Impact analysis of air gap motion with respect to parameters of mooring system for floating platform

In this paper, the impact analysis of air gap concerning the parameters of mooring system for the semi-submersible platform is conducted. It is challenging to simulate the wave, current and wind loads of a platform based on a model test simultaneously. Furthermore, the dynamic equivalence between the truncated and full-depth mooring system is still a tuff work. However, the wind and current loads can be tested accurately in wind tunnel model. Furthermore, the wave can be simulated accurately in wave tank test. The full-scale mooring system and the all environment loads can be simulated accurately by using the numerical model based on the model tests simultaneously. In this paper, the air gap response of a floating platform is calculated based on the results of tunnel test and wave tank. Meanwhile, full-scale mooring system, the wind, wave and current load can be considered simultaneously. In addition, a numerical model of the platform is tuned and validated by ANSYS AQWA according to the model test results. With the support of the tuned numerical model, seventeen simulation cases about the presented platform are considered to study the wave, wind, and current loads simultaneously. Then, the impact analysis studies of air gap motion regarding the length, elasticity, and type of the mooring line are performed in the time domain under the beam wave, head wave, and oblique wave conditions.


Introduction
During the lifetime, the design of a floating platform is mainly based on the extreme response analysis due to the loads by the components. The external loads can induce the extreme air gap response and potential deck impact to the floating structure. It is important to predict air gap response of platforms accurately in order to check the strength of local structures. The strength should meet the class requirements considering the wave slamming load. According to Offshore Standard DNV-OS-C103 (DNV, 2012b), the air gap response analysis of a platform should be calibrated against relevant model test results if available. Besides, the analysis should also take the effects of interacting systems into account such as mooring systems and risers. In general, the positive air gap should be required for waves with a 10 -2 annual probability of exceedance under ultimate limited state condition. An unnecessary increase in air gap will considerably affect the stability of structure and project cost. However, local wave impact may be accepted if it is docu-mented that such loads are adequately accounted for in the structural design. It is believed that allowing wave impacts on some places is more sensible from overall consideration than avoiding any wave hitting the deck (Kazemi and Incecik, 2007). Therefore, it is extremely important to predict air gap response of a platform for checking the local structure strength, which could withstand wave slamming due to the negative air gap.
In recent years, air gap response of a floating platform has been investigated based on model test and theory methods. Huo et al. (2015Huo et al. ( , 2016 studied the sensitivity of wave slamming load on wind load for the floating platform through the model test and numerical simulation methods. Liang and Yang (2010) applied VOF method to capture the free surface and used DeepC software to predict air gap response of the moored floating platform. Simos et al. (2008) performed small-scale model tests of air gap response on a floating semi-submersible and found that standard first-order numerical analysis seriously underestimated run-up ef-fects in the region near the columns except for low wave steepness. Kazemi and Incecik (2005) presented a comparison between moored test results and those obtained based on a hybrid method. The second order effects of diffracted and radiated waves were neglected while nonlinear terms of the incident wave were included. Sweetman and Winterstein (2001) used commercial program WAMIT in which second order nonlinearities were included to predict air gap response of a floating platform. The model can calculate the correct location of the highest wave elevation and has obviously improved the results compared with linear potential theory. Matsumto (2010) and Lwanowski (2009) applied the commercial CFD code ComFLOW based on fully nonlinear methods to investigate air gap distributions around a large volume semi-submersible platform. This code used finite volume method to solve N-S equations, with the support of the VOF model to capture the free surface simultaneously. They found that the whole nonlinear method could obtain more accurate results compared with the WAMIT second order extension.
The main purpose of this paper is to reveal the sensitivity of air gap with respect to the mooring system for the floating platform. According to the model test, the numerical model is tuned and validated by the modification of the radiation damping and viscous drag. Meanwhile, the wind load and current load are simulated based on the results of wind tunnel model test. According to the tuned numerical model, the impact analysis has been conducted for air gap concerning the length, elasticity and type of mooring line in 17 cases. The results have demonstrated that the parameters of mooring system are sensitive for the minimum negative air gap. With the expanding of the working water depth, there are differences regarding the components and length of platform mooring lines under different working water depth conditions, which will aggravate the stiffness difference of the mooring system. Therefore, the effect of the mooring system on air gap cannot be ignored either.

Floating platform properties
The presented platform was a deep water semi-submersible DP drilling rig and suitable for operations worldwide.
The geometry properties and hydrostatical data are listed in Table 1 and Table 2, respectively.

Model test
The model tests were carried out in FORCE's 240 m× 12 m×5.4 m (length×width×depth) towing tank equipped with a double flap hydraulically driven wave generator at one end and an absorbing beach at the other. The model scale was 1:38.9. The model was held by a simple 4-line symmetrical horizontal soft mooring system, as shown in Fig. 1. Mooring lines were attached in 0.77 m above the baseline. At the same time, each mooring line was composed of 2 mm Dynema line with springs inserted near the tank wall. The system was designed so that the natural period of the mooring and model will not be interfered with the periods of the wave spectrum.
The stiffness of the mooring system was examined by a restoring force test in the x and y directions of the tank. The results are presented in Fig. 2.
The wind tunnel test was conducted in FORCE Technology Company, and the model scale was 1:38.9. The wind was simulated by NPD spectrum based on the wind tunnel test results. The height of the wind speed reference was 10 m above the sea surface.    Fig. 4. To simulate the influence of viscous drag of the pontoons, braces, and columns, a number of tubular and disc elements are included in the numerical model. These elements are subjected to Morison loading.
The pontoons and braces were discredited into many longitudinal sections based on their section sizes. And the columns were discredited into some vertical sections, simultaneously. Fig. 5 shows the tubular and disk elements.

Mooring system
Three types of mooring lines are applied in the numeric-al simulation based on the practical engineering projects and this model platform test. The chain mooring system is used in 300 m water depth, commonly. The chain tanker, the winch and the fairlead for the chain are not arranged on this platform, while the wire system is involved. Therefore, the types of the chain mooring system and the wire mooring system have been analyzed. As for the model test of this practical engineering system, the simple spring mooring system is used. Thus, the spring mooring lines are used for the simulation of the model test system. The mooring lines of the model test are attached to the corner column points based on the model test, and the mooring arrangement is illustrated in Fig. 6. The mooring simulating springs have been given stiffness equal to the model test.
The mooring arrangement of chain mooring system is a symmetrical 8-point mooring system. The fairlead positions and line ranges are shown in Table 3. Each mooring line consisted of a 1600 m chain. The properties are listed in Ta-    SHEN Zhong-xiang et al. China Ocean Eng., 2017, Vol. 31, No. 2, P. 141-150 ble 4. The pretension is 820 kN and Fig. 7 illustrates the mooring arrangement.
The mooring arrangement of the wire mooring system was similar to the chain mooring system. Each mooring line consisted of a 2600 m wire, and the properties are listed in Table 3. The fairlead positions and the bearing were the same as the chain mooring system, and the pretension was also 820 kN in the mooring system.

Thruster system
The survival condition made use of a mooring system based on the automated thruster assist (ATA). The thrusters were represented as a constant force in the numerical simulation. Based on the mooring system analysis results of the practical engineering system for this platform, evaluation of the mean components of the environmental forces was conducted that the maximum deliverable thrust was needed.

Interest points of air gap response
According to the symmetry of the semi-submersible and the results of the engineering project, the interest points of air gap response are selected on the starboard side in this paper. Air gap registration points are presented in Fig. 8. The points of interest for the paper have been umbers.

Tuning the numerical simulation results
The analysis model is tuned to match the response from the model test in survival sea state. Besides, simulations have also been carried out in the wave system as used during the model tests. These simulations are used to validate the periods of motion in irregular waves, tune viscous drag and radiation damping.
Viscous drag is not directly included in potential theory, and radiation damping is a pure dampening effect, while viscous drag will both contribute to excitation and damping of the structure motion. The effects of viscous drag and radiation damping must be included properly in the simulations. Therefore, one can not replace the other.

Natural periods of the model test and numerical simulation
The natural periods of the platform in test and simulation under still water condition are presented in Table 5. It can be seen that only small differences could be observed between the numerical model and test model. Nonlinear evaluation of the hydrodynamics in severe motion amplitudes shows a large influence on the natural period of pitch. Under large wave condition, the pontoon bow parts, and the braces occasionally emerge, which can increase the pitch restoring force and reduce the natural pitch period. The pitch response peak period is obviously lower than the still water natural period.

Viscous drag
The Morison elements have drag coefficients accounting to the local geometry properties and appropriate KC numbers (DNV, 2010). Disc elements are used to achieve different drags in the horizontal and vertical directions for braces. The values are tuned towards the model tests.

Radiation damping
Though AQWA NAUT can calculate the hydrostatic and Froude-Krylov forces at each time-step based on the actually submerged geometry, the calculation of the radiation terms is based on the initial frequency domain. The calculated wave radiation is based on the initial position of the platform with the pontoons deeply submerged. The pontoons and braces are partly emerging through the free surface both in the model test and the time domain simulations in the survival sea state. Wave radiation strongly depends on submergence of the pontoons as well as emergence/immergence through the free surface. Wave radiation energy is obviously underpredicted in the diffraction-radiation database based on SWL. According to the comparison, a value of 3×10 9 Nm/(rad/s) of the added pitch damping is used.

Wave system
The wave system used to validate the numerical model is derived from the wave calibration test. The wave surface elevation is used to make a wave spectrum to develop the wave system in the time domain simulation.
The time history of surface elevation from the undisturbed calibration in the model test is read into AQWA which then produces a wave spectrum based on it. A comparison between the two power densities of the wave height is shown in Fig. 10.
The wave realization of an irregular sea state in AQWA NAUT consists of second order asymmetric waves. Wave asymmetry (crest height divided by wave height) of the 100 largest waves in the survival sea state for the model test and AQWA simulation is shown in Fig. 11. The average wave asymmetry value for these 100 waves is 0.556 for the model test and 0.548 for AQWA. Therefore, it is concluded that wave asymmetry is well presented in the analysis. And one difference is that the wave asymmetry has a bigger scatter in the model test, which includes some breaking waves.

Mooring force and motion response comparisons
The comparison of the mooring force between the model test and the simulation is illustrated in Fig. 12. It can be seen that the mooring force is well presented in numerical simulation for the model test.
To investigate the periods of the platform motion in heave and pitch, responses in the frequency and time domain are presented in Fig. 13 and Fig. 14, and a value of 3×10 9 Nm/ (rad/s) of the added pitch damping is used for the simulation.
The model test of the heave motion has more peak response around the peak wave period, while the simulation has more response around the heave natural period. The  . 9. Comparison of the pitch with different dampings (Case 1: 2×10 9 , Case 2: 3×10 9 , Case 3: 4×10 9 ).    pitch response in the simulations has slightly more energy around both spectral peaks than that in the model test. In terms of periods and energy content, the agreements for heave and pitch motion are proved to be good.

Impact analysis
The viscous drag coefficients and radiation damping are tuned for the numerical simulation model based on the model test results. The impact analysis studies of the air gap with respect to the mooring system parameters have been carried out based on the tuned numerical model.
Seventeen cases are simulated with the same wave, wind, and current speeds. The detail information of analysis cases has been presented in Table 6. Owing to the instability in a time domain, each case has been carried out with ten sub-case wave conditions within 3-hour duration in order to obtain accurate results. Meanwhile, wave speeds are the same for each case.

Wind and current loads
ISO wind spectrum is used in the time domain. The height of the wind speed reference is 10 m above the sea surface. Both the wind and current drag are calculated in a similar manner from a set of user-derived environmental load coefficients, covering a range of heading angles. The force is calculated at each time step as: where, F j is the force vector for the degree of freedom j (1, 2, 3, 4, 5 and 6); C j (θ) is the value of the wind and current coefficient under θ direction load condition; u is the wind velocity; and u s is the platform absolute velocity. The wind or current velocity in the above expression u-u s is calculated to be the relative velocity between the absolute wind or current velocity and the velocity of the platform. C j (θ) is used according to the results of the wind tunnel.
The wind and current load coefficients for these simulations are obtained from the wind tunnel model tests (Huo, 2015).

Sea states
The JONSWAP spectrum is used in the simulation of the stochastic wave. The Conditional Modeling Approach (Bitner-Gregersen, 2005) and the inverse reliability method (Winterstein, 1993) are applied to calculating the 100-yearreturn period environmental contour of the North Atlantic. Meanwhile, a steepness criterion is calculated based on the DNV-RP-C103 (2012a). In this paper, the sea state (H s = 17.3 m, T z =16.5 s) is chosen for the analysis based on the limited steepness and environmental contour of the North Atlantic.

Impact analysis results
The maximum for every key result is assumed to be well approximated by a Gumbel distribution and the results from each sea state are defined for a 90% confidence level at the same time. The simulation results are illustrated in Tables 7 and 8. The detailed results of Case 01 are shown in Table 9.

Impact analysis with respect to the length of the mooring line
According to the results of Case 01 through Case 12, it can be seen that the effect of the length of the mooring line for the air gap is obvious under beam wave, head wave, and oblique wave conditions. The minimum air gap of 90% Gumbel distribution and the mean value of the minimum air gap are of both the aggravating trend with the increase of the mooring line length. Under the head wave condition, the mean value of the minimum air gap in the 10 sub-cases of P_05, P_14 and P_37 is aggravated from -0.278 m, -0.197 m and -0.115 m to -0.820 m, -0.664 m and -0.539 m, respectively. Moreover, the minimum air gap of 90% Gumbel distribution in the 10 sum-cases of P_05, P_14 and P_37 is aggravated from -2.466 m, -2.384 m and -2.301 m to -3.231 m, -3.079 m and -2.748 m, respectively. As for the sub-cases Case 01_01 to Case 12_01, the power spectral densities of air gap for the critical interest point, roll, heave and pitch motions of COG location under the beam wave, head wave, and oblique wave conditions are presented from Fig. 15 to Fig. 20. The air gap motion of P_05 for the sub-cases Case 01_01, Case 02_01, Case 03_01 and Case 04_01 is presented from Fig. 25 to Fig. 28 in Appendix A. The mooring length is only the difference in the four sub-cases. It can be found that the minimum air gaps are -0.2165 m, -0.3394 m, -0.5134 m and -0.5972 m, respectively. Thus, the difference is obvious and it shows the effect of the length of the mooring line on the air gap motion, which is close to the natural periods of heave, pitch and roll.

Impact analysis with respect to the elasticity of the mooring line
The results of the impact analysis with respect to the elasticity of mooring line are presented in Table 10 and Table 11. It can be seen that the effect of elasticity of the mooring line on air gap is obvious under head wave condition. The minimum air gap of 90% Gumbel distribution and the mean value of the minimum air gap are both improving trend with the increase of the mooring line elasticity. The mean value of the minimum air gap in the 10 sum-cases of P_05, P_14 and P_37 is aggravated from -0.411 m, -0.289 m and -0.180 m to -0.016 m, 0.053 m and 0.113 m, respectively. Moreover, the minimum air gap of 90% Gumbel distribution in the 10 sum-cases of P_05, P_14 and P_37 is ag-  As for the sub-cases Case 02_01, Case 13_01 and Case 14_01, the power spectral densities of air gap for the critical interest point the heave and pitch motions of COG location under head wave condition are presented in Fig. 21 and Fig. 22. It can be found that the effect of mooring system on air gap motion is close to the natural period of heave, and the effect is slightly near the natural period of pitch and the effect of elasticity of the mooring line on the pitch motion is obvious.

Impact analysis with respect to the mooring line type
According to the results of Case 15, Case 16 and Case 17, it can be seen that the effect of mooring line type on air gap is obvious. The minimum air gap of 90% Gumbel distribution about point P_01 is -2.703 m, -3.829 m and -3.209 m, respectively. The chain mooring system is the best in the     air gap motion analysis. The difference of the minimum negative air gap is 1.126 m between Case 15 and Case 17. Meantime, there are large differences of the mean elevation of interest points in different cases.
The power spectral densities of air gap for point P_01, heave and pitch motions are presented in Fig. 23 and Fig. 24 for Case 15_1, Case 16_1 and Case 17_1. It shows that the effect of mooring system on air gap motion is close to the natural period of heave, and the effect is slightly near the natural period of pitch. The effect of different mooring system on the platform heave and pitch motions is obvious near the natural periods of heave and pitch, respectively.

Conclusions
The wind tunnel model test and the sea-keeping model test of a drilling platform are performed in wave tank. And the effect of scale mooring system has been ignored. According to the model test results, a numerical analysis model is established by the modification of the radiation damping and viscous drag: the simulation is done in ANSYS AQWA software. Based on the tuned numerical model, the impact analysis investigates the air gap motion with respect to the parameters of the mooring system which are carried out by the numerical simulation method. The numerical simulation of air gap response considers the wind, wave, and current load simultaneously. Meanwhile, the full-scale mooring system and thruster force are considered. The following conclusions are drawn.
The mooring system affects air gap of the floating platform, especially for the stiffness of the mooring system. The effect of the mooring system is significant when its period close to the natural period of heave, roll, and pitch under the beam wave, head wave and oblique wave conditions. The length, elasticity and the type of the mooring line affect obviously the roll, pitch and heave motions of the platform. Because of the expanding of the working water depth, there are differences in terms of the components and length of platform mooring lines under different working water depth conditions, which will aggravate the stiffness difference of the mooring system. Therefore, when the air gap response of the platform is being calculated, the effect of the mooring system parameters for air gap motion cannot be ignored.