,

(School of Naval Architecture and Ocean Engineering,Jiangsu University of Science and Technology,Zhenjiang 212003,China)

Abstract:This paper is aimed to investigate ice load for a new Chinese polar research vessel,including level ice resistance and ice floe impact force.Estimation of ice load is most important for both ship designers and shipbuilders.Empirical methods are applied to calculate level ice resistance for the vessel.Ice model tests of the vessel are conducted,and the test data are compared with the empirical results.It is found that both calculated and experimental level ice resistances increase with ship speed and that the empirical method can make a reasonable prediction of level ice resistance.The vessel performance curve,i.e.the speed the vessel may attain in different level ice thicknesses,is also presented.In addition,the 3D oblique-type collision between the vessel and a circular-shaped ice floe is considered.An analytical method is applied to estimate ice floe impact forces for the vessel.The effects of the impact location,the normal frame angel and the ice floe size on the impact forces are also studied.Some discussions and suggestions are presented.

Key words:new Chinese polar research vessel;level ice resistance;ice floe;impact force

0 Introduction

Due to increased need in polar scientific research,a new Chinese polar research vessel has been built to research marine environments and resources.Understanding and calculating ice load for the vessel are important in preliminary stage of design process.

Estimation of level ice resistances is highly related to a vessel’s global performance.It can be used for selection of the propeller and propulsion system which meets the power requirement of the vessel.Many researchers have investigated level ice resistance by empirical,experimental and numerical methods.Lindqvist[1]proposed a formula to predict ice resistance on the basis of many full scale tests in the Bay of Bothnia.This formula was further developed by Riska et al[2]to calculate level ice resistance with some empirical parameters.Suyuthi et al[3]estimated ice resistance for level ice based on full scale measurement on KV Svalbard during expedition in March,2007.The results of ice resistance at particular speeds and ice thicknesses,in addition to the ship performance diagram were presented.Heinonen[4]carried out an experimental study on the effect of speed on the ice resistance of a ship based on both full scale and model tests.Information about the ice breaking process at high speeds was also gathered for future research.Wang[5]proposed a numerical method to simulate the interaction between moving level ice and a fixed conical structure.A numerical simulation method was presented by Hu and Zhou[6]to calculate ice resistance.The calculated results were compared with model test results,and the comparison showed that the numerical method could make a reasonable prediction of ice resistance in time domain.However,the numerical simulation method is a relatively complex method considering the bow shape.

Estimation of ice floe impact forces against the vessel is also important for ship design.The consequences of ice floe impact can be severe in terms of structural integrity,the safety of personnel and the pollution of environment.Hence,ship-ice floe impact modeling has been continuously developed over recent decades.Timco[7]summarized all available data related to ice floe impacts on structures,including forces from small icebergs,first-year and multi-year ice.He found a good correlation between the impact force and the kinetic energy.However,there was a wide range of ice forces in his predictive formulations due to several uncertain factors,notably the strength variation and the failure model of the ice.Popov et al[8]pioneered the work on accessing the ice impact loads on ships.Simplified analytical approach has been proposed by considering the 3D motions of ships and ice features in a simple manner.The friction during impact is not considered and it is assumed that the impact impulse coincides with the normal direction at contact point.Due to its simplicity,it has been implemented into regulations on calculating the ice impact load[9-12].Matskevitch[13]studied the eccentric impact of a floating ice feature interacting with a rigid wide structure.An approximate analytical solution for the maximum impact force and impact duration was obtained,in which force-penetration curves for the ice were needed.The motion of the impacting body was assumed to be planar.Experience has shown that ship-ice floe impacts are most likely to take place at the ship bow,so a non-vertical contact surface and sliding effect should be taken into account.

This paper focuses on the estimation of ice load for the new Chinese polar research vessel.Due to the simplicity,the empirical methods are applied to calculate the level ice resistance,and the calculated results are compared with model test data.The effects of ship speed and ice thickness on the level ice resistance are studied.The vessel performance curve is presented.In addition,the 3D oblique-type collision between the vessel and a circular-shaped ice floe is considered.In order to predict the ice floe impact force,the analytical method proposed by Song et al[14]which takes into account 6D motions of ship and ice and sliding effect is used in this paper.The effects of the impact location,the normal frame angel and the ice floe size on the impact forces are also investigated.

1 Level ice resistance

1.1 Empirical methods

There are many empirical formulas[15-17]available to calculate level ice resistance.Two of them are presented as follows:

(1)Lindqvist formulas

Lindqvist proposed simple formulas on the basis of the full scale tests in the Bay of Bothnia.In this formula,the ice resistance is divided into three components:crushing,bending and submersion.The formula is an equation of main dimensions,hull form,ice thickness,ice friction,ship speed and bending strength.The ice resistance formulas are expressed as

whereRice,Rc,RbandRsare total ice resistance,crushing resistance,bending resistance and resistance due to submersion respectively;σbis ice bending strength;hiis ice thickness;μ,φ,αandψare the friction coefficient,stem angle,waterline entrance angle and flare angle respectively;gis the gravity acceleration;ρwandρiare water and ice density respectively;Eis Young’s modulus;vis Poisson’s ratio;B,T,andLare ship’s breadth,draught and waterline length;andVis ship speed.

(2)Jeong formulas

Jeong formulas were proposed to predict ice resistance for standard icebreaker model ships and model test results to full-scale using calculated non-dimensional coefficients.The formulas are presented as follow:

whereRIis total ice resistance;CB,CcandCBRare coefficient of ice buoyancy resistance,coefficient of ice clearing resistance and coefficient of ice breaking resistance respectively;FrandSNare Froude number and strength number;αis index of Froude number;βis index of Strength number;ρiis ice density;Δρis water density minus ice density;andσfis the flexural strength of ice.The constants used are shown in Tab.1.

Tab.1 Constants in Jeong formulas for level ice resistance

1.2 Model tests

The ice model tests of the new Chinese polar research vessel were conducted at Aker Arctic.The model of the vessel was deployed in the model tests with a scaling factor of 1:22.76.The main particulars of the ship and the model are presented in Tab.2.The tests were performed in model level ice corresponding to a sea ice thickness of 1.57 m.In order to define a regression to the ice resistance,tests were also conducted in 0.97 m thick ice.An example of model tests is shown in Fig.1.

Fig.1 Test in level ice thickness of 1.57 m

Tab.2 Main particulars of the ship and the model

The performance tests in level ice were conducted at three different power levels.In the tests,the revolutions per minute(r/min)of Azipod units were first set to the target values and then the model was let to run freely.The model was free except yaw and sway,which were restricted by the guides to make the model run straight.The test distance was long enough to allow the speed to settle and this constant range speed was used in the analysis.

1.3 Results

The calculated ice resistances based on Lindqvist formulas and Jeong formulas are presented in Fig.2 and Fig.3 along with the ice model test results.It can be seen that both calculated and experimental ice resistances increase with ship speed,which indicates that the ice resistance is speed dependent.The comparisons also show that Jeong formulas overestimate the ice resistances in level ice thicknesses of both 1.57 m and 0.97 m.Lindqvist formulas predict that ice resistances are in good agreement with the model test data.Therefore,Lindqvist formulas are used to calculate ice resistances in different level ice thicknesses,i.e.,varying from 0.5 m to1.57 m.

Fig.2 Comparison of calculated and experimental ice resistances in 1.57 m thick level ice

Fig.3 Comparison of calculated and experimental ice resistances in 0.97 m thick level ice

Fig.4 shows the calculated ice resistance curves and the net thrust curve.It can be observed that the level ice resistance increases with speed for all cases,and the level ice thickness affects its rate of growth:a thick level ice results in a large rate of growth.The net thrust curve represents the thrust available to overcome the ice resistance after the open water resistance has been deducted.Therefore,the speed at the intersection point of the net thrust curve and the resistance curve represents the speed the vessel can achieve in the particular ice condition.

Fig.4 Ice resistance in level ice and the net thrust curve

The new Chinese polar research vessel performance is presented in Fig.5.It is shown that the vessel can reach the speed of 6.4 m/s in level ice thickness of 0.5 m and the speed of 1.67 m/s in level ice thickness of 1.57 m.The new Chinese polar research vessel performance at full power in level ice were required to achieve a speed of 1.03 m/s in level ice thickness of 1.5 m with a 20 cm thick snow layer.The results indicate that the vessel fulfills the requirements.In addition,the limitation of level ice thickness for this vessel is approximately 1.88 m on the basis of its performance curve.

Fig.5 New Chinese polar research vessel’s performance

2 Ice floe impact forces

2.1 Analytical method

When the ice floe collision happens at the bow of a ship,considerable motions in sway,yaw and roll may be produced.It is interesting to estimate the ice floe impact forces for the new Chinese polar research vessel.The analytical method proposed by Song et al[14]is applied here to calculate ice floe impact forces.The calculation procedure consists of the following steps(see Fig.6).First,a full 3D model is applied to assess the energy dissipation in a ship bow-ice floe collision on the basis of impulse momentum and energy conservation.Secondly,the force-and energy dissipation-indentation relationships are determined by introducing the pressure-area relationship and the contact area-indentation relationship.Thirdly,the impact forces are derived by using the calculated dissipated energy and the force/energy-indentation relationship from the previous two steps.Ref.[14]can be referred to for the details.

Fig.6 Methodology to estimate ice impact forces

The new Chinese polar research vessel is categorized as Polar Class PC3.According to IACS rule,the ice pressure-area relationship for PC 3 condition isP=3.2A-0.1.The crushing class factor becomes

withP0=3.2.Therefore,the design vessel speed is 2.95 m/s.

The 3D oblique-type collision between the new Chinese polar research vessel and a circularshaped ice floe is considered.It is assumed that the ice floe has a radius of 15 m and a thickness of 2 m,and the ice floe is at rest before collision.The vessel has a speed of 2.95 m/s.The coefficient of friction between the ice floe and the vessel is assumed to be 0.15.

The force-indentation and the energy-indentation relationships for a circular-shaped ice floe are derived on the basis of the local geometry of the ice floe by the following procedure.

The indentation is assumed to end up with a triangle contact area.The contact width is given by

whereδis indentation.The contact height is expressed as

whereβ′is the normal frame angle of the hull,and the hull angles defined by IACS rule are shown in Fig.7.The normal area is presented as

Fig.7 Definition of hull angles

When the indentationδis small relative to the ice floe radius,the norma contact area can be expressed as

By introducing the ice pressure-area relationshipP=3.2A-0.1,the normal force becomes

Hence,the energy dissipation is found by integrating the force:

2.2 Effect of impact location

In IACS rule,the waterline length of the bow region is generally to be divided into 4 sub-regions of each length.To investigate the effect of impact location,four impact points which are at the mid-length position of each sub-region are considered,see Fig.8.The normal frame angleβ′and the waterline angleαat different impact points are listed in Tab.3.

Fig.8 Illustration for impact location

Tab.3 Impact points

Fig.9 shows the calculated impact forces for the different impact locations.r^xis the longitudinal distance from the impact point to the COG of the vessel andLis the waterline length of the vessel.It is found that the calculated impact force(i.e.,5.62 MN)is the largest when the impact location is closest to the forward perpendicular.The impact force for Impact Point 2(i.e.,5.33 MN)is close to that for Impact Point 3(i.e,5.25 MN),which indicates that there is a little difference in impact forces when the new Chinese polar research vessel-ice floe collision happens at this area.The minimum impact force is 4.84 MN at Impact Point 4.

Fig.9 Ice floe impact forces for different impact locations

2.3 Effect of normal frame angle

It is interesting to see how the ice floe impact force depends on the normal frame angle.It is assumed that the collision between the new Chinese polar research vessel and the ice floe happens at Impact Point 1.Fig.10 shows the calculated ice floe impact force versus the normal frame angle.It is seen that the normal frame angle has a significant effect on the impact force.A large normal frame angle results in a small impact force.The results indicate that a normal frame angle is a very important parameter for polar vessels’design with respect to ice floe impact force.For the new Chinese polar research vessel,the normal frame angle is 51.77° at this impact point,which results in good performance with respect to both level ice resistance and ice floe impact force.

Fig.10 Ice floe impact force versus normal frame angle

2.4 Effect of ice floe size

A sensitivity study is carried out for uncertain sizes of ice floe.Five sizes of ice floe are considered.The collision between the new Chinese polar research vessel and the ice floe with different sizes at Impact Point 1 is assumed.The radius of ice floe varies from 10 m to 30 m,and the mass ratio( )Mice/Mshipincreases from 0.04 to 0.34.The results of the ice floe impact force are plotted in Fig.11.It is shown that the impact force increases with the mass ratio.It can be concluded that the size of ice floe plays an important role for determining the design ice load.

Fig.11 Ice floe impact force versus mass ratio

3 Conclusions

Level ice resistance and ice floe impact force for the new Chinese polar research vessel were investigated by using empirical and analytical methods in this paper.The ice model tests of the vessel in level ice thicknesses of 1.57 m and 0.97 m were conducted.The comparisons between the calculated level ice resistance(Lingdqvist formulas)and the model test results show a good agreement.Jeong formulas predict the larger resistances compared to the model test results.Both the empirical and experimental results show that the level ice resistance is speed dependent as it increases linearly with speed,and its rate of growth is affected by level ice thickness,that is a thick ice results in a large rate of growth.The calculated vessel performance curve based on Lindqvist formulas is also achieved.The results indicate that the new Chinese polar research vessel fulfills its requirements,as it can achieve a forward speed of 1.67 m/s in 1.57 m thick level ice.Estimation of the ice floe impact forces against the new Chinese polar research vessel and study of the effects of the impact location,the normal frame angle and the size of ice floe on the impact force show that the calculated impact force is the largest when the impact location is closest to the forward perpendicular,and that the normal frame angle is a significant parameter for polar vessel’s design with respect to ice floe impact force.In addition,a knowledge of ice floe size in polar area is very important for determining the design ice load.Therefore,in order to predict a more reasonable ice load,it is suggested to gather more information on ice floe shape,size,thickness and strength in the polar shipping area.