Hydroelastic responses and interactions of mega floating fuel storage modules 8

Conclusions and Recommendations 8.1 Summary and Conclusions In this thesis, a numerical model and a hybrid finite-element boundary-element FE-BE method constructed in the frequency domai

Conclusions and Recommendations

8.1 Summary and Conclusions

In this thesis, a numerical model and a hybrid finite-element boundary-element (FE-BE) method constructed in the frequency domain framework have been developed for the hydroelastic analysis of two mega floating fuel storage modules placed side-by-side and protected by floating breakwater under operating condition The hydroelastic responses and interactions of the floating storage modules under wave action were investigated for the first time It is to be noted here that the floating storage facility under survival condition is not addressed in this thesis Interested reader may refer to paper by Suzuki (2005) on the design considerations of FFSF under survival condition

In modelling the fluid-structure interaction problem, the water is assumed to be

a perfect fluid and the fluid motion is irrotational, so that a velocity potential φ exists The fluid motion is then governed by the Laplace equation ∇ φ2 =0 The floating storage modules were modelled as equivalent solid plates using the Mindlin plate theory so that better prediction of deflections and stress resultants may be obtained The equivalent plates were discretised by using non-conforming

quadratic-serendipity (NC-QS) plate elements To obtain the deflection w of the floating plate,

one needs to solve the equation of motion of the plate that unfortunately involves the fluid velocity potential φ In order to determine the velocity potential φ, one needs to solve the Laplace equation which in turn has a water-plate surface

boundary condition that contains the unknown deflection w So one is confronted

with a coupled water-plate problem The modal expansion method was adopted to decouple the water-plate interaction problem In this method, a series of modal functions w

l

c was substituted into the water boundary condition associated with the

water-plate interface, thereby removing the unknown deflection w We then solved

the Laplace equation which was transformed into a boundary integral equation via the boundary element method for the potential φ The computed potential φ was back substituted into the equation of motion of the floating plate as the hydrodynamic force and the plate equation was solved using the finite element method for the complex amplitudes ς of the plate The deflection w of the plate can l

then be obtained by taking the product of the modal functions cˆ l of the freely vibrating plate and the complex amplitudes ς The wave elevations surrounding the l

floating modules could then be computed based on the computed hydroelastic deflections

The validity, convergence and accuracy of the modified NC-QS Mindlin plate element used in computing the hydroelastic deflections and stress resultants of the floating structure were investigated by comparing with some existing results obtained by Yago and Endo (1996) and Wang and Wang (2006) The stress resultants computed from the modified 8-node NC-QS Mindlin plate element were found to be

of better accuracy when compared to the classical 4-node Mindlin plate element

(Wang and Wang, 2006) This is because the modified Mindlin plate element, which adopts the selective integration method and addition of non-conforming modes, aids

in overcoming the rank deficiency and spurious modes in its stiffness matrix By adopting the NC-QS Mindlin plate elements in the design of floating storage modules, the stress distribution on both thin and thick plate models could be computed correctly

The hydroelastic interactions of the floating storage modules and the wave elevations along the channel were validated by experimental test results In order to reduce computational time, a simplified plate model having the same dynamic properties (in terms of vibration modes and natural periods) as the experimental model was used for the hydroelastic analysis The hydroelastic responses computed

on this simplified plate model were found to be in good agreement with the experimental test results Floating breakwaters were found to be very effective in reducing the hydroelastic responses, wave elevations along the channel and steady

drift forces when subjected to wavelengths λ/L less than 0.67 The performance of

the floating breakwater depends on its width to wavelength ratio and the efficiency

of the breakwater in reducing the response of the floating storage modules drops as this ratio decreases Therefore, it is necessary to have breakwaters with an adequate width to be effective in mitigating the wave forces impacting the floating storage modules

The behavior of the floating storage modules under a head sea condition (which

is the worst-case scenario for floating storage modules sited in a narrow channel or near shore) was successfully investigated through comprehensive parametric studies The structural response and wave elevation along the channel were found to

increase with respect to increasing wavelength and they were also found to be larger

at greater water depths due to the corresponding longer wavelengths For a given

wavelength λ/L, the structural response of the floating modules increases as the

water depth decreases because of the enhanced interactions between the seabed and bottom surfaces of the floating storage modules As a result, this increases the pressure acting on the bottom surfaces of the floating storage module However, the difference in the wave elevations at two different water depths is negligible if the difference in the corresponding wavelengths is less than 0.1

The floating modules were found to have maximum heave when both modules are empty The relative deflections between the two floating storage modules were found to be the largest under Load Cases 1 (fully loaded + empty) and 3 (half loaded + empty) This implies that the response of the floating bodies is significantly affected by the loads in the storage modules that increase the added mass, thereby further damping the motion of the floating bodies These findings are significant especially during the loading and offloading operations of fuel The responses of the floating modules could be minimised by constructing floating breakwater around the floating modules

The wave elevations along the channel were investigated and the computed wave elevations were used in designing the minimum freeboard and channel spacing

of the floating modules so as to prevent green water on deck The freeboard of the storage modules could be enhanced significantly by having a parapet wall around the perimeter deck of the storage module As a rule of thumb, the minimum freeboard

of the floating module has to be kept to at least twice the wave amplitude in order

to avoid green water If the floating modules are loaded to having a freeboard less

than 2A, the floating modules should be spaced farther apart The channel spacing

that prevents green water could be determined such that the normalised

(wmax +ηmax)/FB is less than 1.0 For example, if the floating modules with parapet

wall and surrounded by floating breakwater are loaded to d/h = 0.90 and leaving a freeboard of FB = 1.5A (see Fig 6.11), the floating modules should be spaced at λ/L

greater than 0.23 in order to prevent green water on deck However, by placing the floating modules too far apart means that a larger sea space is required as well as the number of mooring dolphins has to be increased On the other hand, by placing the floating modules too close to each other, one has to contend with large hydroelastic responses and wave elevations along the channel The design of a suitable channel spacing thus involves a trade-off between limited sea space, minimum hydroelastic responses and maximum loading capacities of the storage modules The study on the effect of channel spacing on the response of the floating modules interestingly revealed that the structural response increases at certain expanded channel spacings due to undesirable interactions between the modules From the study, it is recommended that the floating modules be spaced in the range

of s/L = 0.10 to 0.25 in order to minimise the undesirable interactions The suitable channel spacing of the storage modules (when the modules are loaded to d/h = 0.90)

that minimises the undesirable response of the floating modules and avoids green

water on deck should be s/L = 0.23 to 0.25 Note that if the minimum freeboard of

the floating modules is kept to at least twice the wave amplitude, the width of the

channel spacing can have a wider range λ/L = 0.10 to 0.25

The steady drift forces acting on the floating storage modules that accounted for the hydroelastic interactions were also investigated based on the near-field

approach (pressure integration method) In the near-field approach, the mean forces were evaluated at the instantaneous position of the floating bodies The steady drift forces computed from the near-field method were found to be in good agreement with Watanabe et al (2000) results obtained from the far-field method The near-field method is a more robust tool for predicting the steady drift forces on the storage modules when compared to the far-field method as the former method enables the evaluation of steady drift forces acting on each floating module As opposed to the Longuet-Higgins (1977) far-field method that requires a good guess for the reflected coefficient, the near-field method solves for the drift coefficient numerically without having to make such an assumption Besides that, the near-field method also takes into considerations the interactions behavior between the storage modules

The steady drift forces acting on the storage modules were found to increase with respect to the wave frequency When the floating modules are subjected to a sea state with a large wave frequency, an increase in the diffracted and radiated wave elevations is observed The formulation of the steady drift forces based on the near-field approach showed that the drift forces acting on the floating modules increase proportionally with increasing wave elevations Parametric studies on the effect of channel spacing on the steady drift force showed that the proposed channel

spacings λ/L = 0.23 to 0.25 (that minimises the undesirable response of empty

modules while maximising the loading capacities) were found to be adequate in reducing the steady drift forces The computed steady drift forces could then be used to design the mooring dolphin fender system by referring to the manufacturer’s performance curves of rubber fenders

In sum, the developed numerical model, formulation, solution technique and computer code provide analysts with a robust analytical tool to investigate the hydroelastic response, interactions behavior and wave field surrounding floating storage modules in a mega floating fuel storage facility The solution techniques presented in Chapter 2 and 3 could also be used to solve for the hydroelastic response, wave field and drift forces for multiple storage modules placed adjacent to each other Engineers and naval architects can confidently design the mega floating fuel storage facility by taking into account the effects of floating breakwater, wave period, loading combinations, channel spacing, water depth and wave angle on the structural response and wave field The effect of hydroelastic interactions towards the steady drift forces could also be investigated and the computed drift forces could

be used in designing the mooring dolphin fender system for restraining the horizontal movement of the floating modules

8.2 Recommendations

There are some interesting directions for future studies in this area initiated by the author of this thesis They include:

• Wave-structure-liquid interaction – It is necessary to consider the free surface effect due to the sloshing behavior of fuel in the storage modules The free surface effect might be crucial towards the response of the floating storage module especially when resonance occurs Some research studies have been made on the sloshing of liquid in tankers but without considering the coupled interaction of liquid-structure with the wave action Moreover, the structure

is usually assumed to be rigid body in these studies Wave-structure-fluid

interaction that takes into account the elastic behavior of the structure is a challenging topic for researchers

• Non-linear analysis and irrotational flow – The frequency domain analysis and linear potential theory is not valid in extreme situation such as in a large storm Such an extreme event has to be considered in the FFSF design for safety and survivability reasons More work should be done to investigate the non-linear response such as the transient response of FFSF under large wave impact

• Arbitrary shaped VLFS – As opposed to the conventional rectangular shaped floating storage module, the storage modules could also be constructed in complicated shapes Research work is needed to develop efficient hydroelastic analysis method to handle complicated shapes of FFSF

• Hydroelastic analysis using Navier-Stokes equation – Vorticity and viscous effects are usually neglected in the hydroelastic analysis using the potential theory However, high vorticity of fluid is expected from tsunami waves impacting FFSF or in the case of FFSF fitted with anti-motion devices such as bilge keels and submerged plates In such situations, the fluid has to be represented by the Navier-Stokes equation that allows for irrotational flow Studies on the effect of fluid viscosity should also be addressed as the induced drag forces might be significant towards the response of the structure under extreme loading cases

• Slowly varying drift forces – The mooring dolphin systems that hold the floating modules in placed are usually designed based on the drift/mean forces Further research studies are needed to include the slowly varying drift

forces in the design of the mooring dolphin system for the VLFS located in multi-directional random seas Besides that, the drift forces due to the horizontal motion of the floating modules (which could be significant due to the large wave runup along the channel) have to be taken into consideration