Hydroelastic responses and interactions of mega floating fuel storage modules 7

CHAPTER SEVEN Steady Drift Forces on Storage Modules 7.1 Overview In this chapter, we investigate the steady drift forces acting on the floating fuel storage modules described in Section 5.2 by taking into consideration the hydroelastic interactions behavior of the floating modules when they are placed side-by-side The interactions behavior of the modules on the steady drift forces is examined by comparing with their counterparts associated with only a single floating module These steady drift forces are important when designing the mooring dolphin system that keeps the floating storage modules in position In order to evaluate the steady drift forces, we employ the pressure integration method (near-field method) at the instantaneous position of the floating bodies The method involves evaluating the mean forces (also known as the time-average forces over one wave period T ) The numerical scheme in deriving the steady drift forces is based on the second order wave theory as propounded by Utsunomiya et al (2001) and described earlier in Section 3.4 It is to be noted that the linear potential wave theory used for modeling the water motion in the previous chapters cannot be used in evaluating the steady drift forces This is because the mean forces are evaluated at 144 Steady Drift Forces on Storage Modules the mean position of the free surface and the submerged hull surface in the linear potential wave theory and as a result the mean forces are zero We first verify the accuracy of the numerical model in predicting the steady drift forces by comparing the results with existing ones furnished by Watanabe et al (2000) Upon establishing the validity of the numerical model and the correctness of the computer code, we investigate the steady drift forces acting on the two adjacently placed floating storage modules The computed steady drift forces are compared with those obtained by the widely used Longuet-Higgins’ (1977) far-field method For completeness, the mooring dolphin-rubber fender system for the aforementioned floating modules is designed based on the computed steady drift forces 7.2 Verification of Numerical Results We first verify the steady drift forces computed using the proposed numerical model that is based on the near-field method with the results obtained by Watanabe et al.’s (2000) who used the far-field method The far-field method is based on the momentum conservation method in a control volume The method requires the evaluation of incident, reflected and transmitted wave elevations on the artificial fluid boundary at infinity S∞ In the analysis, the floating structure used measures 300m × 60m × 2m and the details of the floating structure are given in Table 4.1 The floating structure encounters a head sea Various wave frequencies are considered 145 Steady Drift Forces on Storage Modules The steady drift forces obtained from the near-field method and the far-field method (Watanabe et al., 2000) are compared in Fig 7.1 The two sets of drift force results agree very well with each other In Fig 7.1, it can also be seen that the steady drift forces increase proportionally with respect to increasing wave frequencies This is because when the floating structure is subjected to a sea state associated with a very high wave frequency (i.e corresponding to a very small wavelength λ/L), the high oscillation of the floating structure will generate more radiated waves Besides that, the incident waves get reflected back by the floating structure when the wavelength is small The interference of the incident, reflected and radiated waves thus results in relatively large wave elevations ζ r(1) , and thus produces a large drift forces according to Eq (3.15) On the other hand, when the wave frequency is very small, the floating body will heave in the same phase as the incoming wave This results in relatively small wave elevations ζ r(1) Therefore, the steady drift forces are negligible under small wave frequencies as can be seen in Fig 7.1 In the next section, the near-field method will be used instead of the far-field method for investigating the steady drift forces because the near-field method allows the evaluation of steady drift forces acting on each of the multiple floating modules when placed side-by-side 146 Steady Drift Forces on Storage Modules Present method (near field method) Watanabe et al (2000, far field method) 0.6 Fy /(ρgA L2 /2) 0.5 0.4 0.3 0.2 0.1 0.0 1/2 ω (L2/2g) Fig 7.1 Steady drift forces on Watanabe et al.’ (2000) VLFS 7.3 Steady Drift Force on Specific Example of a Pair of Storage Modules After establishing the validity and accuracy of the numerical model for predicting the steady drift forces, we investigate the steady drift forces acting on the specific example of a pair of floating storage modules (each module has a dimension of 122m × 50m × 10m and the details are given in Section 5.2) under operating condition The hydroelastic interactions of the adjacently placed storage modules are taken into consideration As for the case of survival condition, it is to be noted here that the first order wave force in addition to the steady wave drift force has to be taken into 147 Steady Drift Forces on Storage Modules consideration in the design of mooring system Figure 7.2 shows the steady drift forces acting on each of the two empty modules with respect to different channel spacings s/L for four different wavelengths, i.e λ/L = 0.20, 0.32, 0.43 and 0.67 Results show that the steady drift forces acting on each of the two adjacently placed floating fuel storage modules decrease with increasing channel spacings The steady drift forces acting on a single floating module are also presented in Fig 7.2 for comparison purposes It can be seen from Fig 7.2 that the interactions between the storage modules have a significant effect on the steady drift forces, and therefore the interaction behavior must be allowed for when evaluating the steady drift forces However, when the floating modules are spaced very far apart, the hydroelastic interactions between the modules are negligible and the drift forces acting on each of the two floating storage modules become similar to those encountered by a single module Next, we investigate the steady drift forces acting on the two adjacently placed fully loaded modules as shown in Fig 7.3 Three different wavelengths, i.e λ/L = 0.32, 0.43 and 0.67 are considered From the results shown in Fig 7.3, the channel spacings s/L = 0.23 to 0.25 as proposed in Chapter (for two floating modules loaded to d/h = 0.90 and protected by floating breakwater) are found to be adequate in reducing the steady drift forces We also investigate the contributions of the velocity term (summation of the 1st, 2nd and 3rd drift force components on the right hand side of Eq 3.12) and the wave runup term (the 4th drift force component on the right hand side of Eq 3.12) towards the total steady drift forces acting on the storage modules When the wavelength is large (i.e λ/L = 0.67), it is found that the steady drift forces are governed by the 148 Steady Drift Forces on Storage Modules wave runup term in Eq (3.12) On the other hand, when the wavelength is small (i.e λ/L = 0.32), there is a pressure drop (see Fig 7.1) because the velocity term becomes significant Thus, this velocity term has to be included in order to predict correctly the steady drift forces 149 1.6 1.2 1.2 Fy/(ρgL1A ) (kN/kN) 0.8 2 Fy/(ρgL1A ) (kN/kN) 1.6 0.4 0.0 0.0 (a) λ/L = 0.20 0.5 1.0 1.5 2.0 2.5 0.8 0.4 0.0 0.0 3.0 s/L (m/m) 2.0 2.5 3.0 1.0 Fy/(ρgL1A ) (kN/kN) 0.8 2 Fy/(ρgL1A ) (kN/kN) 1.5 1.2 1.2 0.4 0.0 0.0 1.0 (a) λ/L = 0.43 0.5 1.0 1.5 2.0 s/L (m/m) 2.5 3.0 0.8 0.6 0.4 0.2 0.0 (d) λ/L = 0.67 0.5 1.0 1.5 2.0 2.5 3.0 s/L (m/m) 150 Fig 7.2 Comparison of steady drift forces for single storage module and two empty storage modules for wave period (a) λ/L = 0.20 (b) λ/L = 0.32 (c) λ/L = 0.43 (d) λ/L = 0.67 Wave amplitude A = 1m Water depth H = 30m Steady Drift Forces on Storage Modules Single module Modules 0.5 s/L (m/m) 1.6 Legends (b) λ/L = 0.32 1.0 0.5 0.0 Fy/(ρgL1A ) (kN/kN) 1.5 Legends -0.5 -1.0 0.0 Components Total Wave runup Velocity 0.2 0.3 1.0 1.0 Fy/(ρgL1A ) (kN/kN) 1.5 0.5 0.0 -0.5 -1.0 0.0 (b) λ/L = 0.43 0.1 0.2 s/L (m/m) 0.3 0.5 0.0 -0.5 -1.0 0.0 (c) λ/L = 0.67 0.1 0.2 0.3 s/L (m/m) 151 Fig 7.3 Steady drift forces on two fully loaded storage modules due to various drift force terms Wavelength (a) λ/L = 0.32 (b) λ/L = 0.43 (c) λ/L = 0.67 Wave amplitude A = 1m Water depth H = 30m Steady Drift Forces on Storage Modules 0.1 s/L (m/m) 1.5 Fy/(ρgL1A ) (kN/kN) (a) λ/L = 0.32 Steady Drift Forces on Storage Modules 7.4 Comparison of Steady Drift Forces Predicted by Near-Field Method and Longuet-Higgins’ Formula (1977) In the offshore industry, engineers normally use the Longuet-Higgins’ formula (1977) to determine the steady drift forces According to this formula, the drift coefficient is given by 4πH / λ   Drift coefficient = K r × 1 +   sinh (4πH / λ ) (7.1) where Kr is the wave reflected coefficient (which is the ratio of the reflected wave elevation to the incident wave elevation), H the water depth and λ the wavelength The drift force is evaluated by multiplying the drift coefficient with ρgL1 A where ρ is the water density, g the gravitational acceleration, A the wave amplitude and L1 the length of the floating structure shown in Fig 2.1 We now compare the steady drift forces predicted by the near-field method and the Longuet-Higgins’ formula (1977) For this comparison study, we use the two floating storage modules design and site parameters given in Section 5.2, and assume that the two storage modules are held in place by mooring dolphin-rubber fending systems as shown in Fig 7.4a The head sea condition is considered since it is the worst-case scenario as reported in Chapters and Cylindrical rubber fenders are proposed for absorbing the drift forces and they are shown in Fig 7.4b 152 Steady Drift Forces on Storage Modules (a) (b) Fig 7.4 (a) FFSF held by mooring dolphin systems in protected channel or near shore (b) cylindrical rubber fenders The steady drift forces acting on the single storage module evaluated using the near-field method and the Longuet-Higgins’ formula (1977) are presented in Table 7.1 The wavelengths considered are λ/L = 0.20, 0.32, and 0.67 Note that Kr in Eq (7.1) can only be obtained from experimental or numerical test For convenience, this unknown coefficient is usually taken as 1.0, i.e by assuming that all the incident waves are reflected back from the floating body It should also be noted that the Longuet-Higgins’ formula does not take into consideration the interactions behavior of the storage modules when they are placed side-by-side Therefore, Table 7.1 shows that the Longuet-Higgins’ formula is only accurate in predicting the steady drift forces for storage modules that are separated very far apart i.e s/L = ∞ (i.e hardly any interaction between storage modules) and when the wavelength is very small, i.e λ/L = 0.20 This is because the incident waves are totally reflected from the floating body under small wavelength This means that by using the LonguetHiggins’ formula (by taking Kr = 1.0) for predicting the steady drift forces of 153 Steady Drift Forces on Storage Modules adjacently placed floating modules under large wavelengths, one may end up with a very conservative design for the mooring dolphin system On the other hand, by using the near-field method, we are solving for the drift coefficient numerically without having to make an assumption This approach provides a better prediction of the steady drift forces In the next section, we employ the steady drift forces obtained from the near-field method for the design of the mooring dolphin-rubber fender system under operating condition Table 7.1 Steady drift forces on two floating storage modules for different channel spacings s/L Drift coefficient, s/L 0.15 0.20 0.25 0.30 0.50 ∞ 7.5 λ/L = 0.20 LonguetNear-field Higgins’ method formula 1.4639 1.2267 1.1654 1.009 1.2192 1.0650 1.100 (kN/kN) ρgL1 A λ/L = 0.32 λ/L = 0.67 LonguetLonguetNear-field Near-field Higgins’ Higgins’ method method formula formula 0.5571 0.6676 0.5905 0.648 0.6225 0.6144 1.077 1.464 0.5097 0.529 0.6273 0.4816 0.4804 0.5245 Fy Design of Mooring Dolphin System for FFSF The drift coefficients obtained from the near field method are used in designing a suitable mooring dolphin-rubber fender system for the FFSF Assuming that the floating modules create a channel spacing s/L = 0.15, one obtains a drift coefficient equal to 1.46 from Table 7.1 Thus, the total drift force = 1.46 × ρgL1 A = 358kN Since there are two mooring dolphins at each end of the floating storage module, the drift force acting on each mooring dolphin system is 358kN/2 = 179kN (see Fig 154 Steady Drift Forces on Storage Modules 7.4a) If we select the Model CSS-1450H_F0 rubber fenders (given by Shibata Marine Products, 2003), the strain caused by 179kN ( ≈ 18 Ton) force is less than 10% (see the performance curve of Model CSS-1450H_F0 rubber fenders in Fig 7.5) Note that the performance of the rubber fenders become unstable when the steady drift forces is larger than the reaction forces against 10% strain (see Chapter of the book by Wang et al., 2008) Thus, the selected rubber fenders for the mooring systems are able to withstand the steady drift forces acting on the storage modules Fig 7.5 Performance curve of rubber fender: Model CSS-1450H_F0 (SHIBATA Marine Products, 2003) The drift forces can also be attenuated by constructing floating breakwaters around the floating storage modules The steady drift forces acting on the floating modules with/without box-like floating breakwater and spaced at s/L = 0.15 are shown in Fig 7.6 The box-like floating breakwater considered has a dimension of 200m × 5m × 2.5m and placed in front of the floating modules as shown in Fig 7.6 The results show that the floating breakwaters are effective in attenuating the drift forces acting on the floating storage modules when the 155 Steady Drift Forces on Storage Modules wavelength λ/L is lesser than 0.67 Hence, by having a floating breakwater protecting the floating modules, we could go for a much smaller and cheaper mooring dolphin-rubber fender system Legends No breakwater With breakwater Fy /(ρgL1A ) (kN/kN) 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 (b) s/L = 0.15 0.0 0.5 1.0 1.5 2.0 2.5 λ/L(cm/cm) Fig 7.6 Steady drift forces on fully loaded storage modules with spacing s/L = 0.15 Wave amplitude A = 1m Water depth H = 30m Draft d = 9m 7.6 Concluding Remarks We have presented the solution technique based on the near-field approach for predicting the steady drift forces acting on a specific example of two floating fuel storage modules that are placed side-by-side The effect of the hydroelastic 156 Steady Drift Forces on Storage Modules interactions of the modules on the steady drift forces was found to be significant when the floating storage modules are placed closer to each other The steady drift forces computed from the proposed near-field approach were found to agree very well with that of Watanabe et al.’s (2000) far-field results The steady drift forces were found to increase with increasing wave frequencies The effect of the channel spacing on the steady drift forces was studied It was found that the drift forces increase when the floating modules are placed closer to each other The channel spacing proposed in Chapter 6, i.e s/L = 0.23 to 0.25 was found to be adequate in reducing the steady drift forces When the floating modules are placed very far apart, the steady drift forces become the same as their counterparts acting on a single floating module Hence, this provides a check on the validity and accuracy of the numerical model and scheme in predicting steady drift forces with allowance for the interactions of storage modules From the parametric study on the effect of channel spacing on the drift forces, it was found that the interactions behavior of the floating modules must be considered; otherwise the estimated steady drift forces are erroneous The steady drift forces were found to be governed by the wave runup term (i.e the 4th drift force component on the right hand side of Eq 3.12) when the floating modules are subjected to large wavelength (i.e λ/L = 0.67) On the other hand, when the wavelengths are very small, the velocity term (which is the summation of the 1st, 2nd and 3rd drift force components on the right hand side of Eq 3.12) becomes significant and must be considered when computing the steady drift forces From the computed steady drift forces, one can readily design the rubber fenders for the mooring system by using the performance chart of rubber fenders 157 Steady Drift Forces on Storage Modules prepared by the manufacturers This does away with the traditional and inaccurate method for estimating the drift forces using the Longuet-Higgins’ formula (1977) The latter approach requires a good guess of the wave reflected coefficient K r which is not easy Moreover, the formula does not take into account the interactions behavior of the storage modules The application of the formula usually leads to an over estimation of the drift forces Hence, the better prediction of the drift forces by using the proposed near-field method leads to a more economical design of the rubber fenders for the mooring system In sum, the developed numerical model based on the near-field approach enables engineers and naval architects to investigate the effect of steady drift forces acting on the floating storage modules when they are placed side-by-side The steady drift force computed using the near-field approach is more accurate as it includes the effect of diffracted and radiated waves as a result from the interactions of the floating storage modules The near-field method is also a more robust tool in computing the steady drift forces as compared to the far-field method because it enables the prediction of steady drift forces acting on each of the floating module separately when there are multiple floating modules placed next to each other 158 ... specific example of two floating fuel storage modules that are placed side-by-side The effect of the hydroelastic 156 Steady Drift Forces on Storage Modules interactions of the modules on the steady... example of a pair of floating storage modules (each module has a dimension of 122m × 50m × 10m and the details are given in Section 5.2) under operating condition The hydroelastic interactions of. .. floating storage modules design and site parameters given in Section 5.2, and assume that the two storage modules are held in place by mooring dolphin-rubber fending systems as shown in Fig 7. 4a