Asymmetric Duct Design for Directional Airflow Delivery in UAV-Assisted Greenhouse Tomato Pollination

Abstract

UAV-assisted greenhouse tomato pollination requires lateral airflow delivery toward flower clusters distributed along the crop canopy. To address this, an asymmetric duct was designed to passively redirect the rotor wake through geometric modification of three inner-wall curvature parameters (R₁, R₂, R₃). Three-dimensional CFD simulations were conducted to evaluate the effects of these parameters on airflow redirection and aerodynamic performance. Compared with a conventional symmetric duct, the asymmetric duct shifted the high-velocity wake from a predominantly vertical direction toward the canopy side. Among the three parameters, R₃ exerted the greatest influence: increasing R₃ from 20 to 65 mm improved the lift-to-drag ratio from 24.7 to 184.2 but reduced the airflow velocity delivered to the pollination region from 6.48 to 2.82 m·s⁻¹. The selected configuration (R₁ = 11 mm, R₂ = 20 mm, R₃ = 25 mm) delivered an airflow velocity of 6.03 m·s⁻¹ at an operating height of 1.44 m, with a lift of 7.04 N and a lift-to-drag ratio of 37.0. These results demonstrate that passive geometric asymmetry can redirect rotor-induced airflow toward the canopy side while balancing airflow delivery, operating height, and aerodynamic performance under greenhouse spatial constraints.

1. Introduction

Greenhouse cultivation has become one of the principal production systems for high-value horticultural crops because it provides precise control of temperature, humidity, irrigation, and nutrient supply, thereby improving crop productivity and fruit quality [1,2]. Among greenhouse horticultural crops, tomato (Solanum lycopersicum L.) is one of the most extensively cultivated vegetable species worldwide [3,4]. Tomato flowers possess poricidal anthers that retain pollen within the anther cone, preventing its effective release by gravity or natural air movement. Pollen is released through apical pores when the anther cone is vibrated at specific frequencies—a mechanism known as buzz pollination that has been extensively characterized in both natural bee-mediated and artificial vibration studies [2,5,6,7]. Consequently, the effectiveness of airflow-based pollination does not depend solely on the airflow velocity magnitude, but on whether the airflow induces flower or inflorescence vibrations of sufficient amplitude and frequency to trigger pollen ejection [7,8]. This mechanistic relationship—from airflow to flower vibration to pollen release—provides the physiological basis for the present study: the asymmetric duct is designed to direct airflow toward the flower-bearing regions of the canopy, where it can generate the required vibratory stimulus. The present work therefore focuses on the aerodynamic problem of directional airflow delivery, while the subsequent vibratory and pollination responses represent the subject of ongoing experimental investigation [8,9].

Several pollination techniques have been adopted in commercial greenhouse production, including bumblebee pollination, mechanical vibration, and hormone application [10,11]. Although bumblebee pollination generally achieves high fruit-setting efficiency, colony performance is sensitive to environmental conditions such as temperature and solar radiation, and colony maintenance increases production costs. Mechanical vibration and hormone application reduce dependence on insect pollinators but remain labor-intensive or operationally inconsistent under commercial greenhouse conditions [10,12]. These practical constraints have stimulated interest in automated pollination technologies suitable for protected cultivation.

Unmanned aerial vehicles (UAVs) are increasingly used for crop monitoring, precision pesticide application, and environmental sensing [13,14,15]. Their mobility and potential for automated operation have also prompted investigation of UAVs as platforms for greenhouse pollination. Previous studies have shown that rotor-induced airflow from multirotor UAVs can successfully stimulate pollen release from tomato flowers, indicating that UAV-assisted pollination is technically feasible [5,16,17,18,19,20,21].

Despite this progress, UAV operation for greenhouse pollination is constrained by the confined spatial environment of protected cultivation. Narrow aisles, dense crop canopies, and limited overhead clearance restrict UAV dimensions, operating height, and maneuverability. The greenhouse at Jiangsu University used to define the design constraints in this study (Figure 1) had a double-row planting layout, approximately 90 cm between planting beds, a 65 cm operating aisle, and approximately 200 cm of vertical clearance between the canopy top and greenhouse film. Large multirotor platforms (wheelbase >600 mm) can generate substantial downwash but are difficult to operate within confined greenhouse spaces, whereas micro-UAVs (wheelbase <200 mm) satisfy dimensional constraints but may provide insufficient airflow for tomato flower stimulation [5,19,20]. Medium-sized UAVs therefore offer a practical compromise between airflow generation and spatial compatibility; however, conventional rotor configurations predominantly direct the wake downward rather than toward flower clusters distributed along the tomato canopy [1,7]. To illustrate this limitation quantitatively: for a representative small quadrotor (≈230 g, 2.5-inch propeller class) hovering at 1.5 m, the turbulent jet model of Bauersfeld et al. [22] predicts a centerline velocity of approximately 4 m·s⁻¹ but a jet half-width of only ~0.15 m, yielding a velocity of less than 0.6 m·s⁻¹ at a lateral offset of 0.325 m—the approximate position of the flower clusters relative to the UAV centerline in a typical 65 cm greenhouse aisle. In contrast, the asymmetric duct developed in the present study delivers 6.03 m·s⁻¹ at the same lateral position. These constraints indicate that UAV-assisted greenhouse pollination depends not only on safe operation within confined spaces but also on delivering sufficient rotor-induced airflow toward flower clusters at crop-relevant positions.

The spatial distribution of rotor-induced airflow is an important determinant of how UAV-generated flow interacts with a crop canopy. Accordingly, multirotor downwash has been widely investigated using computational fluid dynamics (CFD) and experimental measurements [23,24,25]. These studies have clarified how rotor speed, flight altitude, and hovering conditions influence the distribution of the downwash flow field. Furthermore, Raeisi [26] analyzed the effect of duct geometry on the airflow velocity and spatial distribution of downdrafts. Beyond multirotor platforms, numerical and experimental studies have also examined the spatial distribution of downwash from fixed-wing UAVs [27], and studies on single-rotor crop protection UAVs [28] have also been conducted. These studies have improved understanding of rotor wake behavior in agricultural UAV operations, but their primary emphasis has been on characterizing downwash rather than directing airflow toward laterally distributed crop targets.

Ducted rotor systems provide a potential geometric approach for modifying rotor-induced airflow. Ducted fans improve thrust generation, reduce noise, and enhance operational safety, making them increasingly attractive for vertical take-off and landing (VTOL) aircraft [29,30]. Previous optimization studies have demonstrated that duct geometry substantially affects aerodynamic performance through its influence on pressure recovery and flow development within the duct [31,32]. However, these investigations have primarily considered geometrically symmetric ducts designed to maximize thrust or aerodynamic efficiency. Asymmetric duct configurations have received limited attention. For example, wing-tip-tilted asymmetric ducts have been investigated for VTOL drones, but the analysis focused on cruise operation rather than low-altitude hovering for greenhouse pollination [26].

In greenhouse tomato pollination, previous experimental studies have reported relationships between rotor-induced airflow velocity and pollination responses [8,9]. In those studies, airflow redirection was attempted using an external deflector plate to steer the rotor downwash toward the canopy side. However, the accuracy of airflow regulation achievable with a deflector plate was limited, and the UAV platform employed in those experiments had a relatively large wheelbase that did not account for the dimensional constraints of a narrow greenhouse aisle (~65 cm). The present study addresses both limitations by introducing passive geometric asymmetry integrated into the duct itself—rather than relying on an external deflector—to redirect the rotor wake toward the canopy side. This approach eliminates the need for additional flow-control components while operating within the dimensional constraints of a medium-sized UAV platform (wheelbase < 200 mm) suitable for confined greenhouse aisles. Furthermore, the parametric evaluation of three inner-wall curvature parameters (R₁, R₂, R₃) provides a systematic framework for quantifying how duct geometry influences directional airflow delivery, aerodynamic performance, and operating height—a level of geometric analysis that was not undertaken in the earlier deflector-based studies. The present work therefore extends prior research by shifting from external flow redirection to integrated geometric design and by explicitly incorporating greenhouse dimensional constraints into the duct configuration selection process.

To address this research gap, an asymmetric duct was designed to redirect rotor-induced airflow toward the canopy side by modifying three characteristic inner-wall curvature parameters (R₁, R₂, and R₃). The objectives were to (i) develop an asymmetric duct capable of passively redirecting rotor-induced airflow toward the canopy side; (ii) quantify the effects of the inner-wall curvature parameters R₁, R₂, and R₃ on internal flow development, aerodynamic performance, and airflow delivered to the defined pollination region using three-dimensional CFD simulations; and (iii) select a duct configuration under greenhouse operating constraints by jointly evaluating airflow velocity within the pollination region, operating height, and aerodynamic performance. The findings provide a design basis for asymmetric duct systems intended to deliver directional airflow during UAV-assisted greenhouse tomato pollination and clarify how duct geometry can be selected against both aerodynamic and greenhouse operating requirements.

2. Materials and Methods

An asymmetric duct was developed to redirect rotor-induced airflow toward the canopy side for UAV-assisted greenhouse tomato pollination. The methodological framework combined geometric design, computational fluid dynamics (CFD) [33,34,35], experimental validation, and parametric evaluation to determine how passive geometric asymmetry affects airflow development under hovering conditions. Three characteristic inner-wall curvature parameters, R₁, R₂, and R₃, were defined to represent the upper-wall, lower-wall, and inner-wall regions of the duct, respectively. Their interaction effects on internal airflow, aerodynamic performance, and airflow delivery to the defined pollination region were subsequently evaluated. The CFD predictions were first compared with experimental airflow measurements before the single-factor and combined parameter analyses were conducted.

2.1. Design Concept of the Asymmetric Duct for Directional Airflow Delivery

Rotor-induced airflow generated by conventional multirotor UAVs is predominantly directed downward. This airflow pattern is suitable for operations such as pesticide spraying [36,37] but provides limited lateral airflow toward flower clusters distributed along the tomato canopy. The design objective was therefore to redirect part of the rotor-induced airflow toward the canopy side rather than simply increase its intensity.

An asymmetric duct was developed to achieve passive airflow redirection through modification of the internal flow passage. The design did not use additional actuators or active flow-control devices. Instead, geometric asymmetry was introduced into the duct inner wall to modify airflow development within the duct and redirect the rotor-induced airflow as it left the duct.

The asymmetric geometry was parameterized using three characteristic inner-wall curvature parameters, denoted as R₁, R₂, and R₃ (Figure 2). These parameters represent the upper-wall, lower-wall, and inner-wall regions of the duct, respectively. Each parameter defines a different geometric region through which the rotor-induced airflow develops before leaving the duct. Varying these curvatures modifies the local flow passage within the duct, allowing the influence of each geometric region on airflow redirection and aerodynamic performance to be evaluated.

The three curvature parameters were treated as independent design variables while the fixed structural dimensions of the duct and the rotor configuration were maintained. This approach enabled the individual and combined effects of R₁, R₂, and R₃ to be evaluated using a consistent geometric and rotor configuration. The fixed duct dimensions are listed in

Table 1. Geometric parameters of the asymmetric duct.

Item	Value (mm)	Item	Value (mm)
d1	92	h1	10
d2	80	h2	31.5
d3	72	h3	68
		h4	60

, whereas the three curvature parameters were varied in the subsequent parametric analyses. This parameterization provided a consistent geometric framework for examining the effects of duct geometry on airflow development, aerodynamic performance, and airflow delivery to the pollination region.

2.2. Greenhouse Design Constraints and Geometric Model

The asymmetric duct was developed for a medium-sized quadrotor UAV intended to operate within the spatial constraints of a greenhouse tomato production system. The greenhouse used to define the design constraints contained planting beds approximately 90 cm wide and operating aisles approximately 65 cm wide (Figure 3). Approximately 20 cm of lateral clearance was reserved between the UAV and the crop canopy, limiting the maximum vehicle width to about 200 mm. Vine-supporting wires were positioned approximately 2.0 m above the ground. Based on these spatial constraints, the UAV operating height was required to remain below approximately 1.7–1.8 m to avoid interference with the greenhouse structure while maintaining airflow delivery toward the canopy. These dimensions were used to define the geometric and operating constraints for the UAV and asymmetric duct design.

A 3-inch three-bladed propeller was selected as the propulsion unit, and its diameter determined the minimum dimensions of the surrounding duct. The minimum inner radius of the duct was fixed at 40 mm to provide clearance for propeller operation. The inner duct wall began 31.5 mm below the duct inlet, while the outer wall extended downward on the outlet side to provide a longer flow passage before the airflow left the duct. The remaining fixed duct dimensions followed the geometric parameters listed in Table 1, whereas R₁, R₂, and R₃ were treated as variable curvature parameters in the CFD analyses.

The duct and propeller assembly was modelled in SolidWorks 2021 SP2.0. The front, left, top, and isometric views of the duct, together with the three-dimensional model, are shown in Figure 4. The three-dimensional geometry was subsequently used to construct the computational domain for the CFD simulations presented in Figure 5.

2.3. Numerical Methodology

2.3.1. Governing Equations and Turbulence Model

Under hovering conditions, propeller rotation generates a three-dimensional turbulent flow involving pressure redistribution and wake development within and downstream of the asymmetric duct. The airflow was described using the Reynolds-averaged Navier–Stokes (RANS) equations, comprising the continuity and momentum equations (Equations (1)–(3)).

$${\displaystyle \frac{\partial U_i}{\partial x_i}}=0$$

(1)

$$\rho {\displaystyle \frac{\partial U_i}{\partial t}}+\rho U_j{\displaystyle \frac{\partial U_i}{\partial x_j}}=-{\displaystyle \frac{\partial P}{\partial x_i}}+{\displaystyle \frac{\partial }{\partial x_j}}\left[\mu \left({\displaystyle \frac{\partial U_i}{\partial x_j}}+{\displaystyle \frac{\partial U_j}{\partial x_i}}\right)\right]+{\displaystyle \frac{\partial }{\partial x_j}}\left(-\rho \overline{u_i^{\prime }{u}_j^{\prime }}\right)$$

(2)

$$-\rho \overline{u_i^{\prime }{u}_j^{\prime }}={\mu }_t\left({\displaystyle \frac{\partial U_i}{\partial x_j}}+{\displaystyle \frac{\partial U_j}{\partial x_i}}\right)-{\displaystyle \frac{2}{3}}\mathrm{\rho k}{\delta }_{\mathrm{ij}}$$

(3)

where U_i represents the Reynolds-averaged (time-mean) velocity component in the i-th coordinate direction, ρ is the fluid density (air, 1.225 kg·m⁻³), P is the Reynolds-averaged pressure, μ is the molecular dynamic viscosity, and $u_i^{\prime }$ denotes the fluctuating velocity component, $-\rho \overline{u_i^{\prime }{u}_j^{\prime }}$ is the Reynolds stress tensor, μ_t is the turbulent (eddy) viscosity, δ_ij is the Kronecker delta, and k is the turbulent kinetic energy.

The standard k–ε turbulence model was used to close the RANS equations and obtain the time-averaged turbulent flow field around the rotor–duct system. The corresponding transport equations for turbulent kinetic energy (k) and its dissipation rate (ε) are given in Equations (4) and (5).

$$\rho {\displaystyle \frac{\partial k}{\partial t}}+\rho U_j{\displaystyle \frac{\partial k}{\partial x_j}}={\displaystyle \frac{\partial }{\partial x_j}}\left[\left(\mu +{\displaystyle \frac{{\mu }_t}{{\sigma }_k}}\right){\displaystyle \frac{\partial k}{\partial x_j}}\right]+P_k-\mathrm{\rho \epsilon }$$

(4)

$$\rho {\displaystyle \frac{\partial \epsilon }{\partial t}}+\rho U_j{\displaystyle \frac{\partial \epsilon }{\partial x_j}}={\displaystyle \frac{\partial }{\partial x_j}}\left[\left(\mu +{\displaystyle \frac{{\mu }_t}{{\sigma }_{\epsilon }}}\right){\displaystyle \frac{\partial \epsilon }{\partial x_j}}\right]+C_{\epsilon 1}{\displaystyle \frac{\epsilon }{k}}{P}_k-C_{\epsilon 2}\rho {\displaystyle \frac{{\epsilon }^2}{k}}$$

(5)

where P_k is the production of turbulent kinetic energy, σ_k and σ_ε are the turbulent Prandtl numbers for k and ε, respectively, and C_ε1 and C_ε2 are empirical model constants.

Propeller rotation was represented using the sliding mesh technique to resolve the transient interaction between the rotating blades and the stationary flow domain under hovering conditions. The numerical model was implemented in ANSYS Fluent (ANSYS 2021 R1) to simulate airflow development within and downstream of the asymmetric duct.

This study employed the standard k–ε turbulence model. Two-equation RANS turbulence models (including the k–ε and SST k–ω series) have been widely applied in CFD simulations of downwash flow fields generated by agricultural drones [24,25,28]; these models have demonstrated satisfactory agreement with experimental measurements in terms of predicting the average flow field. The standard k–ε model has been thoroughly validated in free shear flows and jet configurations and is therefore suitable for the development of the wake at the tube outlet considered in this study. Its robustness and computational efficiency are advantageous for this parametric study, which involves 81 tube configurations and requires consistent convergence across a large number of simulations. The authors acknowledge that the standard k–ε model may have limitations in regions with high streamline curvature, unfavorable pressure gradients, and flow separation, whereas other models (such as SST k–ω) may provide more accurate predictions in these local regions. However, given that the primary objective of this study is to conduct a comparative evaluation of mean airflow redirection and velocity distributions under different duct configurations, the standard k–ε model offers an appropriate balance between physical accuracy and computational feasibility.

The transient simulation was performed with a time step of Δt = 1 × 10⁻³ s at a rotational speed of 27,000 rev·min⁻¹. Each simulation was run for over 400 propeller revolutions, ensuring that the downwash flow field reached a quasi-steady state before data collection. A maximum of 10 inner iterations was performed per time step. Convergence was assessed by monitoring the scaled residuals of the continuity, momentum, k, and ε equations; the solution was considered converged when all residuals fell below 1 × 10⁻³ and remained stable. The pressure-based solver with the SIMPLEC pressure–velocity coupling scheme was employed. Spatial discretization used least-squares cell-based gradient reconstruction, second-order schemes for pressure and momentum, and first-order upwind schemes for turbulent kinetic energy and dissipation rate. Transient time integration was performed using a first-order implicit formulation.

2.3.2. Computational Domain and Boundary Conditions

The numerical model consisted of a rotating region enclosing the propeller and an external stationary flow domain representing the surrounding air (Figure 5). Because the quadrotor is geometrically symmetric and all four propulsion units operate under identical hovering conditions, a single rotor–duct assembly was adopted as the computational model (Figure 5c). This simplification was based on the following considerations. First, the objective of the present study is to evaluate the directional airflow delivery of the asymmetric duct to the laterally positioned pollination region (77.5 cm from the duct centerline, Section 2.6). The duct on the canopy side directs airflow outward, away from the UAV center, and the airflow at this distance is primarily governed by the outlet flow of the individual duct rather than by near-field rotor–rotor interaction. Second, the comparison between symmetric and asymmetric ducts (Section 3.1) was conducted under identical single-duct conditions, ensuring that the observed differences in wake redirection are attributable to duct geometry rather than to multi-rotor effects. The single-duct approach therefore provides a representative and computationally tractable model for isolating the geometric effects of R₁, R₂, and R₃ on directional airflow delivery. The limitations of this simplification with respect to adjacent rotor interference, UAV airframe blockage, and greenhouse boundary effects are discussed in Section 3.8.

The rotating region was defined as a cylindrical domain with a diameter of 100 mm and a height of 40 mm (Figure 5d), enabling propeller motion to be resolved using the sliding mesh technique. The surrounding stationary flow domain measured 1000 mm × 1000 mm × 1000 mm (Figure 5b). The rotating and stationary domains communicated through a sliding interface, enabling continuous transfer of flow variables during the transient simulation.

Pressure inlet and pressure outlet boundary conditions were specified for the external flow domain. Under hovering conditions, the inflow velocity at the computational boundary was set to zero. The propeller blades and duct walls were treated as no-slip walls throughout the simulations. This computational configuration provided the numerical framework for resolving the interaction between the rotating propeller and the asymmetric duct during hovering flight.

2.3.3. Mesh Generation and Quality Assessment

The computational mesh was generated using a locally refined strategy to increase spatial resolution around the propeller, inner duct wall, and wake-development region while maintaining a coarser mesh elsewhere to improve computational efficiency. The rotating domain was meshed with a 2 mm element size, whereas the stationary flow domain employed a 7 mm element size. Additional refinement was applied to the propeller surfaces (0.5 mm) and the inner duct wall (2 mm) to increase spatial resolution in these regions. The overall computational mesh and the locally refined propeller region are shown in Figure 6.

An unstructured tetrahedral mesh generated with the Patch Conforming algorithm was adopted to accommodate the complex geometry of the asymmetric duct. The final computational model consisted of 7,892,153 elements, including 7,495,997 elements in the stationary flow domain and 396,156 elements within the rotating domain.

Mesh quality was evaluated using the Orthogonal Quality metric. As illustrated in Figure 7, all mesh elements exhibited orthogonal quality values greater than 0.30, and most exceeded 0.50, indicating satisfactory mesh quality throughout the computational domain.

2.3.4. Mesh Independence Verification

A mesh independence study was conducted using three progressively refined grids to assess the sensitivity of the numerical results to spatial discretization. The three grids, denoted Mesh-1, Mesh-2, and Mesh-3, are summarized in

Table 2. Grid independence verification results.

Grid	Total Elements	Velocity at 0.5 m (m·s−1)	Velocity at 1.0 m (m·s−1)	Relative Error (%)
Mesh-1	2,456,789	6.21	3.87	9.1/4.9
Mesh-2	7,892,153	6.72	4.02	1.6/1.2
Mesh-3	15,678,234	6.83	4.07	—

Note: Relative errors are calculated with respect to Mesh-3 (the finest grid).

along with the computed airflow velocities at the two validation locations.

The velocity differences between Mesh-2 and Mesh-3 were 1.6% at 0.5 m and 1.2% at 1.0 m, indicating that the results are effectively grid-independent at the Mesh-2 resolution. In contrast, Mesh-1 showed considerably larger deviations (9.1% and 4.9%). Balancing computational accuracy and cost, Mesh-2 (7.89 million elements) was adopted as the uniform grid for all subsequent parametric simulations, ensuring comparability across configurations while avoiding the excessive computational expense of the finest grid for the 81-case parametric study.

2.4. Model Validation

The CFD model was validated by comparing simulated airflow velocities with experimental measurements obtained under representative hovering conditions. Wind speed was measured at two locations positioned 0.5 and 1.0 m below the duct outlet, corresponding to the principal development region of the rotor wake. Three repeated measurements were performed at each location, and the average experimental values were compared with the corresponding numerical predictions. The comparison results are presented in

Table 3. Comparison results of CFD and experimental wind speeds.

Location/m	Value 1/(m·s−1)	Value 2/(m·s−1)	Value 3/(m·s−1)	Experimental Mean/(m·s−1)	CFD Result/(m·s−1)	Absolute Error/(m·s−1)	Relative Error/%
0.5	5.84	5.88	5.56	5.76	6.50	0.74	12.85
1	4.13	4.04	3.90	4.02	4.06	0.04	1.0

.

At both locations, the numerical prediction results were generally in good agreement with the experimental measurements. The CFD validation was conducted using a reference asymmetric duct configuration (R₁ = 15 mm, R₂ = 20 mm, R₃ = 30 mm), which falls within the parameter range of the subsequent parametric study. A significant deviation (12.85%) was observed at the 0.5 m mark, which is attributed to the steep velocity gradients and tip vortex effects in the near-wake region, where point-to-point comparisons are inherently sensitive to subtle differences in measurement locations. This magnitude of near-field deviation is consistent with validation results for simulations of downwash flows from multirotor UAVs, where average relative errors of 10–15% are typically observed in near-field comparisons [38]. At the 1.0 m position, the error decreased to 1.0%, indicating that the model accurately captured the evolution of the average flow field within the region relevant to pollinator airflow transport. Obtaining the complete velocity distribution across the outlet plane would provide a more rigorous validation; however, due to the compact size of the outlet (72 mm inner diameter) and the limited size of the anemometer probes, experimental measurements were restricted to two axial positions to avoid flow disturbances caused by the probes. Therefore, it is recommended that future studies employ more advanced instrumentation to perform spatially resolved measurements of the outlet plane. Based on this, the model is considered sufficient for subsequent parametric analysis of asymmetric ducts.

The validated CFD methodology was subsequently applied to the parametric evaluation of the asymmetric duct configurations. The baseline configuration used for validation (R₁ = 15 mm, R₂ = 20 mm, R₃ = 30 mm) shares the same duct geometry class as the optimized configuration (R₁ = 11 mm, R₂ = 20 mm, R₃ = 25 mm), with R₃ differing by 5 mm. Given the consistent numerical setup and the validated predictive capability at the two measurement locations, the CFD results for the optimized configuration are considered reliable within the scope of the present parametric study. Experimental validation of the optimized configuration under greenhouse conditions is recommended as a topic for future work.

2.5. Parametric Simulation Design

2.5.1. Single-Factor Parametric Analysis

The individual aerodynamic roles of the three curvature parameters were examined using a controlled-variable approach. Each parameter was varied independently while the remaining two parameters were held constant to isolate its influence on airflow development, aerodynamic performance, and airflow delivered to the pollination region. The fixed parameter combinations were defined as follows: R₁ was evaluated with R₂ = 35 mm and R₃ = 30 mm; R₂ was evaluated with R₁ = 15 mm and R₃ = 30 mm; and R₃ was evaluated with R₁ = 15 mm and R₂ = 20 mm.

The investigated ranges were selected to encompass the practical geometric limits of the asymmetric duct while avoiding configurations that produced unrealistic wall profiles or negligible geometric variation. Finer parameter increments were adopted within the curvature ranges exhibiting the greatest geometric sensitivity to improve the resolution of the single-factor analyses. Accordingly, R₁ was evaluated at 10, 11, 13, 14, 15, 20, 25, and 30 mm, R₂ at 15, 20, 25, 30, 35, 40, 45, and 50 mm, and R₃ at 20, 25, 30, 35, 40, 45, 50, 55, 60, and 65 mm. The single-factor analyses were used to compare the responses of airflow and aerodynamic performance to changes in each curvature parameter before the combined parameter analysis.

2.5.2. Quasi-Orthogonal Parameter Combination Design

A combined parameter design was subsequently used to evaluate the configurations formed by R₁, R₂, and R₃ in combination, following the single-factor analyses. The factor levels used in the parameter combinations are listed in

Table 4. Factors and levels for the quasi-orthogonal parameter combination design.

Level	R1 (mm)	R2 (mm)	R3 (mm)
1	10	15	20
2	11	20	25
3	13	25	30
4	14	30	35
5	15	35	40
6	20	40	45
7	25	45	50
8	30	50	55
9	—	—	60

.

The design was constructed as follows. The primary structure consisted of all pairwise combinations of the eight R₁ levels with the nine R₃ levels, yielding 8 × 9 = 72 base configurations. For each of these 72 combinations, an R₂ value was assigned such that each of the eight R₂ levels appeared nine times across the design, ensuring balanced coverage of the R₂ parameter space. Nine additional configurations were incorporated by fixing R₁ = 10 mm and R₂ = 15 mm while varying R₃ across its nine levels, providing supplementary sampling at the lower bound of the R₁ and R₂ ranges. The complete set of 81 configurations is provided in

Table A1. Complete 81-run quasi-orthogonal parameter matrix.

No.	R1 (mm)	R2 (mm)	R3 (mm)	No.	R1 (mm)	R2 (mm)	R3 (mm)	No.	R1 (mm)	R2 (mm)	R3 (mm)
1	15	35	40	28	14	15	50	55	10	15	30
2	13	20	50	29	20	45	35	56	14	50	40
3	14	40	25	30	25	35	35	57	20	15	30
4	25	45	50	31	20	40	45	58	13	15	40
5	15	25	25	32	10	20	30	59	30	15	25
6	25	15	40	33	20	20	40	60	25	25	20
7	10	25	40	34	10	40	35	61	30	30	50
8	30	25	60	35	25	40	60	62	10	15	60
9	10	50	50	36	14	30	35	63	30	50	55
10	25	30	25	37	15	40	50	64	11	45	20
11	11	35	50	38	30	45	45	65	11	50	45
12	13	25	30	39	10	15	20	66	13	35	45
13	11	25	35	40	10	30	60	67	10	15	50
14	13	40	55	41	11	30	40	68	25	20	55
15	10	40	20	42	10	30	45	69	13	45	60
16	15	30	30	43	10	20	45	70	11	15	55
17	15	50	20	44	10	35	25	71	25	15	45
18	11	40	30	45	20	15	25	72	10	45	25
19	13	15	35	46	11	20	25	73	14	45	30
20	13	50	25	47	20	35	20	74	30	20	35
21	14	35	60	48	15	15	35	75	14	25	45
22	15	45	55	49	20	25	50	76	30	40	40
23	10	50	35	50	30	15	20	77	10	35	55
24	25	50	30	51	11	15	60	78	13	30	20
25	15	20	60	52	14	20	20	79	15	15	45
26	10	45	40	53	10	25	55	80	20	30	55
27	20	50	60	54	14	15	55	81	30	35	30

.

The design is referred to as a combined parameter design rather than a strictly orthogonal array because the three factors (R₁, R₂, R₃) were not arranged in a full factorial or balanced orthogonal structure across all factor pairs. Specifically, while R₁ × R₃ and R₂ × R₃ pairs were systematically sampled, the R₁ × R₂ pairing was not independently balanced—R₂ values were assigned within the R₁ × R₃ structure rather than crossed independently with R₁. Consequently, the design does not support reliable estimation of two-factor interactions involving R₁ × R₂. However, the single-factor analyses (Section 2.5.1) had already established the individual effects of each curvature parameter, showing that R₃ exerted the dominant influence on airflow delivery and aerodynamic performance, while R₁ and R₂ produced comparatively smaller main effects. The combined design was therefore intended to explore the parameter space for configurations that simultaneously satisfy the airflow and operating-height criteria, rather than to perform formal statistical inference on interaction effects. The subsequent analysis (Section 3.7) focuses on identifying feasible configurations within the investigated parameter space, and the conclusions regarding the relative importance of R₁, R₂, and R₃ are supported by both the single-factor and combined parameter results.

2.6. Airflow and Aerodynamic Performance Evaluation

The performance of each asymmetric duct configuration was evaluated using five indicators: airflow velocity within the pollination region, UAV operating height, lift, drag, and lift-to-drag ratio (L/D). Airflow velocity within the pollination region was used to evaluate the delivery of redirected rotor-induced airflow to the target region. Operating height represented the vertical position associated with the airflow criterion under the greenhouse conditions considered in this study. Lift, drag, and L/D were used to characterize the aerodynamic performance of the ducted rotor system.

The pollination region was defined as the lateral extent of the tomato planting bed relative to the duct centerline, spanning from the bed edge at 32.5 cm to the bed center at 77.5 cm under the greenhouse layout shown in Figure 3. The planting bed is approximately 90 cm wide, and the 77.5 cm position represents the farthest extent of flower cluster distribution. At this lateral position, a vertical line was extracted from the CFD velocity field, and the airflow velocity within the pollination region was taken as the maximum velocity magnitude along this line. The vertical coordinate at which this maximum occurred defined the corresponding UAV operating height y for each configuration. This sampling approach reflects the physical scenario in which the asymmetric duct redirects rotor-induced airflow toward the canopy side, and the peak velocity delivered to the farthest extent of the planting bed represents the airflow available for flower stimulation. If the airflow satisfies the adopted velocity criterion at this most demanding position, it is inherently sufficient across the entire 32.5–77.5 cm range. The use of velocity magnitude accounts for both the lateral and vertical components of the redirected airflow.

The configurations were evaluated against the airflow and greenhouse operating constraints adopted in this study. Based on the airflow requirement for tomato pollination reported by Shi Qiang et al. [8], the minimum wind speed within the pollination region was specified as:

u ≥ 4.5 m · s⁻¹

(6)

where u represents the velocity magnitude, accounting for both the lateral and vertical components of the redirected airflow, rather than any single velocity component. The adoption of the velocity magnitude is appropriate because the redirected airflow from the asymmetric duct is inherently three-dimensional, and the combined effect of all velocity components contributes to flower stimulation. The threshold of 4.5 m·s⁻¹ was derived from Shi Qiang [8], who reported that rotor-induced airflow velocities exceeding this value produced measurable pollen release from greenhouse tomato flowers. It should be noted that this threshold was established for conventional rotor downwash rather than laterally redirected airflow, and the present study adopts it as an engineering reference for evaluating whether the asymmetric duct delivers sufficient airflow to the crop-relevant position. The relationship between the redirected airflow characteristics and quantitative pollination responses (pollen release rate, fruit set) requires further experimental investigation.

To ensure safe operation within the experimental greenhouse, where the vine-supporting wires were positioned approximately 2.0 m above the ground, the UAV operating height was constrained by:

y < 2.0 m

(7)

All parameter combinations were assessed against these airflow and operating-height criteria. Configurations satisfying both constraints were subsequently compared using lift, drag, and L/D to evaluate their aerodynamic performance and support the selection of a duct configuration for UAV-assisted greenhouse tomato pollination.

3. Results and Discussion

3.1. Comparison Between Symmetric and Asymmetric Ducts

The external airflow distributions generated by the symmetric and asymmetric duct configurations were compared to determine whether geometric asymmetry redirected rotor-induced airflow under identical operating conditions.

The velocity contours (Figure 8) show that the symmetric duct produced a high-velocity region concentrated beneath the rotor, with the wake developing predominantly along the rotor axis and exhibiting limited lateral expansion. In contrast, the asymmetric duct shifted the high-velocity region toward the outlet opening and produced an asymmetric wake distribution extending toward the canopy side. Because the rotor operating conditions remained unchanged, the difference between the two flow fields was associated with the asymmetric duct geometry. This behavior is consistent with previous studies of ducted fan aerodynamics, which show that duct geometry can influence wake development through changes in the internal pressure and flow fields [29,32].

The streamline distributions (Figure 9) show a corresponding change in the downstream transport of the rotor wake. Under the symmetric configuration, the streamlines remained largely aligned with the rotor axis. In contrast, the asymmetric duct redirected the principal flow toward the outlet opening and concentrated the streamlines on the deflection side of the duct, shifting the downstream airflow toward the canopy side. The observed lateral deflection differs from the predominantly axisymmetric downwash reported for conventional multirotor UAVs without ducts [24,25]. Under the identical rotor operating conditions used in the present comparison, the change in wake orientation coincided with the introduction of the asymmetric duct geometry.

At the crop-relevant lateral position (77.5 cm from the duct centerline), the asymmetric duct delivered a velocity magnitude of 6.03 m·s⁻¹, whereas the symmetric duct produced negligible lateral airflow at this offset because its wake remained predominantly aligned with the rotor axis. The visual comparison of the velocity contours (Figure 8) and streamlines (Figure 9) directly demonstrates this redirection effect without requiring an exhaustive numerical comparison of velocity components.

Comparison of the two configurations showed that geometric asymmetry changed the spatial distribution and orientation of the rotor wake rather than simply increasing airflow intensity. The corresponding internal velocity and pressure fields were therefore examined to determine how the asymmetric flow passage produced this directional airflow pattern.

3.2. Internal Flow Characteristics Associated with Directional Airflow Redirection

The external wake comparison showed that the asymmetric duct redirected rotor-induced airflow from a predominantly vertical path toward the canopy side. To examine the internal flow characteristics associated with this redirection, the velocity and pressure distributions within the asymmetric duct were evaluated under a representative operating condition. Previous studies have shown that duct geometry can influence internal airflow through changes in pressure distribution and flow development [29,39], although these investigations mainly considered symmetric configurations. The corresponding velocity and pressure fields are presented in Figure 10.

The velocity contour (Figure 10a) shows that the higher-velocity airflow was concentrated toward one side of the duct outlet. The internal airflow was asymmetrically distributed about the rotor axis and followed the asymmetric flow passage before leaving the duct. The resulting preferential outlet direction was consistent with the laterally shifted external airflow observed in Figure 8 and Figure 9.

The pressure contour in Figure 10b shows a non-uniform pressure distribution across the outlet region of the asymmetric duct. Differences in pressure were observed between the deflection side and the opposite side of the flow passage, corresponding spatially with the asymmetric velocity distribution shown in Figure 10a. Together, the velocity and pressure distributions show that the rotor-induced airflow developed asymmetrically within the duct before leaving the outlet.

The internal flow characteristics therefore indicate that the directional airflow pattern observed downstream of the duct was associated with the redistribution of velocity and pressure within the asymmetric flow passage. Under unchanged rotor operating conditions, this asymmetric internal flow development allowed the rotor-induced airflow to leave the duct with a preferred lateral orientation toward the canopy side. These results extend previous observations that duct geometry influences flow development [28,40] by showing that an asymmetric internal flow passage can redirect rotor-induced airflow without additional active flow-control components.

3.3. Effect of R₁ on Flow Characteristics and Aerodynamic Performance

The influence of the upper-wall curvature parameter R₁ was evaluated under fixed conditions of R₂ = 35 mm and R₃ = 30 mm to determine its effects on internal flow development and aerodynamic performance. The corresponding velocity distributions, pressure distributions, and aerodynamic performance indicators are presented in Figure 11, Figure 12 and Figure 13.

The internal velocity distributions (Figure 11) show that changes in R₁ mainly affected airflow development in the channel between the R₁ and R₂ walls, rather than the velocity distribution within the main duct passage. At smaller R₁ values, the airflow remained tightly attached to the R₁ wall, producing a concentrated high-velocity band along the upper curvature surface, while the velocity near the R₂ wall was comparatively lower. As R₁ increased, the wall-hugging effect weakened: the high-velocity region near the R₁ surface became less concentrated, and the exit angle of the airflow from the R₁−R₂ channel widened. This increase in exit angle indicates that the capability of the duct to deliver airflow laterally toward the canopy side diminished with increasing R₁. These results indicate that R₁ primarily influenced local airflow development in the R₁−R₂ inter-wall channel rather than substantially altering the directional airflow pattern of the main duct. This behavior is consistent with the effects of inlet curvature reported in parametric studies of ducted fans [39], in which local wall geometry influences internal flow development.

The corresponding pressure distributions (Figure 12) reveal the mechanism underlying the velocity-field response. A low-pressure zone developed adjacent to the R₁ wall, while a high-pressure zone formed near the R₂ surface. As R₁ increased, the low-pressure region at R₁ progressively shrank, whereas the high-pressure zone at R₂ remained evident. The pressure distribution within the main duct passage, in contrast, showed comparatively limited variation across the investigated R₁ range. The spatial correspondence between the shrinking low-pressure zone at R₁ and the weakening velocity concentration along the R₁ wall is consistent with the Bernoulli principle: the reduction in the low-pressure region diminished the pressure gradient driving flow acceleration along the R₁ surface, thereby weakening the wall-hugging velocity concentration and widening the exit angle. This pressure–velocity coupling also provides a physical explanation for the flow deflection behavior: the asymmetric pressure distribution between the R₁ and R₂ walls generates a lateral pressure gradient that redirects the internal airflow toward the deflection side of the duct.

The aerodynamic response to R₁ is shown in Figure 13. As R₁ increased from 10 mm to 30 mm, lift decreased from 6.85 N to 6.50 N, while drag decreased from 0.1332 N to 0.0886 N. Consequently, the lift-to-drag ratio increased from 51.41 to 73.39. The increase in L/D therefore resulted from the proportionally greater reduction in drag relative to lift across the investigated R₁ range.

The combined flow-field and aerodynamic results indicate that R₁ primarily regulated airflow development in the R₁−R₂ inter-wall channel. Smaller R₁ values promoted velocity concentration along the R₁ wall and produced a narrower exit angle, favoring lateral airflow delivery; the corresponding low-pressure zone at R₁ was more pronounced, generating a stronger lateral pressure gradient that contributed to flow deflection toward the canopy side. As R₁ increased, the low-pressure zone shrank, the wall-hugging velocity concentration weakened, and the exit angle widened, indicating diminished lateral delivery capability. The accompanying aerodynamic changes—reduced drag and increased L/D—were therefore accompanied by a trade-off in directional airflow performance. Within the investigated range, R₁ acted mainly as a flow-development and aerodynamic-performance parameter rather than the principal geometric parameter controlling directional airflow redirection. This is consistent with the finding that outlet geometry exerts the dominant influence on ducted fan wake characteristics [29].

3.4. Effect of R₂ on Flow Characteristics and Aerodynamic Performance

The influence of the lower-wall curvature parameter R₂ was evaluated under fixed conditions of R₁ = 15 mm and R₃ = 30 mm to determine its effects on internal flow development and aerodynamic performance. The corresponding velocity distributions, pressure distributions, and aerodynamic performance indicators are presented in Figure 14, Figure 15 and Figure 16.

The velocity distributions (Figure 14) show that changes in R₂ mainly affected airflow development in the R₁−R₂ inter-wall channel, with comparatively limited influence on the velocity distribution within the main duct passage. Across the investigated R₂ range, the R₁ wall surface consistently exhibited a concentrated high-velocity region, whereas the velocity near the R₂ wall remained relatively lower. As R₂ increased, the velocity along the R₂ wall surface gradually increased, reducing the velocity contrast between the two walls within the channel. However, the exit angle of the airflow from the R₁−R₂ channel showed no pronounced change with increasing R₂, indicating that R₂ did not substantially alter the directional airflow delivery capability. These results indicate that R₂ influenced local airflow development through the R₁−R₂ channel but produced comparatively limited changes in the overall directional airflow pattern.

The pressure distributions (Figure 15) show corresponding changes in the R₁−R₂ inter-wall channel. A high-pressure zone was observed adjacent to the R₂ wall surface, while the pressure field within the main duct passage remained relatively stable. As R₂ increased, the high-pressure zone at the R₂ wall progressively diminished, consistent with the gradual increase in R₂-wall velocity shown in Figure 14. The pressure-contour results therefore agree with the velocity distributions in showing that the influence of R₂ was concentrated mainly within the R₁−R₂ inter-wall channel, with limited effect on the pressure distribution in the main duct.

The aerodynamic performance indicators (Figure 16) followed a consistent trend. As R₂ increased from 15 mm to 50 mm, lift decreased from 6.81 N to 6.56 N, while drag decreased from 0.1348 N to 0.1083 N. Consequently, the lift-to-drag ratio increased from 50.52 to 60.55. The increase in L/D resulted from the greater relative reduction in drag than in lift across the investigated R₂ range. The magnitude of the aerodynamic changes became smaller at the higher R₂ values, corresponding with the comparatively limited changes observed in the velocity and pressure distributions.

The combined flow-field and aerodynamic results show that R₂ mainly influenced airflow development in the R₁−R₂ inter-wall channel. Increasing R₂ gradually raised the velocity along the R₂ wall and reduced the corresponding high-pressure zone, but produced no pronounced change in the exit angle of the channel airflow. The accompanying aerodynamic changes—a modest increase in L/D from 50.52 to 60.55—were therefore achieved without substantially altering the directional airflow delivery capability. Compared with the changes associated with the upper-wall curvature R₁, the R₂ results show a narrower aerodynamic response, while the overall direction of the airflow leaving the duct remained comparatively stable. Within the investigated duct geometry, R₂ therefore acted primarily as a secondary geometric parameter affecting inter-wall channel flow development and aerodynamic performance [31].

3.5. Effect of R ₃ on Flow Characteristics and Aerodynamic Performance

The influence of the inner-wall curvature parameter R₃ was evaluated under fixed conditions of R₁ = 15 mm and R₂ = 20 mm to determine its effects on internal flow development and aerodynamic performance. The corresponding velocity distributions, pressure distributions, and aerodynamic performance indicators are presented in Figure 17, Figure 18 and Figure 19.

The velocity distributions (Figure 17) show that R₃ strongly influenced airflow development in the main duct passage. At the smallest R₃ value (Figure 17a), a pronounced high-velocity region developed along the R₃ wall surface, producing a concentrated wall-jet effect. However, severe flow separation was observed on the left side of the main duct outlet, indicating that the airflow failed to remain attached to the outlet surface. As R₃ increased, the wall-jet velocity along the R₃ surface progressively decreased, but the flow attachment at the outlet improved markedly. The trade-off between wall-jet intensity and outlet flow attachment was accompanied by a progressive weakening of the directional deflection of the main duct outlet airflow: the larger R₃ values produced a less laterally directed exit flow. These changes indicate that variation in R₃ substantially altered both the flow quality within the main duct and the resulting directional airflow pattern. The pronounced response to R₃ is consistent with previous ducted-rotor studies showing that changes in duct geometry can substantially alter internal flow development and aerodynamic performance [29,32,39].

The pressure distributions (Figure 18) show corresponding changes concentrated at the R₃ wall surface. A low-pressure zone developed adjacent to the R₃ wall, and the pressure field within the main duct passage was shaped by the intensity of this local low-pressure region. As R₃ increased, the low-pressure zone at the R₃ wall progressively diminished, consistent with the gradual reduction in wall-jet velocity observed in Figure 17. The spatial correspondence between the shrinking low-pressure zone and the weakening wall-jet velocity is consistent with the Bernoulli principle: the reduced pressure differential along the R₃ surface weakened the driving force for flow acceleration, thereby lowering the near-wall velocity and improving flow attachment at the outlet. Together, the velocity and pressure contours show that R₃ had a strong influence on internal airflow development near the outlet and on the resulting directional airflow pattern.

The aerodynamic response to R₃ was substantially greater than the responses observed for R₁ and R₂ (Figure 19). As R₃ increased from 20 mm to 65 mm, lift decreased from 7.24 N to 6.54 N, whereas drag decreased markedly from 0.2933 N to 0.0355 N. Consequently, the lift-to-drag ratio increased from 24.67 to 184.24. The marked increase in L/D resulted primarily from the substantially greater reduction in drag relative to lift across the investigated R₃ range. The large L/D values observed at higher R₃ (e.g., L/D = 184.24 at R₃ = 65 mm). At these configurations, the drag was very small (0.007 N), and the L/D ratio was therefore highly sensitive to minor variations in the drag prediction. Furthermore, in hover, the physical significance of L/D differs from that in forward flight, where drag directly opposes the propulsion direction. The L/D values reported here serve primarily as relative indicators of aerodynamic efficiency for comparing duct configurations within the present study rather than as absolute performance metrics.

The combined flow-field and aerodynamic results identify R₃ as the most influential of the three investigated curvature parameters for outlet airflow distribution and aerodynamic performance. Smaller R₃ values produced a strong wall-jet along the R₃ surface driven by a pronounced low-pressure zone, favoring lateral airflow deflection, but at the cost of severe flow separation at the outlet. Increasing R₃ weakened the wall-jet and shrank the low-pressure zone, which improved outlet flow attachment but progressively diminished the directional deflection capability. The aerodynamic response reflected this trade-off: the marked increase in L/D with increasing R₃ was accompanied by a reduction in directional airflow delivery. Previous UAV airflow studies have shown that the spatial distribution of rotor-induced airflow varies with operating conditions and is an important consideration for task-specific agricultural applications [27]. These aerodynamic indicators, however, provide only part of the information required for duct configuration selection. Airflow delivery to the defined pollination region and the corresponding UAV operating height were further examined across the investigated R₁, R₂, and R₃ values.

3.6. Airflow Delivery to the Pollination Region

The practical design objective of the asymmetric duct was not limited to redirecting rotor-induced airflow but also included delivering sufficient airflow to the defined pollination region within the operating-height constraints of the greenhouse. Airflow delivery was therefore evaluated using the airflow velocity within the pollination region and the corresponding UAV operating height. The single-factor results for R₁, R₂, and R₃ were examined to determine how each curvature parameter affected these two application-oriented indicators.

3.6.1. Effect of R₁ on Airflow Delivery

Under fixed conditions of R₂ = 35 mm and R₃ = 30 mm, increasing R₁ generally reduced the airflow velocity within the pollination region while increasing the corresponding UAV operating height (Figure 20). The airflow velocity decreased from 5.83 to 5.36 m·s⁻¹ as R₁ increased from 10 to 30 mm, whereas the operating height increased from 1.83 to 2.36 m. At R₁ = 13 mm, the airflow velocity within the pollination region was 5.89 m·s⁻¹ at an operating height of 1.97 m.

The external airflow distributions (Figure 21) show that smaller R₁ values maintained a more concentrated high-velocity region on the deflection side of the duct, allowing the redirected airflow to reach the pollination region at lower operating heights. As R₁ increased, the high-velocity region became less concentrated, corresponding with the reduction in airflow velocity within the pollination region and the increase in operating height shown in Figure 20. The general downstream flow development retains characteristics reported for multirotor UAV wakes under hovering conditions [24,25], although the asymmetric duct shifted the airflow laterally toward the canopy side. Across the investigated R₁ range, the airflow velocities within the pollination region ranged from 5.36 to 5.89 m·s⁻¹, exceeding the adopted minimum airflow criterion of 4.5 m·s⁻¹ derived from previous greenhouse tomato pollination research [8].

Within the investigated range, R₁ mainly influenced the relationship between airflow delivery to the pollination region and UAV operating height, while producing comparatively limited changes in the overall direction of the redirected airflow.

3.6.2. Effect of R₂ on Pollination Airflow

The effect of R₂ on airflow delivery to the pollination region was comparatively small (Figure 22). When R₂ increased from 15 to 50 mm under fixed conditions of R₁ = 15 mm and R₃ = 30 mm, the airflow velocity within the pollination region remained between 5.82 and 5.93 m·s⁻¹, while the corresponding UAV operating height increased from 1.83 to 2.10 m. The highest airflow velocity, 5.93 m·s⁻¹ occurred at R₂ = 20 mm with an operating height of 1.97 m. Across the investigated R₂ range, airflow velocity varied by only 0.11 m·s⁻¹, indicating a comparatively small response to changes in the lower-wall curvature.

The external airflow distributions (Figure 23) show limited changes in the position and orientation of the high-velocity region across the investigated R₂ values. The overall airflow pattern remained comparatively similar throughout the parameter range, consistent with the small variation in airflow velocity within the pollination region. Although airflow velocity remained above the adopted 4.5 m·s⁻¹ criterion across the investigated R₂ range [8], the corresponding operating height varied from 1.83 to 2.10 m. This variation shows that the effect of R₂ was more evident in operating height than in airflow velocity within the pollination region.

Within the investigated range, R₂ produced relatively small changes in airflow velocity within the pollination region, while its effect was more evident in the corresponding UAV operating height. These results indicate that the lower-wall curvature mainly influenced the operating position associated with airflow delivery, with comparatively limited changes in the overall external airflow distribution.

3.6.3. Effect of R₃ on Airflow Delivery

Among the three curvature parameters, R₃ produced the largest variation in airflow delivery to the pollination region (Figure 24). With R₁ = 15 mm and R₂ = 20 mm, increasing R₃ from 20 to 65 mm reduced the airflow velocity within the pollination region from 6.48 to 2.82 m·s⁻¹, while the corresponding UAV operating height increased from 1.30 to 2.38 m. At R₃ values of 20, 25, and 30 mm, airflow velocities of 6.48, 6.11, and 5.93 m·s⁻¹ were obtained at operating heights of 1.30, 1.58, and 1.97 m, respectively. These airflow velocities exceeded the adopted minimum criterion of 4.5 m·s⁻¹ [8], Across the full investigated range, however, the decrease from 6.48 to 2.82 m·s⁻¹ shows that airflow delivery to the pollination region progressively weakened as R₃ increased.

The external airflow distributions (Figure 25) show that, at smaller R₃ values, the high-velocity region remained concentrated adjacent to the duct outlet and extended toward the canopy side. As R₃ increased, this region progressively spread and became less concentrated, corresponding with the reduction in airflow velocity within the pollination region and the increase in UAV operating height shown in Figure 24. The larger response to R₃, relative to the preceding R₁ and R₂ analyses, identifies the inner-wall curvature as the geometric parameter with the strongest influence on directional airflow delivery within the investigated duct configuration.

The airflow-delivery response to R₃ also contrasts with its aerodynamic response. As R₃ increased from 20 to 65 mm, L/D increased from 24.67 to 184.24, whereas airflow velocity within the pollination region decreased from 6.48 to 2.82 m·s⁻¹, and the corresponding operating height increased from 1.30 to 2.38 m. Thus, the R₃ value associated with greater aerodynamic efficiency did not necessarily provide greater airflow delivery to the pollination region. This result shows the need to consider airflow delivery and operating height together with aerodynamic performance when selecting a duct configuration for greenhouse UAV pollination. Such task-specific consideration of multiple performance criteria is also relevant to the design and operation of UAV systems for agricultural applications [16,17].

3.7. Configuration Selection Under Greenhouse Operating Constraints

The 81 parameter combinations were evaluated to identify an asymmetric duct configuration that satisfied the adopted airflow and greenhouse operating-height criteria while retaining the reported aerodynamic performance. Unlike the single-factor analyses, which examined the individual responses to R₁, R₂, and R₃, the combined parameter analysis evaluated the three curvature parameters in combination. Each configuration was assessed using airflow velocity within the pollination region, UAV operating height, lift, drag, and lift-to-drag ratio. This allowed the airflow-delivery and aerodynamic responses of the candidate configurations to be considered together.

The combined parameter results further showed the importance of R₃ in defining the feasible configuration space. The representative configurations satisfying the adopted criteria were concentrated at R₃ = 25 mm. This result is consistent with the contrasting responses observed in the single-factor analysis, where increasing R₃ increased L/D but reduced airflow velocity within the pollination region and increased the corresponding UAV operating height. Thus, the configurations retained for further comparison were not identified by aerodynamic efficiency alone, but by considering airflow delivery and operating height together with aerodynamic performance. The representative parameter combinations satisfying the adopted criteria are listed in

Table 5. Representative Parameter Combinations Satisfying the adopted airflow and operating-height criteria at R₃ = 25 mm.

No.	R1/mm	R2/mm	R3/mm	Wind Speed in Pollination Area/(m·s−1)	UAV Operating Height/m	Lift/N	Drag/N	Lift-to-Drag Ratio
1	11	20	25	6.032	1.435	7.037	0.190	37.0
2	25	30	25	6.148	1.834	6.674	0.150	44.6
3	30	15	25	6.173	1.833	6.811	0.165	41.3
4	15	25	25	6.185	1.701	6.810	0.171	39.9
5	13	50	25	6.094	1.701	6.741	0.161	42.0
6	10	45	25	5.989	1.568	6.928	0.173	40.0

.

Among the representative configurations listed in Table 5, the combination of R₁ = 11 mm, R₂ = 20 mm, and R₃ = 25 mm provided an airflow velocity of 6.032 m·s⁻¹ within the pollination region at a UAV operating height of 1.435 m, with a lift of 7.037 N, a drag of 0.190 N, and an L/D of 37.0. The selection followed a two-stage evaluation: configurations were first screened against the adopted airflow (u ≥ 4.5 m·s⁻¹) and operating-height (y < 2.0 m) constraints, and the operating height was then minimized among the feasible candidates. This approach prioritized the greenhouse spatial constraint—lower operating height reduces the risk of interference with overhead structures—while treating the 4.5 m·s⁻¹ airflow criterion as a minimum threshold for pollination relevance rather than a quantity to be maximized. Although several other feasible configurations exhibited higher L/D values of 39.9–44.6, they required operating heights of 1.701–1.834 m, which would increase the proximity to the vine-supporting wires under the greenhouse layout. The combined responses formed the basis for the selected configuration within the investigated parameter space.

The distribution of the evaluated parameter combinations is illustrated in Figure 26. The airflow velocity–operating height relationship (Figure 26a) shows the configuration space relative to the adopted airflow criterion, while the parameter projections in Figure 26b–d illustrate the distribution of R₁, R₂, and R₃ in relation to L/D. The representative feasible configurations were concentrated at R₃ = 25 mm, whereas the selected R₁ = 11 mm, R₂ = 20 mm, and R₃ = 25 mm configuration combined an airflow velocity of 6.032 m·s⁻¹ with the lowest operating height among the representative cases in Table 5. The parameter-space analysis therefore shows that configuration selection depended on the combined airflow-delivery, operating-height, and aerodynamic responses rather than on maximizing L/D alone.

Within the investigated parameter space, R₃ = 25 mm defined the region containing the representative configurations that met the adopted airflow and operating-height criteria. The selected combination of R₁ = 11 mm, R₂ = 20 mm, and R₃ = 25 mm delivered 6.032 m·s⁻¹ airflow to the pollination region at an operating height of 1.435 m while producing 7.037 N lift and an L/D of 37.0. These results show that the selected duct geometry was determined by jointly considering directional airflow delivery, greenhouse operating height, and aerodynamic performance. The present optimum was identified among the discrete levels evaluated in the quasi-orthogonal design.

3.8. Design Implications for UAV-Assisted Greenhouse Tomato Pollination

The results show that geometric asymmetry can redirect rotor-induced airflow without additional actuators or active flow-control components. Rather than simply increasing airflow intensity, the asymmetric duct redistributed the internal velocity and pressure fields and shifted the downstream airflow toward the canopy side. This directional airflow pattern addresses a specific limitation of conventional multirotor configurations, which predominantly generate vertically directed downwash for agricultural operations such as pesticide application [16,17,24,25].

For greenhouse tomato pollination, where airflow must be delivered toward flower-bearing regions distributed along the crop canopy, modifying airflow direction provides a distinct design consideration for UAV operation in confined production environments.

The three curvature parameters influenced different regions of airflow development within the asymmetric duct. Changes in the upper-wall curvature R₁ mainly affected airflow development in the upper section of the duct and altered aerodynamic performance, while producing comparatively limited changes in the overall airflow direction. The lower-wall curvature R₂ influenced airflow development through the lower section, with airflow velocity within the pollination region varying by only 0.11 m·s⁻¹ across the investigated range. In contrast, the inner-wall curvature R₃ produced the largest changes in outlet airflow distribution and aerodynamic performance. Increasing R₃ from 20 to 65 mm increased L/D from 24.67 to 184.24, but reduced airflow velocity within the pollination region from 6.48 to 2.82 m·s^−1, and increased the corresponding UAV operating height from 1.30 to 2.38 m. The strong response to changes in this region of the duct is consistent with previous ducted-rotor studies showing that duct geometry can substantially affect internal flow development and aerodynamic performance [29,32,39].

The contrasting aerodynamic and airflow-delivery responses to R₃ have direct implications for duct configuration selection. A higher L/D did not correspond to greater airflow delivery to the pollination region; instead, the increase in L/D across the investigated R₃ range occurred alongside a marked reduction in airflow velocity within this region. The combined parameter analysis therefore considered airflow velocity, UAV operating height, lift, drag, and L/D together rather than selecting a configuration solely on the basis of aerodynamic efficiency. This task-oriented evaluation is relevant to agricultural UAV applications, where the spatial distribution of rotor-induced airflow and the operating conditions required for a specific crop operation must be considered together [27].

Within the investigated parameter space, the selected configuration of R₁ = 11 mm, R₂ = 20 mm, and R₃ = 25 mm delivered an airflow velocity of 6.032 m·s⁻¹ to the defined pollination region at a UAV operating height of 1.435 m. The same configuration produced a lift of 7.037 N, a drag of 0.190 N, and an L/D of 37.0. These results provide a design basis for directing UAV-generated airflow toward the canopy side under the spatial constraints of greenhouse tomato production.

The present analysis considered a single rotor–duct assembly, consistent with the geometric symmetry of the quadrotor platform in which all four propulsion units are identical and operate under the same hovering conditions. This approach enabled the parametric evaluation of 81 duct configurations within feasible computational resources while isolating the geometric effects of individual duct curvature parameters. The reported airflow and aerodynamic indicators are therefore representative of the local behavior of a single propulsion unit. In a compact quadrotor configuration (~200 mm wheelbase), adjacent rotor wakes may interact in the far field, and the combined four-rotor airflow delivered to the pollination region may differ from the superposition of four independent units. Four-rotor coupled simulations are recommended for future work to quantify inter-rotor interference effects on the combined airflow field.

The present simulations were conducted in an open 6 m³ stationary domain, following the standard approach for isolated rotor–duct CFD studies to isolate the geometric effects of duct curvature on internal flow development and wake redirection. This domain choice avoided introducing greenhouse-specific boundary conditions (e.g., wall proximity, canopy porosity) that vary with crop growth stage and planting density, which would confound the parametric evaluation of duct geometry itself. In the actual greenhouse aisle (~65 cm wide), the proximity of crop canopies and structural surfaces may introduce blockage and wall-jet effects that modify the downstream airflow distribution. Incorporating representative greenhouse boundaries into the computational domain is recommended for future work to assess these confined-environment effects on directional airflow delivery under production conditions.

The present study demonstrates that the asymmetric duct geometry can directionally redirect rotor-induced airflow toward the canopy side and that the delivered airflow velocity satisfies the adopted criterion under representative greenhouse operating constraints. The airflow velocity of 6.03 m·s⁻¹ predicted at the pollination region for the optimized configuration exceeds the 4.5 m·s⁻¹ threshold for tomato pollen release reported by Shi et al. [8], and the 77.5 cm lateral delivery offset substantially exceeds the approximately 0.15 m jet half-width predicted by the turbulent jet model of Bauersfeld et al. [22] for a conventional small quadrotor without a duct. These comparisons indicate that the asymmetric duct provides a meaningful gain in lateral airflow delivery relative to unducted configurations evaluated in prior studies. It should be noted, however, that the evaluation is based on CFD-derived airflow and aerodynamic indicators and does not directly assess pollination effectiveness in terms of flower vibration, pollen release, fruit set, or pollination rate. The findings therefore represent an airflow optimization study rather than a proven improvement in pollination performance. Further greenhouse trials are needed to determine how the selected airflow configuration affects flower vibration, pollen release, and subsequent pollination responses, building on previous experimental research on UAV-assisted greenhouse pollination [8,19] and broader developments in UAV-based precision agriculture [6,16,17].

4. Conclusions

This study developed and evaluated an asymmetric duct for greenhouse UAV pollination by using passive geometric modification to redirect the rotor-induced airflow toward tomato flower clusters. Comparison with a symmetric duct showed that the asymmetric duct shifted the high-velocity wake from a predominantly vertical direction toward the canopy side. The internal velocity and pressure fields indicated that this directional airflow redirection resulted from asymmetric redistribution of airflow and outlet pressure within the duct. Among the three curvature parameters, R₃ exerted the strongest influence because it controlled the outlet deflection region, whereas R₁ mainly affected inlet flow conditioning and R₂ served as a secondary transition parameter. Functional performance analysis showed that aerodynamic efficiency alone was insufficient for duct selection, as excessive increases in R₃ improved the lift-to-drag ratio but reduced pollination airflow. The quasi-orthogonal optimization identified R₁ = 11 mm, R₂ = 20 mm, and R₃ = 25 mm as the preferred configuration, producing a pollination wind speed of 6.032 m·s⁻¹, UAV operating height of 1.435 m, lift of 7.037 N, drag of 0.190 N, and lift-to-drag ratio of 37.0. It should be noted that the present evaluation is based on CFD-derived airflow and aerodynamic indicators and does not directly assess pollination effectiveness in terms of flower vibration, pollen release, or fruit set. The parametric analysis considered a single rotor–duct assembly in an open stationary domain; the combined airflow field of a full quadrotor platform and the effects of greenhouse boundaries (e.g., canopy proximity, wall confinement) remain to be quantified. Experimental validation of the optimized configuration, as well as direct assessment of pollination effectiveness, was beyond the scope of this work and represents a necessary direction for future research. These results provide an engineering basis for designing asymmetric duct systems capable of balancing aerodynamic performance with functional airflow delivery for UAV-assisted pollination in confined greenhouse environments.