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On least-order flow representations for aerodynamics and aeroacoustics

Published online by Cambridge University Press:  16 March 2012

Michael Schlegel*
Institut für Strömungsmechanik und Technische Akustik, Technische Universität Berlin MB1, Straße des 17. Juni 135, D-10623 Berlin, Germany
Bernd R. Noack
Institut P′, CNRS–Université de Poitiers–ENSMA, UPR 3346, Département Fluides, Thermique, Combustion, CEAT, 43 rue de l’Aérodrome, F-86036 Poitiers CEDEX, France
Peter Jordan
Institut P′, CNRS–Université de Poitiers–ENSMA, UPR 3346, Département Fluides, Thermique, Combustion, CEAT, 43 rue de l’Aérodrome, F-86036 Poitiers CEDEX, France
Andreas Dillmann
Institut für Aerodynamik und Strömungstechnik, Deutsches Zentrum für Luft- und Raumfahrt, Bunsenstraße 10, D-37073 Göttingen, Germany
Elmar Gröschel
Aerodynamisches Institut, Rheinisch-Westfälische Technische Hochschule Aachen, Wüllnerstraße 5a, D-52062 Aachen, Germany ABB Turbo Systems AG, Bruggerstraße 71a, 5400 Baden, Switzerland
Wolfgang Schröder
Aerodynamisches Institut, Rheinisch-Westfälische Technische Hochschule Aachen, Wüllnerstraße 5a, D-52062 Aachen, Germany
Mingjun Wei
Mechanical and Aerospace Engineering, New Mexico State University, PO Box 30001/Dept 3450, Las Cruces, NM 88003-8001, USA
Jonathan B. Freund
Mechanical Science & Engineering, University of Illinois at Urbana-Champaign, 1206 West Green Street, Urbana, IL 61801, USA
Oliver Lehmann
Northeastern University, Department of Electrical and Computer Engineering, 440 Dana Research Building, Boston, MA 02115, USA
Gilead Tadmor
Northeastern University, Department of Electrical and Computer Engineering, 440 Dana Research Building, Boston, MA 02115, USA
Email address for correspondence:


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, least-biased 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; and (iii) aeroacoustic pressure monitored by a sensor array and emitted from a three-dimensional compressible jet. The most ‘drag-related’, ‘lift-related’ and ‘loud’ structures are distilled and interpreted in terms of known physical processes.

Copyright © Cambridge University Press 2012

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