Experimental Investigation of the Resistance Performance and Heave and Pitch Motions of Ice-Going Container Ship Under Pack Ice Conditions

In order to analyze the ice-going ship’s performance under the pack ice conditions, synthetic ice was introduced into a towing tank. A barrier using floating cylinder in the towing tank was designed to carry out the resistance experiment. The test results indicated that the encountering frequency between the ship model and the pack ice shifts towards a high-velocity point as the concentration of the pack ice increases, and this encountering frequency creates an unstable region of the resistance, and the unstable region shifts to the higher speed with the increasing concentration. The results also showed that for the same speed points, the ratio of the pack ice resistance to the open water resistance increases with the increasing concentration, and for the same concentrations, this ratio decreases as the speed increases. Motion characteristics showed that the mean value of the heave motion increases as the speed increases, and the pitch motion tends to increase with the increasing speed. In addition, the total resistance of the fullscale was predicted.


Introduction
As the global climate is becoming warmer, the northern polar ice cap is gradually thawing. The opening up possibility of the northern shipping lanes is increasing, which will directly change the structure of global oceanic shipping lanes (Lee and Song, 2014). Furthermore, the North Pole is rich in natural resources such as petroleum, natural gas, and coal (Nie et al., 2013). Conventionally, the primary research on ice-going ships focuses on the performance forecasting under the level ice conditions. Thus, research and development on the performance forecasting of ice-going ships under the pack ice conditions is relatively uncommon (Song et al., 2007). In addition, the pack ice drifts continuously because of the effects of wind, waves, and currents, which is especially the case in the straits where the extreme drifting of the pack ice is observed. Drifting ice can pose a serious safety hazard for shipping transports (Marchenko, 2013). Similar to sailing conditions in open water, the motion attitude of ice-going ships changes constantly when ships sail in the pack ice. Therefore, research on the motion of ice-going ships is also crucial. Spencer (1992) categorized the ice-going ship resistance into four components, namely, icebreaking resistance, ice buoyancy resistance, ice-clearing resistance, and open water resistance. Spencer's method is accepted widely, thus, per the request of the Internal Towing Tank Conference's (ITTC) Ice Committee, Derradji-Aouat(2002, 2003 and Derradji-Aouat and Thiel (2004) adopted Spencer's method for conducting the uncertainty analysis of the resistance testing by considering the Canadian Coast Guard Ship Terry Fox as the standard ship model. In broken ice, the uncertainties ranged from 3% to 26%. Under the pack ice conditions, large uncertainties are possible in random pack ice. Thus, the randomness in the pack ice has an important effect on the uncertainties of the pack ice resistance. Kim et al. (2013) calculated the ice resistance for the pack ice conditions based on the LS-DYNA commercial FE package. Then, the numerical analysis was validated in comparison with the model ship performance data from Pusan National University's towing tank and the National Research Council's ice tank. The results show that there exists good consistency among the three cases with regard to the uncertainties in the interaction of the model hull and randomly distributed ice. Su et al. (2010) developed a numerical model to track the icebreaking progress of the ship model under the pitching, yawing, and rotating motions. Tan et al. (2013) expanded the research of Su et al. (2010) by further examination of the icebreaking procedure with six degrees of freedom. Tan et al. (2014) investigated the performance of a dual-direction ship through a numerical procedure simulating continuous-mode icebreaking in the level ice. It is observed that icebreaking pattern largely influences the ice resistance and thus the ship's ice performance. Von Bock und Polach and Ehlers (2011) conducted the level ice tests for ships in the free and restricted modes in order to study the effects of the heave and pitch motions of the ship models during icebreaking on their resistance and the icebreaking patterns. The results show that the heave and pitch motions have a significant impact on the breaking pattern.
China and Europe are each other's biggest trading partner. The nucleus of Sino-European commerce is manufactured goods rather than such raw goods as petroleum, natural gas, and coal. Thus, the container ship transportation plays a critical role in the Sino-European commerce. Therefore, in the present study, the KRISO container ship (KCS) model was adopted. The authors investigated the heave and pitch motions of this ship model. Furthermore, the analysis of the frequency with which the ship encounters ice under different concentrations of the pack ice and its effect on the resistance were described. As the concentration increases, the encounter frequency between the ship model and the pack ice shifts to a higher velocity point that is located in a region of unstable resistance.

Experimental ship model
The ship model used in this experiment is based on the KCS, and is shown in Fig. 1. This hull has a bulbous bow, and we intended to analyze the performance impact of many experiments. The scale ratio, length, and breadth were set to 52.667:1, 4.3671 m, and 0.6114 m, respectively; its parameters are listed in Table 1.

Test facilities
A test with synthetic ice was conducted in the towing tank in Harbin Engineering University (HEU). The HEU towing tank has dimensions of 108 m in the length, 7 m in the width, and 3.5 m in the depth. Dimensions of the towing carriage is of 8 m in the length and 8 m in the width, as shown in Fig. 2. The resistance under the pack ice conditions was measured by using a four-degree freedom dynamometer with a capacity of 300 N (Fig. 3).

Model ice λ
In 1969, Michel mixed polyethylene, vegetable oil, and stearic acid into paraffin to obtain model ice, and called it MOD-ICE. In 1990, the Canadian scholars Beltao et al. developed SYG-ICE model ice, which was made of PVC resin, light exterior stucco, plaster, glass beads, and water (Lau et al., 2007). In 2013, Kim et al. used semi-refined paraffin wax as synthetic ice, and carried out model tests in the towing tank of Pusan National University. The results of these tests were compared with those of tests performed in the ice tank of the Institute for Ocean Technology in Canada. Because the results agreed well with each other, and it was easier to process the semi-refined paraffin wax, we decided to employ a synthetic model ice product made of semi-refined granular paraffin wax. By considering the scale ( = 52.667) from the actual 1.05 m-thick ice, the thickness of the synthetic model ice was set as 20 mm. According to the measurement results, the model ice had an approximate density of 900.1 kg/m 3 , and a friction coefficient of 0.035 between the hull and pack ice.
In the case of resistance test under pack ice conditions, there is barely any breaking and cracking components of pack ice, so the ice breaking forces can be ignored. Since the breaking and cracking of pack ice are not taken into account in our tests, the strength of model ice is not significant. The pack ice size for the North Pole follows the lognormal distribution function (Tuovinen, 1979), and the lognormal distribution graph for model ice of different sizes is shown in Fig. 4. The quantities of model ice of seven sizes are calculated accordingly, as listed in Table 2, and models of the seven sizes are shown in Fig. 5.

Experimental design
The towing tank barriers were set to create a width of 3 m, i.e., nearly 5 times that of the model, because the fence effect was not to be included. According to the primary size and speed requirements of the ship model, and to satisfy the data collection needs for the test, a pack ice area 28 m×3 m was segregated in the tank. An 8 m×3 m buffer zone was installed at one end, with a supporting floating cylinder. This floating cylinder not only prevented the model ice in the pack ice zone from sliding into the buffer zone, but also acted as a support for the barriers cordoning the sides of the towing tank. It prevented the floating cylinders on the sides of the towing tank from drifting toward the middle of the tank. In order to keep the pulling wire under the tension during the tests, the counterweight is used. A sketch of the test setup is shown in Fig. 6.
Under the open water condition, the results of the resistance experiment at the same speed have a very good repeatability. However, under the pack ice conditions, the distribution of the pack ice in the channel changed continuously during the resistance tests at a given velocity point. The repeatability of measuring the ship model resistance value for each speed point was not optimal, similar to the situation with sea ice in real life. Therefore, the resistance test at each speed point was repeated many times.
First, under the open water condition, we carried out the resistance experiment in the towing tank without side barriers, at six model speeds (0.2, 0.4, 0.6, 0.8, 1.0, and 1.2 m/s). Then, we conducted the resistance experiment under the pack ice condition, using the side barriers of the towing tank and synthetic ice at the same six model speeds (0.2, 0.4, 0.6, 0.8, 1.0, and 1.2 m/s), as shown in Table 3.

Prediction method of the full-scale ships
Colbourne, from the Canadian Institute of Ocean Technology (IOT), developed an analysis method to predict the total resistance of the full-scale (Colbourne, 2000). Under the pack ice conditions, assuming that the size of the pack ice is smaller than that of the ship, the breaking of pack ice rarely occurs. Therefore, the resistance resulted from the breaking of ice can be ignored (Kim et al., 2013;Molyneux et al., 2007). Thus, the total resistance under the pack ice conditions consists of two components, namely, the open water resistance and the resistance generated from various motions of the pack ice around the ship body (including submerging, rotating, and sliding); the latter is referred to as the pack ice resistance. The open water resistance can be   GUO Chun-yu et al. China Ocean Eng., 2018, Vol. 32, No. 2, P. 169-178 obtained through the resistance tests in the towing tank. Then, the pack ice resistance can be obtained by subtracting the open water resistance from the total resistance obtained from the resistance tests under the pack ice conditions. The total resistance under the pack ice conditions can be expressed as follows: where R OW is the open water resistance, and R P is the pack ice resistance. According to the basic principle of Colbourne's method, the dimensionless coefficients in the equations are respectively determined after the experimental separation of various resistance components. The expressions for the components of the open water resistance and pack ice resistance are as follows: (2) where C OW is the coefficient of the open water resistance, C P is the coefficient of the pack ice resistance, is the density of the ice, g is the gravitational acceleration, B is the model's width, h i is the thickness of the ice, V is the ship's velocity, C is the concentration of the pack ice, and n is the power of the concentration. The pack ice resistance can be nondimensionalized by using the pack ice resistance coefficient, and the velocity can be nondimensionalized by using the pack ice Froude number. The non-dimensional coefficients are as follows: (4) (1) Determination of C OW The curve of R OW -V 2 is plotted based on Eq.
(2), which is used to determine C OW .
(2) Determination of C P According to the repeated tests conducted by the IOT over the years, lnC P and lnFr P have a linear relationship (Kim et al., 2005). From the graph of lnC P -lnFr P , or the resultant linear equation, the pack ice resistance coefficient C P can be obtained.
(3) Forecasting total resistance of the full-scale Therefore, it is possible to use Eq. (6) to forecast the total resistance of real ships under the pack ice conditions.
where the relevant parameters and the velocity are measured from the full-scale, and the physical properties of the ice are also same as the actual ice parameters. Colbourne initially suggested the adoption of n=3 from the test results based on the floating production storage and offloading vessels and other offshore ships. It was later discovered that n=2 yields results closer to those of actual scenarios with the minimal error when analyzing the pack ice resistance of other ice-going ships. Therefore, in this study, n=2 is considered (Molyneux and Kim, 2007).

Resistance non-stationarity analysis and discussion
From Fig. 7, it is evident that for the same velocities, the total resistance at the 90% concentration is generally larger than that at the 60% concentration. Although sometimes the opposite happens, this can be attributed to the uneven distributions of the pack ice in the channel, which results in the randomness of the collision between the ship model and ice. In Fig. 7a, the ship model velocity is 0.2 m/s, which is smaller than other speeds, and the average of the curve at the 60% concentration approaches a straight line that does not change with time, while the average at the 90% concentration exhibits an increasing trend. This is attributed to the fact that the pack ice is relatively more scattered at the 60% concentration than that at the other concentrations. However, there is some concentrated pack ice at 90% concentration, which gradually piles up and overlaps over time at the bow of the ship model, instead of rotating and submerging. As a result, the resistance gradually increases over time. However, with the increase of the velocity, the trend of the gradual increase in the average resistance with time increases steeply, as seen in Figs. 7b and 7c. The collisions between the ship model and the pack ice intensify at higher velocities, reducing the piling and overlapping of ice in the front of the ship model. Instead, more ice rolls and sinks. At the same time, it is evident that the total resistance often shows negative values, as shown in Fig. 7. Because there are the accelerations and decelerations caused by the collision between the ship and the pack ice, when the ship model collided with the pack ice, the dynamometer dragging the ship model not only provides a towing force that overcomes the resistance of the water, but also overcomes the impact force of the ice on the ship model body, which can result in the resistance increase and speed decrease. After the pack ice moving aside, if there is no more pack ice colliding with the ship model, the ship model accelerates since the drag force of the dynamometer is larger than the water resistance. When the drag force is equal to the resistance, the ship model will move at a constant speed. When the drag force is smaller than the resistance, the ship model begins to slow down. However, the inertia force of the ship model causes the reverse deformation on the strain gauge of the dynamometer, which in turn registers as a negative value in the system. The rapidly repeating shift between the acceleration and deceleration is also demonstrated in the surge motion.
From Fig. 8, it is evident that the total resistance at the 90% concentration is larger than that at the 60% concentration at the same speed. From Figs. 8a and 8b, it is seen that the fluctuations are relatively smooth compared with those of Fig. 8c, except for a few special peak values at 0.8 m/s and 1.0 m/s. Hence, the average resistance graphs are straight lines. Larger peak values appeared abruptly be-cause the bow did not quickly push aside the larger pieces of ice in the front. It knocked the pieces over at 90°, and then pushed them along with the bulbous bow. The thrusting force of the bulbous bow on the pack ice was in equilibrium with the water resistance on the pack ice. The pack ice finally lost its balance because of the collisions with other pieces. Then it rotated, submerged, and separated from the ship model along the body, as seen in Fig. 9. This peak value can be referred to as the "impact peak". Owing to the randomness of the collisions, this phenomenon can occur at both the 60% and 90% concentrations of ice, and the frequency of the occurrence is higher at the 90% concentration.
In Fig. 8c, the trend of the resistance curve at the 60% concentration is similar to the trends seen in Figs. 8a and 8b. But at the 90% concentration, the resistance fluctuation was relatively smooth for the first half of the time period (0-5.5 s). However, the ship model resistance fluctuated at a higher value for the latter time period (5.5-10 s). This is mainly because of the equilibrium between the thrust of the ship model and the water resistance on the pack ice. This equilibrium has not been disturbed for a long time. Instead of an impact peak, the fluctuation has been maintained around a higher value for a long time. The reason for this fluctuation is that the motion of the pack ice faced resistance directly from the water, as if it was surfing. This imbalanced water resistance created the fluctuations. Suddenly, due to the impact of another piece of pack ice, the surfing pack ice was out of the balance and shoved away.  GUO Chun-yu et al. China Ocean Eng., 2018, Vol. 32, No. 2, P. 169-178 5 Analysis and discussion of resistance test data 5.1 Change in the total resistance with the velocity at different pack ice concentrations For the 60% concentration, the pack ice was more sparse than that for the 90% concentration (Fig. 10a). After the resistance tests at each speed, the pack ice in the area through which the ship model had passed had been pushed to the sides (Fig. 10b). Through the observations of the ice piece motion, the pack ice around the hull did not move through the boundaries, thus, the boundaries did not affect the ice piece motion. It was difficult to evenly distribute the pack ice for each test. Manual resetting was necessary to maintain the consistency in the distribution for the resistance test before continuing to the next speed point. Owing to the differences in the distribution of differently sized pack ice for each test, the ship model resistance of repeated experiments for each speed is different, which was similar to the situation with sea ice under the actual sea conditions. Therefore, when plotting the resistance curve, both the average resistance curve and the curves of the smallest and the largest resistance are plotted (Fig. 10c).
From Fig. 10c, it is clear that the total resistance curve close to that of the speed of 0.6 m/s, which is unstable, has a much higher fluctuation than those at the other speeds. Be-cause this is a region of instability for total resistance, 0.6 m/s is referred to as a special speed point. When the velocity is low (i.e. 0.2 m/s), the pack ice is merely slowly pushed aside by the ship model. But at higher velocities (such as 1.0 m/s), the pack ice is abruptly pushed aside by the ship model, with ice rotating and submerging, while the total resistance remains relatively stable. However, in the special region around 0.6 m/s, the frequency of the ship model encountering the pack ice occasionally shows a certain equilibrium between a few factors, namely, the friction between the body and the ice, and the water resistance on the ice. Hence, instead of pushing the ice aside, the ship model brings the ice into motions along with it, resulting in an abrupt increase in the total resistance, as compared with the total resistance at 0.4 m/s. The total resistance reaches the maximum around 0.6 m/s. For the 70% concentration, the pack ice remains sparse compared with that of the 90% concentration. As shown in Fig. 11, a peak resistance is again observed around 0.6 m/s, with the average resistance also showing a peak at this speed. This trend is evidently deviated from the reasonable trend. This indicates that the equilibrium is more apparent and more easily achieved at the 70% concentration for the encounter frequency, which is because of the friction between the ship body and ice and the water resistance on the ice. Thus, the resistance curve appears a peak value rather than a trough value. The speed point of 0.8 m/s is a turning point for the maximum total resistance curve, and also is a low point on the minimum total resistance curve.  This indicates that the phenomenon attributed to the specific encountering frequencies between the ship model and the pack ice at the 70% concentration, which is similar to those at the 60% concentration. However, at the 70% concentration there is a larger instable region, which is a region between 0.6-0.8 m/s. At the same time, the instable region shifts to the right in comparison with that of the 60% concentration.
At the 80% concentration, the curves for the maximum, minimum and average total resistance values all appear troughs at 0.6 m/s (Fig. 12). This indicates that the encountering frequency between the ship and the ice at this point is somewhat weakened as the concentration rises to 80%. However, the peak value occurs at around 1.0 m/s, which is similar to which occurred at 0.6 m/s at the 60% concentration. This indicates that another instable region appears around 1.0 m/s. This is consistent with the trend that the instable region shifts to higher velocity, as observed at the 60% and 70% concentrations.
Because the pack ice at the 90% concentration is denser than that at other concentrations (60%, 70%, 80%). After the resistance test at each speed, the pack ice that had been pushed to the sides quickly returned to fill the ship model's trail. This phenomenon is slow at the 60% concentration. At the speed of 0.6 m/s, only a small trough value is seen in Fig. 13, which is much weaker than those in the preceding three distributions. It is reasonable to draw conclusion that no encountering frequency occurs at this speed. However, the resistance fluctuated largely around 1.2 m/s. This shows that the point of the encountering frequency between the ship model and the pack ice shifts to higher speed as the concentration increases, as shown in Fig. 13. Fig. 14 shows that the total resistance at all the four concentrations follows an increasing trend with the increase of the speed. However, some special speed points appear at 0.6 m/s and 1.0 m/s. For the 70% concentration, the total resistance suddenly increases at 0.6 m/s, and is much larger than that at the 80% and 90% concentrations at the same speed. This implies that the effect of the encountering frequency on the resistance is especially important at 0.6 m/s with the 70% concentration. This is also evident from the analysis described in Section 5.1. At the speed of 1.0 m/s with the 80% concentration, the ship also experiences an encountering frequency, causing the resistance larger than that at the 90% concentration. At the speed of 1.2 m/s with the 90% concentration, the resistance quickly increases, which indicates the fact of another encountering frequency existing at 1.2 m/s. Therefore, from Fig. 14, it is evident that the encountering frequency shifts to a higher velocity as the concentration increases. Fig. 11. Variation curve of the total resistance with the velocity at the 70% concentration. Fig. 12. Variation curve of the total resistance with the velocity at the 80% concentration. Fig. 13. Variation of the total resistance with the velocity at the 90% concentration. Fig. 14. Comparison of the total resistance for different conditions. GUO Chun-yu et al. China Ocean Eng., 2018, Vol. 32, No. 2, P. 169-178 175 Fig . 15 shows the change of the pack ice resistance at four different concentrations. Similar to Fig. 14, the similar conclusion can be obtained. In order to compare the ratio of the pack ice resistance to the open water resistance at various concentrations, these ratios were calculated as listed in Table 4. From Table 4, it is evident that at the same speed, the ratio increases as the concentration increases. For the same concentration, the ratio decreases as the speed increases. This is because that the water resistance is small at a low speed, thus, the pack ice resistance is relatively large, resulting in a higher ratio at a low speed than that at a high speed. Fig. 16 clearly shows that the mean value of the heave motion increases as the speed increases. The mean value of the heave motion under the pack ice conditions is smaller than that in open waters. This is because the wave is restrained by the pack ice. In addition, the impact between the pack ice and the ship model and the pack ice sliding under the bottom of the ship model, provide some support force. By comparing the mean value of the heave motion with the speed increase under four different concentrations, it can be observed that the concentration does not seem to have a great influence on heave. This may be because of the randomness of the impacts between the pack ice and the ship model. From Fig. 17, the mean value of the pitch motion appears its peak value at 1.0 m/s for the 60% and 80% concentrations, while a peak appears at 0.6 m/s for the 70% concentration, and at 0.4 m/s for the 90% concentration. These peaks are attributed to a possible surfing phenomenon. As the bulbous bow pushes against the pack ice, the ice generates an upward lift on the bow and causes the sudden increase in the mean value of the pitch motion. However, the general trends in Fig. 17 show that the pitch motion tends to increase with the increased speed.

Total resistance forecast for the full-scale ships
The curve of R OW -V 2 is plotted in Fig. 18 according to Eq. (2). From the figure, C OW =6.9171. Therefore, the formula for the open water resistance is as follows:    From many years' experience and testing by the IOT, it is known that lnC P and lnFr P have a linear relationship (Colbourne, 2000;Kim et al., 2006). The graph of lnC P -lnFr P is shown in Fig. 19, which shows that it is possible to solve the relationship between the pack ice resistance coefficient C P and the Froude number Fr P : (8) The above equation is applicable not only under the working conditions of the 60%, 70%, 80%, and 90% concentrations of ice, but also at other concentrations.
Thus, the approximation equation for the total resistance of actual ships under the pack ice conditions can be expressed as follows: ρ i where V is the ship velocity, Fr P is the ice Froude number, is the density of the ice, B is the ship width, h i is the ice thickness, and C is the pack ice concentration.
According to Eq. (9), the total resistance of the full-scale at the 60% and 90% concentrations are shown in Fig. 20.

Conclusions
This study is focused on the KCS model. By using synthetic model ice, a pack ice channel was constructed in a towing tank with floating tubes as the boundaries, to con-duct the ship model resistance tests under the pack ice conditions. According to the analysis on the test data and experimental phenomena, we can find some conclusions as follows.
(1) As the concentration varies, the encountering frequencies between the ship model and the pack ice also shift towards a higher speed. At such encountering frequencies, the resistance values around the speed fluctuate dramatically, creating an unstable region of the resistance, and the unstable region shifts to the higher speed with the increased concentration.
(2) For the same speed point, the ratio of the pack ice resistance to the open water resistance increases with the increased concentration. For the same concentration, this ratio decreases as the speed increases.
(3) The mean value of the heave motion increases as the speed increases. The mean value of the heave motion under the pack ice conditions is smaller than that in open waters. The pitch motion tends to increase with the increased speed.