Improving boundary-layer separation prediction by an IDDES turbulence model using a pressure-gradient sensor

Abstract

This work extends a pressure-gradient sensor for boundary-layer separation originally developed for the $k-ω$ shear-stress transport Reynolds-averaged Navier-Stokes (RANS) model (Griffin et al., 2025, J. Turb.) to the Improved Delayed Detached Eddy Simulation (IDDES) turbulence model of Gritskevich et al. (2012, Flow Turbul. Combust.). The pressure-gradient sensor identifies local regions of strong adverse pressure-gradient where the eddy-viscosity is reduced, as in the original RANS model. Additionally, to promote separation in the IDDES model, the elevation term in the IDDES length scale, designed to augment the RANS-mode Reynolds stress in attached flow regions, is turned off where the pressure-gradient sensor is active. The model is applied on various airfoils representative of both wind energy and aerospace applications, and is used in fully turbulent and transitional IDDES model variants. The proposed model improves the prediction of stall onset and post-stall regimes relative to the baseline IDDES model without significant degradation of attached-flow regimes relative to state-of-the-art RANS models or deep-stall regimes relative to state-of-the-art IDDES models. Significant overall improvements are observed in predictions of lift and drag polars across 90 degrees of angle of attack, yielding a unified model able to predict various (two- and three-dimensional) flow regimes. Shortcomings are identified to be related to the underlying RANS pressure-gradient sensor rather than the extension of the sensor to the IDDES model, which is the focus of this work.

Figures (12)

• Figure 1: (a) Coefficient of lift ($C_l$) and (b) coefficient of drag ($C_d$) for the S809 airfoil at $Re_c=650{,}000$ compared between fully turbulent model variants and the experimental data of Butterfield et al. Butterfield92. Note that the drag data from the CSU Wind Tunnel reported in Butterfield et al. Butterfield92 is pressure drag only, thus only qualitative comparisons should be made between drag data.
• Figure 2: Three-dimensional view of isosurfaces of the second invariant of the velocity gradient tensor for the S809 at $\alpha=20^o$. The left plot shows the IDDES model, and the right plot shows the IDDESae model. The isosurfaces visualized at a level of $Q=20U_{\infty}^2/c^2$ and are colored by the instantaneous streamwise velocity $u/U_{\infty}$.
• Figure 3: Contours of the mean velocity magnitude normalized by the freestream velocity ($U/U_{\infty}$) for the S809 airfoil. Contours are compared between the baseline IDDES model (left column) and the proposed IDDESae model (right column). Top row: $\alpha=10^o$; bottom row: $\alpha = 20^o$.
• Figure 4: Mean surface pressure coefficient $(C_p)$ for the S809 airfoil at (a) $\alpha=10^o$ and (b) $\alpha = 20^o$. The IDDES (blue line) and IDDESae (pink line) models are compared with the experimental data reported in Butterfield et al. Butterfield92. The upper and lower airfoil surfaces are shown by the solid and dashed lines, respectively.
• Figure 5: (a) Coefficient of lift ($C_l$) and (b) coefficient of drag ($C_d$) for the NACA0012 airfoil at $Re_c=700{,}000$ compared between transitional model variants and the experimental data of Sheldahl and Klimas Sheldahl81_0012.