The pursuit of advanced drone technology has led to the emergence of trans-medium unmanned aerial vehicles (UAVs), which are capable of operating seamlessly across air and water environments. These vehicles hold immense potential for maritime surveillance, environmental monitoring, and covert reconnaissance. However, one of the most challenging phases in their mission profile is the berthing process near the sea surface, where complex multiphase flow interactions—driven by wind waves and the air-water interface—impose severe aerodynamic and hydrodynamic disturbances on the vehicle’s stability. Understanding these interactions is crucial for improving the reliability and control of next-generation drone technology. In this study, we employ computational fluid dynamics (CFD) based on the lattice Boltzmann method (LBM) to simulate the berthing process of a trans-medium hybrid-wing UAV under realistic sea conditions. The focus is on elucidating the unsteady, nonlinear forces and torques exerted by wave-induced multiphase flows, and how these affect the vehicle’s trajectory and attitude. Through detailed analysis of lift, torque, vorticity, and velocity fields, we reveal the critical role of wave phase, wave height, and wind speed in destabilizing the UAV during its descent. This work provides a foundation for developing robust control strategies that can mitigate the adverse effects of marine environments on drone technology.
1. Vehicle Configuration and Simulation Setup
The trans-medium hybrid-wing UAV under investigation features a compact design optimized for both vertical takeoff and landing and efficient forward flight. Its key geometric and operational parameters are summarized in the following table, which are essential for understanding the aerodynamic and hydrodynamic loads encountered during berthing.
| Parameter | Value | Unit |
|---|---|---|
| Wing area | 2.17 | m² |
| Wingspan | 4.7 | m |
| Fuselage length | 4.2 | m |
| Fuselage width | 2.2 | m |
| Number of rotors | 4 | – |
| Rotor diameter | 0.82 | m |
| Rotor blade count | 3 | per rotor |
| Pitch angle at 0.75R | 20 | ° |
| Rotor rotational speed | 2000 | rpm |
| Airfoil (main wing & tail) | NACA 0010 | – |
The multiphase flow simulation was performed using the lattice Boltzmann method (LBM), which discretizes the Boltzmann equation to solve fluid dynamics at the mesoscale. The governing equation is:
$$
\frac{\partial f}{\partial t} + \mathbf{v} \cdot \nabla f = -\frac{f – f^{eq}}{\tau}
$$
where \(f\) is the particle distribution function, \(\mathbf{v}\) the particle velocity, \(f^{eq}\) the local equilibrium distribution, and \(\tau\) the relaxation time. The computational domain measured 20 m × 20 m × 20 m, housing the UAV model and a representative sea platform. Two-phase flow (air and water) was modeled with water density 998.3 kg/m³, air density 1.225 kg/m³, surface tension 0.072 N/m, and dynamic viscosities of 1 mPa·s (water) and 1.789 × 10⁻⁵ Pa·s (air). The boundary conditions for all rotor blades and fixed-wing surfaces were set as no-slip walls.
To simulate realistic sea states, we employed a second-order Stokes wave model combined with a velocity-inlet boundary method. The wave parameters were set as: significant wave height \(H_w = 3\) m, wind speed \(U_w = 10.7\) m/s, and wave celerity \(c = 10\) m/s. The free-surface evolution follows the second-order Stokes theory, where the surface elevation is given by:
$$
\eta(x,t) = a\cos(kx – \omega t) + \frac{1}{2} k a^2 \cos \big[ 2(kx – \omega t) \big]
$$
with amplitude \(a = H_w/2\), wavenumber \(k = 2\pi/\lambda\), angular frequency \(\omega = 2\pi/T\), and \(\lambda\) the wavelength derived from the dispersion relation. The total simulation time was 2.5 s with a fixed time step of 83.333 μs, allowing high-resolution sampling of rotor forces at every degree of rotation. The mesh consisted of over 2 million cells with two levels of adaptive refinement around the rotors (0.05 m resolution) and a base grid size of 0.1 m. Output frame rate was 200 Hz.
2. Results and Analysis of Multiphase Flow Disturbances
During the berthing process, the UAV descended from an initial altitude of 7 m above the mean sea level to the platform. We recorded the instantaneous lift and torque of each rotor, as well as the vorticity and velocity fields, to characterize the multiphase interaction. The following table categorizes the distinct phases of the descent based on the UAV’s proximity to the wave surface and the observed flow phenomena.
| Time Interval (s) | Altitude Range (m) | Flow Regime | Characteristics |
|---|---|---|---|
| 0 – 0.6 | 7 – 6 | Decoupled aerodynamic phase | Rotor downwash unimpeded by waves; lift and torque stable; minimal wind-wave interference. |
| 0.6 – 1.0 | 6 – 4 | Weak wave interaction | Downwash begins to interact with wave crests; slight fluctuations in aerodynamic forces; onset of unsteadiness. |
| 1.0 – 2.0 | 4 – 1 | Strong multiphase coupling | Rotors directly contact wave crests; intense splashing and spray; severe nonlinear fluctuations of lift and torque; vorticity breakdown. |
| 2.0 – 2.5 | 1 – 0 | Recovery and berthing | UAV clears wave zone; aerodynamic forces stabilize; smooth landing on platform. |
The lift and torque variations for all four rotors over the full simulation are depicted conceptually (without figure numbers) as follows: from 0 to 0.6 s, the four curves nearly overlapped, showing a gradual rise to a steady value of approximately 98 N per rotor. Between 0.6 and 1.0 s, small irregular perturbations appeared with amplitudes up to ±5 N. The most dramatic changes occurred from 1.0 to 2.0 s, where lift exhibited peak-to-peak fluctuations exceeding 40 N and torque variations reached 3 N·m. After 2.0 s, the curves rapidly converged back to the steady-state values, indicating restoration of stable aerodynamic conditions. This evolution confirms that the wave-induced multiphase flow acts as a strong, non-stationary disturbance source for drone technology during near-surface operations.
To visualize the unsteady vortical structures, we examined the vorticity magnitude fields at selected times. At t = 0.2 s, the rotor tip vortices were well-organized and symmetric, with maximum vorticity around 150 s⁻¹. By t = 1.0 s, the downwash impinged upon the wave surface, causing the tip vortices to tilt and partially break into smaller turbulent eddies near the wave crests. At t = 2.0 s, when the rotors were deeply immersed in the wave trough, the vorticity field became highly disorganized, with numerous small-scale structures and strengths exceeding 300 s⁻¹, indicating intense mixing of air and water. Following the UAV’s exit from the wave zone (t = 2.5 s), the vorticity returned to a more ordered helical pattern with reduced peak values of about 120 s⁻¹. This behavior demonstrates that wave interaction enhances vorticity production and promotes turbulence, directly impacting the thrust generation and control margins of drone technology.
Velocity field analysis further reveals the coupling mechanism. At high altitude, the induced velocity field under each rotor was downward and approximately axisymmetric, with a maximum vertical velocity of 12 m/s near the blade tips. As the UAV descended, the wave-induced horizontal velocity component became comparable to the downwash, leading to asymmetric flow patterns. Specifically, when a rotor approached a wave crest, the downwash was deflected laterally, creating a high-speed jet along the wave slope with speeds up to 18 m/s. This jet caused a reaction torque that pitched the vehicle. Additionally, the splashing droplets (up to 5 mm diameter) were accelerated upward by the rotor wake, increasing the effective mass of the surrounding air and altering the apparent density, which contributed to the lift loss and torque spikes quantified in the force data. The volume of fluid (VOF) contour at a mid-descent moment (around 1.5 s) captured the rotor blades cutting through the wave crest, generating a burst of water spray and a temporary cavity in the free surface. The combined effect of these phenomena emphasizes the necessity of adaptive control algorithms for future drone technology operating in maritime environments.
We also derived the instantaneous lift coefficient \(C_L\) for the entire vehicle based on the rotor thrust and the dynamic pressure of the free-stream wind (10.7 m/s). The results are summarized in the following table for the three main phases.
| Phase | Average \(C_L\) | Standard Deviation of \(C_L\) |
|---|---|---|
| High altitude (0–0.6 s) | 1.25 | 0.04 |
| Wave interaction (1.0–2.0 s) | 1.08 | 0.31 |
| Post-wave berthing (2.0–2.5 s) | 1.22 | 0.06 |
The significant increase in standard deviation during wave interaction—by a factor of almost eight—quantifies the degree of unsteadiness introduced by the multiphase flow. The drop in average \(C_L\) suggests a net loss of lifting capability, which must be compensated by increased rotor RPM or collective pitch in real-time control.
3. Implications for Drone Technology Development
The findings of this study have direct implications for the design and control of trans-medium drone technology. First, the strong nonlinearities observed when rotors contact the wave surface indicate that conventional linear control methods may fail during berthing. Instead, non-linear model predictive control or machine learning-based estimators that incorporate multiphase aerodynamic models are required. Second, the asymmetry of loading among the four rotors suggests that differential rotor speed control can be utilized to mitigate the moment disturbances—a technique analogous to cyclic pitch in helicopters but extended to the multiphase regime. Third, the data on vorticity and velocity fields provide benchmark validation for reduced-order models, such as actuator-disk theories extended with wave-induced corrections.
Moreover, the wave height and wind speed used in this simulation correspond to Sea State 5 (rough seas) on the Douglas scale. For operational safety, drone technology deployed in such environments should incorporate real-time wave monitoring (e.g., using onboard radar or lidar) to schedule berthing at wave troughs or during calmer intervals. The second-order Stokes wave model we employed is a reasonable compromise between accuracy and computational cost, but for full-scale simulations, irregular sea spectra (e.g., JONSWAP) should be considered to capture the stochastic nature of real ocean waves.
4. Conclusion
In this work, we have systematically investigated the multiphase flow mechanisms affecting the near-surface berthing process of a trans-medium UAV using LBM-based CFD. The results underscore that wave-induced air-water interaction is the dominant source of unsteady aerodynamic loads on drone technology during descent. The lift and torque data reveal a three-phase behavior: stable, slightly perturbed, and strongly nonlinear. The vorticity and velocity fields illustrate the breakdown of rotor tip vortices and the emergence of high-speed lateral jets that destabilize the vehicle. These insights are critical for advancing drone technology towards reliable maritime operations. Future work will extend the analysis to irregular wave spectra and include fluid-structure coupling to capture the elastic response of the rotors, leading to more robust control frameworks for trans-medium UAVs.