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The dynamic response of the deployment system while deploying a circular cylinder crossing wave surface and the following submerging process are investigated numerically. The present numerical approach is based on the combination of solution methods of cable dynamics and computational fluid dynamics (CFD). For the implementation of the numerical approach, a cosimulation platform based on a CFD code and MATLAB is developed to study the fluid-solid interaction problem in the process. To generate regular waves, a numerical wave tank is built based on a piston-type wave generation method and a wave damping method applying porous media. Numerical simulations are performed based on the cosimulation platform. The sensitivities of cable tension, velocity, and acceleration of deployed body to different input parameters are investigated, including phase angles, wave heights, and periods of regular waves and deploying velocities, and the effects of those input parameters on dynamic responses of the deployment system are also discussed.

In recent years, subsea working systems are widely used in such applications as marine resource development and utilization, maritime exploration, and survey [

This paper mainly pays attention to the dynamic response of a deployment system while deploying a horizontal circular cylinder through wave zone for different deploying velocities and ocean conditions. In the wave impact and water entry process, offshore structures firstly impact on the wave surface, and then are gradually lifted from a dry state (in air) to partially immersed state and, eventually, to a wet state (fully immersed in water), which can be seen in Figure

A circular cylinder lowering through the wave zone: (a) dry state; (b) partially immersed state; (c) fully immersed state.

Hydrodynamic impact problems when solid bodies enter water have been investigated for nearly a century.

Pioneering researches performed by Karman [

In recent years, remarkable progress in computer hardware and software technology and computational fluid dynamics (CFD) has greatly promoted researches in this field. For example, Buckner et al. [

As mentioned above, the prediction of snap load which would result in highly nonlinear tension in deploying cables is very important; in this research field, Niedzwecki and Thampi [

Many researchers utilized commercial software for ocean engineering to implement dynamic analysis of the deployment system, such as Orcaflex, SIMO, and SIMA. Selvåg [

This work is devoted to studying the dynamics of a cable-rigid body system during a circular cylinder lifting through wave zone with different deploying velocities and regular waves with different phase angles and wave heights and periods. Because vertical motion is much more important than motions of other directions for the deploying operation, the cable-rigid body system can be simplified as a 1-degree-of-freedom (1-DOF) mass spring system. For implementation, a cosimulation platform based on CFD codes Fluent and MATLAB is established [

The CFD numerical approaches will be firstly outlined, including governing equations, boundary conditions, wave generation, and absorption methods. Then, a number of numerical tests involving different deploying velocities and different waves are presented, and simulation results are discussed. Finally, conclusions are drawn in Section

For the motion of homogeneous and incompressible fluid, the continuity equation and Navier-Stokes equations are governing equations. Applying the Reynolds decomposition in N-S equations and averaging, the Reynolds-Averaged Navier-Stokes (RANS) equations can be derived:

To fulfill turbulence closures for RANS equations, the standard

Referring to Launder et al.’s work [

To track the wave surface, the Volume of Fluid (VOF) method is employed. If the volume fraction of water and air in each cell is

For (

For the solution of governing equations, appropriate boundary conditions at all boundaries of the domain should be defined. The boundary conditions which need to be satisfied are as follows:

In this work, the wave generation is performed by a piston-type wave-maker. The schematic of a numerical wave tank with a piston wave-maker at the left wall boundary is given in Figure

Numerical wave tank and a moving body.

A paddle moves sinusoidally with the function:

It is necessary to absorb the attenuating incident wave so as to avoid the wave surface of the working zone being disturbed. In this work, at the right part of the flow domain, porous media are used to form an artificial damping zone so that reflected waves are gradually vanished along the direction of wave propagation. Porous media are modeled by the addition of a momentum source term to the standard fluid flow equations, which can be given by

Although the motion of a deployed body has six degrees of freedom of a rigid body, the predominant motion is vertical direction. Compared with accurate but time-consuming multibody dynamics approaches, the 1-DOF dynamic system is more suitable for the present research. Therefore, it is fairly reasonable to assume that the cable-rigid body (circular cylinder) system can be simplified as a 1-DOF system, as shown in Figure

The cable-rigid body system.

Hu et al. [

For the 1-DOF cable-rigid body system, if the deployed body has a vertical motion

Equation (

Hydrodynamic forces

In the 1-DOF cable-rigid body system, the cable can be modeled as a linear spring; if the position of line end of the cable can be obtained, the elongation and thereby the tension on the cable can be determined. For more details, one can refer to the paper by Hu et al. [

The dynamic response of deployment system during a rigid body crossing wave zone is a complex fluid-structure interaction problem, which involves fluid dynamics, mechanical dynamics, and the coupling between them, and thus single solution methods have incapacity to deal with this problem. Therefore, a cosimulation platform is developed based on the CFD software Fluent and MATLAB, and this can also be referred to Hu et al. [

To verify the effectiveness and accuracy of numerical wave generation and dissipation approaches presented in Section

A schematic of numerical wave tank.

Wave surface elevations are probed at four locations (

Wave elevation at four different locations: (a)

A circular cylinder with neutral buoyancy is selected as the rigid body which is to be deployed by the deployment system, parameters of which are as follows: length

To investigate the sensitivity of cable tension and motion parameters of the circular cylinder to regular waves and deploying velocities, different parameters are considered in simulations:

Phase angle =

Wave height

Wave period

Deploying velocity

A simulation example is used to reveal the whole process of water entry of the circular cylinder with considering the influence of waves. Main setups of this example are as follows: the radius of the circular cylinder

Water entry process of a circular cylinder: (a)

Wave impact phase angles can reflect the relative position between the rigid body and wave surface when impact occurs. Figure

Wave impact positions.

From Figures

It can be seen that oscillating periods of cases are nearly approximate but bigger than the natural period, which is mainly due to the complex body-wave interaction.

From curves of tension, it is worth noting that some points or parts of curves are equal to zero; that is to say, cables of these cases are in a slack state, and the occurrence of this phenomenon is because the deploying cable is highly resistible to tension while could hardly bear compression. When the slack state appears, the cable exerts no influence on the motion of the deployed body, and this is a dangerous condition because control methods which play a role by means of the cable cannot make a difference in hostile ocean conditions. It can also be observed that an alternating slack-taut condition of the deploying cable emerges in some cases, including

Figures

Influence of wave impact phase angles (

Influence of wave impact phase angles (

Influence of wave impact phase angles (

According to previous researches, the slamming force

From the case of

Cases with four wave heights of regular waves—1 m, 2 m, 2.5 m, and 4 m—are considered, while periods of regular waves and deploying velocity are determined as 6 s and 1 m/s, respectively.

Figure

Influence of wave heights: (a) tension acting on the cylinder; (b) velocity of the cylinder; (c) acceleration of the cylinder.

Cases with four periods of regular waves—2 s, 4 s, 6 s, and 8 s—are considered, while wave heights of regular waves and deploying velocity are determined as 2.5 m and 1 m/s, respectively.

Figure

Influence of wave periods: (a) tension acting on the cylinder; (b) velocity of the cylinder; (c) acceleration of the cylinder.

In this paper, the dynamic response of a deployment system during a circular cylinder lowering through wave zone is investigated numerically. A 1-DOF approach is applied to represent the dynamic cable-rigid body (circular cylinder) system. Numerical simulations are performed on a cosimulation platform based on CFD code and MATLAB, which can generate regular waves and deal with fluid-solid coupling problems.

The following conclusions can be given, based on analysis of simulation results:

A piston-type wave generation and porous media wave absorption methods are applied to generate regular waves and verified by the comparison with the target wave.

Cases with wave phase angle

Except for some extreme situations, curves of velocity, acceleration, and tension of the circular cylinder oscillate periodically. With wave height increasing and wave period decreasing, the amplitude of variation of curves becomes bigger, and the alternating slack-taut condition occurs when wave height is large enough or wave period is close to the natural period of the dynamic system.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

The authors gratefully acknowledge the support of National Natural Science Foundation of China (Grant no. 51305463), Natural Science Foundation of Hunan Province of China (Grant no. 2017JJ3393), and National Key Research and Development Plan of China (Grant no. 2016YFC0304103).