*5.2. DU06-W-200 Airfoil*

Figure 6 shows the comparison of the experimental coefficients (*CD*, *CL*) of the airfoil measured with the aerodynamic balance and the data from the bibliography. Experimental data from this work are plotted with a red discontinuous line and triangle markers. Up to six complete tests were repeated in an effort to properly characterize the hysteresis zone related to the flow separation. Thus, in this figure, the markers and discontinuous line show the averaged coefficients from all the tests, while the light-red area bounds the maximum and minimum dispersion in the results.

**Figure 6.** Experimental drag and lift coefficients from airfoil DU06-W-200 compared with data from the bibliography.

Regarding the drag coefficient (left plot), the obtained results are significantly higher than those from the "clean" dataset. This can be easily related to the big difference in the mean turbulence level (about 35 times) between both wind tunnels. Nevertheless, the obtained results match remarkably well for the "dirty" dataset, with the exception of the range of low positive angles, in which the obtained coefficients are higher. The reason of this discrepancy may probably lie in the presence of a light dimple in the airfoil shape, close to the leading edge at the pressure side. This defect is a consequence of the deburring of the seam scar produced in the layer shift as the airfoil is 3D-printed. That irregularity may be triggering turbulence transition on the airfoil (precisely in the stagnation point) and, thus, increasing the drag artificially. Furthermore, additional polishing of the area has also slightly modified the local slope of the airfoil, leading to a mismatch with respect to the original geometry.

Meanwhile, the lift coefficient curves (right plot) overlap perfectly for all the datasets at low pitching angles (−6◦ to 6◦), where the flow is completely attached, and the incoming flow turbulence is not relevant. However, at higher angles (−6◦ to −11◦ and 6◦ to 10◦), the "clean" dataset bounds the maximum magnitude of the lift, with the obtained experimental results slightly below and the "dirty" dataset starting to decay due to the early flow separation. At negative angles of attack, both "clean" and "dirty" datasets maintain a slow and progressive detachment when the pitching angle is increased, until they finally drop at −20◦. On the other hand, the experimental data from this work drops earlier at −16◦, after achieving the maximum magnitude of the negative lift. Although our experiments have in fact not been performed to describe the hysteresis cycles, it is significant that the dispersion of the results resemble that phenomenon to some extent. Hence, the width of the hysteresis loop in the reference data is much higher than in the experiments, which practically crosses through the middle, dividing the others in half. This also occurs with the positive side of the curve. However, here, the difference between the lift drop of the "clean" dataset and the two others is much higher with the first one dropping outside the shown range (~22◦) and the other two around 14◦~15◦. Furthermore, despite the experimental data achieving almost the same maximum lift coefficient as the "clean" dataset, the drop zone and hysteresis loop width match better the "dirty" dataset. The existence of a boundary layer on the side walls of the tunnel generating 3D effects at the ends of the tested wing may affect the hysteresis of flow separation on the wing. This could be the reason for the observed large differences between the experiment and CFD calculations at large angles of attack.

Considering the overall results, the aerodynamic balance used in this experiment clearly exhibits a notable accuracy, being able to reproduce the reference dataset both in drag and lift coefficients, and clearly characterizing the flow separation.

A further analysis of the experimental data obtained is discussed with the help of the CFD simulations performed. In Figure 7, the experimental coefficients are compared with the results from CFD simulations for different turbulence models and simulating conditions. Specifically, results from the simulation with the Spalart–Allmaras (S-A) model executed in a steady fashion are represented in dark gray, those computed steadily but for a generalized k-ω (GEKO) model are shown in green, whereas the GEKO unsteady simulations are shown in blue, distinguishing between the coarse mesh (light-blue discontinuous line) and the extra refined mesh (dark-blue continuous line).

Despite the simplifications of the S-A steady simulation, it performs remarkably well in reproducing the lift curve, with only a slight underestimation of the maximum. However, it is clearly unable to predict an accurate drag overshoot. On the other hand, the set of GEKO simulations produce subtle different results among them. The GEKO steady simulation significantly improves the results compared with the S-A, accurately characterizing the drag overshoot as well as the lift curve. Nevertheless, it overestimates both drag and lift magnitude at negative wide angles (−12◦ to −20◦). The results from the GEKO unsteady simulation and with the coarse mesh are enhanced, but show that the initial mesh is not sufficiently accurate to reproduce the lift curve when flow separation starts to be significant. In fact, it is still poorly predicting important flow features when the airfoil stalls, such as the instabilities of the boundary layers and the shedding of trailing vortexes. This is clearly improved with the extra-refined mesh, which produces the best results, especially for negative angles of attack. Yet, it still fails to predict accurate lift drops in the case of fully detached flow.

Since no data were found in the bibliography for the pitching moment, the experimental results have been directly compared with the GEKO unsteady simulation for the refined mesh in Figure 8. Furthermore, as a preliminary approach to evaluate unsteady capabilities of the aerodynamic balance, the RMS value of the fluctuations in the moment coefficient is also represented (dispersion bars) and compared in the figure. In this case, instead of presenting the averaged statistics of the whole dataset as before, only a single measurement has been used to ensure that these fluctuating results are consistent.

**Figure 7.** Experimental drag and lift coefficients from airfoil DU06-W-200 compared with results from CFD simulations for different turbulence models.

**Figure 8.** Experimental moment coefficient and fluctuating moment coefficient from airfoil DU06-W-200 compared with results from the best unsteady CFD model.

As expected, the moment coefficient for low pitching angles, which it is practically zero, matches perfectly between experiments and numerical results (solid and dashed lines). This is coherent with the hypothesis of the airfoil having the center of pressure approximately at 25% of the chord (the same location for the origin of coordinates in the CFD and for the center of the shaft in the experimental prototype). However, as pitching angles increase (both in negative and positive directions), the CFD model predicts a smooth, exponential-like rise in the coefficient magnitude, while the experimental results show a more drastic drop at −16◦ and 13◦, followed by a moderate, linear-slope increase.

In the case of the RMS values, a very low level can be appreciated in the experimental data at low pitching angles. Likewise, the CFD model converges to a unique solution as there is no unsteadiness in the simulations. The flow separation can be easily identified in the figure by the sudden increase in the fluctuations in the experimental dataset, although in the CFD, there is a more progressive increase. Precisely, it was necessary to activate unsteady computations in the CFD model beyond ±8◦ of *AoA* to account for the inherent unsteadiness of the detached flow. This comparison also reveals that the dynamic sensitivity of the balance is enough to perceive the amplitude of the fluctuating forces, despite the structural damping of the wing model. Conversely, accurate frequency values are not feasible due to the high stiffness of the set-up, thus avoiding a complete fast response of the measurements.

For a deeper understanding of the unsteady phenomena involved in these fluctuating forces, the velocity field, pressure coefficient (defined as *Cp* = <sup>2</sup>(*<sup>p</sup>* − *<sup>p</sup>*∞)/*ρv*<sup>2</sup> <sup>∞</sup>), and spectra of the fluctuating moment have been analyzed in detail for four positive pitching angles (8◦, 12◦, 16◦ and 20◦) using the data from the refined GEKO unsteady simulation. The results are shown in Figure 9. The instantaneous velocity field at a particular instant in the simulation is represented on the left part of the figure in non-dimensional terms with respect to the upstream velocity. Meanwhile, on the upper-right plot, the pressure coefficient along the airfoil chord is represented for both suction and pressure sides at that same instant. In addition, shadowed areas have been introduced to illustrate how the coefficient is oscillating during a complete shedding cycle. Finally, on the right lower part, the amplitude and oscillating frequency of the moment coefficient are shown, identifying the peak values.

The maps with the representation of the velocity magnitude allow the identification of the stagnation points in the lower part of the leading edge and show an evident trend towards an early flow separation as the pitching angle is progressively increased, with a remarkable thickening of the boundary layer. A counter-rotating pair of vortices is shed from the airfoil, growing in size as the pitching angle is more pronounced. This vortex shedding is coherent with the frequencies of the fluctuating moment, which show high frequency but low size of the vortex shedding at the lower pitching angles. Conversely, lower frequencies and higher sizes of the vortices are observed at higher angles, once the flow is fully detached. As a consequence, the aerodynamic coefficients are intensively fluctuating with amplitudes up to three times larger than those formed at the separation onset. Regarding the pressure coefficient, there is also a notable increase in the oscillations with the pitching angle, revealed as a progressive build-up of the Cp value in the pressure side, and a shift towards the trailing edge of the airfoil in the suction side. Note that from 12◦ onwards, a wide fluctuation can be observed in the trailing edge due to an oscillatory partial reattachment, which it is also responsible for the periodic variations on both drag and lift coefficients.

Previous assertions are validated by means of the Strouhal number, *St* = *f L*/*v*∞, which relates the vortex shedding of the large turbulent scales and the frequencies of the fluctuating moment. The frequency values (*f*) correspond to the first (fundamental) harmonic in the power spectrum of the fluctuations for the torque coefficient (see plot in the bottom right in Figure 9). The characteristic length (*L*) has been adopted as the maximum value of the integral length scale on the airfoil suction side (see Figure 10 below). The integral scale is estimated from the instantaneous values of the turbulent kinetic energy (*k*) and the turbulent dissipation rate (*ε*) according to *L* = *k*3/2/*ε* [25]. Using the convective inlet velocity (*v*∞ = 16.4 m/s), typical values around 0.2 are found (see Table 3) for all the situations considered between 10 deg (partial detachment) and 20 deg (fully detached flow),

which is a characteristic value observed in separation of bluff-bodies at moderate-to-high Reynolds numbers.

**Figure 9.** Velocity field, pressure coefficients and spectra of the fluctuating moment at *AoA* = 8◦, 12◦, 16◦ and 20◦, obtained from the refined GEKO unsteady CFD simulation.


**Table 3.** Strouhal numbers of the detached flow for different angles of attack.

Figure 10 shows the computed values of integral length scales in the waked regions of the airfoil for different angles of attack. The figure reveals the vortical motion of the largest vortices, identified in a dark-blue color for an instantaneous snapshot, which illustrates the typical turn-out time of the vortices. At a low *AoA*, the size of the vortices is roughly in the order of magnitude of the airfoil thickness, with an intense vortex shedding (high frequency) revealed through the advection transport of the vortices street. For a high *AoA*, the vortices are progressively enlarged, now with a size in the order of magnitude of the airfoil chord, but with a lower shedding frequency (the generation rate of these large flow structures is significantly reduced as shown again in the convective transport along the airfoil wake).

**Figure 10.** Integral length scales in the airfoil wake for positive *AoA* = 10◦, 12◦, 14◦, 16◦, 18◦ and 20◦.

Further insight is now provided with a closer look to the detached regions of the airfoil suction side during a complete oscillation cycle. For that purpose, the longitudinal distribution of the mean pressure coefficients on the suction side of the airfoil is shown in a contour plot in Figure 11, for all the angles-of-attack simulated. A black dashed line identifies the averaged position of the separation point, revealing the severe engrossment of the detached region towards the leading edge for high pitching angles. Moreover, the contour map is complemented by a comprehensive view of the averaged detached regions over the airfoil, for *AoA* going from 6◦ to 20◦ (right plot), in order to illustrate the recirculation zones (identified with negative streamwise velocities).

**Figure 11.** Pressure coefficient in the suction side, boundary layer and flow detachment point, for a wide set of pitching angles simulated with the refined GEKO unsteady model.

As expected, the position of the detachment point (where the wall shear stress equals zero) moves towards the leading edge, leaving a growing detached region. Note that at 20◦, more than 80% of the suction face is exposed to fully detached flow. Although not shown here for brevity, a similar contour map is obtained for the pressure side, but symmetrically flipped with respect to the zero *AoA* and with a small shift, as detachment occurs at slightly higher angles for this side.
