Method for generating sea ice discrete element model based on close-packed hexagonal arrangement

Abstract

The present application relates to a kind of sea ice discrete element model generation method based on close-packed hexagonal arrangement mode, and the particle generation method of innovatively used python and EDEM can be perfectly fused with the particle position information generated by computational fluid dynamics software FLUENT, real-time transmission and mutual calculation of particle position information are realized, so as to consider the influence of fluid on sea ice and structure effect;Using python software, by inputting the position information of particle and the relationship between different layers, the arrangement position of particle can be changed very conveniently, the generation of model is controlled according to demand, so as to realize the simulation of different types of materials.The present application method reduces the overall cost of sea ice discrete element method calculation, and realizes the input of particle position information for computational fluid dynamics, so as to be able to consider the influence of fluid on ice area marine environment, improve the calculation accuracy, so as to realize more reasonable and comprehensive ice load analysis calculation evaluation.

Description

Technical Field

[0001] This invention relates to a shipbuilding and marine engineering technology, and in particular to a method for generating a discrete element model of sea ice based on a close-packed hexagonal arrangement. Background Technology

[0002] Marine structures and ships operating or navigating in icy marine environments are significantly affected by ice loads. Traditionally, research on ice loads has primarily relied on prototype observations and model tests. In recent years, however, researchers have begun to shift towards numerical analysis. Currently, research on ice loads faces several major challenges:

[0003] (1) Prototype observation and model testing require high costs and are limited by the limited data that can be obtained by monitoring technology.

[0004] (2) Due to the inherent characteristics of real sea ice, which is composed of individual ice crystal particles, the discrete element method has a great computational advantage. However, this method is relatively complex, and its research is mainly based on programs developed by individual scholars, which is not conducive to popularization and application.

[0005] (3) In terms of numerical calculation, the mechanical properties of the discrete element model of sea ice constructed by the discrete element method are often not stable enough and are greatly affected by the arrangement rules of the internal particles. A stable particle arrangement method is needed.

[0006] (4) The traditional discrete element model particle arrangement cannot meet the macroscopic mechanical properties of real sea ice, thus failing to simulate the damage caused by the interaction between sea ice and structures in the marine environment, resulting in inaccurate calculations.

[0007] The construction procedures for discrete element models (DEMs) of sea ice are too costly and inconvenient, hindering their promotion and widespread adoption. Existing DEMs of sea ice cannot account for the effects of fluids when calculating interactions with structures, resulting in calculations lacking realism. Current research on ice loads, primarily relying on model experiments and prototype observations, is too costly and limited by the availability of analytical data due to limitations in observation techniques.

[0008] Dalian University of Technology has developed a discrete element method (DEM) program for calculating ice loads. This program can analyze the microscopic parameters of the sea ice discrete element model and their impact on its macroscopic mechanical properties, and based on this, it has calculated the interaction between offshore platforms and various types of sea ice. However, the developed ice load DEM program is costly to use, hindering its widespread adoption and promotion.

[0009] The discrete element method (DEM) program for calculating ice load developed by Dalian University of Technology mainly performs the calculation of the interaction between the discrete element model and the structure, without considering the water flow factor. However, the influence of water flow in the real marine environment is also very important.

[0010] The discrete element method (DEM) program for ice load calculation developed by Dalian University of Technology has fixed particle arrangement and generation methods, making it difficult to easily change the particle arrangement and generation methods according to the needs of the actual model. Therefore, it is not easy to simulate different types of materials. Summary of the Invention

[0011] To address the existing problems in ice load analysis in marine environments, this invention proposes a discrete element method (DEM) for sea ice based on a close-packed hexagonal arrangement. This method combines the traditional general-purpose software EDEM with Python and the DEM technique, generating discrete element sea ice particles based on a regular close-packed hexagonal arrangement. This invention reduces the overall computational cost of the DEM for sea ice and allows for the input of particle position information into computational fluid dynamics, thus considering the impact of fluids on the marine environment in ice-covered areas and improving computational accuracy. Therefore, it enables a more reasonable and comprehensive analysis and evaluation of ice loads.

[0012] The technical solution of this invention is: a method for generating a discrete element model of sea ice based on a close-packed hexagonal arrangement, specifically including the following steps:

[0013] 1) Draw the shape mesh of the discrete element model of sea ice that needs to be filled in the design. The number of meshes corresponds to the number of particles. Determine the number of particles and the coordinates of the center point.

[0014] 2) Using Python software, and with the shape mesh determined in step 1) as constraints, establish a close-packed hexagonal sea ice discrete element model:

[0015] 2.1) Close-packed hexagonal lower-layer planar particle arrangement: Based on the close-packed hexagonal arrangement concept, the XOY plane is defined using the Surface_create plane creation function. A plane is selected as a layer, and two vertices on one side of this plane's mesh are selected. Starting from the vertices, in the X direction, the coordinate values ​​are iterated by increasing by a diameter d each time, where d is the size of one mesh in the X direction; in the Y direction, the coordinate values ​​are iterated by increasing by a diameter d each time. The process is repeated in this manner until the layer is filled with particles;

[0016] 2.2) A discrete element sea ice model is formed by stacking different planar layers:

[0017] Based on the plane established in step 2.1), the Normar function is used to control the stacking of each plane layer with the shape mesh in step 1) as a constraint to complete the construction of the three-dimensional solid. The values ​​of X and Y are increased by a fixed value at the same time and there is a cycle of two layers. The value of Z is increased by a fixed value each time and there is a cycle of one layer.

[0018] 2.3) Determine the specific positional cyclic relationship of particles X and Y in different layers:

[0019] The X and Y coordinates of each particle relative to its corresponding particle in the upper layer are shown, with the value of X increasing with each increment. The value of Y increases by r each time;

[0020] 2.4) Determine the specific positional cyclic relationship of particles Z in different layers:

[0021] For the Z-positional relationship between each particle and its corresponding particle in the upper layer, the particle in the upper layer is actually rotating within a circle centered at the midpoint of the line connecting the centers of the two particles in the lower layer. The radius of this rotation is... The fixed increase in Z is obtained by using the right triangle formed by this rotation.

[0022] 3) Based on the arrangement in step 2), the coordinate information is read using EDEM software to generate a discrete element model of sea ice;

[0023] 4) The generated sea ice discrete element model is calibrated using the mechanical properties of sea ice in the target sea area to obtain the sea ice discrete element model of the target sea area.

[0024] Furthermore, in step 4), parameter calibration involves first determining the macroscopic mechanical properties of sea ice in the target sea area, and then calibrating the microscopic parameters through a three-point bending test and a uniaxial compression test to ensure that the microscopic parameters possess the macroscopic mechanical properties of sea ice in the target sea area.

[0025] Furthermore, in step 4), the mechanical properties are as follows: the contact between particles is calculated and analyzed using the Hertz-Mindlin model; the tangential friction between particles is calculated using Coulomb's friction theory; and the rolling friction between particles is achieved by applying a torque to the contact surface.

[0026] An application of a discrete element model of sea ice based on a close-packed hexagonal arrangement is proposed. The calibrated discrete element sea ice model with the mechanical properties of sea ice in the target sea area is coupled with fluid and structure for calculation and analysis according to the required working conditions, in order to obtain the magnitude of ice load.

[0027] Furthermore, the discrete element sea ice model of the mechanical properties of sea ice in the target sea area interacts with the collision structure. Combined with the flow field velocity vector diagram, the ice load and ice force time history curve of the structure are obtained by calculating the magnitude of the ice load.

[0028] The beneficial effects of this invention are as follows: This invention is based on a discrete element method for generating sea ice models using a close-packed hexagonal arrangement. Based on the discrete element method, this invention can be implemented using both EDEM and Python software, making it simpler and more convenient. Addressing the actual water flow factors in the marine environment, this invention innovatively utilizes Python and EDEM's particle generation method to perfectly integrate the particle position information generated with the computational fluid dynamics software FLUENT, enabling real-time transmission and mutual calculation of particle position information, thus considering the influence of fluids on sea ice and structures. Using Python software, by inputting particle position information and the relationships between different layers, the particle arrangement can be easily changed, controlling model generation according to requirements, thereby achieving simulation of different types of materials. Attached Figure Description

[0029] Figure 1 This is a schematic diagram of the filling shape grid of the present invention;

[0030] Figure 2 This is a schematic diagram showing the position of the planar particles in the first layer of the present invention;

[0031] Figure 3 This is a schematic diagram of the Normal function concept of this invention;

[0032] Figure 4 This is a schematic diagram of the X and Y cycles of the present invention;

[0033] Figure 5 This is a schematic diagram of the Z-cycle of the present invention;

[0034] Figure 6 This is a schematic diagram of the close-packed hexagonal filling method of the present invention;

[0035] Figure 7 This is a schematic diagram of the coordination of close-packed hexagonal particles in this invention;

[0036] Figure 8 This is a schematic diagram of the uniaxial compression parameter calibration test for the sea ice discrete element model of the present invention;

[0037] Figure 9 This is a computational diagram showing the coupling between the structure of this invention and the discrete element sea ice model;

[0038] Figure 10 This is a time history curve of the ice force on the structure calculated by the ice load coupling method of this invention;

[0039] Figure 11This is a model diagram of the ice floe of the present invention;

[0040] Figure 12 This is a diagram illustrating the interaction process between the hourglass-shaped float of the present invention and sea ice;

[0041] Figure 13 This is a vector diagram of the flow field velocity at a fluid velocity of 3 m / s according to the present invention.

[0042] Figure 14 This is a time history curve of ice force on an hourglass-shaped float, simulated by discrete element method according to the present invention.

[0043] Figure 15 This is a time history curve of ice force obtained by measuring the cone pressure cell of the JZ20-2 MUQ platform of the present invention. Detailed Implementation

[0044] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0045] A method for generating discrete element models of sea ice based on a close-packed hexagonal arrangement includes the following steps:

[0046] Step 1: Fill the shape drawing:

[0047] like Figure 1 The diagram shows the shape mesh to be filled, which is used to draw the shape mesh of the discrete element model of sea ice that needs to be filled in the design. The center point coordinate information of these meshes is output through the UDF module of the computational fluid dynamics software.

[0048] Step 2: Implementation of planar particle arrangement in each layer of close-packed hexagonal:

[0049] The program uses Python software to edit the grid center coordinates output in step 1. The main idea is to move from a planar to a three-dimensional structure. Based on the concept of a close-packed hexagonal arrangement, the `Surface_create` function defines three different types of planes: XOY, XOZ, and YOZ. Figure 2 The diagram shows the position of planar particles in a single layer. Taking the XOY plane as an example, two vertices on one side of this planar network are selected. Starting from the vertices, in the X direction, the coordinate values ​​are cyclically increased by a diameter d, where d is the size of one grid cell in the X direction. In the Y direction, the coordinate values ​​are cyclically increased by a diameter d, where d is the size of one grid cell in the X direction. The process is repeated until the layer is filled with particles.

[0050] Step 3: Form a discrete element sea ice model by stacking different plane layers:

[0051] Based on the plane established in step 2, the Normar function is used to control the stacking of each plane layer with the shape mesh from step 1 as a constraint to complete the construction of the three-dimensional solid. For example... Figure 3 The diagram illustrates the logic of the Normal function. The darker particles represent the positions of the first particle in the second layer (filling the gaps in the first layer's xoy plane). This is related to the first particle in the first layer (xoy plane). Figure 3 The relationship between the positions of the light-colored particles (in the middle and lower shades) is the main definition of the Normal function. It can be seen that the values ​​of X and Y increase simultaneously by a fixed value, with each two layers forming a loop. The value of Z increases by a fixed value each time, with each layer forming a loop.

[0052] Step 4: Determine the specific positional cycle relationship of particles X and Y in different layers:

[0053] The specific X and Y positional relationships between each particle and its corresponding particle in the upper layer are as follows: Figure 4 As shown, the value of X can be calculated as increasing each time. The value of Y increases by r each time.

[0054] Step 5: Determine the specific positional cycle relationship of particles Z in different layers:

[0055] The specific Z-position of each particle relative to its corresponding particle in the upper layer is quite complex, such as... Figure 5 The Z-cycle diagram shows that the particles in the second layer are actually rotating within a circle centered at the midpoint of the line connecting the centers of the two particles in the first layer. The radius of this rotation is... Therefore, its position can be determined using the right triangle formed by this rotation, and the result is: This is a fixed increase in Z.

[0056] Step 6: Use EDEM software to read coordinate information and generate a discrete element model of sea ice.

[0057] The particle coordinate information was generated through the above steps and input into the EDEM software, resulting in a close-packed hexagonal sea ice discrete element model with 10 particles in the X direction, 10 particles in the Y direction, and 31 particles in the Z direction, as shown below. Figure 6 As shown.

[0058] The bonding diagram of its internal bonding bonds was read using EDEM, such as... Figure 7 The diagram showing the close-packed hexagonal particle coordination reveals that each particle has a coordination number of 12, meaning that each particle is bonded to 12 other particles, satisfying the close-packed hexagonal arrangement. This verifies the correctness of the program.

[0059] Step 7: calibrate the parameters of the generated sea ice discrete element model:

[0060] Contact analysis between particles was performed using the Hertz-Mindlin (No Slip) model. The tangential friction between particles was calculated using Coulomb's friction theory. Rolling friction τ between particles was also calculated. i This is achieved by applying a torque to the contact surface.

[0061] Interparticle normal force F n Through the normal overlap δ between particles n The function is represented as follows:

[0062]

[0063] Among them, E * For the equivalent Young's modulus, and R * The equivalent radius is defined as follows:

[0064]

[0065]

[0066] E i v i R i and E j v j R j Let i be the Young's modulus, Poisson's ratio, and contact radius of two adjacent particles i and j.

[0067] Normal damping force for:

[0068]

[0069] In the formula, It is the normal component of the relative velocity between particles; It is the equivalent mass, m i and m j β represents the equivalent mass of two adjacent particles i and j; β represents the normal stiffness S. n for:

[0070]

[0071]

[0072] e is the coefficient of restitution between particles.

[0073] Tangential force F t By tangential overlap δ t and tangential stiffness S t Decide:

[0074] F t =-St δ t ;

[0075]

[0076] G * It is the equivalent shear modulus.

[0077] Tangential damping is:

[0078] It is the tangential component of the relative velocity between particles;

[0079] Rolling friction τ between particles i This is achieved by applying a torque to the contact surface:

[0080] τ i =-μ r F n R i ω i ;

[0081] In the formula, ω i R is the vector of the unit angular velocity of the object at the point of contact. i μ is the distance from the contact point to the center of mass. r is the rolling friction coefficient.

[0082] After generating the discrete element model of sea ice, it is necessary to calibrate the values ​​of the micro-parameters in the model through parameter calibration. For example... Figure 8 The diagram shows a uniaxial compression parameter calibration test of the discrete element model of sea ice. The specific method is as follows: first, the macroscopic mechanical properties of sea ice in the target sea area are determined, and then the microscopic parameters are calibrated to make it have the macroscopic mechanical properties of sea ice in the target sea area through three-point bending test and uniaxial compression test.

[0083] Step 8: Perform ice load coupling calculation and analysis:

[0084] A calibrated discrete element sea ice model with the mechanical properties of sea ice in the target sea area was used for coupled computational analysis using EDEM and FLUENT software. Based on the required calculation conditions, coupled computational analysis was performed with fluid and structural parameters to obtain the magnitude of the ice load. For example... Figure 9 The diagram shows the coupled calculation of the structure and the discrete element sea ice model. By reading the calculation results, the ice force time history curve of the ice load on the structure can be obtained, as shown below. Figure 10 The figure shows the time history curve of the ice force on the structure calculated by ice load coupling.

[0085] This invention addresses the generation of discrete element models (DEMs) in the discrete element numerical analysis of ice loads. It proposes a DEM generation method based on a close-packed hexagonal arrangement, suitable for coupled analysis of ice loads and possessing realistic sea ice mechanical properties. Utilizing commonly available commercial software, this method significantly reduces computational costs, improves computational efficiency, ensures accuracy, and is highly efficient and universally applicable, enabling widespread adoption. The generated sea ice DEM model can be coupled with fluid and structural data for computational analysis, thus making the calculations more consistent with the realities of the ice-covered marine environment.

[0086] The following table compares this method with traditional methods:

[0087]

[0088]

[0089] Application examples:

[0090] 1. Output the coordinates of the center point of the model according to step 1.

[0091] 2. Write a program based on steps 2 to 5 and the target model (ice flops).

[0092] 3. Following step 6, use EDEM software to read the program and fill in the sea ice model as follows. Figure 11 As shown:

[0093] 4. Following step 7, the mechanical properties of the sea ice model were calibrated based on the target sea area. Taking the Bohai Sea sea ice as an example, a discrete element model of sea ice was constructed with compressive strength of 5.29 MPa, elastic modulus of 1.78 GPa, and flexural strength of 1.21 MPa. Comparing this to the mechanical properties of real Bohai Sea sea ice (uniaxial compressive strength 5.3 MPa, elastic modulus 1.8 GPa, flexural strength 1.16 MPa), the two are very close.

[0094] 5. After calibration as described in step 7, apply the model to the coupled calculation analysis, as follows: Figure 12 The diagram shows the interaction process between the hourglass-shaped float and sea ice. Figure 13 The vector diagram of the flow field at a fluid velocity of 3 m / s is shown.

[0095] 6. Based on step 8, obtain the time history curve of ice load and ice force on the structure, as shown below. Figure 14 As shown.

[0096] 7. Verification of calculation results:

[0097] Referring to the cone ice force time history curve of the JZ20-2 MUQ jacket platform measured in the Bohai Sea, as shown in the figure... Figure 15 As shown.

[0098] from Figure 15 As can be seen above, the characteristics of the ice load measured by both methods are: pulse-like; after the ice force reaches a certain value, it will be completely unloaded, dropping to zero, followed by another peak ice force that drops to zero again, and so on repeatedly. Due to the use of a scaling ratio, there is a certain degree of scaling in the magnitude of the ice force.

[0099] The comparison results show that the ice force time history curve obtained by the method of this invention, after coupling calculation, has the same characteristics as the ice force time history curve actually measured in the Bohai Sea, which conforms to the actual interaction process between sea ice and structures. Therefore, it can be applied to the analysis of factors affecting ice loads on structures, such as wind speed, current velocity, structural form, ice floe size, contact area, etc., thereby providing design suggestions for structures working in ice-covered marine environments and has a good engineering application background.

[0100] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A method for generating discrete element models of sea ice based on a close-packed hexagonal arrangement, characterized in that, Specifically, the steps include the following: 1) Draw the shape mesh of the discrete element model of sea ice that needs to be filled in the design. The number of meshes corresponds to the number of particles. Determine the number of particles and the coordinates of the center point. 2) Using Python software, and with the shape mesh determined in step 1) as constraints, establish a close-packed hexagonal sea ice discrete element model: 2.1) Close-packed hexagonal lower-layer planar particle arrangement: Based on the close-packed hexagonal arrangement concept, the XOY plane is defined using the Surface_create plane creation function. A plane is selected as a layer, and two vertices on one side of this plane's network are selected. Starting from the vertices, in the X direction, the coordinate values ​​are iterated by increasing by a diameter d each time, where d is the size of one grid in the X direction; in the Y direction, the coordinate values ​​are iterated by increasing by a diameter d each time. This process is repeated until the layer is filled with particles of a radius of [missing information]. r ; 2.2) A discrete element sea ice model is formed by stacking different planar layers: Based on the plane established in step 2.1), the Normar function is used to control the stacking of each plane layer with the shape mesh in step 1) as a constraint to complete the construction of the three-dimensional solid. The values ​​of X and Y are increased by a fixed value at the same time and there is a cycle of two layers. The value of Z is increased by a fixed value each time and there is a cycle of one layer. 2.3) Determine the specific positional cyclic relationship of particles X and Y in different layers: The X and Y coordinates of each particle relative to its corresponding particle in the upper layer are shown, with the value of X increasing with each increment. The value of Y increases each time. r ; 2.4) Determine the specific positional cyclic relationship of particles Z in different layers: For the Z-positional relationship between each particle and its corresponding particle in the upper layer, the particle in the upper layer is actually rotating within a circle centered at the midpoint of the line connecting the centers of the two particles in the lower layer. The radius of this rotation is... The increase in Z is determined by using the right triangle formed by this rotation. ; 3) Based on the arrangement in step 2), use EDEM software to read the coordinate information and generate a discrete element model of sea ice; 4) The generated sea ice discrete element model is calibrated using the mechanical properties of sea ice in the target sea area to obtain the sea ice discrete element model of the target sea area.

2. The method for generating discrete element models of sea ice based on a close-packed hexagonal arrangement as described in claim 1, characterized in that, Step 4) Parameter calibration: First, determine the macroscopic mechanical properties of sea ice in the target sea area, and then calibrate the microscopic parameters to make them have the macroscopic mechanical properties of sea ice in the target sea area through three-point bending test and uniaxial compression test.

3. The method for generating discrete element models of sea ice based on a close-packed hexagonal arrangement as described in claim 2, characterized in that, In step 4), the mechanical properties are as follows: the contact between particles is calculated and analyzed using the Hertz-Mindlin model; the tangential friction force between particles is calculated using Coulomb's friction theory. Rolling friction between particles is achieved by applying a torque to the contact surface.

4. An application method for a discrete element model of sea ice based on a close-packed hexagonal arrangement, characterized in that, The calibrated discrete element sea ice model generated by the sea ice discrete element model generation method based on the close-packed hexagonal arrangement of any one of claims 1 to 3 is used to perform coupled calculation and analysis with fluid and structure according to the required working conditions to obtain the magnitude of ice load.

5. The application method of the sea ice discrete element model based on the close-packed hexagonal arrangement according to claim 4, characterized in that, The discrete element sea ice model of the target sea ice mechanical properties interacts with the colliding structure. Combined with the flow field velocity vector diagram, the ice load and ice force time history curve of the structure are obtained by calculating the ice load through the magnitude of the ice load.

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