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LONG-TIME EVOLUTION OF THE INCOMPRESSIBLE THREE-DIMENSIONAL TAYLOR-GREEN VORTEX AT VERY HIGH REYNOLDS NUMBER

Felix S. Schranner
Institute of Aerodynamicss Technische Universitat Munchen Garching, Germany

Xiangyu Y. Hu
Institute of Aerodynamics and Fluid Mechanics, Technische Universitat Munchen, 85748 Garching, Germany

Nikolaus A. Adams
Chair of Aerodynamics and Fluid Mechanics, Department of Mechanical Engineering, Technical University of Munich, 85748 Garching bei München, Germany

Résumé

For this study a spatially high-order, shock capturing non-oscillatory finite volume method is combined with a weakly compressible flow modeling. As an alternative to methods based on the incompressibility assumption this weakly compressible high-resolution approach is both robust to underresolution and spatially highly accurate. The implicit subgrid-scale (SGS) model permits physically consistent underresolved simulations of incompressible, isotropic turbulent flows at very high Reynolds numbers.
Underresolved three-dimensional Taylor-Green vortex (TGV) simulations at finite Reynolds numbers are compared to reference data. Hereby, direct numerical simulation (DNS) data for Re ≤ 3000 is used to assess the accuracy and physical consistency. Large eddy simulation (LES) predictions with two explicit as well as one implicit SGS model help to benchmark the SGS modeling capabilities. The weakly compressible high-resolution approach gives most accurate predictions for the viscous TGV even when resolution is very low. In contrast to the LES our implicit LES predict the laminar-turbulent transition physically consistently. The dissipation rates compare to those of the reference implicit LES, however, at much lower computational costs and mathematical complexity.
As our weakly compressible high-resolution approach is designed for the physically consistent simulation of very high Re turbulent flows, an infite Re TGV is studied for an extended period of time. Thereby, the evolution at times beyond the obviously temporary quasi-isotropic state are of particular interest. For the high and infinite Re TGV flows, transition to the isotropic state is observed. Its onset and end are identifiable from a macroscopic energy redistribution within the low-modes. Subsequently, the inertial subrange scales according to E(k) ∝ k−5/3 and is self-similar in time.