Aerodynamic Interference of Lift Surfaces During Transition Phase for VTOL Fixed-Wing UAVs with Canard Configuration

Abstract

The compound lift and thrust Vertical Take-Off and Landing (VTOL) fixed-wing Unmanned Aerial Vehicle (UAV) has generated considerable interest in configuration research due to its unique application advantages. This investigation examines the aerodynamic phenomena between the rotors and the main wings, as well as canards, during the transition phase through numerical simulations, thereby advancing the understanding of canard configurations in such UAVs. Based on a systems engineering approach, a 6 kg canard-configured compound lift and thrust VTOL fixed-wing UAV was preliminarily designed for evaluation. Computational Fluid Dynamics (CFD) methods were employed to study the aerodynamic interference under various freestream velocities and rotor speeds during the transition phase. The reliability of the CFD methodology was validated through rotor thrust experiments. Simulations were conducted with freestream velocities ranging from 3 m/s to 15 m/s and rotor speeds from 4000 to 10,000 RPM. The results indicate that the interference of the rotating rotor during the transition phase initially reduces lift, then increases lift, and finally reduces lift again for the wing, while it increases lift for the canard. This phenomenon results from the coupled influence of freestream velocity and rotor-induced flow effects.

1. Introduction

Lift-thrust compound VTOL UAVs represent a prevalent configuration of hybrid fixed-wing rotorcraft, characterized by integrated architectures that synergistically combine fixed wings and rotorcraft elements. This configuration inherits the aerodynamic advantages of fixed-wing UAVs, such as high cruise velocity and long endurance, while incorporating the operational versatility of multi-rotor systems, including vertical takeoff/landing capabilities and precision hovering performance [1]. Owing to these unique operational advantages, VTOL UAVs enable broader application scenarios, consequently driving comprehensive research efforts in UAV design optimization [2,3,4]. However, achieving optimal aerodynamic performance while maintaining these operational advantages presents significant design challenges [5]. This is particularly evident during the complex transition flight phase, where aerodynamic interactions between rotors and fixed-wing components become increasingly pronounced.

Contemporary lift-thrust compound VTOL UAVs predominantly utilize conventional tail configurations in their fixed-wing systems. Extensive investigations of the aerodynamic characteristics between rotors [6] and between rotors and wings [7,8,9,10,11,12] have been conducted using numerical simulations and wind tunnel experiments. For conventional-layout UAVs, Gesang Nugroho et al. [13] numerically analyzed the aerodynamic characteristics of various tails under rotor-off conditions.

Compared with the conventional tail-aft configuration, the canard layout offers distinct aerodynamic advantages, such as completely avoiding deep stall, achieving higher aerodynamic efficiency, and reducing structural weight [14]. Consequently, extensive research has been carried out on its aerodynamic characteristics and performance of canard-configured aircraft [15,16,17]. Through numerical investigations, Liu Zhanhe [18] employed FLUENT simulations and demonstrated that a twin-fuselage canard UAV exhibits superior lift-to-drag performance. Sun Wei [19] conducted unsteady numerical simulations of a full aircraft with rotating wings in forward flight using an overset mesh technique, showing that the interference of the rotors with the canard and vertical tail is relatively weak. Pedro S [20] investigated four VTOL canard aircraft configurations and quantified their performance, revealing that, compared with the clean configuration, a fully exposed VTOL system significantly deteriorates the lift-to-drag ratio. Based on blade element theory and wind tunnel test results, Honggang Gao [21] developed an aerodynamic model of the main rotor system and analyzed the flight dynamics of a canard aircraft in helicopter mode, concluding that with increasing forward flight speed, the canard and horizontal tail can provide considerable lift. Zhao et al. [22] designed a scaled lift-cruise vehicle featuring a canard lift configuration, conducting flight simulation experiments to support subsequent hardware-in-the-loop simulations and prototype flight tests.

Significant aerodynamic coupling exists between the rotor and fixed wing of UAVs, exhibiting increasingly complex characteristics during the transition phase. Previous studies have extensively investigated these interactions through numerical simulations. Mi Baigang [23] investigated the aerodynamic characteristics of a joined-wing compound UAV using CFD, and the results indicated that forward flight speed is a key parameter in the takeoff-to-transition stage, where rotor deceleration and propeller acceleration induce slipstream and downwash interference, directly leading to notable force and moment perturbations. Longjin Ai [24] employed CFD to study the influence of rotor position on the lift and drag of the fixed wing during transition, identifying the rotor location that minimized wing lift and drag fluctuations. Liu Jiahao [25] conducted numerical simulations on rotor–wing aerodynamic interference during the tiltrotor transition phase, demonstrating that the induced slipstream of the rotor provides a certain lift benefit to the wing in the mid-transition stage, whereas no significant lift gain occurs in the early and late stages, with negative gain even observed in the initial phase. Wang Mengtian [26] utilized overset-mesh-based CFD simulations to investigate the aerodynamic performance variations of a tiltrotor rotor–wing system under different transition states, and found that the wing lift and drag coefficients decrease with increasing tilt angle, while the degree of variation diminishes as the advance ratio increases. Daud Filho A. C. [27] employed a dynamics model based on rigid-body motion equations to investigate the transition-flight performance of a VTOL lift-wing quadrotor aircraft with various wing–canard incidence angle combinations, and proposed that such a configuration could be applied to missions currently performed by multirotor UAVs. However, these investigations did not examine the complex aerodynamic configurations in canard-configured VTOL fixed-wing UAVs or adequately address the dynamic transition flight regime.

Despite extensive research on VTOL aircraft aerodynamics, several critical knowledge gaps remain. First, the majority of existing studies focus on conventional tail configurations, with limited attention to canard-configured VTOL systems. Second, most investigations examine either stationary hover conditions or steady forward flight, with insufficient analysis of the dynamic transition phase where the most complex aerodynamic interactions occur. Third, the specific aerodynamic coupling phenomena between rotors and both canard and main wing surfaces in canard-configured VTOL aircraft remain poorly understood. The complex three-dimensional flow interactions, wake interference patterns, and their impact on overall vehicle performance require systematic investigation to enable optimal design and control strategies.

To address these knowledge gaps, the present study conducts a CFD-based investigation of rotor-induced aerodynamic effects on canard-configured VTOL fixed-wing UAVs during constant-altitude transition flight. A validated CFD model is employed to simulate and analyze the effects of rotor-induced flow on the aerodynamic performance of the main wing and canard during constant-altitude transition flight. The main wing and canard are selected as the primary subjects of investigation, with five combinations of rotor rotational speed and freestream velocity examined. Through the analysis of lift generation characteristics and aerodynamic coupling interactions, the underlying aerodynamic variation mechanisms and potential physical phenomena occurring in the transition phase are elucidated. The results provide a more comprehensive understanding of rotor–fixed-wing interactions for the canard VTOL configuration, thereby offering enhanced design guidance and potential optimization strategies for transition-phase control.

2. Models and Methods

2.1. Numerical Simulation Methods

This study employs Fluent 2021R1 software, which is based on the Finite Volume Method (FVM). The finite volume method discretizes the solution domain into a finite number of small control volumes using computational grids. The Reynolds-Averaged Navier-Stokes (RANS) equations employed in this investigation are given by the following formulation:

$${\displaystyle \frac{\partial }{\partial t}}\mathit{E}+\nabla F_{\mathrm{I}}+\nabla F_{\mathrm{V}}=\mathit{Q}$$

(1)

where: $t$ denotes time, $\mathit{E}$ represents the conservative variable, $F_{\mathrm{I}}$ indicates the inviscid flux, $F_{\mathrm{V}}$ corresponds to the viscous flux, and $\mathit{Q}$ stands for the source term generated by rotation.

Considering the complex flow features and computational cost in the present study, it is noted that the k-ε model exhibits limited accuracy in predicting turbulence within separated flow regions. Although the k-ω model is suitable for near-wall flow prediction, it is relatively sensitive to initial conditions and may yield non-physical results. Therefore, the negative-form Spalart–Allmaras (SA-neg) one-equation turbulence model was adopted in this work. This variant is based on the original formulation proposed by Spalart and Allmaras (1992) [28], with the inclusion of a negative-value treatment to enhance numerical stability in strongly separated flows. Owing to its favorable capability in predicting separation and maintaining numerical robustness, the SA-negative model has been successfully applied in both external aerodynamic flows and rotating machinery problems [25,28,29,30,31,32,33]. The transport equation is given as follows:

$${\displaystyle \frac{\partial \tilde{\nu }}{\partial t}}+U_j{\displaystyle \frac{\partial \tilde{\nu }}{\partial x_j}}=C_{b1}\left[1-f_{t2}\right]\tilde{S}\tilde{\nu }+{\displaystyle \frac{1}{\sigma }}\left\{\nabla \cdot \left[\right(\nu +\tilde{\nu })\nabla \tilde{\nu }]+C_{b2}(\nabla \tilde{\nu }{)}^2\right\}-\left[C_{w1}{f}_w-{\displaystyle \frac{C_{b1}}{{\kappa }^2}}{f}_{t2}\right]{\left({\displaystyle \frac{\tilde{\nu }}{d}}\right)}^2+f_{t1}\Delta U^2$$

(2)

where: $\tilde{\nu }$ is the modified turbulent kinematic viscosity, $\nu$ is the molecular kinematic viscosity, $d$ denotes the distance to the nearest wall, $U_j$ represents the velocity components, and $\tilde{S}$ is the modified magnitude of the strain rate, $f_w$, $f_{t1}$ and $f_{t2}$ are empirical functions, while $\sigma$, $C_{w1}$, $C_{b1}$, $C_{b2}$ and $\kappa$ are model constants.

2.2. Computational Model

The computational model is based on a 6 kg canard-configuration VTOL fixed-wing UAV designed using a systems engineering approach, with its primary parameters presented in

Table 1. The design parameters of the 6 kg-class canard-configuration VTOL fixed-wing UAV.

Parameters	Value
Wing Airfoil Section	NACA4412
Canard Airfoil Section	MH114
Wing Span	2.028 m
MAC	0.207 m
Canard Span	0.65 m
Canard Chord Length	0.07 m
Wing Installation Angle	4.219°
Canard Installation Angle	4.593°
Cruise Speed	18 m/s

.

The propulsion system was matched with Qianfeng 12 × 6-inch rotors, where the numbers 12 and 6 denote the 12-inch diameter and 6-inch pitch. Its diameter is approximately 0.3048 m, as shown in Figure 1a. A 3D scanner was employed to capture the rotor geometry, from which the three-dimensional rotor model was reconstructed as shown in Figure 1b. As the hub section does not contribute to lift generation, the geometric details at the hub location were simplified. The model of the 3D scanner is Tianyuan UE7 (Beijing Tianyuan Three-Dimensional Technology Co., Ltd., Beijing, China), with a scanning accuracy of no more than 0.02 mm.

2.3. Numerical Simulation

2.3.1. Computational Domain

The computational domain for the CFD model was divided into three distinct fluid regions: one outer stationary domain and two inner rotating domains, each containing a propeller. The external stationary domain was configured as a rectangular box structure, with dimensions set at 12–20 times the characteristic length of the study object, following the guidelines established in reference [6]. An interface was established between the outer stationary and inner rotating domains, employing sliding mesh technology to accurately capture fluid interactions. The inner rotating domains were positioned approximately 5 m from the velocity inlet and pressure outlet boundaries, and 3 m from the upper/lower boundaries. All CFD models employed identical external flow field dimensions to ensure consistency. Figure 2 illustrates the computational domain configuration used in the CFD simulations, incorporating symmetry planes, velocity inlet, and pressure outlet boundaries. The blue annotations in the figure denote cross-section locations analyzed in subsequent sections: Section 1 is located below the rotor plane, while Section 2 passes through the rotor axis parallel to the freestream direction. Additional boundary conditions included no-slip conditions on propeller surfaces and free-slip conditions on outer stationary domain walls to prevent non-physical velocity solutions.

2.3.2. Mesh Generation

The mesh generation process was divided into four regions of the computational domain: the outer stationary domain, the core body of interest (BOI), and two inner rotating domains. All mesh generation was conducted using ANSYS FLUENT 2021R1. The core body was designed to enhance mesh quality in the region below the propellers, thereby improving the capture of propeller wake characteristics. Volume sizing was used for mesh generation, with a maximum cell size of 4 × 10⁻² m. For the inner rotating domains, surface sizing was used to ensure uniform mesh dimensions at the contact interfaces between the outer stationary domain and the inner rotating domains, ensuring computational accuracy at the interface boundaries. Both internal and external domain surfaces at the interface were assigned a maximum element size of 2 × 10⁻⁴ m to maintain mesh uniformity across all computational regions. Surface sizing was employed to mesh the propeller surfaces, with a maximum cell size of 1 × 10⁻³ m. Eleven boundary layers were applied to the wing, canard, and propeller surfaces, with the first layer height set to 2 × 10⁻⁶ m and a growth rate of 1.3, ensuring that the dimensionless wall distance (y+) at 75% blade radius is approximately 1. The specific mesh setup for the model is shown in Figure 3.

2.3.3. Mesh Independence Study

To achieve an optimal balance between computational accuracy, stability, and efficiency, a grid independence study was conducted to determine an appropriate mesh density. At a freestream velocity of 12 m/s, four computational grids were generated, as listed in

Table 2. Total number of cells and nodes in the computational domain.

	Number of Cells	Number of Nodes
Mesh 1	10,868,830	26,709,659
Mesh 2	12,590,818	31,130,816
Mesh 3	14,124,195	35,253,722
Mesh 4	18,738,984	47,188,400

, by successively refining the mesh resolution over the wing surface, canard surface, propeller surface, inner rotating region, and fuselage core. Figure 4 illustrates the variation in wing lift coefficient as a function of mesh count. The results show that when the number of mesh reaches 14 million, the calculated lift becomes stable, indicating that the mesh independence has been achieved. Therefore, the 14.12-million-cell mesh was selected for all subsequent calculations.

2.3.4. Solver Settings

Two principal CFD approaches are commonly used for simulating rotating flows: the Multiple Reference Frame (MRF) method and the sliding mesh technique. The MRF method is a steady-state approach that, in many cases, provides the initial condition for sliding mesh simulations. Although transient techniques generally yield more accurate predictions, they entail significantly higher computational costs. Due to the periodic flow field fluctuations induced by rotor rotation, transient simulation methods are necessary to obtain accurate aerodynamic data, despite constant inflow conditions and rotor speed. This study employs the MRF approach for steady-state computations, as this method has been extensively validated in numerous previous studies investigating propeller performance [34,35,36,37]. The converged steady-state results serve as initial conditions for subsequent transient simulations using the sliding mesh method.

Velocity inlet boundary conditions are specified as 3, 6, 9, and 15 m/s to simulate the low-speed flight regime during the VTOL-to-cruise transition phase. Both forward and aft rotors are configured to operate within the 4000–10,000 RPM range. Interface boundaries are established between the rotating and stationary zones to facilitate data interpolation and exchange. The Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm is implemented for pressure-velocity coupling. Spatial discretization employs second-order pressure interpolation and second-order upwind schemes for the momentum equations, turbulence kinetic energy, and turbulence dissipation rate. Temporal discretization utilizes a second-order implicit upwind formulation. To maintain a temporal resolution of 1° rotor rotation per time step while satisfying the Courant number constraint (CFL < 5), time step sizes are carefully selected as 4.17 × 10⁻⁵, 3.33 × 10⁻⁵, 2.78 × 10⁻⁵, 2.38 × 10⁻⁵, 2.08 × 10⁻⁵, 1.85 × 10⁻⁵, and 1.67 × 10⁻⁵ s for different rotational speed conditions. The maximum number of iterations per time step is set to 20 to ensure adequate solution convergence within each time step. Convergence was achieved when both computational step residuals fell below 10⁻³ and the percentage error in lift coefficients between corresponding time steps of two consecutive rotor cycles remained below 8%. Figure 5 presents the percentage error in lift coefficients between corresponding time steps of two consecutive complete rotor revolutions for the wing and canard, demonstrating that the maximum variation remains within the 8% convergence criterion.

All simulations were performed on a dual-processor server equipped with two AMD EPYC 7763 64-core processors (Advanced Micro Devices, Inc., Santa Clara, CA, USA) operating at 2.45 GHz and 256 GB of RAM. The computations were parallelized using 128 cores with domain decomposition to optimize computational efficiency. Each complete rotor revolution required approximately 3 h of wall-clock time.

2.4. Validation of Numerical Method

To validate the accuracy and reliability of the computational methodology, experimental rotor data were used to verify CFD results through comparative analysis of thrust measurements. Validation was performed on an isolated propeller operating under static air conditions. As illustrated in Figure 6a, the rotor thrust test rig comprises a dynamometer (Mayatech MT10, Overall error: ±0.02%FS), diffuse reflection photoelectric sensor (Jingjiake LZ-MK10 Measurement accuracy: ±0.01% + 1 digit), RPM Display, servo controller, lithium battery, propeller, and brushless motor (JFU3510S, 700 Kv). The servo controller transmits pulse-width modulation (PWM) signals to the electronic speed controller (ESC) connected to the motor for precise propeller speed regulation, while rotor speed and thrust data are simultaneously acquired through the dynamometer and photoelectric sensor. Figure 6c shows the thrust error range of the individual propeller, based on both experimental measurements and CFD simulations. The data were obtained over a rotational speed range of 3000 to 9000 RPM, with six sets of propeller thrust experiments conducted. The results indicate a high degree of agreement between the CFD predictions and experimental data, with a maximum error of 9.36%. These results validate the CFD model’s accuracy and establish confidence in subsequent simulations involving dual-propeller and wing-canard configurations.

3. Results and Discussion

3.1. Effects of Freestream Velocity and Rotor Speed on Wing and Canard Lift and Drag Characteristics

Based on the aerodynamic principles governing vertical take-off and landing (VTOL) fixed-wing UAVs, this study carefully selects feasible combinations of freestream velocity and rotor rotational speed that are representative of practical transition phase conditions. The research analyzes the variations in lift coefficients for both the wing and canard surfaces under these selected inflow conditions and rotor operating parameters. For the calculation of aerodynamic parameters, data were time-averaged over one complete rotor revolution for each component (rotor, wing, and canard), and the results were visualized through contour mapping. For flow field analysis, instantaneous data corresponding to the moment when the rotor axis is aligned parallel to the fuselage axis were selected to investigate the underlying mechanisms of lift variation on the lifting surfaces, with detailed examination of pressure and velocity distributions at cross-sections.

Figure 7 illustrates the nonlinear variations in lift coefficients for the wing and canard under varying freestream velocities and rotor rotational speeds. Figure 7a shows the contour plot of the wing lift coefficient distribution. The dotted lines represent the lift coefficient required by the wing to maintain the flight altitude when the rotor is in a stationary state. Compared to the stationary rotor condition, the wing lift coefficient demonstrates a variation pattern: it decreases during the initial and final stages of increasing freestream velocity while a temporary, transitional increase occurs at intermediate velocities. Figure 7b displays the contour distribution of the canard lift coefficient, revealing a decreasing trend in canard lift coefficient as the freestream velocity increases.

The contour plots of drag coefficient variations for both the wing and canard surfaces are presented in Figure 8. As the freestream velocity increases, the wing drag coefficient demonstrates a gradual decreasing trend, while the canard drag coefficient exhibits a progressive increasing trend.

3.2. Aerodynamic Characteristics and Formation Mechanisms of Lift and Drag Variations in Rotor-Wing-Canard Systems During the Transition Phase

Figure 9 presents the variation of total lift under different freestream velocities and rotor rotational speeds, where the L = 30 N contour line represents the equilibrium condition in which the total lift balances the aircraft weight, thereby identifying the optimal freestream velocity and rotor rotational speed combinations required for altitude maintenance during the transition phase.

To investigate the aerodynamic effects during the steady-altitude transition phase of the UAV, five representative operating conditions corresponding to the L = 30 N contour line in Figure 9 were selected based on matched freestream velocity and rotor rotational speed combinations. The associated aerodynamic parameters, including rotor rotational speed, front rotor lift, rear rotor lift, wing lift, canard lift, and total lift, are presented in

Table 3. The matching conditions of freestream velocity and rotor rotational speed during the transition phase.

Parameters	Value					Unit
Freestream Velocity	3	6	9	12	15	m/s
Rotational Speed	8000	8000	7000	6000	4000	RPM
Front Rotor Lift	13.741	14.168	11.508	9.045	4.886	N
Rear Rotor Lift	13.502	13.548	10.529	7.983	4.034	N
Wing Lift	0.611	3.690	8.397	11.406	17.592	N
Canard Lift	0.511	1.392	2.000	2.504	3.257	N
Total Lift	28.365	32.798	32.434	30.938	29.769	N

.

Figure 10 presents the variations of lift and drag coefficients for the wing and canard under three configurations: isolated wing-canard configuration, wing-canard combination with a stationary rotor, and wing-canard combination with a rotating rotor. As shown in Figure 10a, compared to the isolated wing case, the presence of the canard with a stationary rotor reduces the wing’s lift coefficient, while the rotating rotor induces more pronounced variations in the wing lift coefficient. The wing lift coefficient initially increases and then decreases with freestream velocity, exhibiting lift reduction during both initial and final transition phases, but demonstrating lift enhancement during the mid-transition phase. Figure 10b demonstrates that the canard’s lift coefficient remains largely unaffected by the stationary rotor when compared to the isolated canard case. However, the rotating rotor significantly enhances the canard’s lift coefficient, although this effect diminishes with increasing freestream velocity.

Compared to the stationary rotor condition, Figure 11 demonstrates the influence of rotor rotation on the drag coefficients of both wing and canard. The wing drag coefficient initially increases before decreasing, while the canard drag coefficient exhibits a significant reduction. The rotor’s effect on canard drag diminishes as freestream velocity increases.

Figure 12 presents the distributions of pressure coefficients on the upper and lower surfaces of the wing and canard. Compared with the rotor-static condition, during the early stage of transition (incoming flow velocity 3 m/s), the pressure coefficients near the rotor on the wing’s trailing-edge upper surface and the canard’s lower surface exhibit a sharp increase. In the mid-stage of transition (incoming flow velocity 9 m/s), the pressure coefficient near the rotor on the wing’s trailing-edge upper surface decreases, while that near the leading edge increases; pressure coefficients on other regions of the wing’s upper surface generally decrease. On the wing’s leading-edge lower surface, low-pressure regions appear near the front rotor, whereas other areas show increased pressure coefficients. The canard’s lower surface near the leading edge and rotor also exhibits high-pressure regions. In the late stage of transition (incoming flow velocity 15 m/s), the pressure coefficient on the wing’s leading-edge upper surface near the rotor increases significantly, while low-pressure regions persist on the leading-edge lower surface, and the high-pressure regions on other areas decrease compared with the mid-stage. The pressure coefficients on the upper and lower surfaces of the wing and canard demonstrate complex variations in magnitude and affected regions, indicating the simultaneous presence of both lift-enhancing and lift-reducing effects.

The regions with complex pressure variations on the upper and lower surfaces of the wing and canard are primarily located near the rotor positions. Figure 13 presents the pressure coefficient contours on the upper and lower surfaces at Section 2 of the wing and canard, illustrating the distribution changes induced by rotor rotation (Figure 13b) compared with the rotor-static condition (Figure 13a). During the early stage of transition (incoming flow velocity 3 m/s), the high-pressure region on the wing’s trailing-edge upper surface is generated by the rotation of the rear rotor, while a reversal of high- and low-pressure regions begins to occur on the wing’s leading-edge surfaces: a high-pressure zone appears on the upper surface and a low-pressure zone on the lower surface. In the mid-stage of transition (incoming flow velocity 9 m/s), the suction effect from the rear rotor further reduces the pressure coefficients on the wing’s upper surface, expanding and shifting the low-pressure region rearward, while the leading-edge pressure reversal becomes more pronounced. In the late stage of transition (incoming flow velocity 15 m/s), the low-pressure region on the wing’s upper surface decreases in magnitude and area, but the leading-edge pressure reversal persists. Throughout the transition, the rotation of the front rotor generates significant pressure differences on the canard’s upper and lower surfaces; however, as the incoming flow velocity increases, these high- and low-pressure regions shrink and shift rearward, which may explain the reduction in canard lift augmentation at higher velocities. The blowing and suction effects induced by the aft rotor rotation are likely responsible for the nonlinear variation of the wing lift coefficient during the transition phase, which first decreases, then increases, and subsequently decreases again.

To illustrate the pressure differential variations on the wing surfaces near the rotor position, Figure 14 presents the pressure distribution along the chordwise direction at Section 2 (Figure 3) under different freestream velocities. Blue and red areas represent negative and positive lift contributions, respectively, with the black curve indicating the pressure distribution under stationary rotor conditions. As shown in Figure 14a–c, at freestream velocities ≤ 9 m/s, the rear rotor’s suction effect on the wing surface flow significantly increases the pressure differential compared to the stationary case. The wing’s negative lift is generated by both leading and trailing edges, with the leading edge’s influence limited to the forward 20% chord. With increasing freestream velocity, the trailing edge pressure differential decreases in both magnitude and affected area. Although the pressure differential near the trailing edge increases, the combined effect with the leading edge shows no net lift enhancement. Figure 14d,e demonstrates that at freestream velocities > 12 m/s, the trailing edge negative lift disappears, leaving only the leading edge contribution with significantly increased pressure differential compared to low-speed conditions. The reduced suction effect at higher velocities, combined with persistent interference from the front rotor’s rotation, leads to markedly decreased pressure differential relative to the stationary case, resulting in lift reduction. Consequently, pressure variations in other wing regions become the dominant factor affecting lift performance. As evidenced by Figure 12, the substantially increased pressure differential in other wing regions during mid-transition explains the observed lift enhancement, while decreased differentials during initial and final phases account for the lift reduction.

To elucidate the underlying causes of the pressure variations on the upper and lower surfaces of the wing and canard, Figure 15 presents the velocity contours at Sections 1 and 2, along with magnified views in the vicinity of the wing and canard. As shown in Figure 15a, a low-velocity zone appears behind the front rotor, with the rotor wake significantly affecting the wing. Figure 15b demonstrates that during the initial and intermediate transition phases, the incoming flow experiences strong rotor suction, altering its direction. Figure 15c reveals that the front rotor’s suction reduces the effective angle of attack of the wing, with the flow velocity on the upper surface near the leading edge being lower than on the lower surface. This explains the pressure reversal at the wing leading edge shown in Figure 13, resulting in negative lift generation. At 9 m/s freestream velocity, a distinct low-velocity region forms on the wing’s lower surface, enhancing lift. Figure 15d indicates that the front rotor’s rotational suction creates a positive angle of attack for the canard, strengthening the high- and low-pressure regions at its leading edge (Figure 12) and thereby increasing lift through an enhanced effective angle of attack. At 15 m/s freestream velocity, the tip vortices from the front rotor and the trailing-edge vortices on the canard’s upper surface dissipate, while the freestream angle decreases, suggesting that higher velocities reduce rotor interference with the canard.

To illustrate the effects of rotor wake interactions, Figure 16 presents vorticity contour plots at different stages of the transition phase. At lower freestream velocities, the rotor wake vortices are primarily confined beneath the rotor disk. Within the wake’s influence region, the rotor downwash directly impinges on the wing surface, significantly altering the flow characteristics over the upper wing surface. During the final transition stage (at 15 m/s freestream velocity), the rotor wake vortices become entangled with the wing structure, creating substantial flow interference patterns. Additionally, the rotational effects of the rotor further modify the flow patterns near the canard wingtips, potentially suppressing spanwise flow and consequently mitigating the influence of tip vortices.

In summary, the combined effect of freestream velocity and rotor rotation constitutes the primary factor influencing the lift characteristics of both the wing and canard during the transition phase. At low freestream velocities, the rotor suction effect becomes pronounced, subsequently altering the inflow angle, whereas at high freestream velocities, the deflection of the rotor wake significantly modifies the interference intensity on wing and canard surfaces. These two distinct mechanisms collectively govern the lift variations. The suction effect of the rear rotor accelerates the freestream velocity over the wing surface, resulting in positive lift effects; the front rotor’s suction increases the effective angle of attack of the canard, producing positive lift effects; while the impingement of rotor wake on the wing surfaces generates negative lift effects. Regarding the wing’s lift evolution during the transition phase, three distinct stages can be identified: during the initial stage, the positive contribution from the rear rotor’s freestream suction is outweighed by the combined negative effects of both rotors; the intermediate is characterized by the rear rotor’s positive effect dominating over the rotors’ combined negative influence; while the final stage is primarily governed by the front rotor’s adverse effect. In contrast, the canard’s lift variation remains consistently influenced by the front rotor’s positive contribution across all transition stages. The complex lift variations during transition impose heightened demands on flight control strategies. Based on the present aerodynamic simulation results, targeted design improvements could be implemented during detailed development phases. For instance, increasing the rear rotor-wing separation distance may mitigate initial-stage interference effects. Furthermore, the control strategy could be specifically optimized during flight simulation phases to accommodate these aerodynamic characteristics and enhance overall flight performance.

4. Conclusions

This paper investigates the aerodynamic effects of rotors on wings and canards during the transition phase of a canard-configuration VTOL fixed-wing UAV using RANS-based CFD methodology. The investigation yields the following conclusions:

(1)

The rotors exhibit a lift-enhancing effect on the canard, primarily attributed to airflow suction induced by the front rotor’s rotation, with this enhancement diminishing as freestream velocity increases.

(2)

The rotors’ influence on the wing exhibits a triphasic lift variation pattern: initial reduction, followed by enhancement, and subsequent reduction. During the early transition phase, lift reduction results from the combined effects of both forward and aft rotors. The mid-transition lift enhancement is primarily governed by the aft rotor’s suction effect on the airflow. During late transition, lift reduction is dominated by the forward rotor’s influence, completing the characteristic aerodynamic interference sequence.

(3)

The combined effects of freestream velocity and rotor operation constitute the primary factors governing wing and canard lift characteristics during the transition phase. At low velocities, rotor-induced suction dominates by modifying flow incidence angles, whereas at high velocities, wake deflection alters the interference intensity on wing and canard surfaces. These dual mechanisms collectively drive the observed lift variations across both aerodynamic surfaces.

The current model does not account for the aerodynamic effects of the fuselage, pusher propeller, and control surfaces on fixed-wing and rotor interactions, as the thrust propeller is positioned at the rear of the airframe with rearward-directed airflow. However, such effects are present in actual flight conditions and merit consideration in future studies. The periodic influence of rotor rotation on wing and canard lift characteristics warrants further investigation. Regarding the study and application of canard configurations, future research will focus on optimizing the relative positioning between fixed-wing and rotor components, followed by prototype fabrication and flight testing to validate the numerical findings.