Study on Characteristics and Mechanism of Positioning Mode on Air Gap of Floating Semi-submersible Platforms

,,（1a.School of Civil Engineering and Architecture;b.School of Naval Architecture and Ocean Engineering;Jiangsu University of Science and Technology,Zhenjiang 212100,China;2.College of Harbor，Coastal and Offshore Engineering,Hohai University,Nanjing 210098,China;.School of Naval Architecture and Ocean Engineering,Dalian Maritime University,Dalian 116026,China）

Abstract:Combined with model test and numerical reconstruction model,a floating semi-submersible platform is used as an example to carry out time-domain full coupling analysis,and the sensitivity of mooring location and dynamically-assisted anchor positioning to the air gap of the platform is studied.The mechanism and influence characteristics of different positioning methods on the air gap of the platform are explored in depth.It is concluded that,compared with that of the pure anchor platform,the vertical constraint of mooring lines on the ATA(antomatic thruster assistance system)positioning platform is relatively small,and the ATA positioning platform has better following behaviour with wave in the vertical direction so that the relative motion of the gap between the platform and the water quality point is reduced,and the air gap is improved.Under the same working conditions,the probability of a negative air gap in the mooring mode is higher than that in the ATA positioning mode,and the wave slamming is more intense than that of the ATA positioning mode.In the numerical simulation of platform air gap,the influence of location difference on platform safe operation should be fully considered.

Key words:positioning mode;floating semi-submersible platforms;air gap;wave slamming

0 Introduction

The marine environment of deep-sea floating platforms is extremely bad,and air gap performance is a key problem in the process of platform design.Floating platforms serving in harsh environments require mooring systems to effectively control their movements and maintain their positions at sea level.At present,anchorage positioning and dynamic positioning are widely used in two ways.Anchorage positioning is generally used in areas with a shallow water depth,and dynamic positioning(DP)is used in areas with deep water.With the increase of water depth of platform service,the anchorage operation,installation and arrangement have become difficult,the mooring system weight has increased dramatically,its installation cost has become higher,the platform positioning ability has been greatly limited[1],and the positioning accuracy has been significantly reduced.Although DP system can be applied to deep water,the dynamic positioning structure system is extremely complex,and the cost of operating at sea is quite high.Compared with anchorage positioning system,dynamic positioning is easy to fail.At this time,the advantages of the power-assisted anchorage positioning system(automatic thruster assistance system,ATA)are immediately reflected,the ATA system can choose the propeller power according to the environmental conditions,and the capability of positioning is good[2].Although the existing specifications clearly need to consider the influence of anchorage system in the numerical simulation of air gap,they do not consider the difference of the influence of different positioning modes containing anchorage on air gap.The platform of a power-assisted anchorage positioning system is generally composed of a multi-point suspension line anchorage system and a dynamic positioning system,because the ATA positioning platform has been fitted with a power positioning system,and the thrust provided by its thrusters can assist the anchorage system,so for resisting the same external environmental load,the parameter standards such as chain length,diameter,unit length mass and axial stiffness of the ATA positioning platform may be smaller than the chain parameter standard of the pure anchoring positioning platform,and the anchorage parameters have a significant effect on the characteristics of anchorage lines.Therefore,under the same environmental load,the anchorage motion characteristics of the two positioning modes will also produce significant differences.

In recent years,many scholars at home and abroad have carried out a lot of experiments and theoretical research on floating platform air gap.For example,Matsumto et al[3]used a completely nonlinear method,which shows that the air gap response distribution of large column semi-submersible platform is analyzed.Computational display standard linear analysis is easy to lead to serious errors in air gap calculation.With the gradual increase of wave steepness,the boundary element model is extended to the second order,and its calculation results can be significantly improved.Naess et al[4]carried out a model test on the floating semi-submersible platform in a certain sea area,and the hydrodynamic performance of the platform under different limit environmental disturbance forces was studied,and the air gap distribution and wave slamming load at each location of the platform were emphatically concerned.Yan and Yang et al[5]proposed a method for dynamic evaluation of air gap response of large semi-submersible platforms based on deep water test pools,and conducted a series of tests on platform scale models based on regular and irregular wave conditions.The air gap values of the 11 positions on the deck under the action of the oblique waves were calculated and statistically processed.Kim and Park et al[6]conducted numerical studies on the design height and layout of lifeboats in offshore floating production plants under various environmental loads such as waves,winds and currents,taking into account the effects of air gaps on lifeboats.Dong et al[7]conducted an in-depth analysis of the factors affecting the air gap of the South China Sea TLP platform.Huo(2016)[8]studied the sensitivity analysis of parameters such as wind speed and direction on the air gap motion of the platform.Shen et al[9]made a comparative analysis of the effects of mooring system characteristics on the air gap of the platform,the analysis results show that the parameters of an anchorage system have a significant effect on the air gap motion of the platform.Shen et al(2018)[10]compared and analyzed the influence of the operating water depth on the air-gap of the power-assisted anchoring platform and the anchoring platform.At present,the research on the influence of positioning mode on the air gap motion of the platform at home and abroad is still scarce.

In this paper,according to the floating platform of anchorage system positioning and the difference of floating platform motion characteristics of dynamic auxiliary anchorage location,under the same working conditions,based on the numerical reconstruction model,the anchoring position of the platform and the power-assisted anchoring position are numerically extrapolated.The floating semi-submersible platform is used as an example to verify the time-domain fully coupled analysis.The sensitivity of the anchoring position and the power-assisted anchoring positioning method to the air gap of the platform are studied respectively,and the influence characteristics and laws of the difference of the positioning mode on the air gap of the platform are deeply explored.

1 Theory of platform air gap forecast

The air gap refers to the vertical clearance between the bottom of the lower deck of the offshore platform or the bottom of the lifeboat platform and the surface of the ocean wave[2],as shown in Fig.1.The air gap at the momenttof the platform moving in the wave is calculated by

Fig.1 Definition of air gap change

wherea0is the static water platform air gap,η(t)is the response wave height of the platform,δ(t) is the vertical displacement of the platform,andr(t) is the relative wave

surface of the platform elevation.The DNV-RP-C205[11]specification stipulates that if the instantaneous air gap of the platform’s attention point is less than 0 at the momentt,the wave slamming phenomenon occurs in the structure.

2 Numerical reconstruction and extrapolation of floating platform based on experiment

2.1 Pool test

In this paper,based on the platform model test,the numerical model was further reconstructed and extrapolated.The platform model pool test was conducted in the towing pool,and the similarity theory needed to be satisfied in the model test of the marine engineering structure positioning system.The model similarity ratio was 1:38.9,and the test model is shown in Fig.2.

Fig.2 Model in pool test

Test method:the end of each of the four strong horse lines was first connected to the spring at four suitable positions on the pool wall with the purpose of avoiding the influence of the slow drift motion of the platform system on the wave frequency motion of the structure and fixing the other end of the anchorage line on the baseline of the platform model.Four of the root mooring lines were of the same length,stiffness and pre-tension.The mooring points were arranged symmetrically,and as far as possible,kept in a horizontal state,and the vertical mooring position of the mooring line in its model was highly consistent with its center of gravity.In the course of the implementation of the experiment,four of the root mooring lines were in a tightening state.The entire system was tested in still water,including a degree of freedom decay test and a chain system stiffness test,and the recovery force of the mooring system in the model test is shown in Fig.3.

Fig.3 Restoring force of mooring system in model test

2.2 Wind tunnel test

At present,the model test is the most accurate calculation method for wind and flow load.Based on the wind tunnel test data of a semi-submersible platform model,the wind flow load coefficient of the numerical model was reconstructed in this paper.The main dimensions of the wind tunnel laboratory were 8.5 m long,3 m wide and 3 m high,the wind speed range was 3～93 m/s,and the turbulent strength was 0.1%.The main component of the semi-submersible platform test model was ABS,which had good strength and stiffness,and was ensured that it was similar to the geometry of the object in appearance.The main instruments and equipment used in wind tunnel test were as follows:hot-wire anemometer,load sensor and data sampling system.The proportion of wind tunnel models was 1:130.The wind tunnel test was mainly implemented under three conditions:self-storage,towing and operation.

The wind field of the wind tunnel test is shown in Fig.4,and its test model is shown in Fig.5.

Fig.4 Wind tunnel for test

Fig.5 Model in wind tunnel test

The main steps of the experiment are as follows:

(1)Install a turntable at the plane center of the test to simulate sea level,place the model in the center of the turntable,and install the generator,such as generators simulating the characteristics of the atmospheric boundary layer,at the test entrance.

(2)Connect the model to the strain balance and rotate the turntable to change the attitude angle of the model so that the wind load direction of the model changes.The hotline anemometer is used to measure the simulated wind profile in the wind tunnel,and the wind and flow loads and their dimensionless coefficients are collected by the load sensor(a strain balance containing 6 components).

(3)Collect data and make analysis by computer-controlled data sampling system.

2.3 Numerical simulation

(1)Platform overview

The main parameters of the floating semi-submersible platform in this example are shown in Tab.1,and the hydrostatic parameters are shown in Tab.2.

Tab.1 Parameters of the platform

(2)Panel model and viscous damping unit

In this paper,the motion response of the floating platform was simulated by the method of combining potential flow theory with Morison formula.The panel model(panel unit)was calculated by using the potential flow theory,and the panel model is shown in Fig.6.The Morison model of platform struts,pontoons and columns was established to effectively correct the viscous damping of the structure,and the Morison model is shown in Fig.7.Because the drainage volume of the structure was considered in the panel model,the section size had been reduced when the Morison model was established,and the drag force coefficient was amplified in the same proportion,which effectively ensured that the towing force load would not be affected under the condition of a constant platform displacement.

Fig.6 Panel model of platform

Fig.7 Tubular and disk model

(3)Mooring system

The floating platform in this paper was positioned by axisymmetric arrangement of eight mooring lines as shown in Fig.8.Each mooring line consisted of a 1 600 m chain and a 200 m steel wire with a preload of 820 kN,and the parameters of the chain and steel wire are shown in Tab.3 and Tab.4.

Fig.8 Arrangement of mooring lines

Tab.3 Fairlead positions and line ranges

Tab.4 Segment properties

(4)Propulsion systems

In the numerical simulation of the dynamic assisted anchorage positioning system,the propeller worked at the maximum thrust and the thrust direction was optimized according to the average environmental disturbance force of the platform.In the numerical simulation,the thrust was expressed as a constant force,that is,when the propeller was installed on the platform,the optimized maximum thrust was used to simulate the efficiency of the propeller in its horizontal direction,and was used together with the mooring system to improve the positioning capacity and efficiency of the platform.

(5)Natural period

Natural period of the platform in still water is an important index to measure its motion response,and the natural periods of heaving,rolling and pitching of the platform studied in this paper are shown in Tab.5.

Tab.5 Natural period of platform

2.4 Numerical model reconstruction and extrapolation

Combined with the results of pool test and wind tunnel test,a‘replication’simulation of the numerical model was carried out,that is,the numerical model adopted the same working conditionand anchorage system in the pool test,and by reconstructing the wind flow load coefficient and hydrodynamic parameters of the numerical model,the dynamic simulation of the model after the numerical reconstruction was carried out in the time domain.Compared with the results of the pool test,the longitudinal motion response analysis of the platform is shown in Fig.9,and the pendulum motion response is shown in Fig.10.From the comparative analysis,it can be seen that the numerical model simulation is in good agreement with the motion response of the pool test.Therefore,the reconstructed numerical model can accurately simulate the motion response of the platform.

Fig.9 Comparison of pitch motion response

Fig.10 Comparison of heave motion response

Under the condition that the calculated results of the motion response of the numerical model are the same as the experimental results,the simultaneous action of the wind and wave flow load was simulated,then,the numerical extrapolation of the platform was carried out.The fully bathymetric mooring system platform is shown in Fig.11.The damping,dynamic characteristics,horizontal stiffness and motion of the fully bathymetric mooring system can be simulated.

Fig.11 Full size numerical model after reconstruction and extrapolation

3 Time-domain coupling analysis of floating semi-submersible platform under different positioning modes

3.1 Calculation conditions

According to the reconstructed numerical model,4 sets of working conditions were selected under the same chain preload force,chain length and environmental load conditions,and the platform air gap response was compared under different positioning modes.Caculation conditions are shown in Tab.6 and Tab.7,where A-Case represents the ATA positioning mode,B-Case represents the anchorage positioning mode,and the two positioning modes serve as water depth of 300 m and the chain elastic stiffness of 65 213 t.

Tab.6 Calculation conditions under ATA positioning mode

Tab.7 Calculation conditions under anchorage positioning mode

Tab.6(Continued)

3.2 Platform air gap time domain coupling calculation

According to the long-term monitoring data of the North Atlantic Sea conditions,the sea conditions of the North Atlantic in 100 years were calculated by using the JONSWAP spectrum.In order to effectively observe the change of platform air gap under various working conditions,based on the symmetry of floating semi-submersible platform structure and the results of engineering test,seven points are arranged at the edge position of the lower deck of the platform for observation,and the detailed distribution of observation points is shown in Fig.12.In order to ensure that the analysis would not be affected by other anchorage parameters,the anchorage system with the same type and characteristics was used to change the anchor position of 300 m water depth and 500 m water depth,so that the cable angle of chain in vertical direction was the same at different water depths.

Fig.12 Observation points for air gap in deck box bottom

Eight sets of calculation conditions(80 sub-conditions)under the environmental head wave and beam wave loads were selected in this paper,and the influence of ATA positioning mode and anchorage positioning mode on platform air gap and wave slamming under different working water depths was studied respectively.In view of the instability of platform wave simulation in time domain,10 different random wave sea conditions were selected as the sub-conditions of each set of calculation conditions.The same random wave was used for 3 hours numerical simulation of all the sub-conditions.Based on the recommendation in specification[12],it was assumed that the smallest gap value of each group of platforms would obey the Gumbel distribution,and the 90%Gumbel distribution value of 10 sub-conditions was selected as the analysis result of the platform’s smallest gap under this condition.Tab.8 shows the average of the smallest gap response for two different positioning platforms,and Tab.9 indicates the Gumbel distribution value of 90% of the smallest gap response for two different positioning modes.Under the same wave and transverse load,the negative gap value of the ATA positioning platform is greater than that of the points of the anchorage positioning platform,which indicates that the situation of occuring negative gap of the points under anchorage location is relatively serious.

Tab.8 Mean value of min air gap response

Tab.9 90%Gumbel distribution of min air gap response

3.3 Study on the influence characteristics of positioning modes on platform air gap

(1)Platform wave slamming forecast

In order to explore the influence of different positioning modes on ATA positioning mode platform and wave slamming of anchorage positioning platform,the platform was discussed in detail under the load of wave and wind.The slamming times of the platform’s observation points under this condition were forecasted and analyzed.

In Fig.13 and Fig.14,the numbers of slamming on the platforms under head sea and beam sea were displayed respectively.

As shown in Fig.13,under head sea because the number of negative gap at the points of the anchorage positioning platform with 1 590 m chain length or 1 610 m chain length was smaller than that at the corresponding points of the ATA positioning platform,the numbe of slamming at the observation points of the ATA positioning platform was decreased as compared with that of the ancnorage positioning platform.Specifically,in Fig.3(a)for the points ofN-03,N-05 andN-07,the numbers of slamming were decreased by 33 and 38,there were reductions of 49.2% and 60.3% respectively.In Fig.13(b)for the points ofN-03,N-05 andN-07 the numbers of slamming were decreased by 39,29 and 42,there were reductions of 40.2%,36.7% and 48.2% respectively.From above analysis,it is concluded that the ATA positioning platform has a better influence on reducing wave slamming than the anchorage positioning platform under the same head sea condition.

Fig.13 Prediction of slamming times at the points in head sea

As shown in Fig.14,under beam sea the number of negative gap at the points of the anchorage positioning platform with 1 590 m chain length or 1 610 m chain length was smaller than that of the ATA positioning platform.The number of occuring slamming at the observation points of the ATA positioning platform was decreased as compared with that of the anchorage positioning platform.In Fig.14(a),for the points ofN-01,N-02 andN-03 the numbers of slamming were decreased by 24,32 and 46,there were reductions of 17.6%,17.9% and 29.1% respectively.In Fig.14(b),for the points ofN-01,N-02 andN-03 the numbers of slamming were decreased by 23,15 and 36,there were reductions of 15.2%,7.5%and 19.3%respectively.Similarly it is concluded that the ATA positioning platform has a better influence on reducing wave slamming than the anchorage positioning platform under same beam sea condition.

Fig.14 Prediction of slamming times at the points in beam sea

(2)Energy spectrum analysis of platform motion response under different positioning modes

In order to further analyze the influence of different positioning modes on the floating semisubmersible platform air gap wave slamming,the time-domain value energy spectrum analysis of the platform response was carried out.Figs.15(a)-(b)show the response energy spectra of the heave motion of two different chain length platforms under the action of the head waves,Fig.16 shows the response energy spectra of the heave motion of two different chain length platforms under the action of beam waves.According to the graph,in the direction of head wave and beam wave,the difference of positioning mode has a significant effect on the energy spectrum of the platform’s pendulum motion response,because the vertical motion of the platform includes the longitudinal shaking and rolling part of the energy,and its influence is mainly concentrated in the vicinity of the platform resonance zone.

Fig.15 Motion response of the platform in head sea

Fig.16 Motion response of the platform in beam sea

(3)Energy spectrum analysis of air gap response of platform observation points under different positioning modes

Figs.17(a)-(c)are the air gap response energy spectra at the points ofN-03,N-05 andN-07 in the case of the head wave conditions,Figs.18(a)-(c)are the air gap response energy spectra at the points ofN-01,N-02,andN-03 under beam wave conditions respectively.According to the graphs,under the action of head wave and beam wave,the difference of air gap response energy spectra of three observation points in different positioning modes are obvious,which further proves the significant influence of positioning mode on the platform air gap.

Fig.17 Response spectra of air gap at the points of N-03,N-05 and N-07 for A-Case 01 and B-Case-01

Fig.18 Response spectra of air gap at the points of N-01,N-02 and N-03 for A-Case 05 and B-Case-05

3.4 Mechanism of the influence of positioning method on the air gap of the platform

In order to further analyze the influence mechanism of ATA positioning and anchorage positioning on the air gap of the floating platform,the mooring force of the platform under different positioning modes is analyzed.Fig.19 shows a mooring force variation characteristic curve of ATA and anchorage positioning platform,which represents five motion directions of the platform.According to the graph,the effect of chain length on mooring force is significant under the same positioning mode.The increase of chain length leads to the decrease of the stiffness of the platform mooring system,that is,the recovery force of the mooring system becomes smaller,which makes the platform motion enhance,the vertical displacement of the platform is easy to change,so that the platform produces the negative air gap.

Fig.19 Mooring force curve of platform

Under the same operating conditions,the mooring force of the anchorage positioning platform is larger than that of the ATA positioning platform,which is related to the auxiliary propeller in ATA,because the propeller can provide partial thrust to improve mooring force finally.At the same time,ATA positioning platform is compared with the pure anchorage positioning platform.For the ATA positioning platform,the platform’s constrained load of mooring line in vertical direction is relatively small,and there exists a good following behavior of the platform with wave.The relative motion between the ATA positioning platform and water particles decreases,and the probability of slamming at the bottom of the platform reduces.

4 Conclusions

In this paper,combined with model test,the numerical reconstruction of platform model is used to extrapolate the different positioning modes of floating platform.Taking a floating semi-submersible platform as an example,the time domain full coupling analysis is carried out.The influence characteristics of anchorage positioning and ATA positioning on the platform air gap are studied respectively,and the influence law of the positioning modes on the platform air gap is explored.Based on the study of the influence characteristics of different positioning methods on the mooring force of the platform,the mechanism of the influence on the air gap is revealed.The following conclusions are obtained from the study:

(1)The ATA positioning mode is better than the pure anchorage positioning mode as the former has a good effect on the air gap of the floating platform.According to the average of the smallest gap of the platform under two different positioning modes and the calculation results of 90% of the Gumbel distribution values,it can be seen that the probability of negative air gap occurring in the anchorage positioning platform is greater than that of ATA positioning platform under the same wind and wave conditions.In the numerical simulation of the platform air gap,the influence of different positioning modes on platform safety operation should be fully considered.

(2)Based on the study of the influence characteristics of different positioning modes on the mooring force of the floating platform,it is proved that the mooring force of ATA positioning platform is less than that of anchorage positioning platform because of the force provided by the propeller of ATA positioning platform.Compared with that of the pure mooring positioning platform,the vertical constraint of chains on the ATA positioning platform is relatively small.For the ATA positioning platform,the following behavior of the platform with the waves in the vertical direction is better,which reduces the relative motion of the air gap between the platform and the water particles and reduces the probability of a negative air gap.

The different positioning modes of the floating platform affect the performance of the platform itself.In the design of platforms,according to the environment condition of platform operation,it is very important to select a positioning system reasonably for both safety and service of the platforms.The conclusion is usefull to actual engineering designs.