High Reynolds Number Flow around Airfoil in Deep Stall

Flows Around Bodies

Underlying Flow Regime 2-11

Evaluation

Comparison of CFD Calculations with Experiments

A dramatic improvement in solution fidelity for DES compared to URANS, first reported by Shur et al. [‌22], was observed in the extensive cross-validation exercise carried out in the EU FLOMANIA project [‌4]. Figure 4 depicts the relative deviation from experimental drag achieved by DES and URANS within this work.

Figure 4: Comparison of URANS and DES for the prediction of mean drag coefficient for the NACA0012 airfoil at α = 60°. Results of 11 different simulations conducted by different partners with different codes and turbulence models within the EU FLOMANIA project [‌4]. Experimental data cited by Hoerner [‌6] are used as reference.

The effect of spatial and temporal numerical schemes on DES was investigated for the NACA0012 case at α = 45° by Shur et al. (2004) [‌23]. Using a localised "hybrid" convection scheme [‌29] (in which 4^th order central differences are applied within the vortical wake region) and a 2^nd order temporal integration was seen to resolve fine turbulent structures to a scale near to that of the local grid spacing. Switching the convection scheme to 3^rd order upwind or, to a lesser extent, the temporal scheme to 1st order was seen to strongly damp the fine vortices in the wake (Figure 5). Correspondingly, a strong under- prediction of the Power Spectral Density (PSD) of the drag and lift forces at higher frequencies was observed. The effect on the mean forces and pressure distributions was however comparatively mild for this case.


Figure 5: Effect of different spatial and temporal numerical schemes on the resolved wake structures of the NACA0012 at α = 45° [‌23]. "Hybrid" refers to the localized blending between 4^th order central and 3^rd or 5^th order upwind convection schemes proposed by Travin et al. [‌29]

Having clearly demonstrated the benefits of DES compared to URANS [‌4, 22] (Figure 4), no further URANS computations were carried out in the successor EU project DESider [‌5], and the focus shifted to cross-comparison of different turbulence-resolving approaches. Figure 6 compares flow visualizations from 3 simulations carried out with the use of different approaches (k – ω SST SAS and DES based on SA and CEASM RANS models) in the form of instantaneous fields of the vorticity magnitude. They reveal quite similar flow and turbulent structures thus supporting a marginal sensitivity of the simulations to the turbulence modelling approach and numerics used.


Figure 6: Comparison of snapshots of vorticity magnitude from three simulations

The same is to a major extent correct regarding the PSD of the lift coefficient and mean pressure distributions over the airfoil shown in Figure 7. Figure 7(a) also suggests that all the simulations are capable of predicting the experimental spectra, particularly the main shedding frequency and its harmonic, fairly well, whereas Figure 7(b) reveals a systematic difference between the predicted and measured pressure on the suction side. Note also that SAS results somewhat deviate from those of SA DES and are closer to the experiment. The same trend is observed for the integral lift and drag forces (Table 5). A concrete reason for the difference between the SAS and DES predictions is not clear but, in any case, it is not significant when compared to e.g. the differences between DES and URANS or between different URANS approaches (see Figure 4). This justifies the above conclusion on the weak sensitivity of the predictions to the turbulence modelling approach and numerics used in different turbulence-resolving simulations.


(a)	(b)
Figure 7: Comparison of PSD of the lift coefficient (left) and mean pressure distributions over the airfoil (right) from three simulations with experimental data [‌27, 28]

**Table 5:** Predicted and measured mean lift and drag coefficients with statistical 95% confidence intervals
Partner and approach	μ [C_l]	Statistical 95% CI^*)	μ [C_d]	Statistical 95% CI^*)
ANSYS (k – ω SST SAS, L_z=4	0.915	±0.017	1.484	±0.030

Contributed by: Charles Mockett; Misha Strelets — CFD Software GmbH and Technische Universitaet Berlin; New Technologies and Services LLC (NTS) and Saint-Petersburg State University