Mean flow properties

At first two-dimensional simulations were performed to investigate the effect of Gurney-flaps on the mean flow quantities. Results can be compared to experiments by Bechert et al. [7] who studied the HQ17 airfoil at the same Reynolds number.

Fig. shows the mean lift coefficient for varying angle of attack. The mean lift clearly increases with the height of the Gurney-flap. This gain remains constant over a wide range of incidence ( $0^{\circ} \le \alpha \le 8^{\circ}$). The relation between flap height and lift however is not linear but seems to reach saturation for very large Gurneys. The experimental results [7] show the same behavior not only in the linear part of the polar but also for higher angle of attack and the agreement between both emphasizes the applicability of the LLR $k$-$\omega$ for such kind of flow. Similar results are reported for other airfoils assembled with Gurney-flaps (e.g. [2,20]).

Figure: Lift coefficient over angle of attack for the HQ17 profile with Gurney-flap of varying flap height at $Re=10^6$ compared to experiments by Bechert et al. [7].

The effect of Gurney-flaps on the mean flow quantities is mostly governed by the flow conditions in the trailing edge region and in the near wake. Though the Kutta condition dominates the lift, in the case of bluff trailing edges its meaning remains more or less nebulous because the angle of downwash $\gamma$ is not inevitably dictated by the geometry. Based on the numerical simulations however, the angle $\gamma$ can be determined (fig. ) and can be compared to the flap height. According to potential flow theory changes of $\gamma$ directly affect the circulation around the airfoil and thereby the mean lift. Fig. , right shows that lift depends linearly on $\gamma$ and the drag quadratically.

Figure: Streamlines in the mean flow field with angle of downwash behind an HQ17 with Gurney-flap (upper figure: $h/c=0.5\%$, lower figure: $h/c=2.0\%$) and relation between angle of downwash and the lift- and drag coefficients.

Comparisons between steady and unsteady numerical simulations indicate that the lift coefficient can be predicted accurately based on steady computations whereas reliable results for the drag can only be obtained from unsteady computations [20]. Only these are able to capture the dynamics of flow structures in the wake which play an important role for the drag.

As expected, the drag-coefficient increases with growing flap heights similar to the lift which can be observed in fig. . Here the augmentation of drag increases remarkably for Gurney-flaps larger than $h/c>0.5\%$. The effect only occurs for low angles of incidence ( $\alpha \le 4^{\circ}$) whereas in the case of high incidence and high lift, the drag is dominated by flow separation in the trailing edge region on the suction side.

Compared to the measured drag coefficients [7], significant derivations are observed. These are due to 3d effects in the experiments as well as, to a certain extent, to insufficient mesh resolution according to the results from previous computations of the clean HQ17 profile [11]. For qualitative comparison however, the obtained accuracy is satisfactory as at least the trend of varying Gurney heights can be predicted by the numerical simulation.

Figure: Lift- over drag coefficient for the HQ17 profile with Gurney-flap of varying flap height at $Re=10^6$ compared to experiments by Bechert et al. [7].

Summarizing the effect of Gurney-flaps on the mean flow, it is apparent that lift can be increased by up to $57\%$ using a flap height of maximum $h/c=2\%$. Unfortunately the drag coefficient also climbs simultaneously by $110\%$. The optimum lift/drag ratio is still obtained by the clean profile. Investigations with Gurney-flaps mounted on other profiles, however have shown improved glide ratios in the case of small Gurneys of about $h/c \approx 0.5\%$ [20].

In order to better understand how Gurney-flaps influence the mean lift, the mean pressure distribution is investigated: Comparison between the clean and the flapped configuration show that the pressure on both the suction and the pressure side of the airfoil depend on the flap height (fig. ). Although the flap is mounted on the pressure side the main impact on the lift is caused by reduced $c_p$ over the complete suction side. Here the downstream motion of the stagnation point leads to strengthening of the suction peak. At the same time, the pressure in front of the flap increases due to stagnation effects. Both effects together are relevant for the enhanced mean lift. In contrast to standard airfoils, especially those with sharp trailing edges, a significant difference in the trailing edge pressure between top and bottom sides contribute to the additional lift. Gurney-flaps are also responsible for an increased moment coefficient.

The problem of unsatisfactory agreement between experimental and computational $c_p$ in the rear part of the pressure side (fig. ) arises from a laminar separation bubble that can not be captured by the numerical simulations.

Figure: Pressure distribution for the HQ17 at $\alpha=4^\circ$ with Gurney-flaps of varying flap height at $Re=10^6$ compared to experiments by Meyer [18].