Author Contributions
Conceptualization, L.Z.; methodology, L.Z.; software, L.Z. and M.S.; validation, L.Z. and S.D. and Y.H.; formal analysis, L.Z. and F.D.; investigation, L.Z; resources, L.Z. and F.D.; data curation, Y.H.; writing—original draft preparation, S.D; writing—review and editing, L.Z.; visualization, M.S.; supervision, L.Z.; project administration, L.Z.; funding acquisition, L.Z. and S.D. All authors have read and agreed to the published version of the manuscript.
Figure 1.
Discretization of the waterline.
Figure 1.
Discretization of the waterline.
Figure 2.
Calculation loop of the icebreaking force.
Figure 2.
Calculation loop of the icebreaking force.
Figure 3.
Illustration of the ice resistance and net thrust.
Figure 3.
Illustration of the ice resistance and net thrust.
Figure 4.
Ice tank of the Krylov State Research Center (KSRC).
Figure 4.
Ice tank of the Krylov State Research Center (KSRC).
Figure 5.
Photographs of the ship model. (a) Bow view (b) Stern view.
Figure 5.
Photographs of the ship model. (a) Bow view (b) Stern view.
Figure 6.
Side view illustration of the test system.
Figure 6.
Side view illustration of the test system.
Figure 7.
Model test of ahead running.
Figure 7.
Model test of ahead running.
Figure 8.
Initial positions of the ship and ice field.
Figure 8.
Initial positions of the ship and ice field.
Figure 9.
Time series of the total ice force and ice force components.
Figure 9.
Time series of the total ice force and ice force components.
Figure 10.
The breaking process of the ice-hull interaction from 2.5~9.5 s (a) t1 = 2.5 s (b) t2 = 8.1 s (c) t3 = 9.5 s.
Figure 10.
The breaking process of the ice-hull interaction from 2.5~9.5 s (a) t1 = 2.5 s (b) t2 = 8.1 s (c) t3 = 9.5 s.
Figure 11.
Part of the total ice force and ice force components.
Figure 11.
Part of the total ice force and ice force components.
Figure 12.
The breaking process of the ice-hull interaction from 65.7~67.4 s (a) t4 = 65.7 s (b) t5 = 66.4 s (c) t6 = 66.7 s (d) t7 = 67.4 s.
Figure 12.
The breaking process of the ice-hull interaction from 65.7~67.4 s (a) t4 = 65.7 s (b) t5 = 66.4 s (c) t6 = 66.7 s (d) t7 = 67.4 s.
Figure 13.
Simulated ice resistance as a function of the time step length.
Figure 13.
Simulated ice resistance as a function of the time step length.
Figure 14.
Computation time as a function of the time step length.
Figure 14.
Computation time as a function of the time step length.
Figure 15.
Simulated global ice load as a function of Cl.
Figure 15.
Simulated global ice load as a function of Cl.
Figure 16.
Simulated global ice load as a function of Cf.
Figure 16.
Simulated global ice load as a function of Cf.
Figure 17.
Time series of the ice forces during the ahead running operation in ice sheet with a thickness of 1.3 m. (a) Test 11 (b) Test 12. (c) Test 13 (d) Test 14.
Figure 17.
Time series of the ice forces during the ahead running operation in ice sheet with a thickness of 1.3 m. (a) Test 11 (b) Test 12. (c) Test 13 (d) Test 14.
Figure 18.
Time series of the ice forces during the ahead running operation in ice sheet with a thickness of 1.6 m. (a) Test 21 (b) Test 22. (c) Test 23 (d) Test 24.
Figure 18.
Time series of the ice forces during the ahead running operation in ice sheet with a thickness of 1.6 m. (a) Test 21 (b) Test 22. (c) Test 23 (d) Test 24.
Figure 19.
Comparison of the ice resistance for the ahead running mode.
Figure 19.
Comparison of the ice resistance for the ahead running mode.
Figure 20.
Time series of the ice forces during the astern running operation in ice sheet with a thickness of 1.3 m. (a) Test 15 (b) Test 16. (c) Test 17 (d) Test 18.
Figure 20.
Time series of the ice forces during the astern running operation in ice sheet with a thickness of 1.3 m. (a) Test 15 (b) Test 16. (c) Test 17 (d) Test 18.
Figure 21.
Time series of the ice forces during the astern running operation in ice sheet with a thickness of 1.6 m. (a) Test 25 (b) Test 26 (c) Test 27 (d) Test 28.
Figure 21.
Time series of the ice forces during the astern running operation in ice sheet with a thickness of 1.6 m. (a) Test 25 (b) Test 26 (c) Test 27 (d) Test 28.
Figure 22.
Comparison of the ice resistance for the astern running mode.
Figure 22.
Comparison of the ice resistance for the astern running mode.
Figure 23.
Simulated ice resistance and evaluated thrust as a factor of ship speed for ahead running.
Figure 23.
Simulated ice resistance and evaluated thrust as a factor of ship speed for ahead running.
Figure 24.
Measured ice resistance and evaluated thrust as a factor of ship speed for ahead running.
Figure 24.
Measured ice resistance and evaluated thrust as a factor of ship speed for ahead running.
Figure 25.
h–v curves from the measurement and the simulation using the static method for ahead running.
Figure 25.
h–v curves from the measurement and the simulation using the static method for ahead running.
Figure 26.
Simulated ice resistance and evaluated thrust as a factor of ship speed for astern running.
Figure 26.
Simulated ice resistance and evaluated thrust as a factor of ship speed for astern running.
Figure 27.
Measured ice resistance and evaluated thrust as a factor of ship speed for astern running.
Figure 27.
Measured ice resistance and evaluated thrust as a factor of ship speed for astern running.
Figure 28.
h–v curves from the measurement and the simulation using the static method for astern running.
Figure 28.
h–v curves from the measurement and the simulation using the static method for astern running.
Figure 29.
Simulated time series of the dynamic ship speed in the ice sheets with different thicknesses for ahead running.
Figure 29.
Simulated time series of the dynamic ship speed in the ice sheets with different thicknesses for ahead running.
Figure 30.
h–v curves from the measurement and the simulation using the dynamic method for ahead running.
Figure 30.
h–v curves from the measurement and the simulation using the dynamic method for ahead running.
Figure 31.
Simulated time series of the dynamic ship speed in ice the sheets with different thicknesses for astern running.
Figure 31.
Simulated time series of the dynamic ship speed in ice the sheets with different thicknesses for astern running.
Figure 32.
h–v curves from measurement and simulation using the dynamic method for astern running.
Figure 32.
h–v curves from measurement and simulation using the dynamic method for astern running.
Table 1.
Main parameters of the arctic tanker.
Table 1.
Main parameters of the arctic tanker.
Parameter | Value | Unit |
---|
Beam o.a. | 44 | m |
Length p.p. | 259.2 | m |
Fore draught | 15.00 | m |
Midship draught | 15.00 | m |
Aft draught | 15.00 | m |
Length by waterline | 270 | m |
Wetted surface area | 16,604 | m2 |
Displacement | 136,385 | m3 |
block coefficient | 0.765 | - |
Waterplane area coefficient | 0.892 | - |
Midship section coefficient | 0.995 | - |
Longitudinal center of buoyancy (from Lpp/2) | 7.593 | m |
Table 2.
Test matrix.
Test No. | Ice Thickness (m) | Tanker Speed (kn) | Operation Mode |
---|
11 | 1.3 | 1.27 | Ahead running |
12 | 1.3 | 1.90 |
13 | 1.3 | 2.54 |
14 | 1.3 | 3.80 |
21 | 1.6 | 1.27 |
22 | 1.6 | 1.90 |
23 | 1.6 | 2.54 |
24 | 1.6 | 3.80 |
15 | 1.3 | 1.27 | Astern running with operating propellers |
16 | 1.3 | 1.90 |
17 | 1.3 | 2.54 |
18 | 1.3 | 3.80 |
25 | 1.6 | 1.27 |
26 | 1.6 | 1.90 |
27 | 1.6 | 2.54 |
28 | 1.6 | 3.80 |
Table 3.
Ice parameters used in the simulation.
Table 3.
Ice parameters used in the simulation.
| Value | Unit |
---|
Elastic modulus | 2000 | MPa |
Bending strength | 500 | kPa |
Crushing strength | 2300 | kPa |
Poisson ratio | 0.3 | |
Ice-hull friction coefficient | 0.1 | |
Water density | 1025 | kg.m−3 |
Ice density | 900 | kg.m−3 |
Gravity acceleration | 9.81 | m.s−2 |
Table 4.
Comparison of the ice resistance for all tests from the model test and simulation.
Table 4.
Comparison of the ice resistance for all tests from the model test and simulation.
Test No. | Model Test (kN) | Simulation (kN) | Absolute Error (%) | Operation Mode |
---|
11 | 3036 | 2953 | 2.7 | Ahead running |
12 | 3376 | 2996 | 11.3 |
13 | 3478 | 3119 | 10.3 |
14 | 4396 | 4133 | 6.0 |
21 | 3495 | 3782 | 8.2 |
22 | 3842 | 4268 | 11.1 |
23 | 4055 | 4362 | 7.6 |
24 | 5007 | 5172 | 3.3 |
15 | 2900 | 2716 | 6.3 | Astern running with operating propellers |
16 | 3089 | 2782 | 9.9 |
17 | 3150 | 2855 | 9.4 |
18 | 3770 | 3798 | 0.7 |
25 | 3324 | 3374 | 1.5 |
26 | 4013 | 3840 | 4.3 |
27 | 3943 | 3906 | 0.9 |
28 | 5136 | 4433 | 13.7 |
Table 5.
Calculated and measured icebreaking capability.
Table 5.
Calculated and measured icebreaking capability.
Items | Ahead Running | Astern Running |
---|
Model test (m) | 1.52 | 1.47 |
Simulation by static method (m) | 1.53 | 1.52 |
Simulation by dynamic method (m) | 1.45 | 1.42 |