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Title:Optimal two-dimensional models for wake flows
Author(s):Balachandar, S.; Najja, Fady M.
Subject(s):Eddy Viscosity
Vorticity Eigenmodes
Abstract:In the case of nominally two-dimensional (2D) cylinders of arbitrary cross-section in cross flow, the three-dimensionality of the wake manifests in the form of quasi-streamwise vortices. These three-dimensional (3D) features profoundly influence lift and drag forces. However, a two-dimensional projection of such a flow, where the effects of three-dimensionality are modeled, will be computationally very attractive. One can consider the two-dimensional projection as the limiting case of large eddy simulation, where the spanwise direction has been completely averaged out. The transport equation for the span-averaged spanwise component of vorticity, wz, is considered; the 3D effects to be modeled appear as a subgrid scale flux of torque. It is shown that simple minded eddy viscosity type models that assume the flux vector to be proportional to the spatial gradient of w: are inadequate. Here we extend the optimal modeling formalism to address issues pertaining to complex flows with multiple directions of inhomogeneity. We present optimal closures for subgrid flux modeled in terms of wz distribution, based on linear and quadratic stochastic approximations. These ideas are tested using the data-base of flow over a flat plate held normal to a cross flow . It is observed that even the optimal model has about 70% normalized error, indicating that the subgrid flux is only about 30% deterministic. Furthermore, it is observed that local models are inadequate, but there exists an optimal region of nonlocality for model dependence. Higher order nonlinearities however do not seem to improve the model's predictability.
Issue Date:2000-03
Publisher:Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report:TAM R 931
Genre:Technical Report
Sponsor:National Science Foundation; Air Force Office of Scientific Research; Center for Simulation of Advanced Rockets
Rights Information:Copyright 2000 Board of Trustees of the University of Illinois
Date Available in IDEALS:2021-11-04

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  • Technical Reports - Theoretical and Applied Mechanics (TAM)
    TAM technical reports include manuscripts intended for publication, theses judged to have general interest, notes prepared for short courses, symposia compiled from outstanding undergraduate projects, and reports prepared for research-sponsoring agencies.

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