3.1. Flow Visualization Results
To study the full range of potential flight conditions, experiments are run for
—varying from 1 m/s to 5 m/s in 1 m/s increments—and the Reynolds number based on the propeller tip (
, where
denotes the angular velocity of the rotors (rad/s),
represents the rotor radius,
is the rotor chord, and
is the kinematic viscosity of air) is varied from 3 × 10
4 to 8 × 10
4 in increments of 10
4. In the case of forward flight, the advance ratio is also commonly used to delineate the flow regimes as it considers the forward flight speed and rotor speed simultaneously where the advance ratio is
, where
is the rotations per second of the propeller. The advance ratios that correspond to the experimental flight conditions are 0.04
0.54. For the results shown in
Figure 3 and
Figure 4, the red arrow indicates the direction of
while yellow arrows highlight and draw attention to significant flow features.
Considering low
and moderate to high
Retip values (low advance ratios), it can be seen in
Figure 3 that the rotor wake dominates the flow, resulting in large disturbances below the multi-rotor UAV.
Figure 3a shows the wake below the multi-rotor UAV with
= 1 m/s and
Retip = 8 × 10
4 (
= 0.04) which is the combination of the lowest simulated flight speed and highest rotor speed. This low
and high
Retip results in strong jets being expelled from the front rotors, beneath the multi-rotor, which extend to the tunnel wall, initiating wall effects that indicate this configuration is beyond the limit of the experimental configuration. As the rotor speed is reduced to
Retip = 5 × 10
4, (
= 0.06), as shown in
Figure 3b, there is still a noticeable jet from the rotors, but
decreased considerably and is well above the tunnel wall. Furthermore, the angle
that the wake propagates from the front rotor is noticeably greater for the
= 0.04 condition. As the advance ratio increases to
= 0.06,
decreases and
decreases. In each of the cases, the streamlines are deflected as they are pulled into the rotors and there is a disturbance that extends slightly above the UAV. The disturbance looks minimal, especially in comparison to
, but warrants its own investigation in which the FOV of the experiments is focused on the top of the multi-rotor UAV.
For flight conditions characterized by high flight speed, presented in
Figure 4, the influence of the rotors is much less discernable than in the previous figure where low freestream speed was considered.
Figure 4a,b present the wake from the multi-rotor UAV operating when
= 5 m/s and
Retip = 3 × 10
4 (
= 0.54) and
Retip = 8 × 10
4 (
= 0.20), respectively. In both cases, the bottom streamline remains minimally disturbed and continues parallel to the background flow. Although the advance ratio is significantly decreased, there is not a large discrepancy in the wake characteristics in
Figure 4b compared to
Figure 4a. The increase in rotor speed slightly increases
of the wake expelled from the rotors and minimally affects
. Aside from these differences, the wake in the two cases is similar.
As previously discussed, and from what can be seen in
Figure 3 and
Figure 4, changes in
and rotor speed,
Retip, have a clear impact on both
and
.
Figure 5 shows how
and
are affected as
is varied for selected values of
Retip. Error bars are provided in both figures based on an estimated 10-pixels of uncertainty (
) in the vertical measurements for the determination of
and
, and 2-pixels of uncertainty in horizontal measurements as they are easier to obtain. For these uncertainties, a measurement of
was used to determine that for a 12 MP camera, each pixel equals 1.53 mm. Similar trends are observed for both
and
as
is simply the angle between
and
, the diameter of the multi-rotor UAV. As the
Retip is increased—in other words, as the rotor speed increases—for a constant
there is an increase in
and
. There is much greater sensitivity to
in the measurement of
due to the 10-pixel uncertainty for lower
as
increases. As
is increased, the disturbance distance is reduced, and the wake is expelled from the front rotors at a shallower angle.
and
are omitted for
Retip values when
is extended beyond the illuminated FOV or clearly interacted with the tunnel wall.
The results from all of the flow visualization experiments are shown in
Figure 6. Each forward flight speed, 1–5 m/s in 0.5 m/s increments, is considered with varying
Retip values, 3 × 10
4–8 × 10
4 in 1 × 10
4 increments, leading to an advance ratio range of 0.04–0.54. The disturbance distance below the multi-rotor,
is shown in
Figure 6a for different freestream speeds under consideration with varying
Retip values with error bars, again based on 10-pixel uncertainty. Clearly, as
is increased, the distance the wake disturbance propagates below the multi-rotor UAV decreases. As expected, as the rotor speed is increased, the disturbance distance increases. The error bars presented in
Figure 6a are small compared to the overall scale of the plot being presented. The 10-pixel uncertainty under consideration is almost negligible when considering the full scale of
observed over the full range of advance ratios. As the
is increased,
is substantially reduced, as seen in
Figure 6b. Alternatively, as the rotor speed is increased for a constant
,
increases but is not as sensitive as in the case of a change in
. Furthermore, at
2.5 m/s,
approaches a constant value that is dependent on
Retip. The errors in the jet angle are more considerable at low jet angles, as seen previously, but for the higher jet angles, the 10-pixel uncertainty is rather negligible. The trends seen in
and
are strikingly similar as expected given
In both cases, different combinations of freestream speeds and rotor speeds result in similar outcomes which indicates that
is dependent on the ratio of freestream speed to rotor speed, which is taken into account in the advance ratio.
The dependency of
and
on the advance ratio is clearly seen in
Figure 7 where the results from
Figure 6 of several experiments with varying
and
Retip collapse to a single curve that predict
and
as a function of
. In
Figure 7a, as
increases,
sharply decreases from the maximum value of 10
for
0.1 and approaches 2.5
for
0.2. From the data, a function for the disturbance distance as a function of the advance ratio,
, is considered and shown in solid black in
Figure 7a. This data fit can be used to influence sensor placement or predict potential proximity effects. A similar trend is observed in
Figure 7b, where
decreases from a maximum value of 75° for low
and approaches a constant of ~10° for
0.2. In both figures, as the advance ratio exceeds 0.2, further increases do not yield as drastic of a change in either the
or
, as was indicated in
Figure 4. Error bars are omitted in
Figure 7 for clarity as they make the results difficult to see and have been shown previously.
In addition to below the multi-rotor UAV’s body, during forward flight there is also a disturbance above the body as depicted in
Figure 8a,b which show flow visualization above the UAV for
= 1 m/s and
Retip = 3 × 10
4 (
= 0.11) and
Retip = 8 × 10
4 (
= 0.04), respectively. In each case, there is a deflection of the streamlines closest to the multi-rotor UAV as the freestream flow is pulled into the rotors. At the lower rotor speed,
Figure 8a shows that although all of the streamlines above the vehicle are affected, in comparison to a higher rotor speed as shown in
Figure 8b, they are less modified.
As the flight speed increases, the rotors have less of an effect on the flow above the multi-rotor UAV which can be seen in
Figure 9a,b where
Retip = 8 × 10
4 and
is increased to 3 m/s (
= 0.12) and 5 m/s (
= 0.20), respectively. At
= 0.20, only the nearest streamline to the multi-rotor UAV is significantly deflected into the rotors. Additionally, the upper streamline within the FOV remains nearly parallel to the background flow, showing little signs of modification caused by the rotors. This shows that, even at high rotor speeds,
is able to dominate the flow and the flow above the UAV remains relatively unaffected. A preliminary conclusion that can be drawn from this is that above the multi-rotor UAV is the optimal location for integration of in-situ instrumentation, especially when the unmanned vehicle is operated at
0.20.
The distance above the multi-rotor vehicle where the flow returns to
,
can be estimated from the flow visualization results. In
Figure 10a,
, is plotted versus
for three
Retip considerations. It should be noted that
< 1.5 m/s is not presented in the plots as
extends beyond the illuminated FOV and an accurate estimation of disturbance distance cannot be obtained. Low values of
result in measurable disturbances at distances of up to 8
above the multi-rotor, even for low
Retip. As
is increased,
decreases for each
Retip and approaches a constant value as it becomes independent on
.
Figure 10 shows the trend of
versus both
and
Retip, with 10-pixel uncertainty error bars. As
Retip is increased,
increases for a constant
, which is expected as more of the incoming flow is pulled into the rotors. As previously mentioned,
and
Retip can be simultaneously described through the advance ratio,
.
Figure 10c depicts
versus the
where as
is increased,
is decreased and approaches a constant value of approximately 3 for
0.35. The disturbance distance above the multi-rotor UAV can be expressed as
, shown as a black solid line in
Figure 10c. As previously mentioned, this expression can be used to determine where to place in-situ instrumentation and predict proximity effects on a multi-rotor UAV.
Table 1 presents the values for
Lb/R and
La/R at
J = 0.10 and
J = 0.55, in addition to the range of the disturbance distances over this range of advance ratios, based on the expressions derived from the flow visualization data. At low advance ratios, there is a greater disturbance predicted above the multi-rotor UAV which more rapidly reduces. At high advance ratios, the disturbance distances above and below the multi-rotor vehicle are relatively similar, resulting in a larger range for
La/R. Clearly, the disturbance distance above the multi-rotor UAV is more sensitive to changes in the advance ratio. Additionally, if in-situ instrumentation is to be integrated onto the multi-rotor, it should be placed well outside of the wake and the UAV should be flown at high advance ratios to avoid corrupting data collected by the instrumentation.
3.2. PIV Results
Based on the results from the flow visualization experiments, it is clear that both
and rotor speed (
) have large impacts on multi-rotor UAV rotor–wake interactions and the corresponding disturbance distances (
). The effect of each of these parameters is captured through advance ratio, therefore 10 advance ratios are considered for PIV testing. Since PIV experiments are more resource intensive—including setup, experimentation, and data processing—a range of advance ratios similar to the considered flow visualization parameters are considered in order to capture a wide array of flight conditions.
Table 2 shows the considered advance ratios and the corresponding wind tunnel and rotor speeds. The advance ratios encountered during operation are dependent on the design and the mission; however, the presented range of advance ratios can be used to inform designers and users in addition to being used to obtain a general understanding of wake propagation in forward flight.
Unlike flow visualization, to obtain high-resolution quality PIV results, the size of the FOV is much more limited. Based on this, results from the flow visualization experiments are used to determine the optimal FOV location for the PIV experiments.
Figure 11a,b shows the FOV designated by the red box for forward flight PIV experiments that was focused below and above the body of the multi-rotor UAV respectively. Both FOVs are selected to capture the detailed flow field in the vicinity of the body.
As can be seen from
Table 2, higher advance ratios are generally achieved in the experiments with higher
(flight speed) while keeping
relatively constant, which results in
dominating the flow around the body of the UAV, while at lower advance ratios, the rotor jets tend to dominate the flow and there is considerable disturbance that extends beneath it. As
increases, the rotor jets become less dominant and
is reduced.
Figure 12a shows the PIV results below the multi-rotor UAV for
= 0.09 and a jet is clearly visible that is expelled from the front rotors. Due to the limited extent of the FOV, the location where the flow returns to
cannot be determined. In addition, there is an evident recirculation zone directly beneath the body of the multi-rotor UAV which was not visible from the flow visualization experiments. As
is increased to 0.24, as shown in
Figure 12b, there is still a clear area of elevated velocity below the multi-rotor, but the rotor jet observed in
Figure 12a is much less discernable and is more reminiscent of bluff body flow. In this case, the flow within the FOV approaches the inlet state farther away from the multi-rotor, but streamlines throughout the FOV are modified by the rotor wake, although minimal at the outer extent. Lastly, at
= 0.54, as depicted in
Figure 12c, the flow further resembles bluff body flow with a clear deficit near the multi-rotor, surrounded by a shear layer, and then the flow returns to
at
~ 0.
. In summary, when multi-rotors are operated at higher advance ratios, in situ instrumentation can be mounted closer to the body (as low as around 0.8
for the extreme case of
= 0.54) and the chance of ground effect on the vehicle is greatly reduced.
Below the multi-rotor UAV, as shown in
Figure 12, the flow exhibits drastic velocity changes throughout the FOV that are associated with the interaction of the rotor jets with the background flow.
Figure 13a shows the vertical velocity,
at
x = 92 mm, for varying
. This location is selected as it is in the center of the multi-rotor UAV, which is the ideal location for stability for most in-situ sensors. At higher advance ratios,
is not significant. Alternatively, low advance ratios show significant deviations in
that trends towards 0 as the distance from the multi-rotor UAV increases. In particular, the
= 0.09 case exhibits
0 in the recirculation zone seen in
Figure 12a and then passes through a shear layer at
~−1 at which point
0 in the rotor jet region. This case is somewhat unique in that is the only
that has a recirculation zone.
Figure 13b shows the horizontal velocity,
versus the vertical distance from the multi-rotor,
, for varying
, at the same location
= 92 mm. Once again, low
cases exhibit complex flow behavior characterized by an extended region of velocity deficit directly below the multi-rotor UAV followed by strong shear and the formation of a horizontal jet where the flow is accelerated before returning to the background flow conditions. As
approaches 0.24, the flow converges to a
profile that has a clear velocity deficit immediately below the multi-rotor UAV that extends downward 0.5
before approaching a constant of
throughout the remainder of the FOV. This may be a result of blockage in the tunnel or could be a consequence of the limited FOV in the PIV experiments. Experiments run in an open tunnel environment or CFD simulations could prove useful in determining the true reason for this phenomenon.
As mentioned previously, alongside the obvious disturbance below the multi-rotor, there is a more subtle modification of the flow above the multi-rotor UAV as air is pulled into the rotors. Although this was observed in the flow visualization, PIV is required to obtain detailed observations of the flow field in the vicinity of the multi-rotor UAV. To accomplish the PIV measurements, the multi-rotor vehicle is mounted upside down in the tunnel test-section to provide sufficient laser illumination of the FOV. For low advance ratios such as
= 0.09, as presented in
Figure 14a, the streamlines are deflected throughout the FOV. As
is increased to 0.24, as shown in
Figure 14b, the streamlines within the FOV are not as significantly affected; however, they are still deflected throughout the FOV. For the extreme case tested in this study,
= 0.54, the flow returns to
at
~ 0.8
, as depicted in
Figure 14c. Near the multi-rotor, inconsistent and low velocity regions can be seen for all cases, but they become more prevalent as
increases. These low-velocity regions are not physical and are caused by reflections off of the motors and body of the multi-rotor UAV.
Flow visualization and PIV experiments show that below the multi-rotor UAV is a much less suitable location for integrated in-situ sensors compared to the top of the multi-rotor UAV. Furthermore, directly above the center of the multi-rotor UAV is an ideal location in order to minimize flow disturbance and maintain vehicle stability during operation. This does not suggest that the area above the multi-rotor UAV is absent flow disturbance, rather that it is minimized there. To obtain accurate velocity sensor data, the velocity components require correction as shown in
Figure 15a,b where
and
are plotted, respectively, for various
versus the vertical distance from the multi-rotor,
, at
x = 100 mm. In
Figure 15a, as
is increased, a drastic reduction in
is observed, further suggesting the multi-rotor UAV should be operated at higher
to reduce errors in in situ sensor velocity measurements. In this range of
0.24, for a given
,
is nearly constant over
making the velocity correction rather simple. At
0.24,
exhibits a stronger dependency on
and large gradients near the multi-rotor UAV. In contrast as shown in
Figure 15b,
is nearly constant throughout the FOV, differing by only around 5% in most cases with the exception of the
= 0.09 case which shows a significant deviation from
and high dependency on
. This deviation is likely due to a transition of regimes at
0.14, where the balance of momentum tips from the freestream towards the rotor jets.
PIV is able to provide quantitative data that are not obtained from running flow visualization experiments alone. The velocity profiles provided in
Figure 13 and
Figure 15 can be used to determine velocity correction factors for instrumentation integrated onto the multi-rotor vehicle. Although PIV provides useful information in the form of more accurate velocity measurements, its limited FOV is a clear drawback and indicates the usefulness of flow visualization experiments. The increased FOV of flow visualization experiments allows disturbance distances to be determined. If only PIV experiments were carried out, the disturbance distances could not be found as they are over 2
R below and above the multi-rotor UAV and would therefore not be contained in the PIV FOV. As they do not require post-processing and are easier to set up, flow visualization experiments can be carried out quicker and they do not require excessive storage space. In order to obtain disturbance distances from PIV experiments, more simulations would need to be run with varying FOVs to cover the full space that is captured through flow visualization. This would require an excessive amount of time and data to accomplish making it much less efficient than flow visualization techniques. As the results of the flow visualization and PIV are both useful, it is recommended to use both strategies to obtain disturbance distances over a large FOV while obtaining accurate velocity data near the multi-rotor vehicle which can provide velocity correction factors.