3.2. Flow Field Analysis
This section presents a discussion of the main results obtained by the stereo PIV flow surveys. Figure 7
shows a comparison of the ensemble-averaged non-dimensional freestream velocity component (
) between the single propeller and side-by-side propellers for both advance ratios tested.
For the lower advance ratio test case (i.e., J = 0.4), the upper propeller wake boundary in side-by-side configuration shows an expansion with respect to the single propeller test case (see Figure 7
b). Indeed, the aerodynamic interaction of the nearby rotating propeller avoids a natural contraction of the wake boundary profile (see Figure 7
a). Moreover, due to the interaction and to the co-rotation of the two propellers, the flow field of the side-by-side propellers observed in the measurement region is not completely symmetric. For the higher advance ratio tested (i.e., J = 0.4), the wake boundaries of the single propeller case and the upper propeller in the side-by-side configuration are almost similar (see Figure 7
c,d). Indeed, the aerodynamic interaction at fast cruise speed is negligible, as confirmed by the quite symmetrical behavior of the flow field for the side-by-side propeller configuration.
Detailed insight about the effects of the side-by-side aerodynamic interaction on the tip vortex topology and distribution is provided in the following using the flow fields evaluated by phase-locked stereo PIV measurements. The choice to present the phase-locked measurement results for a singular blade azimuthal angle is for the sake of consistency but does not affect the main findings of the work. As the PIV surveys were phase-locked with the upper propeller blade azimuthal angle, the phase-averaged flow fields show consistent tip vortex structures issued by the upper propeller blades in the higher region, while the lower region is characterised by a uniform flow region bounded by traces of the tip vortices issued by the lower propeller, as the lower propeller works in the free-run condition, analogously to what was observed from the ensemble-averaged results. Nevertheless, the focus of the following discussion is on investigating the effects of an aerodynamic interaction on the tip vortex topology of the upper propeller by comparison with the phase-locked results obtained for the single propeller configuration. Figure 8
shows a comparison of the phase-averaged non-dimensional vorticity magnitude (
) between the single propeller and side-by-side propellers computed by phase-locked PIV surveys performed at blade azimuthal angle
for both advance ratios tested.
The flow features in the upper propeller wake are characterised by consistent tip vortex structures that were periodically issued by rotating blades (i.e., identified by numbered yellow capital letters in the figures). As expected, the number of tip vortices captured by the PIV investigation window for the low advance ratio J
= 0.4 is doubled with respect to the high advance ratio J
= 0.8 due to the different freestream velocities dragging the vortices downstream (see Figure 8
a,c). As also shown by the flow surveys performed by Zhou et al. [5
] in hover for a similar test case and an equal separation distance between propellers, a wave-shaped flow structure related to the periodical shedding of lower propeller tip vortices is highlighted by the vorticity contour representation for the side-by-side propeller configuration at both advance ratios (see Figure 8
For the low advance ratio J
= 0.4, the vorticity field representation shows that the side-by-side interaction does not alter the vorticity magnitude of the vortices in the inner part of the upper propeller wake (i.e., vortices #A1 and #B1) while the tip vortices in the outer wake (i.e., vortices #C1 and #D1) are more diffused due to the interaction with respect to the single propeller test case (see Figure 8
a,b). Indeed, for the low advance ratio, the upper propeller wake was attracted and bent toward the adjacent side-by-side propeller. This interactional effect, particularly apparent in the outer region of the wake, provides a higher diffusion of the tip vortices in this region. Nevertheless, the vortex structures for the test cases characterised by a low wind tunnel freestream velocity do not loose their coherence, different from the results in Zhou et al. [5
] in the hover condition. For the high advance ratio J
= 0.8, the effect of the side-by-side interaction on the upper propeller wake is negligible both in terms of vorticity magnitude level and core displacements of the tip vortices (see Figure 8
c,d). Due to the higher freestream velocity that characterises the test case at J
= 0.8, the vorticity magnitude level observed for the tip vortices is higher than the one evaluated for low advance ratio test cases (i.e., J
= 0.4). Moreover, the vorticity contour representation clearly shows the presence of pairs of shear layers generated by merging the boundary layers from blades upper and lower surfaces. No interactional effects on vorticity sheets can be observed for both advance ratio test cases considered by the wind tunnel campaign, as shown by the negligible differences of their topology observed between a single propeller and the side-by-side propeller test case.
In order to quantitatively evaluate the effect of a side-by-side interaction on wake boundaries, Figure 9
shows a comparison of the tip vortex core displacements for both advance ratios tested. The vortex core positions were evaluated in correspondence with the peaks of vorticity magnitude [19
]. The vortex core positions were plotted for all phase-locked blade positions considered by PIV measurements, i.e.,
. A maximum displacement of the vortex core position below 1% D was found both in the horizontal and vertical directions by considering the instantaneous flow fields collected for each phase-locked measurement. These small displacement values were found to be common for both single and side-by-side propeller configurations, thus slightly affecting the following discussion concerning wake boundary comparisons.
As previously indicated by the ensemble-averaged PIV results, for the lower advance ratio test case, Figure 9
a shows a quite apparent expansion of the upper propeller wake boundary profile in the side-by-side configuration with respect to the single propeller test case. In particular, for this advance ratio, the wake boundary profile resumes almost the same single propeller profile behavior in the inner region up to
= 0.1, while an 8% propeller diameter increase in the wake boundary is observed downstream from the propeller disk at
= 0.8. On the other hand, for the higher advance ratio tested, the wake boundary profiles of the single and side-by-side propeller show the same pattern, confirming the negligible effect of this interaction on the wake topology at fast cruise speed. Generally, the wake dragging effect provided by the influence of the flow field generated by nearby propellers is reduced by increasing the flight speed. This result is consistent with the outcomes of the PIV surveys performed by Zhou et al. [5
] in the hover condition, showing a higher dragging effect due to the aerodynamic interaction.
Detailed insight on the flow physics characterising side-by-side interaction can be achieved from the comparison of the contours of the phase-averaged non-dimensional three velocity components (u
) shown in Figure 10
and Figure 11
measured at blade azimuthal angle
for both advance ratios tested.
The freestream velocity component representation of the flow field clearly highlights the presence of the tip vortices issued by the upper propeller rotating blade and the wave-shaped wake boundary provided by the lower side-by-side propeller. The freestream velocity component variations with respect to flight speed (
) provided by the rotating blades inside the propeller wakes are lower for the test case with a higher advance ratio (J
= 0.8). In order to quantitatively investigate the effect of the lower propeller on the upper propeller tip vortices, Figure 12
and Figure 13
show a comparison of the freestream velocity component profiles extracted in correspondence with the tip vortex core locations (
), evaluated as in Figure 9
, for blade azimuthal angle
. The standard deviations in the velocity components computed considering the instantaneous flow fields collected during phase-locked measurements were added as error bars on the velocity profiles.
For the lower advance ratio test case J
= 0.4, the comparison of the freestream component velocity profiles extracted in the inner wake of the upper propeller at tip vortex core location #A1 shows that the aerodynamic interaction of the nearby propeller produces an increase of the lower peak of velocity value with respect to single propeller case, while the slope of the profiles remains unaffected (see Figure 12
a). The error bars among the vortex region and particularly around the lower peak are similar for both single and side-by-side propellers, thus confirming the findings concerning interactional effects in this area. The velocity profile for the side-by-side configuration approaches a lower value of the freestream velocity
outside the wake boundary of the upper propeller, while a large positive variation in u
velocity is experienced while going through the lower propeller wake boundary, where also an increase in the velocity standard deviation is observed with respect to the single propeller test case. The analysis of velocity profiles extracted at the tip vortex core positioned downstream of the upper propeller disk shows that the nearby propeller aerodynamic interaction produces a decrease in both the peak-to-peak velocity values and the curve slope with respect to the single propeller test case. This effect increases for tip vortices further downstream from the propeller wake (see Figure 12
b,c,d for vortices #B1, #C1, and #D1, respectively). Consequently, due to the side-by-side interaction, the tip vortices in the outer wake of side-by-side propellers are characterised by lower circulation and a lower vorticity level with respect to the single propeller test case. Nevertheless, a slightly higher standard deviation of the velocity is observed among the outer vortices region (i.e., #C1 and #D1) for the side-by-side propeller. Thus, the interactional effect concerning vorticity level could be affected by the higher level of unsteadiness observed in this flow region. Moreover, the velocity profiles extracted towards the outer propeller wake approaches the freestream velocity value
outside the wake boundary of the upper propeller more rapidly, while the amplitude of the positive variation in the u
velocity experienced through the lower propeller wake boundary remains almost the same.
For the higher advance ratio test case J
= 0.8, the comparison of the freestream velocity component profiles extracted at tip vortex core locations, i.e., #A2 and #B2, shows negligible effects for the nearby propeller aerodynamic interaction. Indeed, the profiles extracted for the side-by-side propeller configuration through the vortex core resemble both the peak-to-peak velocity values and slopes of the curves observed for the single propeller test case (see Figure 13
a,b). This behavior is consistent with the similar vorticity magnitude observed in Figure 8
c,d for the single and side-by-side propeller configurations. Additionally, in this case, the error bars for the side-by-side propellers are slightly higher among the vortex region with respect to a single propeller, confirming a higher unsteadiness level for the interaction. Nevertheless, the main finding concerning negligibility of the interactional effects for the fast cruise speed should not be affected. Moreover, for both tip vortices #A2 and #B2, the velocity profiles rapidly approach the freestream velocity value
in the flow field region between the side-by-side propeller wake boundaries, while as previously anticipated, the positive variation in the u
velocity experienced by the lower propeller wake boundary has a lower amplitude with respect to the test case at a lower advance ratio. Additionally, for the higher advance ratio, an increase in the velocity standard deviation is observed for the lower propeller wake boundary.
The comparison of vertical velocity component v
contours shown in Figure 10
c,d and Figure 11
c,d clearly indicates that, for both advance ratios tested, the side-by-side aerodynamic interaction provides negligible effects on this variable. Indeed, no effective variations in the vertical velocity component v
can be observed inside the upper propeller wake boundary, while a slight positive variation in this velocity component is appreciable for J
= 0.4 in the lowest part of the PIV investigation area, locally related to the lower propeller wake boundary region (see Figure 10
d). Thus, a quantitative comparison of the v
velocity profiles at tip vortex cores locations is not presented for the sake of consistency.
On the other hand, the comparison of the out-of-plane velocity component w
contours presented in Figure 10
e,f and Figure 11
e,f, clearly shows, for both advance ratios tested, a region with remarkable positive w
velocity in the lower propeller wake boundary related to the swirl provided by propeller blade rotations. In particular, a higher positive value of w
is observed in this flow region for the lower advance ratio tested. Moreover, for J
= 0.4, a more pronounced effect on the out-of-plane velocity can be observed on the upper propeller tip vortices due to the nearby lower propeller rotation (see Figure 10
f). In order to achieve a quantitative evaluation on the side-by-side aerodynamic interaction on the out-of-plane velocity component, Figure 14
and Figure 15
show a comparison of the w
velocity component profiles extracted in correspondence with the tip vortex core locations (
) for both advance ratios tested. In particular, for J
= 0.4, the velocity profiles extracted for the two intermediate tip vortices only, i.e., #B1 and #C1, are presented, as analogous findings can be deduced from the analysis of the outer tip vortices captured by the PIV investigation area.
For the lower advance ratio test case J
= 0.4, a comparison of the out-of-plane component velocity profiles shows that the aerodynamic interaction of the nearby propeller produces a reduction in the negative w
velocity peak value with respect to the single propeller case in the upper flow region of both the #B1 and #C1 vortices (see Figure 14
a,b). An opposite effect is observed in the lower flow region of vortex #B1, while the flow region the between side-by-side propeller wake boundaries is characterised by an almost null out-of-plane velocity. The standard deviations of the out-of-plane velocity assume almost the same values throughout the vortex region, thus slightly affecting the main findings concerning side-by-side interactional effects.
For the higher advance ratio test case J
= 0.8, the w
velocity profiles for the upper propeller tip vortex core is quite similar between the side-by-side and single propeller configurations. A slight increase in the positive peak of the w
velocity is observed for vortex #B2 due to a nearby propeller interaction (see Figure 15
b). Analogous to what was observed for the free-stream velocity profile comparison showing higher unsteadiness among the vortex regions for the higher advance ratio, the error bars for the side-by-side propellers are slightly higher with respect to a single propeller, thus indicating that the small effects observed for the out-of-plane velocity profiles due to the interaction should be negligible. Moreover, also for the out-of-plane velocity component, the positive variation experienced by lower propeller wake boundary is lower at J
= 0.8 with respect to the test case at a lower advance ratio.