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On the need for a nonlinear subscale turbulence term in POD models as exemplified for a high-Reynolds-number flow over an Ahmed body

Published online by Cambridge University Press:  23 April 2014

Jan Östh ,
Bernd R. Noack ,
Siniša Krajnović ,
Diogo Barros  and
Jacques Borée
Jan Östh*
Affiliation:
Division of Fluid Dynamics, Department of Applied Mechanics, Chalmers University of Technology, SE-412 96 Göteborg, Sweden
Bernd R. Noack
Affiliation:
Institut PPRIME, CNRS – Université de Poitiers – ENSMA, UPR 3346, Départment Fluides, Thermique, Combustion, CEAT, 43 rue de l’Aérodrome, F-86036 Poitiers CEDEX, France
Siniša Krajnović
Affiliation:
Division of Fluid Dynamics, Department of Applied Mechanics, Chalmers University of Technology, SE-412 96 Göteborg, Sweden
Diogo Barros
Affiliation:
Institut PPRIME, CNRS – Université de Poitiers – ENSMA, UPR 3346, Départment Fluides, Thermique, Combustion, CEAT, 43 rue de l’Aérodrome, F-86036 Poitiers CEDEX, France PSA Peugeot Citroën, Centre Technique de Velizy, 78943 Vélizy-Villacoublay CEDEX, France
Jacques Borée
Affiliation:
Institut PPRIME, CNRS – Université de Poitiers – ENSMA, UPR 3346, Départment Fluides, Thermique, Combustion, CEAT, 43 rue de l’Aérodrome, F-86036 Poitiers CEDEX, France
*
†Email address for correspondence: [email protected]
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Abstract

We investigate a hierarchy of eddy-viscosity terms in proper orthogonal decomposition (POD) Galerkin models to account for a large fraction of unresolved fluctuation energy. These Galerkin methods are applied to large eddy simulation (LES) data for a flow around a vehicle-like bluff body called an Ahmed body. This flow has three challenges for any reduced-order model: a high Reynolds number, coherent structures with broadband frequency dynamics, and meta-stable asymmetric base flow states. The Galerkin models are found to be most accurate with modal eddy viscosities as proposed by Rempfer & Fasel (J. Fluid Mech., vol. 260, 1994a, pp. 351–375; J. Fluid Mech. vol. 275, 1994b, pp. 257–283). Robustness of the model solution with respect to initial conditions, eddy-viscosity values and model order is achieved only for state-dependent eddy viscosities as proposed by Noack, Morzyński & Tadmor (Reduced-Order Modelling for Flow Control, CISM Courses and Lectures, vol. 528, 2011). Only the POD system with state-dependent modal eddy viscosities can address all challenges of the flow characteristics. All parameters are analytically derived from the Navier–Stokes-based balance equations with the available data. We arrive at simple general guidelines for robust and accurate POD models which can be expected to hold for a large class of turbulent flows.

JFM classification

Nonlinear Dynamical Systems: Low-dimensional models Turbulent Flows: Turbulence simulation Wakes/Jets: Wakes
Type
Papers
Information
Journal of Fluid Mechanics , Volume 747 , 25 May 2014 , pp. 518 - 544
Copyright
© 2014 Cambridge University Press 

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