The finite element model of the jacket platform is established as shown in Figure 2 , which is based on the jacket platform in JZ oil field in Jinzhou, Liaoning province in China. The environmental loads, including wind, wave, and current, are calculated in this section, and then, they are applied into the established finite element model to calculate the dynamic responses.
According to the design data, the height from the water surface to the top deck of the platform is 15 m, and the OWC device is installed on the legs and submerged with a draft depth d. The wind loads f wind can be calculated by the following formula Li, :.
Ignoring the interaction with the remaining OWCs and the jacket platform, the wave force acting on a single OWC, as shown in Figure 1 , is calculated by the analytical solutions using the linear potential-flow theory and eigenfunction expansion technique, referenced by the established model of authors Zhou et al. The part below the water surface of the wave energy conversion device can be simplified as shown in Figure 3.
The Cartesian coordinate system is taken, with the still water surface set as the coordinate plane and the ordinate axis passing through the center of the air chamber. The air in the chamber is considered to be motion isentropic and compressible, and all of the time-dependent variables are assumed to be harmonic. Thus, the air pressure p in the chamber is:. A Wells turbine is installed at the top of the air chamber, and the mass flux rate of air across the turbine is proportional to the air pressure, and within the framework of a linear theory, the relationship between the turbine characteristics and the air mass flux is:.
Based on the linear theory, the volume flux of the chamber is the sum of volume fluxes as a result of wave radiation and diffraction. The wave radiation is caused by the wave motion purely generated by the oscillating air pressure of the chamber. The wave diffraction is caused by the scattering of incident waves when the air pressures are identical inside and outside of the chamber. Thus, the complex amplitude of volume flux q 0 is:. For the radiation solution, an added mass coefficient C and damping coefficient B can be obtained Evans, , , so the amplitude of volume flux q R is:.
Through substituting Equations 4 and 5 into Equation 3 , the air pressure in the chamber can be obtained:. The fluid is assumed as incompressible, inviscid, and flow irrotational; the solution of boundary value problem shown in Figure 3 is considered. The amplitude of volume flux can be calculated using the free-surface integration:. Assuming that the current profile is uniform, the current loads f current can be calculated by the following formula Li, :.
The wind and wave directions are all along the positive direction of X -axis. The depth of six times the pile diameter below the mud line is regarded as rigid fixed constraint.
The dynamic analysis of the jacket platform is carried out under the working conditions wind velocity is The ANSYS software is used to calculate the displacement, velocity, and acceleration responses of the top node of jacket platform as shown in Figure 2.
The calculation results are shown in Table 1. Owing to the wind and current load set as the constant loads during the calculation, the velocity and acceleration responses are 0, and the velocity and acceleration responses of the structure are all caused by wave load. To apply the OWC device integrated to the jacket platform in engineering practice, the reasonable structural parameters of OWC device are needed to be determined based on the actual sea conditions.
The optimization criteria are set as follows: the device is subjected to the minimum wave force while the device has the highest wave energy capture efficiency. According to the design data of the jacket platform in the sea area, the diameter of pile legs and wave conditions of the sea area have been determined.
As shown in Figure 4 , the water depth h is taken as Figure 4. Wave energy capture efficiency under different oscillating water column OWC structural parameters. Based on the optimization model above, series values of draft depth d and chamber radius d 1 are given according to the practice project.
The draft depth d , the air chamber radius d 1 , and the wave force F are non-dimensionalized, as shown in Table 2. The results of wave energy capture efficiency under different chamber radius, draft depth, and wave frequencies are shown in Figure 4. The results of wave force are shown in Figure 5. Figure 5. Wave force under different oscillating water column OWC structural parameters.
According to Figure 4 , under each combination of draft depth and chamber radius, the wave energy capture efficiency increases from 1 to the maximum and then decreases to 0 as the incident wave frequency increases. The smaller radius could make the incident wave frequency, which generates maximum wave energy capture efficiency, become larger. The reason of wave energy capture efficiency initially starting from 1 is that the incident wave frequency is in the region of low frequency long wave, and the wave length is much larger than the geometry size of OWC device, so the wave surface in the air chamber cannot be affected by the interface wave.
The frequency corresponding to the maximum wave energy capture efficiency is exactly equal as the incident wave frequency when the piston resonance motion occurs in the OWC device. According to Figure 5 , under each combination of draft depth and chamber radius, the wave force increases from 0 to the maximum value and then decreases to 0 as the incident wave frequency increases.
The larger draft depth could make the incident wave frequency that generates maximum wave force become smaller. In summary, when the draft depth is constant, the smaller air chamber radius could make the resonance frequency of incident wave and wave energy capture efficiency become larger and make the wave force become smaller. Therefore, the slenderer the air chamber, the better the wave energy capture efficiency and the smaller the wave force.
However, when the air chamber radius is constant, the larger is the draft depth, the larger is the maximum wave energy capture efficiency at the resonance frequency, and the larger is the wave force. In a word, the optimization objective function needs to be solved aiming to get the optimal OWC structure parameters. Therefore, the two optimization objective functions are combined into one:. Based on the calculation results shown above, the optimization objective function of Equation 19 is solved and shown in Figure 6.
Figure 6. Based on the design data of the jacket platform shown in Dynamic Response Calculation above, the wave period of working conditions is 5. The minimum value is 0. This is the optimal OWC device structural parameters under the working condition.
If the OWC wave energy conversion device is installed in the other sea area, the optimal structural parameters could also simply be selected based on the wave frequency and Figure 6. Based on the optimal structural parameters of the OWC device under the working conditions shown above, the device could be integrated into the jacket platform, and the influence of integration on the dynamic response of platform is analyzed.
Under the combined action of wind, wave, and current, considering the working conditions, and extreme working conditions, the dynamic response of the jacket platform with and without OWC device is calculated. The influence of OWC device integration on the dynamic response of the jacket platform is studied to provide references for actual construction of project.
Under the action of working condition with regular waves, the time histories of dynamic response of top node of the jacket platform integrated with OWC device Node No.
In addition, the contours of maximum structural dynamic responses, including the velocity, acceleration, and displacement are shown in Figure 8. The results of dynamic responses of the jacket platform with and without OWC device are compared in Table 4A.
Figure 7. Time histories of dynamic responses under working condition with regular waves. A Velocity; B acceleration; C displacement. Figure 8. Dynamic response contours under working condition with regular waves. However, the overall dynamic response is still at a very small value level, which is similar with the results of Zhang and Liu In addition, the contours of maximum structural dynamic responses, including the velocity, acceleration, and displacement are shown in Figure The results of dynamic responses of the jacket platform with and without OWC device are compared in Table 4B.
Figure 9. Time histories of dynamic responses of working condition with irregular waves. A velocity; B acceleration; C displacement. Figure Dynamic response contours under working condition with irregular waves. To assess the safety of the jacket platform under extreme condition, the structure parameters of OWC device are kept unchanged, and the dynamic responses are calculated under the extreme condition. Under the action of extreme condition with regular waves, the results of dynamic responses of the jacket platform with and without OWC device are compared in Table 5A.
Under the action of extreme condition with irregular waves, the results of dynamic responses of the jacket platform with and without OWC device are compared in Table 5B.
In a word, the effect of OWC device integration into the jacket platform is almost negligible on the dynamic response under extreme condition.
In this paper, based on the design data of a jacket platform working in JZ oil field in Jinzhou, Liaoning province in China, an OWC device integrated into the jacket platform is proposed, the optimal structure parameters of OWC device are determined, and the dynamic responses of platform with and without OWC device are compared under the working and extreme conditions.
The main conclusions are obtained as follows:. In general, the jacket platform integrated with OWC device can introduce green wave energy while causing almost negligible effects of the dynamic responses. Therefore, the economic benefit of platform oil exploitation can be improved, and it has certain feasibility in the practice application. However, the integrated device may introduce some strength and fatigue problems, which also need to be checked in the future.
The datasets generated for this study are available on request to the corresponding author. DQ and DN proposed the concept and research framework.
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June This serves to accelerate the air so that it reaches its optimum velocity and pressure as it passes the turbine. The pressure within the chamber is fully controlled through the valves system see Figure 03 and turbine blade pitch control to achieve the optimum conversion efficiency. Figure Ocean waves contain enormous quantities of energy and harnessing this energy in the most efficient and productive way is the objective of the Aquanet Power technology.
At the heart of the technology there are 3 simple elements:. As waves rise within the OWC, it replicates the action of a piston, driving a column of air ahead of it and through the turbine. The enhanced design reduces turbulence at the entry to the OWC and drag inside the chamber, resulting in considerable increase in capturing wave power and system efficiency.
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