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Wang, J.; Derradji-Aouat, A.
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POAC11-172
Numerical Assessment for Stationary Structure (Kulluk)
in Moving Broken Ice
J. Wang and A. Derradji-Aouat
Institute for Ocean Technology, National Research Council, St. John’s, CANADA
ABSTRACT
Fluid-Structure Interaction (FSI) is vital to analyze many hydrodynamic associated multi-physics problems such as structure-ice-water interaction. In pack ice condition, broken ice pieces are floating around the structure and they affect the structure’s stationkeeping performance particularly a moored structure. Generally a moored structure should be supported by good ice management and the typical size of managed ice would be about 10 - 50 m. For this scenario, major parameters for the performance assessment would be appropriate hydrodynamic simulation, accurate ice friction calculation and ice clearing behavior.
The aim of this paper is to assess the global loads of the moored structure (known as Kulluk) by moving broken ice floes that are basically managed ices. For hydrodynamic simulation, ALE (Arbitrary Lagrangian Eulerian) is used to assess the Fluid Structure Interaction (FSI) problem based on the penalty method. Combined hydrodynamic and structural assessment would provide better understanding of multi-physics problems without significant simplification. Three different ice concentrations (low, medium and high) are simulated and numerical results are compared and discussed with full-scale measurement data (Wright et al., 1999 and 2000).
1. INTRODUCTION
The Kulluk is a moored, downward breaking conical drilling vessel and it was designed to withstand the impact of 1.2 m thick level ice (Wright, 1999 and 2000). The Kulluk was operated in the Beaufort Sea in late 1980s to early 1990s and extensive ice interactions were indirectly measured in the field. These full-scale data are very valuable to reassess this type of structure in different ice-covered areas. Consequently comprehensive data analysis were carried out by Wright (1999 and 2000) in order to estimate global ice loads on a moored structure in the field of the Grand Banks, which is located off Canada’s East Coast. It was also mentioned that the current trend for future oil field development on the Grand Bank is to use a floating system.
Floating drilling vessels (such as the Kulluk) or self-propelled drillships have a number of benefits such as less capital cost and fast installation compared to Gravity Based Structures (GBS). In the deep sea, these floating vessels would be more attractive because GBS is not commercially available. In early 2010, a drillship was used for an exploration well in deep water (about 2600m) in the Orphan Basin, which is about 400 km northeast St. John’s. Recently, the
POAC’11
Montréal, CanadaProceedings of the 21st International Conference on
Port and Ocean Engineering under Arctic Conditions July 10-14, 2011 Montréal, Canada
Flemish Pass in the Grand Banks, which is about 500 km off Newfoundland and Labrador, is about to be explored and its water depth is from 1100 m to 2900 m. Pack ice or small
iceberg/bergy bits occurrence is expected in these areas and accurate ice load assessment is required.
In this research, the idealized form of Kulluk is numerically assessed based on three different pack ice concentrations; 20 %, 50 % and 80 % using a commercial Finite Element package (LS-DYNA, www.lstc.com). Pack ice is assumed to have the drift speed of 1 knot (0.51 m/s). Water and air are modeled with the Eulerian method whereas the Kulluk and pack ice are modeled with the Lagrangian method. Both contact (between Lagrangians) and coupling (between Lagrangian and Eulerian) are based on the penalty method. Full-scale measurement data from Wright (1999 and 2000) are used to validate the numerical results. Details of Finite Element formulation including penalty method are omitted here and referred to Wang and Derradji-Aouat (2010) and LS-DYNA theory manual (2006).
2. PREPARATION FOR NUMERICAL MODELING 2.1 Finite Element (FE) Model for the Kulluk
The Kulluk model was created by using ANSYS Workbench Ver. 12.1. A half of the 2D model was sketched and rotated with regard to the vertical axis (z) to generate the 3D model. Uniform Quad/Tri elements are used with the mesh size of 1 m. The aspect ratio is about 1. No mooring lines were modeled. Main dimension for the Kulluk is shown in Table 1.
Table 1: Dimension of the Kulluk in Full Scale
Diameter at deck 81 m
Diameter at waterline 70 m
Diameter at hull bottom 62 m
Depth 18.4 m
Draft 11.5 m
Displacement 28000 tonnes
Cone angle 31.4 degree
2.2 Numerical Ice Model
For the managed ice interaction problem, ice friction would be one of the major parameters to affect the global ice load. Small size managed ice pieces are expected to pass along the Kulluk rather than to be broken with flexural bending failure. Ice is modelled as a rigid body and the Young’s modulus of 5.0 GPa is used.
2.2.1 Ice-Structure Friction Coefficient
Gagnon and Molgaard (1991) carried out crushing friction experiments on freshwater ice. Their finding was that the friction coefficient was a decreasing function of increasing sliding speed and temperature. Mild steel was used to measure the friction against the ice and its surface roughness
was 0.5 ~ 0.7 m. They had three different temperatures (-5°C, -10°C, and –19°C) and four different sliding speeds (0.06 m/s, 0.17 m/s, 0.4 m/s and 0.82 m/s). They used different ice types such as small grain (~0.7cm diameter), large grain (>3 cm diameter) columnar-grained bubble-free ice and randomly oriented fine-grain ice. They also showed that these textures, fabric or the presence of bubbles did not affect the frictional coefficient. In this report, therefore, sea ice was assumed to have similar frictional coefficient as that of freshwater ice. Regression equations for these frictional coefficients are in Table 2. Since full-scale measurement from Wright (2000) was corrected to the air temperature of –10°C, the frictional curve at –10°C was used for the present calculation.
Table 2: Regression Equations for Ice Frictional Coefficient
Temperature (x) -5°C -10°C -19°C Regression Eq. ) 1997 . 1 exp( 0394 . 0 x y ) 1016 . 1 exp( 0649 . 0 x y ) 1897 . 1 exp( 0932 . 0 x y
2.3 Ice Shape and Flow
In the field, ice around the structure was managed by two icebreakers and the typical size of broken ice pieces was from 10 m to 50 m (Wright, 2000). For this numerical simulation, the nominal length of ice used is 15 m. It is also able to consider the interaction between ices more easily. For example, 20 % ice concentration can be determined as 20 % of the Kulluk contacted with ice and the contact length is roughly 15 m (20 % of the diameter of the Kulluk at the waterline). In order to simulate ice drifting motion, water (fluid) domain moves at a constant velocity of 0.51 m/s. Ice drift speed in the field was from 0.2 m/s to 0.5 m/s. Ice is then floating and drifting due to the moving water.
2.4 Simulation Conditions
The main interest in this simulation is to assess interaction behaviour between the Kulluk and ice that occurred mainly at the free-surface. Since significant ice submergence did not happen in several preliminary numerical tests, the depth of water domain and the height of air domain are 6 m and 2 m, respectively. Water and air domains are 128 m wide and 112 m long. A front half of Kulluk was modelled. Four sides (left, right, front and back) of water and air domain have been covered by thin “Reservoir” elements that act as a non-reflecting boundary condition. The front part of water and air domains has two reservoirs with pressure outflow option and the rest of the parts have reservoirs with pressure inflow option. Water elements have a constant velocity of 0.51m/s (current speed) towards the Kulluk (See Fig. 1). The Kulluk was modelled as a rigid and fixed structure.
Figure 1: Details of numerical domain, 150,000 elements
3. NUMERICAL SIMULATION
3.1 Numerical Results with Square Shaped Ice
Three different concentrations were used: 20 % 50 % and 80 % (Fig. 2). Most ice pieces have a square shape and some ices at the edge have rectangle shape in order to match the given
concentration. All ice pieces are slightly tilted in the lateral direction to derive nature ice movement.
Figure 2: 80%, 50% and 20% concentration (1) 80 % concentration
Total 100 sec simulation time was used. Simulation snapshots of 38.5 sec, 63.2 sec and 99.3 sec are shown in the Fig. 3. The figure also shows the load curve with time. During the multiple interactions/accumulations, the average loads are from 3 to 5 MN. It is noted that peak loads are measured at 38.5 sec, 63.2 sec and 99.3 sec.
At 38.6 sec, first row of ice started to accumulate with next row of ices and the measured loads are up to 5 MN.
At 63.2 sec, another peak load was measured. Some of first row ices in front are still accumulated and interacted with the structure. The load of 5 MN is measured. At 99.3 sec, some of the first row ices still stay and affect. Third row of ice starts to
It is noted that the result graph (4) in Fig. 3 the load seems to keep increasing near 100 sec, but multiple ice pieces are already accumulated and ice pressure is built up. Consequently the
concentration is increasing (more than 80 %). In the field, this accumulation/ice pressure build-up can only happen when the ice concentration is more than 90 % (Wright et al., 2000).
With current ice concentration, ice pieces are easily accumulated. When the ice started to be accumulated, the concentration is not valid anymore because at the contact area, concentration would be more than the initial concentration and consequently ice pressure will be built up. Since the ice is modeled as a rigid body, ice cannot be deformed to relief its pressure and it may cause the higher possibility to accumulate ice pieces. It could be one of the demerits for the current rigid modeling.
Figure 3: 80% Concentration at 38.6 sec (1), 63.2 sec (2), and 99.3 sec (3) and result (4) (2) 50 % and 20% concentration
Except for the ice concentration, all the simulation conditions are identical to the 80 %
concentration case. For 50 % case, there are several peak loads at 20 sec, 49.8 sec, and 70.2 sec. Total load with time series is shown in Fig. 4 and the average load level is from 0.5 to 2 MN. For 20% case, there are no significant peak values, and the average load range of this concentration is from 0.2 to 0.8 MN. Fig. 4 shows the load curve with time.
(1) (2)
Figure 4: Numerical Results for 50% (left) and 20% (right) Concentrations
3.2. Numerical Results with Random Shaped Ice
Random shape of ice pieces are generated and simulated with the same condition as those in square shaped ice cases. The interaction behavior and load levels are similar to those with the rectangle ice cases. Ice shape is not likely a major parameter to consider in the current simulation. Three different concentrations are shown in Fig.5 and numerical results for 80% and 50% are shown in Fig. 6.
Figure 5: 80%, 50%, and 20% concentrations with random shaped ice
3.3 One Square Shaped Ice Simulation
A rationale behind this simulation is to avoid any ice-ice interaction that can cause an “ice pressure” event (ice accumulation) at the lower concentration (80%). Again, in the field, this infrequent ice pressure build-up can only happen when the ice concentration is more than 90 % (Wright et al., 2000). Part of the reason for occurring an ice pressure event in the present simulation is due to the rigid modeling as explained earlier. For the clarification of the term of “ice pressure,” below phrase shows a good example to describe the meaning of “ice pressure” from the field data:
“A significant ice pressure event that occurred in mid December (when strong persistent onshore winds compressed the pack ice against the nearby landfast ice edge) caused global loads of more than 400 tonnes, …(Wright, 1998)”
This simulation would be useful to evaluate the ice loads without ice pressure effect. The calculated unit ice load will be linearly extrapolated based on the concentration. In the present simulation, one ice block is 15 m long and the diameter of the Kulluk (or a projected length of the Kulluk in x-direction) is 70 m. 20 % ice concentration means 20 % of the Kulluk, which is 14 m, will experience the ice loads and it can be simulated using one ice block (15 m) multiplied by 0.933 (14/15). At the same way, 50 % and 80 % concentration would need 2.3 and 3.7 ice blocks. The total loads without interaction of ice pieces are then unit ice load multiplied by the number of ice blocks corresponding to the ice concentration.
Fig. 7 shows the simulation snapshot at 49.2 sec (maximum load is recorded) and the load curve with time. The ice piece is interacting with the Kulluk from 37 sec to 75 sec. The average load is 0.34 MN (34.6 tonnes) and its standard deviation is 0.25 MN (25.1 tonnes). Table 3 shows the load estimation using one ice load (unit ice load) against the Kulluk and each concentration is considered using multiplier based on the contact area.
Table 3: Load Estimation using One Ice Load with Multiplier Based on the Concentration Multiplier Average Load (MN) Standard Deviation (MN)
One ice piece 1 0.34 0.25
20% 0.93 0.32 0.23
50% 2.33 0.79 0.57
80% 3.73 1.27 0.92
3.4 Comparison with Full Scale Measurement
Simulation results are compared with full-scale measurement data by Wright (2000) based on the pack ice concentration. In Figs. 8 and 9, all black solid squares are full-scale measurements from Fig. 4.9 in Wright (2000) and numerical results are overlaid on the figure. A black solid line in the figures shows the upper bound of the full-scale measurement. The error bars indicate a
standard deviation (SD). For the field data, it was reported that ice drifting speed was varied from 0.2 m/s to 0.5 m/s and sometimes a convergent (pressured) ice can lead far more than the average magnitude, which were not included in Fig. 4.9 in Wright (2000). The full-scale measurement data used in these figures include more than 600 ice interaction events in various pack ice concentrations without ice pressure. Brief explanation for ice pressure is addressed in 3.3. The left figure in Fig. 8 shows the comparison between the numerical results from the squared shaped ice and full-scale measurement. For lower concentration (up to 50 %), comparison shows a reasonable agreement. For the higher concentration (80 %) numerical results show higher load than the measurement. The main reason would be ice accumulation and this can increase the ice pressure and concentration at the contact area. The right figure in Fig. 8 shows the comparison of the random shaped ice simulation results. At the lower concentration, it shows fairly good
agreement. At the 80 % concentration, the load level is still slightly higher than measured value. Again, higher concentration can make higher ice pressure and accumulation, which can lead higher ice load. In the full-scale measurement, data did not include the load with ice pressure. From squared shaped ice and random shaped ice simulations, both results do not show distinctive differences with regard to the load level. However, due to the rigid modeling, unusual ice shape can be easily stuck in other ice pieces and elevate the load level significantly.
Pack Ice Concentration
Loa d (t onne s ) 2 4 6 8 10 0 50 100 150 200 250 300 350 400 450 500 550 Numerical (Square)
Pack Ice Concentration
Loa d (t onne s ) 2 4 6 8 10 0 50 100 150 200 250 300 350 400 450 500 550 Numerical (Random)
Figure 8: Comparison between Squared (left) and Random Shaped (right) Ice Simulation and Full-scale Measurement
Fig. 9 shows the one ice piece simulation with multiplier based on contact area corresponding to the concentration (see Table 3). Since the full-scale data did not include any ice pressure case, this simulation result shows excellent agreement with full-scale measurement. As the
concentration is higher, interaction between ice pieces is more inevitable and ice pressure cases are easily occurred.
Pack Ice Concentration L oa d (t on ne s ) 2 4 6 8 10 0 50 100 150 200 250 300 350 400 450 500 550
Numerical (One Ice)
Figure 9: Comparison between One Square Shaped Ice Simulation and Full-scale Measurement
4. CONCLUSIONS AND RECOMMENDATIONS
A downward breaking conical structure, Kulluk, in pack ice condition is simulated using explicit finite element method (LS-DYNA). Three different pack ice conditions are used and ice is moving at 0.51 m/s towards the Kulluk. Both water and air are included in the calculation to present appropriate hydrodynamic effect. Square ice blocks, which are 15 m long, 15 m wide and 1 m thick are slightly tilted horizontally and deployed to float in the water.
For the full simulation (half model), rigid ice was used. Three different ice concentrations are considered based on the area ratio between field area and ice area. For lower concentration (up to 50 %) numerical simulation and full-scale measurement showed a good agreement. For the high concentration (80 %) numerical results showed slightly higher average value due to ice
accumulation. From the one ice piece simulation without consideration of interaction between ice pieces, it shows good agreement with the full-scale measurements. These estimates would be valid if there is no ice accumulation/ice pressure at lower concentration, but the concentration is close to 100 % then appropriate ice accumulation/ice pressure consideration is required.
Ice accumulation or pressure will be associated with several important features such as cohesion, friction and interlocking. At this time, only friction is considered because the simulation
condition has up to 80% ice concentration. As a future work, in order to evaluate more severe case such as ice pressure ridge interaction, more elaborate ice modeling is required.
From the present study, some recommendations are as follows:
Deformable body modeling for ice with appropriate failure model
Mooring line modeling for the Kulluk
- Fixed model and moored model would have difference with regard to physical behavior and load level.
More realistic ice shape
- It could derive better results, i.e. actual satellite image in upstream could be a good input data.
CFD coupled flow evaluation
- More elaborate fluid modeling would result more reliable assessment.
5. ACKNOWLEGEMENT
This is a part of collaborative research between the National Research Council Canada’s Institute for Ocean Technology (NRC-IOT) and American Bureau Shipping (ABS). ABS’s financial support is gratefully acknowledged.
6. REFERENCES
Gagnon, R. and Molgaard, J., 1991, “Crushing Friction Experiments on Freshwater Ice,” Proc. IUTAM-IAHR Symposium, S. Jones et al., ed., Springer, Berlin, pp.405-421.
LS DYNA Theory Manual, 2007, Livermore Software Technology Corporation
Wang, J. and Derradji-Aouat, A., 2010 “Ship Performance in Broken Ice Floes – Preliminary Numerical Simulation,” IOT Report, TR-2010-24.
Wright, B., 1998, “Moored Vessel Stationkeeping in Grand Banks Pack Ice Conditions,” PERD/CHC Report 26-189.
Wright, B., 1999, “Evaluation of Full Scale Data for Moored Vessel Stationkeeping in Pack Ice,” PERD/CHC Report 26-200.
Wright, B., 2000, “Full Scale Experience with Kulluk Stationkeeping Opoeration in Pack Ice (With Reference to Grand Banks Developments),” PERD/CHC Report 25-44.
