Direct numerical simulation of unsheared turbulence diffusing towards a free-slip or no-slip surface

Abstract

The physics involved in the interaction between statistically steady, shearless turbulence and a blocking surface is investigated with the aid of direct numerical simulation. The original configuration introduced by Campagne et al. (G. Campagne, J.B. Cazalbou, L. Joly, and P. Chassaing, Direct numerical simulation of the interaction between unsheared turbulence and a free-slip surface, in ECCOMAS CFD 2006, P. Wesseling, E. Onate, and J. Periaux eds., TU Delft, The Netherlands, 2006) serves as the basis for comparing cases in which the blocking surface can be either a free-slip surface or a no-slip wall. It is shown that in both the cases, the evolutions of the anisotropy state are the same throughout the surface-influenced layer (down to the surface), despite the essentially different natures of the inner layers. The extent of the blocking effect can thereby be measured through a local (surface) quantity identically defined in the two cases. Examination of the evolution and content of the pressure–strain correlation brings information on the mechanisms by which energy is exchanged between the normal and tangential directions. In agreement with an earlier analysis by Perot and Moin (B. Perot and P. Moin, Shear-free turbulent boundary layers. Part 1. Physical insight into near-wall turbulence, J. Fluid Mech. 295 (1995), pp. 199–227), it appears that the level of the pressure–strain correlation is governed by a splat/antisplat disequilibrium, which is larger in the case of the solid wall due to viscous effects. However, in contradiction with the latter, the pressure–strain correlation remains as a significant contributor to both Reynolds-stress budgets; it is argued that the net level of the splat/antisplat disequilibrium is set, in the first place, by the normal-velocity skewness of the interacting turbulent field. The influence of viscous friction on the intercomponent energy transfer at the solid wall only comes in the second place and part of it can also be measured by the skewness. The remainder seems to originate from interactions between the strain field and ring-like vortices in the vicinity of the splats.

Keywords:

• wall-bounded turbulence
• direct numerical simulation
• intercomponent energy transfer
• blockage effect
• Reynolds-stress budgets

Acknowledgments

Preliminary computations were carried out under the HPC-EUROPA++ project (project number: 1187), with the support of the European Community Research Infrastructure Action of the FP7 ‘Coordination and Support Action’ program. Final computation was carried out on the IBM/POWER6 supercomputer at the IDRIS computing centre of the CNRS (project number: 92283).