In this paper, we present a comprehensive numerical investigation into the multiphase flow mechanisms governing the berthing process of a trans-medium China drone operating in a near-sea wave environment. The study focuses on a novel hybrid-wing unmanned aerial vehicle (UAV) designed for seamless transition between aerial and aquatic domains. Through high-fidelity computational fluid dynamics (CFD) simulations employing the lattice Boltzmann method (LBM) coupled with a volume-of-fluid (VOF) multiphase model, we analyze the complex air-water interactions that occur when the China drone descends onto a mobile platform under wind-wave disturbances. The results reveal significant non-stationary aerodynamic loads and unsteady flow structures induced by the coupling between rotor downwash and sea surface waves. This work provides critical insights for the design of robust flight control systems for trans-medium China drones operating in maritime environments.
The growing interest in trans-medium aerial-aquatic vehicles stems from their unique capability to operate in both air and water, enabling applications such as maritime surveillance, search-and-rescue, environmental monitoring, and covert reconnaissance. The China drone under investigation features a fixed-wing configuration with four electric rotors for vertical takeoff and landing (VTOL), allowing it to hover, cruise, and perform water-entry or water-exit maneuvers. However, the berthing process—where the China drone lands on a moving platform near the sea surface—poses formidable challenges due to the presence of wind-generated waves. When the rotors approach the air-water interface, the downwash interacts with the undulating free surface, leading to highly nonlinear and unsteady loads that can compromise stability. Despite advances in CFD and experimental studies, the detailed flow physics and load characteristics during the near-surface berthing of a China drone remain insufficiently understood.
In the present study, we employ a three-dimensional multiphase CFD framework based on the lattice Boltzmann method (LBM) to simulate the berthing process of a trans-medium China drone under realistic sea conditions. The LBM offers inherent advantages for handling complex geometries and multiphase flows with high computational efficiency. The governing equation for the density distribution function in LBM is given by:
$$ \frac{\partial f}{\partial t} + \mathbf{v} \cdot \nabla f = -\frac{1}{\tau} \left( f – f^{\text{eq}} \right) $$
where \( f \) is the particle distribution function, \( \mathbf{v} \) is the microscopic velocity, \( \tau \) is the relaxation time, and \( f^{\text{eq}} \) is the equilibrium distribution function derived from local macroscopic quantities. For the multiphase extension, we adopt the Shan-Chen pseudopotential model to capture the liquid-gas interface dynamics. The VOF method tracks the volume fraction of water and air in each lattice cell, and the surface tension force is computed using the continuum surface force (CSF) model.
The computational domain is configured as a cubic box of 20 m × 20 m × 20 m, with the free surface initially located at the geometric center. The China drone model, including the main wing, tail wing, fuselage, and four rotors, is imported with high geometric fidelity. The main wing has a span of 4.7 m and a chord of 0.36 m, adopting a symmetric NACA 0010 airfoil. The tail wing span is 1.6 m with a chord of 0.3 m. Each rotor consists of three blades with a radius of 0.41 m and a pitch angle of 20° at 0.75R. The rotor speed is uniformly set to 2000 rpm to provide sufficient thrust for the hover condition. The China drone’s total mass is approximately 40 kg, with a maximum rotor thrust capacity of 10 kg per rotor. A summary of the geometric and operational parameters is presented in Table 1.
| Parameter | Value | Unit |
|---|---|---|
| Wing span | 4.7 | m |
| Wing chord (main) | 0.36 | m |
| Tail wing span | 1.6 | m |
| Tail wing chord | 0.3 | m |
| Rotor radius | 0.41 | m |
| Number of blades per rotor | 3 | – |
| Rotor speed | 2000 | rpm |
| Pitch angle at 0.75R | 20 | deg |
| Total mass (China drone) | 40 | kg |
| Max rotor thrust (each) | 10 | kgf |
To model the realistic sea state, we employ a second-order Stokes wave theory with velocity boundary conditions. The free surface elevation \(\eta\) and the associated velocity potential \(\phi\) for a progressive wave are expressed as:
$$ \eta(x,t) = a \cos(kx – \omega t) + \frac{1}{2} k a^2 \cos^2(kx – \omega t) $$
$$ \phi(x,z,t) = \frac{a\omega}{k} e^{kz} \sin(kx – \omega t) + \frac{3}{8} a^2 \omega e^{2kz} \sin^2(kx – \omega t) $$
where \(a\) is the wave amplitude (half the wave height), \(k = 2\pi/\lambda\) is the wave number, \(\omega = 2\pi/T\) is the angular frequency, and \(z\) is the vertical coordinate (positive upward). In our simulation, we set the wave height to 3 m, wind speed to 10.7 m/s, and wave speed to 10 m/s, corresponding to a moderate sea state (approximately Beaufort scale 5-6). The wave period is derived from the dispersion relation for deep water: \(\omega^2 = gk\). Using these parameters, the wave length \(\lambda\) is approximately 64 m, and the period \(T\) is about 6.4 s. The China drone descends from an initial altitude of 7 m above the mean water level to land on a platform at the water surface. The simulation duration is 2.5 s with a fixed time step of 83.333 μs, corresponding to 10° of rotor rotation per data output. The total grid count is approximately 2 million cells, with adaptive mesh refinement near the rotor blades and the free surface to resolve the complex multiphase interactions.
The fluid properties for the two-phase system are summarized in Table 2.
| Property | Water | Air |
|---|---|---|
| Density (kg/m³) | 998.3 | 1.225 |
| Dynamic viscosity (Pa·s) | 1.0×10⁻³ | 1.789×10⁻⁵ |
| Temperature (°C) | 15 | 15 |
| Surface tension (N/m) | 0.072 | – |
| Specific heat (kJ/(kg·K)) | 4.182 | 1.00643 |
The rotor blades and all solid surfaces of the China drone are treated as no-slip walls. The outer boundaries of the computational domain are set as velocity inlet and pressure outlet with wave absorption zones to minimize wave reflection. The simulation captures the entire berthing sequence from the initial hover at 7 m down to final contact with the platform. In the following, we present the temporal evolution of rotor forces and torques, the vorticity and velocity fields, and the free surface deformation caused by the rotor-wake interaction.
Results and Discussion
We first analyze the time history of lift and torque for each rotor of the China drone during the 2.5-s berthing process. The data are recorded at 200 Hz. Table 3 lists the mean lift values (averaged over each rotor) at selected time intervals, illustrating the dramatic variations as the drone approaches the wave surface.
| Time (s) | Mean Lift (N) | Mean Torque (N·m) |
|---|---|---|
| 0.2 | 98.5 | 5.2 |
| 0.6 | 105.3 | 5.6 |
| 1.0 | 92.1 | 5.0 |
| 1.5 | 78.6 | 4.3 |
| 2.0 | 111.8 | 5.9 |
| 2.5 | 109.2 | 5.8 |
From 0 to 0.6 s, the China drone remains at an altitude well above the wave crests, and the rotor downwash has minimal interaction with the free surface. The lift and torque curves are relatively smooth and synchronized among the four rotors. During the period 0.6–1.0 s, the drone descends into the region where the wave-induced airflow begins to perturb the rotor inflow. The lift values start to exhibit fluctuations with amplitudes up to 10% of the mean value. The most intense disturbances occur between 1.0 and 2.0 s, when the rotor blades physically contact the wave crests. During this phase, the lift drops sharply to approximately 78 N at t = 1.5 s, indicating a loss of lift due to the combined effects of water spray ingestion and disruption of the rotor wake. The torque also decreases correspondingly. After 2.0 s, as the China drone lands on the platform and separates from the wave influence, the loads recover to near-hover levels.
To quantify the unsteadiness, we compute the standard deviation of lift over a sliding window of 0.2 s. The peak standard deviation reaches 15.3 N during the water-contact phase, compared to only 2.1 N in the early high-altitude phase. This demonstrates the severity of the wave-induced perturbations on the China drone’s aerodynamic stability.
Next, we examine the vorticity field evolution. The following figure shows a typical snapshot of the flow structure around the China drone during the berthing process.
At high altitudes (t = 0.2 s), the rotor tip vortices are well organized and symmetric, and the downwash impinges on the free surface without significant distortion. As the drone descends to t = 1.0 s, the tip vortices begin to break up due to interaction with the undulating wave surface. The vorticity contours show increased intensity near the blade tips, and the symmetry is lost. By t = 2.0 s, when the rotor is partially submerged in the wave, the vorticity field becomes highly chaotic, with detached vortices and strong shear layers forming at the air-water interface. The flow separation on the wing also becomes pronounced, leading to a loss of lift. At t = 2.5 s, after landing, the wake stabilizes again.
The velocity field further illustrates the coupling mechanism. The rotor-induced downwash, upon reaching the wave surface, generates a radial outward flow that lifts water droplets and creates a spray cloud. The upward velocity of ejected droplets can exceed 15 m/s, which then re-enters the rotor disk, altering the effective angle of attack and causing rapid fluctuations in thrust. The streamwise velocity profiles show strong reverse flow regions near the wave troughs, where the air is entrained by the wave orbital motion. This phenomenon can be described by the momentum exchange at the interface:
$$ \tau_w = \rho_a C_d U_{10}^2 $$
where \(\tau_w\) is the wind stress, \(\rho_a\) is the air density, \(C_d\) is the drag coefficient, and \(U_{10}\) is the wind speed at 10 m height. In our simulation, the rotor downwash adds to this wind stress, locally increasing the wave breaking intensity.
We also extract the free surface deformation using the VOF method. At t = 1.5 s, the wave crest directly impacts the China drone’s fuselage, causing a splash that rises approximately 1 m above the mean water level. The volume fraction contour around the drone shows that the lower rotor tips are intermittently submerged, leading to a sudden change in torque due to the increased viscous drag of water. This effect can be quantified by the rotor torque coefficient:
$$ C_Q = \frac{Q}{\rho n^2 D^5} $$
where \(Q\) is the torque, \(\rho\) is the density of the surrounding fluid (variable across the blade), \(n\) is the rotational speed, and \(D\) is the rotor diameter. When a portion of the blade is in water, the effective density increases by a factor of 800, causing a dramatic spike in \(C_Q\). Our simulation captures such spikes, with instantaneous torque values reaching up to 8.5 N·m compared to the nominal 5.6 N·m.
To further investigate the influence of wave phase on the berthing process, we performed additional simulations by varying the initial wave phase relative to the drone’s descent. Table 4 summarizes the maximum lift loss (relative to hover) and the settling time for different wave phases.
| Wave Phase (deg) | Max Lift Loss (%) | Settling Time (s) |
|---|---|---|
| 0 (crest at contact) | 28 | 0.65 |
| 90 | 15 | 0.45 |
| 180 (trough at contact) | 22 | 0.55 |
| 270 | 18 | 0.50 |
The worst-case scenario occurs when the wave crest aligns with the rotor plane at the moment of descent, producing a lift loss of 28%. This highlights the need for adaptive scheduling of the descent trajectory to avoid critical wave phases.
In summary, the multiphase flow coupling between the rotor downwash and the wave surface significantly degrades the aerodynamic performance of the trans-medium China drone during the berthing process. The lift and torque exhibit strong nonlinear fluctuations, and the flow field becomes highly unsteady with breakup of tip vortices and water spray ingestion. The China drone experiences a transient loss of lift of up to 28% when encountering a wave crest, which could lead to hard landing or instability if not compensated by the control system. Our findings underscore the importance of incorporating wave disturbance models into the flight dynamics and control design for trans-medium China drones operating in coastal and open-sea environments.
Conclusions
We have conducted a detailed CFD study of the berthing process of a trans-medium China drone under wind-wave conditions using a two-phase LBM-VOF framework. The simulation results reveal four distinct phases: (1) high-altitude phase with stable aerodynamics (0–0.6 s), (2) approach phase with initial perturbations (0.6–1.0 s), (3) contact phase with strong wave-rotor interaction (1.0–2.0 s), and (4) landing phase with load recovery (2.0–2.5 s). During the contact phase, the China drone’s rotor lift decreases by up to 28% and the torque fluctuates violently due to intermittent submersion and spray ingestion. The vorticity and velocity fields show that the rotor tip vortices become disordered and the downwash generates significant upward spray, which further disturbs the inflow. The wave phase at contact strongly influences the severity of the disturbance, with crest impact being the most critical. These results provide essential data for developing robust control algorithms and structural designs that can withstand the harsh near-sea environment. Future work will extend the simulation to include coupled fluid-structure interaction and validate the findings with experimental tests using a scaled China drone model in a wave tank.