A flexible fiber fluid-structure interaction method

Abstract

The present invention belongs to the technical field of simulation of flexible fiber washing and conveying, and relates to a flexible fiber fluid-structure interaction method. First, a fluid model containing flexible fibers and a flexible fiber model are respectively constructed; then, based on the flexible fiber model and the fluid model, a two-way fluid-structure interaction system is constructed; then, the motion evolution form of a single flexible fiber in the flow field is simulated and physically experimented by using the two-way fluid-structure interaction system, and evaluation indexes of the bending degree of the flexible fiber flow field and the vibration amplitude of the flexible fiber flow field are proposed; finally, the flexible fiber fluid-structure interaction model is corrected through the evaluation indexes, and further exploration is carried out on the bending and winding, entanglement into clusters, and opening of the flexible fibers. The flexible fiber fluid-structure interaction method of the present invention can effectively realize the simulation of the motion evolution behavior of flexible fibers in the flow field, and has good scalability and adaptability.

Description

Technical Field

[0001] The present invention belongs to the technical field of flexible fiber water washing transportation simulation, and relates to a flexible fiber fluid-solid coupling method. Background Art

[0002] The large-production-capacity flexible fiber water transportation technology is one of the key technologies for producing green fibers. It has the advantages of high efficiency, large capacity, strong adaptability, and small environmental impact, and is of extremely important significance to the new energy strategy. However, the forces acting on flexible fibers in the flow field are complex, and their motion postures are unpredictable. During the transportation process, due to the interaction between fibers and fluids and the mutual contact and collision between fibers, the fiber morphology changes, such as bending, winding, and agglomeration. This directly affects the quality of fiber products and poses a risk of production line stoppage, seriously affecting production efficiency and cost.

[0003] Flexible fibers are prone to bending, winding, entanglement, and loosening during the water washing transportation process, which cannot be observed during the actual production preparation process. It is necessary to show through simulation results the tendency of flexible fibers to bend, wind, entangle, and loosen during the water washing transportation process. However, currently in actual production, there is a lack of theoretical guidance, and it is difficult to study the flow evolution behavior.

[0004] To solve the above problems, the literature (Influence of the flow field state in the wool conveying pipe on the opening treatment effect of fiber bundles [J]. Advanced Textile Technology, 2024, 32(3): 29-37. DOI: 10.19398 / j.att.202308011) used the fluid simulation software Cradle CFD to perform a coupled calculation on the movement process of fiber bundles in the flow field of the wool conveying pipe, compared the distribution characteristics of the flow field at different positions of the wool conveying pipe and the fiber movement trajectories at different times, and explored the opening mechanism of fiber bundles during transportation in the wool conveying pipe and the influence of the flow field state in the wool conveying pipe on fiber movement. However, this simulation method does not consider the mechanical properties of flexible fibers and cannot accurately correct the coupled model, and the simulation results are not persuasive.

[0005] Therefore, it is of great significance to study a flexible fiber fluid-solid coupling method to solve the problems existing in the prior art. Summary of the Invention

[0006] The purpose of the present invention is to solve the problems existing in the prior art and provide a flexible fiber fluid-solid coupling method.

[0007] To achieve the above purpose, the technical solution adopted by the present invention is as follows:

[0008] A flexible fiber fluid-structure interaction method is applied to the dynamic simulation of the motion evolution characteristics of the water-washing transportation of flexible fibers with a large aspect ratio. The large aspect ratio means that the aspect ratio is 100 - 500. For example, for Lyocell short-cut fibers, the length is commonly 6 - 50 mm (usually 38 mm in enterprise production and preparation), and the fiber diameter is commonly 60 - 100 μm. The flexible fiber fluid-structure interaction method includes the following steps:

[0009] Step 1: Construct a fluid model containing flexible fibers based on the Computational Fluid Dynamics (CFD) method;

[0010] Step 2: Describe the flexible fibers by using the Discrete Element Method (DEM) combined with the sphere-column unit model to obtain multiple fiber sphere-column units with the same length. The multiple fiber sphere-column units with the same length are connected and combined to form a flexible fiber model;

[0011] Step 3: Introduce the porosity of the fluid phase and establish a mass control volume equation containing the fluid and the flexible fibers; introduce the interaction force between the fluid and the flexible fibers into the source term of the force in the momentum control volume equation to obtain a momentum control volume equation containing the source term of the flexible fiber acting force;

[0012] Step 4: The fluid model containing flexible fibers and the flexible fiber model are mutually interpolated and coupled through the trilinear method in the finite element volume method. The fluid model containing flexible fibers and the flexible fiber model together constitute a two-way fluid-structure interaction system; there is an interaction force between the flexible fiber model and the fluid model in the two-way fluid-structure interaction system; the coupling simulation process is as Figure 1 shown; through the divided finite element mesh, the flow field is spatially discretized, and trilinear interpolation is used to transfer data between the fluid mesh nodes and the discrete particle positions. The steps are as follows:

[0013] Through the divided finite element mesh, the flow field is spatially discretized, and trilinear interpolation is used to transfer data between the fluid mesh nodes and the discrete particle positions. The steps are as follows:

[0014] ① Locate the fluid mesh unit where the fiber is located, and locate the grid unit it is in according to the fiber coordinates The vertex coordinates of the unit are to , and find the eight vertex coordinates of the unit and their corresponding fluid variable velocities;

[0015] ② Calculate the distance between each finite element mesh node and the particle center position. The relative distances (weight coefficients) in each direction are:

[0016] ;

[0017] Among them, , and calculate in the same way.

[0018] ③Vertex weight calculation: The weight of each vertex is the product of the weight coefficients in three directions. For vertex , its weight calculation formula is:

[0019] ;

[0020] ④According to the trilinear interpolation formula, the values of the eight vertices of the grid are weighted and summed to obtain the interpolation result at the fiber position. Let the values of the eight vertices be , and the interpolation formula is:

[0021] ;

[0022] Expanding it gives:

[0023] ;

[0024] Among them, is the coordinate is the weight value of the vertex;

[0025] is the coordinate of the vertex.

[0026] In the two-way coupling, the fluid variables at time t are interpolated to the fiber position, and the force on the fiber also needs to be fed back to the fluid grid. At this time, the interpolation weight is also determined by the weight of the trilinear interpolation. The force of each particle will be distributed to the surrounding eight nodes, and the force received by each node is the fiber force multiplied by the corresponding weight to obtain the interpolation result at the fiber position. Subsequently, at time t + 1, time t + 2, time t + 3... until the calculation time is reached.

[0027] Step 5: Use the two-way fluid-structure coupling system to simulate and physically experiment on the motion evolution form of a single flexible fiber in the flow field to obtain the minimum bending amount of the flexible fiber at any time (i.e., the bending distance between the two endpoints when the amplitude displacement of the flexible fiber is the largest) and the maximum displacement amount and the minimum displacement amount of the end point of the flexible fiber, and then calculate the indexes for evaluating the interaction force between the fluid and the flexible fiber, namely the bending degree of the flexible fiber in the flow field and the amplitude of the flexible fiber in the flow field;

[0028] In the simulation process, the motion posture animation of the flexible fiber in the flow field is decomposed into frames at 0.001 s and saved. Through image processing technology, the value of the minimum bending amount is measured, and it is substituted into the following formula (1) to obtain the value of the bending degree of the flexible fiber in the flow field; through image processing technology, each frame result is measured to obtain the maximum value and the minimum Value, substitute its two values into the following formula (2) to obtain the central axis of the amplitude of the flexible fiber flow field , on the central axis of the amplitude of the flexible fiber flow field , measure the displacement of the flexible fiber in the time series (at each continuous time interval) , substitute it into the following formula (3) to obtain the amplitude of the flexible fiber flow field.

[0029] Step 6: Introduce a drag force model correction factor into the source term of the force in the momentum control volume equation , correct the strength of the force between the fluid and the flexible fiber through the evaluation index in Step 5, and perform simulations according to the number of fibers in the actual working condition, so as to judge the bending and winding, entanglement and loosening of the flexible fiber;

[0030] The calculation formula for the curvature of the flexible fiber flow field is as follows:

[0031] (1);

[0032] Among them, S is the curvature of the flexible fiber flow field, is the initial length of the flexible fiber, with the unit of mm, is the minimum bending amount of the flexible fiber at any moment, with the unit of mm;

[0033] The calculation formula for the amplitude of the flexible fiber flow field is as follows:

[0034] (2);

[0035] (3);

[0036] Among them, is the central axis of the amplitude of the flexible fiber flow field, with the unit of mm, is the maximum displacement of the end point of the flexible fiber, with the unit of mm, is the minimum displacement of the end point of the flexible fiber, with the unit of mm, is the amplitude of the flexible fiber flow field in the time series (the time series is the simulation time interval, and the simulation time interval in the present invention is set to 0.001 s), with the unit of mm, is the displacement of the flexible fiber in the time series, with the unit of mm.

[0037] As a preferred technical solution:

[0038] For a flexible fiber fluid-structure interaction method as described above, the specific steps for constructing the fluid model in Step 1 are as follows:

[0039] Step 1.1: Based on the physical geometry model of the conveying pipeline, extract the fluid domain, divide it using the finite element method to obtain fluid meshes, introduce the volume fraction occupied by the flexible fibers in the fluid meshes, and obtain the fluid model;

[0040] Step 1.2: Discretize the fluid dynamics equations based on the finite element method to obtain a nonlinear equation system with the grid node parameter values as the solution variables; solve the nonlinear equation system to obtain the velocity and pressure changes of the flow field at the grid nodes;

[0041] Step 1.3: Based on the fluid meshes, establish a fluid model containing fibers.

[0042] For a flexible fiber fluid-structure interaction method as described above, in the flexible fiber model of Step 2, each fiber sphere-column unit is composed of a cylinder and two end spheres at both ends, as Figure 3 shown. Adjacent fiber sphere-column units are connected by sphere elastic members. Forces and torques are transmitted through the spherical nodes in the fiber sphere-column units. The fiber sphere-column units can undergo morphological evolutions such as bending, torsion, and stretching under the external forces received, thereby changing the flexibility of the fibers.

[0043] For a flexible fiber fluid-structure interaction method as described above, the flexible fiber model in Step 2 includes the dynamic equations of the fluid's action on the flexible fibers. The dynamic equations of the fluid's action on the flexible fibers include the force translation equation and the torque rotation equation;

[0044] The force translation equation is described as:

[0045] (4);

[0046] The torque rotation equation is described as:

[0047] (5);

[0048] Where, is the mass of a single flexible fiber;

[0049] is the translational velocity of the th fiber node sphere;

[0050] is the rotational angular velocity vector of the node sphere;

[0051] is the gravitational acceleration;

[0052] is the time;

[0053] is the moment of inertia;

[0054] is the contact force of the flexible fiber and ;

[0055] is the total drag force of the fluid on the flexible fiber;

[0056] is the flexible fiber and tangential moment;

[0057] is the flexible fiber and normal moment.

[0058] A flexible fiber fluid-structure interaction method as described above, the calculation formula is:

[0059] (6);

[0060] wherein, is the drag force of the th flexible fiber;

[0061] is the fluid unit volume;

[0062] is the number of flexible fibers in the fluid unit;

[0063] is the interpolation weight function (distributing the contribution of fibers to surrounding grid nodes according to trilinear interpolation method);

[0064] is the position of the flexible fiber;

[0065] is the fluid grid center coordinate.

[0066] A flexible fiber fluid-structure interaction method as described above, based on the finite element volume element method, solves equations (4) and (5), and the steps are as follows:

[0067] First, equations (4) and (5) are respectively simplified to:

[0068] (7);

[0069] (8);

[0070] In the formula, is the acceleration of fiber i; is the moment of inertia of fiber i, is the angular acceleration of fiber i; is the force exerted on fiber i, is the resultant external moment;

[0071] Then, by integration, the velocity of the fiber at time t is obtained:

[0072] (9);

[0073] In the formula, is the acceleration of fiber i at time; is the angular acceleration of fiber i at time;

[0074] Integrate again to update the motion attitude of the fiber:

[0075] (10);

[0076] In the formula, is the displacement of fiber i obtained by solving, is the displacement of fiber i at time; By integrating with respect to time, the displacement of the fiber at the next moment is obtained, and so on, to obtain the change in fiber displacement within the simulation time series;

[0077] is the rotation angle of fiber i obtained, is the rotation angle of fiber i at time; By integrating with respect to time, the rotation angle of the fiber at the next moment is obtained, and so on, to obtain the change in fiber rotation angle within the simulation time series.

[0078] As described above, in a flexible fiber fluid-structure interaction method, the mass control volume equation of the fluid and the flexible fiber and the momentum control volume equation including the source term of the flexible fiber acting force in step 3 are shown in equations (11) and (12) respectively;

[0079] (11);

[0080] The momentum conservation equation including the source term of the flexible fiber acting force is described as:

[0081] (12);

[0082] Among them, is the fluid porosity (the fluid porosity represents the volume fraction of the fluid in the control volume);

[0083] is the fluid density;

[0084] is the fluid velocity;

[0085] is the fluid pressure;

[0086] is the Hamiltonian operator;

[0087] is the fluid viscosity;

[0088] is the time;

[0089] is the acceleration due to gravity;

[0090] is the stress tensor;

[0091] is the reaction force of the flexible fiber on the fluid, where and satisfy Newton's third law, and there is a relationship between the action force and the reaction force, that is ;

[0092] The fluid porosity The calculation formula is:

[0093] (13);

[0094] The sum of the fiber volume fraction and the fluid volume fraction in the entire control volume is 1, that is, the fiber volume is distributed to the adjacent fluid grid nodes or the centers of the grid elements according to its position in the fluid grid;

[0095] Among them, is the volume of the k-th ball-column unit fiber in the control volume;

[0096] V is the volume of the control volume;

[0097] is the interpolation weight function (distributing the contribution of the fiber to the surrounding grid nodes according to the trilinear interpolation method);

[0098] is the position of the fiber;

[0099] is the coordinate of the fluid grid center.

[0100] A flexible fiber fluid-structure interaction method as described above. In step 2, the discrete element method is used in combination with the ball-column unit model to describe the flexible fiber, which means using physical property parameters and mechanical property parameters for description. The physical property parameters are fiber diameter, fiber length, fiber density, fiber number, fiber elastic modulus and fiber Poisson ratio. The mechanical property parameters are: the normal force of the ball-column unit and the tangential force , the normal force at the nodal ball , tangential force , torsional torque , bending moment , total torsional torque Combined bending moment ;

[0101] The parameters of the flexible fiber are obtained based on the actual fiber measurement of the research object. The fiber diameter is 60~120μm, the fiber length is 5~100mm, and the fiber density is 750~2000kg / m 3 , the number of fibers is 1~9999, the fiber elastic modulus is 100~260MPa, and the fiber Poisson's ratio is 0.2~0.35;

[0102] The calculation formulas for various mechanical property parameters are as follows:

[0103] (14);

[0104] (15);

[0105] (16);

[0106] (17);

[0107] (18);

[0108] (19);

[0109] (20);

[0110] (twenty one);

[0111] in, is the elastic modulus of the flexible fiber;

[0112] is the node ball damping coefficient, the value is 0.035;

[0113] is the shear modulus of the flexible fiber, , v is Poisson’s ratio;

[0114] is the cross-sectional area of the spherical column unit;

[0115] is the polar moment of inertia of the spherical cylindrical unit section, is the radius of the spherical cylinder element;

[0116] and are the normal displacement and tangential displacement of the spherical-cylindrical element, respectively;

[0117] and are the normal stiffness and shear stiffness at the spherical node, respectively;

[0118] is the distance between the spherical nodes;

[0119] and are the torsional stiffness and bending stiffness at the spherical node, respectively;

[0120] is the mass and the moment of inertia of the relative normal velocity between two spherical nodes;

[0121] is the mass and the moment of inertia of the relative tangential velocity between two spherical nodes;

[0122] is the mass and the moment of inertia of the relative torsional angular velocity between two spherical nodes;

[0123] is the mass and the moment of inertia of the relative bending angular velocity between two spherical nodes.

[0124] For a flexible fiber-fluid-solid coupling method as described above, the calculation formula for the drag force of the mutual force between the flexible fiber model and the fluid model in the two-way fluid-solid coupling system in step 4 is:

[0125] (22);

[0126] where the momentum exchange coefficient between the fluid and the fiber phase is expressed as:

[0127] (23);

[0128] The drag coefficient C D is expressed as:

[0129] (24);

[0130] The calculation formula for the Reynolds number Re is:

[0131] (25);

[0132] wherein, is the fluid velocity;

[0133] is the flexible fiber velocity;

[0134] is the fluid porosity;

[0135] is the fluid density;

[0136] is the flexible fiber diameter;

[0137] is the fluid viscosity;

[0138] is the acceleration of gravity.

[0139] A flexible fiber fluid-structure interaction method as described above, a drag force model correction factor is introduced into the source term of the force in the momentum control volume equation, and the expression of the corrected drag force model is:

[0140] (26).

[0141] A flexible fiber fluid-structure interaction method as described above, in step 4, the mutual interpolation coupling calculation is carried out by the trilinear method in the finite element volume method. Specifically, equations (7) and (8) are rewritten as a general formula:

[0142] (27);

[0143] wherein, the fluid density vector with porosity is expressed as:

[0144] (28);

[0145] The convective terms of the three components in the spatial coordinate system in the fluid model , and are respectively expressed as:

[0146] (29);

[0147] (30);

[0148] (31);

[0149] The viscous fluxes of the three components in the spatial coordinate system in the fluid model , and is expressed as:

[0150] (32);

[0151] (33);

[0152] (34);

[0153] is the force source term, including the interaction force between the fiber and the fluid:

[0154] (35);

[0155] wherein, is the component of the fluid velocity on the axis in the space coordinate system;

[0156] is the component of the fluid velocity on the axis in the space coordinate system;

[0157] is the component of the fluid velocity on the axis in the space coordinate system;

[0158] is the convection term on the axis in the fluid dynamics equations;

[0159] is the convection term on the axis in the fluid dynamics equations;

[0160] is the convection term on the axis in the fluid dynamics equations;

[0161] is the viscous flux on the axis in the fluid dynamics equations;

[0162] is the viscous flux on the axis in the fluid dynamics equations;

[0163] is the viscous flux on the axis in the fluid dynamics equations;

[0164] is the fluid porosity, is the fluid pressure, is the fluid viscosity tensor;

[0165] , , are respectively the force source terms in three spatial directions;

[0166] is the viscous force perpendicular to the axis and along the axis direction;

[0167] is the viscous force perpendicular to the axis and along the axis direction;

[0168] is the viscous force perpendicular to the axis and along the axis direction;

[0169] is the viscous force perpendicular to the axis and along the axis direction;

[0170] is the viscous force perpendicular to the axis and along the axis direction;

[0171] is the viscous force perpendicular to the axis and along the axis direction;

[0172] is the viscous force perpendicular to the axis and along the axis direction;

[0173] is the viscous force perpendicular to the axis and along the axis direction;

[0174] is the viscous force perpendicular to the axis and along the axis direction.

[0175] Advantageous effects:

[0176] (1) A flexible fiber fluid-structure interaction method of the present invention, based on the ball-column element model modeling method, establishes a flexible fiber fluid-structure interaction system, which can effectively simulate the motion evolution behavior of flexible fibers in a fluid field, and has good scalability and adaptability, and is applicable to the simulation of the motion evolution characteristics of large aspect ratio flexible bodies in a fluid field.

[0177] (2) A flexible fiber fluid-structure coupling method of the present invention. The discrete element method (DEM) is used to study particle dynamics, which can effectively simulate the dynamic characteristics of particles with different shapes. The computational fluid dynamics (CFD) method can accurately capture fluid field information. By self-defining a coupling program, the CFD-DEM model can simulate the solid-liquid two-phase flow system, capture particle collision and position attitude information, and realize the numerical simulation of fluid-solid interaction. This method provides a new theoretical basis for the entanglement behavior and agglomeration characteristics of flexible fibers with a large length-diameter ratio in the flow field, and provides guidance for the future industrial application of fibers in new energy. Description of the Drawings

[0178] Figure 1 It is the coupling calculation flow chart of the flexible fiber fluid-structure coupling method of the present invention;

[0179] Figure 2 It is the schematic diagram of the bending degree and amplitude of a single fiber in the flow field of the present invention; among them, Figure 2 (a) in it is the schematic diagram for solving the bending degree, Figure 2 (b) in it is the maximum displacement in the y-axis direction of the amplitude, Figure 2 (c) in it is the minimum displacement in the y-axis direction of the amplitude; the dotted line represents the amplitude central axis T, and the red line represents the fiber;

[0180] Figure 3 It is the schematic diagram of the flexible fiber model based on the sphere-cylinder unit model of the present invention;

[0181] Figure 4 It is the experimental scheme diagram for verifying the flexible fiber fluid-structure coupling method of the present invention;

[0182] Figure 5 It is the comparison diagram of the simulation and experiment of the motion form evolution of a single fiber in the flow field of the present invention;

[0183] Figure 6 It is the change diagram of the amplitude index of the fiber flow field under different correction factors of the present invention;

[0184] Figure 7 It is the change diagram of the bending degree index of the fiber flow field under different correction factors of the present invention;

[0185] Figure 8 It is the evolution behavior and velocity distribution diagram of the fiber in the flow field at different times. Among them, Figure 8 (a) in it is the evolution behavior and velocity distribution of the fiber at 0.025 s, Figure 8 (c) in it is the evolution behavior and velocity distribution of the fiber at 0.038 s, Figure 8 (e) in it is the evolution behavior and velocity distribution of the fiber at 0.089 s, Figure 8 (g) in it is the evolution behavior and velocity distribution of the fiber at 0.165 s,Figure 8 In (b), Figure 8 In (d), Figure 8 In (f), and Figure 8 In (h) are respectively Figure 8 In (a), Figure 8 In (c), Figure 8 In (e), and Figure 8 The partial enlarged views at the corresponding moments of (g) in the figure;

[0186] Wherein, 1 - node ball, 2 - ball - column unit, 3 - water source, 4 - aluminum profile frame, 5 - CCD high - definition camera, 6 - background board, 7 - lighting lamp, 8 - water flow velocity meter, 9 - universal rotary pipe fixing clamp, 10 - wool - conveying pipe, 11 - recovery tank. Specific embodiments

[0187] The present invention will be further described below in conjunction with specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and not to limit the scope of the present invention. In addition, it should be understood that after reading the content taught by the present invention, those skilled in the art can make various changes or modifications to the present invention, and these equivalent forms also fall within the scope defined by the appended claims of this application.

[0188] A flexible fiber fluid - solid coupling method is applied to the dynamic simulation of the movement evolution characteristics of the water - washing and conveying of flexible fibers with a large length - to - diameter ratio. The large length - to - diameter ratio means that the length - to - diameter ratio is 100 - 500. The flexible fiber fluid - solid coupling method includes the following steps:

[0189] Step 1: Construct a fluid model containing flexible fibers based on the computational fluid dynamics method (CFD), specifically as follows:

[0190] Step 1.1: Based on the physical geometric model of the conveying pipeline, extract the fluid domain, divide it by the finite - element method to obtain fluid meshes, and introduce the volume fraction occupied by the flexible fibers in the fluid meshes to obtain the fluid model;

[0191] Step 1.2: Discretize the computational fluid dynamics equations based on the finite - element method to obtain a non - linear equation set with the grid node parameter values as the solution variables; solve the non - linear equation set to obtain the velocity and pressure changes of the flow field at the grid nodes;

[0192] Step 1.3: Based on the fluid meshes, establish a fluid model containing fibers.

[0193] Step 2: Describe the flexible fibers by using the discrete - element method (DEM) combined with the ball - column unit model to obtain a plurality of fiber ball - column units with the same length, and the plurality of fiber ball - column units with the same length are connected and combined to form a flexible fiber model;

[0194] The discrete element method combined with the spherical-cylindrical element model is used to describe flexible fibers, which means using physical property parameters and mechanical property parameters for description. The physical property parameters are fiber diameter, fiber length, fiber density, fiber quantity, fiber elastic modulus, and fiber Poisson's ratio. The mechanical property parameters are: the normal force of the spherical-cylindrical element and the tangential force , the normal force at the nodal sphere , the tangential force , the torsional moment , the bending moment , the combined torsional moment and the combined bending moment ;

[0195] The parameters of the flexible fibers are obtained by measuring the physical fibers of the research object. The fiber diameter is 60 - 120 μm, the fiber length is 5 - 100 mm, the fiber density is 750 - 2000 kg / m 3 , the fiber quantity is 1 - 9999, the fiber elastic modulus is 100 - 260 MPa, and the fiber Poisson's ratio is 0.2 - 0.35;

[0196] The calculation formulas for each mechanical property parameter are as follows:

[0197] (14);

[0198] (15);

[0199] (16);

[0200] (17);

[0201] (18);

[0202] (19);

[0203] (20);

[0204] (21);

[0205] Among them, is the elastic modulus of the flexible fiber;

[0206] is the damping coefficient of the nodal sphere, and the value is 0.035;

[0207] is the shear modulus of the flexible fiber, , v is Poisson's ratio;

[0208] is the cross-sectional area of the spherical column unit;

[0209] is the polar moment of inertia of the spherical column unit cross-section, is the radius of the spherical column unit;

[0210] and are the normal displacement of the spherical column unit and the tangential displacement of the spherical column unit respectively;

[0211] and are the normal stiffness and shear stiffness at the node ball respectively;

[0212] is the distance between the node balls;

[0213] and are the torsional stiffness and bending stiffness at the node ball respectively;

[0214] is the mass and moment of inertia of the relative normal velocity between two node balls;

[0215] is the mass and moment of inertia of the relative tangential velocity between two node balls;

[0216] is the mass and moment of inertia of the relative torsional angular velocity between two node balls;

[0217] is the mass and moment of inertia of the relative bending angular velocity between two node balls;

[0218] Each fiber spherical column unit is composed of a cylinder and spheres at both ends, as Figure 3 shown, adjacent fiber spherical column units 2 are connected by node balls 1;

[0219] The flexible fiber model includes the dynamic equations of the fluid acting on the flexible fiber. The dynamic equations of the fluid acting on the flexible fiber include the force translation equation and the moment rotation equation;

[0220] The force translation equation is described as:

[0221] (4);

[0222] The torque rotation equation is described as:

[0223] (5);

[0224] Wherein, is the mass of a single flexible fiber;

[0225] is the translational velocity of the th fiber node sphere;

[0226] is the rotational angular velocity vector of the node sphere;[[ID=2(1]]

[0227] is the gravitational acceleration;

[0228] is the time;

[0229] is the moment of inertia;

[0230] is the contact force between the flexible fiber and ;

[0231] is the total drag force of the fluid on the flexible fiber;

[0232] is the tangential torque of the flexible fiber and ;

[0233] is the normal torque of the flexible fiber and ;

[0234] The calculation formula of

[0235] is: (6);

[0236] Wherein, is the drag force of the th flexible fiber;

[0237] is the fluid unit volume;

[0238] is the number of flexible fibers in the fluid unit;

[0239] is the interpolation weight function;

[0240] is the position of the flexible fiber;

[0241] are the central coordinates of the fluid grid;

[0242] Based on the finite element volume element method, equations (4) and (5) are solved as follows:

[0243] First, equations (4) and (5) are respectively simplified to:

[0244] (7);

[0245] (8);

[0246] where is the acceleration of fiber i; is the moment of inertia of fiber i, is the angular acceleration of fiber i; is the force on fiber i, is the resultant external torque;

[0247] Then, integration is performed to obtain the velocity of the fiber at time t:

[0248] (9);

[0249] where, is the acceleration of fiber i at time; is the angular acceleration of fiber i at time;

[0250] Integrate again to update the motion attitude of the fiber:

[0251] (10);

[0252] where, is the displacement of fiber i obtained by solving, is the displacement of fiber i at time; is the rotation angle of fiber i obtained, is the rotation angle of fiber i at time.

[0253] Step 3: Introduce the porosity of the fluid phase and establish the mass control volume equation including the fluid and the flexible fiber; introduce the interaction force between the fluid and the flexible fiber into the source term of the force in the momentum control volume equation to obtain the momentum control volume equation including the source term of the flexible fiber acting force;

[0254] The mass control volume equation containing fluid and flexible fibers and the momentum control volume equation containing the source term of the acting force of the flexible fibers are shown in equations (11) and (12) respectively;

[0255] (11);

[0256] The momentum conservation equation containing the source term of the acting force of the flexible fibers is described as:

[0257] (12);

[0258] where, is the fluid porosity (the fluid porosity represents the volume fraction of the fluid in the control volume);

[0259] is the fluid density;

[0260] is the fluid velocity;

[0261] is the fluid pressure;

[0262] is the Hamiltonian operator;

[0263] is the fluid viscosity;

[0264] is the time;

[0265] is the gravitational acceleration;

[0266] is the stress tensor;

[0267] is the reaction force of the flexible fibers on the fluid, where, and satisfy Newton's third law, and there is a relationship of action and reaction, that is ;

[0268] The fluid porosity The calculation formula of is:

[0269] (13);

[0270] The sum of the fiber volume fraction and the fluid volume fraction in the entire control volume is 1, that is, the fiber volume is distributed to the adjacent fluid grid nodes or the centers of the grid elements according to its position in the fluid grid;

[0271] where, is the volume of the k-th spherical column unit fiber in the control volume;

[0272] V is the volume of the control volume;

[0273] is the interpolation weight function (allocating the contribution of fibers to the surrounding grid nodes according to the trilinear interpolation method);

[0274] is the position of the fiber;

[0275] is the center coordinate of the fluid grid;

[0276] Step 4: The fluid model containing flexible fibers and the flexible fiber model are coupled by mutual interpolation calculation using the trilinear method in the finite element volume method. The fluid model containing flexible fibers and the flexible fiber model together constitute a two-way fluid-structure interaction system;

[0277] By performing mutual interpolation coupling calculation using the trilinear method in the finite element volume method, specifically, equations (7) and (8) are rewritten as a general formula:

[0278] (27);

[0279] Among them, the fluid density vector with porosity is expressed as:

[0280] (28);

[0281] The convective terms of the three components in the spatial coordinate system of the fluid model , and are respectively expressed as:

[0282] (29);

[0283] (30);

[0284] (31);

[0285] The viscous fluxes of the three components in the spatial coordinate system of the fluid model , and are expressed as:

[0286] (32);

[0287] (33);

[0288] (34);

[0289] is the force source term, including the interaction force between the fiber and the fluid:

[0290] (35);

[0291] wherein, is the component of the fluid velocity on the axis in the space coordinate system;

[0292] is the component of the fluid velocity on the axis in the space coordinate system;

[0293] is the component of the fluid velocity on the axis in the space coordinate system;

[0294] is the convective term on the axis in the fluid dynamics equations;

[0295] is the convective term on the axis in the fluid dynamics equations;

[0296] is the convective term on the axis in the fluid dynamics equations;

[0297] is the viscous flux on the axis in the fluid dynamics equations;

[0298] is the viscous flux on the axis in the fluid dynamics equations;

[0299] is the viscous flux on the axis in the fluid dynamics equations;

[0300] is the fluid porosity, is the fluid pressure, is the fluid viscosity tensor;

[0301] and and are respectively the force source terms in the three directions of space;

[0302] is the viscous force perpendicular to the axis and along the axis direction;

[0303] The viscous force is perpendicular to the axis and along the axis direction;

[0304] The viscous force is perpendicular to the axis and along the axis direction;

[0305] The viscous force is perpendicular to the axis and along the axis direction;

[0306] The viscous force is perpendicular to the axis and along the axis direction;

[0307] The viscous force is perpendicular to the axis and along the axis direction;

[0308] The viscous force is perpendicular to the axis and along the axis direction;

[0309] The viscous force is perpendicular to the axis and along the axis direction;

[0310] The viscous force is perpendicular to the axis and along the axis direction;

[0311] There is an interaction force between the flexible fiber model and the fluid model in the two-way fluid-structure coupling system; the calculation formula for the drag force of the interaction force between the flexible fiber model and the fluid model is:

[0312] (22);

[0313] Among them, the momentum exchange coefficient between the fluid and the fiber phase is expressed as:

[0314] (23);

[0315] The drag coefficient C D is expressed as:

[0316] (24);

[0317] The calculation formula for the Reynolds number Re is:

[0318] (25);

[0319] Wherein, is the fluid velocity;

[0320] is the flexible fiber velocity;

[0321] is the fluid porosity;

[0322] is the fluid density;

[0323] is the flexible fiber diameter;

[0324] is the fluid viscosity;

[0325] is the acceleration of gravity.

[0326] The coupling simulation process is as follows Figure 1 shown. A 90° straight pipe model is established in a 3D modeling software and the stp file is saved. The geometric model file is imported into Spaceclaim to extract the fluid domain, and the fluid domain file is saved. Then it is imported into fluent for mesh generation to obtain the fluid model. Set the CFD fluid model parameters, define the fluid domain as water, the inlet condition as velocity inlet, and the outlet as pressure outlet by default. Select the model, and use the SIMPLE method to perform numerical simulation calculations within the given time step, with iterative loops. Define the number of calculation time steps as 1000, the time step as 0.001, and the maximum number of iterations as 20 to perform convergent calculation of the fluid force to obtain the fluid phase velocity field and pressure field information; in the discrete element DEM environment, establish a flexible fiber model, define the flexible fiber model parameters, including physical properties and mechanical properties, solve the fiber dynamics equation, calculate the contact force between fibers, and update the fiber velocity and position.

[0327] Through the divided finite element mesh, the flow field is spatially discretized, and trilinear interpolation is used to transfer data between the fluid mesh nodes and the discrete particle positions. The steps are as follows:

[0328] ① Locate the fluid mesh element where the fiber is located. According to the fiber coordinates locate the mesh element it is in. The vertex coordinates of the element are to , and find the eight vertex coordinates of the element and their corresponding fluid variable velocities;

[0329] ② Calculate the distance between each finite element mesh node and the particle center position. The relative distances (weighting coefficients) in each direction are:

[0330] ;

[0331] Among them, , similarly calculate .

[0332] ③ Vertex weight calculation, the weight of each vertex is the product of the weight coefficients in three directions. Taking vertex as an example, its weight calculation formula is:

[0333] ;

[0334] ④ According to the trilinear interpolation formula, the values of the eight vertices of the grid are weighted and summed to obtain the interpolation result at the fiber position. Let the values of the eight vertices be , and the interpolation formula is:

[0335] ;

[0336] Expanding it gives:

[0337] ;

[0338] Among them, is the coordinate is the weight value of the vertex;

[0339] is the coordinate of the vertex.

[0340] In the two-way coupling, the fluid variables at time t are interpolated to the fiber position, and the force on the fiber also needs to be fed back to the fluid grid. At this time, the interpolation weight is also determined by the weight of the trilinear interpolation. The force of each particle will be distributed to the surrounding eight nodes, and the force received by each node is the fiber force multiplied by the corresponding weight to obtain the interpolation result at the fiber position. Subsequently, at time t+1, time t+2, time t+3... until the calculation time is reached, the calculation ends.

[0341] Step 5: Use the two-way fluid-structure interaction system to simulate and physically experiment on the motion evolution form of a single flexible fiber in the flow field, to obtain the minimum bending amount of the flexible fiber at any time (i.e., the bending distance between the two endpoints when the amplitude displacement of the flexible fiber is the largest) and the maximum displacement amount and the minimum displacement amount of the end point of the flexible fiber, and then calculate the indexes for evaluating the interaction force between the fluid and the flexible fiber, namely the bending degree of the flexible fiber in the flow field and the vibration amplitude of the flexible fiber in the flow field;

[0342] Step 6: Introduce the drag model correction factor , modify the strength of the force between the fluid and the flexible fiber through the evaluation index in step 5, and perform simulations according to the number of fibers in the actual working conditions, so as to judge the bending, entanglement and opening of the flexible fiber;

[0343] Introduce a drag force model correction factor into the source term of the force in the momentum control volume equation , and the expression of the modified drag force model is:

[0344] (26);

[0345] Among them, Coefficient of momentum exchange between fluid and fiber phase;

[0346] The calculation formula for the curvature of the flexible fiber flow field is as follows:

[0347] (1);

[0348] Among them, S is the curvature of the flexible fiber flow field, is the initial length of the flexible fiber, in mm, is the minimum bending amount of the flexible fiber at any time, in mm;

[0349] The calculation formula for the amplitude of the flexible fiber flow field is as follows:

[0350] (2);

[0351] (3);

[0352] Among them, is the central axis of the amplitude of the flexible fiber flow field, in mm, is the maximum displacement of the end point of the flexible fiber, in mm, is the minimum displacement of the end point of the flexible fiber, in mm, is the amplitude of the flexible fiber flow field in the time series (the time series is the simulation time interval, and the simulation time interval in the present invention is set to 0.001 s), in mm, is the displacement of the flexible fiber in the time series, in mm.

[0353] Among them, in the simulation process, the motion posture animation of the flexible fiber in the flow field is decomposed and saved in frames of 0.001 s, and through image processing technology, the minimum bending amount value is measured over the entire time, and substituting it into equation (1) to obtain the value of the curvature of the flexible fiber flow field; by measuring the results of each frame through image processing technology, the maximum value and the minimum Value, substitute its two values into Equation (2) to obtain the central axis of the amplitude of the flexible fiber flow field , on the central axis of the amplitude of the flexible fiber flow field , measure the displacement of the flexible fiber in the time series (at each continuous time interval) , substitute it into Equation (3) to obtain the amplitude of the flexible fiber flow field. The schematic diagram is as Figure 2 shown.

[0354] The following uses specific embodiments to illustrate a flexible fiber fluid-structure interaction method of the present invention, specifically as follows:

[0355] To further verify the correctness of the model, the motion evolution form of a single flexible fiber flow field is simulated and the experiment is corrected and verified. In the CFD environment, the fluid domain is defined as water, the inlet condition is a velocity inlet, and the flow velocity is 4 m / s. The outlet is defaulted to a pressure outlet. In the DEM environment, the fiber diameter is defined as 60 μm, the fiber length is 38 mm, and the fiber density is 1750 kg / m 3 , the fiber generation speed is 0.05 kg / s, the fiber elastic modulus is 122 MPa, and the fiber Poisson's ratio is 0.3.

[0356] The experimental scheme is as Figure 4 shown. A flexible fiber fluid-structure interaction physical experimental platform is built. The experimental platform consists of a water source 3, an aluminum profile frame 4, a CCD high-definition camera 5, a background board 6, a lighting lamp 7, a water flow meter 8, a universal rotating pipe fixing clip 9, a highly transparent acrylic hair conveying pipe 10, and a recovery tank 11. Among them, the size of the aluminum profile frame 4 is 400 mm × 400 mm × 400 mm, the specification of the water flow meter 8 is a 4-inch thread G1 / 2 water flow sensor tachometer, the water pressure resistance is less than 1.75 MPa, the accuracy is ±5%, and the measuring temperature thermistor is 50 kΩ. The background board 7 is matte black to avoid the wall reflection interfering with the shooting effect of the fiber flow field. The designed experimental conditions are the same as the numerical simulation calculation conditions. In order to prevent air from entering the pipeline during the experiment and affecting the fiber flow change, the pipeline interface is sealed with waterproof raw tape.

[0357] When performing numerical simulation calculations of flexible fiber fluid-structure interaction, by changing the drag model correction factor of the interaction source in the momentum equation over a large range, a large number of numerical simulation calculations are carried out, and the values of the evaluation indexes of the mutual force of the fiber flow field, the curvature and the amplitude, are made to approximate the values obtained from the experiment as much as possible. Through continuous simulation calculations, when the drag model correction factor is obtained, the experimental and numerical simulation results are relatively close, and the error is within 5%. Moreover, in the experiment and numerical simulation calculations, the motion characteristics and evolution behaviors of the fiber in the flow field are relatively consistent. The comparison between the physical experiment and the numerical simulation process is as Figure 5As shown; under different drag force model correction factors, the comparison results of the amplitude of the evaluation index between physical experiments and numerical simulations are as Figure 6 shown. Under different drag force correction factors, the comparison results of the curvature of the evaluation index between physical experiments and numerical simulations are as Figure 7 shown.

[0358] Therefore, when the drag force model correction factor is adopted in the present invention, numerical simulation of the evolution characteristics of flexible fiber flow field during fiber transportation is carried out. Under the working conditions of fiber generation speed of 0.05 kg / s and water flow speed of 2 m / s, during the transportation process, the fiber evolution behaviors at different times are as Figure 8 shown. It can be seen from the figure that the fiber starts to flow vertically along the water. When passing through the 90° elbow group, due to the change in the flow field form, the fiber undergoes irregular bending and deformation evolution, laminar flow and turbulent flow phenomena occur in the flow field, and the fiber is involved in the turbulent flow and undergoes winding and knotting behaviors.

[0359] The present invention realizes the simulation visualization of the flexible fiber transportation process in production. Given the fiber generation speed of 0.05 kg / s and the water flow speed of 4 m / s under the initial conditions, simulation is carried out, and model correction and experimental verification are carried out. The actual production and preparation process of fiber water washing and transportation is simulated and reproduced, providing theoretical guidance for studying the phenomena of fiber bending, winding, entanglement and opening in the flow field. It shows that the present invention can be well applied to the research of engineering problems in actual production transportation, has certain academic significance and engineering value, and is expected to promote wider application in the industry and promote the development of industry towards science and efficiency.

Claims

1. A flexible fiber fluid-structure interaction method, characterized in that: Dynamic simulation of the movement evolution characteristics of flexible fibers with a large aspect ratio applied to water washing and conveying. The large aspect ratio refers to an aspect ratio of 100 - 500. The flexible fiber fluid-structure interaction method includes the following steps: Step 1: Construct a fluid model containing flexible fibers based on the hydrodynamic method; Step 2: Use the discrete element method combined with the sphere-cylinder element model to describe the flexible fibers, obtaining multiple fiber sphere-cylinder units of the same length. The multiple fiber sphere-cylinder units of the same length are connected and combined to form a flexible fiber model; Step 3: Introduce the porosity of the fluid phase and establish a mass control volume equation containing the fluid and flexible fibers; introduce the interaction force between the fluid and flexible fibers into the source term of the force in the momentum control volume equation to obtain a momentum control volume equation containing the source term of the flexible fiber acting force; Step 4: The fluid model containing flexible fibers and the flexible fiber model are coupled and calculated through mutual interpolation by the trilinear method in the finite element volume method. The fluid model containing flexible fibers and the flexible fiber model together constitute a two-way fluid-structure interaction system; there is an interaction force between the flexible fiber model and the fluid model in the two-way fluid-structure interaction system; Step 5: Use the two-way fluid-structure interaction system to simulate and conduct physical experiments on the motion evolution of a single flexible fiber in a flow field, and obtain the minimum bending amount of the flexible fiber at any moment and the maximum displacement of the end point of the flexible fiber and the minimum displacement , and then calculate the indexes for evaluating the interaction force between the fluid and the flexible fiber, namely, the bending degree of the flexible fiber in the flow field and the vibration amplitude of the flexible fiber in the flow field; Step 6: Introduce a drag force model correction factor into the source term of the force in the momentum control volume equation , correct the strength of the force between the fluid and the flexible fibers through the evaluation index in Step 5, and perform simulations according to the number of fibers in the actual working conditions, so as to judge the bending and winding, entanglement into clusters, and opening of the flexible fibers; The calculation formula for the curvature of the flexible fiber flow field is as follows: （1）； Wherein, S is the bending degree of the flexible fiber flow field, is the initial length of the flexible fiber, is the minimum bending amount of the flexible fiber at any time; The calculation formula for the amplitude of the flexible fiber flow field is as follows: （2）； （3）； Among them, is the central axis of the amplitude of the flexible fiber flow field, is the maximum displacement of the end point of the flexible fiber, is the minimum displacement of the end point of the flexible fiber, is the amplitude of the flexible fiber flow field in the time series, is the displacement of the flexible fiber in the time series.

2. The flexible fiber fluid-structure interaction method according to claim 1, characterized in that The specific steps for constructing the fluid model in Step 1 are as follows: Step 1.1: Based on the physical geometric model of the conveying pipeline, extract the fluid domain, divide it by the finite element method to obtain fluid meshes, and introduce the volume fraction occupied by the flexible fibers in the fluid meshes to obtain a fluid model; Step 1.2: Discretize the hydrodynamic equations based on the finite element method to obtain a nonlinear equation system with the grid node parameter values as the solution quantities; solve the nonlinear equation system to obtain the velocity and pressure changes of the flow field at the grid nodes; Step 1.3: Based on the fluid meshes, establish a fluid model containing fibers.

3. A flexible fiber fluid-structure interaction method according to claim 2, characterized in that In the flexible fiber model of Step 2, each fiber sphere-cylinder unit is composed of a cylinder and two end spheres, and adjacent fiber sphere-cylinder units are connected by sphere elastic members.

4. A flexible fiber fluid-structure interaction method according to claim 3, characterized in that The flexible fiber model of Step 2 includes the dynamic equation system of the force of the fluid on the flexible fibers. The dynamic equation system of the force of the fluid on the flexible fibers includes the force translation equation and the moment rotation equation; The force translation equation is described as: （4）； The moment rotation equation is described as: （5）； Among them, is the mass of a single flexible fiber; is the translational velocity of the th fiber node sphere; is the rotational angular velocity vector of the node sphere; is the acceleration due to gravity; is time; is the moment of inertia; is the contact force of the flexible fiber and ; is the total drag force of the fluid on the flexible fiber; is a flexible fiber and tangential moment; is a flexible fiber and the normal moment 5. A flexible fiber fluid-structure interaction method according to claim 4, characterized in that, The calculation formula is as follows: （6）； Among them, is the drag force of the th flexible fiber; is the volume of the fluid unit; is the number of flexible fibers in the fluid unit; is an interpolation weight function; Position of the flexible fiber; is the central coordinate of the fluid grid.

6. A flexible fiber fluid-structure interaction method according to claim 5, characterized in that Based on the finite element volume element method, solve equations (4) and (5) as follows: First, simplify equations (4) and (5) respectively to: （7）； （8）； In the formula, is the acceleration of fiber i; is the moment of inertia of fiber i, is the angular acceleration of fiber i; is the force acting on fiber i, is the resultant external torque; Then integrate to obtain the movement speed of the fiber at time t: （9）； In the formula, is the acceleration of fiber i at moment; is the angular acceleration of fiber i at moment. Integrate again to update the movement attitude of the fiber: （10）； In the formula, is the displacement of fiber i obtained by solution, is the displacement of fiber i at time; is the rotation angle of fiber i obtained, is the rotation angle of fiber i at time.

7. A flexible fiber fluid-structure interaction method according to claim 6, characterized in that The mass control volume equation containing the fluid and flexible fibers and the momentum control volume equation containing the source term of the flexible fiber acting force in Step 3 are shown in equations (11) and (12) respectively; （11）； The momentum conservation equation containing the source term of the flexible fiber acting force is described as: （12）； wherein, is the fluid porosity; is the fluid density; is the fluid velocity; is the fluid pressure; is the Hamiltonian operator; is the fluid viscosity; is the acceleration due to gravity; is the stress tensor; is the reaction force of the flexible fiber on the fluid; Fluid porosity The calculation formula is as follows: （13）； Among them, is the volume of the fibers of the k-th ball-column unit in the control volume; V is the volume of the control volume; is an interpolation weight function; is the position of the fiber; is the central coordinate of the fluid grid.

8. A flexible fiber fluid-structure interaction method according to claim 7, characterized in that In Step 2, the discrete element method combined with the spherical-cylindrical element model is used to describe the flexible fibers, which means using physical property parameters and mechanical property parameters for description. The physical property parameters are fiber diameter, fiber length, fiber density, fiber quantity, fiber elastic modulus, and fiber Poisson's ratio. The mechanical property parameters are: the normal force of the spherical-cylindrical element and the tangential force , the normal force at the node sphere , the tangential force , the torsional moment , the bending moment , the combined torsional moment and the combined bending moment ; The fiber diameter is 60 to 120 μm, the fiber length is 5 to 100 mm, and the fiber density is 750 to 2000 kg / m 3 , the number of fibers is 1 to 9999, the elastic modulus of the fiber is 100 to 260 MPa, and the Poisson's ratio of the fiber is 0.2 to 0.35; The calculation formulas for each mechanical property parameter are as follows: （14）； （15）； （16）； （17）； （18）； （19）； （20）； （21）； Among them, is the elastic modulus of the flexible fiber; is the damping coefficient of the node ball, with a value of 0.035; is the shear modulus of the flexible fiber, , and v is the Poisson's ratio; is the cross-sectional area of the ball-column unit; is the polar moment of inertia of the spherical column unit cross-section, is the radius of the spherical column unit; and are the normal displacement and tangential displacement of the spherical column unit, respectively; and are the normal stiffness and shear stiffness at the nodal sphere, respectively; is the distance between the nodal spheres; and are the torsional stiffness and bending stiffness at the nodal sphere, respectively; For mass and moment of inertia the relative normal velocity between two nodal spheres; for mass and moment of inertia the relative tangential velocity between two nodal spheres; for the mass and the moment of inertia the relative torsional angular velocity between two nodal spheres; For mass and moment of inertia the relative bending angular velocity between two nodal spheres.

9. A flexible fiber fluid-structure interaction method according to claim 8, characterized in that The calculation formula for the drag force of the interaction force between the flexible fiber model and the fluid model in the two-way fluid-structure interaction system in Step 4 is: （22）； Among them, the momentum exchange coefficient between the fluid and the fiber phase The expression is as follows: （23）； Drag coefficient C D The expression is: （24）； The calculation formula for the Reynolds number Re is: （25）； Among them, is the fluid velocity; is the velocity of the flexible fiber; is the fluid porosity; is the fluid density; is the diameter of the flexible fiber; is the fluid viscosity.

10. A flexible fiber fluid-structure interaction method according to claim 9, characterized in that, Introduce the drag force model correction factor into the source term of the force in the momentum control volume equation , and the expression of the corrected drag force model is as follows: （26）。 11. A flexible fiber fluid-structure interaction method according to claim 10, characterized in that, In step 4, the trilinear method in the finite cell volume method is used for mutual interpolation coupling calculation. Specifically, equations (7) and (8) are rewritten as a general formula: （27）； Among them, the fluid density vector containing the porosity is expressed as: （28）； Convection terms of three components in the spatial coordinate system of the fluid model , and are respectively expressed as: （29）； （30）； （31）； Three-component viscous fluxes in the spatial coordinate system of the fluid model , and are expressed as: （32）； （33）； （34）； is the force source term, including the interaction force between the fiber and the fluid: （35）； Among them, is the component of the fluid velocity on the axis in the space coordinate system; is the component of the fluid velocity in the spatial coordinate system on the axis; is the component of the fluid velocity in the space coordinate system on the axis; For the convective term on the axis in the hydrodynamic equations ; For the convective term on the axis in the hydrodynamic equations ; For the convective term on the axis in the hydrodynamic equations ; for the viscous fluxes on the axis in the hydrodynamic equations ; for the viscous fluxes on the axis in the hydrodynamic equations ; for the viscous fluxes on the axis in the hydrodynamic equations ; is the fluid porosity, is the fluid pressure, is the fluid viscosity tensor; , , are respectively the force source terms in three directions of space; The viscous force is perpendicular to the axis and along the axis direction; The viscous force is perpendicular to the axis and along the axis direction; The viscous force is perpendicular to the axis and along the axis direction; The viscous force is perpendicular to the axis and along the axis direction; The viscous force is perpendicular to the axis and along the axis direction; The viscous force is perpendicular to the axis and along the axis direction; The viscous force is perpendicular to the axis and along the axis direction; The viscous force is perpendicular to the axis and along the axis direction; The viscous force is perpendicular to the axis and along the axis direction.

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