Low-Dimensional Models for Feedback Flow Control. Part I: Empirical Galerkin Models

Noack, Bernd R.; Tadmor, Gilead; Morzyński, Marek

doi:10.2514/6.2004-2408

Cited by 61 publications

(44 citation statements)

References 18 publications

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“…However, although the range of the POD ROM cannot be evaluated precisely, it is well-known that the performances of the model tend to deteriorate quickly with the change of the control parameters [66,13]. Recently, Noack et al [14] reviewed the key enablers to the use of empirical Galerkin models for feedback flow control and suggested the introduction of non-equilibrium modes in the POD expansion as a way to enhance the range of validity of the controlled POD ROM.…”

Section: Accuracy Of the Calibrated Pod Modelmentioning

confidence: 99%

“…Thus, a POD basis cannot contain more information than that contained in the snapshot set. The generation of "good" snapshot set is then crucial to the success of use of POD ROM approach in a bifurcation analysis [12][13][14] or more generally in an optimization setting. Since the POD basis is intrinsic to a particular flow, we need to give special attention to adapt the POD ROM (and the POD basis naturally) to changes in physics when the flow is altered by control.…”

Section: Reduced-order Models In Optimizationmentioning

confidence: 99%

“…To describe two or more operating conditions in a single POD expansion, Noack et al [13,14] proposed to add special modes, called non-equilibrium modes, to the original POD basis functions. Essentially, these non-equilibrium modes will be, either particular modes not taken into account in the original model but known to play a major role in the description of the flow dynamics (stability eigenmodes for example), or translation modes (also called shift modes) that allow the description of the transition (natural or forced) from the uncontrolled configuration to the optimal controlled flow.…”

Section: Pod Basis Functions With Non-equilibrium Modesmentioning

confidence: 99%

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Optimal control of the cylinder wake in the laminar regime by trust-region methods and POD reduced-order models

Bergmann

Cordier

2008

Journal of Computational Physics

174

152

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In this paper, optimal control theory is used to minimize the total mean drag for a circular cylinder wake flow in the laminar regime (Re = 200). The control parameters are the amplitude and the frequency of the time-harmonic cylinder rotation. In order to reduce the size of the discretized optimality system, a Proper Orthogonal Decomposition (POD) Reduced-Order Model (ROM) is derived to be used as state equation. We then propose to employ the Trust-Region Proper Orthogonal Decomposition (TRPOD) approach, originally introduced by Fahl (2000), to update the reduced-order models during the optimization process. A lot of computational work is saved because the optimization process is now based only on low-fidelity models. A particular care was taken to derive a POD ROM for the pressure and velocity fields with an appropriate balance between model accuracy and robustness. The key enablers are the extension of the POD basis functions to the pressure data, the use of calibration methods for the POD ROM and the addition in the POD expansion of several non-equilibrium modes to describe various operating conditions. When the TRPOD algorithm is applied to the wake flow configuration, this approach converges to the minimum predicted by an open-loop control approach and leads to a relative mean drag reduction of 30% at reduced cost.

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Section: Accuracy Of the Calibrated Pod Modelmentioning

confidence: 99%

Section: Reduced-order Models In Optimizationmentioning

confidence: 99%

Section: Pod Basis Functions With Non-equilibrium Modesmentioning

confidence: 99%

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Optimal control of the cylinder wake in the laminar regime by trust-region methods and POD reduced-order models

Bergmann

Cordier

2008

Journal of Computational Physics

174

152

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“…In addition, BiGlobal analysis has been demonstrated to be relevant to bluff body instabilities (Barkley and Henderson 1996;Theofilis, Barkley and Sherwin 2002), as well as to partial features of the flowfield at hand, such as the trailing-edge separation and its potential global instability (Theofilis 1999;Theofilis, Hein and Dallmann 2000). Finally, the significance of BiGlobal instability analysis to reduced-order modeling and flow control has been discussed extensively by and further quantified recently by Noack, Tadmor, and Morzynski (2004).…”

Section: Introductionmentioning

confidence: 99%

Global Instability and Control of Low-Pressure Turbine Flows

Theofilis¹,

Abdessemed²,

Sherwin³

2006

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Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing this collection of information. Send cornments regarding this burden estimate or any other aspect of this collection of information, including suggestions for redudng this burden to Department of Defense, Washington Headquarters Services, Directorate for Information SUPPLEMENTARY NOTES ABSTRACTThis final report covers the 35-month period from Ferbuary 1, 2003, the inception of the grant, to its end on December 31, 2005. Within the present effort BiGlobal primary and secondary (Floquet) instability analyses of Low Pressure Turbine (LPT) flows were performed for the first time. The T-106/300 LPT blade was selected and used for the analyses reported herein. In addition, two-and three-dimensional direct numerical simulations (DNS) were employed respectively in order to provide the nonparallel steady and unsteady two-dimensional basic flows to be analyzed and in order to cross-validate primary and secondary BiGlobal instability analysis results. Calculations were performed at chord Reynolds numbers of 900 and 5000 using both structured and unstructured grids. Finally, the first-ever transientgrowth analysis of a nonparallel flow field was performed in the context of the LPT flow investigated herein. In the entire range investigated, unstable three-dimensional modes were discovered; as the three-dimensional flow approaches the two-dimensional limit, the time-periodic basic state is recovered. FINAL REPORT Grant F49620-03-1-0295 (Theofilis) -"Global instability and control of low-pressure turbine flows"

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“…A common approach referred to as the method of "snapshots" introduced by Sirovich (1987) is employed to generate the basis functions of the POD spatial modes from flow-field information obtained using either experiments or numerical simulations. This approach to controlling the global wake behavior behind a circular cylinder was effectively employed by Gillies (1998) and Noack et al (2004) and is also the approach followed in the current research effort.…”

Section: Introductionmentioning

confidence: 99%

A Methodology Based on Experimental Investigation of a DBD-Plasma Actuated Cylinder Wake for Flow Control

Cohen¹,

Aradağ²,

Siegel³

et al. 2012

Low Reynolds Number Aerodynamics and Transition

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Low-Dimensional Models for Feedback Flow Control. Part I: Empirical Galerkin Models

Cited by 61 publications

References 18 publications

Optimal control of the cylinder wake in the laminar regime by trust-region methods and POD reduced-order models

Optimal control of the cylinder wake in the laminar regime by trust-region methods and POD reduced-order models

Global Instability and Control of Low-Pressure Turbine Flows

A Methodology Based on Experimental Investigation of a DBD-Plasma Actuated Cylinder Wake for Flow Control

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