An evaluation of the force and moment predictions is presented in this section. Where possible, an attempt is made to explain the non-linear characteristics of this data based on the flow behaviour shown in the previous section. The crossplots of lift, drag and moment coefficients are shown in Fig. 4.20.
(a) Initial stages of vortex development (b) Late stages of vortex with breakdown occur- ring over the top surface
Figure 4.17: Liverpool’s predicted flow topology (Baseline k-ω) for the RLE.
(a) PIV at sectioncroot= 0.51 (b) PIV at sectioncroot= 0.70
(c) PMB at sectioncroot= 0.51 (d) PMB at sectioncroot= 0.70
(e) ENSOLV at sectioncroot= 0.51 (f) ENSOLV at sectioncroot= 0.70 Figure 4.18: CFD data comparison with PIV measurements for the RLE model at
α= 16◦
(a) PIV at sectioncroot= 0.51 (b) PIV at sectioncroot= 0.70
(c) PMB at sectioncroot= 0.51 (d) PMB at sectioncroot= 0.70
(e) ENSOLV at sectioncroot= 0.51 (f) ENSOLV at sectioncroot= 0.70 Figure 4.19: CFD data comparison with PIV measurements for the RLE model at
α= 18◦
Figure 4.20 (a) shows the lift coefficient values as a function of angle of attack for the SACCON SLE obtained from the experiments and a range of steady flow simu- lations. The plots follow a linear trend up to an angle of attack of 13◦
where they start to follow a shallower path. Beyond 20◦
incidence the plots become relatively flat due to a progressive wing stall. This occurs as the vortex breakdown position travels upstream towards the apex. This movement of breakdown position leads to a progres- sive reduction in the vortex-induced suction force which causes this deficit in lift. It can also be seen that the agreement between the two sets of data is good in the linear and non-linear regions with a slight offset throughout. As mentioned previously, this is due to the effect of the sting, as seen from other SACCON CFD studies [71, 72]. The drag predictions also show a good agreement with the experimental data, with a slight discrepancy beyond 20◦
angle of attack, see Fig. 4.20 (b).
The pitching moment behaviour is the most interesting of the three since it shows a more non-linear behaviour, Fig. 4.20 (c). The measurements show a change in gradient at 3◦
and a linear increase from there up to 12◦
angle of attack. A strong dip is present at 15◦
before the moment coefficient recovers up to a new maximum at 22◦
. The simulations predict the main characteristic drawn from the experiments. The computed coefficient increases linearly up to 10◦
. At this point the tip vortex starts to appear with a pitch down influence, causing the predictions to flatten up to 12.5◦
. The strength of the dip at 15◦
is overpredicted and so is the maximum value of Cm above
20◦
angle of attack.
The dip occurs because the onset of the tip vortex moves suddenly along the middle part of the wing and starts to merge with the apex vortex, at 13◦
angle of attack. This changes the force distribution over the wing very rapidly, to which the Cm is very
sensitive. As the single vortex becomes stronger, due to the increasing incidence, a large region of high vortex-suction occurs at the forward section. For this reason and the fact that the vortex breakdown position moves gradually upstream, the pitching moment coefficient recovers again to a new maximum value. The overprediction in the dip does not result from an excess vortex strength, as the strengths were seen to be similar in Fig. 4.13 (c). The predicted vortex is seen to be located further inboard than the measured vortex, meaning that the onset is likely to be further forward. This suggests that the magnitude of the dip is overpredicted because the vortex onset is too far inboard between 12.5◦
and 15◦
incidence.
The SLE and RLE integral results show noticeable differences, as would be ex- pected from the flow topologies seen in the previous section. Figure 4.11 (a) shows the measured and predicted lift curves. The linear slopes of the two curves are in good agreement apart from the previously mentioned sting offset. The drag coefficient re- sults, Fig. 4.11 (b), also show a very good agreement between the predictions and the experiments for the RLE.
(a)CLagainst angle of attack.
(b) CD against angle of attack.
(c)Cmagainst angle of attack.
Figure 4.20: Integral data from experimental results and PMB computations for the sharp leading edge model.
The pitching moment plot for the RLE has some similarities with that of the SLE although generally the behaviour has more abrupt changes. The reason for the poorCm
agreement at lower angles of attack is not fully understood. Despite the good agreement in Cp shown by the pressure tap measurements there seems to be regions where the
predicted flow is in disagreement. One suggestion points to vortices originating behind the sting not being predicted by the Unsteady RANS (URANS) methods. This could result in low pressure present on the aft bottom surface. In order to locate the regions of the flow around the body affecting the pitching moment plot, the differences inCp
distribution between the two solutions were calculated. Then the influence on the Cm
was obtained by multiplying theCp at each point by the moment arm. By subtracting
theCm distribution from solutions at two given incidences, the non-linearities in Fig.
4.11 (c) can be explained.
Figure 4.21 shows the ∆Cm distribution around the top and bottom of SACCON
for different cases. The positive regions (red) show a pitch up moment contribution, and the negative (blue) represent a pitch down. The experiments show an initial linear part up to an incidence of 10◦
. In Fig. 4.21 (a) and (b) a positive increase in ∆Cm
in the region near the apex can be seen. The negative influence of the outboard, aft section is not large enough to counteract the pitch up moment in this range of angles of attack. As the outer vortex starts to gain strength over the tip section from 10◦
onwards, the pitching moment plots are seen to flatten. Figure 4.21 (c) shows clearly the increase in pitch down effect from the tip section as the angle of incidence is increased from 10◦
to 14◦
. At the same time, the pitch up contribution from the apex region has decreased slightly compared to the lower angles of attack, hence the change in behaviour on the plot. Figure 4.21 (d) shows a pitch up area in the tip section due to the inboard displacement of the vortex between 14◦
and 15◦
incidence. This causes the small spike in pitching moment coefficient before the large drop at 16◦
. Up to this point the baseline k-ω predictions are in good agreement with the experiments with an offset throughout. The drop at 16◦
is similar to that seen for the SLE model and is caused by the sudden movement of the outboard vortex as it shifts inboard merging with the apex vortex. The same vortex behaviour causes this drop on the RLE wing, as shown in Fig. 4.21 (e). The large negative region in the aft part of the middle section of the geometry illustrates how the suction effect from the vortex causes the pitch down moment. The computed results from the baseline k-ω model predict an earlier dip than the measurements. This is due to the early movement of the outer vortex onset along the leading edge. Figure 4.21 (f) shows that the reason for the steep increase in moments from 16◦
to 20◦
is the strong vortex suction over a small elongated region near the apex. Furthermore, it can be seen here that separation from the trailing edge and the separated flow over the midsection also have an effect on the pitching moment.
(a) ∆Cmbetweenα= 0 ◦ and 5◦ (b) ∆Cmbetweenα= 5 ◦ and 10◦ (c) ∆Cmbetweenα= 10 ◦ and 14◦ (d) ∆Cm betweenα= 14 ◦ and 15◦ (e) ∆Cmbetweenα= 15 ◦ and 16◦ (f) ∆Cmbetweenα= 16 ◦ and 20◦
Figure 4.21: Distributions of change in moment over the top and bottom SACCON RLE surfaces.