3.1. Vortex Characterisation
The averaged PIV measurements of the isolated vortex (
Figure 3) show that the vortex core, defined as the flow region delimited by the local extrema in the velocity profile, presents a circular shape, with a radius of
. The circulation, computed by integrating along the core perimeter, is
, corresponding to a vortex Reynolds number
= 19,800. By comparing with literature data from experiments on tip vortices released by helicopter rotor models [
27], the size of the present vortex fits very well in the typical range for tip vortices, while its core circulation is consistent with newly released vortices. Concerning the vortex Reynolds number, which is related to turbulent diffusion and vortex growth rate [
28], the present value falls within the range of measurements for model-scale rotors [
29]. The induced tangential velocity
profile is also reported in
Figure 3 and compared to a Vatistas model [
30]:
where
r is the distance from the vortex centre, normalised to have a core size of
; it can be seen that a close fit to the experimental data is obtained by setting
.
To characterise the dispersion associated with vortex meandering and the repeatability of the generation process, a statistics analysis over all the PIV image couples was performed by considering each couple separately and identifying the vortex centre position through the
criterion [
31]: the results showed that the data from the averaged PIV measurements overestimate the vortex size by less than 1%, with respect to the size determined by statistical analysis on the separate image couples. Therefore, no specific procedure was adopted to align the position of the vortex across all the images prior to the averaging process; such a procedure, moreover, would not have been applicable to the following measurements with the blade model.
In conclusion, the vortex generation process was deemed suitable for the parallel BVI study, being able to reliably produce an isolated, coherent vortex with adequate size and strength.
3.3. Vortex Interaction—Static Airfoil
The measurements of the interaction between the vortex and the blade model show the vortex approaching with a trajectory impinging on the leading edge of the airfoil, and then moving towards the suction side and along it. During the interaction, the vortex remains coherent, with a core region which is clearly identifiable, although distorted into a more oval shape; the dimensions of the core also increase slightly.
In
Figure 5 the sequence of the interaction with the airfoil at incidence
shows how the main effect of the vortex passage is a very noticeable thickening of the boundary layer along the suction side of the airfoil, as indicated by the vorticity contours. At first, the thickening is more severe at the chord-wise positions corresponding to and immediately downstream of the vortex position, while it reduces drastically immediately upstream: this behaviour is expected given the counter-clockwise rotation of the vortex, as the induced velocity field tends to displace the flow away from the airfoil surface ahead of the vortex, and towards the surface behind it. Once at approximately the mid-chord position, the upstream edge of the increased thickness region appears to lag behind the vortex, while its downstream edge continues to correspond to the vortex position: this results in the widening of the region and, at later times, in the formation of two almost separate “bubbles” of increased vorticity; in this region, moreover, the vorticity has opposite sign to that of the airfoil and is comparable in magnitude. As the vortex gets closer to the trailing edge, a portion of recirculating flow can be identified as associated with the vorticity bubble. This viscous behaviour is consistent with the observations by [
36] and the analysis of [
37,
38], concerning the vortex interaction with a wall: these authors report the formation of a similar vorticity bubble and indicate its cause in the adverse pressure gradient produced by the presence of the vortex, which induces a suction peak beneath the core. The fact that no “eruption” of this bubble can be seen may be attributed to the different flow conditions of the present case, with an airfoil at incidence, with respect to a plane wall.
Similarities can also be found with the results of the LES computations of [
15], which report thickening of the boundary layer, with laminar separation and the formation of a counter-rotating vortical disturbance. While detailed comparisons are difficult to make, given the lower incidence of the airfoil and the much larger interacting vortex that they used in the work, the mechanism of flow separation presently observed is likely to be similar.
The description just presented can be applied to the behaviour of the interaction with the airfoil at
, as shown in
Figure 6, with the main differences being that in the latter case, the thickness increase does not reduce downstream, thus not forming a bubble as definite as in the former case; and that recirculating flow regions are clearly visible, starting from earlier interaction times. In particular, the boundary layer is more severely displaced and the separated region extends from around 50% of the chord, persisting well after the vortex has passed the trailing edge of the blade. This behaviour could be expected given that the incidence is closer to the stall condition and the boundary layer would be more prone to separating under disturbances. While the appearance of separated flow regions, both for
and
, could be explained in terms of the essentially inviscid effect of the vortex induced velocity increasing the effective incidence of the airfoil, viscous effects also play a significant role, as shown by the vorticity distribution in the boundary layer being heavily influenced by the passage of the vortex, with the appearance of secondary structures and their subsequent evolution.
The measurements of the interaction in the case with the airfoil at
, presented in
Figure 7, show that the above reasoning can still be applied, but the effect of the vortex is much reduced, with the vorticity bubble being smaller and more localised, and no separation of the flow being evident.
From the PIV measurements, therefore, it can be concluded that the interaction produces a thickening of the airfoil boundary layer, with the development of a vorticity bubble; this effect is local, limited to a region which moves downstream approximately following the vortex chordwise position. The magnitude of this effect, both in terms of the increase in thickness and the size of the affected region, is greater for the higher incidences of the airfoil, particularly for those close to the stall condition. The transiency of the observed phenomenon—that is, the fact that upstream of the vortex, the flow field tends to return to the undisturbed conditions—is to be expected by the nature of the interaction, as explained above. In conclusion, trailing-edge stall-like separation is observed as a result of the parallel blade–vortex interaction for high incidences of the airfoil, close to the maximum lift conditions. This is consistent with the interpretation of the effect of the vortex as inducing an increase in incidence, given also the comparatively smooth stall behaviour observed from the airfoil polar. This reasoning, however, is too simplistic since the behaviour cannot be reduced to a mere variation of incidence in unperturbed conditions, but the unsteadiness of the phenomenon must be taken into account. By projecting the results shown here, moreover, it could be argued that a vortex of higher circulation could disrupt more severely the boundary layer downstream of it in such a way that even the restoring influence of the upstream induced velocity is not able to reattach the flow, which would produce a separated condition all over the airfoil chord. This hypothesis could not be tested with the present test rig, as the strength of the vortex is limited by the pitching motion of the vortex generator.
Other works in the literature [
10,
11,
13] presented flow separation as a result of parallel BVI, also in the case of highly loaded airfoil only, already close to the stall conditions. The behaviour of the interaction in those cases, however, differed from the present as it triggered a separation bubble in the leading edge region, which then propagated downstream. This difference could be explained by the overall blade model behaviour, which, as already mentioned, did not feature a definite laminar separation bubble, suggesting a more turbulent flow; three-dimensional effects could also modify the flow conditions.
More insight on the effects of the interaction can be gained from the time histories of the aerodynamic coefficient computed from the pressure measurements. To better show this, the variation
in the lift coefficient is introduced as
where
is the lift coefficient in the baseline condition; the same reasoning leads to the definition of the variation in the drag coefficient
. Of course, the above definitions are meaningful only where
(and similarly for the
), which is always the case in the proximity of the maximum vortex interaction, as shown below.
Concerning the lift coefficient
during the blade–vortex interaction, as seen in
Figure 8 and from
Table 1, a substantial impulsive increase is evident for all the incidences. This effect is consistent with the behaviour of BVI as described in the literature, and it is usually explained in terms of the induced upwash of the approaching vortex, followed by a corresponding downwash effect, as already mentioned above. Comparison with the PIV measurements shows that the peak in the lift coefficient is found in correspondence with the vortex reaching the leading edge portion of the airfoil, which is also in accord with the findings of similar works [
10,
20]. The time
of the peak occurrence is also very similar for all three incidences, with the slight differences accounting for the variations in position of the airfoil and in induced flow. The lift increase is inversely proportional to the blade incidence, with the highest variation being +38% for
. This effect can be expected as the vortex strength is the same for all three cases, while the magnitude of the induced velocity field of the airfoil increases with its incidence, so that the influence of the vortex, in terms of its induced velocity, is proportionally smaller.
Immediately after the peak, the lift falls briskly to values below the baseline: it can be noticed that this difference with respect to the baseline is greater for , which reaches , while it is similar, although smaller in magnitude, for the two other cases. This trend, which contrasts with the interpretation given above for the lift peak, can be explained by the occurrence of flow separation as observed from the PIV measurements, which differentiates the behaviour at the highest incidence.
The return to the baseline
values, for all cases, is noticeably slower than the sharp peak, taking several time units before reaching a steady state; it can also be noticed how in the case of
, the lift coefficient remains very slightly higher than its baseline value. This persistence of the disturbance following the interaction could be attributed to the relatively slow evolution and eventual disappearance of the secondary vortical structures in the boundary layer of the airfoil. To compute an estimate of this settling time, the following approach was chosen: firstly, the difference
between the lift measured during the interaction and its baseline value is computed for all times; then, starting from the time instant corresponding to the peak induced by the interaction, the settling time
is determined as the time interval after which the maximum variation in
keeps under 2% of the maximum value of the baseline
:
where
is the time value such that
for all
, up to a suitably large time. This strategy allows for a comparison of the settling times between the static airfoil interactions and the following oscillating airfoil interactions, while also accounting for any discrepancies between the steady state and the baseline values.
The computed settling times for the static airfoil interaction cases are reported in the last column of
Table 1. The largest value of
is found in correspondence of
, which might reflect the greater perturbing effect induced by the interaction at this lower incidence. The difference between the settling times in the other two cases can be accounted for by considering the larger flow separation occurring for
. Despite the different behaviours among the three cases, as shown by the PIV measurements, the values of
are relatively similar and the time histories show a comparable trend.
Concerning the drag coefficient , a greater variation in the magnitude of the behaviour can be seen among the three cases. In particular, in the case the interaction has the first effect of reducing the drag value, with a downward peak which exactly corresponds in time to the lift peak, representing the same impulsive variation typical of BVI. Drag falls significantly, to almost . This behaviour can be explained as a suction effect of the low-pressure field associated to the vortex approaching the leading edge of the airfoil. After this peak, the value of rises sharply with a quick succession of two peaks at around , before returning to the baseline value. This trend is qualitatively similar in the other two cases: at first the drag is reduced, more briskly, but to a lesser extent with respect to the previous case, which again indicates the greater relative influence of the interaction at low incidences. Then, the drag rises abruptly in a much more significant way: in particular, for , the variation is as high as . This increase in drag, and its dependence on the incidence, can be associated with the occurrence of separated flow, as also indicated by the PIV measurements, as well as with the suction effect mentioned above. It is to be noticed that the appearance of two definite peaks can be attributed to the relative coarse chord-wise spacing between the pressure taps, which causes a loss of spatial resolution when dealing with a very localised phenomenon such as the vortex passage. Nonetheless, it is interesting to point out that the second peak occurs at around , that is, after the vortex has passed the trailing edge: the load variation can therefore be attributed to the downstream convection of the vorticity bubble or, in general, to secondary structures generated by the vortex interaction.
In conclusion, by examining the pressure data, the effect of the parallel BVI is confirmed as impulsive variations in the aerodynamic loads, with drag being particularly affected. A comparison of the aerodynamic loads time history during the interaction can be made with the results by [
15] for the case of the higher relative encounter between vortex and airfoil: the results, for both lift and drag, are in good agreement, at least qualitatively, while a quantitative comparison is difficult to make, given the differences in the test conditions already mentioned above. From their analysis, moreover, secondary spikes in the loads are found to be associated with the vortical structures generated in the boundary layer because of the BVI, which supports the observations made earlier.
3.4. Vortex Interaction—Oscillating Airfoil
From a qualitative point of view, the flow behaviour during the interaction with the oscillating airfoil shows a similarity with the interaction in the case of the static airfoil discussed above.
Figure 9,
Figure 10 and
Figure 11 present the results from the PIV measurements of the HII cases, showing the thickening of the boundary layer, resulting from the passage of the vortex, with respect to the baseline conditions. A region of separated flow near the trailing edge can be identified, especially for
, but its extent does not appear to be significantly different when compared to the static airfoil cases at the corresponding incidences
; in particular, there is no indication of large separations or other phenomena related to dynamic stall.
Similar remarks can be made for the LII cases, of which
Figure 12 shows the one with
: the perturbation induced by the vortex appears to be less significant than the corresponding HII case at the same
, which is consistent with the fact that the interaction is occurring at a lower incidence, although, at the same time, by comparing with the static case at
a slightly larger trailing edge separation can be seen.
The results of the unsteady pressure measurements during the interaction with the oscillating airfoil are reported in
Figure 13 and
Figure 14 in terms of lift coefficient values as a function of blade model incidence. It can be noticed how the data show a small hysteresis cycle for all baseline cases tested (dashed lines in figure); moreover, the fact that a gap is visible in the BVI graph is to be attributed to the different position of the vortex generator during the blade model oscillation cycle, as discussed above.
By looking at the measurements for the HII, a sharp peak in
can be seen, as expected, followed by an interval where the lift is lower than the baseline values, effectively widening the hysteresis cycle in correspondence of the downstroke motion. This effect is similar to, although not as severe as, dynamic stall behaviour, and it is more evident the higher the incidence.
Table 2 reports the relative variations in
and
along with information on the time of occurrence of the lift peak and the settling time. By comparing with the data in
Table 1 the same trends are generally found:
is very similar for all three HII cases, and the maximum
increase in correspondence of the peak is inversely proportional to the airfoil incidence; the minimum
, however, shows a much greater variation at the highest incidences with respect to the static interaction cases, dropping to almost
for
, which is also the case exhibiting a larger hysteresis cycle. Concerning the drag values, the decrease in
is similar to the static
and 15° cases, while there is a much more significant increase in drag, reaching
for
; this behaviour can be related to the insurgence of flow separation, as the highest values are recorded in correspondence of the vortex passing over the region close to the trailing edge of the airfoil. In terms of the settling time
, very little difference is found among the three HII cases; comparing to
Table 1, moreover, it can be seen that these cases present a
lower than in the static interactions.
Table 2 also reports the data from the measurements in the LII cases, while the corresponding trends in
are shown in
Figure 14. Concerning the airfoil lift, the variations for
and 6° are similar, and slightly larger in magnitude than the previously described cases, which is expected since the interaction is occurring at lower incidences. The case
shows a much more detrimental effect, which, again, can be tied to the trailing edge flow separation as shown by the PIV measurements. By looking at the
variations, it can be seen that a very large drop is recorded for all LII cases, as low as
; while such values are comparable to the
for the
static airfoil case, the following peak is considerably higher than the corresponding case. The settling times are significantly larger than in the HII cases, also affecting part of the upstroke motion of the blade model; this difference could hint to a possible restoring effect by the down-stroke motion dynamics itself. For both kinds of interaction, however, the trends confirm that the effects of BVI can be considered to have vanished in less than a period of oscillation, justifying the choice of the motion history for the vortex generator.
By extrapolating the trends described above in the case of the interactions with the static airfoil, it can be suggested that the BVI behaviour is not fundamentally different from that seen in the case of the oscillating blade model when compared at a similar incidence at the moment of interaction. The most noticeable difference, a general increase in drag, can be associated with the insurgence of flow separation at lower incidences than would be the case if the airfoil were static, although the pitching motion seems to affect only weakly the overall effects.