**1. Introduction**

Abundant mineral resources, power sources, and biological resources are conserved in the ocean, which is meaningful for economic development [1]. Because of the dark and hypoxic environment underwater, the need for an unmanned machine to replace people to complete underwater inventions is imperative. Autonomous underwater vehicles (AUVs) have a wide range of applications in oceanic geoscience, and they were created to accomplish resource exploration tasks on the seabed, including energy exchange, pipeline inspection, and roaming the deep-sea seabed [2]. AUVs have revolutionized our ability to detect and image the seabed with the real-time ability to exchange high-resolution, oceanographic, photomosaic information at abyssal depths [3–5]. However, conventional axisymmetric, torpedo-shaped AUVs have poor maneuverability when swaying and yawing because the added mass and added moment of inertia of the slender body dominates, which causes unstable AUV motions due to the occurrence of the Munk e ffect. In addition, motion instability in heave situations results from ine fficient surface control in low-velocity conditions. Thus, the conventional horizontal, axisymmetric AUVs cannot e ffectively and e fficiently accomplish unplanned super-mobile hovering tasks, for example, random landing and launching on the seabed, random hovering at some specified oceanic depth, providing services for a submarine mobile observation network, exploring submarine resources, connecting submarine operating point data in a specified smaller seabed area, and so on.

An autonomous underwater hovering vehicle (AUH), with a vertical, symmetric structural design, is a novel, dish-shaped, multi-functional, ultra-mobile submersible in the AUV family. AUHs are subject to high demands, for example, high-level and autonomous functionality, enhanced maneuverability in horizontal and vertical planes, adaptive landing and launching on the seabed, and the need to easily hover in the deep sea. The disk-shaped AUH was proposed at the Ocean College of Zhejiang University in 2016 to greatly enhance the motion stability during heaving, enable the AUH to hover in the deep sea, and improve the maneuverability of conventional, slender AUVs in yawing and swaying, including an enhanced anti-flow ability in the deep sea [6,7].

The structural design of the AUH is shown in Figure 1. This AUH could transmit data between base stations on the deep-sea bottom to communicate with scientific research ships near the free surface. The conceptual design of the AUH includes a symmetric, disk-shaped hull form, a pressure hull of 15 MPa, an energy power system, a control system, a navigation system, a communication system, and mission payload technology, e.g., recovering, landing, and launching models. The mission payload technology design in this study, i.e., airborne-launched technology, can enhance the e ffectiveness and efficiency of AUH missions. Thus, the study of the water entry impact forces on the disk-type AUH hull, with di fferent water entry velocities and attitudes from a certain height, shall be carried out in this paper.

**Figure 1.** Conceptual design of the disk-type autonomous underwater hovering vehicle (AUH).

Research on launch and recovery systems for AUVs is significant to aid in the overall design process and guarantees successful, smooth deployment and operation of the AUH from the free surface to the deep sea [8]. The AUH hull was mounted with precise sensors, which were often damaged and lost from excessive water impact forces when the AUH was deployed and launched.

Traditionally, two main methods of AUV deployment are often adopted, i.e., a shore-based deployment or deployment by a scientific research ship [9]. Shore-based deployment technology is relatively mature; however, this needs excellent hardware support and good sea weather. Deployment by a scientific research ship is more di fficult and brings about grea<sup>t</sup> uncertainty under atrocious sea conditions and other restrictions. Deployments by a scientific research ship include several forms: Deployment of a scientific research ship, an underwater vehicle (UV), and/or an unmanned surface

vehicle (USV). An automated launch and recovery system for AUVs from an unmanned surface vehicle was proposed by Edoardo and Manhar [10].

Scientific research ships can be mounted with several launch and recovery devices, including conventional crane forms, A-shaped cranes, dedicated single-arm cranes, sliding cranes, and integrated cranes. Conventional forms are advantageous because of their simple structures and low costs; however, the operation is complex, and they are not as safe. A-shaped cranes have been widely adopted because of their simple operation. Dedicated single-arm crane systems are very safe, as shown in Figure 2. They greatly simplify operation processes and save costs [11]; however, time-consuming deployment and its ine fficiency to quickly launch multiple AUVs to target sea areas are its weaknesses. Sliding-type crane systems are mainly used to continuously lay equipment or di fferent types of remotely operated vehicle (ROV) cables. An integrated layout and recovery system operates, more or less, independently from the scientific research ship and has a high safety factor. Deployment of AUVs is better from a submarine than from a scientific research ship; however, recovering the AUVs is di fficult. USV- and UV-based deployments need further improvement in order to be practical and reliable [10].

**Figure 2.** Conventional launching and recovery system of a single-arm crane.

In particular, airborne launch methods that use planes or helicopters to quickly launch AUVs into target sea areas have received more attention by scientists and strategists recently [11–21]. Scholars have conducted a lot of research to investigate water entry impact forces, trajectory deflection, and damage to an airborne-launched AUV, especially when the maximum impact loads occur in the initial entry stages [11].

Xia et al. [15] studied the water entry impact forces of an inclined, axisymmetric, slender body with a horizontal velocity and multiple degrees of motion freedom on the free surface. The e ffects of horizontal velocity, angle of attack, and inclined angle on the motion characteristics of the axisymmetric slender body were studied. A circuitous phenomenon was found when the angle of attack was greater than 22◦.

Wang et al. [17] established an oblique water entry impact model, coupled with dynamic ballistic models, which was based on the theory of potential flow and the precise shape of the coupling surface between the fluid and the solid.

Qiu et al. [18] carried out simulations of the water entry impact forces on axisymmetric bodies, which was based on water entry dynamics and ballistic theories, to obtain the maximum impact load. The initial water entry conditions and the relationship between water entry impact loads were simulated. The simulation tests implemented relevant water entry processes for the revolution bodies (e.g., flat head, cone head, and round head), using commercial computational fluid dynamics (CFD) software FLUENT technologies, including dynamic mesh, user-defined functions (UDFs), and a mixture (MIXTURE) process model. The e ffects of velocity and head shape on the impact load and shape of cavitation were studied.

Qi et al. [19] presented the impact load of an AUV model under various water entry conditions as well as the varied rules of axial and radial forces during water infiltration through experiments and viscous CFD simulation methods. Reference data on the structural design and projection conditions of the AUV were provided.

Shi et al. [20] designed an inlet cap for an AUV and analyzed the influence of the bu ffer cap's structural design, material density, bu ffer distance, water flow velocity, and bu ffer e ffect of initial bu ffer on the water entry angles.

Ma et al. [21] implemented experimental investigations and analyzed the vertical water entry of a sphere. During water entry, the velocities, accelerations, and drag coe fficients of the spheres were studied. The investigated results showed that the motion trajectory of the spheres presented highly nonlinear characteristics and notable fluctuations of the motion parameters, which were proportional to the entry speed.

In this paper, research on simulated water entry impact forces of an airborne-launched disk-type AUH based on the CFD method was implemented. The creative AUH hull form was di fferent from the above water entry geometric shapes in literature. The STAR-CCM+ CFD Reynolds-averaged Navier–Stokes (RANS) solver was adopted to simulate air-launched AUH dynamic motions with di fferent water entry speeds and immersion angles using the STAR-CCM+ volume of fluid (VOF) method, overlapping grid technology, and user-defined functions (UDFs). The simulation analysis was carried out under di fferent water entry speeds and angles of the launched AUH in calm sea conditions. The variations of load and velocity of the disk-type AUH versus di fferent states were obtained, i.e., in di fferent initial free-fall velocities and water entry immersion angles. This study can provide an important reference for the disk-type, vertical, axisymmetric body of the AUHs to improve the structural design and adapt to the launching conditions, and it can enhance the e ffectiveness and efficiency of AUV deployments in order to smoothly carry out more complex tasks on the seabed.

#### **2. Configuration of the AUH**

In this paper, research on simulated water entry impact forces of the hung, air-launched AUH was carried out. The main parameters of the AUH are shown in Table 1, and the disk-shaped AUH prototype in the test pool is shown in Figure 3. Both Earth-fixed and body-fixed coordinates were established to describe the water impact loads and motion of the AUH, as shown in Figure 4. In the body-fixed coordinates, the hydrodynamic forces (surge, sway, and heave) and moments (roll, pitch, and yaw) exerted on the AUH in six-degrees of freedom can be designated as X, Y, Z, K, M, and N, respectively. The impact forces on the AUH were estimated in the body-fixed coordinate in this study, including the surge force (expressed in terms of X-force) and heave force (expressed as Z-force).


**Table 1.** Main parameters of the disk-shaped AUH.

**Figure 3.** ZJU (Zhejiang University) AUH physical prototype.

**Figure 4.** Earth-fixed and body-fixed coordinates.

#### **3. Numerical Simulation of the Impact on Water Entry**

This section describes the basic principles of solving the Navier–Stokes (N-S) equation by using the *k* − ε model. It also introduces the setting to calculate the AUH water domain and boundary conditions (BC).

#### *3.1. N-S Governing Equations and Turbulence Models*

Reynolds-averaged Navier–Stokes (RANS) equations were solved by a numerical method using the software STAR-CCM+ as follows [22]:

$$\frac{\partial(\overline{u\_i})}{\partial \mathbf{x}\_i} = \mathbf{0},\tag{1}$$

$$\frac{\partial(\rho \overline{u\_i})}{\partial t} + \rho \overline{u\_j} \frac{\partial \overline{u\_i}}{\partial \mathbf{x\_j}} = \rho \overline{F\_i} - \frac{\partial \overline{P}}{\partial \mathbf{x\_i}} + \frac{\partial}{\partial \mathbf{x\_j}} \left( \mu \frac{\partial \overline{u\_i}}{\partial \mathbf{x\_j}} - \rho \overline{u\_i' u\_j'} \right) \tag{2}$$

where *ui* denotes the component of the average speed, *ui* denotes the turbulent fluctuation velocity component relative to the hourly average flow velocity, *Fi* denotes the component of the mass force, *P* denotes the pressure, μ is the fluid dynamic viscosity coefficient, and <sup>ρ</sup>*<sup>u</sup>iuj* denotes the Reynolds average stress.

The RANS equations are the current focus of computational fluid dynamics research. This method introduces fewer assumptions and is a method to calculate the viscous flow field with higher accuracy. Since RANS equations are not closed by themselves, a supplementary equation needs to be introduced to close it. Three of the most popular two-equation turbulence models, i.e., *k* − ε model, *k* − ω model, and *k* − τ model, have been introduced in the literature [23]. In this paper, the *k* − ε turbulence model and the STAR-CCM+ CFD solver were integrated with the volume of fluid (VOF) method, overlapping grid technology, and user-defined functions (UDFs) to simulate different situations of the disk-type AUH immersing into water, including varying the water entry velocities and angles of the AUH.

The two-equation turbulence model *k* − ε, i.e., turbulent kinetic energy *k* and turbulent dissipation rate ε, is expressed as follows [24]:

$$k = \frac{\overline{u\_i' u\_j'}}{2} = \frac{1}{2} (\overline{u^{r^2}} + \overline{v^{r^2}} + \overline{w^{r^2}}) \tag{3}$$

$$
\varepsilon = \frac{u}{\rho} \overline{\left(\frac{\partial u'\_j}{\partial \mathbf{x}\_k}\right)} \bigg(\frac{\partial u'\_i}{\partial \mathbf{x}\_k}\bigg). \tag{4}
$$

In the two-equation turbulence model *k*−ε, the corresponding transport equation can be expressed as follows:

$$\begin{cases} \frac{\partial(\rho k)}{\partial t} + \frac{\partial(\rho k u)}{\partial x\_i} = \frac{\partial}{\partial x\_j} \Big[ (\mu + \frac{\mu\_l}{\sigma\_k}) \frac{\partial \mathbf{k}}{\partial x\_j} \Big] + G\_k + G\_b - \rho \varepsilon - Y\_M + S\_k\\ \frac{\partial(\rho \varepsilon)}{\partial t} + \frac{\partial(\rho \varepsilon u\_i)}{\partial x\_i} = \frac{\partial}{\partial x\_j} \Big[ (\mu + \frac{\mu\_l}{\sigma\_\ell}) \frac{\partial \varepsilon}{\partial x\_j} \Big] + G\_{1\varepsilon} \frac{\varepsilon}{k} (G\_k + G\_{3\varepsilon} G\_b) - G\_{2\varepsilon} \rho \frac{\kappa^2}{k} + S\_\ell \end{cases} \tag{5}$$

where *Gk* denotes generation of turbulent kinetic energy; *k* is caused by the average speed gradient; *Gb* denotes generation of turbulent kinetic energy caused by buoyancy; *YM* is the contribution of pulsatile expansion in compressible turbulence; *G*1<sup>ε</sup>, *G*2ε, and *G*3ε denote the empirical constants; σ*k* and σε denote the Prandtl numbers corresponding to the turbulent kinetic energy *k* and dissipation rate ε*,* respectively; and *Sk* and *S*ε denote the user-defined source items.

The VOF method was adopted to tackle the problem of free surfaces. Both the liquid phase (water) and the gas phase (air) above the free surfaces are treated clearly by putting forward a (liquid) volume fraction α1 and gas volume fraction α2. The combined volume fraction of both phases should satisfy the conservation property. A conservation equation was solved to transport the volume fraction of one of the phases in this study. The density, ρ, and viscosity, μ, at any point are acquired by averaging volume phases as follows [25]:

$$\begin{cases} \rho = a\rho\_{water} + (1-\alpha)\rho\_{air} \\ \mu = a\mu\_{water} + (1-\alpha)\mu\_{air} \end{cases} \tag{6}$$

A single momentum equation was solved for the whole domain, resulting in a shared velocity field for both phases. The VOF defines a step function, α, equal to unity at any point occupied by water, and zero elsewhere, such that for volume fraction α, three conditions are considered as follows:

$$a = \begin{pmatrix} 1 & \text{if} & \text{cell} & \text{is} & \text{full} & \text{of} & \text{water} \\ 0 & \text{if} & \text{cell} & \text{is} & \text{full} & \text{of} & \text{air} & \text{...} \\ 0 < a < 1 & \text{if} & \text{cell} & \text{contains} & \text{both} & \text{water} & \text{and} & \text{air} \end{pmatrix} \tag{7}$$

The VOF method adopted to treat two-phase flows has been given in detail in Hirt and Nichols (1981) [26]. Tracking the interface between air and water is completed by solving a volume fraction continuity equation as follows:

$$\frac{\partial \alpha}{\partial t} + \mathcal{U}\_j \frac{\partial \alpha}{\partial \mathbf{x}\_j} = 0. \tag{8}$$
