Horizontal Wind Effect on the Aerodynamic Performance of Coaxial Tri-Rotor MAV

Abstract

The coaxial Tri-rotor micro air vehicle (MAV) is composed of three coaxial rotors where the aerodynamic characteristics of is complicated in flight especially when the wind effect is introduced. In this paper, the hovering performance of a full-scale coaxial Tri-rotor MAV is analyzed with both the simulations and wind tunnel experiments. Firstly, the wind effect on the aerodynamic performance of coaxial Tri-rotor MAV is established with different rotor speed (1500–2300 rpm) and horizontal wind (0–4 m/s). Secondly, the thrust and power consumption of coaxial Tri-rotor (L/D = 1.6) were obtained with low-speed wind tunnel experiments. Furthermore, the streamline distribution, pressure distribution, velocity contour and vortex distribution with different horizontal wind conditions are obtained by numerical simulations. Finally, combining the experiment results and simulation results, it is noted that the horizontal wind may accelerate the aerodynamic coupling, which resulting in the greater thrust variation up to 9% of the coaxial Tri-rotor MAV at a lower rotor speed. Moreover, the aerodynamic performance is decreased with more power consumption at higher rotor speed where the wind and the downwash flow are interacted with each other. Compared with no wind flow, the shape of the downwash flow and the deformation of the vortex affect the power loading and figure of metric accordingly.

1. Introduction

Compared with traditional Quad-rotor or Hex-rotor, the coaxial Tri-rotor the coaxial Tri-rotor has a much wider class including a compact structure without redundancy device since the vehicle mass is related to the rotor arm where the Quad-rotor or Hex-rotor is limited with more rotors to avoid rotor conflict. Also, it provides the unique capability of being able to resist any applied wrench or wind gust or failure tolerance with coaxial rotors (If one rotor, even three rotors, fails the system, it still has the freedom of movement). For a coaxial Tri-rotor MAV, the three coaxial rotors are evenly distributed along with the vehicle center. The aerodynamic interference is mainly including two parts: the rotor interference between the upper rotor and lower rotor and adjacent coaxial rotors [1,2,3,4,5,6]. When the horizontal wind is introduced, the whole aerodynamic environment will be affected by the horizontal wind during flight. Therefore, the objective of the present work is to explore wind effect on the aerodynamic performance on a full-scale coaxial Tri-rotor MAV.

Currently, the research on the multi-rotor MAV is mainly focused on the control strategies. Pflimlin, Zhang and Kirsch [7,8,9] designed the adaptive backstepping sliding mode controllers and realized attitude, velocity and position control of the Hex-rotor MAV. Salazar and Arellano-Muro [10,11] adopted the dynamic model of a multi rotor MAV to analyze the attitude and translation and estimate the aerodynamic forces and moments acting of a hexarotor MAV in flight. Shi [12] presented an indoor path planning algorithm and overcome the drawbacks of Global Positioning System (GPS). So the shortest trajectory for the Hex-rotor MAV in the complex terrains is obtained. Ma [13] designed a 4 channels PID controller to achieve the attitude control of a miniature Hex-rotor MAV. Chen [14] proposed a controller with cascaded structure, which has the ability to maintain the flight state of MAV. Zhao [15] presented a novel Hex-Rotor MAV based on the unique configuration of its six driving rotors and overcame the effect of the under-actuation and strong coupling characteristics on the flight performance. Salazar-Cruz [16] proposed the dynamical model of an original coaxial Tri-rotor MAV and applied a nested saturations control law to control the roll and the forward displacement, resulting in the better behavior of controller. Mohamed [17] and Chiou [18] proposed the design and control of the single tilt tri-rotor and shown the effectiveness of the controllers design scheme through nonlinear simulation model. Brossard, Mystkowski and Tunik [19,20,21] discussed a nonlinear robust control design procedure to micro air vehicle, resulting in the stable flight of MAV in the presence of perturbations.

Therefore, only a few studies lay emphasis on the aerodynamic characteristics of a Multi-rotor MAV or even to consider the wind effect. Lei et al. studied the hover performance of a Multi-rotor MAV by means of the combination of experiment and simulation [22,23]. Zhao promoted a method to analyze the effects of airflow disturbance and rotor interference on the control scheme, which is based on the dynamic experiment of the Hex-rotor MAV [24]. Hrishikeshavan reviewed the hover capability of MAV with varying solidity, collective, operating RPM and planform [25]. The results of the above studies are all conducive to analyze the aerodynamic characteristics of the coaxial Tri-rotor MAV. However, there are no aerodynamic studies of the coaxial Tri-rotor MAV with the Horizontal wind so far. Hence, this paper presents the aerodynamic characteristics of a coaxial Tri-rotor MAV with the effect of the horizontal wind.

2. Theoretical Analysis

2.1. Structure

Structure of the coaxial Tri-rotor MAV is shown in Figure 1.

Figure 1 shows the structural model of the coaxial Tri-rotor MAV. An inertial reference frame o_e (x_e, y_e, z_e), an Euler angle in inertial frame (φ, θ, γ) and a body reference frame o_b (x_b, y_b, z_b) that indicates a set of coordinate fixed to the MAV, are defined in Figure 1. The coaxial Tri-rotor MAV is composed of three coaxial rotors units. The connecting line between the centers of three coaxial rotors forms an equilateral triangle, which is center-symmetric. In addition, compared with traditional rotor arrangement, the Tri-rotor MAV is more compact with less rotors in a same plane.

2.2. Flow Field Model

Flow model of the coaxial Tri-rotor MAV considering the horizontal wind is shown in Figure 2.

In the Figure 2, it can be observed that the flow field of the coaxial Tri-rotor system will shift along the incoming flow direction in a horizontal wind. Compared with no wind effect, it can be found that the downwash flows are coupled with each other besides the interference between upper and lower rotor of coaxial rotors. In this case, the wake vortices of the front rotors directly affect the flow of the rear rotors. In this case, the wind may aggravate the aerodynamic interference among rotors with varied power consumption accordingly.

In the natural environment, the wind speed is usually less than 5.0 m/ s. Furthermore, the light breeze (1.6–3.3 m/ s) and the gentle breeze (3.4–5.4 m/s) frequently appear in the natural environment. The average values of the wind, 2.5 m/s and 4 m/s are selected as the horizontal incoming wind speed. Therefore, it is conducive to study the influence of the horizontal wind on the aerodynamic performance of the rotor system. In the meanwhile, the situation of the horizontal wind at 0 m/s is also taken as the comparison to analyze the effect of the horizontal wind.

2.3. Force Analysis

Taking a rotor as an example, the airflow model with the presence of the horizontal airflow is shown in Figure 3.

In Figure 3, v is the horizontal wind velocity, W is the weight of rotor, T is the thrust of rotor, L is the relative lift of rotor and α is the angle of attack. With the horizontal airflow, the rotor disk will tilt at a certain angle. Because the rotor is required to generate relative force (to balance the horizontal force) and lift (to overcome the rotor gravity), resulting in stable hovering state. Clearly, the induced power changes with the angle of attack. To derive the effect of the horizontal wind velocity on induced power, the induced velocity v_i for a rotor can be obtained as follow [26]:

$$v_i=\frac{v_h{}^2}{\sqrt{{(v\cos \alpha )}^2+{(v\sin \alpha +v_i)}^2}},$$

(1)

where α is the angle of attack, v is the horizontal wind velocity, v_h is the induced velocity in hover [26].

$$v_h=\sqrt{\frac{T_1}{2\rho A}},$$

(2)

where ρ is the air density, kg/m3; A is rotor disk area, m². By applying the energy conservation, the power required is obtained as follow:

$$P=T\left(v_i+v\sin \alpha \right).$$

(3)

Therefore, the horizontal wind may cause more power consumption resulted by the induced velocity and affect the flight efficiency eventually.

2.4. The Parameters of Aerodynamic Performance

2.4.1. Power Loading

The total hover efficiency of a MAV can be quantified by means of effective power loading (PL). The PL is defined as the ratio of the thrust to power required [27]:

$$PL=\frac{T}{P}.$$

(4)

The thrust coefficient C_T and power coefficient C_P are defined as [28]:

$$C_T=\frac{T}{\rho A{\Omega }^2{R}^2},$$

(5)

$$C_P=\frac{P}{\rho A{\Omega }^3{R}^3}=\frac{Q\Omega }{\rho A{\Omega }^3{R}^3}=\frac{Q}{\rho A{\Omega }^2{R}^3}.$$

(6)

Therefore, the power loading (PL) can be written as:

$$PL=\frac{C_T}{\Omega R{C}_P}=\frac{T}{Q\Omega },$$

(7)

where T is the thrust, N; A is the area of the rotor, m²; P is the power, W; Ω is rotational speed of the rotor, r/min; R is the rotor radius, m; Q is the torque, Nm; ρ is the fluid density, kg/m3; C_T is the thrust coefficient; C_P is the power coefficient.

To maximize the PL, that is, for a given thrust, the power demand is minimum. When designing a vehicle it is wanted to maximize the power loading such that energy requirements are minimized. This will give the vehicle the best endurance or payload capabilities possible.

2.4.2. Hover Efficiency

A figure of merit (FM) is adopted to characterize the hover efficiency. It is regarded as the ratio of the ideal power demand to the actual power demand. In addition, by means of the measured quantities, the figure of merit equation is defined as [29]:

$$FM=\frac{C_T{}^{3/2}}{\sqrt{2}{C}_P}=\frac{T^{3/2}}{Q\Omega \sqrt{2\rho A}},$$

(8)

where T is the thrust, N; Ω is rotational speed of the rotor, r/min; Q is the torque, Nm; C_T is the thrust coefficient; C_P is the power coefficient.

3. Experiment

3.1. Experiment Setup

In order to obtain the performance of the MAV in the horizontal wind, wind tunnel tests were carried out to simulate the environment of MAV at 0 m/s, 2.5 m/s and 4 m/s. Experiment process of the coaxial Tri-rotor MAV considering the horizontal wind is shown in Figure 4.

The dimensions of rectangular test section of wind tunnel are 3 m (length) × 3 m (width) × 2.5 m (height), ensuring sufficient space for maneuvering the multirotor platform. A settling chamber is attached before the test section to characterize the output wind. Wind is generated with two 3 m diameter, 45 kW fans. For the current low Reynolds number experiments the maximum testing velocity is 12.5 m/s. According to the theoretical analysis, the power, rotor speed and thrust of the coaxial Tri-rotor MAV with the horizontal wind are obtained accordingly to convert into the power loading and FM. In the test, propeller is specially made with unidirectional carbon fiber fabrics as stiffener based on the airfoil of C5.5/4.5, with 15.7 cm of pitch and 2.8 cm of chord at 75% position. The rotational speed range of rotor is 1500–2300 r/min. The motor is brushless DC motor(model: MSYSLRK 195.03). The main measuring equipment is as follows: (1) speed controller (model: BL-6); (2) tachometer (model: DT-2234C, accuracy: 6 ± (0.05% + 1D)); (3) thrust sensor (model: CZL605, accuracy: 0.02% F.S.).

3.2. Experimental Results

Figure 5 shows the thrust and power variation.

The thrust and power consumption at 0 m/s is set as the reference value to obtain the increment the variation with the wind effect. According to the Figure 5, it can be observed that the thrust increased with the wind effect, especially at 4 m/s. At the same time, it can be noted that the thrust increment approached to 0 m/s at a higher rotor speed for 2.5 m/s. This is because the rotor interference is much stronger at 2.5 m/s for a rotor speed ranging from 2000 to 2300 r/min. With an increased wind speed, this interference is not domain the aerodynamic environment. In addition, it also can be observed that the required power of coaxial Tri-rotor is also increased 2–4% with the wind speed. This extra power consumption may be generated by the introduced rotor interference when the horizontal wind is considered in this case. However, the thrust increment is higher than the power increment, especially at a lower rotor speed. Clearly, it is advantageous to promote the power loading and the coupling interference is offset to the minimum in the horizontal wind.

Figure 6 shows the variation of the power loading.

In Figure 6, it can be noted that the variation of power loading gradually decreases with the rotor speed especially for 4 m/s. Also, it can be observed that the power loading with incoming flow is greater than that of no wind effect between 1500 and 1800 r/min. In this case, the horizontal airflow will improve the aerodynamic performance of the coaxial Tri-rotors to a certain extent. However, the decreased power loading at a higher rotor speed indicated that the rotor interference is coupled with each other. At this point, the external airflow aggravates the aerodynamic interference between the rotors. For a light breeze, the coaxial Tri-rotor presented a good wind resistance. When the working speed is 2200 r/min, the power loading variation at 2.5 m/s and 4 m/s is about −0.5% and −2%, respectively.

Figure 7 shows the FM increment with the wind effect.

In Figure 7, it can be noted that the hover efficiency in the horizontal wind is higher at lower thrust where the power increment is relatively low. It can be seen that the intervention of the horizontal airflow can promote the aerodynamic coupling between rotors and improve the hover efficiency of the coaxial Tri-rotor. In addition, it can be observed that the hover efficiency is slightly higher when the horizontal airflow velocity at 2.5 m/s, which indicates that the hover efficiency of the coaxial Tri-rotor can be improved by the intervention of the horizontal wind.

4. Simulation Analysis

4.1. Computational Fluid Dynamics (CFD) Setup

Sliding-mesh is applied to solve for the motion of the rotors due to the highly unsteady nature of flow involved in the study and the time-step size is 10e-5. The meshing distribution of the entire computing domain is shown in Figure 8.

The whole computational domain is divided into 7 regions including 1 cylinder stationary region and 6 cylinder rotating regions to capture the flow detail of rotors with refined mesh. Also, the MAV is located at the left region of the domain to obtain the detail of the downwash flow along with the wind direction. Mesh parameters are showed in the

Table 1. Mesh parameters.

Nodes	Elements	Average Skewness	Turbulence Model	Pressure Interpolation	Spatial Discretization
1164307	6472340	0.21734	Spalart-Allmaras	Standard	Second-order upwind

.

To validate the effectiveness of the CFD method, the comparison of CFD and experimental results is showed in

Table 2. Comparison of Computational Fluid Dynamics (CFD) and experiments.

Cases	CT Experiment	CT Simulation	Relative Error (%)	CP Experiment	CP Simulation	Relative Error (%)
1	0.404	0.385	4.94	0.198	0.181	9.39
2	0.578	0.562	2.85	0.215	0.196	9.69
3	0.783	0.742	5.53	0.218	0.197	10.66
4	0.854	0.878	−2.73	0.274	0.248	10.48
5	0.924	0.952	−2.94	0.408	0.375	8.80
6	0.968	0.988	−2.02	0.524	0.572	8.39
7	0.925	0.945	−2.12	0.798	0.764	4.45
8	0.965	0.925	4.32	0.834	0.848	−1.65

. Both the C_T and C_P in experiment and simulation showed that they are generally in good agreement.

4.2. Simulation Results

4.2.1. Velocity Contour

The velocity contour of the coaxial Tri-rotor considering the horizontal wind is shown in Figure 9.

In Figure 9, it can be clearly noted that the downwash flow is moved along with the wind direction. Compared with the case with no wind effect, the velocity variation becomes even more complex, which will affect the aerodynamic performance of the coaxial Tri-rotor. Moreover, with the increase of the horizontal wind velocity, the downwash velocity of the coaxial Tri-rotor gradually decreases and the velocity gradient arrangement of downwash becomes closer, leading to the strong rotor interference. It can be seen that the aerodynamic coupling will be affected by the external airflow and aggravate the aerodynamic interference between the rotors. Moreover, the enhancement of aerodynamic interference will bring the increase of required power. This also verifies that in Figure 5 and Figure 7, the overall power consumption of the coaxial Tri-rotor system with the influence of external airflow is significantly greater than that without airflow.

4.2.2. Streamline Distribution

The streamline distribution of the coaxial Tri-rotor with the horizontal airflow is shown in Figure 10.

In Figure 10, it can be observed that compared with no-flow environment, the streamline deformed with more vortices around the rotor tip in the horizontal wind environment. The streamline is squeezed and deformed, resulting in the vortices under the rotor being deformed and the streamline inclined distribution. At the same time, with the increase of the horizontal wind speed, the streamline arrangement is more compact and the aerodynamic interference between rotors is more intense in this case. Therefore, it can be seen that the horizontal airflow will move the coupling interference between rotors and affect the overall aerodynamic performance. In addition, it can be also noted that compared with the horizontal wind at 4 m/s, the streamline distribution with the horizontal wind at 2.5 m/s is more uniform. The more uniform the streamline arrangement, the better the aerodynamic performance, which also verifies that the power loading of the horizontal wind at 2.5 m/s is greater than that of the horizontal wind at 4 m/s in Figure 6.

4.2.3. Vortex Distribution

The vortex distribution of the coaxial Tri-rotor considering the horizontal wind is shown in Figure 11.

As shown in the Figure 11, it is observed that the vortex will shift to the rear when it is affected by the horizontal airflow. With the increase of the horizontal wind velocity, the vortex shape inclines to the rotor plane. In the meanwhile, it can be noted that with the increase of horizontal wind velocity, the vortex shape becomes slenderer and the vortex overlap area of rotors is larger. Hence, it can be seen that the coupling interference between rotors will be moved with the horizontal airflow, so as to aggravate the aerodynamic interference, which will affect the overall aerodynamic performance of the coaxial Tri-rotor. Above also verifies that when working speed at 2200 r/min, the power loading of the horizontal airflow at 2.5 m/s is greater than that of the horizontal wind at 4 m/s in Figure 6.

4.2.4. Pressure Contour

The pressure contour of rotor tip in coaxial rotors is shown in Figure 12.

In Figure 12, it can be observed that the pressure difference between the upper and lower surfaces of the rotor tip is higher with the horizontal wind which indicated a higher thrust. Also, it can be seen that a part of the thrust produced by the coaxial Tri-rotor MAV with the horizontal airflow needs to be adopted to balance the external force, resulting in the weakened thrust of the rotor. This also verifies that in Figure 6 and Figure 7. With the influence of the horizontal wind, the thrust growth rate of the coaxial Tri-rotor is low, resulting in the poor hover efficiency. In addition, with the increase of the horizontal wind speed, the thrust growth rate of the coaxial Tri-rotor becomes lower and lower.

4.2.5. Velocity Variation Figures

The velocity variation of the lower rotor plane is shown in the Figure 13.

In Figure 13, the lower rotor plane of the coaxial Tri-rotor system is applied to obtain the velocity distribution contour of the horizontal wind at 2.5 m/s and 4 m/s and extract the relevant velocity values for analysis. The distance between the reference point and the coordinate origin is expressed by s. It is interesting to note that the minimum of the downwash velocity will move with the horizontal airflow. When the horizontal airflow is larger, the airflow around the rotor will flow faster and the rotor needs to increase the angle of attack to maintain its overall stability. This also verifies that in Figure 5, with the influence of the horizontal airflow, the thrust growth rate of the coaxial Tri-rotor is relatively low.

5. Conclusions

In this paper, low-speed wind tunnel tests and numerical simulations are performed to obtain the aerodynamic performance of the coaxial Tri-rotor MAV with the horizontal wind ranged from 0 to 5 m/s. Conclusions are as follows:

(1) For a lower rotor speed ranging from 1500 to 1800 r/min, the power required is constant, while the thrust increased up to 9%, which indicated that the coaxial Tri-rotor system with lower speed has larger power loading and better aerodynamic performance. In fact, part of the rotor interference is offset by the horizontal inflow.

(2) The velocity and streamline distribution proved that the required power increment is the result of the downwash deformation with the horizontal wind effect. At the same time, the greater the deformation of downwash comes along with a larger the horizontal wind, which will decrease the whole flight efficiency. Combined with the pressure distribution, it also can be seen that the aerodynamic performance is related to the instantaneous thrust variation.

(3) Compared with the case of no wind, the horizontal wind can promote the aerodynamic coupling between the rotors and improve the aerodynamic performance of the coaxial Tri-rotor system at a lower speed. Conversely, the interaction between rotor tip vortices is stronger with a higher rotor speed, thus the interaction between rotors is transferred by the horizontal wind, resulting in reduced thrust. In this case, the stronger coupling interference directly affects the rear rotor with the action of the horizontal wind, which may lead to the rotor vibration with extra power consumption.

(4) For the rotor speed ranging from 1900 to 2300 r/min, part of the horizontal flow is interacted with the downwash flow, resulting in stronger interference to form an unstable flight. Hence, further study will focus on the compensation of the control strategy, considering a lager wind speed.