JP6711344B2 - Method and apparatus for analyzing motion state of fibrous substance in fluid - Google Patents

Description

The present invention relates to a method of analyzing a motion state of a fibrous substance in a fluid and an analyzing apparatus therefor.

Conventionally, when particles contained in a fluid are almost spherical, various calculations are performed based on the fluid information (flow field distribution, fluid viscosity, etc.) and particle information (particle diameter, initial position, etc.). By the method, it was possible to analyze the movement and rotation of particles by computer simulation with relatively high accuracy. On the other hand, when the substance contained in the fluid is a fibrous substance, due to the complicated shape change and behavior of the fibrous substance in the fluid, the movement state and the deformation state of the fibrous substance are calculated by computer simulation. However, it has been difficult to analyze the distribution state, the orientation state, etc. accurately and in a short time. Therefore, in recent years, various methods have been studied in order to perform a highly accurate simulation of the motion state of the fibrous substance in the fluid.

For example, in Japanese Patent Application Laid-Open No. 5-314091 (Patent Document 1), the movement and/or deformation and/or orientation of particles contained in a fluid substrate is determined by the various characteristics of the substrate and particles, the flow field of the substrate. Of the particle size and the initial position and orientation of the particle in the flow field of the substrate, and the like, and a method of analyzing using a CAE/CAD/CAM system so as to obtain an overall shape simulating the shape of the particle. A sphere assembly in which a plurality of spheres are mutually connected in one-dimensional, two-dimensional or three-dimensional directions is used as a model for analyzing the particles (using a sphere assembly model), and each sphere constituting this sphere assembly is Is the translation and/or rotation of each sphere, with the degree of freedom of the bond length corresponding to the tensile elasticity of the particles and/or the degree of freedom of the bond angle corresponding to the bending elasticity of the particles set between adjacent spheres. And a method of analyzing the movement and/or deformation and/or orientation of the particles from the calculation result of the movement and/or deformation and/or orientation of the entire sphere aggregate, which is the sum of the calculation results of these spheres, is disclosed. Has been done. The analysis method as described in Patent Document 1 can be adopted as a method for simulating the motion state of the fibrous substance, but it is not always sufficient in terms of the accuracy of the analysis result.

In addition, the analysis result of the motion state of the fibrous substance in the fluid obtained by such a simulation shows, for example, molding conditions of a composite material such as fiber reinforced resin (FRP) or fiber reinforced metal (FRM), a molding die. Since it can be an important design guideline, etc., and can be an effective data for controlling the distribution and orientation of dispersed particles in electrorheological fluids, magnetic fluids, etc., it is used as a method for analyzing the motion state of fibrous substances in fluids. , It is desired to develop a method capable of more accurate simulation. In addition, as a method of analyzing the motion state of such fibrous substances in a fluid, it is desirable to develop a method that enables more efficient simulation in a shorter time than the conventional method. It is rare.

JP-A-5-314091

The present invention has been made in view of the above problems of the prior art, and a fibrous substance in a fluid capable of simulating a motion state of a fibrous substance in a fluid in a shorter time and with higher accuracy. It is an object of the present invention to provide a method for analyzing a motion state of the above and an apparatus for analyzing a motion state of a fibrous substance in a fluid capable of executing such an analysis method.

As a result of intensive studies to achieve the above-mentioned object, the present inventors have obtained the analysis results including the following steps (a) to (c) and performing a coupled analysis of the motion of the fluid and the motion of the fibrous substance. By sequentially analyzing the motion of the fluid and the motion of the fibrous material until a specific time elapses, the motion state of the fibrous material in the fluid can be calculated in a shorter time and more accurately. The inventors have found that it is possible to perform high simulation, and have completed the present invention.

That is, the method of analyzing the motion state of the fibrous substance in the fluid of the present invention uses the equation of motion of the fluid and the equation of motion of the particles to calculate the movement of the fibrous substance and the fluid. And an analysis method for simulating the motion state of the fibrous substance in the fluid based on the information of the fluid, comprising the following steps (a) to (c):
Step (a): The fibrous substance after a lapse of a minute time from a specific time by using a calculation method using a sphere aggregation model assuming that the fibrous substance is composed of a sphere assembly in which a plurality of spheres are bonded. Is a step for analyzing the movement of
Based on the information of the velocity of the fluid, calculate the fluid resistance force of each sphere of the fibrous substance and the torque that each sphere of the fibrous substance receives from the fluid,
Calculate the binding force between each sphere of the fibrous material and the restoring torque for the bending deformation between each sphere of the fibrous material,
Fluid resistance of each sphere of the fibrous material, torque that each sphere of the fibrous material receives from the fluid, binding force between each sphere of the fibrous material, and bending between each sphere of the fibrous material. The position, velocity and angular velocity of each sphere of the fibrous substance and the bending angle between adjacent spheres forming the fibrous substance are calculated after a lapse of a minute time from a specific time based on the information of the restoring torque for the deformation. , Fibrous material motion analysis step;
Step (b): The force that the fluid receives from the fibrous substance is calculated based on the fluid resistance force information of each sphere of the fibrous substance calculated in step (a), and the fluid is the fibrous substance. Considering the force received from the substance and the volume fraction of the fibrous substance in the fluid, calculate the velocity of the fluid after a lapse of a minute time from a specific time, the movement of the fluid and the movement of the fibrous substance Coupled analysis step;
Step (c): Utilizing the information on the transient motion states of the fluid and the fibrous substance, which are already obtained in the steps (a) and (b), the steps (a) and (b) are newly added. An iterative operation step in which the process of sequentially executing the calculation is repeatedly executed until a predetermined condition is satisfied;
The motion of the fluid and the motion of the fibrous substance are sequentially used by sequentially using the transient analysis result after a lapse of a minute time obtained by analyzing the motion of the fluid and the motion of the fibrous substance during the iterative calculation step. This method is characterized by performing a coupled analysis and analyzing the motion state of the fibrous substance in the fluid.

Further, in the above-described method of analyzing the motion state of the fibrous substance in the fluid of the present invention, in the motion analysis step of the fibrous substance, the fluid lubricating force and the mechanical contact force related to the interaction force between the fibrous substances are calculated. Instead, it is preferable to calculate the position, velocity and angular velocity of each sphere of the fibrous substance and the bending angle between adjacent spheres that form the fibrous substance after a lapse of a minute time from a specific time.

Further, the analysis apparatus of the motion state of the fibrous substance in the fluid of the present invention uses the equation of motion of the fluid and the equation of motion of the particles to calculate the movement of the fibrous substance and the fluid. And an analysis device for simulating a motion state of a fibrous substance in a fluid based on information of the fluid,
Using a calculation method using a sphere assembly model assuming that the fibrous material is composed of a sphere assembly in which a plurality of spheres are bonded, the movement of the fibrous material after a lapse of a minute time from a specific time is analyzed. Is a calculation means for calculating the fluid resistance force of each sphere of the fibrous substance and the torque that each sphere of the fibrous substance receives from the fluid, based on the information of the velocity of the fluid, The binding force between the spheres and the restoring torque for bending deformation between the spheres of the fibrous substance are calculated, and the fluid resistance force of each sphere of the fibrous substance, the torque that each sphere of the fibrous substance receives from the fluid. , The binding force between the spheres of the fibrous substance, and based on the information of the restoring torque for the bending deformation between the spheres of the fibrous substance, each of the fibrous substance after a lapse of a minute time from a specific time First calculation means for calculating the position, velocity and angular velocity of the sphere, and the bending angle between adjacent spheres forming the fibrous substance;
The force received by the fluid from the fibrous substance is calculated based on the information on the fluid resistance force of each sphere of the fibrous substance calculated by the first computing means, and the fluid receives from the fibrous substance. Second computing means for calculating the velocity of the fluid after a lapse of a minute time from a specific time in consideration of the force and the volume fraction of the fibrous substance in the fluid;
Utilizing the information on the transitional motion states of the fluid and the fibrous substance already obtained by the first computing means and the second computing means, the first computing means and the second computing are newly added. Determination means for determining whether or not the condition is satisfied in order to execute an iterative operation step in which the process of sequentially executing the calculation by the means is repeated until a predetermined condition is satisfied;
The motion of the fluid and the motion of the fibrous material are sequentially used by sequentially using the transient analysis result after a lapse of a minute time obtained by analyzing the motion of the fluid and the motion of the fibrous material during the iterative calculation step. It is characterized by performing a coupled analysis and analyzing the motion state of the fibrous substance in the fluid.

Furthermore, in the above-described device for analyzing the motion state of the fibrous substance in the fluid of the present invention, the first computing means does not calculate the fluid lubrication force and the mechanical contact force related to the interaction force between the fibrous substances. It is preferable that the arithmetic means is for calculating the position, velocity and angular velocity of each sphere of the fibrous substance after a lapse of a minute time from a specific time, and the bending angle between adjacent spheres constituting the fibrous substance.

According to the present invention, there is provided an analysis method of a motion state of a fibrous substance in a fluid and such an analysis method, which makes it possible to simulate a motion state of a fibrous substance in a fluid in a shorter time and with higher accuracy. It becomes possible to provide an apparatus for analyzing the motion state of fibrous substances in a fluid that can be executed.

It is a block diagram which shows typically one suitable embodiment of the analyzer of the motion state of the fibrous substance in the fluid of this invention. 1 is a flowchart of a preferred embodiment of a method for analyzing a motion state of a fibrous substance in a fluid of the present invention. It is a schematic sectional drawing which shows typically the dispersion system of the fibrous substance in a simple shear flow. It is a schematic diagram which shows typically the long and slender linear fibrous substance which is one suitable embodiment of a fibrous substance, and the spherical aggregate model which is a model for the analysis. It is a schematic diagram which shows the state before and after applying a tensile stress to two adjacent spheres in a sphere assembly model. It is a schematic diagram which shows the state before and after applying bending stress (force to a bending direction) to two adjacent spherical bodies in a spherical body aggregate model. 7 is a follow chart of an analysis method adopted in a conventional technique (one embodiment of an analysis method of a motion state of a fibrous substance in a fluid). 4 is a graph showing the analysis results of Example 1 and Comparative Example 1, which is a graph regarding the time change of the fiber orientation tensor Axx after the shear stress is applied. FIG. 7 is a graph showing the analysis results of Example 2 and Comparative Example 2, which is a graph relating to the time change of the fiber orientation tensor Axx (a value obtained by making time dimensionless by a shear rate, that is, strain) after applying a shear stress. 5 is a graph showing a calculation time ratio of the analysis performed in Example 1 and Comparative Example 1 and a calculation time ratio of the analysis performed in Example 2 and Comparative Example 2.

Hereinafter, with reference to the drawings, preferred embodiments of a method and an apparatus for analyzing a motion state of a fibrous substance in a fluid of the present invention will be described in detail. In the following description and drawings, the same or corresponding elements will be denoted by the same reference symbols, without redundant description.

The method for analyzing the motion state of the fibrous substance in the fluid of the present invention and the device for analyzing the motion state of the fibrous substance in the fluid of the present invention are as described above. FIG. 1 shows a block diagram of a preferred embodiment of the apparatus for analyzing the motion state of fibrous substances in a fluid according to the present invention.

The analysis apparatus of the embodiment shown in FIG. 1 includes an input unit 1 for inputting initial conditions and the like, an arithmetic processing unit 2 for executing an arithmetic operation based on data input by the input unit 1, and an analysis result. And an output unit 3 for outputting.

The input unit 1 is not particularly limited as long as it can input desired setting conditions and the like. For example, in addition to a keyboard and a mouse, a hard disk or a ROM in which various data are stored in advance. A storage medium such as (Read Only Memory) may be used.

The output unit 3 is also not particularly limited as long as it can output the calculation result (analysis result) by the calculation processing unit 2 as data. For example, a storage medium for storing data, a printer for printing on paper, a screen It may be in any form such as a monitor for display.

The arithmetic processing unit 2 is mainly configured by a computer in which a computer program for executing each step described below is installed. That is, the arithmetic processing unit 2 executes hardware including a CPU (Central Processing Unit) and a memory for executing calculation (calculation) of each step to be described later, and each step (these steps will be described later together with mathematical expressions). And a computer program (software) installed for the purpose.

Examples of such a CPU include a central processing unit, a processing unit, an arithmetic unit, a processor, a microprocessor, a microcomputer, a DSP (Digital Signal Processor), and the like.

As such a memory, for example, a non-volatile memory such as a RAM (Random Access Memory) as a temporary storage area, a ROM (Read Only Memory), a flash memory, an EPROM (Erasable Programmable ROM), an EEPROM (Electrically EPROM), or the like. It may be a volatile semiconductor memory, a magnetic disk such as a hard disk or a flexible disk, or an optical disk such as a mini disk, a CD (Compact Disc), a DVD (Digital Versatile Disc), or the like. .. It should be noted that the memory configuring the arithmetic processing unit 2 has an initial condition (basic information: for example, an initial position of each sphere of a sphere assembly model of fibrous substances and an initial condition of each sphere). It is preferable that a region for storing information such as a rotation angle) is formed.

Further, the arithmetic processing unit 2 includes a first arithmetic unit 21, a second arithmetic unit 22, and a determination unit 23.

The first computing means 21 as described above uses a calculation method using a sphere assembly model in which the fibrous substance is assumed to be a sphere assembly in which a plurality of spheres are bonded, and a minute time elapses from a specific time. It is a calculating means for analyzing the movement of the fibrous substance afterwards, and based on the information of the velocity of the fluid, the fluid of each sphere of the fibrous substance (each sphere of the sphere aggregate model of the fibrous substance). Calculate the torque that each sphere of the fibrous material receives from the fluid, calculate the binding force between each sphere of the fibrous material and the restoring torque for bending deformation between each sphere of the fibrous material, Fluid resistance of each sphere of the fibrous material, torque that each sphere of the fibrous material receives from the fluid, binding force between each sphere of the fibrous material, and bending between each sphere of the fibrous material. Based on the information of the restoring torque for the deformation, the position, velocity and angular velocity of each sphere of the fibrous substance after a lapse of a minute time from a specific time, and the bending angle (angle) between adjacent spheres forming the fibrous substance Is a calculation means (for example, means for causing a CPU to execute calculation (calculation) processing by a program stored in a memory for executing the calculation processing).

As the information on the velocity of the fluid used for such calculation, if there is already information (data) on the calculation result calculated by the second calculation means, the calculation result is used, When the fluid velocity is not calculated by the second calculation means (during the first calculation), the fluid velocity information input as the initial condition may be used, or the fluid velocity information input as the initial condition may be used. It may be calculated based on the information obtained. Further, by the calculation method using such a sphere aggregate model, based on the information of the velocity of the fluid, the fluid resistance force of each sphere of the fibrous substance and the torque that each sphere of the fibrous substance receives from the fluid are calculated. A specific method of calculating and a method of calculating the binding force between the spheres of the fibrous substance and the restoring torque for the bending deformation between the spheres of the fibrous substance will be described later. Incidentally, as a method for calculating the binding force between the spheres of the fibrous substance and the restoring torque for the bending deformation between the spheres of the fibrous substance, a known method (for example, described in JP-A-5-314091). Method) may be applied as it is.

Further, the first computing means 21 analyzes the movement of the fibrous substance after a lapse of a minute time from a specific time (time: t+Δt). In the present invention, in such an analysis, the fluid resistance of each sphere of the fibrous substance obtained by the above calculation, the torque that each sphere of the fibrous substance receives from the fluid, the inter-sphere of the fibrous substance Using the information on the binding force of the fibrous substance and the restoring torque for the bending deformation between the spheres of the fibrous substance as it is, the position, velocity and angular velocity of each sphere of the fibrous substance after a lapse of a minute time from a specific time and The bending angle (bending angle) between the adjacent spheres forming the fibrous substance is calculated. Then, in such a calculation, without calculating the fluid lubrication force and the mechanical contact force related to the interaction force between the fibrous substances, the sphere of each of the fibrous substances after a lapse of a minute time from a specific time is calculated. It is preferable to calculate the position, velocity and angular velocity, and the bending angle between adjacent spheres that make up the fibrous material. As described above, the first calculating means 21 does not calculate the fluid lubrication force and the mechanical contact force related to the interaction force between fibrous substances, and each sphere of the fibrous substance after a lapse of a minute time from a specific time. It is preferable that the arithmetic means is for calculating the position, velocity and angular velocity, and the bending angle between adjacent spheres constituting the fibrous substance. As described above, in the present invention, the first computing means 21 does not calculate the two-body interaction between fibrous substances (fluid lubricating force and mechanical contact force related to the interaction force between fibrous substances), Positions, velocities and angular velocities of the spheres of the fibrous substance (each sphere of the sphere aggregate model of the fibrous substance) after a lapse of a minute time from a specific time, and adjacent spheres (the fibers Bending angles between adjacent spheres, which are spheres that form a sphere aggregate model of a spherical substance, can be calculated. Therefore, according to the present invention, the motion state can be simulated in a shorter time. The specific calculation method and the like will be described later.

Further, the second calculation means 22 calculates the force that the fluid receives from the fibrous substance, based on the information on the fluid resistance force of each sphere of the fibrous substance calculated by the first calculation means 21. The calculation means for calculating the velocity of the fluid after a lapse of a minute time from a specific time in consideration of the force that the fluid receives from the fibrous substance and the volume fraction of the fibrous substance in the fluid. (For example, means for causing the CPU to execute the calculation (calculation) processing by the program for executing the calculation processing stored in the memory). By such a calculation, it is possible to calculate the velocity of the fluid by performing a coupled analysis of the force that the fibrous substance receives from the fluid and the force that the fluid receives from the fibrous substance. Then, in the present invention, until the determination means 23 described later determines that the predetermined condition is satisfied, the transient analysis results after a lapse of a minute time are sequentially used to newly use the first calculation means 21. The calculation and the process of executing the calculation by the second calculation means 22 are repeated. As a result, the transient analysis result after a lapse of a minute time obtained by coupled analysis of the motion of the fluid and the motion of the fibrous substance (for example, the velocity of the fluid, the position of each sphere of the fibrous substance in the fluid, the velocity It is possible to analyze the motion state of the fibrous substance in the fluid by sequentially utilizing the angular velocity, the displacement information such as the bending angle between the adjacent spheres forming the fibrous substance, and the like). In such an analysis method, since the interaction between fibrous substances is not calculated, it becomes possible to simulate the motion state in a shorter time. Further, according to such an analysis method, since the motion of the fluid and the motion of the fibrous substance are coupled and analyzed, it is possible to perform a more accurate simulation.

The determining means 23 uses the information on the transient motion states of the fluid and the fibrous substance, which have already been obtained by the first calculating means and the second calculating means (for example, the above-mentioned information used by the first calculating means 21). Using the fluid velocity obtained by the second computing means as the fluid velocity), the processing of sequentially executing the calculations in the first computing means 21 and the second computing means 22 is repeatedly executed until a predetermined condition is satisfied. In order to do so, it is a means for determining whether or not the condition is satisfied. As a method of determining such a condition, for example, it is possible to set the number of times of repeated calculation as the predetermined condition and determine whether the number of times of repeated calculation satisfies the set number of times, or Since the calculation by the calculating means 21 and the second calculating means 22 is to obtain the calculation result at the time when a minute time (Δt) is added from the predetermined time t, the final time (T _end ) as the predetermined condition. Every time the processing of sequentially setting the values and setting the calculation by the first calculation means 21 and the second calculation means 22 is completed, the time (t+Δt) for obtaining the calculation result is shorter than the set time (T _end ). You may judge whether a predetermined condition is satisfied by judging whether it is small. Note that such a determination may be performed by inputting conditions into a determination program stored in the memory and causing the CPU to execute the determination. Further, in the present invention, if the predetermined condition is not satisfied after the condition is judged by the judging means 23, a process of sequentially executing the calculation by the first calculating means 21 and the second calculating means 22 is performed. , Repeatedly executed until a predetermined condition is satisfied. From such a viewpoint, it is preferable that the determination unit 23 also function as a unit for executing the iterative calculation according to the condition. Note that the arithmetic processing unit 2 in the present embodiment uses the calculation results of the first arithmetic unit 21 and the second arithmetic unit 22 when the determining unit 23 determines that the predetermined condition is not satisfied, A computer program for newly executing the calculations in the first calculating means 21 and the second calculating means 22 in sequence; when the judging means 23 judges that a predetermined condition is satisfied, the calculation results up to that time are output. A computer program for storing the program may be stored in the memory.

Hereinafter, based on the flowchart shown in FIG. 2 (a preferred embodiment of the method for analyzing the motion state of the fibrous substance in the fluid of the present invention), the method for analyzing the motion state of the fibrous substance in the fluid of the present invention will be described. A preferred embodiment and a specific calculation method of the calculation by the calculation means will be described. It should be noted that the analysis processing method as described in such a flowchart causes the analysis processing program stored in the memory of the arithmetic processing unit 2 to be executed when the user instructs via the input unit 1 to perform the analysis processing. You may start by doing that. Further, the preferred embodiment of the method for analyzing the motion state of the fibrous substance in the fluid of the present invention described below is a motion state of the fibrous substance in the fluid when a shearing force is applied (in a shear field). (For example, a method of analyzing the orientation state of fibrous substances in a fluid).

In such an analysis, first, in step S1, initial conditions (basic information) are input to the arithmetic processing unit 2 via the input unit 1.

Such an initial condition (basic information) is information on the fibrous substance and the fluid necessary for calculating the motions of the fibrous substance and the fluid using the equation of motion of the fluid and the equation of motion of the particles, For example, information on the calculation mesh (calculation grid: calculation cell) necessary for calculating the fluid, information on the physical properties of the fibrous material necessary for modeling the fibrous material into the spherical aggregate model described below, Information on fluid boundary conditions such as physical properties of fluid necessary for analyzing motion, and the like. Such "fluid motion equations" include not only continuity equations (mass conservation) and Navier-Stokes equations (Navier-Stokes equations) but also for calculating fluid motions and fibrous material motions. Also, it is a concept including various calculation formulas and the like, which will be described later, which are necessary to calculate fluid motions in a coupled manner. Further, the “particle motion equation” is used to calculate the motion of the fibrous substance, such as the formula (7) or the formula (7′) and the formula (8), and This is a concept including various calculation formulas described later, which are necessary to calculate fluid motions in a coupled manner.

With regard to such a calculation mesh, in order to analyze the state in which the fibrous substance is dispersed in the fluid, it is sufficient to divide the analysis region into a finite number in an appropriate range, and the conditions for performing such division are A known method may be adopted and appropriately set according to the object to be analyzed.

Further, as the information of the fibrous substance to be input as the initial condition (basic information), for example, the number of fibrous substances, the diameter of the fibrous substance, the aspect ratio of the fibrous substance, the density of the fibrous substance (ρ ^p ) , Information about the Young's modulus of the fibrous substance can be given.

Further, as the information of the fluid to be input as the initial condition (basic information), for example, the density (ρ ^f ) of the fluid, the viscosity coefficient (μ), the pressure (p) in the fluid, the velocity of the fluid (wall surface velocity, u f _^i: speed when the t _{n (n} = 0) as the initial condition (fibrous material not yet considered) boundary conditions, etc.), information such as the size of the computational domain and the like. Regarding the pressure (P) in the fluid, for example, in the case of a calculation method assuming an incompressible fluid, the pressure is determined so that the mass of the fluid is preserved, so that a special initial condition is required. do not do. In addition, when inputting information (velocity and angular velocity) related to fluid motion among the fluid information used as the basic information, the continuous equation (mass conservation) and the Navier-Stokes equation (Navier-Stokes equation) are used. You may utilize the value analyzed based on it. The information about the motion of the fluid (velocity or angular velocity) may be calculated by the CPU of the arithmetic processing unit 2 based on the information about the characteristic of the fluid or the information about the boundary condition. Here, for example, a shear flow field as shown in FIG. 3 (a dispersion system of a fibrous substance in a simple shear flow: U _{0 in} FIG. 3 indicates the velocity of a moving plate (plate), and 2δ is Taking shown) the length of one side of the computational domain as an example, the velocity of the fluid ^(u _{f i),} the information of the _{U 0} and [delta] (delta) (shear rate (= _{U 0} / [delta]) information) Based on the equation of continuity (conservation of mass) and Navier-Stokes equation (Navier-Stokes equation).

As such an initial condition, at least information on the physical property value of the fibrous substance (information necessary for modeling the fibrous substance into a spherical aggregate model: diameter of fibrous substance, aspect ratio, Young's modulus, etc.) , Input information of initial position and velocity of fibrous material, physical properties of fluid and boundary conditions (slip-free condition on wall surface (non-slip boundary condition), periodic boundary condition (information of calculation mesh), initial velocity of fluid) There is a need to.

When inputting such initial conditions, for example, in the case of assuming injection molding of fiber reinforced resin, the Stokes number is generally 1 or less (a value close to 1 (nearly 1) or It is preferable to set the shear rate, the viscosity of the fluid, etc. so that the condition becomes a smaller value). By inputting the value set in this way, the viscous force of the fluid applied to the fibrous substance becomes more dominant than the inertial force applied to the fibrous substance, and the analysis according to the above molding process is numerically stable. It becomes possible to calculate. The condition of the Stokes number is not particularly limited, and the set value may be changed according to the balance between the inertial force applied to the fibrous substance and the viscous force applied to the fibrous substance in the assumed target.

Thus, in step S1, as initial conditions (basic information), the motions of the fibrous substance and the fluid that are necessary to calculate the motions of the fibrous substance and the fluid using the motion equations of the fluid and the motion equations of the particles are used. This is a step of inputting information (information on physical property values of the fibrous substance, information on initial position and velocity of the fibrous substance, physical property values of the fluid and boundary conditions). That is, step S1 is a step of inputting initial conditions (basic information) of the fibrous substance and the fluid, which are necessary for the calculation (including modeling into a spherical body assembly) described later.

Regarding the initial condition (basic information) input by the input unit 1 in this way, for example, some of the information exemplified above is based on other input information and is stored in the arithmetic processing unit 2. Since the CPU may separately calculate, the information necessary for performing the later-described calculation may be appropriately input from the above information according to the type of the analysis program. It should be noted that such initial conditions (basic information) and/or the initial state separately calculated by the CPU are stored in an appropriate area of the memory in the arithmetic processing unit 2 after input, and the information is appropriately calculated at the time of calculation. Should be available.

Further, when executing the analysis method as described in the flowchart shown in FIG. 2, the CPU of the arithmetic processing unit 2 is used by using the initial condition (basic information) input via the input unit 1 in step S1. In, modeling is performed by an aggregate of spheres of the fibrous substance 10. Hereinafter, such a sphere assembly model will be briefly described with reference to the drawings.

FIG. 4 is a schematic diagram schematically showing an elongated linear fibrous substance 10 which is a preferred embodiment of the fibrous substance and a spherical aggregate model 10A which is a model for analysis thereof. Such a sphere assembly model 10A of the embodiment shown in FIG. 4 shows a state in which five spheres having a diameter d _P are linearly connected. When the CPU of the arithmetic processing unit 2 performs modeling of such a sphere aggregate model (Bead model), for example, based on information such as the diameter and aspect ratio of the fibrous substance input as the initial condition (basic information). Then, the diameter, the number, and the like of the spheres may be appropriately calculated and modeled, or the spheres may be modeled by forming sphere aggregates from spheres having sizes set in advance. In the embodiment shown in FIG. 4, the diameter d of the fibrous substance 10 and the diameter d _P of each sphere of the sphere assembly model 10A are set to be the same size, and five spheres having a diameter d _P are linearly formed. The continuous spherical aggregate model is modeled as the fibrous substance 10.

Further, in the calculation of such modeling, for example, when the fibrous substance 10 is linear as shown in FIG. 4, the CPU aggregates a plurality of spheres linearly in the sphere aggregate model. It is modeled as an aggregate 10A. Then, using the sphere assembly model 10A, initial positions such as the positions (positional information in the x, y, z directions, etc.) of the centers O1 to O5 of the spheres of the initial sphere assembly model, the bond angles between the spheres, etc. The position information and the like can be appropriately set according to the simulation target and the like. Here, in order to explain the concepts such as the amount of change in the distance between the centers of adjacent spheres and the bond angle (bending angle) of each sphere, FIGS. 5 to 6 show the sphere aggregate model 10A (in five spheres). 2 schematically shows the state of two adjacent spheres.

FIG. 5 schematically shows a state before and after a tensile stress is applied to two adjacent spheres in the sphere assembly model 10A, and (a) in FIG. 5 shows a state before the tensile stress is applied ( The state of any two adjacent spheres out of the five spheres arranged in a straight line as shown in FIG. 4 is schematically shown, and (b) in FIG. 5 shows that after tensile stress is applied (minute The state after the passage of time) is schematically shown. In addition, in such a sphere assembly model 10A, assuming that there is a restoring force (coupling force) that elastically returns to the original state when a tensile stress is applied and the distance between the spheres extends, Analyze the state of fibrous substances. Then, as the coupling force between the spheres of such a sphere assembly model 10A (the force that tries to return to the original state when the distance between the spheres is extended), the change amount (σ _ij ) of the center-to-center distance of the spheres, A value calculated based on the Young's modulus (E) of the fibrous substance is adopted (a specific calculation method will be described later). Here, the amount of change in center-to-center distance of the sphere (σ _ij ) is a value obtained by subtracting the center-to-center distance r ₀ of the sphere before the stress is applied from the center-to-center distance r ₁ of the sphere after the stress is applied. It can be obtained as (r ₁ −r ₀ ).

Further, FIG. 6 schematically shows a state before and after applying a force to two adjacent spheres in the sphere assembly model 10A (in five spheres) when a force is applied in the bending direction of the fibrous substance. 6A is a state before a force is applied in a bending direction of the fibrous substance (any two adjacent spheres among five spheres linearly arranged as shown in FIG. 4). 6), and (b) in FIG. 6 schematically shows a state after a force is applied in the bending direction of the fibrous substance. In the present invention, the spherical aggregate model 10A is used to calculate the restoring torque (force to return to the original state when the fibrous material is bent) for bending deformation between the spheres of the fibrous material, Calculation is performed based on the bond angle (bending angle: angle between two adjacent spheres) θ _ij (a specific calculation method will be described later).

As described above, in the present invention, the fibrous substance 10 is modeled based on the information given as the initial information. Further, in such modeling, the initial positions (center initial position: center xyz coordinate) of the centers O1 to O5 of the spheres constituting the fibrous substance 10 and the initial rotation angle θij of each sphere are set. It is possible to operate and store the value obtained by the operation in an appropriate area of the memory for use, and a program programmed to perform the operation such as modeling may be appropriately used. .. The calculation by such a program may be achieved by configuring the calculation processing unit 2 as further including a calculation means (not shown) for modeling for performing the calculation. The calculation means 21 may also perform calculation before performing various calculations. This allows the arithmetic processing unit 2 to calculate the initial state by inputting the initial condition (basic information). As a method for modeling such a spherical body aggregate model, a method adopted by a known method described in JP-A-5-314091 may be used.

Further, after the initial condition (basic information) is input to the arithmetic processing unit 2 via the input unit 1 in step S1, the time T is updated by Δt in step S2. By such steps, the position, velocity, and angular velocity of each sphere of the fibrous substance (each sphere forming the fibrous substance) and the space between the adjacent spheres forming the fibrous substance in the first computing means 21. The time T of the calculated value of the bending angle can be set to t _n +Δt (where n is the number of times the calculation is repeated, and the initial value is 0).

Next, in step S3, by using the first arithmetic unit 21, based on the information of velocity of the fluid ^(u _{f i),} a specific time _{t n} (The time _{t n} is represented by T-Delta] t Time: time before updating Δt), the fluid resistance force (f ^h _i ) of the fibrous substance at a specific time t _n and the torque (T ^h _i ) received from the fluid at a specific time t _n are calculated. Then, such a fluid resistance force ^(f _{h i)} and restoring torque ^(T _{h i)} is represented by the following formula (1) to (2):

[In Formulas (1) and (2), f ^h _i represents the fluid resistance force of the sphere of the spherical assembly model, and T ^h _i is the restoring torque of the sphere of the spherical assembly model (torque from the fluid applied to each sphere. ), μ is the viscosity of the fluid, d _P is the diameter of the sphere of the spherical assembly model, u ^f _i is the velocity of the fluid, and u ^P _i is the velocity of the sphere of the spherical assembly model. , Ω ^f _i represents the angular velocity of the fluid, and ω ^P _i represents the angular velocity of the sphere of the spherical assembly model. With respect to each symbol related to the sphere, the subscript i is a number given to each sphere, and when N spheres exist in the calculation area, such i becomes an integer satisfying the condition of i≦N. Further, regarding each symbol related to fluid, the subscript i means that it is a component (for example, xyz or the like) of Cartesian coordinates in each direction. ]
It can be obtained by the calculation formula represented by. The step S3 for performing such calculation is a step that can correspond to one step in the step (a), and based on the information of the velocity of the fluid, the fluid resistance force (eg, Stokes resistance) of each sphere of the fibrous substance is calculated. Force) and the torque each sphere of the fibrous material receives from the fluid. Such calculation is basically the same as the calculation described in paragraphs [0024] to [0025] of JP-A-5-314091.

Regarding the velocity ( ^uf _i ) of the fluid used for such calculation, at the time of the first calculation (the stage before the calculation result by the second calculation means 22 is obtained), the velocity ( When information of a value calculated separately in advance) is input (for example, a value calculated based on the Navier-Stokes equation in advance is input), it may be used. Further, as the velocity of the fluid used for such calculation, the velocity obtained in advance as the initial condition at the time of the first calculation (the stage before the calculation result by the second calculating means 22 is obtained) (preliminarily calculated separately) If there is no information (data) of the specified value), it is assumed that the fibrous substance does not exist in the fluid based on the input initial condition (information about the fluid) and the initial time (t _n : The velocity of the fluid at n=0) may be separately calculated and used. When performing such a calculation, a method of calculating based on the Navier-Stokes equation can be adopted. At the time of the first calculation (before the calculation result by the second calculation means 22 is obtained), the velocity of the fluid calculated by using the equations (111) to (112) described below is used. Good.

Further, the velocity (u ^P _i ) of the sphere of the spherical aggregate model used for such calculation is u at the time of the first calculation (the stage before the calculation result by the second calculation means 22 is obtained). An initial value such as ^P _i =0 may be adopted, or the fluid velocity calculated separately assuming that fibrous substances do not exist in the fluid as described above is used to calculate the fluid velocity of each sphere. The value spatially corrected at the position may be adopted, and the value calculated in step S5 described later can be used at the time of the second and subsequent calculations (at the time of calculation in the repetitive execution step).

Further, the angular velocity (ω ^f _i ) of the fluid used for such calculation is used as described above at the time of the first calculation (the stage before the calculation result by the first calculation means 21 is obtained). A value that can be calculated from the information of the fluid velocity (u ^f _i ) at the time of the first calculation can be used, and at the time of the second and subsequent calculations (at the time of calculation in the repetitive execution step), calculation was performed in step S5 described later. A value that can be calculated from fluid velocity information can be used. In addition, as a specific calculation method of such an angular velocity, for example, the following formula (I):

[In Formula (I), ω ^f _i is an angular velocity, x _j and x _k are Cartesian coordinates, and u ^f _k and u ^f _j are velocities in respective directions of Cartesian coordinates. ]
A method of calculating the calculation formula represented by When the above formula (I) is examined for components in each direction, the following formula:

The calculation formula is

In addition, as the angular velocity (ω ^P _i ) of the sphere of the spherical assembly model used for such calculation, the value input as the initial condition or the value calculated from the input value is adopted in the first calculation. It should be noted that the value of the angular velocity (ω ^P _i ) may be an initial value such as ω ^P _i =0 at the time of the first calculation, or the fibrous substance may be contained in the fluid as described above. It is also possible to use a fluid angular velocity that can be calculated from the fluid velocity calculated separately assuming that it does not exist, and use the value obtained by spatially correcting the fluid angular velocity at the position of each sphere. At the time of calculation), the value calculated in step S5 described later can be used. By calculating using such values, the fluid resistance force (f ^h _i ) of each sphere of fibrous substance and the torque (T ^h _i ) that each sphere of fibrous substance receives from the fluid can be obtained. ..

Next, in step S4, each of the fibrous substances at time t _n (time t _n is a time represented by T−Δt: a time before updating Δt) by using the first calculation means 21. The binding force between the spheres (F ^s _i ) and the restoring torque (T ^b _i ) for the bending deformation between the spheres of the fibrous material at time t _n are calculated. The coupling force (F ^s _i ) and the restoring torque (T ^b _i ) between the spheres are expressed by the following equations (3) to (6):

[In the formulas (3) to (6), F ^s _i represents a binding force between the spheres (a restoring force against tensile deformation or compression deformation generated between two adjacent spheres in the sphere assembly model), and k _s Is a constant for tensile/compressive deformation, E is a Young's modulus (longitudinal elastic modulus), d _p is a diameter of a sphere in a sphere assembly model, and T ^b _i is a bend between spheres of a fibrous material. shows the recovery to deformation torque (restoring torque against occurring between two spheres adjacent in spherical aggregate model bending deformation), k _b represents a constant for bending deformation, sigma _ij is the amount of change in the distance between the centers of the spheres (See FIG. 5), θ _ij indicates a bending angle (bonding angle: angle between two adjacent spheres in the sphere assembly model) (see FIG. 6). For each symbol, the subscripts i and j are the values for the i-th sphere out of five and the j-th sphere next to it, for example, when considered in a sphere assembly model as shown in FIG. (When using the model shown in FIG. 4, i and j are each an arbitrary integer of 5 or less). ]
It can be obtained by the calculation formula represented by. In addition, such calculation formulas (3) to (6) are equations for obtaining the restoring force and the restoring torque according to the deformation amount of each spherical body by using the longitudinal elastic modulus (E). This step is a step that can correspond to one step in the step (a), and calculates a binding force between the spheres of the fibrous substance and a restoring torque for bending deformation between the spheres of the fibrous substance. It is a step.

Further, as σ _ij , a value obtained from the position information (coordinates) of each sphere at time t _n (a value input as the initial condition at the time of the first calculation) can be used, and as θ _ij , each at time t _n can be used. The value of the bending angle between the spheres (the value obtained from the initial condition of each sphere can be adopted in the first calculation) can be used.

Next, in step S5, the position of each sphere of the fibrous substance (for example, xyz coordinates, etc.), velocity (u ^P _i ), angular velocity (ω ^P _i ), and the fiber are used in step S5. The bending angle (θ _ij ) between the adjacent spheres forming the substance is calculated. The calculation in step S5 is performed by calculating the fluid resistance force of each sphere of the fibrous material, the torque that each sphere of the fibrous material receives from the fluid, and the inter-sphere of the fibrous material calculated in steps S3 to S4. Of the fibrous material and the restoring torque for the bending deformation between the spheres of the fibrous substance. The velocities (u ^P _i ) and angular velocities (ω ^P _i ) of each sphere are expressed by the following equations (7) to (10):

[In Formulas (7) to (10), m ^P represents the mass of the sphere, u ^P _i represents the velocity of the sphere i, u ^P _j represents the velocity of the sphere j, and f ^h _i represents the spherical aggregate model. Represents the fluid resistance of the sphere, F ^s _i represents the binding force between the spheres of the fibrous material, T ^b _i represents the restoring torque for bending deformation between the spheres of the fibrous material, and T ^h _i represents Each sphere of the fibrous material represents a torque received from the fluid, f _ij represents a frictional force generated between two adjacent particles, d _p represents a diameter of the sphere in the sphere assembly model, and ω ^P _i represents the sphere. i represents the angular velocity of i, ω ^P _j represents the angular velocity of the sphere j, θ _ij represents the bending angle (bond angle) between the sphere i and the sphere j of the spherical assembly model, t represents the time, and n _ij Indicates a unit vector in the direction from the sphere i to the sphere j connecting the centers of the sphere i and the sphere j of the spherical aggregate model, and n _ji indicates the center of the sphere i and the sphere j of the spherical aggregate model. A unit vector in the direction from the sphere j connecting the two to the sphere i is shown. Note that i and j in the sphere i and the sphere j referred to here are, for example, in the sphere aggregate model as shown in FIG. It means that it is a sphere (when the model shown in FIG. 4 is used, i and j are arbitrary integers of 5 or less). ]
It can be obtained by the calculation formula represented by.

Here, the method of calculating the frictional force (f _ij ) generated between two adjacent spheres is not particularly limited, and a known method can be adopted as appropriate. For example, both sides of the above formula (10) are time-differentiated, Even if a method of calculating by solving a formula in which the frictional force (f _ij ) is arranged by substituting the formulas (7) and (8) by using a convergent solution method such as SOR (Successive Over-Relaxation) method is adopted. Good. That is, the method of calculating the frictional force between the spheres (f _ij ) is not particularly limited, but for example, both sides of the equation (10) are time-differentiated and the equations (7) and (8) are substituted. The following formula (II) obtained by:

[Note that each component on the left side and the right side in the formula (II) is represented by the following formula:

(I, j, k, and 1 in the formula represent the numbers of adjacent spheres that form the fibrous substance.)
It is represented by. ]
May be calculated by solving a value using a convergent solution method such as SOR (Successive Over-Relaxation) method. The method of calculating the frictional force (f _ij ) generated between two adjacent spheres is not limited to the above-described calculation method (exemplified method), and other known calculation methods are appropriately adopted. You may.

The calculation formulas (7) and (8) are equations of the translational motion and the rotational motion of each sphere of the sphere assembly model, and the calculation formula (9) is the sphere i and the sphere which are adjacent to each other and constitute the fibrous substance. Equation (10) is a bending angle equation between j and equation (10) gives a condition (constraint condition) indicating that the sphere does not slip at the connecting point, and by calculating these by simultaneous equations, The velocity (u ^P _i ) and the angular velocity (ω ^P _i ) can be obtained. Then, based on the velocity (u ^P _i ) and the angular velocity (ω ^P _i ) of each sphere, the moving positions of the centers O1 to O5 of each sphere of the sphere assembly model can be calculated. In this way, after short time from a specific time (t _n) (time: T = t n ₊ Δt) at the position of each sphere of the fibrous material, velocity and angular velocity, as well as a particular time (t _n) From the above, it is possible to obtain the bending angle between adjacent spheres constituting the fibrous substance after a lapse of a minute time (time: T=t _n +Δt). Further, by determining the movement of each sphere of such a sphere assembly model, the position moved from the initial position of the centers O1 to O5 of each sphere can be determined, and thereby the orientation state of the fibrous substance is determined. be able to. However, the calculation method regarding the bending angle is not limited to the calculation formula shown in the above formula (9), and the calculation may be performed using a calculation such as a quaternion.

Further, after a lapse of a minute time (time: T=t _n +Δt) from such a specific time (t _n ), the position, velocity and angular velocity of each sphere of the fibrous substance and the fibrous substance are configured. When calculating the bending angle between the adjacent spheres, the above equations (7) to (10) are adopted, without calculating the fluid lubrication force and the mechanical contact force related to the interaction force between the fibrous substances, It is preferable to calculate the position, velocity and angular velocity of each sphere of the fibrous substance and a bending angle between adjacent spheres forming the fibrous substance after a lapse of a minute time from a specific time. In the present invention, as described above, it is possible to omit the calculation of the fluid lubrication force and the mechanical contact force related to the interaction force between fibrous substances, which can significantly reduce the calculation time. Become. In the present invention, for the calculation formula of the interaction force (fluid lubrication force and mechanical contact force) between the fibrous substances which can be omitted from calculation, the conventional fibrous substances in the fluid described later are described. It will be described together with a method of analyzing a motion state.

Such step S5 is a step that can correspond to one step in the step (a), and is the fluid resistance force of each sphere of the fibrous substance, the torque that each sphere of the fibrous substance receives from the fluid, Based on the binding force between the spheres of the fibrous substance, and the information of the restoring torque for the bending deformation between the spheres of the fibrous substance, each sphere of the fibrous substance after a lapse of a minute time from a specific time Is a step of calculating the position, the velocity and the angular velocity, and the bending angle between the adjacent spheres forming the fibrous substance. Thus, ^f _h i in the formula ^{(7) ~ (10),} F s i, T b i, as a value of ^T _{h i} utilizes the values obtained in the steps S3 and S4.

In this way, steps S2 to S5 can be said to be steps for performing a motion analysis of fibrous substances (fibrous substance motion analysis steps) in consideration of the above calculation contents. It is possible to analyze the position (coordinates) of each sphere of the fibrous substance after a lapse of time, the velocity, the angular velocity, and the bending angle between the adjacent spheres constituting the fibrous substance.

Next, in step S6, the force (F ^f _i ) received by the fluid from the fibrous substance is calculated using the second calculation means 22. The calculation of the force (F ^f _i ) received from such a fibrous substance is performed based on the information of the fluid resistance force (f ^h _i ) of each sphere of the fibrous substance calculated in step S3. The force (F ^f _i ) that such a fluid receives from the fibrous substance is represented by the following formula (11):

[In the formula (11), F ^f _i represents the force that the fluid receives from the fibrous substance, V _p represents the volume of one calculation cell, and f ^h _i represents the fluid resistance force (fluid) of each sphere of the fibrous substance. Resistance) to the following part of the formula (11):

Indicates that the total sum is calculated for all the spheres existing within Vp. ]
It can be obtained by the calculation formula represented by. V _p used in such a calculation is the volume of one calculation cell, and can be obtained from the size of the calculation region and the number of divisions of the calculation cell. Further, such a calculation formula (11) is a reaction force that the fluid receives from the fibrous substance, and is a formula for obtaining the sum of f ^h _i in one calculation mesh (calculation cell). It can be said that the force (F ^f _i ) that the fluid receives from the fibrous substance is a reaction force to the Stokes resistance force that the fibrous substance receives from the fluid. Such step S6 is a step that can correspond to one step in step (b), and is information on the fluid resistance force of each sphere of the fibrous substance calculated in step (a) (calculated in step S3). based on fluid resistance of each sphere fibrous material information (f h _^i)), said fluid may correspond to the step of calculating the force applied from the fibrous material.

Then, in step S7, by using the second calculating means 22, the velocity of the fluid after the lapse of short time from a specific time (u f _ⁱ⁾ is calculated. The calculation of the velocity (u ^f _i ) of such a fluid takes into consideration the force (F ^f _i ) that the fluid receives from the fibrous substance and the volume fraction (ε) of the fibrous substance in the fluid. Formulas (12) to (13) below:

In Expression ^{(12) ~ (13),} u f i at time _{t n} minute time from (Delta] t) after (time: _T = _{t n} + Δt) in indicates the speed of the fluid ^{in, u} _{f j} at time _{t n} Indicates the velocity of the fluid, ε indicates the volume fraction of the fibrous substance in the fluid, t indicates the time, x _i and x _j indicate the Cartesian coordinates (x, y, z, etc.), and ρ ^f indicates the fluid. the indicated density (fluid density), P denotes the pressure in the fluid, F ^f _i denotes the force applied fluid from the fibrous material, mu denotes a viscosity coefficient of the fluid. The subscript letters i and j follow Einstein's summation rules. ]
It can be obtained by the calculation formula represented by. The calculation formulas (12) and (13) consider the force (reaction force) that the fluid receives from the fibrous substance and the volume fraction of the fibrous substance in the fluid, and consider the motion of the fluid and the fibrous substance. Is a calculation formula for obtaining the velocity of the fluid by an analysis (coupling analysis) in consideration of the interaction of the movements of the fibers (the force that the fiber receives from the fluid and the force that the fluid receives from the fibrous substance (reaction force)).

The volume fraction (ε) of such a fluid is the ratio of the total volume of each calculation cell at time t _n and the volume of each sphere (each sphere forming a fibrous substance) existing in each cell ( [Total volume of spheres]/[volume of calculation cell]).

Such step S7 is a step that can correspond to one step in the step (b), and the force that the fluid receives from the fibrous substance (calculated value in step S6) and the fibers in the fluid. In consideration of the volume fraction of the particulate matter, it may correspond to the step of calculating the velocity of the fluid after a lapse of a minute time from a specific time. Note that, in consideration of the above calculation contents, such steps S6 and S7 are a step of analyzing the motion of the fluid and the motion of the fibrous material by coupling (the motion of the fluid and the motion of the fibrous material). Even though it is a coupled analysis step), this enables an analysis (coupled analysis) that considers the force that the fiber receives from the fluid and the force that the fluid receives from the fibrous substance (reaction force) from both directions (2 ways). Becomes In addition, since the volume fraction (ε) of the fibrous substance in the fluid is taken into consideration in such a calculation, in the present invention, objects of various concentrations (the fibrous substance The inventors believe that the motion state (orientation state, etc.) of the fibrous substance can be simulated with respect to the fluid containing ().

Next, in step S8, the determination means 23 determines whether or not the time T is a value larger than the time (T _end ) set as the calculation end time. If the time T is smaller than the end time T _end , the time T is converted to the time t _n in step S2, and steps S2 to 7 are newly executed. Then, in step S8, a transient analysis result (transient fluid and fibrous substance) after a lapse of a minute time obtained by analyzing the motion of the fluid and the motion of the fibrous substance until the condition of T _end <T is satisfied. Information of the exercise state) is sequentially used, and the process of newly performing steps S2 to 7 is repeatedly performed. By sequentially repeating steps S2 to 7 in this manner, it becomes possible to repeatedly execute the calculations described in steps S3 to 7 until a predetermined condition is satisfied (iterative calculation). , The transient analysis result (transitional fluid and fibrous material motion state information) after a lapse of a minute time, which is obtained by analyzing the fluid motion and the fibrous material motion, is sequentially used to The motion of fibrous material can be analyzed. In addition, such an iteratively-calculated analysis is bidirectional (2 way) for the interaction between the motion of the fluid and the motion of the fibrous substance (the force that the fiber receives from the fluid and the force that the fluid receives from the fibrous substance (reaction force)). Since this is an analysis (coupling analysis) that takes into consideration the above, it is possible to perform a highly accurate simulation.

Then, in step S8, when the condition that the time T becomes longer than the end time (T _end ) is satisfied (the condition T _end <T), the calculation is ended, and the calculation result is output in step S9. Note that the velocity and angular velocity of each sphere of the fibrous substance (sphere aggregate model) from the initial time to the predetermined time T _end and the bending between the adjacent spheres forming the fibrous substance are calculated by such calculation. Information on the position of the center of each sphere of the fibrous substance (sphere aggregate model) can be output together with the information on the angle, and based on this, the fibers in the fluid from the initial time to the predetermined time T _end can be output. The movement (movement position) of the fibrous substance and the orientation state of the fibrous substance can also be output. Further, by such calculation, information on the velocity of the fluid can also be output. Thus, by analyzing the motion state of the fibrous substance in the fluid, the motions of the fibrous substance and the fluid can be analyzed, and the velocity of the fluid and the velocity of each sphere of the fibrous substance (sphere aggregate model) can be analyzed. In addition to the information on the angular velocity and the bending angle between the adjacent spheres forming the fibrous substance, the moving position and the orientation state of the fibrous substance can be calculated and output based on the analysis information. The output of such a calculation result may be performed by recording data on an external recording medium (one aspect of the output unit 3) or the like, or the analysis result may be displayed on the display (one aspect of the output unit 3) or the like. Visual information (for example, numerical data itself, a graph of numerical data, an image such as a three-dimensional animation created based on the time-dependent motion state information obtained as a calculation result, and the like) May be mentioned).

As described above, steps S2 to S5 (particularly S3 to S5) in the flowchart are steps suitable as the step (a), and steps S6 to S7 in the flowchart are steps suitable as the step (b). The step of repeatedly executing steps S2 to S7 based on the determination result of step S8 in the flowchart is a preferable step as step (c). Then, the method for analyzing the motion state of the fibrous substance in the fluid of the present invention including the steps (a) to (c) is, as described above, calculated by using a computer (electronic computer) to calculate the fluid velocity. The speed, position information, orientation state, etc. of the fibrous substance can be output. As described above, the method of analyzing the motion state of the fibrous substance in the fluid of the present invention is also a method of analyzing the motion state of the fluid and the fibrous substance (including the moving position and the orientation state of the fibrous substance). I can say.

In addition, in the method for analyzing the motion state of the fibrous substance in the fluid including the steps (a) to (c), the form of the fibrous substance may be a so-called fiber-like state. The fiber length, fiber diameter, material, and shape are not particularly limited, and the concept includes fibrous (short fibrous, long fibrous, etc.), needle-shaped, rod-shaped, conical, and tubular shapes. Further, in the method of analyzing the motion state of the fibrous substance in the fluid including the steps (a) to (c), from the viewpoint of the accuracy of the simulation, the fibrous substance has a diameter d of about 1 μm or more. It is preferable that the simulation target is a fibrous material having a size (where the Brownian motion is not dominant) and having a length L not exceeding the calculation region. Therefore, if the aspect ratio (L/d) defined in this range can be calculated in principle. Examples of such fibrous substances include carbon fibers and glass fibers used in fiber-reinforced resins and the like. Further, the fluid used for such a motion analysis is preferably a liquid substance having fluidity, and examples thereof include general resins and water.

From the above-mentioned analysis, for example, the fibrous substance during simple shearing, which is an important target for understanding and modeling of the molding process of fiber reinforced resin (FRP), is schematically shown in FIG. It is possible to carry out a three-dimensional numerical simulation of the orientation behavior of the. In FRP, since the fiber orientation state after molding is an important parameter for the strength and rigidity of the molded product, it is possible to more accurately predict the orientation behavior during the process by such a numerical simulation. Become. As described above, according to the present invention, it is possible to perform a simulation in which the orientation state of the fibrous substance in the fluid can be predicted with higher accuracy and in a realistic calculation time, and it is expected to be applied to optimization of various molding processes.

The preferred embodiment of the method and apparatus for analyzing the motion state of the fibrous substance in the fluid of the present invention has been described above with reference to FIGS. 1 and 2, but the motion state of the fibrous substance in the fluid of the present invention has been described. The analysis method and the apparatus for analyzing the motion state of the fibrous substance in the fluid according to the present invention are not limited to the above embodiment. For example, in the above-described embodiment, in step S8, the process of sequentially executing the calculations in the first calculating means 21 and the second calculating means 22 under the condition of time (the process of sequentially executing the calculations described in steps S3 to 7). The process of sequentially executing the calculations described in steps (a) and (b) above is repeatedly executed, but in the method and apparatus for analyzing the motion state of the fibrous substance in the fluid of the present invention, The condition for repeatedly executing the calculation process is not limited to the time, and for example, the number of times of repeated calculation is set as the condition while setting the size of Δt to a specific size, and the above step (a) is performed. The calculation described in (b) (calculation by the first calculating means 21 and the second calculating means 22) may be repeatedly executed until it is executed a predetermined number of times.

According to the method and apparatus for analyzing the motion state of the fibrous substance in the fluid of the present invention, the motion state of the fibrous substance in the fluid to which the shearing force is applied can be simulated in a shorter time and with higher accuracy. It becomes possible. As described above, the method and apparatus for analyzing the motion state of the fibrous substance in the fluid of the present invention makes it possible to simulate the motion state of the fibrous substance in the fluid in a shorter time and with higher accuracy. Is not necessarily clear, but the present inventors speculate as follows.

Here, first, for comparison with the present invention, a brief description will be given of a conventional method for analyzing the motion state of a fibrous substance in a fluid, as described in the above-mentioned Patent Document 1 (JP-A-5-314091). To do. In such a conventional method of analyzing the motion state of the fibrous substance in the fluid, the analysis is performed in the procedure of steps S21 to S29 as shown in the flowchart of FIG. To briefly describe such analysis, first, steps S21 and S22 are basically the same steps as steps S1 and S2 described in the preferred embodiment of the analysis method of the present invention described above. Next, in step S23, the following equations (111) to (112):

[The symbols in formulas (111) to (112) are the same as the symbols in formulas (12) and (13). ]
First, the velocity of the fluid is calculated without considering the presence or movement of the fibrous substance. As described above, in the conventional method of analyzing the motion state of the fibrous substance in the fluid, the velocity of the fluid is calculated by ignoring the presence of the fibrous substance. Then, using the calculated value of the velocity of the fluid, the fluid resistance of the fibrous substance and the torque received by each sphere of the fibrous substance from the fluid are calculated in step S24. Such calculation in step S24 is described in step S3 described in the preferred embodiment of the above-described analysis method of the present invention, except that the value calculated in step S23 is used as the fluid velocity (u ^f _i ). Adopt the same calculation method as the calculation. Then, in step S25, the binding force between the spheres of the fibrous substance and the restoring torque for the bending deformation are calculated. Such calculation in step S25 adopts the same calculation method as the calculation described in step S4 described in the preferred embodiment of the analysis method of the present invention. Next, in step S26, the fibrous substances that interact with each other are searched for, and the following formulas (113) to (115):

[In Formulas (113) to (115), f ^lub _ij and f ^mec _ij represent the interaction force between fibrous substances, d _p represents the diameter of the sphere in the sphere assembly model, and m ^P represents the sphere's diameter. Mass, u ^P _i represents the velocity of the sphere i of the spherical aggregate model, u ^P _j represents the velocity of the sphere _j of the spherical aggregate model, and n _ij represents the sphere i and the sphere j of the spherical aggregate model. The unit vector in the direction from the sphere i connecting the centers to the sphere j is shown, r _i is the coordinate of the center of gravity of the sphere i, r _j is the coordinate of the center of gravity of the sphere j, and k _s is the tension/compression. shows the constant for deformation, e _d represents the coefficient of restitution between the spheres, f ^P _ij denotes the frictional force generated between the two particles adjacent. ]
The interaction force (two-body interaction) between fibrous substances is calculated by. The concept of such f ^lub _ij and f ^mec _ij is described in Yamamoto, s. et al., J. Chem Phys., 102, 2254 (1995) and Tsuji, Y. et al., Powder Tech., 77. , 79 (1993) can be used. Then, in step 27, using the calculation results of f ^lub _ij and f ^mec _{ij and} the calculation result of f ^P _ij , the following formula (7′):

[In the formula (7′), f ^lub _ij and f ^mec _ij represent the interaction force between the fibrous substances calculated in step S26, and other symbols have the same meanings as those in the above formula (7). is there. ]
The velocity (u ^P _i ) and angular velocity (ω ^P _i ) of each sphere are calculated by the calculation formula represented by the above formula and the calculation formulas represented by the above formulas (8) to (10), and Find the position. Next, in step S28, it is determined whether or not the time T is a value larger than the time (T _end ) set as the end time of the calculation, and the time T is a value smaller than the end time T _end. to converts the time T to the time _{t n} in the step S2, perform the steps S22~27 _again, terminates the operation when the condition is met the _{T end the} <T, it outputs the result in step S29 To do.

As described above, in the conventional analysis method as shown in FIG. 7, after the initial condition is input (step S21), the time is updated (step S22), and the presence of the fibrous substance and its motion are not taken into consideration. The velocity is calculated (step S23), and then the fluid resistance of each sphere of fibrous material and the torque that each sphere of fibrous material receives from the fluid are calculated (step S24) to calculate the distance between each sphere of fibrous material. A restoring torque for the binding force and the bending deformation is calculated (step S25). Next, in order to calculate the two-body interaction between the fibrous substances, a partner that interacts with each other is searched for, and the two-body interaction between the fibrous substances is calculated based on the result (step S26). The forces (interaction forces between fibrous substances) considered as the two-body interaction in step S26 are the fluid lubrication force f ^lub _ij and the mechanical contact force f ^mec _ij described above. Then, the position, velocity, angular velocity, and the like of the fiber are calculated based on the calculation results of steps S23 to S27 (step S27). After that, when the specified condition is not reached, the process returns to step S22 and the same calculation is repeated.

On the other hand, in the embodiment shown in FIG. 2 (a preferred embodiment of the analysis method of the present invention), after inputting the initial conditions (step S1), the time is updated (step S2) and each of the fibrous substances is updated. The fluid resistance of the sphere and the torque that each sphere of the fibrous substance receives from the fluid are calculated (step S3), the binding force between the spheres of the fibrous substance and the restoring torque for bending deformation are calculated (step S4), The position, velocity, angular velocity, etc. of the fibrous substance are calculated based on the calculation result (step S5). Next, the force that the fluid receives from the fibrous substance based on the calculation result of step S3 (a value obtained by summing the reaction forces of the fluid resistance force f ^h _i applied to each sphere present in the calculation cell in one calculation cell) Is calculated (step S6), and the velocity of the fluid is calculated based on the calculation result in consideration of the reaction force received from the fibrous substance (step S7). Then, when the specified condition is not reached, the process returns to step S2 and the same calculation is repeated.

As described above, the difference between the present invention and the conventional technique as described in Patent Document 1 is that the calculation of the two-body interaction calculated in the conventional technique is based on the comparison between the embodiments described in the flowchart and the above calculation formulas. (Step S26) is omitted in the present invention. In the present invention, the calculation result of the two-body interaction when calculating the position, velocity, angular velocity, etc. of the fibrous substance (interaction force between fibrous substances: fluid The point that the lubrication force f ^lub _ij and the mechanical contact force f ^mec _ij are not used (the calculation formula (7) used in the present invention is that the fluid lubrication force f ^lub _ij and the mechanical contact force f in the formula (7′) are used. ^mec values of _ij is the same formula as when a 0), the point in the present invention that taking into account the existence and the movement of the fibrous material to calculate the velocity of the fluid (step 6 and 7: fluid motion and fibers This is in the two-way calculation that considers the interaction of motions (specifically, the force that the fiber receives from the fluid and its reaction force) bidirectionally (2 ways).

Here, when the calculation of the two-body interaction (interaction between particles: interaction force between fibrous substances) adopted in the conventional technique is examined, the two-body interaction such as fluid lubrication or mechanical contact is It is necessary to refer to the positional information and the velocity information of a particle (as a particle A) and another particle (as a particle B) having a particulate matter, and the information of the particle A and the particle B is stored in the memory space of the computer. If they are stored at distant locations in, the communication time for them will take a lot of time. Especially, in the calculation of two-body interaction, when parallel calculation is performed, such communication time tends to be longer. As described above, the calculation of the two-body interaction is the portion with the largest calculation load (which requires a long calculation time) in the above conventional analysis method.

Further, in such a conventional analysis method, since the existence and movement of the fibrous substance are not considered in the calculation of the velocity of the fluid, the orientation of the fibrous substance in the movement of the fibrous substance during shearing is changed from the initial state. It was difficult to simulate the basic orientation behavior that would reach a steady value. On the other hand, in the present invention, such two-body interaction (fluid lubrication or mechanical contact between fibrous substances) is calculated, that is, the interaction force between fibrous substances (fluid lubrication force f ^lub _ij). And the mechanical contact force f ^mec _ij ) is omitted, and as an alternative, the interaction between the fluid motion and the fiber motion (specifically, the force that the fiber receives from the fluid and its reaction force) is considered bidirectionally (2 ways). 2 way calculation is done. Therefore, in the present invention, the present inventors presume that the calculation speed can be significantly improved (the calculation speed can be significantly shortened) without lowering the calculation accuracy.

Further, in the conventional method, the motion state of the fibrous substance in the fluid is analyzed by a one-way (1 way) calculation method in which only the force that the fiber receives from the fluid is considered, but in the present invention, as described above, , Bidirectional interaction between fibrous substance and fluid, focusing on not only the movement of fibrous substance caused by receiving force from fluid, but also the presence of fibers and the movement of fluid affects the movement of fluid. Since the calculation is performed in consideration of (2 ways), the simulation of the basic orientation behavior in which the orientation of the fibrous material reaches a steady value from the initial state in the movement of the fibrous material during shearing is performed. Is also possible. Such a simulation can be suitably used for understanding and modeling the molding process of fiber reinforced resin (FRP) or the like. Further, in such a simulation, since the interaction between the fluid and the fibrous substance is considered in 2 ways as described above, the prediction accuracy of the orientation of the fibrous substance is further improved. As described above, according to the present invention, the interaction between the motion of the fluid and the motion of the fibrous substance (specifically, the force that the fiber receives from the fluid and its reaction force) is considered bidirectionally (2 ways). The present inventors presume that it becomes possible to more accurately predict the orientation state of the fibrous substance during shearing as compared with the conventional method.

As described above, in the present invention, the fluid motion and the fibrous substance are not calculated in the basic equations of the fluid and the fibrous substance without calculating the two-body interaction such as fluid lubrication and mechanical contact that occur between the fibrous substances. Since the 2-way calculation that bidirectionally considers the interaction of the movements of 1 is performed, it becomes possible to more accurately predict the fiber orientation during shearing as compared with the conventional technique. Further, in such an analysis method of the present invention, the calculation of the two-body interaction, which has the largest calculation load in the conventional analysis method, is omitted, and the above-described bidirectional interaction is taken into consideration (fluid motion and fiber The present inventors speculate that the calculation speed is further improved because the motion state of the fibrous substance in the fluid is analyzed instead (by calculating the interaction of the motion of the substance).

Hereinafter, the present invention will be described more specifically based on Examples and Comparative Examples, but the present invention is not limited to the following Examples.

(Example 1)
In Example 1, the following formula was added to a fluid composed of Newtonian fluid:

[In the formula, d _p represents the diameter of the fibrous substance (the diameter of the sphere in the case of a sphere assembly model), γ represents the shear rate, ρ ^p represents the density of the fibrous substance, and μ represents the fluid Viscosity coefficient, St represents Stokes number]
Based on the flowchart shown in FIG. 2, a system in which fibers having a density (ρ ^p ) and a diameter (d _p ) of a fibrous substance such that the Stokes number (St) represented by By performing the calculation described in the equations (1) to (13) and analyzing the motion of the fluid and the motion of the fibrous substance from the start of applying the shearing force, the orientation state of the fibrous substance in the fluid is analyzed. Was analyzed.

The experiment to be analyzed (simulated) in this manner is described in the document “Cieslinski, MJ et al., J. Non-Newtonian Fluid Mech., vol.222, pp. 163-170 (2015)”. A fluid containing a fibrous substance at a volume concentration of 3.8 vol% (Vf=3.8%) using a sliding type rheometer described below in some cases, simply referred to as “Reference 1”. Specifically, the above-mentioned analysis is performed by the sliding rheometer described in Reference 1 (specifically, large deformation and uniform deformation are generated, and time series data is acquired). Using a sliding type rheometer that can be used, a fiber-containing fluid (fluid (polypropylene) and fibrous substance (glass fiber)) in which glass fibers are dispersed in a fluid of polypropylene at a volume concentration (Vf) of 2.2 vol% is used. It was performed as a simulation of an experiment in which a shearing force was applied to it.

In such an analysis, as initial conditions, the density of the fibrous substance (ρ ^p ), the diameter of the fibrous substance (d _p ), and the ratio of the fiber length L to the diameter of the fibrous substance (L/d _p ) Information such as aspect ratio (G=20), number of fibers (690), volume concentration of fibrous substance (Vf=2.2vol%), viscosity coefficient of fluid (μ), shear rate (γ) did. Similar to the experiment described in Reference 1, the Stokes number is approximately 1 (generally 1) or less as a condition under which the inertial force acting on the particles is not dominant and the numerically stable calculation is possible. As such a combination of d _p , ρ ^p , γ, and μ, d _p =25 [μm], ρ ^p =1×10 ⁶ [kg/m ³ ], γ=1000 [1/sec], μ=0 The value of 1 [Pa·s] was input. Moreover, the initial condition of the fiber was input so that the initial fiber orientation in the calculation was set to Axx to 0.5, Ayy to 0, and Azz to 0.5. Here, Axx represents the orientation tensor in the x direction (flow direction), Ayy represents the orientation tensor in the y direction (wall surface vertical direction), and Azz represents the orientation tensor in the z direction (depth direction of the flow channel).

(Example 2)
The number of fibers was changed from 690 to 4140, and the volume concentration value of the fibrous substance under the initial condition was 2.2 vol% (Vf=2.2%) to 12.7 vol% (Vf=12.7%). ) Was changed to analyze the motion of the fluid and the motion of the fibrous substance from the start of applying the shear stress to a predetermined time in the same manner as in Example 1 to determine the orientation state of the fibrous substance in the fluid. Analyzed.

The experiment to be analyzed (simulated) in this way is described in Reference 1 [“Cieslinski, MJ et al., J. Non-Newtonian Fluid Mech., vol.222, pp. 163-170 (2015). Published)] is a model of a fluid containing a fibrous substance at a volume concentration of 13.3 vol% (Vf=13.3%) using a sliding type rheometer described above. Specifically, using the sliding rheometer described in Reference 1, a fiber-containing fluid (fluid (polypropylene)) in which glass fibers are dispersed in a polypropylene fluid at a volume concentration (Vf) of 12.7 vol% is used. And a fibrous substance (glass fiber) was subjected to a shearing force as a simulation of an experiment.

(Comparative Example 1)
Instead of performing the calculations described in the above formulas (1) to (13) based on the flowchart shown in FIG. 2, formulas (1) to (6), formula (7′), and formulas based on the flowchart shown in FIG. In the same manner as in Example 1 except that the calculations described in (8) to (10) and formulas (111) to (115) are performed, the motion of the fluid and the fibrous state from the start of applying the shear stress to the predetermined time. The motion of the substance was analyzed to analyze the orientation state of the fibrous substance in the fluid.

(Comparative example 2)
Instead of performing the calculations described in the above formulas (1) to (13) based on the flowchart shown in FIG. 2, formulas (1) to (6), formula (7′), and formulas based on the flowchart shown in FIG. Except for performing the calculations described in (8) to (10) and equations (111) to (115), in the same manner as in Example 2, the motion of the fluid and the fibrous state from the start of applying the shear stress to the predetermined time. The motion of the substance was analyzed to analyze the orientation state of the fibrous substance in the fluid.

<Analysis result of orientation state>
As a result of the analysis of Example 1 and Comparative Example 1, a graph relating to a time change of the fiber orientation tensor Axx (a value obtained by making time dimensionless by a shear rate, that is, strain) after applying a shear stress is shown in FIG. 8. Note that, in FIG. 8, since the values of the volume fractions of fibrous substances are close to each other, reference 1 [“Cieslinski, MJ et al., J. Non-Newtonian Fluid Mech., vol. 222, p. Page 170 (published in 2015)”], the results of an experiment on a fluid containing a fibrous substance at a volume fraction (ε) of 3.8 vol% using a sliding rheometer are also shown as Reference Example 1. Show.

As described above, the result of the experiment using the sliding rheometer described in Reference 1 described in FIG. 8 for reference is as follows: Glass fiber (fibrous substance) having an average value of 13.3 μm and an aspect ratio G of 105 is dispersed in polypropylene (fluid) at a ratio of the volume concentration (Vf) condition of 3.8 vol %. Is a measurement result in an experiment in which shear is applied under the condition that the shear rate (γ) is 1.0 [1/sec].

In addition, as an analysis result of Example 2 and Comparative Example 2, a graph relating to the time change of the fiber orientation tensor Axx (a value obtained by making time dimensionless by shear rate, that is, strain) after applying the shear stress is shown in FIG. 9. Show. In FIG. 9, since the volume fraction values of the fibrous substance are close to each other, the volume fraction (ε) of the fibrous substance using the sliding rheometer described in Reference 1 is 13.3 vol%. The result of the experiment with respect to the fluid contained in the ratio of is also shown as Reference Example 2.

In addition, the result of the experiment using the sliding rheometer described in the reference 1 described in FIG. 9 for reference as described above shows that the sliding rheometer described in the reference 1 is used and the diameter d Glass fibers (fibrous material) having an average value of 13.3 μm and an aspect ratio G of 105 are dispersed in polypropylene (fluid) at a ratio of 13.3 vol% as a volume concentration (Vf) condition, It is a measurement result in an experiment in which shear is applied under the condition that the shear rate (γ) is 1.0 [1/sec].

As is clear from the results shown in FIGS. 8 and 9, the simulation results obtained by the conventional analysis method used in Comparative Examples 1 and 2 (hereinafter, sometimes referred to as “Int1way”) [volume concentration ( The simulation result when Vf) is 2.2% (Comparative Example 1: FIG. 8) and the simulation result when Vf is 12.7% (Comparative Example 2: FIG. 9)] are described in Reference 1. It became clear that the behavior was completely different from the experimental results. On the other hand, simulation results obtained by the method of analyzing the motion state of the fibrous substance in the fluid of the present invention (hereinafter, sometimes referred to as “Noint2way”) adopted in Examples 1 and 2 [volume integral From the initial values, the simulation result (Example 1: FIG. 8) when the rate (concentration) is Vf is 2.2% and the simulation result when Vf is 12.7% (Example 2: FIG. 9)] The behavior gradually reaches a steady value, and the tendency of the graph is almost the same as the experimental result described in Reference Document 1 above. The analysis result of the alignment state and the observation result of the alignment state by the experiment are almost the same. It turns out that it will be a result. From these results, according to the analysis method (Noint2way) adopted in the present invention, compared with the conventional analysis method (Int1way), the motion state of the fibrous substance in the fluid when shear stress is applied (the It was confirmed that the orientation behavior in the example) can be simulated with higher accuracy.

<About analysis time>
With respect to the analyzes performed in Examples 1 and 2 and Comparative Examples 1 and 2, in a 64 parallel (4 CPU, 16 cores/CPU) environment, a calculation is performed such that the number of repeated calculations is 5000 (time: n at tn: Calculation until reaching 5000: calculation of 5000 steps) was performed and the calculation time was measured. As a result of such calculation, the analysis method adopted in Noint2way (Example 1 or Example 2) in each of the cases where the volume concentration Vf is 2.2% and the volume concentration Vf is 12.7% FIG. 10 shows the calculation time ratio when the calculation time of 1 is 1.

As is clear from the results shown in FIG. 10, when Vf is 2.2%, the calculation method by Noint2way (the analysis method used in Example 1) is the calculation method by Int1way (used in Comparative Example 1). It has been confirmed that the calculation time is about four times faster than that of the analysis method). Further, when Vf is 12.7%, the calculation method by Noint2way (analysis method adopted in Example 2) is larger than the calculation method by Int1way (analysis method adopted in Comparative Example 2). It was confirmed that the calculation time was about 12 times faster. From such results, it was found that the calculation method by Noint2way (the analysis method adopted in the present invention) makes it possible to obtain a simulation result with higher accuracy in a shorter time.

Note that when the volume concentration Vf is further increased (when the number of fibers is further increased), communication to distant positions in the memory space that occurs when calculating the two-body interaction increases. It is considered that the calculation method according to (the analysis method adopted in the present invention) further improves the speed-up effect as compared with the calculation method according to Int1way (conventional analysis method).

<Discussion>
When the range of application of the calculation method by Noint2way (analysis method adopted in the present invention) is examined, generally, the particle concentration is one of the important parameters when discussing the interaction in the calculation of a fluid containing particles. Here, the particle concentrations are generally classified into three systems of a dilute system, a semi-concentrated system, and a concentrated system when arranged in the order of increasing concentration. Then, in the case of a fluid containing fibers as analyzed in the examples, the above-mentioned three systems have the following conditional expressions:

It is known that it can be classified under the conditions represented by (Doi, M. and Edwards, S.F., The Theory of Polymer Dynamics, Oxford Univ. Press, New York (1988)). In this conditional expression, n is the number of fibers per unit volume. In the lean system, the two-body interaction such as mechanical contact omitted in the present invention is not so important (although it can be ignored), but in the rich system, the two-body interaction may be a dominant parameter. There is. Therefore, when the fibers having the aspect ratio L/d=20 simulated in the examples are classified by applying the above-mentioned conditional expressions, it is found that the condition of the concentrated system is the case where the volume concentration Vf is 3.9%. . On the other hand, in Example 2 described above, as is clear from the results shown in FIG. 9, it is confirmed that the simulation can be performed with high accuracy even when the volume concentration Vf is 12.7%. Considering the results of Examples 1 and 2 and the general classification described above, the calculation method by Noint2way (the analysis method adopted in the present invention) can be applied to any concentration classification of diluted system to concentrated system. It is clear that the kinetic state (orientation state, etc.) of the fibrous substance can be analyzed with sufficient accuracy in the range (total range of concentration classification), and can be said to be applicable to any concentration system.

As described above, according to the present invention, a method for analyzing a motion state of a fibrous substance in a fluid that enables a motion state of a fibrous substance in a fluid to be simulated in a shorter time and with higher accuracy, and It is possible to provide a device for analyzing the motion state of a fibrous substance in a fluid, which is capable of executing such an analysis method.

Therefore, the method for analyzing the motion state of the fibrous substance in the fluid of the present invention derives the molding conditions for the composite material such as the fiber reinforced resin (FRP) and the fiber reinforced metal (FRM) and the design guideline for the molding die and the like. It is particularly useful as a simulation method for

DESCRIPTION OF SYMBOLS 1... Input part, 2... Arithmetic processing part, 21... 1st arithmetic means, 22... 2nd arithmetic means, 23... Judgment means, 3... Output part, 10... Fibrous substance, 10A... Fibrous substance Sphere aggregate model.

Claims (4)

Simulation of the motion state of fibrous substance in fluid based on the information of fibrous substance and fluid required to calculate the motion of fibrous substance and fluid using the equation of motion of fluid and that of particle An analysis method for performing the following steps (a) to (c):
Step (a): The fibrous substance after a lapse of a minute time from a specific time by using a calculation method using a sphere aggregation model assuming that the fibrous substance is composed of a sphere assembly in which a plurality of spheres are bonded. Is a step for analyzing the movement of
Based on the information of the velocity of the fluid, calculate the fluid resistance force of each sphere of the fibrous substance and the torque that each sphere of the fibrous substance receives from the fluid,
Calculate the binding force between each sphere of the fibrous material and the restoring torque for the bending deformation between each sphere of the fibrous material,
Fluid resistance of each sphere of the fibrous material, torque that each sphere of the fibrous material receives from the fluid, binding force between each sphere of the fibrous material, and bending between each sphere of the fibrous material. The position, velocity and angular velocity of each sphere of the fibrous substance and the bending angle between adjacent spheres forming the fibrous substance are calculated after a lapse of a minute time from a specific time based on the information of the restoring torque for the deformation. , Fibrous material motion analysis step;
Step (b): The force that the fluid receives from the fibrous substance is calculated based on the fluid resistance force information of each sphere of the fibrous substance calculated in step (a), and the fluid is the fibrous substance. Considering the force received from the substance and the volume fraction of the fibrous substance in the fluid, calculate the velocity of the fluid after a lapse of a minute time from a specific time, the movement of the fluid and the movement of the fibrous substance Coupled analysis step;
Step (c): Utilizing the information on the transient motion states of the fluid and the fibrous substance, which are already obtained in the steps (a) and (b), the steps (a) and (b) are newly added. An iterative operation step in which the process of sequentially executing the calculation is repeatedly executed until a predetermined condition is satisfied;
The motion of the fluid and the motion of the fibrous substance are sequentially used by sequentially using the transient analysis result after a lapse of a minute time obtained by analyzing the motion of the fluid and the motion of the fibrous substance during the iterative calculation step. A method for analyzing the motion state of a fibrous substance in a fluid, which comprises performing a coupled analysis to analyze the motion state of the fibrous substance in the fluid. In the motion analysis step of the fibrous substance, the position of each sphere of the fibrous substance after a lapse of a minute time from a specific time is calculated without calculating the fluid lubrication force and the mechanical contact force related to the interaction force between the fibrous substances. The velocity, angular velocity, and bending angle between adjacent spheres forming the fibrous substance are calculated, and the method of analyzing the motion state of the fibrous substance in the fluid according to claim 1. Simulation of the motion state of fibrous substance in fluid based on the information of fibrous substance and fluid required to calculate the motion of fibrous substance and fluid using the equation of motion of fluid and that of particle An analysis device for
Using a calculation method using a sphere assembly model assuming that the fibrous material is composed of a sphere assembly in which a plurality of spheres are bonded, the movement of the fibrous material after a lapse of a minute time from a specific time is analyzed. Is a calculation means for calculating the fluid resistance force of each sphere of the fibrous substance and the torque that each sphere of the fibrous substance receives from the fluid, based on the information of the velocity of the fluid, The binding force between the spheres and the restoring torque for bending deformation between the spheres of the fibrous substance are calculated, and the fluid resistance force of each sphere of the fibrous substance, the torque that each sphere of the fibrous substance receives from the fluid. , The binding force between the spheres of the fibrous substance, and based on the information of the restoring torque for the bending deformation between the spheres of the fibrous substance, each of the fibrous substance after a lapse of a minute time from a specific time First calculation means for calculating the position, velocity and angular velocity of the sphere, and the bending angle between adjacent spheres forming the fibrous substance;
The force received by the fluid from the fibrous substance is calculated based on the information on the fluid resistance force of each sphere of the fibrous substance calculated by the first computing means, and the fluid receives from the fibrous substance. Second computing means for calculating the velocity of the fluid after a lapse of a minute time from a specific time in consideration of the force and the volume fraction of the fibrous substance in the fluid;
Utilizing the information on the transitional motion states of the fluid and the fibrous substance already obtained by the first computing means and the second computing means, the first computing means and the second computing are newly added. Determination means for determining whether or not the condition is satisfied in order to execute an iterative operation step in which the process of sequentially executing the calculation by the means is repeated until a predetermined condition is satisfied;
The motion of the fluid and the motion of the fibrous material are sequentially used by sequentially using the transient analysis result after a lapse of a minute time obtained by analyzing the motion of the fluid and the motion of the fibrous material during the iterative calculation step. An apparatus for analyzing a motion state of a fibrous substance in a fluid, which performs a coupled analysis to analyze the motion state of the fibrous substance in the fluid. The first computing means calculates the position and velocity of each sphere of the fibrous substance after a lapse of a minute time from a specific time without calculating the fluid lubrication force and the mechanical contact force related to the interaction force between the fibrous substances. The calculation device for calculating the angular velocity and the bending angle between the adjacent spheres forming the fibrous substance, and the apparatus for analyzing the motion state of the fibrous substance in the fluid according to claim 3.