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PROPER ORTHOGONAL DECOMPOSITION ANALYSIS OF TRANSITIONAL CONVECTIVE FLOW SYSTEMS IN COMPLEX GEOMETRIES

DOI: 10.1615/ICHMT.1997.IntSymLiqTwoPhaseFlowTranspPhenCHT.260
page 8

R. A. Sahan
Department of Mechanical Engineering and Mechanics, Lehigh University, 19 Memorial Drive West, Bethlehem, PA 18015-3085, USA

A. Liakopoulos
Department of Mechanical Engineering and Mechanics, Lehigh University, 19 Memorial Drive West, Bethlehem, PA 18015-3085, USA

Résumé

The present investigation reports direct numerical simulation and low-order dynamical representation of transitional flow and heat transfer in a periodically grooved channel relevant to forced convective air (Pr = 0.71)cooling of electronic systems. The governing partial differential equations of the thermo-fluid system are solved by a spectral element method. Time-dependent periodic solutions are calculated for a supercritical value of Reynolds number, Re = 750. Proper orthogonal decomposition is employed to extract the empirical eigenfunctions, to identify the coherent (spatio-temporal) structures and to compress the data. Low-order dynamical systems of non-linear ordinary differential equations are obtained by using the empirical eigenfunctions as basis functions in a truncated series expansion and applying Galerkin projection. It is found that the first four modes for velocity and temperature fields contain almost all flow and temperature fluctuation energy. Eigenfunctions and coherent structures of the thermo-fluid system are identified as standing and traveling waves. In order to develop valid and accurate low-order models of the thermo-fluid system, it is required to retain at least four modes for each field variable in the truncated series expansion.

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