Hydroelastic responses and interactions of mega floating fuel storage modules 5

CHAPTER FIVE Hydroelastic Interactions of Storage Modules 5.1 Overview After establishing the validity, convergence and accuracy of the modified NC-QS element in predicting the hydroelastic deflections and stress resultants on the VLFS in the previous chapter, we will now perform the hydroelastic analysis on a specific example of FFSF in order to better understand the hydroelastic interactions behaviour of the floating modules The dimensions and sea states of the FFSF are given in Section 5.2 Experimental tests were carried out to validate the numerical model and scheme used in accessing the hydroelastic interactions behaviour of the adjacently placed floating modules With the confirmation of the correctness of the numerical model and scheme, extensive parametric studies are then carried out in order to investigate the effects of floating breakwater, channel spacing, draft, water depth and wave angle on the hydroelastic interactions behaviour between floating modules The stress resultants on the floating storage modules due to the interaction behaviour are also investigated 70 Hydroelastic Interactions of Storage Modules 5.2 Problem Definition of Floating Fuel Storage Facility Consider the FFSF comprising of two box-like floating fuel storage modules placed side-by-side at 25m apart (see Fig 5.1) Each module has dimensions of 122m × 50m × 10m, but the modules may have different drafts depending on the amount of fuel stored In an empty module, the draft is assumed to be 1m while in a fully loaded module, the draft is assumed to be 9m Fig 5.1 Specific example of floating fuel storage facility We consider the floating storage modules enclosed by floating breakwaters and the facility is sited in a narrow waterway or near shore as shown in Fig 5.2 Two boxlike floating breakwaters (with cross-sectional dimensions: 2.5m × 2.5m and 5m × 2.5m) are considered in the study in order to investigate the effect of breakwater sizes on the wave induced response of the floating storage modules 71 Hydroelastic Interactions of Storage Modules The incident wave angles considered range from θ = π / to π / , by assuming that the storage modules are shielded from incident waves at θ < π / The wave Module Module periods range from 3s to 9s and the water depth is 15m Fig 5.2 FFSF sited in a narrow waterway or close to shore 5.3 Experimental Test A scaled model test was conducted in the wave basin of the Hydraulic Engineering Laboratory of the National University of Singapore A scale ratio of 1:50 with no distortions in horizontal and vertical dimensions was adopted in modelling the aforementioned floating storage modules and breakwaters The experimental model was made from Perspex with thickness of 5mm Figure 5.3a shows the dimensions of the experimental test models Each floating storage model has dimensions of 2.44m × 1m × 0.2m and consists of a system of longitudinal and transverse bulkheads The models were placed at 0.5m apart The two floating Perspex breakwater models have cross sections of 5cm × 5cm and 10cm × 5cm, respectively, as shown in Fig 72 Hydroelastic Interactions of Storage Modules 5.3b The length and time variables were scaled according to the Froude number Vel gL = constant , where Vel is the velocity of the wave, g the gravitational acceleration and L = L2 The water depth in the wave basin was set to 0.3m, and the wave periods ranged from 0.42s to 1.27s which correspond to wavelengths λ/L = 0.12 to 0.78 The wave paddles were used to generate regular waves that propagated in a head sea direction (a) (b) Fig 5.3 Dimensions of (a) floating storage Perspex model (b) floating Perspex breakwater 73 Hydroelastic Interactions of Storage Modules Figure 5.4 shows the experimental setup in the wave basin of the laboratory Five potentiometers were installed along the centerline of Module (each with a spacing of 0.61m) in order to capture the vertical deflections of the floating module Aluminum brackets were used to prevent horizontal movements of the storage modules and floating breakwater The floating modules were thus allow to move vertically only under wave action or varying fuel load The vertical deflections of the floating Perspex models with and without breakwaters under a head sea condition will be used to check the deflections obtained from the developed numerical model Aluminum Bracket Fig 5.4 Experimental setup in wave basin of Hydraulic Engineering Laboratory, National University of Singapore 5.4 Numerical Model 5.4.1 Simplified Floating Storage Module The detail experimental Perspex model (with longitudinal and transverse bulkheads) consists of a huge number of degrees of freedoms, thereby making the 74 Hydroelastic Interactions of Storage Modules hydroelastic analysis on such model very time-consuming In order to reduce computational time in the hydroelastic analysis, the detail experimental model is usually simplified by an equivalent solid plate A 3-D finite element model of the experimental model is created in the FEM software ABAQUS as shown in Fig 5.5a The longitudinal and transverse bulkheads are modelled as well The particulars of the equivalent solid Mindlin plate shown in Fig 5.5b are obtained by keeping the length, width and height dimensions of the solid plate the same as the 3-D finite element model but the Young’s modulus E adjusted to match the first three vibration modes and natural periods T N of the finite element model as shown in Fig 5.6 Particulars of experimental model Length 2L2 = 2.44m Width 2L1 = 1m Thickness h = 0.2m Perspex Young’s modulus E = 1.27GPa Perspex thickness = 0.005m No of longitudinal bulkheads: No of transverse bulkheads: (a) 3-D FEM model Particulars of equivalent solid Mindlin plate Length 2L2 = 2.44m Width 2L1 = 1m Thickness h = 0.2m Equivalent Young’s modulus E = 38MPa (b) Equivalent solid Mindlin plate Fig 5.5 Figure depicting plan view of (a) 3-D FEM model (b) equivalent solid Mindlin plate 75 Hydroelastic Interactions of Storage Modules 1st vibration mode, TN = 0.0463s 1st vibration mode, TN = 0.0476s 2nd vibration mode, TN = 0.0379s 2nd vibration mode, TN = 0.0368s 3rd vibration mode, TN = 0.0166s 3rd vibration mode, TN = 0.0174s (a) Experimental model (b) Equivalent solid Mindlin plate Fig 5.6 First three vibration modes and natural periods of (a) experimental model (b) equivalent solid Mindlin plate 5.4.2 Simplified Floating Breakwater The equivalent solid plate for the floating breakwater is also obtained in the same manner as for the floating storage modules However, only breakwater B shown in Fig 5.4 is modelled (neglecting floating breakwaters A and C) for the numerical analysis in order to reduce the computational time Figure 5.7 shows the comparison between the deformations of the FFSF with and without breakwaters A and C under a head sea condition Results show that the deformation shapes are the same for the 76 Hydroelastic Interactions of Storage Modules floating structure with and without floating breakwaters A and C The percentage error in the maximum deflection without breakwaters A and C with respect to their counterparts with breakwaters A and C is less than 3.2% Such a small error shows that even by neglecting breakwaters A and C under a head sea condition, a rather high accuracy of the computational results could still be achieved 77 (wmax )i / A = 0.4253 Floating breakwater (wmax )ii / A = 0.4117 Simplified floating breakwater (wmax )ii / A = 1.0383 (b) λ/L = 1.0 Error = (wmax )ii − (wmax )i / (wmax )i = 1.25% 78 Fig 5.7 Deformation shapes and percentage errors in maximum vertical deflection of FFSF with and without floating breakwaters A and C for wavelength (a) λ/L = 0.7 (b) λ/L = 1.0 Water depth H = 0.3m Head sea Hydroelastic Interactions of Storage Modules (wmax )i / A = 1.0514 (a) λ/L = 0.7 Error = (wmax )ii − (wmax )i / (wmax )i = 3.20% Hydroelastic Interactions of Storage Modules 5.4.3 Convergence Tests In performing the hydroelastic analysis of VLFS, the solution of the boundary integral equation (BIE) of the water involves the largest computational time/memory In order to reduce the computational time, we use the constant panel method (CPM) to solve for the BIE where the numerical integration is evaluated at the middle of the boundary element (see Appendix D) A convergence test has to be carried out in order to: • determine the mesh size needed for the convergence of numerical results • assess the rate of convergence of the BIE by using the CPM We carried out a convergence test on the equivalent solid Mindlin plate (obtained from the previous section) under a head sea condition (i.e incident wave angle θ = π / ), wavelength λ/L = 1.0 (i.e λ = L = 2.44 m) and the water depth H of 0.3m For the convergence study, we adopt the reference number of plate elements N which specifies the complicated mesh design with the total number of elements q = ( ) n1 × n + 2n3 n1 + n , where n1 = Integer(2 NL1 / λ ) is the number of elements along the width L1 , n = Integer(2 NL2 / λ ) the number of elements along the length L2 and n3 = Integer( Nh / λ ) the number of elements along the thickness h This number N will be increased, starting from 5, 10, 15, 20, and so on The error between the deflection surfaces associated with subsequent increase of N is defined as ε N +5 = ∫ w N +5 (x ) − w N (x ) dx , ∆ N = 5, 10, 15, 20,… (5.1) 79 Hydroelastic Interactions of Storage Modules 5.6.3 Effect of Draft The effect of draft on the hydroelastic responses of the floating storage modules is investigated The vertical deflections of empty and half loaded floating storage modules for four different wavelengths λ/L = 0.32, 0.55, 0.78 and 1.00 are compared in Figs 5.16a–d Results show that the half loaded floating storage modules heave with smaller amplitudes due to the reduction of pressure distributions on the modules’ bottom surfaces and the increase of added mass and added damping This shows that a larger draft has a significant effect in reducing the deflection of the floating modules This means that the fully loaded storage modules will experience an even smaller deflection as compared to the partially loaded storage modules for a given wave condition provided that resonance does not occur Next, we would like to investigate the interactions of the floating storage modules when they are subjected to five different loading combinations as described in Table 5.2 The maximum vertical deflections of the floating storage modules which correspond to these five sets of loading cases are presented in Fig 5.17 The thin dashed lines ( ), dotted lines ( LL ) and solid lines ( _ 3, respectively; whereas the thick solid ( ) represent Cases 1, and ) and dashed lines ( ) represent Cases and 5, respectively Each set of thin lines shows the maximum vertical deflections for Modules and 2, where Module is represented by the line with close squares ( ) whereas Module by the line with open squares ( ) There are no close or open squares for Cases and (thick solid and dashed lines) as the deflections of Modules and are the same 95 Hydroelastic Interactions of Storage Modules A comparison study between the five sets of results shows that the relative deflections between Modules and are significant under Load Cases and We observed that the sets of thin lines are bounded by the thick solid and dashed lines (except for Load Case when subjected to wavelength λ/L = 0.67), which imply that the responses of the floating modules are greatest when both floating modules are empty and smallest when both modules are fully loaded This shows that the loadings (and hence the drafts) of the floating modules affect the relative motions and maximum vertical responses of the floating modules under wave actions significantly 96 0.10 Empty Half loaded 0.05 0.00 (a) λ/L = 0.32 0.0 0.2 0.4 0.6 0.8 1.0 0.4 wmax /A (cm/cm) wmax /A (cm/cm) 0.15 y/L (cm/cm) 0.0 (b) λ/L = 0.55 0.0 0.2 0.4 0.6 0.8 1.0 0.2 (c) λ/L = 0.78 0.0 0.2 0.4 0.6 0.8 1.0 y/L (cm/cm) wmax /A (cm/cm) 0.8 0.6 0.4 0.2 0.0 (d) λ /L = 1.00 0.0 0.2 0.4 0.6 0.8 1.0 y/L (cm /cm ) 97 Fig 5.16 Maximum vertical deflections of empty and half loaded floating storage modules for wavelength (a) λ/L = 0.32 (b) λ/L = 0.55 (c) λ/L = 0.78 (d) λ/L = 1.00 Water depth H = 0.3m Hydroelastic Interactions of Storage Modules wmax /A (cm/cm) 0.1 1.0 0.3 0.0 0.2 y/L (cm/cm) 0.4 0.1 0.3 Hydroelastic Interactions of Storage Modules Table 5.2 Combinations of loadings for storage Modules and Loading Combinations Module Module Fully loaded Half loaded Empty Empty Case Fully loaded Case Half loaded Case Case Case Fully loaded Empty Empty Fully loaded draft, d = 0.02m (empty), 0.10m (half loaded), 0.18m (fully loaded) 1.4 Loading configurations Case 1.2 wmax /A (cm/cm) 1.0 0.8 0.6 Case Case Case Case Module Module Module Module Module Module Modules & Modules & 0.4 0.2 0.0 0.4 0.5 0.6 0.7 0.8 0.9 1.0 λ /L (cm/cm) Fig 5.17 Maximum vertical deflections of floating storage modules under different loading combinations 98 Hydroelastic Interactions of Storage Modules 5.6.4 Effect of Water Depth Next, we investigate the effect of different water depths H on the hydroelastic responses of the two empty floating storage modules with floating BW2 The regular wave is assumed to propagate in a head sea We plot the normalised maximum vertical deflections at the front end of the empty floating storage modules with respect to its corresponding wavelength λ/L for different water depths (H = 0.2m, 0.4m, 0.6m) in Fig 5.18 It can be seen from Fig 5.18 that there is an increase in maximum deflection of the floating modules with respect to the wavelength λ/L However, the maximum deflection of the floating modules starts to converge to a constant value when the wavelength λ/L > This is because the floating modules are heaving in approximately the same phase as the incident wave at λ/L > For a given wavelength λ/L, the maximum deflection of the floating modules also increases as the water depth decreases This is due to the increase in interactions between the seabed and bottom surfaces of the floating storage modules, resulting in an increase in the pressure acting on the bottom surfaces of the floating storage module 99 Hydroelastic Interactions of Storage Modules 1.4 (wmax)y=0/A (m/m) 1.2 1.0 H = 0.2 m H = 0.4 m H = 0.6 m 0.8 0.6 0.4 0.2 0.0 0.0 0.5 1.0 1.5 2.0 λ /L (m/m) Fig 5.18 Maximum vertical deflection of empty floating storage module for different water depths H 5.6.5 Effect of Wave Angle Next, we carry out hydroelastic analysis on the two empty floating storage modules with and without floating breakwaters for incident wave angles θ = π / (head sea) and π / The floating storage modules that are placed in a narrow waterway/near shore as shown in Fig 5.2 are shielded from wave coming in the beam sea direction, i.e θ = The floating breakwater used has a width of 10 cm The nondimensionless wavelength λ/L is taken as 0.4 The numerical results are shown in Fig 5.19 It can be seen that the reduction of the response due to the presence of floating breakwater is remarkable and the floating storage modules are subjected to the worst-case scenario under head sea condition 100 (b) 101 5.19 Maximum vertical deflections of two empty floating storage modules with and without breakwater at wave angle (a) θ = π / (b) θ = π / Water depth H = 0.3m Wavelength λ/L = 0.4 Hydroelastic Interactions of Storage Modules (a) Hydroelastic Interactions of Storage Modules 5.7 Principal Stresses on Storage Modules The stress resultants on the floating storage modules could be derived from the hydroelastic deflections and bending rotations based on Eqs (2.13a-c) These stress resultants could be used in computing the principal stresses of the floating modules for the design of the structural slabs The principal stress σ ps is given as (Hibbeler, 2000) σ ps = σ x +σ y σ x −σ y +      + τ xy   (5.3) where σ x and σ y are the normal stresses in x and y direction, respectively, and τ xy the shear stress It is to be noted that the normal stresses are derived from the bending moments whereas the shear stresses from the shear forces We consider the same floating fuel storage modules defined in Section 5.2 with each module having dimensions of 122m × 50m × 10m The slabs and bulkheads of the floating storage modules are usually strengthen by using precast or reinforced concrete, but for simplicity, we will assume that the floating modules to be made of plain concrete By carrying out the hydroelastic analysis on the floating storage modules, we found that the top slab of the floating module is in compression whereas the bottom slab is in tension We will only focus on the bottom concrete slab because the plain concrete is weak in tension It is to be noted that the plain 102 Hydroelastic Interactions of Storage Modules concrete has a relatively low allowable tensile stress, i.e σ t = 4.36MPa as compared to its allowable compressive stress i.e σ c = 40MPa (Garber, 2006) By considering that the floating modules having a bottom concrete slab with thickness of 40cm, the principal stresses distributed on the bottom slab of Module are presented in Fig 5.20 We assumed that the floating storage modules are subjected to three different wave periods T = 5, 6, and 7s and three different channel spacings s/L = 0.1, 0.2 and ∞ for comparison purposes Figure 5.20 shows that the principal stresses vanish at the free edges of the concrete slab This is because the bending moments and shear forces satisfy the natural boundary conditions of the free-edge plate (see Eqs 2.13a–c) When the floating storage modules are placed far apart (i.e s/L = ∞ ), the principal stresses distributed on the bottom slab are found to be symmetrical with respect to the module’s centerline This shows that there are hardly any interactions between the floating modules when spaced at s/L = ∞ apart From Fig 5.20, it can be seen that the maximum principal stresses distributed on the bottom slab are very small as compared to the allowable tensile stress, i.e σ t = 4.36MPa For comparison purpose, we carried out a static analysis on the concrete floating storage module in the FEM software ABAQUS The details of the FEM model are given in Table 5.3 The maximum principal stresses distributed on the bottom slab of the floating module are shown in Fig 5.21 Figure 5.21 shows that the maximum stresses due to the static loads (i.e 4.18MPa, see Fig 5.21) are much larger as compared to the maximum stresses due to the hydroelastic response (i.e 103 Hydroelastic Interactions of Storage Modules 0.74MPa, see Fig 5.20), thus the stresses due to the static loads will govern the design of the structural components Table 5.3 Particulars of 3-D finite element model for concrete floating storage modules Dimensions Material Young’s modulus E Poisson’s ratio ν Concrete density No of longitudinal bulkheads No of transverse bulkheads Concrete slab thickness Loadings Buoyancy force 122m × 50m × 10m Plain concrete 24GPa 0.2 2400 kg/m3 40cm • 62784 N/m2 due to fuel loads acting on bottom slab • Selfweight of concrete module 10055.25 N/m 104 λ/L = 0.32 max λ/L = 0.78 = 0.74MPa s/L = ∞ 105 5.20 Principal stresses (due to hydroelastic response) on bottom slab of empty concrete floating storage module under different wavelengths λ/L and channel spacings s/L Water depth H = 0.3m Axis of symmetry at x = Waves propagate in a head sea direction from the left Hydroelastic Interactions of Storage Modules s/L = 0.2 s/L = 0.1 σ ps λ/L = 0.55 106 Hydroelastic Interactions of Storage Modules Fig 5.21 Principal stress (due to static loadings) distributed on bottom slab of floating storage module Hydroelastic Interactions of Storage Modules 5.8 Concluding Remarks We have presented the hydroelastic responses and hydrodynamic interactions of the two specific example of floating storage modules placed side-by-side with the presence of floating breakwaters The hydroelastic interaction behavior between the storage modules was found to be significant in affecting the response of the storage modules In order to reduce computational time, we used an equivalent solid Mindlin plate that has the same dynamic properties as the actual FFSF for the hydroelastic analysis The floating breakwater is also treated as an equivalent plate We have proved herein that these simplified numerical models could be used to obtain the hydroelastic deflections of the FFSF without much loss of accuracy by comparing with experimental test results Besides that, the convergence tests showed that converged deflection results can be achieved with relatively small number of plate elements/meshes, thereby further reduced the computational time needed for the hydroelastic analysis Based on the hydroelastic responses of the floating modules, we found that the presence of floating breakwater significantly decreases the vertical deflections of the floating storage modules especially when the wavelength λ/L is smaller than 0.67 The effectiveness of the floating breakwater in reducing the vertical deflections of the floating modules increases with the width of the floating breakwaters Therefore, it is recommended that floating breakwaters with a larger width be used in order to minimise the motion of the floating storage modules 107 Hydroelastic Interactions of Storage Modules In the parametric studies, we found that the vertical responses of the floating storage modules are also affected by the channel spacing, loading in the floating storage modules, water depth, incident wavelength as well as the direction of the incoming wave We found that the response (either elastic or rigid) of our floating storage modules depends on the incident wavelength and flexural rigidity As a rapid check, we can determine the responses of the floating structure by comparing the ratios of L/λ and L/λc as proposed by Suzuki and Yoshida (1996), where λc is the characteristic length which is a function of the ratio of the flexural rigidity D to the buoyancy force k c , i.e λc = 2π (D / k c ) The response of the floating structure is dominated by the elastic modes if these two ratios are greater than unity and hence, hydroelastic analysis has to be performed in order to simulate the deformation of the structure correctly We found that the worst-case scenario that results in the maximum deflection of the floating storage modules sited in a narrow channel corresponds to the case where the floating modules are empty and encountering a head sea ( θ = π / ) The relative deflections between the two floating storage modules of different loadings were observed to be the largest under Load Cases (fully loaded + empty) and (half loaded + empty) The vertical deflections of the floating storage modules were also found to decrease with increasing channel spacing Under the same sea state, the response of the floating modules is also affected by the changes in water depth We observed that the deflection of the floating modules (when subjected to the same wavelength) increases as the water depth 108 Hydroelastic Interactions of Storage Modules gets smaller This is due to the longer wavelength in shallow waters and the effect of interaction between the seabed and bottom surfaces of the floating structures We also examined the principal stresses on the floating storage modules The principal stresses due to the hydroelastic responses were found to have negligible effect towards the design of the structural components as compared to their counterparts due to static loads In sum, the developed numerical model and computational technique enable engineers and naval architects to investigate the hydroelastic responses and hydrodynamic interactions behavior of the floating storage modules by taking into consideration the effect of floating breakwater As the floating fuel storage modules may be subjected to different drafts due to varying payload, green water might occur on the deck when wave propagates through the channel formed by the two loaded floating storage modules Under such condition, we need to take into consideration the effect of wave runup for the suitable channel spacing design of the floating fuel storage modules This study will be carried out in the next chapter and it involves a trade-off decision between minimising the hydroelastic responses of the empty floating modules and maximising the loading capacities of the floating modules 109 ... 0.4 Hydroelastic Interactions of Storage Modules (a) Hydroelastic Interactions of Storage Modules 5. 7 Principal Stresses on Storage Modules The stress resultants on the floating storage modules. .. Storage Modules 5. 6.1 Effect of Floating Breakwater The effect of floating breakwater on the hydroelastic responses of the floating modules is shown in Figs 5. 8 and 5. 9 Both floating BW1 and BW2 contribute... Hydroelastic Interactions of Storage Modules 5. 6.3 Effect of Draft The effect of draft on the hydroelastic responses of the floating storage modules is investigated The vertical deflections of