The quad tilt rotor aircraft used in this paper is shown in Figure 1 below. The front and rear wings and rotors of this model are of the same size and at the same horizontal height. Different from common tilting rotor models, this model adopts overall tilting of the rotors and part of the wings to avoid the “fountain effect” [11] , which greatly improves the flight efficiency of tilting wing aircraft during vertical takeoff and landing.

In order to study the overall performance of the vehicle, the aerodynamic characteristics between the vehicle’s components must first be studied to provide a basis for further improvement of the type, the overall parameters of the vehicle and the parameters of the propeller are shown in Table 1.

The front and rear wings and rotors of the type are of the same size, so the research object of this article is mainly component based, providing a basis for further improvement of the type, so all the research omits the fuselage, thus saving operations, such as performing separate rotor simulation operations, performing the same simulation operations for separate rotors and wings, and performing different rotor combinations for a pair of front and rear wings and rotors. The flow field calculation watershed used is a cuboid, about 15 times the length of its own size. The generation method of non structural grid is used, and the grid type is polyhedral grid. In order to restore flow details more realistically, the number of grid used is more than 10 million.

In order to fully simulate the flow of the wing and rotor boundary layer, it is necessary to generate a boundary layer mesh on the surface of the wing and rotor, so that y⁺ is close to 1, and the calculation formula of y⁺ is as follows: (1), so as to calculate the grid spacing of the first layer of the grid boundary layer. 15 boundary layer grids were generated, and the mesh growth rate was 1.2. And some details of the local encryption, so that the operation can be better convergence, to achieve better simulation effect, grid diagram as shown in Figure 2.

y + = u ∗ y μ (1)

u ∗ is friction velocity near the wall, y is the distance between the first mesh node and the wall, and μ is the kinematic viscosity of the fluid.

Multiple reference frame is a common computational method, which is one of the simpler multi region computational methods. Different rotational or translational velocities can be assumed in different regions, and the transient problem is solved approximately as a steady state problem. If the region is at rest, the equation is transformed into the form of a stationary system. At the interface of the computational domain, a local reference frame is used to perform flux calculations of flow variables in one region and convert them to adjacent regions. The most important feature of the multiple reference frame method is that it can simulate the model directly, reflect the effect of the blades on the flow field more realistically, save computational resources relatively, and the results are more accurate.

In this paper, the aerodynamic characteristics of each part of the tilting quadrotor were simulated by solving Reynolds mean N-S equation. The turbulence model was selected as SSTK-ω model, the steady-state calculation was selected to solve the N-S equation, and the medium characteristics of the flow field were selected as ideal gas. The numerical solutions could be obtained more accurately through comparison. The quad tilt rotor aircraft calculated in this article has the same rotor specifications and front and rear wings. Therefore, the numerical calculation between components is carried out in this paper, and only one side is selected, excluding the fuselage.

The turbulence model is SSTK-ω model, according to reference [12] , K is used to describe the change of turbulence energy, and the governing equation is as follows:

∂ ∂ t ( k ρ ) + ∂ ∂ x j ( ρ u j k ) = ∂ ∂ x j [ ( μ + σ k μ t ) ∂ k ∂ x j ] + P k − ρ ε (2)

where ρ is the fluid density, k is the turbulent kinetic energy, u j is the velocity component, μ is the dynamic viscosity, σ k is the correction coefficient, μ t is the turbulent dynamic viscosity, P k is the turbulent energy generation term, and ρ ε is the turbulent dissipation rate.

The Omega equation is used to describe the variation of turbulent dissipation rate, and the control equation is:

∂ ∂ t ( ρ ω ) + ∂ ∂ x j ( ρ u j ω ) = ∂ ∂ x j [ ( μ + σ ω μ t ) ∂ ω ∂ x j ] + P ω − C lim ρ ω 2 (3)

ω is the turbulent dissipation rate, σ ω is the correction coefficient, P ω is the turbulent dissipation rate production term, C lim is the limiting factor.

This paper uses the rotor in reference [13] as an example to verify the multiple reference frame method. The main parameters of this type of rotor are shown in Table 2 below.

Figure 3 compares the calculated tension of an isolated rotor at different speeds with experimental values in the literature. Through numerical calculation, it can be seen that the rotor lift force obtained by the numerical simulation of multiple reference frame method is basically consistent with the experimental value on the whole, which can meet the needs of engineering calculation.

This section carries out a study on the influence of an isolated rotor on its aerodynamic performance under conditions of different coaxial flow velocity. The rotor speed is 1600 RPM, and the axial flow velocity is 8 m/s, 15 m/s, 30 m/s, 45 m/s and 60 m/s respectively. This speed range includes the speed under all conditions from take-off to cruise. It provides the basis for further improving the propeller. Grid independence verification was carried out for a single rotor. The number of grids calculated for the first time was 5 million, the number of grids calculated for the second time was 10 million, and the number of grids calculated for the third time was 15 million, and the error of the three calculations was within 5%. Figure 4 shows the force calculated for the three times of the rotor, and Figure 5 shows the moment of force calculated for the three times of the rotor.

It can be seen from the data in the figure that with the increase of the axial flow speed, the tension of the rotor decreases sharply, and the torque of the rotor also decreases. This is because the initial flow velocity is small and the impact on the rotor is also small, which can even be ignored. The rotation speed of the rotor is enough to provide a large pull and torque. On the one hand, the performance of the rotor depends on the speed. As a result, the aerodynamic Angle of attack of the blade element is reduced, which leads to the reduction of the tension and torque of the entire rotor. Therefore, from the practical point of view, the pitch variation of the propeller needs to be considered in the real application, so as to achieve the best performance of the rotor.

The study in this section is to determine the optimal lateral position of the propeller on the wing, so as to maximize the wing lift-drag ratio and minimize the performance loss during the roll. Since the front and rear wings and rotors have the same specifications, only the front wings and rotors are selected as the research object in this section. Start from the outermost position of the wing, that is, the position of the wing tip, which is recorded as the position of 0 m, start from the position of 0.5 m, and move closer to the position of the wing root in turn. Each position of 0.5 m is regarded as the position of a rotor, which is successively placed at the positions of 0.5 m, 1 m, 1.5 m 2 m, and 2.5 m, as shown in Figure 6 below.

The rotors are at different lateral positions on the wing, thus monitoring wing lift and drag, lift-drag ratio, and rotor force are shown in Figures 7, 8, and 9, respectively.

From the above figure, it can be observed that as the rotor moves laterally towards the wing root, the lift of the wing gradually increases while the increase in drag is relatively small. This is because as the rotor gets closer to the wing root, the rotor’s induced flow affects a larger area of the wing, resulting in an increase in the nearby airflow velocity, lift, and drag. Furthermore, from the above figure, it can be seen that although the lift of the wing increases as the rotor gets closer to the wing root, according to Figure 8, the maximum lift-to-drag ratio occurs when the rotor is positioned at 1.5 along the wing. Beyond 2 m the lift-to-drag ratio starts to decrease. This is because at 1.5 m, the rotor’s induced flow affects the largest area of the wing, resulting in an optimal lift-to-drag ratio at that location. Due to the wing’s shape, which has a certain amount of dihedral angle, and the tilt position of the rotor being at the mid-span of the wing, although the rotor at 2.5 m along the wing can provide a greater lift for the wing, during the tilting process, some of the rotor’s downwash flow will act on the fixed section of the wing, resulting in the so-called “fountain effect.”

Therefore, the rotor located at 1.5 m of the wing is the best position, which can not only provide the maximum lift-drag ratio, but also avoid the loss of aircraft performance during the tilt process.

The wing of tilting quadrotor aircraft will be affected by the rotor wake when flying forward, and the rotation direction of the rotor will directly affect the flow direction and speed of the air behind the rotor, which has a great influence on the pressure distribution and aerodynamic load on the wing. Therefore, it is necessary to study the influence of different rotor rotation layout on the aerodynamic characteristics of the whole aircraft. In order to balance the reverse torque, the rotation directions of the two rotors of the tilting quadcopter on the same wing surface should be opposite, so the rotation directions of the rotors are as shown in Figure 10. It is defined that the rotation direction of the rotors towards the wing root is as inward rotation, and the rotation direction towards the wing tip is as outward rotation. Therefore, group (a) means that the rotors rotate inward, group (b) means that the front rotors rotate inward and the rear rotors rotate outward, and group (c) means that the rotors rotate outward. Group (d) The front rotors turn outward and the rear rotors turn inward. In order to save computing resources, only the front and rear wings and rotors on one side of the fuselage are also selected to match, excluding the fuselage, and only the different rotation directions of the front and rear wings and rotors are calculated.

The effects of different rotor direction combinations on wing lift and rotor force are shown in Figures 11 and 12.

As can be seen from Figure 11, the front wing lift increases in spin combination (c) and spin combination (d). In both configurations, the front rotor rotates outward from the nose, while the rear wing lift increases in spin combination (b) and spin combination (c). In both configurations, the rear rotor rotates outward from the nose. It can be seen that the layout in which the rotor rotates outward on the wing can improve the lift of the wing to a certain extent, because the sliding flow of the propeller will increase the lift of the wing, and the left and right sides of the propeller will respectively produce upwash and downwash on the wing, among which the upwash is the main source of the increase in lift. Therefore, when the rotor rotates outward, the lift of the wing can be improved. The upwash produced by the rotor will produce a certain increase in the lift of the wing. As can be seen from Figure 12, the rear rotor tension increases in rotation combination (b) and rotation combination (d). In these two layouts, the rotation direction of the front and rear rotors is opposite, indicating that the front rotor rotation also has a certain influence on the rear rotor force.

From the above figure, it can be seen that the four rotors are arranged in a layout where the rotation directions of adjacent rotor positions are opposite and the rotation directions of diagonal rotor positions are the same, which improves both the tension on the rotor and the lift on the wing. Due to the influence of the rotor, there is a circumferential velocity in the wake of the rotor that is the same as the rotation direction of the rotor, resulting in an additional upward velocity component in the wing flow behind the rotor, which reduces the local wing profile inflow angle, increases the aerodynamic attack angle, and ultimately increases the lift of the entire wing, the same applies to the rotor.