JP2016147440A - Flow simulation method and device for fluid - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method for reproducing behavior of a fluid when the fluid is discharged from a space formed of a movable wall, by shear flow of the fluid formed by movement of the movable wall, using a computer.SOLUTION: A flow simulation method of a fluid comprises: a step for setting a space model 38 which is made a model by dividing a space formed by a movable wall by plural lattices; a step for setting a fluid model formed by modeling of the fluid; and a step for calculating flow of the fluid model, based on a determined condition, in the space model 38. The space model 38 contains a thin film model 40 which has a corresponding boundary plane 40a of the space model 38 corresponding to a boundary plane 40a of the space contacting a surface of the movable wall, and configured to move to a movement direction of the movable wall at speed equal to movement speed of the movable wall, and has uniform thickness along the corresponding boundary plane 40a, and a main space model 42 which rests regardless of the movement speed.SELECTED DRAWING: Figure 4

Description

  The present invention relates to a fluid flow simulation method and apparatus for reproducing, using a computer, the behavior of a fluid when the fluid is discharged from space by a shear flow of the fluid formed by the movement of a moving wall.

  In recent years, various techniques for predicting and calculating fluid flow behavior by numerical simulation using a computer have been performed. For example, a numerical value that reproduces a rolling process in which a viscoelastic fluid such as rubber is subjected to shearing by a moving wall such as a rotating roll, thereby turning the viscoelastic fluid into a fluidized state and processing the fluidized viscoelastic fluid into a sheet shape. Simulation is also being considered.

  For example, a wedge-shaped space formed between two rotating rolls is mesh-divided to create a spatial model, and a fluid model in which a viscoelastic fluid is modeled is set in this spatial model. The flow calculation of the fluid model is performed based on the determined conditions.

  There is also known a fluid flow simulation method for calculating the state of fluid in a chamber having a wall surface using a computer (Patent Document 1). Specifically, a chamber model in which the chamber is modeled with a finite number of elements is set, and a material model in which the fluid is modeled is set. Further, a material model is arranged in the chamber model, and the flow calculation is performed based on a predetermined condition. In the flow calculation, the slip speed of the material model is defined at the contact surface between the material model and the wall surface of the chamber model, and the slip speed is calculated by a specific formula.

JP2013-256026A

However, in the simulation of the behavior of the viscoelastic fluid in the wedge-shaped space between the two rotating rolls as described above, the calculation result of the pressure at which the flow model of the viscoelastic fluid acts on the wall model of the rotating roll is the measurement result. In the pressure calculation result, it was found that the pressure value was very close to zero.
On the other hand, in the above-mentioned method in which the fluid flow simulation is performed by giving a slip speed to the material model at the contact surface between the wall surface of the material model and the chamber model, the flow calculation of the fluid with high viscosity can be stabilized. It can be done. However, in this method, in order to determine the slip speed, there is a complexity in which a constant of Fslip is determined in advance.

  In view of this, the present invention reproduces the behavior of the fluid when the fluid is discharged by the shear flow of the fluid formed by the movement of the moving wall using a computer in a different manner from the conventional method. It is an object to provide a fluid flow simulation method and apparatus that can be reproduced.

In one embodiment of the present invention, the behavior of the fluid when the fluid is discharged from the space formed by the moving wall by the shear flow of the fluid formed by the movement of the moving wall is reproduced using a computer. This is a fluid flow simulation method.
The flow simulation method is
Setting a space model modeled by dividing the space by a plurality of grids;
Setting a fluid model that models the fluid;
Performing a flow calculation of the fluid model based on defined conditions in the spatial model, and
The space model includes a corresponding boundary surface of the space model corresponding to a boundary surface of the space in contact with the surface of the moving wall, and moves in the moving direction of the transfer wall at the same speed as the moving speed of the moving wall. A thin film model having a uniform thickness along the corresponding boundary surface, and a main space model that is stationary regardless of the moving speed.

  The space is a wedge-shaped space in which the space width is gradually narrowed along the moving direction of the moving wall, and the fluid is discharged from a narrow portion where the space width of the wedge-shaped space is the narrowest. It is preferred that

  The thickness of the thin film model is preferably 50% or less of the space width of the narrow portion.

  The thickness of the thin film model is preferably changed according to the space width of the narrow portion.

  In the flow calculation, it is preferable to calculate a pressure at which the fluid model acts on the corresponding boundary surface.

The fluid is a viscoelastic fluid having a viscosity coefficient of 10 to 100,000 Pa · sec,
The moving wall is an outer surface of a rotating roll;
The space is preferably a wedge-shaped space sandwiched between the rotating roll and a non-rotating fixed wall.

The fluid is a viscoelastic fluid having a viscosity coefficient of 10 to 100,000 Pa · sec,
The moving wall is an outer surface of two rotating rolls arranged so that the rotation axis directions are parallel,
The space is a wedge-shaped space sandwiched between the two rotating rolls,
The behavior of the fluid is a rolling behavior of unvulcanized rubber in which the two rotating rolls are rotated in opposite directions and the fluid is discharged from the gap between the two rotating rolls to a belt-like sheet material having a constant thickness. It is preferable that there is.

According to another aspect of the present invention, the behavior of the fluid when the fluid is discharged from the space formed by the moving wall due to the shear flow of the fluid formed by the movement of the moving wall is calculated using a computer. It is a fluid flow simulation device that is reproduced by using it.
The flow simulation device is
A space model setting unit for setting a space model modeled by dividing the space by a plurality of grids;
A fluid model setting unit for setting a fluid model obtained by modeling the fluid;
A calculation unit that performs flow calculation of the fluid model based on a predetermined condition in the spatial model, and
The space model includes a corresponding boundary surface of the space model corresponding to a boundary surface of the space in contact with the surface of the moving wall, and moves in the moving direction of the transfer wall at the same speed as the moving speed of the moving wall. A thin film model having a uniform thickness along the corresponding boundary surface, and a main space model that is stationary regardless of the moving speed.

  According to the fluid flow simulation method and apparatus described above, the behavior of the fluid discharged from the space formed by the moving wall can be easily reproduced by the shear flow of the fluid formed by the movement of the moving wall.

It is a figure explaining the structure of the fluid flow simulation apparatus of this embodiment. It is a figure which shows the form which discharges the fluid from the narrow part where the space width of the wedge-shaped space pinched | interposed by the outer peripheral surface of two rotating rollers became the narrowest. It is a figure which shows an example of the space used as the preparation object of the space model used for this embodiment. It is a figure explaining the movement of the thin film model used by this embodiment. (A) is a figure which shows an example of the pressure distribution of the fluid model which acts on the corresponding boundary surface of the thin film model used by this embodiment, (b) is a figure explaining the definition of roller angle (theta). It is a figure which shows the result of the flow simulation of the conventional fluid model which used the main space model for all the space models, without using the thin film model used for this embodiment. (A) is a figure explaining the experiment which discharges | emits the rubber | gum sheet material from the clearance gap between rotating rollers, (b) is a figure which shows the result of the experiment shown to (a).

  Hereinafter, a fluid flow simulation method and apparatus according to the present invention will be described in detail with reference to the accompanying drawings.

  FIG. 1 is a diagram illustrating a configuration of a fluid flow simulation device (hereinafter simply referred to as a device) 10 according to the present embodiment.

  The device 10 is a device that reproduces the behavior of a fluid when the fluid is discharged from the space formed by the moving wall by the shear flow of the fluid formed by the movement of the moving wall. FIG. 2 is a diagram showing a mode in which fluid is discharged from a narrow portion where the width of the wedge-shaped space sandwiched between the outer peripheral surfaces of two rotating rollers is the narrowest as an example. In the example of FIG. 2, fluid is supplied from two extrusion screw feeders 32a and 32b to a wedge-shaped space formed by the outer peripheral surfaces of the two rotary rollers 30a and 30b. The supplied fluid is subjected to shear stress by the rotation of the rotating rollers 30a and 30b whose rotation axes are arranged in parallel to generate a shear flow. The rotation rollers 30a and 30b are arranged with a gap so that the outer peripheral surfaces thereof do not come into contact with each other. The rotation directions of the rotating rollers 30a and 30b are determined so as to move the supplied fluid toward the gap. However, since the fluid flowing by the shear flow proceeds toward the gap (narrow portion) where the width of the wedge-shaped space is the narrowest, the pressure acting on the fluid gradually increases and the flow velocity of some fluids decreases. However, there is a case where a part of the fluid is made to flow away from the gap (narrow part). Thus, the fluid that has reached the gap (narrow portion) is discharged from the wedge-shaped space in the X direction as a sheet material 31 having a certain thickness. The apparatus 10 performs a simulation that reproduces the behavior of the fluid from the supply to the discharge of the fluid. FIG. 3 is a diagram illustrating an example of a space that is a creation target of the space model used in the present embodiment. This space includes a wedge-shaped space sandwiched between the outer peripheral surfaces of the two rotating rollers 30a and 30b, and includes a space extension portion extending in the X direction from the narrow portion 36 of the wedge-shaped space. It should be noted that in the space that is the target of the model space, a wall that does not deform except for the boundary surface of the space that contacts the outer peripheral surface of the rotating rollers 30a and 30b and the tip of the space extension portion that becomes the sheet material 31 and is discharged in the X direction. It is treated as surrounded by.

The device 10 is configured by a computer, and includes a CPU 12, a memory 14 such as a RAM or a ROM, and an input / output unit 16. By calling and executing the program stored in the memory 14, the space model setting unit 18, the fluid model setting unit 20, and the calculation unit 22 are formed. That is, the space model setting unit 18, the fluid model setting unit 20, and the calculation unit 22 are software modules formed by executing a program, and the space model setting unit 18, the fluid model setting unit 20, and the calculation unit 22 The function is substantially controlled by the CPU.
An input operation system 24 for inputting conditions for an operator such as a keyboard and a mouse to set various conditions is connected to the input / output unit 16, and an input screen for model setting, a created model, A display 26 for displaying the calculation result is connected.

  The space model setting unit 18 sets a three-dimensional space model 38 that is modeled by dividing a three-dimensional wedge-shaped space 34 as shown in FIG. 3 by a plurality of grids in accordance with the set conditions. Here, the set space model includes a thin film model 40 and a main space model 42. The thin film model 40 includes the corresponding boundary surface 40a of the space model 38 corresponding to the outer peripheral surface of the rotating rollers 30a and 30b, that is, the boundary surface of the space in contact with the surface of the moving wall, and has the same speed as the moving speed of the moving wall. It is comprised so that it may move in the moving direction of the said movement wall. The thin film model 40 has a uniform thickness along the corresponding boundary surface 40a. On the other hand, the main space model 42 is a stationary model regardless of the moving speed of the outer peripheral surfaces of the rotating rollers 30a and 30b (in FIG. 4, the mesh division display is omitted from the main space model 42). In other words, the thin film model 40 is a very thin model formed between the corresponding boundary surface 40a on the space model 38 corresponding to the boundary surface between the rotating rollers 30a and 30b and the main space model 42. . The thickness of the thin film model 40 is preferably 50% or less of the space width (gap size) of the narrow portion 36 that is the gap between the rotating rollers 30a and 30b, from the viewpoint of accurately reproducing the behavior of the fluid. . The space model 38 is composed of a three-dimensional Euler element such as a polyhedron cell in addition to a tetrahedron and a hexahedron.

  The fluid model setting unit 20 sets a fluid model obtained by modeling a fluid. In the fluid model, shear viscosity, specific gravity, and the like, which are viscosity coefficients, are set according to the plastic material that becomes the viscoelastic fluid to be analyzed. Furthermore, specific heat, thermal conductivity, etc. are set as needed. The fluid model is set so as to fill the entire created space model 38. As for the shear viscosity, for example, viscoelastic properties (G ′ and G ″) are measured from a fluid to be analyzed under a plurality of temperature conditions, and the measurement result can be converted into a shear viscosity at a desired temperature.

  The calculation unit 22 uses the created space model 38 and the fluid model, and uses the three-dimensional velocity and pressure of the fluid model at the representative points of elements such as nodes in the space model 38 as unknowns, and the Navier-Stokes and mass conservation equations. Is calculated according to the finite element method and is discretized in accordance with the arrangement of the elements constituting the space model 38, and the value of the unknown is calculated. Since such a calculation method is a fluid calculation method using a well-known finite element method, description thereof is omitted.

  Since the thin film model 40 moves relative to the main space model 42, discontinuous elements in which no nodes are shared are formed at the boundary between the thin film model 40 and the main space model 42. For this reason, it is preferable to use a well-known sliding mesh method for passing the physical quantity of the fluid model between discontinuous elements. FIG. 4 is a diagram schematically illustrating the movement of the thin film model 40. The thin film model 40 moves in the same direction as the moving direction of the rotating rollers 30a and 30b at the same speed as the outer peripheral surfaces of the rotating rollers 30a and 30b. At this time, the calculation unit 22 performs the flow calculation of the fluid model when the fluid model comes out from the outlet 44 of the space model 38 under the condition that the thin film model 40 moves. As a boundary condition in the flow calculation, a pressure of atmospheric pressure is applied to a representative point of an element in contact with the outlet 44. Furthermore, conditions such as the supply amount of the fluid model are set in the supply port 46 provided on the opposite side to the outlet 44 in the X direction. In such a flow calculation, the fluid model in the thin film model 40 can reproduce the behavior of the fluid flowing in the same direction as the outer peripheral surface at the same speed as the moving wall that is the outer peripheral surface of the rotary rolls 30a and 30b.

The flow calculation result calculated by the calculation unit 22 is stored in the memory 14, and the calculation unit 22 obtains the velocity distribution at each position of the fluid model, and the fluid model corresponds to the corresponding boundary surface 40 a of the thin film model 40. The pressure of the fluid model acting on is calculated, and the calculation result is displayed on the display 26.
FIG. 5A is a diagram illustrating an example of the pressure distribution of the fluid model acting on the corresponding boundary surface 40 a of the thin film model 40. FIG. 5 (a) also shows the measurement results of the pressure that the rotating rollers 30a and 30b receive from the fluid when the sheet material 31 is actually produced using the rotating rollers 30a and 30b under the same conditions as in the simulation described above. . The horizontal axis of the graph in FIG. 5A indicates the roller angle θ. FIG. 5B illustrates the definition of the roller angle θ. The roller angle θ = 0 is the position of the narrow portion 36 where the space width between the rotating rollers 30a and 30b is the narrowest, and the direction in which the roller angle θ is negative is the direction opposite to the X direction.
As can be seen from FIG. 5A, the calculation result calculated using the space model 38 using the thin film model 40 shows a result approximate to the measurement result.

  FIG. 6 is a diagram showing a flow simulation result of a conventional fluid model in which the main space model 42 is used for all the space models 38 without using the thin film model 40 for the space model 38. In the conventional flow calculation, the same speed as the moving speed of the outer peripheral surface of the rotating rollers 30a and 30b is given as a boundary condition to the corresponding boundary surface of the main space model 42 corresponding to the boundary surface of the space in contact with the rotating rollers 30a and 30b. Flow calculations were performed. As shown in FIG. 6, in the calculation result, the pressure is very small and greatly deviates from the measurement result.

  Thus, since the flow simulation method of this embodiment reproduces the pressure distribution similar to the measurement result, it can be said that the behavior of the fluid is accurately reproduced. Thus, in this embodiment, the behavior of the fluid discharged from the space formed by the moving wall is facilitated by the shear flow of the fluid formed by the movement of the moving wall such as the outer peripheral surfaces of the rotating rollers 30a and 30b. Can be reproduced.

  In this way, the thin film model 40 is formed in the space model 38 because there is a thin film layer that moves at the same speed and does not flow on the outer peripheral surfaces of the rotating rollers 30a and 30b, as will be described later. FIG. 7A shows a state in which the black rubber thin film 50 is formed on the outer peripheral surface of the rotating roller 30a among the rotating rollers 30a and 30b, and the white rubber 52 is replaced with the outer peripheral surface of the rotating roller 30a and the rotating roller 30b. It is a figure explaining the experiment which is supplied to the wedge-shaped space between outer peripheral surfaces, and discharges | emits the rubber | gum sheet material 31 from the clearance gap between rotating rollers 30a and 30b. At this time, it was found that a black rubber layer having a certain thickness was formed on the sheet material 31 without being flowed by the rotation of the rotating rollers 30a and 30b. FIG. 7B is a diagram showing the results of the experiment shown in FIG. 7A, in which the horizontal axis represents the gap between the rotating rollers 30a and 30b, and the vertical axis represents the thickness W of the black rubber layer. FIG. As can be seen from FIG. 7B, the thickness W of the rubber layer in which the rubber near the outer peripheral surface of the rotating roller 30a is formed with a constant thickness without flowing due to the rotation of the rotating rollers 30a and 30b is: It can be seen that it depends on the gap (space width of the narrow portion 36). Therefore, even when the sheet material 31 is produced as shown in FIG. 2 using the rotating rollers 30a and 30b, the thin film layer of the fluid located near the outer peripheral surface of the rotating rollers 30a and 30b has the rotating rollers 30a and 30b. It can be said that the sheet material 31 is discharged as part of the sheet material 31 without being moved by the shear flow. Therefore, as in this embodiment, the uniform thickness along the corresponding boundary surface 40a configured to move in the moving direction of the outer peripheral surface at the same speed as the moving speed of the outer peripheral surfaces of the rotating rollers 30a and 30b. It can be said that the use of the thin film model 38 having the above is appropriate in calculating the fluid flow.

  In the fluid flow simulation method using such an apparatus 10, a spatial model modeled by dividing a space formed by moving walls such as the outer peripheral surfaces of the rotating rollers 30 a and 30 b by a plurality of grids is set. . In addition, a fluid model in which a fluid such as a viscoelastic fluid is modeled is set. In the created spatial model, the fluid model is calculated based on a predetermined condition. At this time, the space model includes the corresponding boundary surface 40a of the space model corresponding to the boundary surface of the above-mentioned space in contact with the surface of the moving wall, and moves in the moving direction of the transfer wall at the same speed as the moving speed of the moving wall. A thin film layer model 40 having a uniform thickness along the corresponding boundary surface 40a, and a main space model 42 that is stationary regardless of the moving speed.

  The above-described space is, for example, a wedge-shaped space in which the space width of the space formed by the moving wall gradually narrows along the moving direction of the moving wall, and the fluid discharge is performed with the narrowest space width of the wedge-shaped space. It is preferable to discharge from the narrowed portion. In this case, the moving wall is not limited to the outer peripheral surface of the rotating roller. The moving wall may be, for example, a flat plate surface or a cylindrical outer peripheral surface having a non-circular cross section such as an ellipse. Further, the above-described space may not be a space between two moving walls as in this embodiment, but may be a space formed by a moving wall and a fixed wall.

  The thickness of the thin film model 40 is preferably 50% or less of the space width of the narrow part 36 where the space width of the wedge-shaped space is the narrowest from the viewpoint of accurately calculating the fluid flow. The thickness of the thin film model 40 is more preferably 30% or less of the space width of the narrow portion 36.

  Further, it is preferable that the thickness of the thin film model 40 is changed in accordance with the space width of the narrow portion 36 described above from the viewpoint of accurately calculating the fluid flow. Actually, when the sheet material 31 is produced, the surface of the sheet material 31 is formed by the fluid that moves following the moving wall without being affected by the flow of the fluid, and the thickness of this portion is shown in FIG. This is because it changes according to the space width (gap) of the narrow portion 36 as shown in FIG.

  In the flow calculation, it is preferable to calculate the pressure at which the fluid model in the space model 38 acts on the corresponding boundary surface.

  The fluid used in the present embodiment is preferably, for example, a viscoelastic fluid having a viscosity coefficient of 10 to 100,000 Pa · sec, such as unvulcanized rubber. In this case, the moving speed of the moving wall is, for example, 1 to 10 m / sec, preferably 2 to 8 m / sec, and more preferably 3 to 7 m / sec. The flow simulation method of the present embodiment is also suitable when the moving wall is, for example, the outer peripheral surface of a rotating roll, and the space is a wedge-shaped space sandwiched between the rotating roll and a non-rotating fixed wall. Can be implemented. Alternatively, the moving wall is, for example, the outer surface of two rotating rolls arranged so that the rotation axis directions are parallel, and the space is a wedge-shaped space sandwiched between the two rotating rolls. At this time, the behavior of the fluid is the rolling of the unvulcanized rubber that rotates the two rotating rolls in the opposite direction and discharges the belt-like sheet material of a certain thickness from the narrow portion where the fluid is sandwiched between the two rotating rolls. It is the behavior.

  The fluid flow simulation method and apparatus of the present invention have been described in detail above, but the present invention is not limited to the above-described embodiment, and various improvements and modifications may be made without departing from the spirit of the present invention. Of course.

10 Flow simulation device 12 CPU
14 Memory 16 Input / output unit 18 Spatial model setting unit 20 Fluid model setting unit 22 Calculation unit 24 Input operation system 26 Display 30a, 30b Rotating roller 31 Sheet material 32a, 32b Screw feeder 34 Wedge-like space 36 Narrow part 38 Spatial model 40 Thin film Model 40a Corresponding interface 44 Exit

Claims (8)

The fluid flow simulation method reproduces, using a computer, the behavior of the fluid when the fluid is discharged from the space formed by the moving wall by the shear flow of the fluid formed by the movement of the moving wall. And
Setting a space model modeled by dividing the space by a plurality of grids;
Setting a fluid model that models the fluid;
Performing a flow calculation of the fluid model based on defined conditions in the spatial model, and
The space model includes a corresponding boundary surface of the space model corresponding to a boundary surface of the space in contact with the surface of the moving wall, and moves in the moving direction of the transfer wall at the same speed as the moving speed of the moving wall. A fluid flow simulation method comprising: a thin film model having a uniform thickness along the corresponding boundary surface, and a main space model stationary regardless of the moving speed.   The space is a wedge-shaped space in which the space width is gradually narrowed along the moving direction of the moving wall, and the fluid is discharged from a narrow portion where the space width of the wedge-shaped space is the narrowest. The fluid flow simulation method according to claim 1, wherein:   The fluid flow simulation method according to claim 2, wherein a thickness of the thin film model is 50% or less of a space width of the narrow portion.   The fluid flow simulation method according to claim 2 or 3, wherein a thickness of the thin film model is changed according to a space width of the narrow portion.   5. The fluid flow simulation method according to claim 1, wherein, in the flow calculation, a pressure applied by the fluid model to the corresponding boundary surface is calculated. The fluid is a viscoelastic fluid having a viscosity coefficient of 10 to 100,000 Pa · sec,
The moving wall is an outer surface of a rotating roll;
The fluid flow simulation method according to claim 1, wherein the space is a wedge-shaped space sandwiched between the rotating roll and a non-rotating fixed wall. The fluid is a viscoelastic fluid having a viscosity coefficient of 10 to 100,000 Pa · sec,
The moving wall is an outer surface of two rotating rolls arranged so that the rotation axis directions are parallel,
The space is a wedge-shaped space sandwiched between the two rotating rolls,
The behavior of the fluid is a rolling behavior of unvulcanized rubber in which the two rotating rolls are rotated in opposite directions and the fluid is discharged from the gap between the two rotating rolls to a belt-like sheet material having a constant thickness. The fluid flow simulation method according to any one of claims 1 to 5. The fluid flow simulation device reproduces, using a computer, the behavior of the fluid when the fluid is discharged from the space formed by the moving wall by the shear flow of the fluid formed by the movement of the moving wall. And
A space model setting unit for setting a space model modeled by dividing the space by a plurality of grids;
A fluid model setting unit for setting a fluid model obtained by modeling the fluid;
A calculation unit that performs flow calculation of the fluid model based on a predetermined condition in the spatial model, and
The space model includes a corresponding boundary surface of the space model corresponding to a boundary surface of the space in contact with the surface of the moving wall, and moves in the moving direction of the transfer wall at the same speed as the moving speed of the moving wall. A fluid flow simulation apparatus comprising: a thin film model having a uniform thickness along the corresponding boundary surface; and a main space model that is stationary regardless of the moving speed.

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