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Internationa! Journal of Naval Architecture and Ocean Engineering 8 (2016) 169—176

http://www.journals.elsevier.com/international-journal-of-naval-architecture-and-ocean-engineering/

Further study on level ice resistance and channel resistance

for an icebreaking vessel

Jian Hu a, Li Zhou b *

a College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China b Aker Solutions, Fornebu 1360, Norway

Received 14 September 2015; revised 24 November 2015; accepted 11 January 2016 Available online 16 March 2016

Abstract

In this paper, further research is carried out to investigate the resistance encountered by an icebreaking vessel travelling through level ice and channel ice at low speed range. The present paper focuses on experimental and calculated ice resistances by some empirical formulas in both level ice and channel ice. In order to achieve the research, extra model tests have been done in an ice basin. Based on the measurements from model test, it is found that there exists a relationship between ice resistance, minimum ice load, maximum ice load and the standard deviation of ice load for head on operation in level ice. In addition, both level ice resistance and channel ice resistance are calculated and compared with model test results.

Copyright © 2016 Society of Naval Architects of Korea. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Keywords: Level ice resistance; Channel ice resistance; Model test data; Icebreaking vessels

1. Introduction

Due to the increased hydrocarbon exploration and exploitation in ice-covered waters, ship transports and operations under ice impact are becoming more and more concerned. It is important to estimate ice loads acting on ice-going vessels under design conditions. For icebreaking vessels, there exist a large number of engineering tools for ice-class ship performance evaluation at the design stage. Lindqvist (1989) developed a formula to calculate ice resistance based on many full scale tests in the Bay of Bothnia. By modifying the formulations of Lindqvist (1989), Riska et al. (1997) proposed a level ice resistance formula with some empirical parameters. Keinonen et al. (1996) did research on resistance of ice-breaking vessels in level ice and developed a formula based on results of a study of escort operations involving five

* Corresponding author.

E-mail address: zhouli209@hotmail.com (L. Zhou).

Peer review under responsibility of Society of Naval Architects of Korea.

icebreaking vessels. Moreover, Jeong et al. (2010) proposed new ice resistance prediction formula for standard icebreaker model using component method of ice resistance and also predicted the model test results to full-scale using calculated non-dimensional coefficients.

How to validate these tools based on model scale data remains an issue. Hu and Zhou (2015) compared model test data and numerical results calculated with several popular empirical and analytical formulas. They found that the empirical methods could predict ice resistance at different accuracy, but none of them could give a good estimation for all cases. In order to further study ice resistance, more model tests have been performed using the same ship model. The model test results with respect to ice resistance in both level ice and channel ice are presented in this paper. The relationships between mean, maximum, minimum and standard deviation regarding ice resistance are found and highlighted based on the model test results. In addition, the ice resistances in both level ice and channel ice are calculated are compared with model test data.

http://dx.doi.org/10.1016/j.ijnaoe.2016.01.004 / pISSN : 2092-6782, eISSN : 2092-6790

2092-6782/Copyright © 2016 Society of Naval Architects of Korea. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

2. Model test description

The icebreaking tanker MT Uikku is a double-hull ice-breaking motor tanker that is owned by Neste Shipping and Kvaerner Masa-Yard's joint venture company, Nemarc. It is shown in Fig. 1. The ship model of MT Uikku was deployed in the model tests with a scaling factor of 1:31.56 (as shown in Fig. 2). The model ice was generated from ethanol (0.3%) doped water solution. The ambient temperature was lowered to approximately —10 °C. The carriage moved continuously from one end to the other of the basin in the spraying process where water-mist was emitted by nozzles. The freezing process continued until the target thickness of the ice was achieved. Then the ambient temperature was increased to around —2 °C and this process continued until the target strength (flexural strength) of the ice was achieved.

The ship model was trimmed to even keel without heel angle, so that the centre of buoyancy and the centre of gravity were in the same longitudinal and transverse location. The ship model was towed straightly through ice fields in all tests. The particulars of the full scale vessel are given in Table 1.

Test matrix with ice type, ice drifting speed and measured ice properties are presented in Table 2. It should be noted that tests with ice sheet I and II (shown in Zhou et al., 2013) are

Fig. 1. Icebreaking tanker MT Uikku.

Fig. 2. Ship model of MT Uikku.

Table 1

Full-scale primary dimensions of MT Uikku.

Item Notation Unit Value

Length L m 150.0

Length of bow Lbow m 39

Length of parallel Lpar m 65

Breadth moulded B m 21.3

Tested draft T m 9.5

Bow waterline angle a deg 21

Bow stem angle f deg 30

average flare angle j deg 58

also included here in order to have more measured data. Two extra ice sheets were made in the ice basin, where level ice and channel ice tests were carried out. Level ice tests means that the ship model was towed straightly in the intact ice sheet. After the ship model travelled through the ice field, a channel would form behind the ship model. The ship model would experience ice resistance from ice floes in the open channel, which is ice channel resistance. In total, three ice drifting speeds were set, namely 0.2, 0.5 and 1.0 m/s. When broken ice slides along the hull, there will be a friction force which is a function of relative speed between ice and hull. It is also proportional to the weight of ice in the water. The ratio of the friction force to the weight of ice is defined as ice-hull friction coefficient. The ice-hull friction coefficient was measured to be 0.04. The measured water density pw is 989 kg/m3 while ice density pi is 906 kg/m3.

3. Model test results and analysis

Ice resistance is defined as average value of all longitudinal forces invoked by ice acting on the structures in time domain. An example of a time history of measured longitudinal ice force is shown in Fig. 3, where the dot dash line denotes the mean ice force or ice resistance, the dot line denotes the minimum ice force and the dash line denotes the maximum ice force.

The dynamic fluctuations of ice force are mainly caused by ice breaking and ice submersion processes. When a structure transit in ice, its hull will break and displaces broken ice wedge. Crushing happens between hull and ice immediately after the ice sheet contacts the hull. The crushing force will keep growing as the contact area increases until its vertical component is large enough to cause a bending failure of ice. After the new ice floes are formed from the intact ice sheet, the advance of ship forces them to turn on edge until parallel with the hull. Then, the floes will become submerged and slide along the hull until they lose contact with the hull and clear away. During those processes, the ice force will fluctuate significantly.

3.1. Ice resistance

The results of all measurements with respect to the mean, standard deviation, maximum and minimum ice forces are given in Table 3.

Table 2

Test matrix and measured ice properties.

Ice sheet Test No. Ice type Ice thickness h¡ [m] Bending strength sb [kPa] Crushing strength [kPa] Elastic Modulous E [MPa] Ice speed V [m/s]

I 103 Level 0.77 724 1748 929 0.2

104 Level 0.76 844 2192 984 0.5

II 205 Level 0.96 920 1840 1685 0.2

206 Level 0.95 912 1862 1701 0.5

III 301 Level 1.04 540 2477 1474 0.2

302 Level 1.04 669 2485 1273 0.5

303 Level 1.04 592 2397 1390 1.0

304 Channel - - - - 0.2

305 Channel - - - - 0.5

306 Channel - - - - 1.0

IV 401 Level 0.63 808 4040 1616 0.2

402 Level 0.63 1029 5389 2058 0.5

403 Level 0.63 903 4616 1805 1.0

404 Channel - - - - 0.2

405 Channel - - - - 0.5

406 Channel - - - - 1.0

In Table 3, the ratios of difference between maximum/ minimum and mean force to the standard deviation of ice force are also included. It is interesting to find that the ratios are relatively concentrated from 2.8 to 3.6 for upper bound and 2.5 to 3.2 for low bound. Then the ratios could be written as

Kmax = (Fmax — Fmea)/Std(F) , ,

Kmin = (Fmea — Fmin)/Std(F)

Where Fmax is the maximum ice force, Fmea is the mean ice force or ice resistance, Fmin is the minimum ice force, Std(F) is the standard deviation of ice force.

Then least squares method is used to obtain the coefficient Kmax and Kmin based on the measured data given in Table 3. It is found that Kmax = 3.26 and Kmin = 2.76. The results of measured and fitted values are plotted in Fig. 4. Both maximum and minimum values are fitted very well with the correlation coefficients 0.998 and 0.986 respectively.

Compared to the measured resistances in level ice, the measured channel ice resistances are relatively small. This is as expected since the ship model needs more energy to break

Table 3

Measured ice forces for all cases (kN).

Case No. Ice type Mean Std. Max Min (Max - Mean)/Std. (Mean - Min)/Std.

1 (Test 103) Level 480 130 920 100 3.4 2.9

2 (Test 104) Level 560 130 990 200 3.3 2.8

3 (Test 205) Level 670 220 1410 100 3.3 2.6

4 (Test 206) Level 720 193 1390 130 3.5 3.2

5 (Test 301) Level 540 88 850 290 3.5 2.8

6 (Test 302) Level 830 130 1200 450 2.8 2.9

7 (Test 303) Level 780 160 1260 370 3.0 2.6

8 (Test 304) Channel 220 65 420 60 3.1 2.5

9 (Test 305) Channel 120 31 210 40 2.9 2.6

10 (Test 306) Channel 210 65 430 40 3.4 2.6

11(Test 401) Level 150 56 350 8 3.6 2.5

12 (Test 402) Level 290 84 590 48 3.6 2.9

13 (Test 403) Level 390 120 720 84 2.8 2.6

14 (Test 404) Channel 98 22 175 30 3.5 3.1

15 (Test 405) Channel 81 25 160 19 3.2 2.5

16 (Test 406) Channel 69 25 140 5 2.8 2.6

— 600

400 Time [s]

Fig. 3. Time history of measured longitudinal ice force.

1600 p

1400 -

1200 -

1000 -

-200 — 0

Measured mean Fitted max — - Fitted min

Measured max A Measured min

2 4 6 8 10

Case No.

Fig. 4. Measured and fitted ice forces.

intact ice sheet and submerge the ice floes newly formed from ice wedge. The maximum channel ice resistance at the lowest ice drifting speed account 50% of maximum level ice resistance in case 8 and 14 as shown in Table 3. As the speed increases, the channel ice resistance tends to decrease due to shortened interaction time between incoming ice floes and the ship.

3.2. Level ice resistance

Level ice resistance could be taken as the summation of the force occurred during ice breaking process at the initial

a. 30 E

1.5 2.0 2.5

Froude number

ice-hull interaction and the force due to submersion and sliding of broken ice from intact ice sheet. It is difficult to measure the global ice breaking force directly since the integration of ice submersion is inevitable. However, the breaking component can be determined by means of a test in pre-sawn ice indirectly. The intact ice sheet is cut into pieces in a similar pattern as observed in the level ice test. Then ice submersion force could be measured and subtracted from the total ice resistance to get the ice breaking force at the same ice drifting speed.

Unfortunately, the pre-sawn test was not included in the present model tests. Herein, one good reference highly related to the present research is introduced to study the ratio of ice breaking component to the total ice resistance. Heinonen (2014) carried out a series of experiments to study on the effect of speed on the ice resistance of a ship. The model of the icebreaker Kontio was used at a scale of 1:20. Both level ice tests and pre-sawn ice tests were performed at four model-scale speeds: 0.23 m/s; 0.69 m/s; 1.38 m/s and 1.84 m/s. The ice breaking forces were calculated as the difference between the resistances measured in level ice and in the pre-sawn ice. The measured percentages of ice breaking component to the total ice resistance as a function of Froude number are shown in Fig. 5. The relationship between the percentage and the Froude number is fitted with a second order polynomial curve based on the measured data. Then the fitted curve is used to calculate the percentages of ice breaking component for the MT Uikku ship model at different speeds. The calculated ice breaking and submersion components are given in Table 4.

The submersion ice resistance is defined as the resistance in pre-sawn ice. According to ITTC (2002), the submersion resistance coefficient Cv is written as

PigBh2

where pi is the ice density,g is the gravity acceleration, B is the ship breadth, h is the ice thickness.

The calculated coefficients are shown in Fig. 6. The coefficients range from 1.5 to 3.2, which are slightly lower than the range 2—4 suggested by ITTC.

Fig. 5. Measured and fitted percentage of ice breaking component for the Kontio model.

Table 4

Calculated ice breaking and submersion components from measured resistance.

Case No. Speed (m/s) Froude Number Breaking comp. (%) Measured total resistance (kN) Breaking comp. (kN) Submersion comp. (kN)

1 (Test 103) 0.2 0.073 37 480 176 304

2 (Test 104) 0.5 0.183 36 560 204 356

3 (Test 205) 0.2 0.065 41 670 273 397

4 (Test 206) 0.5 0.164 41 720 292 428

5 (Test 301) 0.2 0.063 42 540 229 311

6 (Test 302) 0.5 0.157 42 830 352 478

7 (Test 303) 1.0 0.313 42 780 329 451

11 (Test 401) 0.2 0.080 34 150 51 99

12 (Test 402) 0.5 0.201 34 290 98 192

13 (Test 403) 1.0 0.402 33 390 130 260

«л с

«и (у

♦ ▲

24 mm ▲ 30 mm X 33 mm 20 mm

0.0 0.1 0.2 0.3 0.4 Froude number

Fig. 6. Submersion resistance coefficient VS Froude number.

4. Empirical and analytical formulas

4.1. Level ice resistance formula

There are many empirical and analytical formulas available to estimate level ice resistance. Some of them are presented as follows.

a) Lindqvist formula

The Lindqvist formula was developed from research done on full scale tests in the Bay of Bothnia (Lindqvist, 1989). It is a rather simple way of estimating the ice resistance. In this model, the resistance is divided into crushing, bending-induced breaking and submergence. The formula gives resistance as a function of main dimensions, hull form, ice thickness, ice friction and strength. The formula is expressed as:

Rice = (Rc + Rb)[ 1 + 1-4

:)+ R,(

2tan f + m cos f / cos j Rc = 0.5shk-

1 + 9.4

1 — m sin f / cos j

Rb ^ttSbB 64

tan j + m cos f ^ 1 1

cos j sin a \ cos j

12(1 — v2) grw

Rs = (Pw — рдЕЫВ[Т-^2Г + k

T В /11

к = m( 0 .7L — ^ _ ^ — и ^ _—hTcos f cos j/^-2^--2

tan f 4 tan a

Л —[2+——i)

V sin f2 tan a2/

j = arctan -

where Rice, Rc and Rb and Rs are total andice resistance, crushing resistance, bending resistance and resistance due to submersion;sb and hj are respectively ice strength in bending and ice thickness; m, f, a and j are respectively the friction

coefficient, stem angle, waterline entrance angle and flare angle; g is the gravity acceleration; pw and pi are water and ice density; E, and y are Young's modulus and Poisson ratio of sea ice respectively. B, T, and L are ship's breadth, draught and waterline length; V is ship speed.

b) Keinonen formulas

Based on results of a study of escort operations involving five icebreaking vessels, Keinonen et al. (1996) did research on resistance of icebreaking vessels in level ice. In order to investigate low-velocity ice resistance, specific formulas were derived from full scale trials of icebreaker performance in ice at 1 m/s speeds. These prediction formulas include parametric influences for different vessel dimensions, hull forms, hull surface conditions, ice strengths and ambient temperatures. The speed-dependent resistance formula is written as:

R = Cf (0 . 08 + 0 . 017CsChB0, 7L0- 2T01HL 25kik2) к = (1 — 0.0083 (t + 30)) (0.63 + 0.00074sf)

k2 = (1 + 0.0018(90 — j)14) (1 + 0 . 04(4 — 5)1 '5) V

where R is total ice resistance in MN; Cs is water salinity coefficient (0 fresh, 1 saline); Ck is hull condition coefficient (1 inertia, 1.33 bare steel); В, T and L are ship beam at waterline, draft and waterline length in meter; j and4 are average flare angle and buttock angle in degree; t is air temperature; Sf is flexural strength; H is ice thickness; Cf is the correction factor considering the effect of vessel speeds with reference speed Vj = 1 m/s.

c) Riska formulas

Riska et al. (1997) proposed a level ice resistance formula by modifying the formulations of Lindqvist (1989). The formulation is based on a set of empirical coefficients, derived from full-scale tests of a number of ships in ice conditions in the Baltic Sea. The main resistance formula is given in Eq. (5), while constants are found in Table 5.

Table 5

Constants in Riska formulation for ice resistance in level ice.

Symbol Value Unit

fi 0.23 kN/m3

f2 4.58 kN/m3

f3 1.47 kN/m3

f4 0.29 kN/m3

gl 18.9 kN/(m/s*m15)

g2 0.67 kN/(m/s*m2)

g3 1.55 kN/(m/s*m25)

Cl = fi

BLparhi + (1 + 0.021f)

fBh2 + fcLbowh2 + f4BLbawhi)

C2 = (1 + 0.063f) (g,h,L5 + g2Bhi) + gMl + 1-2T/B)p=

where V, B, T and L are vessel speed, breadth, draught and length, ht is ice thickness, f is the stem angle in degrees and Lbow and Lpar are the length of bow and parallel sides section, respectively.

d) Jeong formulas

Jeong et al. (2010) proposed new ice resistance prediction formula for standard icebreaker model using component method of ice resistance and also predicted the model test results to full-scale using calculated non-dimensional coefficients. The formulas are presented as follow:

R, = 13.14V2 + CB DpghiBT + CcF-haPiBhy2 + CBRSNß PiBhtV2

Fh = -V

where RI total ice resistance; CB, CC and CBR are coefficient of

ice buoyancy resistance, coefficient of ice clearing resistance

and coefficient of ice breaking resistance; Fh and SN are Froude number and strength number; a is index of Froude

number; b is index of Strength number; pi and pw are ice and

water density; Dp is water density minus ice density; g is

gravitational constant; hi is ice thickness; B and T are beam

and draft of the ship; V is ship speed; Sf is the flexural strength of ice. The constants used are shown in Table 6.

4.2. Channel ice resistance formulas

When coming to the design point, the rule channel resistance for different ice classes should be taken into account.

According to Juva and Riska (2002), the rule resistance equation is expressed in the following form:

C1 + C2 + C3 [Hf + HM ]2 [B + Cj HF ] C

+ C4LparHF + C5 n0.5

Hf = 0.26 + (HMB) Cm = 0.15 cos f2 + sin j sin a, min 0.45 Cj = 0.047j - 2.115, min 0.0 tan f2

j = arctan BL

C1 = f

+ [1 + 0.021f 1]f2B + f3Lbow + f4BLbow)

C2 = [1 + 0.063f1][g1 + g2 B]+g3

1 + L2 B

Bffi PL

where the term [LT/B2]3 is taken as 20 if it is above 20 and 5 if it is below 5; all other coefficients are shown in Table 7.

5. Comparisons

5.1. Level ice

Ice resistances by empirical and analytical formulas (Eqs. (5)—(7)) are calculated and compared with model test results. The calculated results and model test measurements are shown in Table 8, where the error between measured data and analytical data is also included. The corresponding results are plotted in Fig. 7 for comparison.

From Table 8, it shows that the Lindqvist formulas under-predicts ice resistances for most cases except cases 11 and 12. The average numerical error is —13% for all cases. Riska formulas give the largest predictions among all formulas, which overestimate the ice resistance up to 50% in average. Joeng formulas estimate ice resistance very well with the difference of 7%. Konenien formulas overestimate the ice resistance by 37% in average.

It should be noted that all formulas used in the present paper overestimate the ice resistance significantly for case 11.

Table 7

Coefficients for channel resistance formulas.

Symbol Value Unit

Table 6 fi 23 N/m2

Constants in Jeong formulation for ice f2 4.58 N/m

resistance in level ice. f3 14.7 N/m

f4 gi g2 29 1537.3 N/m2 N

Symbol Value

Cb 0.5 172.3 N/m

Cc 1.11 g3 398.7 N/m15

cbr 2.73 C3 845.576 kg/(m2s2)

a 1.157 C4 41.74 kg/(m2s2)

b 1.54 C5 825.6 kg/s

Rice — C1 + C2V

Table 8

Experimental and calculated level ice resistance.

Case No. Experimental results Calculated results (kN) Numerical error (%)

Lindqvist Riska Jeong Konenien Lindqvist Riska Jeong Konenien

1 (Test 103) 470 320 610 330 510 -32 30 -30 9

2 (Test 104) 560 380 630 520 600 -32 13 -7 7

3 (Test 205) 670 510 800 560 740 -24 19 -16 10

4 (Test 206) 720 560 840 800 810 -22 17 11 13

5 (Test 301) 539 426 892 459 663 -21 65 -15 23

6 (Test 302) 829 538 942 765 783 -35 14 -8 -6

7 (Test 303) 781 572 1025 961 847 -27 31 23 8

11 (Test 401) 152 251 473 259 425 65 211 70 180

12 (Test 402) 291 322 501 300 526 11 72 3 81

13 (Test 403) 391 351 548 542 579 -10 40 39 48

Case No.

Fig. 7. Comparison of experimental and calculated ice resistance.

It is not hard to explain the difference. In case 11, ice is thin and towing speed is low, which may lead to elastic buckling rather than bending failure for the ship model. The resulting ice load is smaller than that occurred during bending process.

5.2. Channel ice

Ice channel resistances calculated with Eq. (7) are shown in Table 9, where the experimental data are also included. From Table 9, it is found that the rule channel ice resistance formula overestimates the resistance and is on the conservative side as expected. It should be noted that the channel ice resistance formula does not take the effect of ice drifting speed into account, but the effect of ice drifting speed may be significant according to the model test. In the model test, all ice channels

Table 9

Experimental and calculated channel ice resistance.

Case No. Model test (kN) Calculation (kN)

8 (Test 304) 220 252

9 (Test 305) 120

10 (Test 306) 210

14 (Test 404) 98 204

15 (Test 405) 81

16 (Test 406) 69

were newly formed with different ice concentrations. For case 10, the ice concentration is very high, above 90% in average. For other channels, it is around 40%. If the case 10 is not considered due to very high concentration, the resistance decreases as the speed increases when comparing cases 8 and 9 or cases 14,15 and 16. This is mainly attributed to shortened time of ice-hull interaction and strong weak at high drifting speed.

6. Conclusions

This paper aims to study level and channel ice resistance exposed to an icebreaker in both numerical and experimental ways. Extra model tests have been carried to get more experimental data. There exists a clear relationship between ice resistance, standard deviation, maximum force and minimum force from the measurements. The maximum ice force is around 3.26 times standard deviation higher than mean ice force while the minimum ice force is around 2.76 times standard deviation lower than the mean ice force. The measured submersion resistance coefficient as a factor of Froude number is slightly lower than that recommended by ITTC. Some empirical and analytical formulas are used to calculate both level ice and channel ice resistance. The calculated results are compared against model test results. Empirical methods mentioned in the present paper predict ice resistance at different accuracy, but Jeong formula gives the best predictions in general. The ice channel resistance are also calculated and compared with experimental results. It shows that the rule ice channel resistance formula is relatively conservative. The measured channel ice resistance is also speed-dependent. This effect is suggested to be included in the ice channel resistance formula as well.

Acknowledgements

Project supported by the National Natural Science Foundation of China (Grant Nos. 11102048, 11302057) and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20132304120028).

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