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Research Papers: Flows in Complex Systems

Drone Scale Coaxial Rotor Aerodynamic Interactions Investigation PUBLIC ACCESS

[+] Author and Article Information
Dhwanil Shukla

School of Aerospace Engineering,
Georgia Institute of Technology,
Atlanta, GA 30318
e-mail: dhwanil.shukla@gatech.edu

Narayan Komerath

Professor
School of Aerospace Engineering,
Georgia Institute of Technology,
Atlanta, GA 30318
e-mail: komerath@gatech.edu

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received August 31, 2018; final manuscript received November 27, 2018; published online January 7, 2019. Assoc. Editor: Timothy Lee.

J. Fluids Eng 141(7), 071106 (Jan 07, 2019) (10 pages) Paper No: FE-18-1574; doi: 10.1115/1.4042162 History: Received August 31, 2018; Revised November 27, 2018

Coaxial rotor uninhabited aerial vehicles (UAVs) are compact compared to single rotor UAVs of comparable capacity. At the low Reynolds numbers (Re) where they operate, the simplifying assumptions from high Re rotor aerodynamics are not valid. The low Re coaxial rotor flowfield is studied including aerodynamic interactions and their effect on performance. The evolution of the wake is captured using high-speed stereo particle image velocimetry (SPIV). Improvement of upper rotor performance due to viscous swirl recovery from the lower rotor is discovered and then verified by analyzing PIV data. Interesting vortex–vortex sheet interactions are observed under the coaxial rotor affecting wake structure spatially and temporally. A qualitative model explaining the observed wake interaction phenomena is presented. Comparison with the performance of high Re rotors shows higher profile and induced drag at low Re for the same thrust coefficient.

FIGURES IN THIS ARTICLE
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Coaxial rotor vehicles were first developed in the early 1900s but did not gain as much popularity as single main rotor vehicles due to mechanical complexities. Nevertheless, numerous theoretical, computational, and experimental studies continued over decades. For instance, Harrington [1] and Dingeldein [2] did performance tests on coaxial rotors in the 1950s in the Langley full-scale wind tunnel. Nagashima and Nakanishi [3] studied coaxial rotor wake geometry, and a relatively recent experimental work by Sunada et al. [4] aimed at maximizing thrust-torque ratio. Saito and Azuma [5], Andrew [6], and Zimmer [7] have attempted to model coaxial rotors computationally. Bagai and Leishman [8] used free wake model to study tandem, tilt-rotor, and coaxial rotor configuration.

Recent advancements in electronics, control systems, and wireless communications have made it possible to create small uninhabited aerial vehicles (UAVs) which have quickly found numerous applications. Coaxial rotor UAVs are the most common after quadrotors. Small UAV designers struggle to obtain satisfactory performance due to energy storage and aerodynamic inefficiencies. Better understanding of the flow field around small low Re coaxial rotors is postulated to enable improvements. Design analyses of large co-axial rotors use simplifying assumptions from aerodynamics at high Re such as neglecting viscous effects away from flow boundaries and assuming thin vortical layers. These are not valid in the low Re, and a primary question in our research is the effect of such features on the flowfield and performance.

In the low Re regime, there have been efforts to come up with optimal low Re airfoil design such as those by Lei and He [9]. A recent work on understanding three-dimensional flow over wings at low Re by Karasu et al. [10] focused on evaluating models for laminar to turbulence transition by comparing the computational results with experiments. Flow separation and stability of shear layer over airfoils is an important factor determining rotor performance. Ziadé et al. [11] investigated shear layer development at low Re experimentally and computationally. Boukenkoul et al. [12] showed significant delay in flow separation over a low aspect ratio wing at low Re, commonly found in micro-air vehicles, by using a moving belt on wing surface for flow control.

Jang et al. [13,14] and Guilmineau et al. [15] studied wake of propellers which share some similarity with helicopter rotors in terms of wake structure. The previous low Re single rotor studies such as those by Ramasamy et al. [16,17] have shown that the vortex core size, trailing edge vortex sheet size, and structure differ significantly from higher Re rotors. This can be compared against the high Re vortex stereo particle image velocimetry (SPIV) data by Krane et al. [18] taken at Garfield Thomas Water Tunnel at Penn State. The differences in rotor wake cause rotor to rotor and rotor to fuselage aerodynamic interactions in low Re coaxial rotors to be different in nature compared to their high Re counterparts.

In our exploratory work on low Re coaxial rotor covered in Ref. [19], some interesting results such as higher than expected figure of merit (FM) of the upper rotor and alternating lower rotor vortex trajectories were reported. While doing performance measurements on high Re rotors at varying vertical separations, Ramasamy [20] mentions the possible role of swirl recovery in improving coaxial rotor performance, stating that there are no known direct or indirect measurements to validate the hypothesis. Later, Brazinskas et al. [21] report 4% improvement in coaxial rotor efficiency due to swirl, which was estimated by comparing performance of a counter-rotating coaxial rotor with that of a co-rotating coaxial rotor. However, there is no mention of the effect of swirl on upper rotor performance in either of these high Re coaxial rotor studies. On the coaxial rotor flow visualization side, Ma et al. [22] studied vortex models, vortex size, and trajectories for a high Re rotor setup in a water tunnel but without performance measurements.

This work aims to address the gap in understanding the physics behind the upper rotor in a low Re coaxial rotor system performing better than a single isolated rotor (as first observed in Ref. [19]), and discovering flow features in low Re coaxial rotor wake for use in computational model building and vehicle design. Performance and high-speed stereo PIV measurements were made on a coaxial rotor setup at two vertical separations at three Re. The paper contains performance data on individual rotors of coaxial system and instantaneous as well as mean high-speed SPIV results. The time-resolved SPIV data and vortex traces help visualize the evolution of the wake and interactions of various prominent flow features. A qualitative vortex–vortex sheet interaction model based on careful observation of hundreds of instantaneous velocity fields from all test cases is also presented here. The model explains dynamics of these coherent structures in the wake. Rotor inflow, rotor outflow, and swirl velocity computations for all test cases are useful in understanding coaxial rotor performance from a momentum perspective.

Facility and Diagnostics.

The coaxial rotor experiments were performed in the John J. Harper memorial wind tunnel at Georgia Tech. The low speed wind tunnel's test section is 2.13  m × 2.74  m (7  ft × 9  ft). The high-speed PIV system for flow diagnostics consisted of two Phantom v341 cameras, a dual head Nd:YLF Photonics (USA) laser (DM30-527), LaVision hi-speed programmable timing unit (PTU-X). and DaVis 8 imaging software. Other equipment included two laser tachometers for feedback based motor speed control, an microcontroller, signal conditioners, and a National Instruments data acquisition (DAQ).

Test Setup.

The test setup used here is identical to that described briefly and used in our previous study [19]. A more detailed description follows. The coaxial rotor setup is composed of two almost identical two-bladed single rotor modules. The upper rotor was suspended from the wind tunnel ceiling, whereas the lower rotor was held from the wind tunnel floor, both using aluminum rods to place the rotors approximately at the center of the test section. The support rods were in-line with the motor and rotor axis to avoid them interacting with the rotor wake. One-kilogram force thrust sensing load cells were also placed on the other end of the rods (away from the rotors) for the same reason.

The rotors were powered by brushless direct current (BLDC) motors run by electronic speed controllers. The rotor speeds were maintained within ±10 rpm of the set values using a microcontroller implementing stepwise proportional control. The microcontroller got speed feedback from the two laser tachometers pointing at the two rotors. The collective pitch on both the rotors could be adjusted independently during test runs through variable pitch assemblies installed on the BLDC motors actuated using servo motors. The servo motors also got their command from the microcontroller. The rotor blades used here are from an off-the-shelf UAV (BLADE mCP-X BL) with simple blade planform and rotor radius in the range of most commercially available multirotor UAVs.

For the torque measurements, the motor mounts were mounted on the rods through friction-less bearings. The rotation about the bearings was restricted by 0.1 kgf load cells placed off-center. This way the counter torque necessary to keep the motor mount from rotating about the bearing due to aerodynamic torque was provided through the 0.1 kgf load cells, indirectly measuring the torque on the rotors. The torques due to frictional losses in the motors and the variable pitch assemblies are internal to the mounts, and hence, they do not contribute to the reading obtained through the arrangement.

All four load cells (two for thrust and two for torque) were provided with a regulated power supply from a signal conditioner. The signals were filtered and amplified to be read by a DAQ. The thrust and the torque data were collected at the rate of 1000 Hz for a span of 60 s. The thrust due to the rotors at a given rpm was controlled by applying collective pitch. The collective pitch of the rotors could be varied remotely in real time through a collective pitch assembly actuated using servos. Figure 1(a) describing the setup is taken from Ref. [19] by permission of the authors. The setup specifications are mentioned in Table 1.

Test Conditions.

The coaxial rotor tests were done for three tip Reynolds numbers at two rotor separations. The Re was changed by changing rotor rpm, and the rotor separations were varied by adjusting the position of the upper rotor. To separate out the effect of rotor loading from the effect due to tip Re, one set of tests was done keeping CT and the other was done keeping T constant while varying Re. The rotor separation of 0.25R and 0.40R was selected based on the range of rotor separations found in commercially available coaxial rotor UAVs such as HAK303, HAK787, Sprite™ [23], and WorkFly™ [24], and the minimum achievable rotor separation in the setup. The test matrix for ducted and unducted rotor experiments is included in Table 1.

The constant CT experiments were performed at the collective thrust coefficient of 0.008 (i.e., an average CT of 0.004 per rotor) and the constant T experiments were performed at collective thrust value of 0.54 N. The target collective CT and T along with net torque balance at the rpms dictated by Re were achieved by adjusting collective pitches on the two rotors.

Uncertainty Estimates.

The hi-speed PIV data were captured at the highest rate of 400 frames per second at the full camera resolution of 4 megapixels. The resultant physical resolution of the images by the cameras was 0.087 mm × 0.087 mm, as a function of the placement of the cameras with respect to PIV plane. For all the PIV, vector computations were done in four passes. The first two passes used interrogation window size of 64 × 64 pixels with 50% overlap, and the next two passes used 32 × 32 pixels with 50% overlap. The computed vector field after the passes has the resolution of 1.375 mm × 1.392 mm, which can be verified to be consistent with the interrogation window size and overlap described earlier.

The air was seeded using atomized mineral oil particle of diameter ranging from 5 to 10 μm. The relaxation time, or the time taken by the seeder particle to follow a step change in air velocity found analytically using stokes flow assumptions, is in the order of 0.25 ms. The smallest characteristic time scale in the flow estimated from the vorticity data is in the order of 1–2 ms. Hence, error in the PIV measurements due to seeder particle lag can be neglected. The seeding density was kept uniform by seeding the whole test section well in advance before commencing the PIV tests. No pockets of unseeded or over seeded regions were found in the raw camera images. Each interrogation window of 32 × 32 pixels covered about 9–12 seeder particles everywhere in the PIV plane.

The standard deviation in the thrust and torque measurements for these tests has been found to be within 5% and 3%, respectively. While all the high frequency noise was filtered using low-pass filters set at 40 Hz, the collected data still show oscillations about the mean due to vibrations. The uncertainty due to DAQ resolution is negligible when compared to the standard deviation. Uncertainty in the velocity vector computation was estimated using the davis software which computes positional disparity of the image of seed particles in two interrogation windows which have been mapped back onto each other (Sciacchitano 2015). Uncertainties in the instantaneous in-plane velocity components in the area of interest are within 5% of the mean velocity values.

The hi-speed PIV was done on a plane 32 mm offset from the rotor center to avoid motor mount shadows. Only the right half of the rotor setup is covered under the assumption of wake symmetry in hover to utilize the available camera resolution more optimally. Figure 1(d) describes the camera and PIV plane orientation with respect to the rotors. Hereon, the test cases corresponding to constant CT are referred to by their Re and vertical separation only without mentioning “Const. CT”. Only the constant T cases are explicitly labeled to show the difference.

Thrust and Torque Measurements.

Table 2 lists all thrust and torque measurement results in nondimensional form along with FM of the upper rotor, lower rotor, and that of the combined system. The FM for the coaxial rotor mentioned here is computed using Eq. (1) as given by Leishman and Syal [25]. This definition accounts for unequal thrust due to the two rotors while balancing torque.

The table also contains thrust and torque results for baseline single rotor cases for comparison. For the single rotor experiments, only the upper rotor was operated with the lower rotor removed. The zero-thrust CQ values for both rotors for 40,000, 60,000, and 80,000 Re cases are 0.00024, 0.00021, and 0.00019, respectively, Display Formula

(1)FMCombined=(CTU3/2+CTL3/2)/2(CQU+CQL)

Comparing the overall FM of the constant CT cases, FM increases with the increase in Re for all. This is just as expected as the viscous parasitic drag losses which do not contribute toward thrust generation are more prominent at low Re, affecting performance. The FM of constant T cases decreases with Re because Re increase is obtained through increasing rotor rpm. This increases the parasitic drag torque though the thrust demanded is the same. The fraction of parasitic drag torque to the overall torque can be gauged by comparing the readings in the table with the zero-thrust CQ for the three Re.

Another easily noticeable trend is that the lower rotor has much lower FM compared to the upper rotor although they are identical in construction. This is due to higher induced losses on the lower rotor as it is operating in the downwash of the upper rotor. The drop in effective angle of attack of the lower rotor blades makes higher pitch angles necessary, causing the lift generated at each blade section to have a significant component in the drag direction.

While comparing the overall FM of coaxial rotors at two different vertical separations, the VS = 0.40 cases tend to have slightly better performance at higher Re as a larger outboard region of the lower rotor experiences flow from the sides. This is because the upper rotor wake gets more space to contract. This effect is not as sharp at lower Reynolds numbers, likely because of higher viscous effects leading to slower wake contraction. Another observation is that the divide between the upper rotor performance and the lower rotor performance is greater for the higher separation, which is consistent with findings by Ramasamy [20] for much higher Re tests. Ramasamy argues that when the vertical separation is low, the lower rotor induces higher inflow through the upper rotor due to the low pressure generated under the upper rotor, increasing induced losses on it (as explained in the previous paragraph). The lower rotor experiences relatively lower downwash from the upper rotor (meaning lower inflow) as the upper rotor is generating lower thrust than what it would have if the vertical separation were greater. This reduces the induced losses on the lower rotor. For all the coaxial rotor cases, the FM is less than that of the single isolated rotor. Coaxial rotors in this study have effective disk loading twice that of the single isolated rotor. It is well known that higher disk loading leads to higher inflow velocities and induced losses.

One very interesting finding from the independent thrust and torque measurements here is that the upper rotor's FM is higher than that of the single isolated rotor for all constant CT cases. This counter-intuitive finding was first reported in Ref. [19] for a couple of exploratory test cases. Going by what is known from the momentum theory for rotors, higher overall disk loading for coaxial rotors should cause higher inflow velocities above the rotors as a whole. In fact, the upper rotor is responsible for a larger share of thrust, and hence, is individually facing much higher disk loading than the isolated rotor already, causing higher rotor inflow velocities. Another way to look at this is that the lower rotor is generating low pressure under the upper rotor, causing more flow through the upper rotor (in other words, higher inflow velocity). Hence, the upper rotor FM should have been lower than the single rotor FM because of the higher induced losses due to higher inflow velocities.

The coaxial rotor tests at high Re such as those by Ramasamy [20] have always had the upper rotor performing worse than the isolated rotor, indicating a role of low Re effects in the current observations. It was hypothesized in Ref. [19] that the upper rotor could be benefiting from swirl induced by the lower rotor, but that hypothesis was left unverified as potential future work. A more detailed analysis done on this matter using mean velocity field data from stereo PIV measurements is presented and discussed later in this paper.

The thrust and torque measurement outcomes from the current low Re coaxial rotor tests are compared with some historic data on big size coaxial rotor by Harrington [1] and computational fluid dynamics study on the coaxial rotor by Schatzman [26] in Fig. 2. Zero thrust torque coefficients for both the coaxial rotors are also marked on the plot to separate out the contribution of parasitic drag from overall drag. It is seen that the difference in high and low Re rotor CQ is more than the difference between their respective single rotor zero thrust CQs. This means that not just profile drag, but induced drag is also higher for low Re rotor. The significant difference in thrust induced torque coefficient may be due to difference in the way low Re rotor wake induces flow over the blades. However, a more precise comparison would need rotors of identical geometries tested at the two significantly different Re ranges.

Particle Image Velocimetry Results
Instantaneous Velocity Field Data and Wake Interactions.

Figure 3 contains instantaneous vorticity contour plots for constant CT cases. The red spots in the contour plots correspond to tip vortices, and the coherent blue streaks correspond to the trailing edge vortex sheets. Three instances of the test cases help in understanding the progression of the wake. One can identify the vortices and vortex sheets from the upper and the lower rotor from Fig. 3 plots by referring the conceptual depiction of instantaneous flow field in Fig. 4 and careful observation.

As the upper and lower rotors in a coaxial rotor rotate in opposite directions, the vortices and the trailing edge vortex sheets form helices of opposite sense, but just shifted vertically. The upper rotor tip vortices impinge inboard on the lower rotor disk due to wake contraction, and hence, mostly interact directly with the lower rotor trailing edge vortex sheet only above a certain vertical separation between the rotors. As the upper rotor tip vortices and lower rotor vortex sheets are parts of helices of opposing sense, the separation between the two ranges from zero to a maximum number at any given instant as one looks around the wake. A graphical depiction of the expected rotor wake structure as described earlier is featured in Fig. 5(a) for aiding visualization. The figure assumes single bladed rotors for clarity, without losing generality.

If the two rotors rotate at the exact same speed, the blade crossings and the vortex-vortex-sheet interactions get locked in the azimuth direction. To get a complete picture of the wake all around the coaxial rotor, the speeds of the individual rotors were kept different by 15 rpm while taking the hi-speed PIV images. In hover or axial flight, this has the same effects as slowly moving around the coaxial rotor setup with the cameras to study each vertical sectional plane of the wake.

Interaction Mechanisms.

Through careful observation of all the instantaneous PIV results for all cases, it was found that there are four specific ways in which the upper rotor wake interacts with the lower rotor wake across the cases. The four observed ways correspond to the four types of azimuthal locations. Figure 5(b) is extracted out from Fig. 5(a) to show these four locations of interaction between the upper rotor tip vortex helix and the lower rotor trailing edge vortex sheet flat helix with more ease. Location A is where the upper rotor vortex is approximately in the middle of two consecutive layers of lower rotor vortex sheets. Location B is where the upper rotor vortex is just above the vortex sheet, which happens when the lower rotor blade passes right before the upper rotor vortex reaches the lower rotor plane. Location C is where the upper rotor vortex is just below the vortex sheet, which happens when the lower rotor blade passes right after the upper rotor vortex crosses the lower rotor plane. Location D is where the upper rotor merges with the vortex sheet which coincides with the lower rotor blade hitting the upper rotor vortex. Though the markers in Fig. 5(b) show only a small region, the region actually extends in the vertical direction. This is because the relative positions of the vortices and vortex sheets do not change much with the progression of wake as the convective speeds are almost the same. The swirl in wake below the coaxial rotor is negligible because of torque cancelation (or swirl recovery). Therefore, the wake structures are found to descend vertically down and not spin about the rotor axis.

At location A, the upper rotor vortex trajectory transitions smoothly downward through the lower rotor disk as the vortices do not have any other structure close to them. The instantaneous vorticity contour plots presented for all the VS = 0.40R cases in Fig. 3 are at such location. At location B, the upper rotor vortices being above the vortex sheet get pushed outboard due to the flow induced by the vortex sheet. On the other hand, the upper rotor vortices at location C being below the vortex sheet get pulled inboard. The instantaneous vorticity plot series presented for 40,000 Re, VS = 0.25R (or z/R = 0.25) case serves as an example for location B, and the series presented for 60,000 Re, VS = 0.25R for location C. The crude model of interaction effects described earlier can be understood better by referring to Fig. 5(c) where the sheet induced flow above and below vortex sheet is shown to push upper rotor vortex away from the original, undisturbed trajectory.

At location D, the upper rotor vortex is seen to get destroyed after merging with the vortex sheet or colliding with the lower rotor blade. No trace of the upper rotor vortex is found below the lower rotor plane if the collision is complete. Imperfect collisions at small azimuthal distances away from the complete collision result in residual high vorticity pockets which do not have vortex-like coherent structure. The instantaneous contour plot series labeled “80,000 Re, z/R = 0.25 Const. CT(a)” is an example for location D.

The upper rotor vortex center trajectories for locations A, B, and C were traced for all the cases. Figure 6 contains representative vortex trajectory plots for two test cases. For tracing the vortex trajectories, vortex centers were identified using the algorithm described by Graftieaux et al. [27]. The algorithm involves defining functions Γ1 and Γ2 which characterize the locations of the center and boundary of a large scale vortex by considering the topology of the velocity field. In Eqs. (2) and (3), P is a fixed point in the measurement domain, S is the area surrounding P, and M is a point in S. The functions effectively find sine of mean angle between position vectors of points neighboring P and flow velocities at those points. The point corresponding to local maximum or minimum of Γ2 (for counter-clockwise and clockwise rotating vortices, respectively) in the region of a vortex is the vortex center. The equations are in discretized form for application to PIV data. The PIV velocity fields were interpolated to increase the resolution threefolds before using the algorithm to identify vortex centers. The uncertainty in the identification of location of vortex centers is within 1 PIV data pixel (1.4 mm or about 1% or the rotor radius) Display Formula

(2)Γ1(P)=1SMS(PMUM)·z||PM||·||UM||=1SMSsin(θM)
Display Formula
(3)Γ2(P)=1SMS(PM(UMŨP))·z||PM||·||UMŨP||

Interaction Effects on Upper Rotor Vortices.

The effect on the upper rotor vortex trajectory due to interaction with the vortex sheet at different locations is easy to observe through the two plots. As expected, the deviations in the trajectories happen only after the vortices cross the lower rotor plane. The effect is independent of vertical separation between rotors, however, the magnitude of trajectory deviation should be a function of vertical separation as vertical separation affects thrust share, downwash from the two rotors, radial location of upper rotor vortices hitting lower rotor plane, vortex sheet strength, etc. The reasons why the upper rotor vortex sheet gets affected the most by lower rotor vortex sheet are (1) the radial location of the upper rotor vortex matches well with the lower rotor vortex sheet location and (2) convection speeds of both are comparable, giving more time to the vortex sheets to affect the vortices. The lower rotor vortices convect down much slower than the upper rotor vortices and the vortex sheets.

It is also observed that the upper rotor vortices convecting down at locations A and C retain coherent structure for much longer duration compared to those convecting down at location B. This is because the vortices at location B are being drawn outboard toward the tip vortices generated by the lower rotor and get disturbed by them. The locations described here are not discrete and they smoothly transition from one to another, which is intuitive through Fig. 5(b). Therefore, the vortex trajectories also vary continuously between the extrema as one looks around the coaxial rotor wake. A similar study of tracking rotor tip vortices using PIV, but on high Re single rotor was done recently by Karpatne et al. [28] where an analytical model was proposed to account for the anisotropic behavior of aperiodic tip vortex motion. Accurate prediction of vortex trajectories and properties is necessary for refined analysis of rotor performance.

Lower Rotor Vortices.

Now shifting focus to the lower rotor tip vortices, it is found that consecutive vortices tend to have different paths for almost all cases and locations. The lower rotor vortices are affected by the upper rotor wake and get shifted from their usual path either radially outward or inward. At some instances, the consecutive lower rotor vortices which are close to each other due to lower convective speeds get triggered by the disturbance and start to roll about each other. In such scenarios, the divide between trajectories of the two is large. Figure 7 shows trajectories of two consecutive set of vortices from the two rotors. The upper rotor vortex trajectory does not change noticeably over time as much as it changes over azimuthal location, whereas the lower rotor vortex trajectory is different within a range for each vortex. The spread in lower rotor vortex trajectories is dependent on radial location. The lowest spread is observed around location B for all cases.

Significance of Wake Interactions on Performance and Design.

The upper rotor wake and features directly affect the lower rotor performance through blade-vortex and blade-vortex sheet interactions upon impingement. These vorticity-laden wake structures are expected to have very strong effect on the spanwise (radial) flow over and under the lower rotor blades depending on the azimuthal locations identified earlier as A, B, C, and D. The spanwise flow is crucial especially at high CT conditions where sections of the lower rotor blades are close to stall. The periodic change in direction and magnitude of the wake-induced spanwise flow can trigger flow separation or reattachment. Factors such as rotor separation, blade geometry, and loading determine the radial location where the wake structures impinge on the lower rotor also affecting the stall characteristics.

In hover, synchronization of the two rotors to fix bladed crossings is not significantly beneficial in terms of performance because the lower rotor blades have to pass through all the upper rotor wake features as it turns one rotation. However, in forward flight, the synchronized rotors can be tuned to take advantage of favorable or avoid unfavorable blade-wake interactions observed here. The blade-wake interactions have implications on vibrations and noise which may be factors of concern in some applications.

The resultant wake left below the lower rotor generally does not hit the rotors again in the case of isolated coaxial rotors. However, the knowledge on the trajectories and strengths of features in the overall wake is important from vehicle design perspective where reducing download on fuselage and/or payload or reducing gusts on sensors needs to be considered. The results from the wake study are also instrumental in developing high fidelity performance prediction codes for low Re rotors along the lines of vortex theory and free wake models for high Re rotors.

Mean Velocity Field Data and an Investigation on High Upper Rotor Performance.

Figure 8 presents mean flow field streamline plots, with VS = 0.25R cases on the left and VS = 0.40 cases on the right. The two horizontal white lines in each plot depict rotor planes. The 200 instantaneous velocity fields cover 18 rotor rotations (or 36 blade passings) for the lowest rpm case. The 200 frames cover rotor rotation in 1.8 deg resolution as the rotor rotates 16.2 deg between two consecutive instantaneous fields, which is not a factor of 360. Therefore, the mean flow field obtained by averaging 200 instantaneous velocity fields should be well representative of the actual mean flow field.

One simple observation through the plots is that the velocities at the upper rotor slipstream are higher than at the lower rotor slipstream across all cases. This is expected as the upper rotor generated more thrust, and hence, causes stronger downwash. There is a notable difference between streamlines entering the upper rotor for VS = 0.25R and VS = 0.40R constant CT cases. For all the three Re, streamlines entering upper rotor of VS = 0.25R have a smaller radial component and higher axial component than their VS = 0.40R counterparts. The inflow streamline pattern at the upper rotor for constant thrust cases at both rotor separations also match that of VS = 0.40R constant CT cases. This behavior is primarily due to flow induced by the lower rotor at upper rotor plane through suction and/or tip vortices. At smaller rotor separations with loaded lower rotor, the lower rotor tip vortices are strong and close to induce some flow at the upper rotor plane outside slipstream. Also, the lower rotor creates higher suction below the upper rotor when the separation is low. At higher rotor separations and at low lower rotor loading conditions, the lower rotor suction and tip vortices do not play a significant role in upper rotor inflow.

The effect of the above difference in upper rotor inflow pattern is visible on the upper rotor performance. The upper rotor is seen to have generally higher FM in VS = 0.40R cases compared to VS = 0.25R cases of constant CT. This is because the upper rotor in VS = 0.40R cases ingests air from the sides which does not have any significant axial velocities/momentum. In VS = 0.25R cases, the mean downward inflow velocities are higher as the air is pulled from above the rotors, causing relatively higher induced losses.

Figure 9 captures inflow and outflow velocity profiles for both rotors for all cases from the time-averaged velocity field. The inflow and outflow data presented here are extracted from a distance of 0.1R above and below the rotors, respectively, for both the rotors. Here, again the difference in the way flow enters upper rotor for the two vertical separation cases is apparent from the inflow velocity profile curves. The upper rotor outflow and the lower rotor inflow velocity profiles are very similar. Both of them tend to be further inboard for all VS = 0.40R cases. The lower rotor outflow profile has two peaks because there are two slip streams at this location. The inboard peak is due to the upper rotor slipstream and the outboard peak is due to lower rotor slipstream. The peak corresponding to the upper rotor wake is higher in magnitude as upper rotor generates more thrust. The divide between radial locations of the peaks is higher for VS = 0.40R cases as expected by observing lower rotor inflow velocity profile.

We now move on to the problem of the upper rotor of a coaxial rotor performing better than an isolated rotor as introduced in the thrust and torque measurement results section. It was hypothesized then that the observation is due to swirl recovery at upper rotor due to lower rotor. To verify the hypothesis, the mean tangential (into the plane/swirl) velocities in a region neighboring the upper rotor disk are integrated to find the spatial average for all constant CT cases and compared with single isolated rotor results. The integration area is 0.2R thick, equally spread on either sides of the rotor disk, and 0.8R in length as marked in Fig. 10 by green box. The figure features one single rotor case and one coaxial rotor case for illustration.

The effect of the lower rotor on swirl close to the upper rotor cannot be compared by comparing the swirl velocities directly. That is because thrusts and torques at the upper rotor vary across cases, and swirl near a rotor is directly related to the torque applied by the rotor. Hence, the integration averaged swirl velocities around the upper rotor are normalized by the upper rotor torque to account for the effect of rotor torque on swirl before comparing different cases for finding swirl induced by the other rotor.

The normalized results from the aforementioned process are tabulated in Table 3. Here, it is seen that except for the outlier case of 40,000 Re VS = 0.25R, all other coaxial rotor cases have the normalized swirl velocities smaller (in magnitude) than their single rotor counterparts. Moreover, the swirl velocity magnitudes for VS = 0.25 cases are smaller than VS = 0.40R cases. This supports the idea that the lower rotor induces counter swirl on the upper rotor, which can be responsible for performance improvement of the upper rotor compared to a single isolated rotor.

The phenomenon of swirl recovery in a coaxial rotor is not new. However, it is always seen to be benefiting the lower rotor performance, but not the other way around as the flow is from upper rotor to the lower rotor. It is believed that reverse swirl recovery phenomenon observed here is typical for low Re coaxial rotors only because viscous forces which are significant compared to momentum in this regime help in transferring swirl from the lower rotor to the upper rotor against downward flow.

The present study on low Re coaxial rotors showed that though most arguments made for large size coaxial rotors on performance hold true for low Re rotors as well, there are some interesting observations which cannot be explained by what is known from high Re rotor aerodynamics.

Just like for high Re coaxial rotors, the upper rotor performance is seen to be much better than the lower rotor performance, and the overall coaxial rotor FM is less than that of an isolated single rotor. However, unlike high Re coaxial rotors, the upper rotor was found to have higher FM than the single isolated rotor for all test cases, which goes against what is expected out of typical momentum based approach. It was later found through the analysis of swirl velocities from the SPIV data that the better than expected upper rotor performance was due to viscous swirl recovery by the counter-rotating lower rotor. Such viscous swirl recovery is unlikely in high Re rotors where strong downwash from the upper rotor does not allow viscous forces to communicate lower rotor swirl in the upward direction.

While comparing the low Re coaxial rotor CT and CQ data with the historic high Re data by Harrington, it is apparent that the parasitic and induced torque coefficients are much higher for the present lower Re rotor cases. The higher induced torque is hypothesized to be due to difference in the way low Re rotor wake induces flow over the blades.

The upper rotor vortices are found to interact with the lower rotor trailing edge vortex sheet in four separate ways in each test case, affecting upper rotor tip vortex trajectories and endurance. Upper rotor tip vortices are seen to get pulled inboards, pushed outboards, disintegrated, or stay unaffected after interaction with the lower rotor vortex sheet depending on if the upper rotor tip vortices land below, above, exactly on, or far away from the lower rotor vortex sheet at the given azimuthal location. These findings on rotor wake are expected to aid design of coaxial rotor UAVs and be instrumental in the development of more accurate performance prediction methods for this regime.

We would like to thank the team of undergraduate researchers in the Experimental Aerodynamics lab at Georgia Tech for their assistance in conducting tests and Georgia Tech A.E. Machine shop for their guidance in building the setup.

The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation thereon. The U.S. Government technical monitor is Mahendra Bhagwat. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Aviation Development Directorate or the U.S. Government.

  • Army Research Office (W911W6-17-2-0002, Funder ID. 10.13039/100000183).

  • c =

    blade chord length

  • CQ =

    coefficient of torque

  • CT =

    coefficient of thrust

  • FM =

    figure of merit

  • Q =

    torque

  • R =

    rotor radius

  • Re =

    tip Reynolds number

  • T =

    thrust

  • VS =

    vertical separation between rotors

Harrington, R. D. , 1951, “ Full-Scale-Tunnel Investigation of the Static-Thrust Performance of a Coaxial Helicopter Rotor,” National Advisory Committee for Aeronautics Langley Aeronautical Laboratory Langley Field,Hampton, VA, Report No. NACA-TN-2318. https://ntrs.nasa.gov/search.jsp?R=19930083001
Dingeldein, R. C. , 1954, “ Wind-Tunnel Studies of the Performance of Multirotor Configurations,” National Advisory Committee for Aeronautics Langley Aeronautical Laboratory Langley Field, Hampton,VA, Report No. NACA-TN-3236. https://ntrs.nasa.gov/search.jsp?R=19930083899
Nagashima, T. , and Nakanishi, K. , 1981, “ Optimum Performance and Wake Geometry of Co-Axial Rotor in Hover,” DGLR Seventh European Rotorcraft and Powered Lift Aircraft Forum, Garmisch-Partenkirchen, Germany, Paper No. 41.
Sunada, S. , Tanaka, K. , and Kawashima, K. , 2005, “ Maximization of Thrust-Torque Ratio of a Coaxial Rotor,” J. Aircraft, 42(2), pp. 570–572. [CrossRef]
Saito, S. , and Azuma, A. , 1981, “ A Numerical Approach to Co-Axial Rotor Aerodynamics,” Seventh European Rotorcraft and Powered Lift Aircraft Forum, Garmisch-Partenkirchen, Germany, Paper No. 42.
Andrew, M. , 1981, “ Co-Axial Rotor Aerodynamics in Hover,” Sixth European Rotorcraft and Powered Lift Aircraft Forum, Bristol, UK, Sept. 16–19, Vol. 5, pp. 163–172.
Zimmer, H. , 1985, “ The Aerodynamic Calculation of Counter Rotating Coaxial Rotors,” Eleventh European Rotorcraft and Powered Lift Aircraft Forum, London, Paper No. 27..
Bagai, A. , and Leishman, J. G. , 1996, “ Free-Wake Analysis of Tandem, Tilt-Rotor and Coaxial Rotor Configurations,” J. Am. Helicopter Soc., 41(3), pp. 196–207. [CrossRef]
Lei, J. , and He, J. , 2016, “ Adjoint-Based Aerodynamic Shape Optimization for Low Reynolds Number Airfoils,” ASME J. Fluids Eng., 138(2), p. 021401. [CrossRef]
Karasu, I. , Özden, M. , and Genç, M. S. , 2018, “ Performance Assessment of Transition Models for Three-Dimensional Flow Over NACA4412 Wings at Low Reynolds Numbers,” ASME J. Fluids Eng., 140(12), p. 121102. [CrossRef]
Ziadé, P. , Feero, M. A. , Lavoie, P. , and Sullivan, P. E. , 2018, “ Shear Layer Development, Separation, and Stability Over a Low-Reynolds Number Airfoil,” ASME J. Fluids Eng., 140(7), p. 071201. [CrossRef]
Boukenkoul, M. A. , Li, F.-C. , Chen, W.-L. , and Zhang, H.-N. , 2018, “ Lift-Generation and Moving-Wall Flow Control Over a Low Aspect Ratio Airfoil,” ASME J. Fluids Eng., 140(1), p. 011104. [CrossRef]
Jang, C.-M. , Furukawa, M. , and Inoue, M. , 2001, “ Analysis of Vortical Flow Field in a Propeller Fan by LDV Measurements and LES—Part I: Three-Dimensional Vortical Flow Structures,” ASME J. Fluids Eng., 123(4), pp. 748–754. [CrossRef]
Jang, C. , Furukawa, M. , and Inoue, M. , 2001, “ Analysis of Vertical Flow Field in a Propeller Fan by LDV Measurements and LES—Part II: Unsteady Nature of Vertical Flow Structures Due to Tip Vortex Breakdown,” ASME J. Fluids Eng, 123(4), pp. 755–761. [CrossRef]
Guilmineau, E. , Deng, G. , Leroyer, A. , Queutey, P. , Visonneau, M. , and Wackers, J. , 2018, “ Numerical Simulations for the Wake Prediction of a Marine Propeller in Straight-Ahead Flow and Oblique Flow,” ASME J. Fluids Eng., 140(2), p. 021111. [CrossRef]
Ramasamy, M. , Leishman, J. G. , and Lee, T. E. , 2007, “ Flowfield of a Rotating-Wing Micro Air Vehicle,” J. Aircraft, 44(4), pp. 1236–1244. [CrossRef]
Ramasamy, M. , Johnson, B. , and Leishman, J. G. , 2008, “ Understanding the Aerodynamic Efficiency of a Hovering Micro-Rotor,” J. Am. Helicopter Soc., 53(4), pp. 412–428. [CrossRef]
Krane, M. H. , Meyer, R. S. , Weldon, M. J. , Elbing, B. , and DeVilbiss, D. W. , 2015, “ Measurements of Loading and Tip Vortex Due to High-Reynolds Number Flow Over a Rigid Lifting Surface,” ASME J. Fluids Eng., 137(7), p. 071301. [CrossRef]
Shukla, D. , Hiremath, N. , and Komerath, N. M. , 2018, “ Low Reynolds Number Aerodynamics Study on Coaxial and Quad-Rotor,” AIAA Paper No. 2018-4118.
Ramasamy, M. , 2013, “ Measurements Comparing Hover Performance of Single, Coaxial, Tandem, and Tilt-Rotor Configurations,” 69th AHS Annual Forum, Vol. 31, Phoenix, AZ, May 21–23, p. 32.
Brazinskas, M. , Prior, S. D. , and Scanlan, J. P. , 2016, “ An Empirical Study of Overlapping Rotor Interference for a Small Unmanned Aircraft Propulsion System,” Aerospace, 3(4), p. 32. [CrossRef]
Ma, Y. , Chen, M. , Zhang, X. , and Wang, Q. , 2016, “ Scale-Model Tests of Coaxial Rotors in Water Tunnel Via Particle Image Velocimetry Technique,” Proc. Inst. Mech. Eng., Part G, 230(3), pp. 426–443. [CrossRef]
Kickstarter, 2018, “ Sprite: Portable and Rugged. A Totally Different Drone,” Brooklyn, New York, accessed June 10, 2018, https://www.kickstarter.com/projects/ascentaerosystems/sprite-the-portable-rugged-totally-different-small
Drone, C. , 2018, “ WorkFly: Datasheet,” Montreuil, France, accessed June 12, 2018, http://www.civicdrone.com/our-rpa/datasheet-of-drones-c10114.html
Leishman, J. G. , and Syal, M. , 2008, “ Figure of Merit Definition for Coaxial Rotors,” J. Am. Helicopter Soc., 53(3), pp. 290–300. [CrossRef]
Schatzman, N. L. , 2018, “ Aerodynamics and Aeroacoustic Sources of a Coaxial Rotor,” Ph.D. thesis, Georgia Institute of Technology, Atlanta, GA.
Graftieaux, L. , Michard, M. , and Grosjean, N. , 2001, “ Combining PIV, POD and Vortex Identification Algorithms for the Study of Unsteady Turbulent Swirling Flows,” Meas. Sci. Technol., 12(9), p. 1422. [CrossRef]
Karpatne, A. , Sirohi, J. , Mula, S. , and Tinney, C. , 2014, “ Vortex Ring Model of Tip Vortex Aperiodicity in a Hovering Helicopter Rotor,” ASME J. Fluids Eng., 136(7), p. 071104. [CrossRef]
Copyright © 2019 by ASME
Topics: Rotors , Vortices , Wakes , Thrust
View article in PDF format.

References

Harrington, R. D. , 1951, “ Full-Scale-Tunnel Investigation of the Static-Thrust Performance of a Coaxial Helicopter Rotor,” National Advisory Committee for Aeronautics Langley Aeronautical Laboratory Langley Field,Hampton, VA, Report No. NACA-TN-2318. https://ntrs.nasa.gov/search.jsp?R=19930083001
Dingeldein, R. C. , 1954, “ Wind-Tunnel Studies of the Performance of Multirotor Configurations,” National Advisory Committee for Aeronautics Langley Aeronautical Laboratory Langley Field, Hampton,VA, Report No. NACA-TN-3236. https://ntrs.nasa.gov/search.jsp?R=19930083899
Nagashima, T. , and Nakanishi, K. , 1981, “ Optimum Performance and Wake Geometry of Co-Axial Rotor in Hover,” DGLR Seventh European Rotorcraft and Powered Lift Aircraft Forum, Garmisch-Partenkirchen, Germany, Paper No. 41.
Sunada, S. , Tanaka, K. , and Kawashima, K. , 2005, “ Maximization of Thrust-Torque Ratio of a Coaxial Rotor,” J. Aircraft, 42(2), pp. 570–572. [CrossRef]
Saito, S. , and Azuma, A. , 1981, “ A Numerical Approach to Co-Axial Rotor Aerodynamics,” Seventh European Rotorcraft and Powered Lift Aircraft Forum, Garmisch-Partenkirchen, Germany, Paper No. 42.
Andrew, M. , 1981, “ Co-Axial Rotor Aerodynamics in Hover,” Sixth European Rotorcraft and Powered Lift Aircraft Forum, Bristol, UK, Sept. 16–19, Vol. 5, pp. 163–172.
Zimmer, H. , 1985, “ The Aerodynamic Calculation of Counter Rotating Coaxial Rotors,” Eleventh European Rotorcraft and Powered Lift Aircraft Forum, London, Paper No. 27..
Bagai, A. , and Leishman, J. G. , 1996, “ Free-Wake Analysis of Tandem, Tilt-Rotor and Coaxial Rotor Configurations,” J. Am. Helicopter Soc., 41(3), pp. 196–207. [CrossRef]
Lei, J. , and He, J. , 2016, “ Adjoint-Based Aerodynamic Shape Optimization for Low Reynolds Number Airfoils,” ASME J. Fluids Eng., 138(2), p. 021401. [CrossRef]
Karasu, I. , Özden, M. , and Genç, M. S. , 2018, “ Performance Assessment of Transition Models for Three-Dimensional Flow Over NACA4412 Wings at Low Reynolds Numbers,” ASME J. Fluids Eng., 140(12), p. 121102. [CrossRef]
Ziadé, P. , Feero, M. A. , Lavoie, P. , and Sullivan, P. E. , 2018, “ Shear Layer Development, Separation, and Stability Over a Low-Reynolds Number Airfoil,” ASME J. Fluids Eng., 140(7), p. 071201. [CrossRef]
Boukenkoul, M. A. , Li, F.-C. , Chen, W.-L. , and Zhang, H.-N. , 2018, “ Lift-Generation and Moving-Wall Flow Control Over a Low Aspect Ratio Airfoil,” ASME J. Fluids Eng., 140(1), p. 011104. [CrossRef]
Jang, C.-M. , Furukawa, M. , and Inoue, M. , 2001, “ Analysis of Vortical Flow Field in a Propeller Fan by LDV Measurements and LES—Part I: Three-Dimensional Vortical Flow Structures,” ASME J. Fluids Eng., 123(4), pp. 748–754. [CrossRef]
Jang, C. , Furukawa, M. , and Inoue, M. , 2001, “ Analysis of Vertical Flow Field in a Propeller Fan by LDV Measurements and LES—Part II: Unsteady Nature of Vertical Flow Structures Due to Tip Vortex Breakdown,” ASME J. Fluids Eng, 123(4), pp. 755–761. [CrossRef]
Guilmineau, E. , Deng, G. , Leroyer, A. , Queutey, P. , Visonneau, M. , and Wackers, J. , 2018, “ Numerical Simulations for the Wake Prediction of a Marine Propeller in Straight-Ahead Flow and Oblique Flow,” ASME J. Fluids Eng., 140(2), p. 021111. [CrossRef]
Ramasamy, M. , Leishman, J. G. , and Lee, T. E. , 2007, “ Flowfield of a Rotating-Wing Micro Air Vehicle,” J. Aircraft, 44(4), pp. 1236–1244. [CrossRef]
Ramasamy, M. , Johnson, B. , and Leishman, J. G. , 2008, “ Understanding the Aerodynamic Efficiency of a Hovering Micro-Rotor,” J. Am. Helicopter Soc., 53(4), pp. 412–428. [CrossRef]
Krane, M. H. , Meyer, R. S. , Weldon, M. J. , Elbing, B. , and DeVilbiss, D. W. , 2015, “ Measurements of Loading and Tip Vortex Due to High-Reynolds Number Flow Over a Rigid Lifting Surface,” ASME J. Fluids Eng., 137(7), p. 071301. [CrossRef]
Shukla, D. , Hiremath, N. , and Komerath, N. M. , 2018, “ Low Reynolds Number Aerodynamics Study on Coaxial and Quad-Rotor,” AIAA Paper No. 2018-4118.
Ramasamy, M. , 2013, “ Measurements Comparing Hover Performance of Single, Coaxial, Tandem, and Tilt-Rotor Configurations,” 69th AHS Annual Forum, Vol. 31, Phoenix, AZ, May 21–23, p. 32.
Brazinskas, M. , Prior, S. D. , and Scanlan, J. P. , 2016, “ An Empirical Study of Overlapping Rotor Interference for a Small Unmanned Aircraft Propulsion System,” Aerospace, 3(4), p. 32. [CrossRef]
Ma, Y. , Chen, M. , Zhang, X. , and Wang, Q. , 2016, “ Scale-Model Tests of Coaxial Rotors in Water Tunnel Via Particle Image Velocimetry Technique,” Proc. Inst. Mech. Eng., Part G, 230(3), pp. 426–443. [CrossRef]
Kickstarter, 2018, “ Sprite: Portable and Rugged. A Totally Different Drone,” Brooklyn, New York, accessed June 10, 2018, https://www.kickstarter.com/projects/ascentaerosystems/sprite-the-portable-rugged-totally-different-small
Drone, C. , 2018, “ WorkFly: Datasheet,” Montreuil, France, accessed June 12, 2018, http://www.civicdrone.com/our-rpa/datasheet-of-drones-c10114.html
Leishman, J. G. , and Syal, M. , 2008, “ Figure of Merit Definition for Coaxial Rotors,” J. Am. Helicopter Soc., 53(3), pp. 290–300. [CrossRef]
Schatzman, N. L. , 2018, “ Aerodynamics and Aeroacoustic Sources of a Coaxial Rotor,” Ph.D. thesis, Georgia Institute of Technology, Atlanta, GA.
Graftieaux, L. , Michard, M. , and Grosjean, N. , 2001, “ Combining PIV, POD and Vortex Identification Algorithms for the Study of Unsteady Turbulent Swirling Flows,” Meas. Sci. Technol., 12(9), p. 1422. [CrossRef]
Karpatne, A. , Sirohi, J. , Mula, S. , and Tinney, C. , 2014, “ Vortex Ring Model of Tip Vortex Aperiodicity in a Hovering Helicopter Rotor,” ASME J. Fluids Eng., 136(7), p. 071104. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

(a) Coaxial rotor setup [19], (b) individual rotor construction, (c) coaxial rotor setup photo, and (d) PIV measurement location

Grahic Jump Location
Fig. 2

Comparison of CT and CQ measurements with coaxial rotor data by Harrington [1] and RotUNS computational fluid dynamics data by Schatzman [26]

Grahic Jump Location
Fig. 3

Instantaneous vorticity contour plots

Grahic Jump Location
Fig. 4

Conceptual sketch of instantaneous vorticity contour plots

Grahic Jump Location
Fig. 5

(a) Graphical depiction of coaxial rotor wake in hover, (b) vortex–vortex sheet interaction locations of interest, and (c) graphic explaining vortex–vortex sheet interaction effects at locations B and C

Grahic Jump Location
Fig. 6

Upper rotor vortex trajectories for at azimuthal locations marked as A, B, and C in Fig. 5 for two test conditions

Grahic Jump Location
Fig. 7

Vortex trajectory plots for VS = 0.25R and VS = 0.40R

Grahic Jump Location
Fig. 8

Time-averaged velocity field streamlines

Grahic Jump Location
Fig. 9

Inflow and outflow velocity profiles for upper and lower rotors

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Fig. 10

Time-averaged swirl velocity field plots with integration box marked in green

Tables

Table Grahic Jump Location
Table 1 Setup and test condition for coaxial rotor experiments
Table Grahic Jump Location
Table 2 Coaxial rotor thrust and torque measurements
Table Grahic Jump Location
Table 3 Integrated normalized swirl velocities

Errata

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