A generalized mean-field model of the natural and high-frequency actuated flow around a high-lift configuration

Luchtenburg, Dirk M.; Günther, Bert; Noack, Bernd R.; King, Rudibert; Tadmor, Gilead

doi:10.1017/s0022112008004965

Cited by 87 publications

(71 citation statements)

References 43 publications

(58 reference statements)

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“…Lift force and drag force fluctuations are most susceptible to variations of the amplitudes of the first odd and even POD modes, which energetically dominate higher odd and even POD modes, respectively (see e.g. Noack et al 2003;Luchtenburg et al 2009). …”

Section: Lift and Drag Optimized Oids Of Cylinder Wake Flowmentioning

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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Section: Lift and Drag Optimized Oids Of Cylinder Wake Flowmentioning

confidence: 99%

On least-order flow representations for aerodynamics and aeroacoustics

et al. 2012

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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%

“…The filter modes contain significant information gained from the URANS solution by the k-ω-model. Following [20,29], the main idea of the ROM is to set up a small size system of ODEs for (a 1 (t), · · · , a 4 (t)) T that rebuilds the computed fluid flow best under the operating conditions. Similarly to the work of Luchtenburg et al [20], the dynamical system consists of the uniformly oscillating of the unactuated and the actuated coefficient pairs (a 1 , a 2 ) respectively (a 3 , a 4 ), which are coupled through the equations for amplified saturation.…”

Section: Reduced-order Model (Rom)mentioning

confidence: 99%

“…A high-lift configuration with observation region Ω presented in Figure 4 was considered, see [20] for details. 19.…”

Section: Reduced-order Model (Rom)mentioning

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%

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Optimal Boundary Control Problems Related to High-Lift Configurations

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Noack

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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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System reduction strategy for Galerkin models of fluid flows

Noack

Schlegel

Morzyński

et al. 2009

Numerical Methods in Fluids

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SUMMARYWe propose a system reduction strategy for spectral and Galerkin models of incompressible fluid flows. This approach leads to dynamic models of lower order, based on a partition in slow, dominant and fast modes. In the reduced models, slow dynamics are incorporated as non-linear manifold consistent with mean-field theory. Fast dynamics are stochastically treated and can be lumped in eddyviscosity approaches. The employed interaction models between slow, dominant and fast dynamics respect momentum and energy balance equations in a mathematically rigorous manner-unlike unsteady Reynoldsaveraged Navier-Stokes models or Smagorinsky-type reductions of the Navier-Stokes equation. The proposed system reduction strategy is employed to the cylinder wake benchmark.

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A generalized mean-field model of the natural and high-frequency actuated flow around a high-lift configuration

Cited by 87 publications

References 43 publications

On least-order flow representations for aerodynamics and aeroacoustics

On least-order flow representations for aerodynamics and aeroacoustics

Optimal Boundary Control Problems Related to High-Lift Configurations

System reduction strategy for Galerkin models of fluid flows

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