Zonal detached eddy simulation (ZDES) of a spatially developing flat plate turbulent boundary layer over the Reynolds number range 3 150 ⩽ Reθ ⩽ 14 000
Authors: Deck Sébastien , Renard Nicolas , Laraufie Romain , Sagaut Pierre 
Published: February 2014

A Wall-Modeled Large Eddy Simulation (WMLES) of a spatially developing zero-pressure gradient smooth flat plate turbulent boundary layer is performed by means of the third mode of the Zonal Detached Eddy Simulation technique. The outer layer is resolved by a Large Eddy Simulation whereas the wall is modeled by a RANS simulation zone, with a RANS/LES interface prescribed at a fixed location. A revisited cost assessment of the Direct Numerical Simulation of high Reynolds numbers (Reθ ⩾ 10 000) wall-bounded flows emphasizes how moderate the cost of the WMLES approach is compared to methods resolving the near-wall dynamics. This makes possible the simulation over a wide Reynolds number range 3 150 ⩽ Reθ ⩽ 14 000, leaving quite enough space for very large scale motions to develop. For a better skin friction prediction, it is shown that the RANS/LES interface should be high enough in the boundary layer and at a location scaling in boundary layer thickness units (e.g., 0.1δ) rather than in wall units. Velocity spectra are compared to experimental data. The outer layer is well resolved, except near the RANS/LES interface where the very simple and robust passive boundary treatment might be improved by a more specific treatment. Besides, the inner RANS zone also contains large scale fluctuations down to the wall. It is shown that these fluctuations fit better to the experimental data for the same interface location that provides a better skin friction prediction. Numerical tests suggest that the observed very large scale motions may appear in an autonomous way, independently from the near-wall dynamics. It still has to be determined whether the observed structures have a physical or a numerical origin. In order to assess how the large scale motions contribute to skin friction, the Reynolds shear stress contribution is studied as suggested by the FIK identity [K. Fukagata, K. Iwamoto, and N. Kasagi, “Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows,” Phys. Fluids 14, L73 (2002)]. Scale decomposition is achieved thanks to the co-spectrum of the Reynolds shear stress in function of the length scale and of the wall distance. The contribution of the large scales to streamwise turbulence intensity and to the Reynolds shear stress is assessed. At the considered Reynolds numbers, the observed largest scales contribute significantly to the Reynolds shear stress in the outer layer but are almost inactive in the sense of Townsend [The Structure of Turbulent Shear Flow (Cambridge University Press, 1976)] closer to the wall. The modeled Cf amounts to only 11% of the total Cf: most of the skin friction is resolved by the present simulations rather than modeled. The large scales, defined by λx &gt; δ, represent the largest contribution to the resolved Cf. It is surmised that there is a correlation between the large scale motions being closer to the experimental data and the better skin friction prediction enabled by a proper interface positioning.