JP2023054638A - Fluid simulation method - Google Patents

Abstract

To provide a fluid simulation method capable of calculating a flow state of a fluid in consideration of a slip velocity that varies according to a proportion of a fluid material in the vicinity of a wall surface.SOLUTION: A simulation method for calculating a state in which a fluid containing multiple types of fluid materials is flowing in a chamber by using a computer includes the steps of: inputting a chamber model having a wall surface; defining a space model in which an internal space surrounded with the wall surface of the chamber model is modeled with a finite number of elements; defining a fluid model including multiple types of fluid material models in the space model; and performing flow calculation of the fluid model. The step of performing flow calculation includes steps of calculating a volume fraction of the multiple types of fluid material models for the fluid model in contact with the wall surface S52; and calculating a slip velocity with respect to the wall surface of the fluid model in contact with the wall surface based on the volume fraction S53.SELECTED DRAWING: Figure 6

Description

The present disclosure relates to a fluid simulation method.

Patent Literature 1 listed below describes a fluid simulation method that uses a computer to calculate the state of a fluid in a chamber having walls. In this method, first, a step of setting a chamber model in which a chamber is modeled with a finite number of elements, and a step of setting a material model in which a fluid is modeled are performed.

Next, a step of placing a material model in the chamber model and performing a flow calculation based on predetermined conditions is performed. In this flow calculation, a linear slip velocity, which is a velocity parallel to the contact surface of the material model, is defined at the contact surface where the material model and the wall surface of the chamber model are in contact.

Japanese Patent No. 5564074

By the way, when the fluid contains a plurality of types of fluid materials, the slip speed of the fluid with respect to the wall surface is considered to change according to the ratio of the fluid materials existing in the vicinity of the wall surface. , it was not possible to calculate the flow state considering such changes.

The present disclosure has been devised in view of the actual situation as described above, and is a fluid simulation capable of calculating the flow state of the fluid in consideration of the slip speed that changes according to the ratio of the fluid material near the wall surface. Its primary purpose is to provide a method.

The present disclosure is a simulation method for calculating, using a computer, a state in which a fluid containing multiple types of fluid materials is flowing in a chamber, wherein the chamber is modeled to create a chamber model having walls. into the computer; defining a space model in which the internal space surrounded by the walls of the chamber model is modeled with a finite number of elements; and modeling the plurality of types of fluid materials in the space model. A step of defining a fluid model including a plurality of types of fluid material models; and a step of the computer performing a flow calculation of the fluid model, wherein the step of performing the flow calculation includes: A fluid simulation method, comprising the steps of: calculating volume fractions of the plurality of types of fluid material models; and calculating a slip velocity with respect to the wall surface of the fluid model in contact with the wall surface based on the volume fractions. .

By adopting the steps described above, the fluid simulation method of the present disclosure can calculate the flow state of the fluid in consideration of the slip velocity that varies according to the proportion of the fluid material near the wall surface.

1 is a perspective view showing a computer for executing the fluid simulation method of this embodiment; FIG. FIG. 4 is a perspective view showing fluid flowing within the chamber; 4 is a flow chart showing a processing procedure of a fluid simulation according to the embodiment; It is a conceptual diagram showing a chamber model and a space model of the present embodiment. It is a partial cross-sectional view of the main chamber model. 4 is a flow chart showing a processing procedure of a flow calculation step of this embodiment; It is a contour diagram showing the flow velocity of the fluid material model of the example. FIG. 5 is a contour diagram showing the flow velocity of a fluid material model of a comparative example;

Hereinafter, embodiments of the present disclosure will be described based on the drawings. It should be understood that the drawings contain exaggerated representations and representations that differ from the dimensional ratios of the actual structures in order to aid in understanding the content of the disclosure. In addition, throughout each embodiment, the same or common elements are denoted by the same reference numerals, and overlapping descriptions are omitted. Furthermore, the specific configurations shown in the embodiments and drawings are for understanding the contents of the present disclosure, and the present disclosure is not limited to the illustrated specific configurations.

In the fluid simulation method of the present embodiment (hereinafter sometimes simply referred to as "simulation method"), a state in which a fluid containing multiple types of fluid materials is flowing in a chamber is calculated using a computer. .

[Computer]
FIG. 1 is a perspective view showing a computer for executing the fluid simulation method of this embodiment. A computer 1 of this embodiment includes a main body 1a, a keyboard 1b, a mouse 1c, and a display device 1d. The main body 1a is provided with, for example, an arithmetic processing unit (CPU), a ROM, a working memory, a storage device such as a magnetic disk, and disk drive devices 1a1 and 1a2. Software and the like for executing the simulation method of this embodiment are stored in advance in the storage device.

[fluid]
FIG. 2 is a perspective view showing the fluid 3 flowing inside the chamber 2. FIG. The fluid 3 of this embodiment contains multiple types of fluid materials 4 . The fluid material 4 is not particularly limited as long as it constitutes the fluid 3 . An unvulcanized rubber material or an uncured resin material is adopted as the fluid material 4 of the present embodiment. Rubber materials include, for example, natural rubber (NR), butadiene rubber (BR), styrene-butadiene rubber (SBR), and the like.

The number of types of the fluid material 4 of this embodiment is not particularly limited. In this embodiment, four types are set, including a first fluid material 4A, a second fluid material 4B, a third fluid material 4C, and a fourth fluid material 4D. These first to fourth fluid materials 4A to 4D have different slip characteristics on the wall surface 7 of the chamber 2 .

[Chamber]
The chamber 2 of this embodiment is formed in a cylindrical shape and has a wall surface 7 that defines an internal space 8 . The chamber 2 of this embodiment includes a branch chamber 5 and a main chamber 6 .

[Branch chamber]
The branch chamber 5 of this embodiment is for flowing the fluid material 4 (first fluid material 4A to fourth fluid material 4D in this example) into the main chamber 6 . One end (upstream side) of the branch chamber 5 of the present embodiment is connected to, for example, a screw extruder (not shown) for supplying the fluid material 4 .

The branching chamber 5 includes a first branching chamber 5A, a second branching chamber 5B, a third branching chamber 5C and a fourth branching chamber 5D. The first branch chamber 5A to fourth fluid material 4D are for allowing the first fluid material 4A to fourth fluid material 4D to flow into the main chamber 6, respectively.

[Main chamber]
The main chamber 6 of this embodiment is for flowing a fluid 3 containing a plurality of types of fluid materials 4 (first fluid material 4A to fourth fluid material 4D in this example). One end (upstream side) of the main chamber 6 is provided with a junction 9 for connecting the other end (downstream side) of the branching chambers 5 (in this example, the first branching chamber 5A to the fourth branching chamber 5D). ing. As a result, an internal space 8 surrounded by a wall surface 7 is continuously formed in the chamber 2 from the branch chamber 5 to the main chamber 6 .

The main chamber 6 contains fluid materials 4 (first fluid material 4A to fourth fluid material 4D in this example) supplied from branch chambers 5 (first branch chamber 5A to fourth branch chamber 5D in this example). ) is supplied. In the main chamber 6, the fluid 3 (plural kinds of fluid materials 4) is extruded from one end (upstream side) to the other end (downstream side).

By the way, as in this embodiment, when the fluid 3 contains a plurality of types of fluid materials 4 (in this example, the first fluid material 4A to the fourth fluid material 4D), the slip speed of the fluid 3 with respect to the wall surface 7 is considered to change according to the ratio of the fluid material 4 existing in the vicinity of the wall surface 7 and the like. Therefore, in order to calculate the flow of the fluid 3, it is important to calculate the flow state in consideration of the change in the slip speed.

[Fluid simulation method (first embodiment)]
In the simulation method of the present embodiment, the flow state of the fluid 3 is calculated in consideration of the slip speed that changes according to the ratio of the fluid material 4 near the wall surface 7 . FIG. 3 is a flow chart showing the processing procedure of the fluid simulation of this embodiment.

[Enter chamber model]
In the simulation method of this embodiment, first, a chamber model is input to the computer 1 (step S1). FIG. 4 is a conceptual diagram showing the chamber model 11 and the space model 12 of this embodiment. FIG. 5 is a partial cross-sectional view of the main chamber model 16. FIG.

The chamber model 11 is a model of the chamber 2 (shown in FIG. 2). In step S1 of the present embodiment, the chamber 2 is modeled (discretized) with a finite number of elements G(i) based on design data (design factors) of the chamber 2 to be analyzed. Thereby, in step S1, the chamber model 11 having the wall surface 19 (shown in FIG. 5) is set.

The chamber model 11 of this embodiment includes a branch chamber model 15 and a main chamber model 16 .

Branch chamber model 15 is a model of branch chamber 5 (shown in FIG. 2). The branching chamber model 15 of this embodiment includes a first branching chamber model 15A, a second branching chamber model 15B, a third branching chamber model 15C and a fourth branching chamber model 15D. These branch chamber models 15A-15D are models of the first branch chamber 5A-fourth branch chamber 5D (shown in FIG. 2), respectively.

The main chamber model 16 is a model of the main chamber 6 (shown in FIG. 2). One end (upstream side) of the main chamber model 16 is provided with a junction 17 for connecting the other end (downstream side) of each of the branch chamber models 15A to 15D. As a result, in the chamber model 11, an internal space 18 (shown in FIG. 5) surrounded by the walls 19 is continuously formed from the branch chamber models 15A to 15D to the main chamber model 16. As shown in FIG.

Element G(i) employs, for example, a two-dimensional surface element or a three-dimensional solid element (in this example, a solid element). The solid element is preferably a hexahedron with good accuracy and easy setting of the contact surface, but a tetrahedron element suitable for expressing a complicated shape may be used. In addition to these solid elements, three-dimensional solid elements that can be used with software may be used as the solid elements. For each element G(i), numerical data such as an element number, a node (not shown) number, and coordinate values of the node are defined. Further, each element G(i) in this embodiment is defined to have such rigidity that it cannot be deformed even when an external force acts on it. Chamber model 11 is stored in computer 1 .

Define Spatial Model
Next, in the simulation method of the present embodiment, the space model 12 is defined by modeling the internal space 18 (shown in FIG. 5) surrounded by the walls 19 of the chamber model 11 with a finite number of elements F(i) ( step S2).

In step S2 of this embodiment, the internal space 18 (shown in FIG. 5) of the chamber model 11 including the branch chamber model 15 and the main chamber model 16 is discretized with a finite number of elements F(i). As a result, a spatial model 12 that is continuous from the branch chamber model 15 to the main chamber model 16 is defined.

The space model 12 of this embodiment includes a main space model 13 and a branch space model 14 . The branched space models 14 include a first branched space model 14A, a second branched space model 14B, a third branched space model 14C and a fourth branched space model 14D.

As shown in FIG. 5, the main space model 13 is defined in the inner space 18 of the main chamber model 16. As shown in FIG. As shown in FIG. 4, the first branch space model 14A to fourth branch space model 14D are defined in each internal space 18 (not shown) of the first branch chamber model 15A to fourth branch chamber model 15D. .

The element division is performed by, for example, three-dimensional elements such as tetrahedrons, hexahedrons, and polyhedral cells (polyhedral grids). In this embodiment, Euler elements are used. In each element F(i), physical quantities such as pressure, temperature and velocity of the fluid model 21, which will be described later, and volume fractions of the fluid material model 22 (first fluid material model 22A to fourth fluid material model 22D) are calculated. be done. Spatial model 12 is stored in computer 1 .

[Define fluid model]
Next, in the simulation method of the present embodiment, a fluid model 21 including multiple types of fluid material models 22 is defined in the space model 12 (step S3). The plurality of types of fluid material models 22 are models of the plurality of types of fluid materials 4 (shown in FIG. 2).

The multiple types of fluid material models 22 of this embodiment include a first fluid material model 22A, a second fluid material model 22B, a third fluid material model 22C and a fourth fluid material model 22D. These first fluid material model 22A to fourth fluid material model 22D are models of the first fluid material 4A to fourth fluid material 4D (shown in FIG. 2), respectively.

The fluid material model 22 of this embodiment is defined by elements (Eulerian elements) F(i) of the space model 12 . Physical quantities of the first to fourth fluid materials 4A to 4D to be analyzed are defined in the first to fourth fluid material models 22A to 22D, respectively. Physical quantities include, for example, shear viscosity, specific heat, thermal conductivity, specific gravity, and the like. These physical quantities are appropriately defined based on the descriptions in, for example, Patent Document 1 and Patent Document (Japanese Patent Application Laid-Open No. 2016-043545). A fluid model 21 (a plurality of types of fluid material models 22) is stored in the computer 1. FIG.

[Set boundary conditions, etc.]
Next, in the simulation method of this embodiment, boundary conditions and the like are set in the computer 1 (step S4). The boundary conditions of the present embodiment include the first fluid material model 22A to the fourth fluid material model 22D supplied from one ends (supply ports 14Ai to 14Di) of the first branch space model 14A to the fourth branch space model 14D, respectively. Inflow and temperature are included.

The inflow rate and temperature can be set, for example, based on experimental results using an actual chamber 2 (shown in FIG. 2) or design values of the chamber 2 . These inflow amount and temperature may be set differently for each of the first fluid material model 22A to the fourth fluid material model 22D, or may be set the same. In this embodiment, the same inflow rate and temperature are set. Furthermore, the boundary conditions of the present embodiment include the pressure (pressure=0) at the other end (exhaust port) 13t of the main space model 13 .

The boundary conditions of this embodiment include the flow calculation (simulation) time step, the number of iterations in internal processing, the calculation end time, and the like. These conditions are arbitrarily determined according to the purpose of the simulation.

The boundary conditions of this embodiment include a wall slip condition with flow velocity in the fluid material model 22 on the wall surface 19 (shown in FIG. 5) of the chamber model 11 . The wall slip condition is defined by the slip velocity V _slip (x) with respect to the wall surface 19 of the fluid model 21 in contact with the wall surface 19 of the chamber model 11 . The slip speed V _slip (x) is calculated by the following formula (1).

ここで、
ｘ：壁面と接触する各要素に割り当てられた番号（自然数）
Ｖ_slip（ｘ）：スリップ速度
α：スリップ率
Ｖ_t（ｘ）：壁面から法線方向に距離Ｄ_wallを隔てた位置での流体モデルの速度成分
Ｖ_wallm（ｘ）：壁面での流体モデルの速度成分
ｉ：各流体材料モデルに割り当てられた番号（自然数）
Ｃ_ｉ：各流体材料モデルの体積分率
η_ｉ：各流体材料モデルの粘度
Ｆ_slipi、ｅ_i：各流体材料モデルのスリップの特性を示す定数

here,
x: Number assigned to each element in contact with the wall (natural number)
V _slip (x): Slip velocity α: Slip rate V _t (x): Velocity component of the fluid model at a position separated by a distance D _wall in the normal direction from the wall surface V _wallm (x): The velocity component of the fluid model at the wall surface Velocity component i: Number assigned to each fluid material model (natural number)
C _i : Volume fraction of each fluid material model η _i : Viscosity of each fluid material model F _slipi , e _i : Constants indicating slip characteristics of each fluid material model

x in the above equation (1) is a number (natural number) assigned to each element F(i) in contact with the wall surface 19 of the chamber model 11 among the elements F(i) of the space model 12 . Thus, the slip velocity V _slip (x) defines the slip velocity at each element F(x) identified by the number x. In this embodiment, the slip speed V _slip (x) is specified by the center point (representative point) 23 of each element F(x) specified by the number x.

V _t (x) in the above equation (1) is a velocity component at a position separated from the wall surface 19 by a distance D _wall in the normal direction for each element F(x) specified by the number x. V _wallm (x) in the above equation (1) is the velocity component on the wall surface 19 for each element F(x) specified by the number x. These velocity components V _t (x) and V _wallm (x) are velocity components of the fluid model 21 parallel to the wall surface 19 . The details of the velocity components V _t (x) and V _wallm (x) are as described in Patent Document 1 above.

i in the above equation (1) is a number (natural number) assigned to each fluid material model 22 (shown in FIG. 4). In this embodiment, a first fluid material model 22A to a fourth fluid material model 22D are included. Therefore, the first fluid material model 22A is assigned "1" as the number i. The second fluid material model 22B is assigned "2" as the number i. The third fluid material model 22C is assigned "3" as the number i. The fourth fluid material model 22D is assigned "4" as the number i.

C _i in the above formula (1) is the fluid material model 22 (first fluid material model 22A to fourth fluid material model 22D) specified by number i in each element F(x) specified by number x. volume fraction. η _i in the above formula (1) is each fluid material model 22 (first fluid material model 22A to fourth fluid material model 22D) specified by number i in each element F(x) specified by number x. is the viscosity of The viscosity in this embodiment is shear viscosity. This viscosity includes the shear viscosities defined in the first fluid material model 22A to the fourth fluid material model 22D (that is, the shear viscosities of the first fluid material 4A to the fourth fluid material 4D ) is used.

F _slipi and e _i in the above equation (1) are constants representing the slip characteristics of the fluid material model 22 identified by the number i. These constants F _slipi and e _i are determined (identified) in advance by experiments based on the same procedure as in Patent Document 1 above.

In this embodiment, in the flow calculation step S5 described later, for each element F(x) of the space model 12 in contact with the wall surface 19, the volume fraction C _i of each of the plurality of types of fluid material models 22A to 22D and the velocity component V _t (x) and V _wallm (x) are substituted into equation (1) above. Thereby, the slip velocity V _slip (x) of the fluid model 21 arranged at each element F(x) is calculated. Such a slip velocity V _slip (x) is obtained by applying the shear viscosities of the first fluid material model 22A to the fourth fluid material model 22D to the first fluid material model 22A to the fourth fluid material model 22A included in the element F(x). It is specified by weighting with the volume fraction of the model 22D. Therefore, in the simulation method of the present embodiment, it is possible to consider the slip speed that changes according to the proportion of the fluid material 4 near the wall surface 19 . The boundary conditions are stored in computer 1 .

[Flow calculation step]
Next, in the simulation method of this embodiment, the computer 1 (shown in FIG. 1) performs flow calculation of the fluid model 21 (flow calculation step S5). In the flow calculation step S5 of the present embodiment, based on the boundary conditions, as shown in FIG. The fluid material model 22A to the fourth fluid material model 22D are introduced respectively. Then, in the flow calculation step S5, the first fluid material model 22A to the fourth fluid material model 22D are merged in the main space model 13, and the fluid model 21 flows to the other end (discharge port) 13t of the main space model 13. The state to push (extrude) is calculated. Such a flow calculation is performed for each unit time Tx of simulation.

The flow calculation is performed, for example, based on a procedure similar to that in the patent document (Japanese Patent Application Laid-Open No. 2016-043545). In this embodiment, at the position of each element F(i) of the space model 12, velocity components u in three directions (x, y, z) specifying the motion state of the fluid material model 22 and the internal state of the material model are Certain unknowns pressure p and temperature T are calculated. Further, in the flow calculation of this embodiment, the Navier-Stoks equation for incompressible flow is used, and the density of the fluid material model 22 is assumed to be constant.

In this embodiment, the fluid material model 22 is treated as a fluid over the entire temperature range. For this purpose, the fluid equations (simultaneous Navier-Stoks equations, mass conservation equations, and energy equations) are solved. Moreover, in this embodiment, mixed phases of a plurality of types of material models with different shear viscosities η are handled. For this reason, in this embodiment, the VOF (Volume of Fluid) method used in the calculation of the flow on the free surface is used.

In the VOF method, the movement of the interfaces of the four first to fourth fluid material models 22A to 22D is not directly calculated, but the volume fractions of the fluid material models 22A to 22D ( fill factor) C _i is defined to represent the free interface averaged.

In the flow calculation step S5 of this embodiment, the calculation is performed until the flow of the fluid model 21 reaches a stable state (that is, until it converges). Thereby, the stable state of the fluid model 21 can be obtained. For flow calculation, for example, commercially available fluid analysis software (eg, ANSYS FLUNET, CFX, etc.) can be used. FIG. 6 is a flow chart showing the processing procedure of the flow calculation step S5 of this embodiment.

[Calculate motion of fluid material model]
In the flow calculation step S5 of this embodiment, first, motions of a plurality of types of fluid material models 22 (first fluid material model 22A to fourth fluid material model 22D) are calculated (step S51). The motion calculation in step S51 can be performed in a conventional procedure. Examples of the motion calculation procedure include steps S51 to S60 of the flow calculation in Patent Document 1 and steps S201 to S210 in the motion calculation step described in Patent Document (JP 2016-043545 A). be done.

[Calculate volume fraction of fluid material model]
Next, in the flow calculation step S5 of the present embodiment, as shown in FIG. 5, the volume fractions of multiple types of fluid material models 22 (shown in FIG. 4) are calculated for the fluid model 21 in contact with the wall surface 19. (step S52). In step S52 of the present embodiment, the first fluid material model 22A to the fourth fluid material model 22A shown in FIG. The volume fractions C _i (i=1-4) of model 22D are calculated respectively. Each volume fraction is calculated based on the VOF method.

In the main space model 13, the flow of the fluid model 21 including the first fluid material model 22A to the fourth fluid material model 22D is calculated. The 22D volume fraction C _i is calculated. On the other hand, in the first branch space model 14A, only the flow of the first fluid material model 22A is calculated. is set to Similarly, in the second branch space model 14B to the fourth branch space model 14D, the volume fraction of the second fluid material model 22B to the fourth fluid material model 22D in the element F(i) in contact with the wall surface 19 is 1.0. are set respectively. The volume fraction is stored in computer 1 .

[Calculation of slip velocity of fluid model 21]
Next, in the flow calculation step S5 of this embodiment, the wall surface 19 of the fluid model 21 in contact with the wall surface 19 is calculated based on the volume fractions C _i (i=1 to 4) of each of the plurality of types of fluid material models 22A to 22D. A slip velocity V _slip (x) for is calculated (step S53).

In step S53 of the present embodiment, for each element F(x) of the space model 12 in contact with the wall surface 19, the volume fraction C _i of each of the plurality of types of fluid material models 22A to 22D, the velocity component V _t (x) and V _wallm (x) is substituted into the above equation (1). The volume fractions C _i (i=1 to 4) of the first fluid material model 22A to the fourth fluid material model 22D calculated in step S52 are used as the volume fractions C _i . The velocity components V _t (x) and V _wallm (x) are calculated, for example, by a procedure similar to that of the prior art, such as Patent Document 1 above. As a result, in step S53, the slip velocity V _slip (x) of the fluid model 21 contacting the wall surface 19 with respect to the wall surface is calculated for each element F(x) of the space model 12 contacting the wall surface 19 .

In the main space model 13 _, the flow of the fluid model 21 including the first fluid material model 22A to the fourth fluid material model 22D is calculated. A slip velocity V _slip (x) is calculated. On the other hand, in the first branch space model 14A, only the flow of the first fluid material model 22A is calculated. Therefore, the volume fraction (=1. 0) is calculated based on slip velocity V _slip (x) only. Similarly, in the second branch space model 14B to the fourth branch space model 14D, the volume fraction (=1. 0) _are calculated respectively. The slip velocity V _slip (x) is stored in computer 1 .

[Determine the stable state of the fluid material model]
Next, in the flow calculation step S5 of this embodiment, it is determined whether or not the flow of the fluid model 21 has reached a stable state (whether the calculation has converged) (step S54). The stable state of the present embodiment is the total supply amount of the first fluid material model 22A to the fourth fluid material model 22D from one end (confluence portion) of the main space model 13, and the fluid at the other end 13t of the main space model 13. A state in which the difference from the emission amount of the model 21 is within a predetermined range. The determination of the stable state is appropriately performed based on, for example, the processing procedure of step S211 of the patent document (Japanese Patent Application Laid-Open No. 2016-043545).

In step S54, when it is determined that the flow of the fluid model 21 has reached a stable state ("Yes" in step S54), the series of processes of the flow calculation step S5 of this embodiment ends, and the next step S6 (Fig. 3) is performed. On the other hand, if it is determined in step S54 that the flow of the fluid model 21 is not in a stable state ("No" in step S54), the simulation unit time Tx is advanced by one (step S55), and steps S51 to Step S54 is performed again. Thus, in the flow calculation step S5, the flow calculation of the fluid model 21 is performed for each simulation unit time Tx until the flow of the fluid model 21 reaches a stable state.

In the simulation method of this embodiment, the slip velocity V _slip (x) is calculated. As a result, in the simulation method of this embodiment, it is possible to calculate the flow state of the fluid 3 in consideration of the slip velocity V _slip (x) that changes according to the proportion of the fluid material 4 near the wall surface 19. . Therefore, in the present embodiment, it is possible to accurately (close to reality) calculate the state in which multiple types of fluid material models 22 merge and the state in which they are pushed out.

[Get Physical Quantity]
Next, in the simulation method of this embodiment, the computer 1 (shown in FIG. 1) acquires physical quantities of the fluid model 21 (step S6). Physical quantities include, for example, the velocity, pressure, and temperature of the fluid model 21 . In this embodiment, these physical quantities are calculated at the other end (discharge port) 13t of the main chamber model 16. FIG. These physical quantities are appropriately calculated using fluid analysis software. Physical quantities are stored in the computer 1 .

[Evaluate physical quantity]
Next, in the simulation method of the present embodiment, it is evaluated whether or not the physical quantities of the fluid model 21 are satisfactory (step S7). Whether the physical quantity is good or bad may be judged by the computer 1 (shown in FIG. 1) or by an operator.

In step S7 of the present embodiment, it is determined whether or not the physical quantity of the fluid model 21 is equal to or less than a predetermined threshold. The threshold value is appropriately set according to, for example, the flow state required for the fluid 3 (shown in FIG. 2) to be analyzed.

If it is determined in step S7 that the physical quantities of the fluid model 21 are good ("Yes" in step S7), a product using the fluid 3 (shown in FIG. 2) is manufactured (step S8). In step S8, the chamber 2 is manufactured based on the design factors of the chamber 2, for example. Then, in step S8, a product having a desired shape is manufactured by causing the fluid 3 containing the fluid material 4 to flow in the chamber 2 that has been manufactured.

On the other hand, if it is determined in step S7 that the physical quantities of the fluid model 21 are not good ("No" in step S7), for example, the design factors of the chamber 2 (shown in FIG. 2) and the physical properties of the fluid material 4 are changed. (step S9), and steps S1 to S7 are performed again. As described above, in the simulation method of the present embodiment, the design factors of the chamber 2 and the physical properties of the fluid material 4 are changed until the physical quantities of the fluid model 21 are improved. It becomes possible to manufacture reliably.

[Fluid simulation method (second embodiment)]
In the flow calculation step S5 of the embodiment so far, as shown in FIG. 4, the state in which the fluid material model 22 merges and the state in which it is pushed out is calculated, but the present invention is not limited to such a mode. In the flow calculation step S5, for example, as in Patent Document 1, a Banbury mixer (not shown) may calculate a state in which a plurality of types of fluid material models 22 are kneaded. Further, in the flow calculation step S5, for example, a state in which the fluid model 21 (plural types of fluid material models 22A to 22D) is molded into a predetermined shape may be calculated. In this embodiment, as in the previous embodiments, the slip velocity with respect to the wall surface 19 is calculated in consideration of the fluid material 4 existing in the vicinity of the wall surface 19, so the kneading state and molding state of the fluid material model 22 , can be calculated with high accuracy (in a state close to reality).

Although the particularly preferred embodiments of the present disclosure have been described in detail above, the present disclosure is not limited to the illustrated embodiments and can be modified in various ways.

Based on the processing procedure of FIG. 3, a computer was used to calculate the state in which the fluid containing multiple types of fluid materials was flowing in the chamber (Example and Comparative Example).

In the example, based on the processing procedure of FIG. 6, the slip velocity with respect to the wall surface of the fluid model in contact with the wall surface was calculated based on the volume fractions of a plurality of types of fluid material models. On the other hand, in the comparative example, the slip velocity was calculated based on the same procedure as before without considering the volume fractions of the multiple types of fluid material models. Common specifications are as follows.
First fluid material model to fourth fluid material model:
Specific gravity: 1.11 x 103 (kg/ ^m3 )
Specific heat: 1.43 x 103 (J/kg K)
Thermal conductivity: 0.323W/m・K
Initial temperature, wall temperature: 100°C
Inflow: 0.05 kg/s
Constants that characterize the slip:
First fluid material model:
F _slip1 : 2.38×10 ⁶
_e1 : 0.235
Second fluid material model:
F _slip2 : 1.34×10 ⁶
_e2 : 0.285
Third fluid material model:
F _slip3 : 3.56×10 ⁶
_e3 : 0.201
Fourth fluid material model:
F _slip4 : 3.01×10 ⁶
_e4 : 0.269

FIG. 7 is a contour diagram showing the flow velocity of the fluid material model of the example. FIG. 8 is a contour diagram showing the flow velocity of the fluid material model of the comparative example. Figures 7 and 8 show the flow velocity when viewed from the outlet side of the main chamber model, and the lighter the color, the higher the flow velocity.

7 and 8, the wall surface on the left side has a large ratio of the first fluid material model 22A due to supply from the first branch chamber model 15A shown in FIG. The upper wall surface has a large ratio of the second fluid material model 22B, the right wall surface has a large ratio of the third fluid material model 22C, and the lower wall surface has a ratio of the fourth fluid material model 22D. is large.

As shown in FIG. 8, in the comparative example, the same slip velocity relative to the wall surface was calculated for the upper wall surface, the left wall surface, the lower wall surface, and the right wall surface. Therefore, in the comparative example, it was not possible to take into account the slip speed that varies according to the proportion of the fluid material near the wall surface.

As shown in FIG. 7, in the example, the slip velocity for the wall surface was calculated to increase in the order of the upper wall surface, the left wall surface, the lower wall surface, and the right wall surface. That is, the slip speed of the second fluid material model 22B was calculated to be the largest, and the slip speed of the third fluid material model 22C was calculated to be the smallest. This is based on the constants F _slip and e that characterize the slip defined for each fluid material model. Therefore, in the example, it was possible to calculate the flow state of the fluid considering the slip speed that varies according to the ratio of the fluid material near the wall surface.

[Appendix]
The present disclosure includes the following aspects.

ここで、
ｘ：壁面と接触する各要素に割り当てられた番号（自然数）
Ｖ_slip（ｘ）：スリップ速度
α：スリップ率
Ｖ_t（ｘ）：壁面から法線方向に距離Ｄ_wallを隔てた位置での流体モデルの速度成分
Ｖ_wallm（ｘ）：壁面での流体モデルの速度成分
ｉ：各流体材料モデルに割り当てられた番号（自然数）
Ｃ_ｉ：各流体材料モデルの体積分率
η_ｉ：各流体材料モデルの粘度
Ｆ_slipi、ｅ_i：各流体材料モデルのスリップの特性を示す定数
［本開示３］
前記流体材料は、未加硫のゴム材料又は未硬化の樹脂材料である、本開示１又は２に記載の流体シミュレーション方法。
［本開示４］
前記流動計算を行うステップは、前記複数種類の流体材料モデルが合流する状態、混合される状態、押し出される状態、及び、成形される状態の少なくとも１つを計算する、本開示１ないし３のいずれかに記載の流体シミュレーション方法。 [Present Disclosure 1]
A simulation method for calculating, using a computer, a state in which a fluid containing multiple types of fluid materials is flowing in a chamber,
modeling the chamber and inputting a chamber model with walls into the computer;
defining a space model in which an internal space surrounded by the walls of the chamber model is modeled with a finite number of elements;
defining a fluid model including a plurality of types of fluid material models modeling the plurality of types of fluid materials in the space model;
said computer performing flow calculations for said fluid model;
The step of performing the flow calculation includes:
calculating volume fractions of the plurality of types of fluid material models for the fluid model in contact with the wall surface;
calculating a slip velocity with respect to the wall of the fluid model in contact with the wall based on the volume fraction;
Fluid simulation method.
[Disclosure 2]
The fluid simulation method according to the present disclosure 1, wherein the slip speed is calculated by the following formula (1).

here,
x: Number assigned to each element in contact with the wall (natural number)
V _slip (x): Slip velocity α: Slip rate V _t (x): Velocity component of the fluid model at a position separated by a distance D _wall in the normal direction from the wall surface V _wallm (x): The velocity component of the fluid model at the wall surface Velocity component i: Number assigned to each fluid material model (natural number)
C _i : Volume fraction of each fluid material model η _i : Viscosity of each fluid material model F _slipi , ei _: Constants indicating slip characteristics of each fluid material model [3 of the present disclosure]
The fluid simulation method according to the present disclosure 1 or 2, wherein the fluid material is an unvulcanized rubber material or an uncured resin material.
[Disclosure 4]
Any one of 1 to 3 of the present disclosure, wherein the step of performing the flow calculation calculates at least one of a state in which the plurality of types of fluid material models merge, are mixed, be pushed out, and be molded. 2. A fluid simulation method according to claim 1.

S52 Step of calculating volume fraction S53 Step of calculating slip velocity

Claims (4)

A simulation method for calculating, using a computer, a state in which a fluid containing multiple types of fluid materials is flowing in a chamber,
modeling the chamber and inputting a chamber model with walls into the computer;
defining a space model in which an internal space surrounded by the walls of the chamber model is modeled with a finite number of elements;
defining a fluid model including a plurality of types of fluid material models modeling the plurality of types of fluid materials in the space model;
said computer performing flow calculations for said fluid model;
The step of performing the flow calculation includes:
calculating volume fractions of the plurality of types of fluid material models for the fluid model in contact with the wall surface;
calculating a slip velocity with respect to the wall of the fluid model in contact with the wall based on the volume fraction;
Fluid simulation method. 2. The fluid simulation method according to claim 1, wherein said slip speed is calculated by the following formula (1).

here,
x: Number assigned to each element in contact with the wall (natural number)
V _slip (x): Slip velocity α: Slip rate V _t (x): Velocity component of the fluid model at a position separated by a distance D _wall in the normal direction from the wall surface V _wallm (x): The velocity component of the fluid model at the wall surface Velocity component i: Number assigned to each fluid material model (natural number)
C _i : Volume fraction of each fluid material model η _i : Viscosity of each fluid material model F _slipi , e _i : Constants indicating slip characteristics of each fluid material model 3. The fluid simulation method according to claim 1, wherein said fluid material is an unvulcanized rubber material or an uncured resin material. 4. The step of performing the flow calculation calculates at least one of a state in which the plurality of types of fluid material models converge, a state in which they are mixed, a state in which they are pushed out, and a state in which they are molded. 2. The fluid simulation method according to item 1 or 2.

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