DOI: 10.1615/TSFP8
LONG-TIME EVOLUTION OF THE INCOMPRESSIBLE THREE-DIMENSIONAL TAYLOR-GREEN VORTEX AT VERY HIGH REYNOLDS NUMBER
SINOPSIS
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.