Quadcopters, hexacopters, and in-plane octocopters appear to dominate the current commercial and recreational markets for Vertical Takeoff Landing UAVs (VTOL UAVs). These configurations offer much higher flexibility in size and placement of rotors and payload when compared with traditional single rotor or coaxial rotor configurations. Research in electronics and controls in the past two decades has made such UAVs more reliable, safer, and easier to control in a variety of flight conditions. A recent paper by Gonzalez et al. [1
] gives an overview of types of UAVs, describes all the necessary subsystems with their importance, and also mentions a few present day applications. Floreano et al. describe the potential of small size UAVs to a great extent and cover all important current challenges on different fronts which need to be addressed, in their review paper [2
]. The authors rightly make an observation that aerial vehicles do not scale down well in terms of aerodynamic efficiency, affecting performance. Hassanalian et al. [3
] also talk extensively about classification, applications, and current challenges of UAVs. Some of the most common present day applications of small size VTOL UAVs are aerial photography, remote sensing, surveying, accident scene investigation etc.
The current aerodynamics knowledge in this small scale regime is limited to design and optimization of isolated rotors, with multirotor configurations being designed largely on an ad hoc basis. A good understanding of rotor-rotor and rotor-body aerodynamic interactions for multirotor UAVs is important for well-informed design optimization to push beyond the current performance limitations. Performance enhancements in endurance, range, payload and/or speed are crucial for utilizing drones in applications such as firefighting, rescue operations, EMS, organ transport, retail delivery and so on, which have potential to cause great socio-economic impact.
Knowledge and tools created over a span of about a century for helicopter rotors are not directly valid for most UAVs due to the huge difference in Reynolds number (Re) range. The approximations used in helicopter rotor theories are primarily based on the assumption that very high Re flows act mostly like inviscid, irrotational flows everywhere except in small regions containing high vorticity. Thin boundary layers and strong, tightly concentrated tip vortices, and thin vortex-sheet wakes are assumed in calculations that use the Blade Element, Prescribed Wake and Free Wake methods. Outside these thin regions of vorticity, the flow is presumed to be inviscid, irrotational and hence amenable to potential flow methods. At low Re, the effects of viscosity become more comparable to inertial effects. Hence helicopter rotor theories based on the above assumption of high Reynolds number cannot be expected a priori to give reliable predictions. To what extent can these methods be trusted, and how much do they affect predictions when there are multiple rotors in close proximity? These are the motivating questions behind the experimental research presented in this paper.
The prior studies relevant to the the problem can be separated into low-Re airfoils, low-Re rotors and large scale multi-rotor vehicles. In the area of low Re rotor, research so far has been on performance measurements, design, optimization, and CFD of micro aerial vehicle (MAV) scale rotors. Bohorquez and Hein [4
] contributed through hover performance tests, Kunz and Rubio [7
] through design and analysis, Lakshminarayan, Schroeder through CFD study [9
]. On the multirotor side, there are some experimental studies by Radhakrishnan [13
] and Ramasamy [14
], computational studies by Griffiths [15
], Gupta [16
], Lee [17
], Rajagopalan [18
], and Yoon [19
]. There have been a couple of aerodynamics studies on quadrotors as well in recent past. Huang et al. [20
] studied aerodynamics, blade flapping and controls of a quadrotor UAV in aggressive maneuvering. Carroll et al. [21
] worked on optimizing rotors for quadrotor arrangement for wake interference by a model using Biot–Savart rule. A more extensive literature review on the low-Re multirotor aerodynamics is covered in our prior papers [22
The current study continues our prior efforts to understand low Re multirotor flows presented in [22
]. The prior effort was focused on the special case of quadrotors and included flow visualization and performance measurements on a small size quadrotor setup. The present work is more generalized for use in any in-plane multirotor configuration. All in-plane multirotors can be interpreted as pairs of rotors placed side-by-side. Hence studying one pair of side-by-side rotors at a range of conditions should provide a fair idea about all possible in-plane configurations. The present study includes high-speed stereo particle image velocimetry and performance measurements on a setup comprising of two counter-rotating side-by-side rotors. Some instantaneous and mean flow field results are presented here for a range of test conditions along with analysis and discussion for use by UAV designers.
The rest of this paper is organized as follows: Section 2
describes test facility, setup, test conditions and estimated uncertainties in the measurements. Section 3
presents performance measurement and flow field results through PIV for all the test cases. The results are interpreted and discussed in Section 4
, highlighting differences and commonality in the cases through velocity profile plots and conceptual sketches.
Starting with the figure of merit plot in Figure 3
, it is seen than the 80k Re cases do not show any noticeable variation in FM over the range of axis shifts. However, the FM of 40k Re cases tends to increase slightly with increase in distance between the rotors. This slight increase for 40k Re cases too is significant only for AS ≤ 2.3R after which it is approximately similar to 80k Re cases.
Studying the instantaneous vorticity contour plots in Figure 4
, it is observed that the rotor tip vortices due to the two adjacent rotors interact with each other for small axis shift values. The tip vortices are seen to deviate from the trajectories expected in a typical rotor wake. They lose their coherent structure in about a rotor rotation and get split into small spots of high vorticity in the region between the rotor wakes. Very often, consecutive tip vortices from the same rotor are seen to roll about each other after getting disturbed from their trajectory by velocity induced by vortices from the neighboring rotor. The direction of vortex roll-up is same as the direction of vorticity in the vortices. These pairs of vortices eventually merge and then split into spots of high vorticity soon after.
Such wake interactions are relatively higher for 40k Re cases compared to 80k Re cases. With increase in axis shift, the trajectories of tip vortices tend to get more predictable and the region between rotor wakes become free of sporadic flow. Lesser wake interactions at higher axis shifts is in a way obvious and expected as velocity induced by vortices decay by a factor of square of distance outside the solid body rotation core area. The wake should in principle become like that of a single isolated rotor as axis shift tends to infinity. Figure 7
contains explanatory sketches for the instantaneous vorticity contour plots in Figure 4
, depicting behaviour of major wake features under a separate range of conditions.
The low Re cases see more wake interactions probably because the tip vortices are weaker in terms of circulation and the downwash convecting them downward is also low. These slow moving vortices with low circulation are more vulnerable to velocities induced by flow features in close proximity such as vortices from the neighboring rotor. At high Re (and hence higher thrust values), the vortices are stronger and they also get lesser time to get affected by other disturbances due to stronger downwash. The relative strength of vortices can be judged by comparing vorticity magnitudes in the instantaneous vorticity contour plots. The time-averaged rotor outflow velocity gradient near the rotor tip is apparent through the plots in Figure 6
, which is also indirectly indicative of the vortex strengths in the two Re cases.
Similar observations were made regarding relatively higher wake interactions for low Re cases in the previous work on quadrotor [23
] where the Re 8630 test case (1280 RPM) showed significantly higher wake interactions compared to Re 16,856 case (2500 RPM) as seen in the Figure 8
. The FM for the lower Re case was also much lower than the other two higher Re cases (see Table 2
) just like it is in the current study where the FM is lower for 40k Re cases at low AS. It is possible that the low rotor performance at small axis shifts at low Re is because of flow that is induced over the blades by interaction with tip vortex cores of the adjacent rotor. Tip vortex cores are known to be larger in size for low Re rotors [25
]. If interactions of rotor blades with adjacent rotor tip vortices is a factor, then phase difference between the rotors should also play an important role in performance. Verifying that will need a setup where the rotors are mechanically linked to allow locking their phase with respect to each other.
Comparing FM data of the current bi-rotor tests in Figure 3
with those from the previous tests on quadrotor in Table 2
, it can be noticed that rotors in the current tests perform worse than the quadrotor rotors despite being operated at a much higher Re. The biggest difference between the two setups (other than size) is blade geometry (which is described in the Table 3
). The blades used in the current setup are symmetric and more like those for large scale helicopters whereas the quadrotor blades are highly cambered. Such highly cambered blades are ideal for low Reynolds number rotors only where the viscous skin friction drag is high enough to afford highly cambered airfoil designs which otherwise would have caused a much larger share of pressure drag.
It is noticed from the streamline plots in Figure 5
that the mean rotor wakes from the two rotors tend to stay farther away from each other for 80k Re cases hinting towards lower wake interactions at higher Re apparent from the instantaneous vorticity contour plots as well. As the Axis shift increases, the flow around the rotors slowly tend to be similar to that expected for an isolated rotor, with 80k Re cases leading the change. The streamline plot for Re 40k, AS = 2.1R is noticeably different from the rest. The first plot shows high velocity magnitudes in the region between the two rotor wakes due to inter-rotor wake interactions, and the streamlines in the last plot (Re 40k, AS = 2.4R) are as if results from two isolated rotors are put side-by-side. All other cases in between show how the interactive rotors evolve with axis shift and Re into two isolated rotors in terms of mean flow.
The inflow and outflow profile plots in Figure 6
contain some common features among cases. Outflow profiles under both rotors are wedge-shaped with velocity magnitude increasing while going from rotor hub to tip, and dropping back to zero steeply right before the tip. The peak in outflow velocity profile is consistently found close to r = 0.9R span-wise location for both rotors for all cases except Re 40k AS = 2.1R where it is seen to be slightly inboard (close to the hub). Such a wedge-shaped feature is common for most rotors, especially if the blades are simple rectangular blades like the ones in this study. As mentioned earlier, inflow and outflow profiles provide an estimate of thrust generated by different sections of rotor, and hence their shape is dependent on rotor blade geometry (taper and twist). Inflow velocity profiles peak around r = 0.75R (and slightly inboard for Re 40k AS = 2.1R case). The outflow velocity profile peaks are much sharper than the inflow velocity peak due to sudden thrust drop near blade tip and the resultant tip vortices.
It should be noted that the velocity profiles, which are non-dimensionalized using rotor tip speed, are almost exactly same for the two Re for AS = 2.2R, 2.3R, and 2.4R. This may mean that at least in this Re range, Re does not have any significant effect on the way inflow and and outflow velocities get induced when the rotors are farther than 2.2R. Out of the two cases on the AS = 2.1R plot, the 80k Re curves still look similar to the other axis shift cases but the 40k Re plots have higher upward directed inflow and outflow velocities between the rotors. But for all cases within the range, it should be possible to come up with a rough estimate of the velocity profiles, and hence span-wise thrust distribution on side-by-side rotors based on the presented results. Figure 9
is a sketch of a typical side-by-side rotor inflow and outflow velocity profiles based on the mean velocity profiles for the test cases presented in Figure 6
The information on outflow or downwash velocity profiles is also instrumental in deciding on fuselage and payload placement under a UAV while designing it. The objective being to minimize download on the rest of the structure and payload from the rotor downwash to reduce rotor thrust lost in internal force.
The interactions between wakes of two side-by-side rotors as a function of distance between the rotors and their Re were looked at from instantaneous as well as mean flow field perspective in this study. A dip in performance was observed for cases with rotors very close to each other at low Re. It was hypothesized that the interaction of rotor blades with the tip vortex cores of the neighboring rotor blades at small axis shifts could be a reason for the effect on efficiency. However, more focused tests are needed to confirm this. The instantaneous flow field measurements indicated high inter-rotor wake interactions for small axis shifts causing rotor wake features to distort, lose coherent form and deviate from their typical trajectories.
The time-averaged streamline and inflow–outflow velocity profiles brought out commonality among the range of tests in this study. Prominent instantaneous flow features and mean velocity profile traits were identified for the test cases which are expected to guide rotor wake and performance estimates on a wider range of vehicle designs and flight conditions.
Briefly summarizing the key findings:
Very close proximity of adjacent rotors adversely affects rotor performance
Blade–vortex interaction hypothesized to be a reason behind the noticed effect on performance.
High inter-rotor wake interaction observed for close proximity rotors at low Reynolds numbers.
Similarities observed in instantaneous and mean flow fields for the range of tested conditions, useful in extending the understanding to a wider range of vehicle configurations.