The rapid adoption of small unmanned aerial vehicles (UAVs) in precision agriculture, particularly in hilly and mountainous regions, has revolutionized crop protection practices. These agricultural UAVs offer enhanced adaptability and flexibility, enabling efficient pesticide application in challenging terrains. However, the complex aerial environment during operation introduces significant challenges related to droplet deposition, drift, and evaporation, which can compromise spraying efficacy. Understanding the interplay between the downwash airflow generated by agricultural UAV rotors and droplet motion is critical for optimizing application parameters, improving pesticide utilization, and minimizing environmental impact. This study focuses on numerically simulating and analyzing the downwash airflow field and droplet dispersion patterns of a small quadrotor agricultural UAV, with the aim of elucidating the underlying mechanisms that govern droplet deposition and providing actionable insights for field operations.
The core of this investigation lies in the fluid dynamics of the downwash airflow, which is generated by the rotating rotors of the agricultural UAV. This airflow significantly influences the trajectory, dispersion, and ultimate deposition of sprayed droplets. To model this phenomenon, a comprehensive computational fluid dynamics (CFD) approach is employed, utilizing the Navier-Stokes (N-S) equations, the realizable k-ε turbulence model, and the Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) algorithm. The discrete phase model (DPM) is applied to simulate the motion of individual droplets within the continuous airflow field. The agricultural UAV under study is a custom-built quadrotor system, representative of platforms commonly used in small-scale farm operations.
The aerodynamic performance of the agricultural UAV is foundational to the study. The quadrotor configuration consists of four rotors arranged symmetrically, with diagonally opposite rotors rotating in the same direction to balance torque. The lift force generated by each rotor is a function of its rotational speed, air density, and aerodynamic characteristics. The total lift sustaining the agricultural UAV is the vector sum of these individual forces. For a rotor, the lift ($f_i$) can be expressed as:
$$ f_i = \frac{1}{2} C_L \rho v_L^2 S $$
where $C_L$ is the lift coefficient, $\rho$ is the air density, $v_L$ is the rotational speed of the rotor, and $S$ is the rotor disk area. The interplay of these forces allows the agricultural UAV to maintain stable flight and execute precise maneuvers during spraying operations.
To simulate the downwash airflow field, a three-dimensional computational domain is constructed. The domain is a rectangular volume measuring 3 m × 3 m × 2 m, encapsulating the agricultural UAV positioned 1.5 m above the ground plane during initial simulations. The UAV geometry, including the fuselage and rotors, is simplified to reduce computational complexity while preserving key aerodynamic features. The rotors are modeled as rotating cylindrical zones using a sliding mesh technique to account for their motion. The computational mesh is highly refined, particularly near the rotors and the spray nozzle, with inflation layers applied to wall boundaries to accurately capture boundary layer effects. The total mesh count exceeds 7.5 million elements to ensure resolution of the complex flow features. Boundary conditions are set as follows: the ground is a no-slip wall, the top and sides of the domain are pressure outlets, and the rotor zones are defined as rotating fluid regions.
The governing equations for the fluid flow are the Reynolds-Averaged Navier-Stokes (RANS) equations. In a rotating reference frame attached to the agricultural UAV’s rotors, these equations incorporate source terms to account for rotational effects. The integral form of the conservation equations is:
$$ \frac{\partial}{\partial t} \iiint_{\partial V} \mathbf{W} dV + \oiint \left( \mathbf{F}(\mathbf{W}) – \mathbf{G}(\mathbf{W}) \right) dS = \iiint_{\partial V} \mathbf{Q} dV $$
where $\mathbf{W}$ is the vector of conservative variables $[\rho, \rho u, \rho v, \rho w, \rho E]^T$, $\mathbf{F}$ and $\mathbf{G}$ are the inviscid and viscous flux vectors, respectively, and $\mathbf{Q}$ is the source term vector containing Coriolis and centrifugal forces due to rotation. Here, $\rho$ is density, $u, v, w$ are velocity components, $E$ is total energy per unit mass, and $V$ and $S$ denote volume and surface area.
The motion of droplets, treated as a discrete phase, is governed by Newton’s second law, accounting for various forces. The equation of motion for a droplet particle is:
$$ m_p \frac{d\mathbf{v}_p}{dt} = \mathbf{F}_g + \mathbf{F}_D + \mathbf{F}_{VM} + \mathbf{F}_P + \mathbf{F}_S $$
where $m_p$ is the droplet mass, $\mathbf{v}_p$ is droplet velocity, $\mathbf{F}_g$ is gravity, $\mathbf{F}_D$ is drag force, $\mathbf{F}_{VM}$ is virtual mass force, $\mathbf{F}_P$ is pressure gradient force, and $\mathbf{F}_S$ is Saffman lift force. The drag force is typically the most significant and is given by:
$$ \mathbf{F}_D = \frac{1}{2} \rho_f C_d A_p |\mathbf{v}_f – \mathbf{v}_p| (\mathbf{v}_f – \mathbf{v}_p) $$
with the drag coefficient $C_d$ often expressed as a function of the droplet Reynolds number $Re_d$:
$$ C_d = \frac{24}{Re_d} (1 + 0.15 Re_d^{0.687}) \quad \text{for} \quad Re_d < 1000 $$
and $Re_d = \rho_f d_p |\mathbf{v}_f – \mathbf{v}_p| / \mu_f$, where $d_p$ is droplet diameter, $\mathbf{v}_f$ is fluid velocity, and $\mu_f$ is dynamic viscosity. The momentum exchange between the discrete droplets and the continuous air phase is modeled via source terms in the fluid momentum equations, creating a two-way coupled simulation.
The characteristics of the downwash airflow field are first analyzed without droplet injection. The simulation reveals a complex velocity structure beneath the agricultural UAV. The high-speed rotating rotors induce a strong downward jet of air, which interacts with the UAV fuselage and the ground. Velocity contours on horizontal planes at various heights below the rotors show distinct patterns. Table 1 summarizes key flow zone identifications based on velocity magnitude and direction.
| Zone Name | Location Relative to Rotors | Flow Characteristics | Typical Velocity Range (m/s) |
|---|---|---|---|
| Core Downwash Zone | Directly below rotor disks | High-velocity, vertically downward flow | 5 – 15 |
| Airflow Induction Zones | Between adjacent rotors (inward sides) | Air is entrained inward and downward | 3 – 10 |
| Airflow Export Zones | Outer sides of rotors | Air flows outward and downward | 2 – 8 |
| Ground Interaction Zone | Near ground surface | Flow decelerates and spreads radially | 0 – 3 |
| Recirculation Zone | Below UAV fuselage center | Low-velocity, complex vortical structures | 0 – 2 |
The downwash airflow accelerates to a maximum velocity at approximately 1.0 m below the rotor plane, after which it decelerates due to ground effect and viscous dissipation. The presence of the spray system assembly on the agricultural UAV fuselage causes flow blockage and deflection, leading to the formation of distinct “airflow introduction zones” and “airflow export zones” between the rotors. These zones play a crucial role in channeling the sprayed droplets.
To validate the numerical model, field measurements of downwash velocity were conducted using a calibrated anemometer. Velocity profiles were recorded at multiple vertical positions directly beneath the rotor center and in the inter-rotor regions of a stationary, hovering agricultural UAV operating at a constant rotor speed. The comparison between simulated and experimental velocity magnitudes showed good agreement, with the relative error generally within 20%. The largest discrepancies occurred in regions of high shear and near the ground, attributable to measurement limitations and simplifications in the geometric model. This level of agreement confirms the feasibility and reliability of the CFD model for predicting the downwash airflow of this agricultural UAV.
The interaction between the downwash airflow and the sprayed droplets is the central focus. The agricultural UAV was equipped with a centrifugal atomizer nozzle producing droplets with a volumetric median diameter (VMD) in the range of 90-130 μm. The nozzle was positioned centrally beneath the fuselage. Droplet trajectories, dispersion, and deposition patterns were simulated under various operational heights. The initial droplet velocity from the nozzle is primarily horizontal, but the strong vertical downwash rapidly alters their momentum.
Simulation results for droplet concentration distribution on horizontal slices at different heights reveal a non-uniform deposition pattern. Immediately after release (near the nozzle), droplets are dispersed in a wide, hollow cylindrical pattern. As they descend, the downwash airflow concentrates them into the two airflow induction zones and two airflow export zones, forming four preferential deposition bands on the ground. The concentration in the induction zones is generally higher than in the export zones. The central region directly below the agricultural UAV fuselage receives comparatively fewer droplets due to the initial spray pattern and the recirculating flow in that area. The maximum lateral displacement of droplets from the centerline was found to be approximately 0.6 m under the simulated conditions.
The effect of operational height on deposition uniformity and drift potential is critical for agricultural UAV applications. Simulations were conducted with the agricultural UAV flying at heights of 0.5 m, 0.8 m, 1.0 m, 1.5 m, and 2.0 m above ground level (AGL). Key deposition metrics are summarized in Table 2.
| Flight Height (m AGL) | Avg. Deposition Rate (μL/cm²) | Deposition Uniformity (Coeff. of Variation %) | Estimated Drift Potential (% of spray mass beyond 1m from center) | Max. Droplet Lateral Spread (m) |
|---|---|---|---|---|
| 0.5 | 1.25 | 45.2 | 5.1 | 0.55 |
| 0.8 | 1.08 | 38.7 | 8.3 | 0.65 |
| 1.0 | 0.92 | 42.1 | 12.7 | 0.75 |
| 1.5 | 0.61 | 58.9 | 25.4 | 1.10 |
| 2.0 | 0.40 | 72.3 | 38.6 | 1.50 |
The data indicates a clear trade-off: lower flight heights for the agricultural UAV result in higher deposition density and lower drift but may suffer from poorer uniformity due to strong airflow concentration effects. Higher flight heights improve swath width but drastically increase drift potential and reduce deposition density. The optimal compromise for this specific agricultural UAV and spray system appears to be in the range of 0.8 m to 1.0 m AGL, where deposition is reasonably high and uniform, while drift is controlled.
The physics of droplet entrainment can be further described by analyzing the forces. The droplet acceleration in the vertical direction ($j$) at a time step $k+1$ can be approximated from the force balance:
$$ a_{p,j}(k+1) = \frac{\pi \mu_f d_p C_d Re_j(k+1)}{4 C_e m_p} (v_{f,j} – v_{p,j}(k+1)) $$
where $C_e$ is a Cunningham slip correction factor (important for very small droplets). The trajectory is computed by integrating velocity: $v_{p,j}(k+1) = v_{p,j}(k) + a_{p,j}(k) \Delta t$. The dominance of the drag force, proportional to $(v_f – v_p)$, means droplets quickly attain the vertical velocity of the downwash, but their horizontal momentum can cause significant lateral movement before being fully entrained.
The performance of an agricultural UAV is also influenced by environmental factors. While this study primarily considered calm conditions, crosswind would interact with the downwash, skewing the deposition pattern and increasing drift. Future models for agricultural UAV operation must incorporate ambient wind vectors. The downwash itself can be modeled as a momentum source. The total momentum imparted to the air by the agricultural UAV rotors can be related to the thrust $T$:
$$ T = 2 \rho A v_i V_h $$
where $A$ is total rotor disk area, $v_i$ is induced velocity at the rotor, and $V_h$ is the hover induced velocity. In the far-field, the downwash velocity $w$ below the agricultural UAV can decay according to potential theory for a point momentum source:
$$ w(z) \propto \frac{1}{z} \quad \text{for} \quad z \text{ sufficiently large} $$
where $z$ is the vertical distance from the rotor plane. However, near-field interactions with surfaces and the UAV body make the full CFD simulation essential for accurate droplet prediction.
To generalize findings, dimensionless analysis can be useful. Key parameters influencing agricultural UAV spray deposition include the Stokes number ($St$), which compares droplet response time to flow time scale, and the Froude number ($Fr$), relating inertial to gravitational forces. For a droplet in the downwash:
$$ St = \frac{\tau_p}{\tau_f} = \frac{\rho_p d_p^2 / (18 \mu_f)}{D_r / V_t} $$
$$ Fr = \frac{V_t}{\sqrt{g D_r}} $$
where $\tau_p$ is droplet relaxation time, $\tau_f$ is flow characteristic time (e.g., rotor diameter $D_r$ divided by tip speed $V_t$), and $g$ is gravity. Droplets with $St \ll 1$ follow the airflow closely, while those with $St \gg 1$ are less affected. For typical agricultural UAV droplets (100 μm, density ~1000 kg/m³) and downwash (~10 m/s, $D_r$ ~0.24 m), $St$ is on the order of 0.1-1, indicating moderate coupling. This explains why droplets are not perfectly following the streamlines but are significantly redistributed by the flow.
Operational guidelines derived from this study emphasize the importance of flight height calibration for any agricultural UAV system. The optimal height is a function of rotor size, rotational speed, nozzle type, and droplet spectrum. For the small agricultural UAV modeled, maintaining a flight attitude parallel to the ground and an altitude between 0.8 m and 1.0 m is predicted to maximize deposition on target while minimizing off-target drift. This finding must be validated across different crop canopies, as plant architecture will further interact with the downwash, affecting deposition and penetration.
Future work should involve more sophisticated turbulence models like Large Eddy Simulation (LES) to capture transient vortical structures in the agricultural UAV wake, which can influence fine droplet dispersion. Furthermore, extensive field trials measuring deposition using tracers like water-sensitive paper or fluorescent dyes are necessary to calibrate and refine the numerical models for various agricultural UAV designs and operating conditions. The integration of real-time meteorological data and adaptive flight control could lead to next-generation intelligent agricultural UAV spray systems that dynamically adjust parameters for optimal performance.
In conclusion, this numerical investigation provides detailed insights into the complex fluid dynamics governing droplet transport in the presence of an agricultural UAV’s downwash airflow. The validated model demonstrates how the airflow structures—specifically the induction and export zones—channel droplet deposition into distinct patterns. The strong dependence of deposition efficiency and drift on operational height was quantified. These results underscore the necessity of tailored operational protocols for agricultural UAVs to ensure effective and responsible pesticide application. As agricultural UAV technology continues to evolve, such physics-based simulations will be indispensable tools for design optimization, regulatory assessment, and the development of best management practices for aerial crop protection.