A hierarchy of low-dimensional models for the transient and post-transient cylinder wake

Noack, Bernd R.; Afanasiev, Konstantin; Morzyński, Marek; Tadmor, Gilead; Thiele, Frank

doi:10.1017/s0022112003006694

Cited by 875 publications

(789 citation statements)

References 30 publications

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“…The obtained OID modes represent mainly the first and the second flow harmonics (see Noack et al 2003). This is shown in figure 3, where the axis of the streamwise direction is denoted by x and the axis of the transverse direction by y.…”

Section: Lift and Drag Optimized Oids Of Cylinder Wake Flowmentioning

confidence: 96%

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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Section: Lift and Drag Optimized Oids Of Cylinder Wake Flowmentioning

confidence: 96%

On least-order flow representations for aerodynamics and aeroacoustics

et al. 2012

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“…POD is often employed to capture the dominant features of the flow by a low number of basis functions or modes, which can be used to elaborate reduced order models (Berkooz et al 1993;Ma & Karniadakis 2002;Noack et al 2003). It may be an efficient tool to identify the main elements of wake unsteadiness and connect them to spatial patterns of the flow (e.g.…”

Section: Flow Patternsmentioning

confidence: 99%

The onset of vortex-induced vibrations of a flexible cylinder at large inclination angle

Bourguet

Triantafyllou

2016

J. Fluid Mech.

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The onset of the vortex-induced vibration (VIV) regime of a flexible cylinder inclined at 80 • within a uniform current is studied by means of direct numerical simulations, at Reynolds number 500, based on the body diameter and inflow velocity magnitude. A range of values of the reduced velocity, defined as the inverse of the fundamental natural frequency, is examined in order to capture the emergence of the body responses and explore the concomitant reorganization of the flow and fluid forcing. Additional simulations at normal incidence confirm that the independence principle, which states that the system behavior is determined by the normal inflow component, does not apply at such large inclination angle. Contrary to the normal incidence case, the free vibrations of the inclined cylinder arise far from the Strouhal frequency, i.e. the vortex shedding frequency downstream of a fixed rigid cylinder. The trace of the stationary body wake is found to persist beyond the vibration onset: the flow may still exhibit an oblique component that relates to the slanted vortex shedding pattern observed in the absence of vibration. This flow component which occurs close to the Strouhal frequency, at a high and incommensurable frequency compared to the vibration frequency, is referred to as Strouhal component; it induces a high-frequency component in fluid forcing. The vibration onset is accompanied by the appearance of novel, low-frequency components of the flow and fluid forcing, which are synchronized with body motion. This second dominant flow component, referred to as lock-in component, is characterized by a parallel spatial pattern. The Strouhal and lock-in components of the flow coexist over a range of reduced velocities, with variable contributions, which results in a variety of mixed wake patterns. The transition from oblique to parallel vortex shedding, that occurs during the amplification of the structural responses, is driven by the opposite trends of these two component contributions: the decrease of the Strouhal component magnitude, associated with the progressive disappearance of the high-frequency force component, and simultaneously, the increase of the lock-in component magnitude, which dominates once the fully-developed VIV regime is reached and the flow dynamics is entirely governed by wake-body synchronization.

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“…an extension of POD to data compression of multiple operation points, see [17] for sequential POD or [30] for DPOD. We follow an alternative approach suggested in [20,22] of a canonical reduction with parameter identification. Here, a very small system of nonlinear ODEs is adapted to the computed flows in the actuated and non-actuated case.…”

Section: Model Reductionmentioning

confidence: 99%

“…[2,18,19,35]. A reduced-order model (ROM) is considered in Section 3 due to [20] and [22]. The numerical application of this technique is explained in Section 3 and first test examples are presented.…”

Section: Introductionmentioning

confidence: 99%

Optimal Boundary Control Problems Related to High-Lift Configurations

John

Noack

Schlegel

et al. 2010

Active Flow Control II

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We investigate two control problems related to the aerodynamic optimization of flows around airfoils in high-lift configurations. The first issue is the steady state maximization of lift subject to restrictions on the drag. This leads to a boundary control problem for the 2D stationary Navier-Stokes equations with constrained controls functions belonging to L 2 (Γ ) under an integral state constraint. We derive optimality conditions and treat the problem numerically by direct solution of the associated nonsmooth optimality system. The second part is based on a k-ω-WILCOX98 turbulence model. To deal with the curse of dimension, we discuss a reduced-order model by adapting a small system of ODEs to solutions computed with the full model.

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A hierarchy of low-dimensional models for the transient and post-transient cylinder wake

Cited by 875 publications

References 30 publications

On least-order flow representations for aerodynamics and aeroacoustics

On least-order flow representations for aerodynamics and aeroacoustics

The onset of vortex-induced vibrations of a flexible cylinder at large inclination angle

Optimal Boundary Control Problems Related to High-Lift Configurations

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