Equivalent ice layer conversion method for snow in the continuous icebreaking resistance of icebreakers

Abstract

This invention discloses a method for converting snow into equivalent ice layer thickness in the continuous icebreaking resistance of an icebreaker. The method includes: dividing icebreaking resistance into impact resistance, bending failure resistance, and submersion resistance; determining the conversion relationship between the actual snow layer thickness and the equivalent ice layer thickness when calculating impact resistance, bending failure resistance, and submersion resistance; calculating the icebreaking resistance of snow using the formula for icebreaking resistance of ice, wherein the ice layer thickness in the formula for icebreaking resistance of ice is equal to the equivalent ice layer thickness of snow. The method of this invention provides a more accurate estimation of icebreaking resistance.

Description

Technical Field

[0001] This invention relates to the field of shipbuilding technology, and in particular to a method for converting snow into equivalent ice layers in the continuous icebreaking resistance of an icebreaker. Background Technology

[0002] The polar regions are rich in resources, and polar shipping routes can significantly shorten the voyage from Asia to Europe, leading to increasingly frequent economic activities in the polar regions. Whether icebreakers or vessels capable of autonomous navigation in the polar regions, a certain level of icebreaking capability is essential. Predicting icebreaking resistance is a key technology in polar vessel design, determining the vessel's hull form and main engine power. Current methods for resistance prediction include empirical formulas and numerical simulations, assessing the icebreaking resistance performance of vessels under layered ice conditions. In reality, polar shipping lanes contain not only layered ice but also snow on top of it. The physical properties of snow differ from those of ice, resulting in different forms of resistance during icebreaking. Since the physical properties of snow are difficult to construct in numerical simulations, a common international approach is to simplify the snow model, equating a specified snow thickness to a layer of ice of a certain thickness, and then performing numerical simulations or empirical formula conversions on a single layer of ice mode. This approach greatly simplifies the evaluation process but has accuracy limitations. In a typical icebreaking process, the resistance exerted by ice on a ship can be mainly divided into four parts: impact resistance, ice bending failure resistance, ice potential energy reduction resistance, and frictional resistance between ice and the ship's hull. Among these four parts, the bending failure strength of snow is much lower than that of ice, while the coefficient of friction of snow is greater than that of ice. Snow melts in water, but ice still exerts significant frictional resistance on the ship's hull. Therefore, the different physical properties of snow and ice result in distinctly different resistance exerted by snow on ships during icebreaking. Simply equating snow thickness with ice thickness is flawed in its assessment principle and cannot guarantee the accuracy of the results.

[0003] With the increasing number of ships navigating polar regions, the assessment of icebreaking resistance has become increasingly important. Currently, common assessment techniques include empirical formulas and numerical simulations. Empirical formulas, which are frequently used, divide icebreaking resistance into three parts: impact resistance, ice bending failure resistance, and submersion resistance (including ice potential energy changes and frictional resistance between the ice and the hull). However, empirical formulas only consider ice thickness, omitting snow thickness. Since a certain thickness of snow covering the ice is common in polar regions, this empirical formula has limitations. To address the assessment of snow-induced ship resistance, the International Towing Tank Conference (ITTC) introduced the concept of equivalent ice thickness, equating snow to a certain thickness of ice for resistance assessment, h′. i =h i +k e *h SN , where h i It is the thickness of the ice, h SN It's the thickness of the snow, k e Empirical coefficient, h′ i It is the equivalent total ice thickness that takes into account the snow thickness.

[0004] For k e International scholars have proposed their own methods for estimating the value of k, for example, given k e The value range is 0.5 to 1.5. Some scholars have suggested a value of 1 / 3, while others believe that if the snow is fresh, the value should be 0.

[0005] Some also believe that the density of snow is assumed to be 400 kg / m³. 3 The density of ice is 920 kg / m³. 3 Then k e The value is approximately 1.83.

[0006] Some scholars have also proposed the following calculation method: k e =0.284 + 0.575 * 10 -3 SWB -0.164 h I -0.048V, where V is the ship's speed and S WB It is the wet bottom area.

[0007] In summary, the estimated equivalent ice thickness for snow ranges widely, from about 1 / 3 to 1.8 meters. If the snow thickness is taken as 0.3 meters, the equivalent ice thickness can range from 0.1 meters to 0.5 meters, which is quite large and unfavorable for estimating ice-breaking resistance. If the equivalent ice thickness is too small, the ice-breaking capacity may be insufficient; if it is too large, the installed power configuration may be too large, resulting in increased initial investment or wasted main unit power.

[0008] Existing methods for estimating the equivalent ice thickness of snow have the following drawbacks:

[0009] Most equivalent conversion formulas are relatively simple, failing to reflect the compositional mechanism of snow or ice in icebreaking resistance, nor do they account for the differences in physical and mechanical properties between snow and ice. Furthermore, different estimation methods yield significant numerical discrepancies. Such input conditions lead to overestimation of icebreaking resistance. Using a snow thickness of 0.3 meters as a basis, the equivalent ice thickness ranges from 0.1 meters to 0.5 meters. Adding a 2.0-meter ice layer thickness, the ice layer thickness used to calculate icebreaking resistance ranges from 2.1 meters to 2.5 meters, a difference of nearly 20%. Based on the components of icebreaking resistance, different resistance components have different relationships with ice layer thickness. According to empirical formulas, the impact ice load component of icebreaking resistance has a quadratic relationship with ice thickness, the resistance component caused by ice bending failure has a 1.5-power relationship, and the frictional resistance component has a linear relationship. Therefore, a 20% difference in ice thickness can result in a difference of over 20% in the estimated total resistance value. Such a fluctuation is unacceptable for ship design and may lead to significant changes in hull design. Summary of the Invention

[0010] The technical problem to be solved by the present invention is to overcome the above-mentioned defects in the prior art and provide a method for converting snow into equivalent ice layer in the continuous icebreaking resistance of icebreakers.

[0011] The present invention solves the above-mentioned technical problems through the following technical solution:

[0012] A method for converting snow into equivalent ice layers in the continuous icebreaking resistance of an icebreaker, comprising:

[0013] Ice-breaking resistance is divided into impact resistance, bending failure resistance and immersion resistance. The conversion relationship between the actual snow layer thickness and the equivalent ice layer thickness is determined when calculating impact resistance, bending failure resistance and immersion resistance.

[0014] The ice-breaking resistance of snow is calculated using the same formula as the ice-breaking resistance of ice, where the thickness of the ice layer is equal to the equivalent thickness of the snow layer when it is formed into ice.

[0015] Furthermore, when calculating impact resistance, the actual snow layer thickness H SN Equivalent ice thickness H′ of snow ICE The relationship between them is: H′ ICE =k c *H SN ;

[0016] Where, k c The impact drag equivalent coefficient, k = σ SN / σ ICE ; where σ ICE σ is the bending failure strength of ice. SN The bending failure strength of snow.

[0017] Furthermore, in the ice-breaking resistance of snow, the impact resistance R C The calculation formula is:

[0018]

[0019] Where σ0 is the flexural breaking strength of ice, and μ is the coefficient of friction of ice. α is the inclination angle of the first column, and α is the waterline angle. H1=H′ ICE .

[0020] Furthermore, when calculating the bending failure resistance, the actual snow layer thickness H SN The equivalent ice thickness H″ of snow ICE The relationship between them is: H″ ICE =k b *H SN ;

[0021] Where, k b The equivalent coefficient for bending failure resistance; k = σ SN / σ ICE ; where σ ICE σ is the bending failure strength of ice. SN The bending failure strength of snow.

[0022] Furthermore, in the ice-breaking resistance of snow, the bending failure resistance R b The calculation formula is:

[0023]

[0024] Where σ0 is the flexural breaking strength of ice, and μ is the coefficient of friction of ice. α is the inclination angle of the first column, and α is the waterline angle. H2 = H″ ICE B is the ship's waterline width;

[0025] m=E / (12*(1-v 2 )*g*ρ sea ;

[0026] Where E is Young's modulus, v is Poisson's ratio, g is gravitational acceleration, and ρ is... sea This is the density of seawater.

[0027] Furthermore, when calculating immersion resistance, the actual snow layer thickness H SN Equivalent ice thickness H″′ of snow ICE The relationship between them is: H″′ ICE =k s *H SN ;

[0028] Where, k s This is the equivalent coefficient for immersion resistance;

[0029] k s =(ρ sea -ρ snow ) / (ρ sea -ρ ice );

[0030] Where, ρ sea ρ is the density of seawater. snow ρ is the density of snow. ice This is the density of ice.

[0031] Furthermore, in the ice-breaking resistance of snow, the submersion resistance R s The calculation formula is:

[0032]

[0033] Where, δ ρ ρ is the density difference between water and ice; g is the acceleration due to gravity;

[0034] H3=H″′ ICE ;

[0035] T is the ship's draft; B is the ship's waterline width; μ is the coefficient of friction of ice; A μ A is the area of ​​the flat bottom of the ship; f Area of ​​the bow section; α is the inclination angle of the first column, and α is the waterline angle.

[0036] The beneficial effects of this invention are as follows: This invention provides methods for calculating the equivalent ice thickness of snow based on the ice-breaking mechanism and the physical properties of ice and snow for different ice-breaking resistance components; the equivalent ice thickness estimation methods given by this invention for different ice-breaking mechanisms are more accurate than the calculated value of the equivalent ice thickness of a single snow, and the ice-breaking resistance estimation results obtained by using this invention to estimate the equivalent ice thickness of snow are more accurate. Attached Figure Description

[0037] Figure 1 This is a schematic diagram of the main features of the hull according to a preferred embodiment of the present invention. Detailed Implementation

[0038] The present invention will be described more clearly and completely below with reference to a preferred embodiment and the accompanying drawings.

[0039] A method for converting snow into equivalent ice layers in the continuous icebreaking resistance of an icebreaker, comprising:

[0040] Ice-breaking resistance is divided into impact resistance, bending failure resistance and immersion resistance. The conversion relationship between the actual snow layer thickness and the equivalent ice layer thickness is determined when calculating impact resistance, bending failure resistance and immersion resistance.

[0041] The ice-breaking resistance of snow is calculated using the same formula as the ice-breaking resistance of ice, where the thickness of the ice layer is equal to the equivalent thickness of the snow layer when it is formed into ice.

[0042] In this method, ice-breaking resistance is divided into impact resistance, bending failure resistance, and immersion resistance, and calculated in three parts.

[0043] Part 1: When calculating impact resistance, the actual snow layer thickness H SN Equivalent ice thickness H′ of snow ICE The relationship between them is: H′ ICE =k c *H SN ;

[0044] Where, k c The impact drag equivalent coefficient, k = σ SN / σ ICE ; where σ ICE σ is the bending failure strength of ice. SN The bending failure strength of snow.

[0045] Of the ice-breaking resistance of snow, impact resistance R C The calculation formula is:

[0046]

[0047] Where σ0 is the flexural breaking strength of ice, and μ is the coefficient of friction of ice. α is the inclination angle of the first column, and α is the waterline angle. H1=H′ ICE .

[0048] First column inclination angle And the waterline angle α, such as Figure 1 As shown.

[0049] Figure 1 In this context, T represents the ship's draft, L represents the ship's waterline length, and B represents the ship's waterline width.

[0050] Part Two: When calculating the bending failure resistance, the actual snow layer thickness H SN The equivalent ice thickness H″ of snow ICE The relationship between them is: H″ ICE =k b *H SN ;

[0051] Where, k b The equivalent coefficient for bending failure resistance; k = σ SN / σ ICE ; where σ ICE σ is the bending failure strength of ice. SN The bending failure strength of snow.

[0052] In the ice-breaking resistance of snow, the bending failure resistance R b The calculation formula is:

[0053]

[0054] Where σ0 is the flexural breaking strength of ice, and μ is the coefficient of friction of ice. α is the inclination angle of the first column, and α is the waterline angle. H2 = H″ ICE B is the ship's waterline width;

[0055] m=E / (12*(1-v 2 )*g*ρ sea ;

[0056] Where E is Young's modulus, v is Poisson's ratio, g is gravitational acceleration, and ρ is... sea This is the density of seawater.

[0057] Part Three: When calculating immersion resistance, the actual snow layer thickness H SN Equivalent ice thickness H″′ of snow ICE The relationship between them is: H″′ ICE =k s *H SN ;

[0058] Where, k s This is the equivalent coefficient for immersion resistance;

[0059] k s =(ρ sea -ρ snow ) / (ρ sea –ρ ice );

[0060] Where, ρ sea ρ is the density of seawater. snow ρ is the density of snow. ice This is the density of ice.

[0061] In the ice-breaking resistance of snow, the submersion resistance R s The calculation formula is:

[0062]

[0063] Where, δ ρ ρ is the density difference between water and ice; g is the acceleration due to gravity;

[0064] H3=H″′ ICE ;

[0065] T is the ship's draft; B is the ship's waterline width; μ is the coefficient of friction of ice; A μ A is the area of ​​the flat bottom of the ship; f Area of ​​the bow section; α is the inclination angle of the first column, and α is the waterline angle.

[0066] Figure 1 The parameters mentioned above are shown in the figure.

[0067] Based on the ice-breaking mechanism and the composition of its resistance, this invention addresses the impact resistance R. C Bending failure resistance R b Submersion resistance R S The equivalent ice thickness is given respectively.

[0068] This invention innovates the method for estimating the equivalent ice thickness of snow in ice-breaking resistance estimation:

[0069] 1. Based on the morphological characteristics of ice breaking, ice breaking resistance is divided into impact resistance, bending failure resistance and submersion resistance, and the equivalent ice thickness conversion method for snow is given for each.

[0070] 2. In the calculations related to the characteristic values ​​of the hull form, an exhaustive calculation was performed based on the mainstream characteristic value range of icebreaker hull forms. The average value was given based on the results with small fluctuation range, realizing a unified equivalent ice thickness calculation method under different hull form characteristic values. This simplifies the calculation while ensuring conversion accuracy.

[0071] 3. The conversion method allows users to define the bending failure strength of the ice layer. Because the bending failure strength of current-year ice and multi-year ice differs significantly, this ensures the consistency between the conversion result of the equivalent ice thickness of snow and the actual operating conditions, thus guaranteeing the accuracy of the resistance estimation.

[0072] The present invention has the following advantages:

[0073] 1. For different ice-breaking resistance components, based on their ice-breaking mechanisms and referring to the physical properties of ice and snow, methods for converting snow into equivalent ice thickness are given respectively.

[0074] 2. The equivalent ice thickness estimation methods given for different ice-breaking mechanisms are more accurate than the equivalent ice thickness calculation value of a specified snow. The ice-breaking resistance estimation results obtained by using the equivalent ice thickness estimation of snow using the present invention are more accurate.

[0075] While specific embodiments of the present invention have been described above, those skilled in the art should understand that these are merely illustrative examples, and the scope of protection of the present invention is defined by the appended claims. Those skilled in the art can make various changes or modifications to these embodiments without departing from the principles and essence of the present invention, but all such changes and modifications fall within the scope of protection of the present invention.

Claims

1. A method for calculating the equivalent ice layer in the continuous icebreaking resistance of an icebreaker, characterized in that, It includes: Ice-breaking resistance is divided into impact resistance, bending failure resistance and immersion resistance. The conversion relationship between the actual snow layer thickness and the equivalent ice layer thickness is determined when calculating impact resistance, bending failure resistance and immersion resistance. When calculating impact resistance, the actual snow layer thickness H SN Equivalent ice thickness H′ of snow ICE The relationship between them is: H′ ICE =k c *H SN ; Where, k c The impact drag equivalent coefficient, k = σ SN / σ ICE ; where σ ICE σ is the bending failure strength of ice. SN The bending failure strength of snow; When calculating the bending failure resistance, the actual snow layer thickness H SN The equivalent ice thickness H″ of snow ICE The relationship between them is: H″ ICE =k b *H SN ; Where, k b The equivalent coefficient for bending failure resistance; k = σ SN / σ ICE ; where σ ICE σ is the bending failure strength of ice. SN The bending failure strength of snow; When calculating immersion resistance, the actual snow layer thickness H SN Equivalent ice thickness H″′ of snow ICE The relationship between them is: H″′ ICE =k s *H SN ; Where, k s This is the equivalent coefficient for immersion resistance; k s =(ρ sea -r snow ) / (ρ sea -r ice ); Where, ρ sea ρ is the density of seawater. snow ρ is the density of snow. ice The density of ice; The ice-breaking resistance of snow is calculated using the same formula as the ice-breaking resistance of ice, where the thickness of the ice layer is equal to the equivalent thickness of the snow layer when it is formed into ice.

2. The method for calculating the equivalent ice layer in the continuous icebreaking resistance of an icebreaker as described in claim 1, characterized in that, Of the ice-breaking resistance of snow, impact resistance R C The calculation formula is: Where σ0 is the flexural breaking strength of ice, and μ is the coefficient of friction of ice. α is the inclination angle of the first column, and α is the waterline angle. H1=H′ ICE .

3. The method for calculating the equivalent ice layer in the continuous icebreaking resistance of an icebreaker as described in claim 1, characterized in that, In the ice-breaking resistance of snow, the bending failure resistance R b The calculation formula is: Where σ0 is the flexural breaking strength of ice, and μ is the coefficient of friction of ice. α is the inclination angle of the first column, and α is the waterline angle. H2=H″ ICE ; B is the width of the ship's waterline; m=E / (12*(1-v 2 )*g*r sea ; Where E is Young's modulus, v is Poisson's ratio, g is gravitational acceleration, and ρ is... sea This is the density of seawater.

4. The method for calculating the equivalent ice layer in the continuous icebreaking resistance of an icebreaker as described in claim 1, characterized in that, In the ice-breaking resistance of snow, the submersion resistance R s The calculation formula is: Where, δ ρ ρ is the density difference between water and ice; g is the acceleration due to gravity; H3=H″′ ICE ; T is the ship's draft; B is the ship's waterline width; μ is the coefficient of friction of ice; A μ A is the area of ​​the flat bottom of the ship; f Area of ​​the bow section; α is the inclination angle of the first column, and α is the waterline angle.

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