JP6524686B2 - Method and apparatus for fluid flow simulation - Google Patents

Description

  The present invention relates to a fluid flow simulation method and apparatus that reproduces, 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 the behavior of fluid flow by numerical simulation using a computer have been performed. For example, a numerical value that reproduces a rolling process in which a visco-elastic fluid such as rubber is subjected to shear by a moving wall such as a rotating roll to make the visco-elastic fluid into a fluid state and processing this visco-elastic fluid into a sheet Simulation is also being considered.

  For example, a wedge-like space formed between two rotating rolls is divided into meshes to create a space model, and a fluid model that models a viscoelastic fluid is set in the space model, and in this space model, The flow calculation of the fluid model is performed based on the defined conditions.

  In addition, a fluid flow simulation method is also known in which the state of fluid in a chamber having a wall surface is calculated using a computer (Patent Document 1). Specifically, a chamber model in which a chamber is modeled with a finite number of elements is set, and a material model in which a fluid is modeled is set. Furthermore, a material model is disposed in the chamber model, and flow calculation is performed based on predetermined conditions. In the flow calculation, the slip velocity of the material model is defined at the interface between the material model and the wall of the chamber model, and the slip velocity is calculated by a specific equation.

JP, 2013-256026, A

However, in the simulation of the behavior of the visco-elastic fluid in the wedge-like space between two rotating rolls as described above, the calculation result of the pressure at which the flow model of the visco-elastic fluid acts on the wall model of the rotating roll is a measurement result It did not correspond, and it turned out that the value of pressure has become a value near 0 very much by the calculation result of pressure.
On the other hand, in the above-mentioned method of carrying out fluid flow simulation of a fluid by giving a slip velocity to the material model at the interface between the material model and the wall surface of the chamber model, it is possible to stabilize the fluid flow calculation of high viscosity fluid. It is supposed to be possible. However, in the method, there is a complication of predetermining the Fslip constant in order to determine the slip speed.

  Therefore, the present invention uses a computer to reproduce 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. It is an object of the present invention to provide a fluid flow simulation method and apparatus that can be reproduced.

One aspect of the present invention is a space formed by a moving wall, and a narrow portion of the wedge-like space whose space width is gradually narrowed along the moving direction of the moving wall, the narrowing portion having the narrowest space width. from the behavior of the fluid in the fluid is discharged Rutoki by shear flow of the fluid to be formed by the movement of the moving wall, a flow simulation method of the fluid reproduced using computer.
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 flow calculation of the fluid model based on defined conditions in the space model;
The space model includes a corresponding boundary of the space model corresponding to the boundary of the space in contact with the surface of the moving wall, and moves in the moving direction of the moving wall at the same speed as the moving speed of the moving wall. The thin film model having a uniform thickness along the corresponding interface, and the main space model which is stationary regardless of the moving speed.

  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.

  Preferably, in the flow calculation, a pressure at which the fluid model acts on the corresponding interface is calculated.

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

The fluid is a visco-elastic fluid having a viscosity coefficient of 10 to 100,000 Pa · s,
The moving wall is the outer surface of two rotating rolls arranged such that the rotational axis directions are parallel.
The space is a wedge-like space sandwiched by the two rotating rolls,
The behavior of the fluid is a behavior of rolling of unvulcanized rubber in which the two rotating rolls are rotated in the opposite direction to discharge the fluid from the gap between the two rotating rolls and a strip-shaped sheet material of a certain thickness. Preferably.

Another aspect of the present invention is a space formed by a moving wall, wherein the space width is the narrowest among the wedge-like spaces whose space width gradually narrows along the moving direction of the moving wall. The fluid flow simulation apparatus reproduces, using a computer, the behavior of the fluid when the fluid is discharged from the narrowed portion by the shear flow of the fluid formed by the movement of the moving wall .
The flow simulation device is
A space model setting unit configured to set a space model modeled by dividing the space by a plurality of grids;
A fluid model setting unit configured to set a fluid model that models the fluid;
A calculation unit for performing flow calculation of the fluid model based on defined conditions in the space model;
The space model includes a corresponding boundary of the space model corresponding to the boundary of the space in contact with the surface of the moving wall, and moves in the moving direction of the moving wall at the same speed as the moving speed of the moving wall. The thin film model having a uniform thickness along the corresponding interface, and the main space model which is stationary regardless of the moving speed.

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

It is a figure explaining the composition of the flow simulation device of the fluid of this embodiment. It is a figure which shows the form which discharges | emits a fluid from the narrow part where space width of the wedge shaped space pinched | interposed by the outer peripheral surface of two rotation rollers became the narrowest. It is a figure which shows an example of the space used as creation object of the space model used for this embodiment. It is a figure explaining 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 | compatible interface 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 space models, without using the thin film model used for this embodiment. (A) is a figure explaining the experiment which discharges the sheet material of rubber from the crevice of a rotation roller, and (b) is a figure showing the result of the experiment shown to (a).

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

  FIG. 1 is a view for explaining the configuration of a fluid flow simulation apparatus (hereinafter simply referred to as an apparatus) 10 according to the present embodiment.

  The apparatus 10 is an apparatus that reproduces 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. FIG. 2 is a view showing an example in which the fluid is discharged from the narrow portion where the space width of the wedge-like space sandwiched by the outer peripheral surfaces of the two rotating rollers is the narrowest. In the example of FIG. 2, the fluid is supplied from the two extrusion screw feeders 32a and 32b to the wedge-like space formed by the outer peripheral surfaces of the two rotating rollers 30a and 30b. The supplied fluid is subjected to shear stress by rotation of the rotating rollers 30a and 30b whose rotation axes are arranged in parallel to form a shear flow. The rotating rollers 30a and 30b are disposed with a gap so that the outer peripheral surfaces thereof do not contact. The rotating rollers 30a and 30b are oriented in rotation so as to move the supplied fluid toward the gap. However, since the fluid flowing by the shear flow travels toward the narrowest gap (narrowed portion) of the space width of the wedge-like space, the pressure acting on the fluid gradually increases and the flow velocity of some fluid decreases. The fluid may stagnate, and part of the fluid may create a flow away from the gap (the narrow portion). Thus, the fluid that has reached the gap (narrowed portion) is discharged from the wedge-shaped space in the X direction as a sheet 31 having a constant 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 showing an example of a space to be a creation target of a space model used in the present embodiment. This space includes a wedge-like space sandwiched between the outer peripheral surfaces of the two rotating rollers 30a and 30b, and includes a space extension extending in the X direction from the narrow portion 36 of the wedge-like space. In the space to be the target of the model space, a wall which does not deform except for the boundary surface of the space contacting the outer peripheral surface of the rotating rollers 30a and 30b and the tip of the space extension portion discharged as the sheet material 31 in the X direction. Treated as enclosed by.

The apparatus 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. The space model setting unit 18, the fluid model setting unit 20, and the calculation unit 22 are formed by calling and executing a program stored in the memory 14. 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 functions are substantially controlled by the CPU.
The input / output unit 16 is connected to an input operation system 24 for inputting conditions for an operator such as a keyboard and a mouse to set various conditions, and further, an input screen for model setting, a created model, and the like. A display 26 for displaying the calculation result is connected.

  The space model setting unit 18 sets a three-dimensional space model 38 modeled by dividing the three-dimensional wedge-like space 34 as shown in FIG. 3 by a plurality of grids according to the set conditions. Here, the space model to be set includes the thin film model 40 and the main space model 42. The thin film model 40 includes the corresponding boundary surface 40a of the space model 38 corresponding to the moving 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. In the moving direction of the moving wall. The thin film model 40 has a uniform thickness along the corresponding interface 40a. On the other hand, the main space model 42 is a model which is stationary regardless of the moving speed of the outer peripheral surface of the rotation rollers 30a and 30b (in FIG. 4, the mesh division display of the main space model 42 is omitted). 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 with the rotating rollers 30a and 30b and the main space model 42. . It is preferable that the thickness of the thin film model 40 is 50% or less of the space width (size of the gap) of the narrow portion 36 which 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 tetrahedrons, hexahedrons, etc., and three-dimensional Euler elements such as polyhedron cells.

  The fluid model setting unit 20 sets a fluid model obtained by modeling a fluid. In the fluid model, a shear viscosity, a specific gravity, or the like, which is a viscosity coefficient, is set in accordance with a plastic material to be a viscoelastic fluid to be analyzed. Furthermore, specific heat, thermal conductivity and the like are set as necessary. The fluid model is set to fill the entire space model 38 created. The shear viscosity can be converted, for example, from the fluid to be analyzed to the shear viscosity of a desired temperature based on the measurement of the visco-elastic properties (G ′ and G ′ ′) under a plurality of temperature conditions.

  The calculation unit 22 uses the generated space model 38 and the fluid model to calculate the Navier-Stokes and mass conservation equations with 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. Is formulated according to the finite element method, and the value of the above unknown is calculated from an equation discretized in accordance with the arrangement of the elements constituting the space model 38. Such a calculation method is a calculation method of a fluid using a known finite element method, so the description thereof is omitted.

  In addition, since the thin film model 40 moves relative to the main space model 42, a discontinuous element in which no node is shared is 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 physical quantities of 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 at the same speed as the outer peripheral surface of the rotating rollers 30a and 30b, and in the same direction as the moving direction of the rotating rollers 30a and 30b. At this time, the calculation unit 22 performs flow calculation of the fluid model when the fluid model exits from the outlet 44 of the space model 38 under the condition that the thin film model 40 moves. A pressure of atmospheric pressure is applied to a representative point of the element in contact with the outlet 44 as a boundary condition in the flow calculation. Furthermore, conditions such as the supply amount of the fluid model are set in the outlet 44 and the supply port 46 provided on the opposite side in the X direction. In such 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 which is the outer peripheral surface of the rotating rolls 30a and 30b.

The result of the flow calculation 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 interface 40a of the thin film model 40. The pressure of the fluid model acting on the surface is calculated, and the calculation result is displayed on the display 26.
FIG. 5A is a view showing an example of the pressure distribution of the fluid model acting on the corresponding interface 40 a of the thin film model 40. FIG. 5A 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 manufactured using the rotating rollers 30a and 30b under the same conditions as the above-described simulation. . The horizontal axis of the graph of FIG. 5A indicates the roller angle θ. FIG. 5B is a view for explaining 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 30 a and 30 b 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 the result approximating the measurement result.

  FIG. 6 is a view showing the result of flow simulation of the conventional fluid model using the main space model 42 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 boundary speed as the movement speed of the outer peripheral surface of the rotary rollers 30a and 30b is given as the 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 rotary rollers 30a and 30b. The flow was calculated. As shown in FIG. 6, in the calculation result, the pressure is extremely small and largely deviates from the measurement result.

  As described above, the flow simulation method of the present embodiment reproduces the pressure distribution similar to the measurement result, so that it can be said that the reproduction of the behavior of the fluid is performed with high accuracy. As described above, in the present embodiment, the shear flow of the fluid formed by the movement of the moving wall such as the outer peripheral surface of the rotating rollers 30a and 30b facilitates the behavior of the fluid discharged from the space formed by the moving wall. Can be reproduced.

  Thus, in the space model 38, the thin film model 40 is formed because the thin film layer which is moved at the same speed and does not flow is present on the outer peripheral surface of the rotating rollers 30a and 30b, as described later. FIG. 7A shows that the white rubber 52 is formed on the outer peripheral surface of the rotating roller 30a and the rotating roller 30b in a state where 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. It is a figure explaining an experiment which is supplied to the wedge-like space between outer peripheral surfaces, and is made to discharge sheet material 31 of rubber from a crevice between rotation rollers 30a and 30b. At this time, it was found that a black rubber layer having a predetermined thickness was formed on the sheet material 31 without being flowed by the rotation of the rotating rollers 30a and 30b. FIG. 7 (b) is a graph showing the results of the experiment shown in FIG. 7 (a), with the gap between the rotating rollers 30a and 30b as the horizontal axis and the thickness W of the black rubber layer as the vertical axis. FIG. As can be seen from FIG. 7B, the thickness W of the rubber layer formed with a constant thickness without the rubber in the vicinity of the outer peripheral surface of the rotating roller 30a flowing by the rotation of the rotating rollers 30a and 30b is It can be seen that it is determined according to the gap (the space width of the narrow portion 36). Therefore, even when the sheet material 31 is manufactured as shown in FIG. 2 using the rotating rollers 30a and 30b, the thin film layer of the fluid located in the vicinity of the outer peripheral surface of the rotating rollers 30a and 30b is the rotating rollers 30a and 30b. It moves with the outer peripheral surface of the sheet, and is discharged as a part of the sheet material 31 without flowing by the shear flow. Therefore, as in the present 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 surface of the rotating rollers 30a, 30b. The use of the thin film model 38 having the following equation is appropriate for calculating the fluid flow.

  In a fluid flow simulation method using such an apparatus 10, a space model modeled by dividing a space formed by moving walls such as outer peripheral surfaces of the rotating rollers 30a and 30b by a plurality of grids is set. . Also, a fluid model that models a fluid such as a visco-elastic fluid is set. In the created space model, flow calculation of the fluid model is performed based on predetermined conditions. 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. The thin film layer model 40 having a uniform thickness along the corresponding interface surface 40a, and the main space model 42 stationary regardless of the moving speed.

  The above-mentioned space is, for example, a wedge-like 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 discharge of the fluid is the narrowest space width of the wedge-like 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, the surface of a flat plate or a cylindrical outer peripheral surface having a non-perfect circular cross section such as an ellipse. Further, the above-mentioned space may not be a space sandwiched by two moving walls as in the present embodiment, but may be a space formed by the moving wall and the fixed wall.

  The thickness of the thin film model 40 is preferably 50% or less of the space width of the narrowest narrow portion 36 of the space width of the wedge-shaped space 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.

  In addition, it is preferable to change the thickness of the thin film model 40 in accordance with the space width of the narrow portion 36 described above, from the viewpoint of accurately performing the fluid flow calculation. In fact, when producing the sheet material 31, the surface of the sheet material 31 is not influenced by the flow of the fluid, but is formed by the fluid moving following the moving wall, and the thickness of this portion is as shown in FIG. As shown in the graph, the width changes according to the space width (gap) of the narrow portion 36.

  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 interface.

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

  As mentioned above, although the fluid flow simulation method and apparatus of the present invention were explained in detail, the present invention is not limited to the above-mentioned embodiment, and various improvements and changes may be made within the scope of the present invention. Of course.

10 Flow simulation device 12 CPU
14 memory 16 input / output unit 18 space model setting unit 20 fluid model setting unit 22 calculation unit 24 input operation system 26 display 30a, 30b rotary roller 31 sheet material 32a, 32b screw feeder 34 wedge shaped space 36 narrow portion 38 space model 40 thin film Model 40a corresponding interface 44 exit

Claims (7)

The space formed by the moving wall, of the wedge-like space whose space width gradually narrows along the moving direction of the moving wall, the movement of the moving wall from the narrow portion where the space width becomes the narrowest wherein the behavior of the fluid of the fluid is discharged Rutoki, a flow simulation method of the fluid reproduced using computer by shear flow of the fluid to be formed by,
Setting a space model modeled by dividing the space by a plurality of grids;
Setting a fluid model that models the fluid;
Performing flow calculation of the fluid model based on defined conditions in the space model;
The space model includes a corresponding boundary of the space model corresponding to the boundary of the space in contact with the surface of the moving wall, and moves in the moving direction of the moving wall at the same speed as the moving speed of the moving wall. A fluid flow simulation method of a fluid comprising: a thin film model having a uniform thickness along the corresponding interface; and a main space model which is stationary regardless of the moving speed. The thickness of the film models, wherein more than 50% of the space widths of the narrow portions, flow simulation method of a fluid according to claim 1. The thickness of the thin film model changes depending on the spatial width of the narrow portion, the flow simulation method of a fluid according to claim 1 or 2. The fluid flow simulation method according to any one of claims 1 to 3 , wherein in the flow calculation, a pressure of the fluid model acting on the corresponding interface is calculated. The fluid is a visco-elastic fluid having a viscosity coefficient of 10 to 100,000 Pa · s,
The moving wall is an outer surface of a rotating roll,
The fluid flow simulation method according to any one of claims 1 to 4 , wherein the space is a wedge-like space sandwiched by the rotating roll and a non-rotating fixed wall. The fluid is a visco-elastic fluid having a viscosity coefficient of 10 to 100,000 Pa · s,
The moving wall is the outer surface of two rotating rolls arranged such that the rotational axis directions are parallel.
The space is a wedge-like space sandwiched by the two rotating rolls,
The behavior of the fluid is a behavior of rolling of unvulcanized rubber in which the two rotating rolls are rotated in the opposite direction to discharge the fluid from the gap between the two rotating rolls and a strip-shaped sheet material of a certain thickness. The flow simulation method of the fluid according to any one of claims 1 to 4 . The space formed by the moving wall, of the wedge-like space whose space width gradually narrows along the moving direction of the moving wall, the movement of the moving wall from the narrow portion where the space width becomes the narrowest A fluid flow simulation apparatus for reproducing the behavior of the fluid when the fluid is discharged by the shear flow of the fluid formed by using a computer,
A space model setting unit configured to set a space model modeled by dividing the space by a plurality of grids;
A fluid model setting unit configured to set a fluid model that models the fluid;
A calculation unit for performing flow calculation of the fluid model based on defined conditions in the space model;
The space model includes a corresponding boundary of the space model corresponding to the boundary of the space in contact with the surface of the moving wall, and moves in the moving direction of the moving 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 interface; and a main space model which is stationary regardless of the moving speed.

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