On Capturing Laminar/Turbulent Regions Over a Wing Using WMLES

Wall-modeled large-eddy simulation (WMLES) is performed for flow over a wing with a focus on documenting grid resolution requirements to predict both the laminar and turbulent regions accurately. Flow over a spanwise extruded NACA0012 airfoil at 0-degree angle of attack and freestream chord-based Reynolds numbers of 3 million is simulated using an unstructured-grid finite-volume solver. An equilibrium wall function with the first off-wall grid point as the exchange location is used. Two scenarios are simulated wherein either the entire airfoil surface, or only a portion of it, is assumed turbulent based on linear stability calculations. For the latter scenario, the regular no-slip wall boundary condition is imposed in laminar regions. Using the same grid that was employed in the fully turbulent case, WMLES captured the skin friction in the turbulent region close to the RANS results. However, the skin friction is not well captured in the laminar region, due to far few grid points inside the boundary layer. When the near-wall grid was refined in the wall normal direction, the laminar region was captured accurately, but the turbulent region was not resolved well because the first off-wall point moved below the buffer-layer. To reconcile differing resolution requirements in the laminar and turbulent regions, a grid was generated based on the varying boundary layer thickness estimated from a precursor RANS simulation with a specified transition location. This grid produced improved results in the laminar region but resulted in a delayed transition location. Unsteady disturbances with the most amplified frequencies were introduced upstream of the neutral point. The transition process in the laminar region and the skin friction in the turbulent region were then captured satisfactorily.

💡 Research Summary

This paper investigates the capability of wall‑modeled large‑eddy simulation (WMLES) to predict both laminar and turbulent regions on a NACA0012 airfoil at a chord‑based Reynolds number of 3 × 10⁶ and zero angle of attack. The authors focus on documenting the grid‑resolution requirements that allow accurate capture of the laminar‑to‑turbulent transition, a problem that is especially challenging for WMLES because the optimal wall‑normal spacing differs dramatically between thin laminar boundary layers and fully turbulent logarithmic layers.

Two primary WMLES scenarios are examined. In the first, the entire airfoil surface is assumed turbulent and a standard equilibrium wall model (Spalding log‑law) is applied with the first off‑wall cell used as the exchange location. In the second, a linear‑stability/N‑factor analysis is performed to locate the most amplified disturbance frequencies and the transition onset (critical N = 9). The transition point is set at x ≈ 0.36 c, and the flow is treated as laminar upstream (no‑slip wall) and turbulent downstream (wall‑model).

A structured C‑type grid is used for the fully turbulent case, with a nominal wall‑normal spacing that places the first cell roughly in the middle of the log layer for the downstream region. This grid resolves the turbulent skin‑friction coefficient (Cf) well when compared with RANS and wall‑resolved LES (WRLES) results, but it contains only one or two points inside the thin laminar boundary layer near the leading edge, leading to large errors in the laminar Cf.

Refining the wall‑normal spacing uniformly improves the laminar region but pushes the first cell below the buffer layer (y⁺ < 5) in the turbulent region, degrading the wall‑model performance there. To reconcile these conflicting requirements, the authors generate an unstructured grid whose wall‑normal spacing follows the boundary‑layer thickness obtained from a precursor RANS simulation that includes a prescribed transition location. This “variable‑thickness” grid provides y⁺ ≈ 1–2 in the laminar part and y⁺ ≈ 30–50 in the turbulent part, thereby capturing the laminar Cf accurately while still delivering reasonable turbulent Cf. However, the transition location predicted by WMLES on this grid is slightly downstream of the RANS‑based estimate.

To further improve the transition prediction, the authors introduce unsteady disturbances at the most amplified frequency (F₀ ≈ 6.5 × 10⁻⁵, wavelength ≈ 0.011 c) upstream of the neutral point. Direct‑numerical‑simulation‑based forcing shows that these disturbances grow exponentially from x ≈ 0.10, matching linear‑stability predictions and leading to a satisfactory capture of both the transition process and the turbulent skin‑friction distribution. Simulations without forcing exhibit natural numerical noise that only triggers transition much farther downstream (x ≈ 0.60), highlighting the potential delay of sensor‑based transition detection.

The study concludes that accurate WMLES of flows with co‑existing laminar and turbulent regions requires a hybrid grid strategy: (1) fine wall‑normal resolution in the laminar region to resolve the thin boundary layer, (2) placement of the first off‑wall cell within the logarithmic layer for the turbulent region, and (3) a grid that varies in thickness according to the local boundary‑layer growth predicted by a RANS precursor. Additionally, deliberate low‑amplitude forcing at the most amplified frequencies can be used to “trip” the boundary layer at the intended location, reducing the sensitivity of the transition prediction to grid‑induced delays. These findings provide practical guidelines for applying WMLES to high‑Reynolds‑number wing simulations where viscous effects and transition location critically influence aerodynamic performance.