Numerical Investigation of Aerodynamic Interaction for a Quad-Rotor UAV Configuration
3 Results and Discussion
3.1 Configuration and Computational Mesh
The quad-rotor UAV configuration adopted in the present study is shown in Fig. 1. The vehicle has four identical fixed-pitch rotors mounted at the end of four equally-space arms attached to the flat form. Out of the four rotors, two pairs are spinning in the opposite direction to maintain the vehicle in balance. The length from one rotor tip to the other rotor tip in the opposite side is 0.48 meters. The rotor adopted in the present study is the EPP1045 rotor produced by the Maxx Products International Inc. Each rotor is consisted of two blades that have an aspect ratio of 5.508. The diameter of the rotor is 10 inches, and the pitch length is 4.5 inches per revolution. The rotor is driven by Robbe ROXXY 2827-35 motor and BL-Ctrl V1.2 speed controller. The rotor rotates at 300rad/sec. The total weights of the UAV configuration with and without the battery are 8.5064N and 6.2132N, respectively.
In Fig. 2, the computational mesh is presented. The overset mesh is constructed with five mesh blocks; four sub-blocks covering each of the four rotors, and a main block representing the overall computational domain. To simulate the aerodynamic interactions between the rotors more accurately, fine cells are distributed around the rotor blades. The mesh consists of and the connecting arms are not modeled in the present study.
Fig. 1 Quad-rotor UAV configuration.
(a) Overset mesh blocks for four rotors
(b) Computational mesh around each blade
Fig. 2 Computational mesh for quad-rotor UAV.
3.2 Hovering Flight
At first, the aerodynamic interaction in the hovering flight condition was analyzed. In Fig.
3, the wake structure of the quad-rotor is presented by the 2-criterion when the blades are located at the azimuth angle of zero degree.
It is observed that helically shaped vortex structures are formed under each rotor. It is shown that in this hovering flight there is not much interaction, at least a direct intersection between the wakes from each rotor, even though the wakes still influence the other rotors in close proximity.
(a) Top and side views
(b) Perspective View
Fig. 3 Rotor wake structure represented by iso-surface of2-criterion for hovering flight.
In Fig. 4, the vertical downward velocity contours are presented at a plane half chord length below the rotor disk and at the vertical plane along the center of the first and third rotors for the hovering flight condition. It is observed that the velocity contours are almost symmetric along the diagonal lines between the rotors. There exist slight differences in the velocity contours as marked by the dotted and dash-dot lines. This is because each pair of the rotors is rotating in the opposite direction from the other one. At the vertical plane, the velocity contours appear almost symmetric. It is also observed that a slight upwash flow region exists at the center between the rotors as induced by the tip vortices from the rotor blades.
In Fig. 5, the blade sectional thrust distribution along the span is presented for a typical rotor for one rotor revolution. All four rotors exhibit a similar sectional thrust variation in this hovering flight. It is shown that even for the hovering flight condition, a significant fluctuation of the blade loading exists along the rotor azimuth angle, particularly near the blade tip around 45◦, 135◦, 225◦, and 315◦. This is because the rotor interacts with the other rotors, and the blade effective angle of attack is locally influenced by their wakes.
Numerical Investigation of Aerodynamic Interaction for a Quad-Rotor UAV Configuration
CEAS 2013 The International Conference of the European Aerospace Societies
(a) Plane at half chord length below rotor disk
(b) Vertical center plane
Fig. 4 Vertical downward velocity contours for hovering flight.
Fig. 5 Sectional thrust contour along blade span for one rotor revolution for hovering flight.
Fig. 6 Unsteady thrust variations of rotors for hovering flight.
Table 1. Time-averaged thrust of rotors and total moments on the vehicle for hovering flight.
Time-averaged value
Thrust
Rotor 1 1.09817 N
Rotor 2 1.09843 N
Rotor 3 1.09675 N
Rotor 4 1.09583 N
Moment Pitch 0.00064 Nm
Roll -0.00071 Nm
In Fig. 6, the unsteady thrust variations of the four rotors are presented for one rotor revolution.
It is shown that all rotors are in almost identical thrust variations, exhibiting a periodic change due to the aerodynamic interaction as described in Figs. 4 and 5, even though the magnitude of variation is small.
In Table 1, the time-averaged thrust of each rotor and the total moments on the vehicle by the four rotors are represented. It is again confirms that the time-averaged thrusts of all rotors are almost same. As a result, the time-averaged pitch and roll moments of the vehicle are near zero. For comparison, the calculation for an isolated rotor was also made. It showed that the thrust of an isolated rotor is 1.12489N, approximately 2.5% higher than the present rotors, again confirming the effects of the mutual aerodynamic interaction between the rotors.
3.3 Forward Flight
To investigate the mutual aerodynamic interaction of the rotors in forward flight,
calculation was performed for the rotors when the vehicle flies at a freestream velocity of 5m/s.
In the present calculation, the vehicle was assumed to be at an angle of attack of negative five degrees to the incoming freestream. The operating blade tip speed is 38.31m/s, and the tip advancing ratio is 0.174.
Figure 7 shows the wake structure behind the rotors as represented by the 2-criterion when the blades are located at the azimuth angle of zero degree. In the figure, the rotors 1 & 3 rotate clockwise, and the rotors 2 & 4 rotate counter-clockwise. The rotor 1 is the upmost one against the incoming freestream. It is shown that the rotors at the downstream are strongly influenced by the tip vortices trailed from the upstream rotors. It is also evident that the rotor disk vortices are formed at the sides of the rotor disk plane, and these disk vortices from upstream rotors strongly interact with those and also with the individual tip vortices of the downstream rotors. For example, the disk vortices from rotor 1 induce upwash to rotors 2 and 4 by increasing the effective angle of attack of the blades of those rotors, but increase the downwash on rotor 3. On the contrary, the wake from rotors 2 and 4 works in the direction of reducing the downwash for rotor 3.
In Fig. 8, the vertical downward velocity distributions at half chord length below and above the rotor disk plane are presented. It shows that relatively high downward velocity exists behind the rotor blades as induced by the wake of the individual rotor itself. In contrast, fairly high upwash is observed between the rotors as marked by the dash-dot region and the dotted region. This upwash is induced by the rotor disk vortices, and the magnitude is slightly higher between rotor 1 and rotor 4 as both rotor disk vortices are from the advancing sides. In contrast, the upwash with a less strength exists for a wider region between the rotor disk vortices from the retreating sides of rotors 1 and 2. The downstream rotor 3 is affected by all three upstream rotors. However, the influence by the three downstream rotors on upstream rotor 1 is relatively small.
(a) Top and side views
(b) Perspective view
Fig. 7 Rotor wake structure represented by iso-surface of2-criterion in forward flight.
(a) Plane at half chord length below rotor disk
(b) Plane at half chord length above rotor disk
Fig. 8 Vertical downward velocity contours at half chord length below and above rotor disk plane in
forward flight.
Numerical Investigation of Aerodynamic Interaction for a Quad-Rotor UAV Configuration
CEAS 2013 The International Conference of the European Aerospace Societies In Fig. 9, the sectional thrust contours over
the rotor disk plane are presented for one blade.
It is observed that rotor 3 has relatively smaller thrust loading than rotor 1 due to the higher induced downwash induced from the upstream rotors. It is also observed that the maximum thrust loading is obtained at the azimuth angles near 110 and 20 degrees for rotors 1 and 2, respectively. In contrast, in the case of rotors 3 and 4, the maximum thrust loading, slightly higher than that of rotors 1 and 2, is observed near the azimuth angles of 120 and 30 degrees as they interact with the wakes from the upstream rotors at the advancing side. It is also shown that higher thrust loading is distributed over a wider area for rotors 2 and 3 than rotors 4 and 1, particularly around the azimuth angles of 135 and 225 degrees.
In Fig. 10, the unsteady thrust variations of each rotor are presented for one rotor revolution.
The phase difference of 90 degrees between the rotors in the figure is because the setting of the reference azimuth angle is different for each rotor. In general, the thrust obtained from rotor 3 is lower than that of rotor 1, although locally higher value exists. This again confirms that higher downwash flow is induced on rotor 3 as it is affected by the wake from the upstream rotors. It is also shown that higher thrust values are obtained for rotors 2 and 4, which is due to the upwash flow induced by the wake of rotor 1.
Rotor 2 exhibits higher thrust loading than rotor 4 at two regions from 135◦ azimuth angle to 180◦ and from 315◦ azimuth angle to 360◦. This is again due to the higher upwash induced by the tip vortex from the retreating side of rotor 1.
In Table 2, the time-averaged thrust of each rotor for one rotor revolution and the moments acting on the vehicle are presented. As discussed in Fig. 10, the time-averaged thrusts of rotors 2 and 4 are higher than that of rotor 1, and rotor 3 produces the smallest time-averaged thrust. As each rotor exhibits different time-averaged thrust behavior, a finite value of pitch and roll moments about the center of the four rotors is generated. This demonstrates that the attitude stability of the quad-rotor UAV can be deteriorated in forward flight due to the aerodynamic interaction between the rotors,
which should be considered seriously in designing the autonomous flight control system of the vehicle.
Fig. 9 Sectional thrust contours for one rotor revolution in forward flight.
Fig. 10 Unsteady thrust variations of rotors in forward flight.
Table 2 Time-averaged rotor thrust and total moments on the vehicle in forward flight.
Time-averaged value
Thrust
Rotor 1 1.49772 N Rotor 2 1.59025 N Rotor 3 1.46264 N Rotor 4 1.55175 N
Moment Pitch 0.00963 Nm
Roll -0.0106 Nm