## LES and DES investigations of turbulent flow over a sphere at Re = 10,000.(English)Zbl 1113.76354

Summary: Large Eddy Simulation (LES) using a dynamic Smagorinsky type subgrid stress (SGS) model and Detached Eddy Simulation (DES) are applied to prediction and investigation of the flow around a sphere at a Reynolds number of 104 in the subcritical regime. In this regime the boundary layers at separation are laminar, and transition to turbulence occurs farther downstream in the separated shear layers via Kelvin-Helmholtz (K-H) instabilities. The dynamic eddy viscosity model of M. Germano, U. Piomelli, P. Moin and W. H. Cabot [Phys. Fluids, A 3, No. 7, 1760–1765 (1991; Zbl 0825.76334)] is used in the LES, while the current implementation of the DES employs a formulation based on the Spalart-Allmaras (S-A) model. DES is a hybrid approach in which the closure is a modification to the production/destruction term of the original Reynolds-Averaged Navier-Stokes (RANS) model, reducing to RANS in the attached regions, and to LES away from the wall. In the present work where we simulate the flow over a sphere in the subcritical regime in which the boundary layers at separation are laminar, DES can be viewed as LES with a different SGS model. Effects of the discretization scheme used to approximate the convective terms are considered, along with sensitivity of predictions to changes in the additional model coefficient, $$C_{\text{DES}}$$, in the DES formulation. DES and LES yield similar predictions of the wake structure, large-scale vortex shedding and the Strouhal number associated with the low frequency mode in the wake. Predictions of quantities such as the drag coefficient, wake frequencies, position of laminar separation on the sphere, and the mean pressure and skin-friction distributions along the sphere are in good agreement with the measurements of E. Achenbach [J. Fluid Mech. 54, 565–575 (1972)]. Predictions of the primary Reynolds shear stress, turbulent kinetic energy, eddy viscosity, and turbulent dissipation for the two models are also similar. In addition, both models successfully resolve the formation of the vortex tubes in the detached shear layers along with the value of the Strouhal number associated with the high frequency instability mode, provided that the level of numerical dissipation introduced by the discretization scheme remains sufficiently low. Flow physics investigations are focused on understanding the wake structure in the subcritical regime.

### MSC:

 76F65 Direct numerical and large eddy simulation of turbulence 76M25 Other numerical methods (fluid mechanics) (MSC2010)

Zbl 0825.76334
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