Tri-Rotor Propeller Design Concept, Optimization and Analysis of the Lift Efficiency During Hovering

This study introduces the simulation of a tri-rotor contra-rotating propeller for thrust force and hover lift efficiency during vertical take-off. Vertical take-off or landing is a method used by many aircraft and makes the vehicle more convenient and easier to use. The second rotor revolved in the opposite direction of the first and third rotors. The proposed multi-rotor system has NACA 0012 untwisted and symmetric airfoil and includes three rotors with two blades for each. The airflow analysis was optimized with computational fluid dynamics simulation by using different pitch combinations to achieve the highest hover lift efficiency with sufficient overall thrust value. The critical angle of attack for the chosen airfoil gave the boundary conditions for the pitch of rotors. The results showed us that the most efficient combinations for three rotors work better with an increase of pitch angle from top to bottom so that there is a difference of at least two degrees between propellers. Experiments with angles of attack within the boundary conditions showed that the blade combinations starting from three degrees and increasing values gave positive and adequate results in many cases. In addition, the results showed that a regular increase in the angle of attack does not relate to a regular increment in thrust force.


Introduction
The vast majority of unmanned aerial vehicles (UAVs) have a multi-rotor configuration to complete the hovering and vertical take-off or landing [1]. There are several examples of coaxial-rotor designs, such as curved rotors and other VSTOL (vertical/short take-off-landing) that have proven suitable for helicopters [2]. A coaxial propeller design has some cases ( Fig. 1) with fixed wing aircraft such as the Supermarine Spitfire (mk.XIX), Tupolev Tu-95 bomber (known as the bear), the Fairey Gannet and the Avro Shackleton [3]. Rotor efficiency of VTOL vehicles is high compared with other lifting aircrafts due to the massive mass flow through the rotors during hovering. Even in the low speed the coaxial helicopter rotors have better performance than single rotors. Considering this advantage, Kamov coaxial-rotor helicopters were developed, as shown in Fig. 1b [4]. Regarding modern helicopter systems, conventional and multi-rotor configurations have advantages of they own. For conventional helicopters, a single main rotor or single tail rotor can be given as an example while multi-rotor configurations express tandem or tilt-rotor aircraft. Both systems are widely used in military and civil applications [5].
However, considerable performance is achievable with a well-designed propeller which is the essential factor of the system [2]. Similarly, the cruise efficiency can rise with the proper propeller design parameters by increasing the propeller efficiency during the cruise flight [6]. Likewise, coaxial design alleviates the detrimental effects of the retreating blade of conventional helicopters, high-speed performance and critical cruise efficiency [7][8][9][10][11]. A coaxial-rotor helicopter layout shows substantial advantages compared with the conventional single-rotor configuration. It is known that double-rotor, contra-rotating propeller applications are increasing in the military field. In helicopters, the torque of a coaxial-rotor system can be balanced by the two contrarotating rotors, taking over the need for a tail rotor. Thus, the additional weight and power consumption associated with the tail rotor can be saved [8].
Additionally, a coaxial-rotor design has the potential to lighten the adverse effects of retreating blade stalls. The rotor disc has two main areas, namely the advancing side and the retreating side. And the relative airflow during the forward speed of the helicopter is higher over the advancing side, but lower at the retreating side. Moreover, this situation occurs with a higher angle of attack at high-speed flights and restricts the propulsive flight speed of a helicopter. In this regard, a second contra-rotating propeller helps to offset the lift towards both sides of the rotor disc [11,12].
Moreover, the coaxial rotor has three essential advantages in a helicopter. The first one is that it removes the requirements for an anti-torque system, the second one is the rotor diameter can be scaled down when compared with a single rotor and the third one is not having the instability region that causes the "settling with power" condition [13]. Experimental analysis showed that instabilities in the single-rotor design [14] can be eliminated by the addition of a second rotor. The second propeller reduces the instability of the first propeller, by reducing the instability in the vortex ring state [15]. These three advantages give the possibility of more efficiency at most flying conditions while providing a smaller size of the aircraft. In addition, the coaxial layout offers more advantages [2,16,17]. It can provide higher forward speeds than a conventional helicopter. In a tilt-rotor layout, a coaxial-rotor propeller may present some benefits [18], such as better aerodynamic and weight efficiency [7,19,20]. The research of Coleman [21] studied a summary of aerodynamic performance and wake characteristics of the coaxial rotor regarding experimental and theoretical findings; Ramasamy [22] found a 5% reduction in a stacked rotor power by using 7% diameter axial space while the thrust is the same with a coplanar rotor; Serrano et. al. [1] explained the multi-rotor vehicle condition in the case of forwarding flight. It creates a propeller thrust parameter by tilting the rotor disc in the direction of motion. Ferguson [23] made a research on multiple helicopter configurations in terms of performance, dynamic stability, manoeuvrability and handling qualities and investigated the development of compound helicopter configurations. This proved that compounding configuration for thrust increases the forward propulsion thanks to the axial thrust the propellers provide. In addition, the addition of wings to the design has adverse effects on the hover performance of the component helicopter. Another critical performance-related consequence is that it displays unstable longitudinal movements at high-speed flights. Furthermore, a compound helicopter has more promising results in terms of manoeuvrability than a conventional one.
Likewise, the coaxial propeller system has some advantages over the smaller-sized aircraft design when compared to two single rotors mounted side by side. Thus, the efficiency of the contra-rotating propeller system during a forwarding flight needs more detailed research for better recognition [24]. Moreover, the advantages and high performance of the coaxial propeller are the main reasons to study multirotor propellers in this research. The benefits of this system over the other designs claimed to research another version of this design; the tri-rotor system. One of the most notable advantages of this design is a third propeller that reduces the diameter of the propellers while increasing the system ergonomics. Furthermore, it is aimed to design a tri-rotor propeller as an alternative to the coaxial propeller and it has been ensured that this unimplemented design leads to innovations based on the results it has. Therefore, in this study, the aim was to simulate three coaxial rotors using CFD (computational fluid dynamics) method. A solution whether the same or greater efficiency can be achieved with the smaller rotor area provided by the tri-rotor propeller beyond the coaxial propeller is going to be portrayed. One of the main goals of this design is to divide the power between the three rotors so that technical malfunction during flight may lower the effect in flight performance. With flow simulation, it is possible to calculate the thrust force with several different angle values. A wide variety of blade angle combinations were evaluated to understand the aerodynamic performance of the tri-rotors. The optimization process aims (1) to optimize our contra-rotating propeller design; (2) to perform the airflow analysis of the entire design for the different pitch angles, calculate the thrust and torque values for each propeller; and finally (3) to choose the most efficient configuration of the system by calculating hover lift efficiency during hovering.

Geometry Description of the Propeller Design
The first step in the propeller design is to define the aircraft type and desired working condition. All assumptions and determined values are given in Table 1. All the details about the chosen values are explained in this section. The graph shown in Fig. 2 can be used to determine the aircraft type. As seen from this graph, DL (disc loading) and HLE (hover lift efficiency) values are the major values to be identified. Disc loading represents the average pressure change through rotor disc. Hover efficiency is the relation between the weight of an aerial vehicle and the power required to keep it suspended in the air. Our design targets tilt-rotor performance.
As defined before, tilt-rotor values are the target, and in this case, as seen from the graph, the HLE value must be around 3-4. Similarly, DL can be chosen from Fig. 1. On the other hand, the UH1 helicopter is the reference system for our innovative design, because this helicopter is already in use of the military and has valid tilt-rotor efficiency. Its design condition and parameters have been used to create a new propeller system. The required values, such as Mach   [26]. The values used in this design are given in Table  2. In the following steps, how these values are found will be explained.
Taking into consideration to an innovative design, the diameter of the tri-rotor system was calculated using the same disc loading value of the UH1. The disc loading value for a hovering helicopter is determined by dividing the helicopter weight (G) by the area swept by the blades of a rotor ( ).
For this, the gross weight of UH1 and the thrust area of the current blades were used. As known, the weight of a UH 1 helicopter is 3651 kg, and power can reach a maximum of 1000 HP due to the torque limiter [26].
(1) Then, the same disc loading value was used to calculate the propeller diameter. Design assembly for the tri-propeller design is referenced from [27].
where "k" is the safety factor here and "g" is gravity. From the calculations above, we found out that our radius is 1.315 m, and we can calculate our angular velocity as 188.32 rad/s. Then, the thrust force (F) needs to be obtained from the propeller calculation, and design geometry is also referenced from [27]. Thrust force is equal in this study to the gross weight of the helicopter (vertical force) divided by the number of rotors. In the case of the lift, thrust force is higher than the gross weight, and the helicopter would take off.
The missing data in Table 1 were completed, and the final values were obtained resulting in the values given in Table 3.
Afterwards, it is time to choose the proper airfoil which affects thrust force substantially. We preferred to use NACA 0012 airfoil ( Fig. 3) with untwisted geometry, as it was used in other studies [28,29].

Implementation of the Propeller Design
Two blades were used in each rotor as UH1. One of the most critical factors of the three-rotor propeller is the rotor distance. There are several studies where different ratios are applied [31][32][33]. According to these references and after a few simulations, we decided to use a distance equal to 13.3% of the rotor. The multi-rotor system was designed by using three multi-blade rotors. The first rotor blade was designed to rotate clockwise direction. Therefore, the second rotor rotates in an anticlockwise direction, and the bottom rotor rotates at the same direction as the top rotor (Fig. 4).

Simulation Environment
A simulation environment and simulation settings must be validated to simulate the tri-propeller design. To prove the   validity of the CFD (computational flight dynamics) simulation, the rotor of the UH1C "HUEY" helicopter was simulated (Fig. 5). Therefore, SolidWorks Flow Simulation was preferred as a software to find out the lift performance and torque values. The data were taken from Tables 1, 2, 3 and 4. As a reference value, simulation results were evaluated according to the graph that shows the hover lift efficiency and disc loading in Fig. 2.
We created a pilot simulation environment to validate the simulation. One of the most important factors in these kinds of simulations is the environmental conditions. Therefore, this study used the same values for UH1 (taken from ISA atmosphere calculator) [34] given in Table 4. Figure 6 and Table 5 show the results with our simulation settings. As seen from the result, lighter green areas show lower pressure and yellow areas means higher pressure underside which proves the lift. And according to numerical results (Table 5), the desired lifting force is easily obtained by adjusting the attack angle.

Aerodynamic Simulation of Tri-Rotor Propeller System
We have implemented the same simulation settings on the tri-rotor propeller design. The proposed tri-rotor propeller design has three rotors which mean each rotor can have its angle of attack.

First Simulation
One of the most important parameters for each rotor is the angle of attack. To choose the collective pitch for the initial value, we used results from the research of Kusyumov et al. [35] as a reference. In the first simulation, an angle of attack of 3.3 DEG was chosen for the first propeller. For the second and third propellers, we chose 5.3 DEG and 3.3 DEG, respectively. The combinations of the blade settings are working better at + 2°/−2° [15]. In addition, the rotational speed and direction of the rotors are represented in Fig. 7. According to these settings, force and torque results are given in Table 6 Angle configuration display of blades is shown in Fig. 8. The thrust value of the first simulation with the tri-rotor layout is 2924 N, and the power of the triple rotor is 258 HP.   According to these values, efficiency is lower than desired range. To increase the system lift efficiency, angular speed was decreased to create less power for each rotor. This situation was possible by the reduction of the Mach number. As a result, it had to be optimized to obtain the best values.

Second Simulation
According to the first simulation results, the power (HP) of the rotors has to be decreased. For these reasons, we optimized the angular velocity value. This optimization can be achieved by changing the Mach number (M). In the new case, we defined the Mach number as 0.657, and according to this given value, the new angular velocity was 154.682 rad/s. These new values were compared with the UH1C helicopter in Table 7.
With these new values and same environmental conditions, we performed our simulation once again (Fig. 9). Figure 10 shows the airflow around the blades along the y-axis. Distribution of airflow area has decreased due to the reduced angular velocity but shows more vortices formed towards the tip of the propeller. Also, the air velocity decreased.
In this simulation case, the second and third propellers showed positive thrust values because of more pressure under  (Fig. 11). Numerical results (Table 8) showed global force and the total power of the tri-rotor together. The efficiency could not reach the desired value in the initial simulation.
As regards these results, the thrust value and power of the system decreased. On the other hand, HLE slightly increased. In conclusion, the hover lift efficiency still was not sufficient to reach the tilt-rotor standards. We performed several combinations to optimize the results to reach the targeted values. For this reason, an optimization method is performed to find the best design for the entire system.

Optimization of the Three Propeller Layout
The main objective is to find the tri-rotor design which provides optimum hover lift efficiency. To achieve that, the pitch of the rotors is the main parameter. For the tri-rotor, we needed to perform each combination of the blade angles according to the critical angle of attack of the chosen airfoil to find the best efficiency. Critical angle of attack is 8 DEG for NACA 0012 (Fig. 12) [36]. Thus, the blade pitch angle changed between 0°and 8°, and power and thrust coefficient calculations were done with different combinations. The angle-of-attack combination for the rotor blades was performed with a step of 1 DEG.
An exhaustive search method was used for the propeller design optimization. Exhaustive search, also called bruteforce research, is a common problem-solving method aimed at generating and testing the problem [37,38]. It includes an algorithmic approach that calculates all combinations systematically and analyses the results. All the possibilities were overseeing according to this method until reaching the best outcome. All simulations were performed by using the same boundary conditions. Identification of combinations was achieved by giving each rotor an angle from 0 to 8.

Results
Calculation outcome demonstrated that the propulsion efficiency of the propeller increases with the rotor angle-ofattack (AOA) increment [1]. Simultaneously, in this study, the results showed that the highest thrust was obtained by increasing the attack angles of the propellers from the first propeller to the third, or when the third propeller had a higher attack angle than the first and second propellers. Similarly, it is proven that each added rotor increases the overall thrust, even though it produces less force than the previous rotor [39]. However, there is a wide variety of angle-of-attack combinations with triple rotors, and the results are not as constant   as in a single-rotor design; concluding that a coaxial arrangement produces less thrust when compared with a single rotor at the same propulsion power [40]. In addition, we know that the two systems have the same Mach number (0.657) (the first one is the single rotor with 4.5 m diameter of the disc and the other one is a tri-rotor with 2.6 m diameter); the smaller disc area produces less thrust (Table 9). In previous studies, it was stated that the loss of efficiency with decreasing the propeller diameter has been searched, and it was found out that the diameter of the propeller affects the efficiency of the rotor system. Thus, we found out that the same or closer efficiency values can be reached with smaller diameter values thanks to an increase of the number of rotors. Finally, when these two systems are compared, the efficiency of the first one is 1.976 and the tri-rotor efficiency is 1.511. Efficiency is more dependent on diameter, rather than angular speed [40].

Thrust Force and Hover Lift Efficiency
According to the results obtained from the simulations under all the combinations stated before, some essential inferences are: 1. In the case of 1 DEG for the first propeller, when we used a higher angle at the second and third propeller subsequently, the first propeller always showed a negative thrust (Fig. 13). This intrigued us to try with higher angles for the first propeller. An example of the pressure distribution created by using 1 DEG in the first propeller is shown in Fig. 14. Moreover, the thrust force graph (Fig. 13a) proves the negative results of the first propeller. Likewise, the global force values (Fig. 13b) and hover lift efficiency (Fig. 13c) are not sufficient for these configurations.
However, the pressure distribution results further establish that the first propeller has lower pressure on the underside than the upside, contrary to the second and third propellers; this situation means the first propeller works to create downforce while others create lift. This situation is shown in all 1 DEG combinations.
2. As the angle of attack of the third propeller decreased, the hover lift efficiency started to reduce. The results of the third propeller with 1 DEG combinations are shown to understand this extreme loss of thrust force. The third propeller always gives a negative value when 1 DEG combination is used (Fig. 15a). Also, efficiency is insufficient and below 1.5 (Fig. 15c).
In this case, there is a higher pressure found on the upper side of the airfoil of the third propeller. This caused a negative thrust overall (Fig. 16a, b). Also, the first and second propellers do not have regular results. In some cases, the first propeller may have a negative result overall (Fig. 16a).
Apart from these combinations, the results in the case of sliding the degree of the third propeller are given in Fig. 17a, b. Again, the third propeller was found to not provide high values at low degrees. Moreover, the hover lift efficiency decreased as the third propeller angle value was reduced from 8 to 1. It is worth noticing that the second propeller was  Fig. 17a and 8 DEG in Fig. 17b. This specific part of the combination is shown in the latter graphs for a better understanding of the behaviour of the propellers.
3. When the AOA (angle of attack) increased in the first, second and third rotor, respectively, the system gave sufficient thrust for the lift values, especially at high angles in the second and third propeller. Moreover, the HLE is closer to the desired limits (between 3 and 4). But, in many combinations all propellers are not working in harmony since at least one of them showed a negative thrust (Fig. 18). However, the pressure results of 3-7-7 DEG combination have the best lift performance for the second propeller and a higher pressure as shown in Fig. 19. These results showed a conflict between the second and third propellers when having an equal angle-of-attack value. 4. Finally, for the best result scenario, in the case of increased rotor angles, we found sufficient thrust at certain angles, and the best results were outlined. The average value of hover lift efficiency is close to 3 for the successful combinations. In these combinations, each propeller gave positive results (Fig. 20) which represents the lift. The propeller on such combinations created a balanced force, while in others, a single propeller produced a higher lift. In the cases where a single propeller produces high thrust, the other propellers do not show strong results. In instances where two propellers create sufficient thrust, the thrust force of the third propeller is negligible. Additionally, HLE values are average between 2.5 and 3. Finally, from the flow velocity behaviours of the best propeller designs, the first and third propellers produced a higher lift force (Fig. 21). The second propeller, being the only propeller that rotates in the opposite direction, must both provide balancing and assist the thrust force. Therefore, its performance is more unstable in some cases.
Additionally, the blue areas in Fig. 21 are mostly more specific on the upside of the propellers. The highest pressure appears at the leading edge of the propellers. Moreover, there is a high rate of vortices at the trailing edge.

Thrust and Power Coefficient
The lift and power coefficient values were calculated to verify the numerical results of our design and to compare it with other studies. These values are independent of the number of blades or rotors used, as well as the type of airfoil used. The formula as defined in Eq. x is used, where T is the thrust force, P is the power, ρ is the air density, A is the disc area and V tip is the tip speed of the propeller.
This analysis was performed for combinations showing increased angles of attack; even if the ascending of coefficient values are not regular, they will show an irregular increment against an increment in attack angles (Fig. 22).
Ramasamy [5] compared the hover performance of single, coaxial, tandem and tilt-rotor configurations. Likewise, the NACA 0012 airfoil was used as the untwisted airfoil, similar to our study, but an additional highly twisted (xv-15) airfoil was used for each design. When we consider it as a similarity of design, it would be logical to compare the coaxial-rotor results. The coefficient of power (C P ) value is in the 0.0001-0.0008 range, while the coefficient of thrust (C T ) is in the 0-0.008. These ranges are the results for untwisted blades. Considering the twisted blades, C P is in the 0.0002-0.001 range, while C T is between 0 and 0.01. In another study, Tang et al. [41] analysed the contra-rotating propeller with high-lift airfoil S1223. CFD analysis gave them the efficiency of the design. C T takes values between 0.03 and 0.13, and C P values are between 0.006 and 0.0016. Gur [42] made a research on contra-rotating configuration.
According to the Harrington test, C T values are from 0 to 0.006 and C P is between 0 and 0.0005. Haider et al. [43] studied single-rotor design for an agricultural unmanned helicopter. In this study, three types of blade configurations have been investigated. They used V1505A and V2008B airfoils on these configurations. Also, untwisted and twisted versions of these designs have been analysed. As a result, each design showed results in the same range of values: 0.3-1.2 for C T and 0.04-0.26 for C P . Finally, Kusyumov et al. [35] studied with a single rotor and made CFD analysis of the single-rotor propeller which was used NACA 0012 airfoil. It has been Hover LiŌ Efficiency c found out when the thrust is equal to the weight of the helicopter, the thrust coefficient is equal to 0.0055. The graph in Fig. 22 shows that C T has values around 0.005-0.018, while C P is between 0.00055 and 0.00125. A comparison of our results with other studies is given in Table 10. Moreover, C T and C P showed close results, especially with studies using the NACA0012 airfoil. An increment in torque is the result of raised induced power due to the induced drag at a high angle of attack [43]; these values are valid compared with other current studies with NACA0012 airfoil with both types of designs, twisted and untwisted. As a result, the results show similar results with a general range between 0.0001 and 0.0125 compared with the studies using NACA0012.
Finally, the numerical results of coefficients for sufficient angle-of-attack combinations shown an increment in values but not proportionally. The biggest reason for this pattern is the diversity in the angle-of-attack combinations, and this is more complicated in the triple rotor system. Coefficients of thrust and power represent similar results but as seen at some points an abnormal decrease in strength is observed at some combinations such as (3-6-7), (4-7-8), (6-6-7) and (7-7-7) (Fig. 23).

Discussion
This study shows the results of the propeller design that used a symmetrical and untwisted basic airfoil. These results must  Hover LiŌ Efficiency c be considered according to the limitations of the NACA 0012 airfoil, especially regarding the angle of attack. As seen from the results, generally, one of the rotors gave negative thrust force in many tested combinations, even if the total force of the propeller is sufficient. Consequently, these outputs showed that the results are not constant for these specific variables and settings. But still, this design gave us some major information to understand the performance of a tri-rotor propeller in a wider aspect. Also, this basic design might be a pioneer of noticing out which points need to be improved in the multi-propeller design in the future.

Conclusions
The most important deduction that can be drawn from all the results shown is that the diameter of the rotor has decreased by 42.27% when compared with the single-propeller version of the same design parameters. The single-propeller diameter value is calculated as 4.5 m for this study. This value gives us one of the important advantages of this system, the reduction in the frontal drag area. The results proved that even if this trirotor propeller system produces sufficient thrust for hovering, in many situations, there is a conflict between the second and third propeller which is stronger at high angle combinations (6 DEG, 7 DEG and 8 DEG for NACA 0012). Additionally, the coaxial design does not manage to support the power to the total system all the time. One reason for this might be because of the lower propeller performing a prop wash for the upper unit [40]. That is the problem that shows the point that needs to be improved in this design. That is because only the second propeller needs to involve in balancing and creating thrust force in the opposite direction to the other two propellers. The only disadvantage compared to the dual contra-rotating rotor system is that two propellers need to be balanced with one.
Nevertheless, the entire system gave positive results and sufficient thrust force at a few intervals. By considering combinations where this conflict does not exist, a certain working area can be determined or the interactions between different types of airfoils can be studied. Consequently, this design has great potential, because the propellers compensate for each    other's performance drops, just to eliminating instabilities. In addition, the results showed that at least two angles of increment between the propellers is the key point for better efficiency.
Author Contributions All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by LP and MS. The first draft of the manuscript was written by MS, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
Funding Open access funding provided by Alma Mater Studiorum -Università di Bologna within the CRUI-CARE Agreement. The authors declare that no funds, grants, or other support was received during the preparation of this manuscript.

Data Availability
The datasets generated during and/or analysed during the current study are not publicly available but are available from the corresponding author on reasonable request.

Conflict of interest
The authors have no relevant financial or nonfinancial interests to disclose.
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