Lift–Drag Performance of a New Unmanned Aerial Vehicle in Di ﬀ erent Media and Ground E ﬀ ect

: Water–air trans-media unmanned vehicle is a kind of aircraft, which can freely ﬂ y in the air, sail in the water and pass through free surface. For trans-media aircrafts, the development process from air–surface to air–underwater and from submarine-launched drive to autonomous drive is investigated. By analyzing the characteristic of manta ray, ﬂ ying ﬁ sh and existing aircraft, this paper proposes a new water–air trans-media unmanned vehicle with ﬂ at dish-airfoil-shaped main body and telescopic NACA-type wing. Then the numerical method to calculate the lift and drag forces is established and validated by the results of classic NACA cases. On this basis, the ﬂ ow ﬁ eld around the new vehicle is numerically simulated, and its lift–drag performances in di ﬀ erent media (air and water) and ground e ﬀ ect are analyzed, comparing it with a model inspired by the Black-wing Unmanned Aerial Vehicle (UAV). The ﬁ ndings illustrate the superior performance of the new vehicle in terms of lift and drag forces, o ﬀ ering an innovative design framework for water–air trans-media UAV applications.


Introduction
The increasing complexity of maritime operating environments has led many researchers to focus on high-performance aircraft suitable for marine conditions, offering promising applications in both military and civilian sectors.Furthermore, in order to expand the working environment and application scope of existing aircraft, the researchers have turned their attention to the trans-media aircraft with amphibious capabilities [1].
Research on water-air amphibious aircraft involves a developmental progression from operating on the air surface to functioning underwater and from being launched from submarines to autonomous operation [2].The seaplane is an amphibious aircraft that can operate in the air and on the water surface, as shown in Figure 1a, and does not achieve underwater navigation.Zha [3] conducted numerical simulations on the water surface for seaplanes.This aircraft has been extensively utilized in the military domain, with the United Kingdom and the United States leading the development efforts and deploying a significant number of these aircraft into active service.The relative research about the seaplane has stepped into maturity.Its special modes of take-off and landing consider the interactive effect between the plane and waves, which can provide certain technical reference for the trans-media UAV.With the development of technology, Liu [4] used numerical methods to study the water ejection process under different launching conditions.As shown in Figure 1b, the United States led the world in the research of the submarine-launched UAV.For example, the Black wing UAV that the U.S. military has already installed is a kind of UAV that can be launched underwater by submarine and cruise in the air [5], which has good performance in relay communication, surface search and rescue, etc.This UAV cannot achieve autonomous propulsion and operate independently in the water and air, but the design idea of variable wing can support the waterair trans-media method for the technique development of self-driven UAVs [2].For example, Lock et al. [6] proposed a bionic flapping amphibious drive wing.The Blackwing UAV uses a variable-sweep wing.Qi et al. [7] have conducted a detailed study on the control of this structural deformation.To increase the operational range underwater, numerous institutions are conducting research on water-air trans-media unmanned aerial vehicles (UAVs) capable of autonomous operation in both underwater and aerial environments, as illustrated in Figure 2. Yin et al. [10] created a visual simulation of a trans-media aircraft based on the Creator and Vega platforms.The simulation results can provide theoretical basis and research measures for the general design of the trans-media aircrafts.Various research institutions have proposed their own experimental prototypes based on the principle of bionics.For example, Lock et al. [6] studied the application of bionics in multimodal motion.Xingbang et al. [11] and Wang et al. [12] from Beihang University have successively developed the trans-media aircrafts by referring to the flying fish and booby.Gao [13] proposed a bionic flying fish-inspired cross-domain unmanned aerial vehicle as shown in Figure 2a.Ma et al. [14], in the Robert Wood research group of Harvard University, proposed an insectlike flapping-wing amphibious aircraft.Siddall and Kovac [15] from Imperial College London designed a diving UAV inspired by the propulsion of squid and the water-entry characteristics of the booby, applying principles of bionics.Izraelevitz and Triantafyllou [16] from Mechanical Engineering at MIT proposed the concept of a water-air amphibious multi-mode bionic prototype.Hou [17]  The information of three kinds of water-air amphibious aircrafts has been summarized and is listed in Table 1.Therein, the self-driven trans-media UAV with the widest application range and best performance has been in the conceptual design stage and has not yet been converted to an engineering model.The existing concept primarily features a slender body shape, with the wing responsible for supplying the overall lift force of the aircraft, based on its shape and performance characteristics.Therefore, the wing should be designed to be very large, which may bring large difficulty to the design of variant wings for the trans-media processes.Drawing from the characteristics of manta rays, flying fish, and current aircraft designs, a novel flat dish-airfoil shape is proposed to replace the traditional slender-body form.This new shape aims to enhance lift force while minimizing drag.The length of the wing can be shortened, which can reduce the design difficulty of variant wing.Therefore, this study proposes a novel water-air trans-media UAV with a flat main body and discusses the performance characteristics of lift and drag forces as crucial indicators.The lift and drag forces not only determine the aircraft's payload capacity but also influence its flight speed and maneuverability [18].The rest of this paper is organized as follows: in Section 2, the new water-air transmedia UAV with a flat dish-airfoil-shaped main body and telescopic NACA-type wing is described.In Section 3, the numerical method to calculate the lift and drag force is established and validated by the results of classic NACA cases.In Section 4, the flow field around the new UAV is numerically simulated, and its lift-drag performance in two media (air and water), as well as in ground effect, is analyzed and compared with a model resembling the Blackwing UAV.In Section 5, key conclusions of the current work are drawn.

Description of New Water-Air Trans-Media UAV
Currently, research on water-air trans-media UAV mostly adopts the form of wings combined with a cylindrical fuselage.When navigating underwater, the fuselage cannot provide lift and relies on propulsion devices for control.There is a plan to design a vehicle that combines wings and fuselage, so that the vehicle still possesses a certain amount of lift and drag underwater, enhancing its maneuverability underwater.During the process of surfacing, the existing lift can help the vehicle transition from underwater to near the water surface without the need to adopt a vertical surfacing method, utilizing its own lift to generate upward force, lifting the watercraft above the water surface, and smoothly transitioning to a near-surface navigation state, rendering it more concealed.
This paper introduces a new concept for the water-air transmedia UAV by analyzing the characteristics of manta rays, flying fish, and existing aircraft.The study proposes a new main body shape in the form of a flat, dish-like airfoil, designed to provide lift force compensation while operating in the air or underwater.A Romanian team [19] is developing a dish-shaped ultrahigh-speed aircraft which achieves all-directional flight in the air.Chen et al. [20] from Beihang University developed a manta-like underwater vehicle in water, which can prove the adaptability of the flat vehicle in the air or water environment.In the process of sailing of UAV, the trans-media problem through water surface can be solved by means of the morphing wing by Siddall [13], which includes folded and telescopic ways.From the aspect of bionics, the design of variant wings can be referred to the form to imitate the gannet and flying fish by Ropert et al. [21], Liang et al. [22] and Gao [13].When the aircraft enters the water, the wings can shrink and fold like a flying fish or a gannet to achieve a change in lift and drag forces.
By analyzing the characteristic of the manta ray, flying fish and existing aircraft, this paper proposes a new water-air trans-media unmanned vehicle with a flat dish-airfoilshaped main body and telescopic NACA-type wing, as shown in Figure 3.The main body of the new UAV is basically dish-shaped.Furthermore, in order to provide more lift compensation, the design of the dish adopts an airfoil-like design with a slightly convex upper surface compared to the lower surface.The connection between the main body and the wings adopts the method of telescopic wing [23].The wings can be ejected from the inside of the main body.The technique of the telescopic wing is relatively mature, and can be applied in the UAV under complex environments.
The designed aircraft has an approximate mass of around 1.8 kg and is mainly used for exploration and reconnaissance functions.We hope that this aircraft has the ability to switch freely between three working modes and achieve attitude control by adjusting the angle of attack.Due to the significant underwater resistance and the difficulty of deploying the wings timely upon surfacing, conventional aircraft use propellers to provide upward thrust to achieve vertical surfacing and deploy the wings after surfacing to generate lift.However, such a mechanism lacks concealment.Our design is an aircraft with a blended wing-body design, allowing it to have some lift to control attitude when the wings are retracted underwater, and emerging with a smaller angle of attack when surfacing using propellers.Due to ground effect near the water surface, the body will gain additional lift to help stabilize the aircraft.In terms of ground effect, this working mode not only allows the aircraft to surface at a higher initial speed and quickly maintain stability with higher lift, but also, due to the curvature of the Earth, radar has blind spots on the water surface, making low-level water navigation more concealable.When the new UAV is cruising in the air, its two wings are stretched out and can fly in the air like ordinary aircraft, as shown in Figure 3.As the aircraft prepares for entering the water, the wings retract, as shown in Figure 4a.When the UAV is entering the water, the two wings are contracted in the main body, as shown in Figure 4b, then it enters into the water and sails underwater.The design method can effectively protect the wings from the impact failure.By adjusting the lift force of the main body, the new UAV can freely achieve floating and diving.Different functions can be achieved by adjusting the attitude of the wing through the motor and transmission device inside the main body.When entering the water, the wings retract through a telescopic device to reduce the impact during entry and the resistance when navigating underwater.The technology for wing retraction is currently quite mature, and Li [24] has conducted structural research on this technology, which can be applied to this new type of vehicle, as shown in Figure 5.This technology has already been widely patented, and Zhu [25] researched a new one, it is a patented achievement of a retractable variable wing.The diagram depicts a device that uses linkages to operate the retractable aircraft wing.Aviation Technology Co., Ltd., in the High-Tech Zone of Zhuhai, China, has designed an unmanned aerial vehicle with retractable wings that can operate underwater [26].The retractable wings are connected to the fuselage through an axle system.Some scholars [27] have researched a cross-media variant wing watertight device and a cross-media variant aircraft, effectively solving this issue and obtaining a patent.

Numerical Simulation Method to Calculate the Lift and Drag Forces
In order to study the characteristic of lift-drag forces of the UAV, the numerical simulation method based on the Star CCM+2022.1 platform is taken here.Then, the convergence and accuracy of the method are validated by comparing with the results of classic cases of NACA airfoils.

Description of Numerical Method
The numerical method in this paper is based on the Star CCM+ platform.By referring to the cruising speed 80~160 km/h of the Blackwing UAV, the speed is lower than Mach 0.3.The flow field around the UAV in the air can be handled as an incompressible fluid, and the density and viscosity coefficients of air are both constant.
The governing equations of flow field in the air and water based on the law of conservation of mass and momentum can be described as follows: where u, v and w are the components of the fluid velocity vector along the three coordinate axes of x, y and z, respectively.S x, S y and S z are the source terms of the momentum equation.P is the fluid pressure, ρ is the fluid density, which is constant, and µ is the dynamic viscosity of the fluid.
The boundary conditions include velocity inlet boundary, pressure outlet boundary, symmetry boundary, and wall boundary.For the velocity inlet boundary condition, the parameters of velocity should be set according to the actual situation.The pressure outlet boundary condition should be usually far away from the perturbation-causing location in the flow field, at which the static pressure should be given.The symmetry boundary condition can be used to solve symmetric physical problems, which can reduce the size of computational domain.At the symmetry boundary, the gradients of fluid variables along the normal direction are zero.On the wall boundary, the fluid flow needs to satisfy the principle of "impenetrability".Furthermore, no-slip boundary conditions are used, which means that the relative velocity of the fluid particle and the wall is zero.
In order to deal with the turbulent performance of fluid field, the turbulent models should be applied in the numerical simulations.Based on the theoretical and empirical studies, S-A and SST k-ω turbulent models are more suitable for the numerical simulation about the flow field around aircraft.Therein, the S-A turbulent model is appropriate to simulate the flow characteristic in the boundary layer of airfoil wall.The SST k-ω turbulent model combines the k-ω model's strengths in the near-wall region and the k-ε model's advantages in the far-field one.It also accounts for the transport process of turbulent shear stress, making it well-suited for studying the flow field around an airfoil.Thus, the above two turbulent models should be further discussed regarding the feasibility to calculate the lift and drag forces in Section 3.2.
When an aircraft is flying close to the water surface, there will be a phenomenon known as the ground effect.Ground effect refers to the aerodynamic disturbances caused by the ground on moving objects when they are close to the ground.This results in a reduction in induced drag and an increase in lift-to-drag ratio for the aircraft.Since the aircraft is flying close to the water surface rather than a solid surface, the Volume of Fluid method (VOF) is a numerical method that can be used to simulate interface behavior in multiphase flow.By using the VOF method to simulate the liquid surface when the aircraft is flying, the aerodynamic performance of the aircraft flying close to the water surface can be obtained.
The Volume of Fluid (VOF) method is a numerical technique used in computational fluid dynamics to track and locate free surfaces or fluid interfaces.It employs a static or grid that is migrated in a specific determined form to adapt to the evolution of the interface shape, being a form of Eulerian method.In the VOF method, different fluids are identified by tracking the volume fractions of different phases in the computational grid.Typically, a phase function is used to represent the distribution of each phase in each cell, such as the distribution of water and air in a container.The process of identifying fluids using the phase function generally involves the following steps:

Validation on the Convergence and Accuracy of the Method
Here, classic models of NACA0012 airfoil with Reynolds number Re = 1.6*10 5 and 1.0*10 6 are taken as test cases.The NACA airfoil was designed by the National Advisory Committee for Aeronautics (NACA), and the performance parameters of the airfoil are obtained through wind tunnel tests conducted by the National Aeronautics and Space Administration (NASA), according to the experimental data used in this article from official data sources [28].The computational domain and boundary conditions are established, as shown in Figure 6.Then, the numerical meshes are created, the global mesh scheme is shown in Figure 7a, and the local meshes in the front, middle and rear of the airfoil are refined to ensure precise calculation, as shown in Figure 7b.Based on the principle of y + = 1, four numerical grid schemes with different mesh size are selected for the analysis on mesh convergence, and the lift coefficients of the airfoil with attack angle 10° and Re = 1.0*10 6 are numerically calculated, as listed in Table 2.It can be found that as the number of grids becomes larger, the lift coefficient tends to converge when the number of meshes increases to 96,214.Considering the calculation accuracy and efficiency, grid scheme 3 (96,214) is selected to discuss the feasibility of turbulent model and the accuracy of the method.On this basis, the lift coefficients of the NACA0012 airfoil with Re = 1.6*10 5 and 1.0*10 6 are numerically calculated by the two turbulent models and compared with the experimental data [28,29], as shown in Figure 8. From Figure 8a, it can be found that for the cases of Re = 1.0*10 6 , the results by the two turbulent models are basically consistent with the experimental data.However, for the cases of Re = 1.6*10 5 in Figure 8b, the result by standard S-A turbulent model is different from the experimental data, and the solution by SST k-ω turbulent model agrees well with the experimental result.Therefore, the SST k-ω turbulent model is adopted in the numerical method to calculate the lift-drag coefficients in the flow field around the airfoil.Furthermore, the results of lift and drag forces of NACA0012 airfoil with Re = 1.0*10 6 are numerically calculated and compared with the experimental data to validate the method, as shown in Figure 9.It can be seen from Figure 9 that the lift and drag coefficients by the numerical method of this paper have little difference with the experimental results, which can validate the accuracy of the numerical method of this paper.

Three-Dimensional Simulation and Convergence Analysis
The two-dimensional experimental data and simulation results are in good agreement, but two-dimensional simulations cannot simulate the actual state of the aircraft in a three-dimensional environment.In a three-dimensional environment, the most typical feature of an aircraft is the wingtip effect at the end of the wing.Vortices are generated at the wingtip of the aircraft, increasing the induced drag of the aircraft.As shown in Figure 10, Cheng [30] simulated the phenomenon of wingtip vortices on the wing, and it was observed that the wake vortices experienced a process of first increasing and then decreasing during the entire evolution process.The SST k-ω turbulent model is adopted for the numerical simulation calculation of the model.According to the computational method for calculating the aerodynamic performance of the airfoil based on two-dimensional simulation, as shown in Figure 11a, the computational domain grid is refined from sparse to dense to accurately obtain performance data.Regarding the size of the computational domain, the distance of the aircraft from the inlet and the top, bottom, left, and right boundaries of the computational domain is set to 10 times the characteristic length.The distance of the tail from the outlet of the computational domain is set to 15 times the characteristic length to allow for sufficient development of the flow field at the aircraft's tail during its flight.The computational field is 17 m long, 14 m wide and 14 m high.The surface of the cuboid is divided, and the inlet, outlet, bottom, top and two side boundaries are set.The basic grid size is set to 0.4 m.As shown in Figure 11b, when performing ground effect simulation calculations, since it is a calm water surface, there is no large wave height disturbance.A cuboid with a height of 0.1 m is created on the water surface.This area is the interface between gas and liquid.In order to better capture the interface between gas and liquid, and near the free liquid surface, the velocity and pressure gradients are large, so it is necessary to encrypt in the height direction, which is designed to be 3.125% of the basic size.The design calculation time is 10 s, the time step is 0.001 s, and it is iterated 10 times in one time step.Due to the influence of wingtip vortices, the calculation results will have a certain amplitude.When the amplitude divided by the calculation result is less than 0.5%, it is considered that the calculation has basically converged.During the aircraft's flight process, prism layers are applied at the wall to ensure accurate development of the flow field at the wall.According to the VOF theory, due to the significant density variation and rapid transition between gas and liquid, and considering that the simulation is conducted with a static water surface, the phase function in the VOF method should exhibit a nearly vertical change at the gas-liquid interface, with a significant variation in the phase function.As shown in Figure 12, the numerical method employed in our simulation effectively simulates the changes in the phase function at the interface.Based on the principle of y + = 1, four numerical grid schemes with different grid sizes are selected for grid convergence analysis.The lift of the aircraft at an angle of attack of 0 degrees is chosen for analysis, as shown in Table 3.It can be observed that when the grid size is 3,155,571, the number of grids has already converged.This grid scheme is selected for the analysis and calculation of the aircraft's performance.By using this grid scheme to simulate the new aircraft, as shown in Figure 13, it is observed that the wingtip vortex also undergoes a process of first increasing and then decreasing throughout the entire evolution process.Similar to the phenomenon observed by Cheng [30], this grid scheme is able to simulate three-dimensional phenomena that were not present in the two-dimensional grid, enabling a more accurate numerical simulation of the aircraft's flight state in three dimensions.

Parameters of New Conceptual Model and Comparative Model
Here, the Black wing UAV is chosen as the comparative model to analyze the lift and drag forces of the UAV.The Black wing is a submarine-launched UAV as shown in Figure 14, which is relatively mature and has been installed.Its parameters are listed in Table 4 by referring to Sun [5].In order to maintain the same functionality of the UAVs, based on the volume of main body and the size of the front wings, the new water-air trans-media UAV with a flat dishairfoil-shaped main body and telescopic NACA-type wing is presented, whose parameters are listed in Table 5.From Tables 4 and 5, it can be found that the volumes of the main body for the two UAVs are equal, which can carry the same equipment.The diameter of the Blackwing drone(AeroVironment, America) is 7.62 cm.However, due to the necessity of accommodating the retractable wings at the lower end of the fuselage of the aircraft, most of the housing space within the fuselage only has half the diameter in height.Figure 15 depicts the maximum longitudinal height of the cross-medium drone in the vertical section as 4.35 cm.The height dimension of modular components such as laser radar and batteries does not exceed 3 cm.This design can meet the requirements of some normal equipment use, and the narrow part at the edge of the drone can accommodate the layout design of electrical wires.Small components such as rod linkages and electrical wiring can be placed at the internal edges and narrow areas of the fuselage.
Figure 16 depicts the internal layout of the preliminary design of the watercraft.The equipment in the diagram is shown to scale, this is a schematic representation.Further research is needed for the actual internal layout, and we hope this will answer your questions.2) is a camera for photography and reconnaissance purposes.( 3) is a motor for controlling the camera's rotation.( 4) is a laser radar.( 5) is the fuselage bulkhead which houses the retractable wings externally using a motor.The wings retract and shorten when in operation, folding into the fuselage.( 6) is the component for retracting the wings, rotating to drive the internal components for wing retraction; for specific retraction methods, please refer to relevant patents.( 7) is a motor driving the wing retraction mechanism.( 8) is a propeller providing thrust for the UAV.( 9) is the motor driving the propeller.( 10) is the speed controller regulating the motor.( 11) is the control chip managing the devices.( 12) is the battery supplying the required energy.
Furthermore, the wings of the new UAV are the same size as the front wings of the Black wing UAV, which means that the new concept can reduce the wing area by nearly half compared to the Black wing UAV.Moreover, the models of the Black wing UAV and new UAV are created as shown in Figure 17.Therein, the Black wing UAV has two front wings and two rear wings, and the new UAV only has two wings which are same as the front wing.

Analysis on the Lift-Drag Performance of the Models in Air
Here, the flow fields around the two UAV models in the air are numerically simulated by the CFD method, which have various attack angles from 0° to 5° and cruising speed of 160 km/h.When the UAVs fly in the air, the air flows through the body surface.The streamline diagrams and velocity contours of the two UAVs can be obtained as shown in Figures 18 and 19  From Figure 18, the airflows reach the front of the UAVs and then flow backwards around the body surface.In the case of the Blackwing UAV, the configuration of the main body and the auxiliary structure designed to safeguard the retracted wings may lead to vortex and streamline fluctuations in the UAV's front end, potentially impacting its aerodynamic lift-to-drag performance.For the new UAV, the streamlines in the flow field are smoother, which can make the aerodynamic performance more stable.The airflows on the top surface of the main body have obvious high velocity, which can cause the main body to produce effective lift for the new UAV.Additionally, it can be observed in Figure 19a that the rear wings are situated within the wake generated by the front wings, thereby influencing the lift-to-drag performance of the Blackwing UAV.The flow field around the main body has a long wake and is different from the field around the wings.From Figure 19b, the difference in the air velocity near the main body and wings is smaller, and the flow field around the new UAV is more stable.
Throughout UAV flights, streamline diagrams and velocity contours, as depicted in Figures 18 and 19, play a crucial role in defining the pressure distribution on the UAVs' body surfaces, exemplified in Figure 20.For the Black wing UAV, the pressures on the front surface of the UAV are large, especially for the auxiliary structure, which should mainly affect the drag performance of the UAV.The lift of the UAV is mainly provided by the wings.For the new UAV, the leading edge of the main body still bears the maximum pressure, but the pressure transition along the body surface is relatively gentle, and the difference in the pressure on the front and back surface is relatively smaller.Both the main body and the wings can produce the lift for the new UAV.On this basis, the lift forces on the new UAV at the attack angles of 0° and 5° can be obtained, which are listed in Table 6 and shown in Figure 21, along with the results of the Black wing UAV.From Table 6 and Figure 21, the calculated lift forces of the Blackwing UAV are about 22.6 N at attack angle 0° and 55.6 N at 5°, respectively.According to the reference material [5], its full-load weight is about 3 kg, and the numerical model of the Black wing UAV can stably achieve the cruise function in the state of small attack angle, which better shows the performance of the real aircraft by the numerical method.On the other hand, the results of the new UAV are 28.6 N at 0° with the increase of about 26.5% compared with the Blackwing UAV.The lift is 64.3 N at 5° with a performance improvement of about 15.6%.Therefore, the concept of new UAV can not only reduce the wing area by about half to greatly decrease the trans-media difficulty but also effectively improve the lift performance in the cruising state with a small angle of attack.
Furthermore, the drag performance of the two UAVs are further achieved and discussed.The total drag F can be divided into frictional resistance F f and differential pressure drag F p, which are listed in Table 7 and shown in Figure 22.From Table 7 and Figure 22, it can be found that the attack angle has little influence on the frictional resistance and large effect on the differential pressure drag.Furthermore, the frictional resistance of the new UAV is smaller than that of the Black wing UAV by about 35%.As the attack angle tends to zero, the new conceptual design should minimize the differential pressure drag and total drag of the UAV.The total drag of the new UAV can significantly decrease to about 40% of the Black wing UAV under the attack angle 0°.Therefore, the new UAV can effectively reduce the total drag compared with the Blackwing UAV.

Analysis on the Lift-Drag Performance of the Models in Water
When the two UAVs are sailing in the water, in order to reduce the drag, the wings should be contracted in or hidden under the main body.Therefore, for the lift-drag performance of the trans-media UAVs when sailing in water, here the main body should be only considered.In this paper, the main bodies of the two UAVs are put into the water to numerically simulate the lift-drag performance under the sailing speed of 6 kn.The same as aerial flight simulation, environmental setup is conducted using single-phase flow.The streamline diagrams and velocity contours of the two UAVs can be obtained as shown in Figures 23 and 24  From Figure 23, it can be found that when the two UAVs are sailing in water, the flow field near the Black wing UAV is more chaotic, which will cause a higher pressure differential resistance.Comparatively speaking, the streamline around the new UAV is much smoother.Furthermore, In Figure 24a, the Black wing UAV has a larger change in flow velocity near the tail during the sailing process.However, in Figure 24b, the fluid velocity in the flow field around the new UAV has smaller and more natural changes.Moreover, from the influence range of the flow field for the two UAVs, the influence area for the Blackwing UAV is much larger than the new UAV, which shows that the new UAV has better concealment when navigating underwater.
On this basis, pressure distribution on the body surface of the UAVs is shown in Figure 25.From the figure, the local and overall pressures on the body surface of the Black wing UAV are higher than those of the new UAV, which needs higher requirements for the material strength.The performances of the UAVs in water are calculated and listed in Tables 8 and 9 and Figure 26.

Attack Angle
Blackwing UAV (N) New UAV (N) 0 0.7 31.8 −2.5 −1.2 11.9 −5 −3.1 −6.9The data in Tables 8 and 9, as well as Figure 26, suggest that as the attack angle shifts from 0° to −5°, the change in lift force for the Blackwing UAV is 3.8 N compared to 38.7 N for the new UAV, indicating a higher sensitivity of the lift force to the attack angles in the new UAV.Thus, it is easier to adjust the ascending and descending of the new UAV through the angle of attack, i.e., the flexibility and sensitivity of the new UAV is better.On the other hand, the lift force of the Black wing UAV does not obviously change in the water, and the UAV can be controlled only by adjusting the buoyancy, which should cause the lag and delay.Moreover, in terms of drag, for the Black wing UAV, the differential pressure drag is much larger than the frictional resistance, and the total drag is mainly determined by the differential pressure drag.For the new UAV, the differential pressure drag can be largely decreased and is very close to the frictional resistance.Therefore, compared with the Black wing UAV, the new UAV can more effectively reduce the total drag by about 70% when sailing in the water.

Analysis on the Lift-Drag Performance of the Models near Free Surface in Ground Effect
After the UAV emerges from the water, it enters a phase of near-surface navigation to fully utilize the ground-effect state, which can help the vehicles to generate sufficient lift near the water surface and smoothly transit to normal flying mode.In CFD simulations, when an aircraft is flying close to the water surface, the VOF method is required to track the changes of the water-air interface.Assuming that the environmental wind and flow speed around the aircraft are both 160 km/h, this is used to simulate the UAV's constant-speed flight close to the water surface.The VOF model is employed to calculate the volume fraction in each cell, solve the fluid flow equations, update the volume fraction, simulate the changes in different phase interfaces, and obtain the performance of flying near the water surface.Here the lift-drag performances of the two UAVs are analyzed near the water surface.
According to the wingspan of the UAVs at 0.3 m, the UAVs can be assumed to fly at a height of 0.15 m above the water surface, which enables the aircraft to more fully utilize the ground effect.During near-surface navigation, both the Black wing UAV and the new UAV experience a certain performance improvement, attributed to the presence of the ground effect which can generate an increase in lift.In terms of lift performance as listed in Table 10, although the new UAV lacks a pair of rear wings compared to the Black wing UAV, it still exhibits performance advantages.With an increase in the angle of attack within a certain range, the lift performance of the new UAV has weakened to some extent.Furthermore, based on the numerical results as listed in Table 11, the new UAV still maintains a certain advantage in terms of the drag performance.With zero angle of attack, the drag of the new UAV is only 43% of the Black wing UAV.As the angle of attack increases, the pressure drag also increases, leading to a slight overall increase in the total drag of the new UAV, reaching around 60% of the Black wing UAV.The lift of the new UAV during low-altitude water surface flight without an angle of attack has increased by 13.6% compared to the airborne cruising state, as listed in Table 12.As shown in Figure 27, this is the pressure distribution along the longitudinal crosssection of the aircraft during low-altitude flight near the water surface.It can effectively reflect the variations in the pressure difference above and below the aircraft in ground effect conditions compared to aerial flight.This is because during the low-altitude water surface flight process, the expansion of the high-pressure area at the lower part has increased the lift performance.Drag performances of the new UAV in air and ground effect are listed in Table 13.During low-altitude water surface flight, there is an abnormal increase in drag force compared to aircraft near the wall surface, primarily attributed to the rise in pressure drag.Thus, the characteristics of pressure drag should be discussed in the following section.During the flight of an aircraft, wingtip vortices are generated as shown in Figure 28.The airflow over the upper surface of a typical wing travels faster, resulting in lower pressure and generating lift in an upward direction.The pressure on the lower wing surface is higher than on the upper wing surface.Under the influence of the pressure difference between the upper and lower wing surfaces, the airflow from the lower wing surface flows around the wingtip towards the upper surface, forming wingtip vortices.The generation of wingtip vortices leads to a decrease in lift and an increase in drag on the aircraft.It is worth noting that as the airflow from the lower wing surface flows around the wingtip towards the upper surface, a trend of up wash in the airflow can be observed by capturing the lateral velocity at the wingtip.From Figure 29, it is evident that the up wash airflow at the wingtip is weakened.This should lead to a reduction in the drag, which is same as the ground effect of the wall surface.However, the results in Table 13 show that the weakening of wingtip vortices may not significantly improve the drag performance.On the other hand, by using the VOF method to track the change in water surface as shown in Figure 30, it can be found that the new UAV will generate the surface wave phenomenon at the tail during low-altitude water surface flight.Obviously, this is caused by the work carried out by the aircraft on the water surface, and the object will experience higher resistance due to the water waves generated by the high-speed UAV.In conclusion, when an aircraft navigates near the water surface, the new UAV has certain performance advantages compared to the Black wing UAV.Furthermore, during navigation near the water surface, the lift performance is improved compared to the aerial cruising state, and there is a certain weakening of the wingtip vortex.However, due to the existence of wave drag, the resistance of the aircraft will increase to some extent compared to in the air.

Conclusions
In order to reduce the difficulty of variable wing for the trans-media process and improve the lift-drag performance during the cruising process, this paper presents a new conceptual UAV with innovative dish-airfoil-shaped main body and telescopic NACAtype wing.Then, the numerical method to calculate the lift and drag forces are presented and validated.Furthermore, based on the functions of the Black wing AUV, a new dishairfoil-shaped UAV can be achieved and discussed by numerical methods.The lift-drag performances of the two UAVs in air and water are numerically calculated and compared.Finally, many useful conclusions can be made as follows.
(1) Compared to the Blackwing UAV, the new UAV has a reduced size in the vertical direction.The diameter of the Blackwing UAV is 7.5 cm, and the height of the UAV body is 4.35 cm.Considering the dimensions of the main equipment available on the market, the new UAV can meet the requirements and requires a specific design for the cabin layout.We have made preliminary designs for the layout of the cabin to ensure that the design meets basic functional requirements.With the progress of miniaturization of equipment, the new UAV can carry the same equipment as conventional cylindrical UAVs and perform tasks effectively.
(2) When the UAVs fly in the air, the streamlines in the flow field around the new UAV are smoother compared to the Blackwing UAV, resulting in improved aerodynamic performance and stability.Furthermore, the airflows on the top surface of the main body have obvious high velocity, which can cause the main body to produce effective lift for the new UAV.For the test cases with cruising speed of 160 km/h, the lift force of the new UAV at 0° attack angle can increase by about 26.5% compared with the Black wing UAV.The new UAV concept not only reduces the wing area by approximately half, significantly decreasing trans-media difficulty, but also effectively enhances lift performance in the cruising state at a small angle of attack.
(3) When the UAVs fly in the air, compared with the Black wing UAV, the new UAV avoids the disturbance problem of the front wings to the rear wings.Its pressure transition along the body surface is relatively gentle, and the pressure difference of the front and back surface is relatively smaller.For the test cases with cruising speed of 160 km/h, the total drag of the new UAV can significantly decrease to about 40% of the Black wing UAV under the attack angle 0°.Thus, the new dish-airfoil-shaped main body can effectively reduce the total drag of the UAV in air compared with the Black wing UAV.

Figure 4 .
Figure 4. New concept of unmanned aerial vehicle cruises in water after retracting its wings.(a) Wing retraction.(b) Sailing underwater.

( 1 )
Define the phase function: Choose an appropriate phase function to represent the volume fractions of different phases at different locations.The phase function for liquid is defined as 1 and for gas is defined as 0. (2) Initialize the phase function: Initialize the phase function in the computational grid, usually based on initial conditions and boundary conditions.(3) Update the phase function: Calculate the evolution of the phase function in each cell at different time steps by solving the fluid dynamics equations.(4) Identify fluids based on the phase function: Determine the fluid phase occupying each cell based on the calculated phase function values, thus simulating multiphase fluid behavior.

Figure 9 .
Figure 9.Comparison of lift and drag coefficients by numerical and experimental methods under Re = 1.0*10 6 .(a) Lift coefficient.(b) Drag coefficient.

Figure 12 .
Figure 12.The changes in the phase function at the interface.

Figure 13 .
Figure 13.The development of wingtip vortices in the new unmanned aerial vehicle.

Figure 15 .
Figure 15.Longitudinal section of the new UAV.

Figure 16 .
Figure 16.The internal layout diagram of the preliminary design of the aircraft.Equipment number (1) is a signal receiver device for receiving external signals.(2) is a camera for photography and reconnaissance purposes.(3) is a motor for controlling the camera's rotation.(4) is a laser radar.(5) is the fuselage bulkhead which houses the retractable wings externally using a motor.The wings retract and shorten when in operation, folding into the fuselage.(6) is the component for retracting the wings, rotating to drive the internal components for wing retraction; for specific retraction methods, please refer to relevant patents.(7) is a motor driving the wing retraction mechanism.(8) is a propeller providing thrust for the UAV.(9) is the motor driving the propeller.(10) is the speed controller regulating the motor.(11) is the control chip managing the devices.(12) is the battery supplying the required energy.

Figure 17 .
Figure 17.Models of the Black wing UAV and new UAV.(a) Black wing UAV.(b) New UAV. .

Figure 18 .Figure 19 .
Figure 18.Streamline diagrams of the Black wing UAV and new UAV.(a) Black wing UAV.(b) New UAV.

Figure 20 .
Figure 20.Pressure distribution on the body surface of the Black wing UAV and new UAV.(a) Black wing UAV.(b) New UAV.

Figure 21 .
Figure 21.Lift performance of the two UAVs under different attack angles.

Figure 22 .
Figure 22.Drag performance of the two UAVs under different attack angles. .

Figure 25 .
Figure 25.Pressure distribution of the two UAVs in water.(a) Blackwing UAV.(b) New UAV.

Table 8 .
Comparison of the lift forces for the two UAVs in the water.

Figure 26 .
Figure 26.Lift and drag performance of the two UAVs under different attack angles.(a) Lift force.(b) Drag force.

Figure 27 .
Figure 27.Pressure distribution of the new UAV in air cruise and ground effect.(a) Aerial cruising.(b) Navigating near the water surface.

Figure 28 .
Figure 28.Tip vortices of the new UAV.

Figure 29 .
Figure 29.Contour of lateral velocity near the wingtip of the new UAV.(a) Aerial cruising.(b) Navigating near the water surface.

Figure 30 .
Figure 30.Surface wave due to the ground-effect navigation of the new UAV.

Table 1 .
Comparison of characteristic versus water-air amphibious aircrafts.

Table 2 .
Lift coefficients of the airfoil versus different mesh scheme.

Table 3 .
Lift of the airfoil versus different mesh scheme.

Table 4 .
Main parameters of the Black wing UAV.
Length (cm)Width (cm) Diameter of Main Body (cm) Volume of Main Body (cm 3 ) Cruising Speed (km/h)

Table 5 .
Main parameters of the new UAV.

Table 6 .
Comparison of the lift forces for the two UAVs in the air.

Table 7 .
Comparison of the drag forces for the two UAVs in the air.

Table 9 .
Comparison of the drag forces for the two UAVs in the water.

Table 10 .
Comparison of the lift forces for the two UAVs in the ground effect.

Table 11 .
Comparison of the drag forces for the two UAVs in the ground effect.

Table 12 .
Lift forces on the new UAV in two conditions of air and ground effect.

Table 13 .
Drag performance of the new UAV in air and ground effect.