ENGINEERING AND CFD

Both Wind turbine and aircraft industry rely on numerical optimization to reach high performances in ever shorter times to market. Current simulation strategies are based upon statistically averaged, so-called Reynolds-Averaged Navier-Stokes (RANS) to represent the time-average effect of the stochas-tic flow structures known as turbulence. Furthermore, due to the need for calibration, RANS can only be reliably used near the design point, and moreover requires vast experience of the design engineer. In order to cope with these uncertainties, industry wants to complement RANS with Large-Eddy Simulation (LES) for verification and off-design predictions.

LES directly resolves the most energetic turbulent flow structures, and only models the smallest. However, its cost rises rapidly with the Reynolds number due the growing disparity between turbu-lence in the inner part of the boundary layer and that in outer flow features. Therefore, fully resolved LES is to date unfeasible for realistic geometries and conditions.

At off-design operating conditions, resolving turbulence close to the wall in the boundary layer may not be so critical. Therefore hybrid approaches that combine a model for the inner part of the boundary layer to LES further away from the wall are seen as a viable alternative for the next decade. These “wall-modeled” LES (wmLES) need to be validated with respect to “wall-resolved” LES (wrLES) computations. This is the goal of the current research.

This project provided a high resolution wrLES of the NACA4412 airfoil, a widely used test case for turbulence model validation, at near stall conditions (angle of attack of 12°) and at high Reynolds number (Re=1.6Mio). Based upon a detailed analysis of the boundary layer, guidelines were specified regarding the required minimum span extent and the most appropriate wall-models for boundary lay-ers subjected to moderate adverse pressure gradients. In addition to serving as validation case for the development of wall-modeled LES at Cenaero, the results are also being compiled as reference data-base for future model development, including RANS, by other researchers.

At the computed conditions, the results can be compared to two experiments [HW87, W87], four wall-resolved LES [J95, J96, KC95, SFT01] and two wall-modeled LES [FSHCW16, PM14]. All computations aimed at reproducing the wind tunnel tests. Due to the uncertainties and the lack of knowledge on specific conditions in the wind tunnel, these computations differ slightly in their setup: span extent, transition forcing, tunnel blockage compensation, among other. Also, the numerical setup differs in method, mesh refinement, statistical averaging window, et cetera. Therefore, the redundancy is only in appearance, and the comparison enables us to check sensitivity with respect to discretization and setup. Furthermore, the current approach differs from the previous ones in the sense that it allows some deviations with respect to wind tunnel conditions in favor of a fully numerically reproducible setup to arrive at a solid basis for comparison.

Computations were previously performed on the in-house cluster zenobe at Cenaero for a small span of 1% and published by Frère et al. [FHCW18]. The computational resources made available on JUQUEEN in the R2Wall project were used to investigate the impact of the span extent and grid re-finement. A ten times larger span was considered and a grid sensitivity analysis was performed to ensure independence of the turbulent flow structures observed in the boundary layer.

Up to the separation point, there was no noticeable effect on the evolution of the boundary layer, as illustrated in Figure 1. Noticeable differences appear however in the separated wake, leading to an artificially coherent vortex street in the 1% case. This in turn impacts the reattachment point at the trail-ing edge of the airfoil. One of the main observations is that wall-model development can rely on small span computations up to a point where the boundary layer height becomes comparable to the span extent. This considerably relaxes the computational cost. The results were presented at PASC confer-ence [FRH18] and PRACE days [HRF18]. Currently, a paper is in preparation for FTAC [FHCW19] to present results together with the accompanying database.