Method for predicting the response of a marine vessel to movement in an ice ridge field

Abstract

The application discloses a kind of ship in ice ridge field movement response forecasting method, comprising the following steps: establishing ice ridge structure simplified model;Based on ice ridge structure simplified model, establish ice ridge field probability model;According to ice ridge structure simplified model and ice ridge field probability model, establish ship motion equation;Establish ship ice resistance calculation model, ship net thrust model, ship hydrodynamic model, ship rudder external force model;Through ship motion equation, ship ice resistance calculation model, ship net thrust model, ship hydrodynamic model, ship rudder outside force model calculation obtains the movement response of ship in ice ridge field.The present application is based on simplified analytical method, considering the influence of ship speed on ice resistance, proposes a kind of method for simulating the movement response of icebreaker under the impact of ice ridge, can predict the navigation performance of ship under ice ridge field, further analyzes the average speed and navigation ability that ship can reach, to evaluate the icebreaking performance of polar ship.

Description

Technical Field

[0001] This invention belongs to the field of polar vessel technology and relates to dynamic evaluation technology of polar vessel icebreaking navigation performance, specifically to a method for predicting the motion response of a vessel in an ice ridge field. Background Technology

[0002] The polar regions possess abundant resources such as oil and natural gas. Due to the continuous melting of glaciers, the transportation and development of these energy resources have become pressing issues. As human research into the polar regions deepens, the Northeast Passage has become a reality during the summer. The development of polar vessels has received significant attention from countries worldwide, with many major powers possessing their own icebreaker fleets.

[0003] Ice ridges are among the most challenging obstacles ships encounter during polar navigation. In the frigid subarctic regions, keel depths can reach 25 meters or more, while in the Arctic, they can exceed 50 meters. When encountering an ice ridge, a ship is highly likely to be unable to break through and become stuck in the ice, causing significant structural damage, potentially drifting into shallower waters, running aground, and endangering the safety of personnel. To date, the main methods used to study ship-ice ridge collisions include the finite element method and the discrete element method.

[0004] Since calculating the interaction between ships and ice ridges using numerical simulation methods is very time-consuming, a new technical solution is needed to address this problem. Summary of the Invention

[0005] Purpose of the invention: To overcome the shortcomings of existing technologies, this invention provides a method for predicting the motion response of ships in ice ridge fields. Based on a simplified analytical analysis method, it considers the influence of ship speed on ice resistance and proposes a method to simulate the motion response of icebreakers colliding with ice ridges. This method can predict the navigation performance of ships in ice ridge fields and further analyze the average speed and navigation capability that ships can achieve in order to evaluate the icebreaking performance of polar ships.

[0006] Technical Solution: To achieve the above objectives, this invention provides a method for predicting the motion response of ships in ice ridge fields, comprising the following steps:

[0007] S1: Establish a simplified model of the ice ridge structure;

[0008] S2: Based on the simplified model of ice ridge structure, establish a probability model of ice ridge field;

[0009] S3: Based on the simplified model of the ice ridge structure and the probability model of the ice ridge field, establish the equations of motion for the ship;

[0010] S4: Establish models for calculating ship ice resistance, ship net thrust, ship hydrodynamics, and ship rudder external force.

[0011] S5: The ship's motion response in the ice ridge field, such as velocity, acceleration, displacement, ice resistance, and net thrust, is calculated by using the ship's motion equations, ship ice resistance calculation model, ship net thrust model, ship hydrodynamic model, and ship rudder external force model.

[0012] A simplified model of an ice ridge structure includes a solidified layer, a sail, and a keel. Ice ridge structures are more complex, typically modeled in trapezoidal or triangular forms, where the base width w... s When the value is 0, it can be simplified to a triangular model. This invention establishes a simplified model of the ice ridge structure in the form of a triangle. The simplified model of the ice ridge structure includes the sail height h. s Keel depth h k 、sail width w s , keel width w k These are some of the characteristics.

[0013] Furthermore, this invention analyzes measured data on the geometric characteristics of over 300 one-year-old ice ridges in the Arctic, subpolar, and Barents Sea regions, constructing a geometric relationship and size probability model for the one-year-old ice ridge structure. Within a certain ice zone, multiple ice ridges are simulated and generated according to a probability function; ships navigating within this zone will collide with the generated ice ridges. The method for establishing the ice ridge field probability model is as follows:

[0014] Keel width w k With Hodaka H s The average ratio is expressed as:

[0015] w k =16.7h s (1)

[0016] sail width w s With Hodaka H s The average ratio is expressed as:

[0017] w s =3.75h s (2)

[0018] The maximum sail height follows a Gamma distribution, and its probability density function is expressed as:

[0019]

[0020] Among them, h s The maximum value of the sail height is given by parameter β, which is called the shape parameter and affects the shape of the curve, with a value of 2.42; parameter α is called the scale parameter and affects the location of the distribution, with a value of 1.14.

[0021] The maximum ratio of ice ridge keel depth to sail height follows a Gamma distribution, and its probability density function (PDF) can be given by the following expression:

[0022]

[0023] Among them, h k / h s The maximum ratio of keel depth to sail height is given by a shape parameter β of 3.05 and a scale parameter α of 1.70.

[0024] The thickness of the consolidation layer follows a Gamma distribution, and its probability density function (PDF) can be expressed as follows.

[0025]

[0026] Among them, h c The thickness of the consolidation layer is given by a shape parameter β of 2.97 and a scale parameter α of 0.54.

[0027] The spacing between ice ridge keels can be modeled using an exponential distribution:

[0028] p(d;μ(h c ))=μ(h c )exp(-μ(h c )d) (6)

[0029] In the formula, d is the distance between ice ridge keels; μ is the shape parameter of the distribution, i.e. the expected number of keels per kilometer.

[0030] Furthermore, the reference frames used are a fixed body reference frame and a fixed ground reference frame, both of which satisfy the right-hand rule. The ship's fixed frame, denoted as G-xyz, is fixed to the ship, with its origin coinciding with the ship's center of gravity, and Gx representing the ship's direction of travel. The Earth's fixed frame, denoted as O0-x0y0z0, is fixed to the Earth, and in the initial stage of the simulation, the fixed object frame coincides with the Earth's fixed frame.

[0031] In step S3, the ship's equation of motion is the ship's three-degree-of-freedom equation of motion, expressed as:

[0032]

[0033] In the formula, M is the diagonal mass matrix; A is the additional mass matrix; U(t), and These are displacement, velocity, and acceleration vectors, respectively. F(t) considers ice resistance, propeller net thrust, rudder external force, and hydrodynamic force. F(t) is equal to the superposition and summation of ice resistance, propeller net thrust, rudder external force, and hydrodynamic force. Ice resistance, propeller net thrust, rudder external force, and hydrodynamic force are calculated using ship ice resistance calculation model, ship net thrust model, ship rudder external force model, and ship hydrodynamic model, respectively. C and K are the damping matrix and stiffness matrix, respectively.

[0034] Since ships are covered by ice when navigating in ice ridges, and neglecting hydrodynamic damping and restoring forces, the ship's equation of motion simplifies to:

[0035]

[0036] Among them, the mass matrix Additional mass matrix

[0037] In the formula, m is the mass of the hull; I 66 Let A be the moment of inertia along the z-direction; 11 A 22 A 66 These represent the added mass in the x-direction, the added mass in the y-direction, and the added moment of inertia in the z-direction, respectively.

[0038] In the initial design phase of the ship A 11 A 22 A 66 and I 66 It can be calculated using the following expression:

[0039]

[0040]

[0041]

[0042]

[0043] In the formula, L is the ship's length, B is the ship's beam, T is the ship's draft, and C... b For the ship's block coefficient, Let g be the ship's displacement and g be the acceleration due to gravity.

[0044] Based on the linear acceleration assumption of the NewMark method, the following three equations can be obtained:

[0045]

[0046]

[0047]

[0048] In the formula, δ t t represents the time interval for numerical integration. k This represents the k-th time step.

[0049] Furthermore, in step S4, the ship ice resistance calculation model consists of a smooth ice resistance model and an ice ridge resistance model. The ice ridge resistance model is divided into solidified layer resistance, sail resistance, and ice ridge keel resistance. Solidified layer resistance is calculated using the smooth ice resistance model. Ice ridge keel resistance includes bow keel resistance and midship keel resistance.

[0050] The resistance model for smooth ice consists of three parts: fracturing, bending, and submersion, expressed by the following formula:

[0051]

[0052]

[0053]

[0054]

[0055]

[0056]

[0057] Among them, R l R s R b R c These are the total ice resistance during leveling, ice resistance during immersion, ice resistance during bending failure, and ice resistance during compression, respectively; σ b h represents the flexural strength of ice. i The thickness of the smooth ice is represented by u, φ, ψ, and α, which are the coefficient of friction, bow inclination angle, outward drift angle, and waterline angle, respectively; g is the acceleration due to gravity; ρ w ρ i Here, E represents the density of seawater and sea ice; V represents Young's modulus; B, T, and L represent the ship's beam, draft, and waterline length, respectively; and V represents the ship's speed.

[0058] The resistance of a sail includes friction and the cohesive force of the ice freezing, and can be expressed as:

[0059] F sail =p s w s =(p sg +p sc )w s (twenty two)

[0060] In the formula, p s This refers to the load per unit width of the sail, expressed in kN / m; p sg This represents the load per unit width of the sail, calculated based on its weight and height, expressed in kN / m; p sc The load per unit width of the sail due to cohesion is expressed in kN / m, and the cohesion is c. sThe unit is kPa.

[0061] A soil mechanics model was used to simulate the load per unit width of the sail under friction and cohesion:

[0062]

[0063] p sc =2c s (h s )K ps (twenty four)

[0064] In the formula, γ is the unit weight of ice, with units of kN / m3 (γ=γg); n represents the porosity of the sail (n=0.3);

[0065] K ps Rankin's passive earth pressure coefficient can be expressed as:

[0066] K ps =(1+sinψ) s ) / (1-sinψ s (25)

[0067] In the formula, ψ s It is the internal friction angle of the ice block in the sail;

[0068] The cross-sectional length of the sail at the waterline can be expressed as:

[0069] L ps =H s tan(φ+ψ s / 2) (26)

[0070] In the formula, φ = 45° is the angle when the sail is stationary.

[0071] The bow keel resistance takes into account the effect of ship speed and is expressed as:

[0072]

[0073] Among them, h r (x) represents the local ice ridge thickness; C p It is a constant.

[0074] The midhull keel resistance of a ship takes into account the effect of ship speed and is expressed as:

[0075]

[0076] in, It is a non-negative number, C m It is a constant.

[0077] During the process of a ship reversing and accelerating forward again, it is mainly affected by ice breakage resistance. The ice breakage resistance in the waterway can be expressed as:

[0078]

[0079] Among them, H M The ice resistance in the channel is δ, the slope angle of the ice fragment sidewall is ρ. Δ A represents the density difference between ice and water. WF F is the waterline area at the bow of the ship. n H is a Froude number. F The thickness of the ice floe as the bow shifts and moves towards the side parallel to the midship; when B > 10m and H M When H > 0.4m, F =0.26+(BH) M ) 0.5 ;

[0080] Furthermore, in step S4, the ship net thrust model is used to calculate the total force acting on the ship at each time step. The net thrust is the thrust that overcomes ice resistance after subtracting open water resistance.

[0081] The net thrust formula in the ship net thrust model is expressed as:

[0082]

[0083] Among them, v ow For open water velocity; v n T represents the velocity component in the direction of the icebreaker's movement; when the ship's speed is the open-water speed, the net thrust is zero; n It is the tie rod tension, which is defined as:

[0084] T pull =K e (P s D p ) 2 / 3 (31)

[0085] Among them, P s Power; D p K is the propeller diameter; e It is a dimensionless coefficient.

[0086] Furthermore, the movement of the ship in the ice ridge field in step S5 is as follows:

[0087] When a ship becomes stuck in an ice ridge and cannot move forward, its speed drops to zero. It will then use reverse thrust to reverse the ship a predetermined distance. After reversing the predetermined distance, the ship will propel itself forward with maximum power, accelerating again to collide with the ice ridge. This collision process will be repeated until the ship sails out of the ice ridge. If the ship does not have enough thrust to propel itself forward, it will eventually become stuck in the ice ridge.

[0088] Furthermore, the ship rudder external force model is used to calculate the loads that the ship experiences during motion, namely the rudder external force.

[0089] Furthermore, the method for establishing the ship hydrodynamic model in step S4 is as follows: the net propeller thrust and rudder external force are combined and decomposed into the ship's pitch, sway, and yaw directions, respectively, as shown in the following formulas:

[0090]

[0091] In the formula, T net Indicates net thrust; C L and C D These represent the lift and drag coefficients of the rudder, respectively; V f Indicates fluid velocity; A r Represented as rudder area; x r This indicates the longitudinal position of the rudder; that is, the distance from the center of the rudder's force to the ship's center of gravity. The stern rudder is a negative value.

[0092] The hydrodynamic forces acting on a ship are calculated using empirical formulas as follows:

[0093]

[0094] In the formula, R n =uL / ν represents the Reynolds number; u represents the longitudinal velocity of the ship; L represents the ship's length; ν represents the kinematic viscosity of seawater; ρ w S represents the density of seawater. w Indicates the wetted surface area of ​​the hull; C D (x) represents the drag coefficient of each longitudinal section of the hull; that is, the resistance coefficient of fluid passing through an infinitely long cylinder equivalent to the cross-sectional area of ​​each longitudinal section of the hull; D(x) represents the draft of each longitudinal section of the hull; v(x) represents the lateral velocity at each longitudinal section of the hull.

[0095] The method for calculating the ship's motion response in the ice ridge field in step S5 is as follows:

[0096] The ship's ice resistance, net thrust, hydrodynamic force, and rudder force were calculated using the ship ice resistance calculation model, ship net thrust model, ship hydrodynamic model, and ship rudder force model, respectively.

[0097] The total forces acting on a ship are obtained by summing up the ice resistance, net thrust, hydrodynamic forces, and rudder forces.

[0098] Based on the total forces acting on the ship, information such as the ship's speed, acceleration, and displacement can be obtained through the ship's equation of motion.

[0099] This invention calculates the ship's motion response in an ice ridge field, such as speed, acceleration, displacement, ice resistance, and net thrust, using the ship's motion equations, ship ice resistance calculation model, ship net thrust model, and ship hydrodynamic equations. It also considers the influence of ship speed on ice resistance and specifically analyzes the change in average speed during ship navigation to evaluate the icebreaking performance of polar ships.

[0100] Beneficial Effects: Compared with existing technologies, this invention proposes a method for simulating the motion response of icebreakers colliding with ice ridges. This method can predict the navigation performance of ships under ice ridge conditions and further analyze the average speed and navigation capability achievable by the ship to evaluate the icebreaking performance of polar vessels. After establishing the program, this invention can calculate multiple ice ridge collision scenarios in approximately 2 seconds, generating information such as net thrust, speed, acceleration, and ice resistance when the ship is navigating in an ice ridge field. The results can be output as a .txt file for subsequent data processing. If the size of the ship or ice ridge changes, only the input parameters need to be modified. Therefore, the method proposed in this invention has the advantages of simplicity and efficiency, completely solving the problem of the time-consuming calculation of ship-ice ridge interactions in existing numerical simulation methods. Attached Figure Description

[0101] Figure 1 This is an operation flowchart of the present invention;

[0102] Figure 2 This is a simplified model diagram of the ice ridge structure in an embodiment of the present invention;

[0103] Figure 3 This is the ship reference coordinate system in the embodiment of the present invention.

[0104] Figure 4 This is a graph showing the change of velocity with displacement under different ice thicknesses in an embodiment of the present invention;

[0105] Figure 5 These are the maximum, average, and minimum average ship speeds under 100 simulations with different ice thicknesses in the embodiments of this invention. Detailed Implementation

[0106] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. After reading this invention, any modifications of the invention in various equivalent forms by those skilled in the art will fall within the scope defined by the appended claims.

[0107] like Figure 1 As shown, the present invention provides a method for predicting the motion response of ships in ice ridge fields, comprising the following steps:

[0108] S1: Establish a simplified model of the ice ridge structure:

[0109] A simplified model of an ice ridge structure includes the solidified layer, the sail, and the keel. Ice ridge structures are more complex and are typically modeled in trapezoidal or triangular forms, such as... Figure 2 As shown, when the bottom width w s When the value is 0, it can be simplified to a triangle model.

[0110] This invention establishes a simplified model of the ice ridge structure in the form of a triangle. The simplified model of the ice ridge structure includes the sail height h. s Keel depth h k 、sail width w s , keel width w k These are some of the characteristics.

[0111] S2: Based on the simplified model of ice ridge structure, establish a probability model of the ice ridge field:

[0112] Keel width w k With Hodaka H s The average ratio is expressed as:

[0113] w k =16.7h s (1)

[0114] sail width w s With Hodaka H s The average ratio is expressed as:

[0115] w s =3.75h s (2)

[0116] The maximum sail height follows a Gamma distribution, and its probability density function is expressed as:

[0117]

[0118] Among them, h s The maximum value of the sail height is given by parameter β, which is called the shape parameter and affects the shape of the curve, with a value of 2.42; parameter α is called the scale parameter and affects the location of the distribution, with a value of 1.14.

[0119] The maximum ratio of ice ridge keel depth to sail height follows a Gamma distribution, and its probability density function (PDF) can be given by the following expression:

[0120]

[0121] Among them, h k / h s The maximum ratio of keel depth to sail height is given by a shape parameter β of 3.05 and a scale parameter α of 1.70.

[0122] The thickness of the consolidation layer follows a Gamma distribution, and its probability density function (PDF) can be expressed as follows.

[0123]

[0124] Among them, h c The thickness of the consolidation layer is given by a shape parameter β of 2.97 and a scale parameter α of 0.54.

[0125] The spacing between ice ridge keels can be modeled using an exponential distribution:

[0126] p(d;μ(h c ))=μ(h c )exp(-μ(h c )d) (6)

[0127] In the formula, d is the distance between ice ridge keels; μ is the shape parameter of the distribution, i.e. the expected number of keels per kilometer.

[0128] S3: Establish the equations of motion for the ship:

[0129] The reference frames used are a fixed-body reference frame and a fixed-ground reference frame, both satisfying the right-hand rule. The ship's fixed frame, denoted as G-xyz, is fixed to the ship, with its origin coinciding with the ship's center of gravity, and Gx representing the ship's direction of travel. The Earth's fixed frame, denoted as O0-x0y0z0, is fixed to the Earth, and in the initial stage of the simulation, the fixed-body frame coincides with the Earth's fixed frame.

[0130] like Figure 3 As shown, the equations of motion for a ship with three degrees of freedom can be expressed as:

[0131]

[0132] In the formula, M is the diagonal mass matrix; A is the additional mass matrix; U(t), and These are displacement, velocity, and acceleration vectors, respectively; where F(t) considers ice resistance, propeller net thrust, rudder external force, and hydrodynamic forces, and C and K are the damping matrix and stiffness matrix, respectively.

[0133] Since ships are covered by ice when navigating in ice ridges, and neglecting hydrodynamic damping and restoring forces, the ship's equation of motion simplifies to:

[0134]

[0135] Among them, the mass matrix Additional mass matrix

[0136] In the formula, m is the mass of the hull; I 66Let A be the moment of inertia along the z-direction; 11 A 22 A 66 These represent the added mass in the x-direction, the added mass in the y-direction, and the added moment of inertia in the z-direction, respectively.

[0137] In the initial design phase of the ship A 11 A 22 A 66 and I 66 It can be calculated using the following expression:

[0138]

[0139]

[0140]

[0141]

[0142] In the formula, L is the ship's length, B is the ship's beam, T is the ship's draft, and C... b For the ship's block coefficient, Let g be the ship's displacement and g be the acceleration due to gravity.

[0143] Based on the linear acceleration assumption of the NewMark method, the following three equations can be obtained:

[0144]

[0145]

[0146]

[0147] In the formula, δ t t represents the time interval for numerical integration. k This represents the k-th time step.

[0148] S4: Establish a model for calculating ship ice resistance:

[0149] The ship ice resistance calculation model consists of a smooth ice resistance model and an ice ridge resistance model. The ice ridge resistance model is divided into solidified layer resistance, sail resistance, and ice ridge keel resistance. Solidified layer resistance is calculated using the smooth ice resistance model. Ice ridge keel resistance includes bow keel resistance and midship keel resistance.

[0150] The resistance model for smooth ice consists of three parts: fracturing, bending, and submersion, expressed by the following formula:

[0151]

[0152]

[0153]

[0154]

[0155]

[0156]

[0157] Among them, R l R s R b R c These are the total ice resistance during leveling, ice resistance during immersion, ice resistance during bending failure, and ice resistance during compression, respectively; σ b h represents the flexural strength of ice. i The thickness of the smooth ice is represented by u, φ, ψ, and α, which are the coefficient of friction, bow inclination angle, outward drift angle, and waterline angle, respectively; g is the acceleration due to gravity; ρ w ρ i Here, E represents the density of seawater and sea ice; V represents Young's modulus; B, T, and L represent the ship's beam, draft, and waterline length, respectively; and V represents the ship's speed.

[0158] The resistance of a sail includes friction and the cohesive force of the ice freezing, and can be expressed as:

[0159] F sail =p s w s =(p sg +p sc )w s (twenty two)

[0160] In the formula, p s This refers to the load per unit width of the sail, expressed in kN / m; p sg This represents the load per unit width of the sail, calculated based on its weight and height, expressed in kN / m; p sc The load per unit width of the sail due to cohesion is expressed in kN / m, and the cohesion is c. s The unit is kPa.

[0161] A soil mechanics model was used to simulate the load per unit width of the sail under friction and cohesion:

[0162]

[0163] p sc =2c s (h s )K ps (twenty four)

[0164] In the formula, γ is the unit weight of ice, with units of kN / m3 (γ=γg); n represents the porosity of the sail (n=0.3);

[0165] K ps Rankin's passive earth pressure coefficient can be expressed as:

[0166] K ps =(1+sinψ) s ) / (1-sinψ s (25)

[0167] In the formula, ψ s It is the internal friction angle of the ice block in the sail.

[0168] The cross-sectional length of the sail at the waterline can be expressed as:

[0169] L ps =H s tan(φ+ψ s / 2) (26)

[0170] In the formula, φ = 45° is the angle when the sail is stationary;

[0171] The bow keel resistance takes into account the effect of ship speed and is expressed as:

[0172]

[0173] Among them, h r (x) represents the local ice ridge thickness; C p It is a constant.

[0174] The midhull keel resistance of a ship takes into account the effect of ship speed and is expressed as:

[0175]

[0176] in, It is a non-negative number, C m It is a constant.

[0177] When a ship becomes stuck in an ice ridge and cannot move forward, its speed drops to zero, and it will use reverse thrust to back up approximately 1.5 times its length. After backing up the predetermined distance, the ship will propel itself forward with maximum power, accelerating again to ram the ice ridge. This ramming process repeats until the ship moves out of the ice ridge. If the ship does not have sufficient thrust to move forward, it will eventually become stuck in the ice ridge. During the backflip and subsequent acceleration forward, the ship is primarily affected by the drag of breaking ice.

[0178] Channel ice breakage resistance can be expressed as:

[0179]

[0180] Among them, H M Let ρ be the ice resistance in the channel, and δ be the slope angle of the ice fragment sidewall (δ = 26°). ρΔ is the density difference between ice and water, and A is... WF F is the waterline area at the bow of the ship. n H is a Froude number. F The thickness of the floating ice as the bow shifts and moves towards the side parallel to the midship. When B > 10m and H M When H > 0.4m, F =0.26+(BH) M ) 0.5 .

[0181] S5: Establish a ship net thrust model:

[0182] The ship net thrust model is used to calculate the total force acting on the ship at each time step; net thrust is the thrust that overcomes ice resistance after subtracting open water resistance.

[0183] The net thrust formula in the ship net thrust model is expressed as:

[0184]

[0185] Among them, v ow For open water velocity; v n T represents the velocity component in the direction of the icebreaker's movement; when the ship's speed is the open-water speed, the net thrust is zero; n It is the tie rod tension, which is defined as:

[0186] T pull =K e (P s D p ) 2 / 3 (31)

[0187] Among them, P s Power; D p K is the propeller diameter; e It is a dimensionless coefficient.

[0188] S6: Establish the ship's hydrodynamic equations; the combined decomposition of the propeller's net thrust and the rudder's external force into the ship's pitch, sway, and yaw directions are shown in the following equations:

[0189]

[0190] In the formula, T net Indicates net thrust; C L and C D These represent the lift and drag coefficients of the rudder, respectively; V f Indicates fluid velocity; A r Represented as rudder area; x rThis indicates the longitudinal position of the rudder; that is, the distance from the center of the rudder's force to the ship's center of gravity. The stern rudder is a negative value.

[0191] The propeller net thrust and rudder external force here are calculated by the ship net thrust model and the ship rudder external force model, respectively.

[0192] The hydrodynamics of a ship are calculated using empirical formulas as follows:

[0193]

[0194] In the formula, R n =uL / ν represents the Reynolds number; u represents the longitudinal velocity of the ship; L represents the ship's length; ν represents the kinematic viscosity of seawater; ρ w S represents the density of seawater. w Indicates the wetted surface area of ​​the hull; C D (x) represents the drag coefficient of each longitudinal section of the hull; that is, the resistance coefficient of fluid passing through an infinitely long cylinder equivalent to the cross-sectional area of ​​each longitudinal section of the hull; D(x) represents the draft of each longitudinal section of the hull; v(x) represents the lateral velocity at each longitudinal section of the hull.

[0195] S7: Calculate the ship's motion response in an ice ridge using the ship's equation of motion, ship ice resistance calculation model, ship net thrust model, ship rudder external force model, and ship hydrodynamic equations respectively.

[0196] The ship's ice resistance, net thrust, hydrodynamic force, and rudder force were calculated using the ship ice resistance calculation model, ship net thrust model, ship hydrodynamic model, and ship rudder force model, respectively.

[0197] The total forces acting on a ship are obtained by summing up the ice resistance, net thrust, hydrodynamic forces, and rudder forces.

[0198] Based on the total forces acting on the ship, information such as the ship's speed, acceleration, and displacement can be obtained through the ship's equation of motion.

[0199] As can be seen from the above, the method of the present invention takes into account the influence of ship speed on ice resistance, and specifically analyzes the change of average speed during ship navigation in order to evaluate the icebreaking performance of polar ships.

[0200] Based on the above, in order to verify the effectiveness of the present invention, the following implementation examples are provided:

[0201] The main parameters of the ship are as follows:

[0202] Main dimensions of the ship:

[0203] Waterline boat width 21m Draft 7.7m bow waterline angle 40° bow angle 20° Mean outward tilt 29.5° propeller diameter 4.25m Main unit power 2X7.5MW Discharge 13999t Maximum open water speed 9.66m / s

[0204] The main parameters of the ice ridge field and the calculation conditions are as follows:

[0205] Calculation conditions:

[0206]

[0207]

[0208] Based on the main parameters of the ship and the ice ridge, the simplified analytical method established in this invention is used to solve the ship's motion response, specifically analyzing the change in the ship's average speed.

[0209] Figure 4 The curves show the change in ship speed with displacement under different thicknesses of smooth ice. Figure 5 The maximum, average, and minimum average ship speeds were obtained from 100 simulations conducted under different ice thicknesses. Figure 4 and Figure 5 The results show that the greater the thickness of the smooth ice, the lower the ship's speed becomes with increasing displacement, and the ice thickness has a significant impact on the ship's navigation performance. Therefore, the calculation results obtained by the method of this invention are reasonable.

[0210] Comparison data on computation time:

[0211] The numerical model of a ship colliding with a single ice ridge (ice field area of ​​40m) using the Ls-dyna nonlinear finite element software takes more than 20 hours with 16 CPUs working simultaneously. When the size of the ship or ice ridge changes, the finite element model needs to be rebuilt, making the modeling and calculation work very time-consuming. When multiple ice ridges need to be considered, the computational workload increases significantly due to the increased model range and the increased number of elements in the model. For example, when calculating the collision of a ship with two ice ridges (ice field area of ​​80m), it takes more than 60 hours.

[0212] According to the method proposed in this invention, after establishing the program, it only takes about 2 seconds to calculate the working condition of a ship colliding with multiple ice ridges (ice field range of 1000m). It can generate information such as net thrust, speed, acceleration, and ice resistance when the ship is sailing in the ice ridge field, and the results can be output as a .txt file for subsequent data processing. If the size of the ship or ice ridge field changes, only the input parameters need to be modified. It can be seen that the method proposed in this invention has the advantages of simplicity and high efficiency.

[0213] This embodiment also provides a prediction system for the motion response of ships in ice ridge fields. The system includes a network interface, a memory, and a processor. The network interface is used to receive and send signals during the process of sending and receiving information with other external network elements. The memory is used to store computer program instructions that can be run on the processor. The processor is used to execute the steps of the consensus method described above when running the computer program instructions.

[0214] This embodiment also provides a computer storage medium storing a computer program that, when executed by a processor, can implement the methods described above. The computer-readable medium can be considered tangible and non-transitory. Non-limiting examples of non-transitory tangible computer-readable media include non-volatile memory circuitry (e.g., flash memory circuitry, erasable programmable read-only memory circuitry, or masked read-only memory circuitry), volatile memory circuitry (e.g., static random access memory circuitry or dynamic random access memory circuitry), magnetic storage media (e.g., analog or digital magnetic tape or hard disk drive), and optical storage media (e.g., CD, DVD, or Blu-ray disc). The computer program includes processor-executable instructions stored on at least one non-transitory tangible computer-readable medium. The computer program may also include or depend on stored data. The computer program may include a basic input / output system (BIOS) for interacting with the hardware of a dedicated computer, device drivers for interacting with specific devices of the dedicated computer, one or more operating systems, user applications, background services, background applications, etc.

[0215] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

Claims

1. A method for predicting the motion response of ships in ice ridge fields, characterized in that, Includes the following steps: S1: Establish a simplified model of the ice ridge structure; S2: Based on the simplified model of ice ridge structure, establish a probability model of ice ridge field; S3: Based on the simplified model of the ice ridge structure and the probability model of the ice ridge field, establish the equations of motion for the ship; S4: Establish models for calculating ship ice resistance, ship net thrust, ship hydrodynamics, and ship rudder external force. S5: The ship's motion response in an ice ridge field is calculated using the ship's motion equations, ship ice resistance calculation model, ship net thrust model, ship hydrodynamic model, and ship rudder external force model. In step S1, the simplified model of the ice ridge structure includes the solidified layer, sail, and keel. The simplified ice ridge structure model is established using a triangular form, and includes the sail height. Keel depth , sail width keel width ; The method for establishing the ice ridge field probability model in step S2 is as follows: Keel width With Hodaka The average ratio is expressed as: （1）； sail width With Hodaka The average ratio is expressed as: （2）； The maximum sail height follows a Gamma distribution, and its probability density function is expressed as: （3）； in, For the maximum sail height, the parameter is... For shape parameters; parameters For scale parameters; The maximum ratio of ice ridge keel depth to sail height follows a Gamma distribution, and its probability density function is given by the following expression: （4）； in, The maximum ratio of keel depth to sail height, shape parameters The value is 3.05, scale parameter The value is 1.70; The thickness of the consolidation layer follows a Gamma distribution, and its probability density function is expressed as: （5）； in, For the thickness and shape parameters of the consolidation layer The value is 2.97, scale parameter The value is 0.54; The spacing between the ice ridge keels is modeled using an exponential distribution: （6）； In the formula, This refers to the distance between the ice ridge keels; The shape parameter of the distribution is the expected number of keels per kilometer.

2. The method for predicting the motion response of a ship in an ice ridge field according to claim 1, characterized in that, In step S3, the ship's motion equations are the ship's three-degree-of-freedom motion equations, expressed as: （7）； In the formula, A is the diagonal mass matrix; A' is the additional mass matrix. , and These are displacement, velocity, and acceleration vectors, respectively; where, Ice drag, propeller net thrust, rudder external force, and hydrodynamics were considered, with C and K being the damping matrix and stiffness matrix, respectively.

3. The method for predicting the motion response of a ship in an ice ridge field according to claim 2, characterized in that, The ship motion equations established in step S3 are simplified as follows, since the ship is covered by ice when sailing in an ice ridge, and hydrodynamic damping and restoring forces are ignored: （8）； Among them, the mass matrix Additional mass matrix ; In the formula, m is the mass of the ship; Let be the moment of inertia along the z-direction; , , These represent the added mass in the x-direction, the added mass in the y-direction, and the added moment of inertia in the z-direction, respectively. During the initial design phase of the ship , , and Calculated using the following expression: （9）； （10）； (11)； （12）； In the formula, L is the ship's length, B is the ship's beam, and T is the ship's draft. For the ship's block coefficient, Where is the ship's displacement, and g is the acceleration due to gravity. Based on the assumption of linear acceleration in the NewMark method, the following three equations are obtained: (13)； (14)； (15)； In the formula, The time interval for numerical integration; This represents the k-th time step.

4. The method for predicting the motion response of a ship in an ice ridge field according to claim 1, characterized in that, In step S4, the ship ice resistance calculation model consists of a smooth ice resistance model and an ice ridge resistance model. The ice ridge resistance model is divided into solidified layer resistance, sail resistance, and ice ridge keel resistance. Solidified layer resistance is calculated using the smooth ice resistance model. Ice ridge keel resistance includes bow keel resistance and midship keel resistance. The resistance model for smooth ice consists of three parts: fracturing, bending, and submersion, expressed by the following formula: (16)； （17）； （18）； （19）； （20）； （21）； in, , , , These are the total ice resistance during leveling, ice resistance during immersion, ice resistance during bending failure, and ice resistance during compression. The bending strength of ice; To even out the ice thickness; u, ψ, α are the coefficient of friction, bow inclination angle, outward drift angle, and waterline angle, respectively; g is the acceleration due to gravity; ρ w ρ i Here, E represents the density of seawater and sea ice; V represents Young's modulus; B, T, and L represent the ship's beam, draft, and waterline length, respectively; and V represents the ship's speed. Sail resistance includes friction and the cohesive force of ice freezing, expressed as: (22)； In the formula, This represents the load per unit width of the sail, expressed in kN / m. This represents the load per unit width of the sail, calculated based on its weight and height, expressed in kN / m. The load per unit width of the sail due to cohesion is expressed in kN / m, and the cohesion is... The unit is kPa; A soil mechanics model was used to simulate the load per unit width of the sail under friction and cohesion: (23)； (24)； In the formula, γ is the unit weight of ice; n represents the porosity of the sail. Rankin's passive earth pressure coefficient is expressed as: (25)； In the formula, It is the internal friction angle of the ice block in the sail; The cross-sectional length of the sail at the waterline is expressed as: (26)； In the formula, The angle when the sail is stationary; The bow keel resistance takes into account the effect of ship speed and is expressed as: （27）； in, This refers to the thickness of a local ice ridge; It is a constant; The midhull keel resistance of a ship takes into account the effect of ship speed and is expressed as: （28）； in, It is a non-negative number. It is a constant; During the process of a ship reversing and then accelerating forward again, it experiences ice breakage resistance. The ice breakage resistance in the channel is expressed as: （29）； in, For ice resistance in the waterway, The slope angle of the ice floe sidewall. Due to the density difference between ice and water, The waterline area at the bow of the ship. For Froude number, The thickness of the ice floe as the bow shifts and moves towards the side parallel to the midship; when B > 10m and When >0.4m, .

5. The method for predicting the motion response of a ship in an ice ridge field according to claim 1, characterized in that, In step S4, the ship net thrust model is used to calculate the total force acting on the ship at each time step. The net thrust is the thrust that overcomes ice resistance after subtracting open water resistance. The net thrust formula in the ship net thrust model is expressed as: （30）； in, For open water speed; This represents the velocity component in the direction of the icebreaker's movement; when the ship's speed is the open water speed, the net thrust is zero. It is the tie rod tension, which is defined as: （31） in, Power; The diameter of the propeller; It is a dimensionless coefficient.

6. The method for predicting the motion response of a ship in an ice ridge field according to claim 1, characterized in that, The movement of the ship in the ice ridge field in step S5 is as follows: When a ship becomes stuck in an ice ridge and cannot move forward, its speed drops to zero. It will then use reverse thrust to reverse the ship a predetermined distance. After reversing the predetermined distance, the ship will propel itself forward with maximum power, accelerating again to collide with the ice ridge. This collision process will be repeated until the ship sails out of the ice ridge. If the ship does not have enough thrust to propel itself forward, it will eventually become stuck in the ice ridge.

7. The method for predicting the motion response of a ship in an ice ridge field according to claim 1, characterized in that, The method for establishing the ship hydrodynamic model in step S4 is as follows: the net propeller thrust and rudder external force are combined and decomposed into the ship's pitch, sway, and yaw directions, respectively, as shown in the following formulas: （32）； In the formula, T net Indicates net thrust; C L and C D These represent the lift and drag coefficients of the rudder, respectively; V f Indicates fluid velocity; A r Represented as rudder area; x r This indicates the longitudinal position of the rudder; that is, the distance from the center of the rudder's force to the ship's center of gravity. The stern rudder is a negative value. The hydrodynamic forces acting on a ship are calculated using empirical formulas as follows: （33）； In the formula, =uL / ν represents the Reynolds number; u represents the longitudinal velocity of the ship; L represents the ship's length; ν represents the kinematic viscosity of seawater; Indicates the density of seawater; Indicates the wetted surface area of ​​the hull; This represents the drag coefficient of each longitudinal section of the hull; that is, the resistance coefficient of fluid passing through an infinitely long cylinder equivalent to the cross-sectional area of ​​each longitudinal section of the hull. Indicates the draft of each longitudinal section of the hull; This indicates the lateral velocity at each longitudinal section of the hull.

8. The method for predicting the motion response of a ship in an ice ridge field according to claim 1, characterized in that, The method for calculating the ship's motion response in the ice ridge field in step S5 is as follows: The ship's ice resistance, net thrust, hydrodynamic force, and rudder force were calculated using the ship ice resistance calculation model, ship net thrust model, ship hydrodynamic model, and ship rudder force model, respectively. The total forces acting on a ship are obtained by summing up the ice resistance, net thrust, hydrodynamic forces, and rudder forces. Based on the total forces acting on the ship, the ship's velocity, acceleration, and displacement are obtained through the ship's equation of motion.

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