave-cancelling nature of boundary layer flow control
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2018 (English)In: Theoretical and Computational Fluid Dynamics, ISSN 0935-4964, E-ISSN 1432-2250, Vol. 32, no 5, p. 593-616Article in journal (Refereed) Published
Abstract [en]

This work deals with the feedforward active control of Tollmien-Schlichting instability waves over incompressible 2D and 3D boundary layers. Through an extensive numerical study, two strategies are evaluated; the optimal linear-quadratic-Gaussian (LQG) controller, designed using the Eigensystem realization algorithm, is compared to a wave-cancellation scheme, which is obtained using the direct inversion of frequency-domain transfer functions of the system. For the evaluated cases, it is shown that LQG leads to a similar control law and presents a comparable performance to the simpler, wave-cancellation scheme, indicating that the former acts via a destructive interference of the incoming wavepacket downstream of actuation. The results allow further insight into the physics behind flow control of convectively unstable flows permitting, for instance, the optimization of the transverse position for actuation. Using concepts of linear stability theory and the derived transfer function, a more efficient actuation for flow control is chosen, leading to similar attenuation of Tollmien-Schlichting waves with only about 10% of the actuation power in the baseline case.

Place, publisher, year, edition, pages
Springer, 2018
Keywords
Boundary layer control, Flow control, Instability control, LQG controllers, Inversion controllers
National Category
Other Engineering and Technologies
Identifiers
urn:nbn:se:kth:diva-235102 (URN)10.1007/s00162-018-0469-x (DOI)000443412500003 ()2-s2.0-85049125322 (Scopus ID)
Note

QC 20180917

Available from: 2018-09-17 Created: 2018-09-17 Last updated: 2020-05-08Bibliographically approved
2. A realizable data-driven approach to delay bypass transition with control theory
Open this publication in new window or tab >>A realizable data-driven approach to delay bypass transition with control theory
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2020 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 883, article id A33Article in journal (Refereed) Published
Abstract [en]

The current work presents a realizable method to control streaky disturbances in boundary layer flows and delay transition to turbulence by means of active flow control. Numerical simulations of the nonlinear transitional regime in a Blasius boundary layer are performed where streaks are excited in the boundary layer by means of a high level of free-stream turbulence. The occurring disturbances are measured by means of localized wall-shear-stress sensors and damped out using near-wall actuators, which resemble ring plasma actuators. Each actuator is powered by a time-varying signal whose amplitude is computed by processing signals from the sensors. The processed signal is the result of two control laws: the linear quadratic Gaussian regulator (LQG) and the inverse feed-forward control technique (IFFC). The use of the first control method, LQG, requires a state-space representation of the system dynamics, so the flow is described by means of a linear time-invariant operator that captures only the most relevant information of the dynamics and results in a reduced-order model (ROM). The ROM is computed by means of the eigensystem realization algorithm (ERA), which is based on the impulse responses of the real system. Collecting such impulse responses may be unfeasible when considering free-stream turbulence because of the high dimensionality of the input forcing needed for a precise description of such a phenomenon. Here, a new method to identify the relevant system dynamics and generate the needed impulse responses is proposed, based on additional shear-stress measurements in an upstream location. Transfer functions between such measurements and other downstream sensors are obtained and allow the derivation of the ERA system, in a data-driven approach that would be realizable in experiments. Finally, in order to discuss the advantages of the LQG based on the ROM and analyse its performance, the implemented LQG is compared to the IFFC, which consists of wave cancellation. The work (i) presents a systematic and straightforward way to deal with high-dimensional disturbances in order to build ROMs for a feasible control technique, and (ii) shows that even when considering practical constraints, such as the type and size of actuators and sensors, it is possible to achieve at least as large delay of bypass transition as that obtained in more idealized cases found in the literature.

Place, publisher, year, edition, pages
CAMBRIDGE UNIV PRESS, 2020
Keywords
boundary layer control, drag reduction, transition to turbulence
National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-267149 (URN)10.1017/jfm.2019.793 (DOI)000508121500033 ()
Note

QC 20200217

Available from: 2020-02-17 Created: 2020-02-17 Last updated: 2020-05-08Bibliographically approved
3. On the role of actuation for the control of streaky structures in boundary layers
Open this publication in new window or tab >>On the role of actuation for the control of streaky structures in boundary layers
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2020 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 883, article id A34Article in journal (Refereed) Published
Abstract [en]

This work deals with the closed-loop control of streaky structures induced by free-stream turbulence (FST), at the levels of 3.0% and 3.5 %, in a zero-pressure-gradient transitional boundary layer, by means of localized sensors and actuators. A linear quadratic Gaussian regulator is considered along with a system identification technique to build reduced-order models for control. Three actuators are developed with different spatial supports, corresponding to a baseline shape with only vertical forcing, and to two other shapes obtained by different optimization procedures. A computationally efficient method is derived to obtain an actuator that aims to induce the exact structures that are inside the boundary layer, given in terms of their first spectral proper orthogonal decomposition (SPOD) mode, and an actuator that maximizes the energy of induced downstream structures. All three actuators lead to significant delays in the transition to turbulence and were shown to be robust to mild variations in the FST levels. Integrated total drag reductions observed were up to 21% and 19% for turbulence intensity levels of 3.0% and 3.5 %, respectively, depending on the considered actuator. Differences are understood in terms of the SPOD of actuation and FST-induced fields along with the causality of the control scheme when a cancellation of disturbances is considered along the wall-normal direction. The actuator optimized to generate the leading downstream SPOD mode, representing the streaks in the open-loop flow, leads to the highest transition delay, which can be understood due to its capability of closely cancelling structures in the boundary layer.

Place, publisher, year, edition, pages
CAMBRIDGE UNIV PRESS, 2020
Keywords
boundary layer control, drag reduction, transition to turbulence
National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-267150 (URN)10.1017/jfm.2019.893 (DOI)000508121500034 ()
Note

QC 20200217

Available from: 2020-02-17 Created: 2020-02-17 Last updated: 2020-05-08Bibliographically approved
4. Experimental control of Tollmien-Schlichting waves using pressure sensors and plasma actuators
Open this publication in new window or tab >>Experimental control of Tollmien-Schlichting waves using pressure sensors and plasma actuators
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2020 (English)Report (Other academic)
Abstract [en]

This manuscript shows the successful application of the inverse feed-forwardcontrol (IFFC) technique for the cancellation of Tollmien–Schlichting (TS)waves. Active wave cancellation of two-dimensional broadband TS disturbancesis performed with a single dielectric barrier discharge (DBD) plasma actuator.The measurements required for the IFFC are performed with microphones,instead of hot wires most used for this task, in order to reduce the spaceoccupied by the sensors and assess the suitability of simpler and cheaperdevices. The experiments are conducted in an open-circuit wind-tunnel witha NACA0008 wing profile. An attenuation of the TS-wave amplitude of oneorder of magnitude is achieved. Direct numerical simulations (DNS) are alsoperformed, and compared to the outcome of the experiments. The modeling ofboth actuator and sensors in the DNS is not based on data from the presentexperiments. The plasma actuator used is a mapping of the force field inFabbiane et al., J. Fluid Mech. 2015, to the NACA0008 wing profile, whereasthe microphones are modeled as pressure probes. Despite these modellingchoices, a remarkable level of agreement between the DNS and the experimentsis achieved. However, the control performance is better in the DNS, withattenuations of three orders of magnitude of TS-wave amplitude. Furtheranalysis of experiments and simulations shows that the limiting factor in theexperiments is the ambient low-frequency acoustic waves in the wind tunnel,which are sensed by the microphones, acting as noise in the analysis of TS-waveevolution and thus leading to lower coherences between sensors and actuators.This in turn leads to a suboptimal control kernel in the experiment.179

National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-273161 (URN)
Note

QC 20200511

Available from: 2020-05-08 Created: 2020-05-08 Last updated: 2020-05-11Bibliographically approved
5. On the relevance of Reynolds stresses in resolvent analyses of turbulent wall-bounded flows
Open this publication in new window or tab >>On the relevance of Reynolds stresses in resolvent analyses of turbulent wall-bounded flows
2019 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 867, p. 969-984, article id PII S0022112019001964Article in journal (Refereed) Published
Abstract [en]

The ability of linear stochastic response analysis to estimate coherent motions is investigated in turbulent channel flow at the friction Reynolds number Re-r = 1007. The analysis is performed for spatial scales characteristic of buffer-layer and large-scale motions by separating the contributions of different temporal frequencies. Good agreement between the measured spatio-temporal power spectral densities and those estimated by means of the resolvent is found when the effect of turbulent Reynolds stresses, modelled with an eddy-viscosity associate with the turbulent mean flow, is included in the resolvent operator. The agreement is further improved when the flat forcing power spectrum (white noise) is replaced with a power spectrum matching the measures. Such a good agreement is not observed when the eddy-viscosity terms are not included in the resolvent operator. In this case, the estimation based on the resolvent is unable to select the right peak frequency and wall-normal location of buffer-layer motions. Similar results are found when comparing truncated expansions of measured streamwise velocity power spectral densities based on a spectral proper orthogonal decomposition to those obtained with optimal resolvent modes.

Place, publisher, year, edition, pages
CAMBRIDGE UNIV PRESS, 2019
Keywords
turbulent boundary layers
National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-249766 (URN)10.1017/jfm.2019.196 (DOI)000463073000001 ()2-s2.0-85063881975 (Scopus ID)
Note

QC 20190429

Available from: 2019-04-29 Created: 2019-04-29 Last updated: 2020-05-08Bibliographically approved
6. Forcing statistics in resolvent analysis: application in minimal turbulent Couette flow
Open this publication in new window or tab >>Forcing statistics in resolvent analysis: application in minimal turbulent Couette flow
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(English)Manuscript (preprint) (Other academic)
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-273163 (URN)
Available from: 2020-05-08 Created: 2020-05-08 Last updated: 2020-05-11Bibliographically approved
7. The colour of forcing statistics in resolvent analyses of turbulent channel flows
Open this publication in new window or tab >>The colour of forcing statistics in resolvent analyses of turbulent channel flows
(English)Manuscript (preprint) (Other academic)
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-273164 (URN)
Note

QC 20200511

Available from: 2020-05-08 Created: 2020-05-08 Last updated: 2020-05-11Bibliographically approved

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