Zonal detached eddy simulation (ZDES) of a spatially developing flat plate turbulent boundary layer over the Reynolds number range 3 150 ⩽ Reθ ⩽ 14 000

Abstract

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 > 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.

Experimental Study of the Corner Flow Separation on a Simplified Junction

“…Eventually, the improved knowledge of the corner flow separation as well as the collection of dedicated databases such as the present experimental one should allow the development and implementation of reliable RANS models to provide aircraft designers with affordable yet accurate tools. Investigations on this matter are underway at ONERA, including the use of QCR for RANS models [26,27] and zonal detached eddy simulation mode 3 (which operates as a wall modeled LES) [28].…”

“…RANS models based on the Boussinesq closure (which are the standard ones used in aircraft design) are not able to capture corner flow separations and one must turn to non-linear closures such as quadratic constitutive relation (QCR [25][26][27]), explicit algebraic Reynolds stress models (EARSM) or Reynolds stress models (RSM). Hybrid RANS/LES methods [28] are also promising. Nevertheless, all these studies are limited by the lack of experimental data to validate the CFD.…”

High-fidelity simulations of unsteady civil aircraft aerodynamics: stakes and perspectives. Application of zonal detached eddy simulation

“…They are called very-large-scale motions (VLSM) or superstructures. The role played by these structures in the boundary layer dynamics is still unclear, but Deck et al [11,52] have recently emphasized how significant the contribution of the VLSM to mean wall shear stress is. The computational cost of a WRLES (or quasi-DNS) is extremely expensive because of the very small Figure 9.…”

“…ASL, atmospheric surface layer; PBL, planetary boundary layer. The largest wall turbulence simulation performed with ZDES (both in WMLES [11] and in WRLES [52] operating modes) in 2014 is emphasized along with the corresponding grid size. Note that the Reynolds number range achieved corresponds to the one commonly observed in subscale wind tunnels and that the use of WMLES allows a CPU cost reduction factor close to 30 compared with a complete WRLES simulation.…”

“…Mode 1 concerns flows where the separation is triggered by a relatively abrupt variation in the geometry; mode 2 is retained when the location of separation is induced by a pressure gradient on a gently curved surface; and mode 3 is for flows where the separation is strongly influenced by the dynamics of the incoming boundary layer. This latter mode is often referred to as WMLES mode (see [11,16]). The ZDES method aims to treat all classes of flow problems and typical associated applications (indicated in figure 3) in a single model, which defines a hybrid length scaleL that enters any turbulence model (because the eddy viscosity ν t ≈ V × L is the product of a velocity scale V and a length scale L) and reads as…”