Continuous Mode Interpolation for Control-Oriented Models of Fluid Flow

Morzyński, Marek; Stankiewicz, Witold; Noack, Bernd R.; King, Rudibert; Thiele, Frank; Tadmor, Gilead

doi:10.1007/978-3-540-71439-2_16

Cited by 23 publications

(26 citation statements)

References 33 publications

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“…Remedies include: (i) augmented mode sets derived from transients, multiple datasets (see figure 2), Navier-Stokes residuals and sensitivity analysis [26][27][28], (ii) online adaptation [29,30], and (iii) pre-computed interpolated bases, which is the topic of this section [31,32].…”

Section: Galerkin Models With Deformable Modes (A) Evolving Coherent mentioning

confidence: 99%

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Reduced-order models for closed-loop wake control

Tadmor

Lehmann

Noack

et al. 2011

Phil. Trans. R. Soc. A.

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We review a strategy for low-and least-order Galerkin models suitable for the design of closed-loop stabilization of wakes. These low-order models are based on a fixed set of dominant coherent structures and tend to be incurably fragile owing to two challenges. Firstly, they miss the important stabilizing effects of interactions with the base flow and stochastic fluctuations. Secondly, their range of validity is restricted by ignoring mode deformations during natural and actuated transients. We address the first challenge by including shift mode(s) and nonlinear turbulence models. The resulting robust least-order model lives on an inertial manifold, which links slow variations in the base flow and coherent and stochastic fluctuation amplitudes. The second challenge, the deformation of coherent structures, is addressed by parameter-dependent modes, allowing smooth transitions between operating conditions. Now, the Galerkin model lives on a refined manifold incorporating mode deformations. Control design is a simple corollary of the distilled model structure. We illustrate the modelling path for actuated wake flows.

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Section: Galerkin Models With Deformable Modes (A) Evolving Coherent mentioning

confidence: 99%

“…Linear (including geodesic) interpolation of POD modes [31,32] is a natural option. An effective variant for harmonically dominated flows is to compute equation (4.1a) as an a-dependent harmonic expansion (allowing incommensurate frequencies!…”

Section: (C) Parametrization and Harmonic Modesmentioning

confidence: 99%

Reduced-order models for closed-loop wake control

Tadmor

Lehmann

Noack

et al. 2011

Phil. Trans. R. Soc. A.

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“…On least-order flow representations for aerodynamics and aeroacoustics 369 (Morzyński et al 2007) and double POD (Siegel et al 2008), or the consideration of incomplete data sets (see e.g. Willcox 2006).…”

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confidence: 99%

On least-order flow representations for aerodynamics and aeroacoustics

et al. 2012

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We propose a generalization of proper orthogonal decomposition (POD) for optimal flow resolution of linearly related observables. This Galerkin expansion, termed 'observable inferred decomposition' (OID), addresses a need in aerodynamic and aeroacoustic applications by identifying the modes contributing most to these observables. Thus, OID constitutes a building block for physical understanding, leastbiased conditional sampling, state estimation and control design. From a continuum of OID versions, two variants are tailored for purposes of observer and control design, respectively. Firstly, the most probable flow state consistent with the observable is constructed by a 'least-residual' variant. This version constitutes a simple, easily generalizable reconstruction of the most probable hydrodynamic state to preprocess efficient observer design. Secondly, the 'least-energetic' variant identifies modes with the largest gain for the observable. This version is a building block for Lyapunov control design. The efficient dimension reduction of OID as compared to POD is demonstrated for several shear flows. In particular, three aerodynamic and aeroacoustic goal functionals are studied: (i) lift and drag fluctuation of a two-dimensional cylinder wake flow; (ii) aeroacoustic density fluctuations measured by a sensor array and emitted from a two-dimensional compressible mixing layer; † Email address for correspondence: michael.schlegel@tu-berlin.de

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“…Further investigations include the extension of the range of applicability of the model by parametrization of mode bases using Continuous Mode Interpolation [30]. Such approach will allow modeling of the §ow under varying operating conditions, like di¨erent Mach numbers and §ight altitudes.…”

Section: Discussionmentioning

confidence: 99%

“…The changing element shapes might be taken into account using continuous mode interpolation [29,30].…”

Section: Projection Of Convective Term In Arbitrary Lagrangian Eulerimentioning

confidence: 99%

Arbitrary Lagrangian-Eulerian approach in reduced order modeling of a flow with a moving boundary

Stankiewicz

Roszak

Morzyński

2013

Progress in Flight Physics

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Flow-induced de §ections of aircraft structures result in oscillations that might turn into such a dangerous phenomena like §utter or bu¨eting. In this paper the design of an aeroelastic system consisting of Reduced Order Model (ROM) of the §ow with a moving boundary is presented. The model is based on Galerkin projection of governing equation onto space spanned by modes obtained from high-¦delity computations. The motion of the boundary and mesh is de¦ned in Arbitrary Lagrangian Eulerian (ALE) approach and results in additional convective term in Galerkin system. The developed system is demonstrated on the example of a §ow around an oscillating wing.

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Continuous Mode Interpolation for Control-Oriented Models of Fluid Flow

Cited by 23 publications

References 33 publications

Reduced-order models for closed-loop wake control

Reduced-order models for closed-loop wake control

On least-order flow representations for aerodynamics and aeroacoustics

Arbitrary Lagrangian-Eulerian approach in reduced order modeling of a flow with a moving boundary

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