JPH11211744A - Mixing data analysis system - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a mixing data analysis system which enjoys a large degree of design freedom and can cut a design term and design costs. SOLUTION: A particle-tracking analyzing part 3 combines data by interpolation calculation on the basis of discrete flow velocity field data obtained as a result of a heat flow analysis at a heat flow-analyzing part 2, thereby obtaining data on path of particle. A mixing data-evaluating analyzing part 4 calculates for each flow locus line a change of a vector connecting a point on the path of particle and points on a group of path of particles present within a predetermined distance from the point after a predetermined time, obtains a transformation matrix representing the change of the vector by linear approximation, sets as an extension rate of an optional three-dimensional area at the section a maximum component of a specific value corresponding to a maximum extension rate in a specific vector direction of the area transformed by the transformation matrix, repeatedly obtains the extension rate via every predetermined time up to a predetermined position of the path of particle, and indexes a history of mixture along the flow locus lines with an average value of the extension rates.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a mixer such as an extruder screw or a stirrer and a mixing performance analysis system for evaluating the mixing performance of a part of the mixer by software.

[0002]

2. Description of the Related Art As a method for quantitatively evaluating the mixing performance, there has been conventionally a method of judging based on an experimental result of a dispersion state of a tracer injected in a minute amount into an apparatus.
Vector representation of concentration distribution in the apparatus (Chemical Engineering Transactions, 1986 Edition, No. 12, p. 459), information entropy (Chemical Engineering, 1974 Edition, No. 38,
815).

[0003]

However, in the above-mentioned conventional evaluation method, the judgment is made based on the experimental result of the dispersion state of the tracer injected into the apparatus in a very small amount. Each time, it is necessary to repeat the experiment under the same conditions, and it takes time and effort to evaluate one condition. In addition, for a system having a complicated mixer shape, it is difficult to adopt this evaluation method from the viewpoint of difficulty in manufacturing a prototype and evaluating the results. In addition, when using for design, a prototype must be created for each different design parameter, and there is a problem that the degree of freedom of design is small, the cost is high, and the development time is long.

SUMMARY OF THE INVENTION The present invention has been made to solve the above-mentioned problems, and its object is to evaluate the mixing performance using the concept of eigenvalues based on the flow velocity field data obtained as a result of the heat flow analysis, thereby designing the design. An object of the present invention is to provide a mixed performance analysis system having a large degree of freedom and capable of reducing a design period and a design cost.

[0005]

In order to solve the above-mentioned problems, a mixing performance analysis system of the present invention uses a polyhedral cell element to form a flow path of an object to be mixed with a target mixing system.
The three-dimensional components of the continuous mesh, motion equation, energy equation, and constitutive equation governing heat flow are divided into predetermined three-dimensional components and the physical property data of the mixture to be mixed. By solving under the above conditions, for each grid point of the mesh, a heat flow analysis unit that obtains flow velocity field data consisting of its coordinates and flow velocity,
Initially place a predetermined number of virtual particles having no physical size and mass at a predetermined position in the mixture flow path, based on the discretized flow velocity field data obtained as a result of the heat flow analysis. A particle tracking analysis unit that obtains trajectory data of each virtual particle by interpolating or extrapolating the flow velocity at the virtual particle position, and a trajectory of each virtual particle obtained by the particle tracking analysis unit And a point on the trajectory,
A change after a predetermined time (development time) of a vector connecting a point on a nearby trajectory group existing within a predetermined distance from this point is calculated, and a conversion matrix representing the change of the vector is obtained by linear approximation. The maximum component of the eigenvalue corresponding to the maximum value of the stretch rate in the eigenvector direction of the area when an arbitrary three-dimensional area is converted by the conversion matrix is defined as the stretch rate of the area in the section, and this stretch rate is set to the predetermined value. Iteratively obtains to the predetermined position of the trajectory every time, indexes the mixing history along each trajectory by the average value, and mixes by the average value of the index value data obtained for each trajectory. A mixed performance evaluation analysis unit for analyzing the performance of the system.

[0006]

Embodiments of the present invention will be described below with reference to the drawings.

FIG. 1 is an overall configuration diagram of a mixing performance evaluation and analysis system according to the present invention, which is roughly divided into a model shape creating section 1, a heat and fluid analysis section 2, a particle tracking analysis section 3, and a mixing performance evaluation and analysis section 4. It is constituted by.

FIG. 2 shows a more specific configuration of the model shape creation unit 1 and the heat flow analysis unit 2. Model shape creation unit 1
Is a preprocessor that divides the flow path of the mixture into a three-dimensional minute area using a polyhedral (hexahedral or tetrahedral) cell element for the target mixing system, and creates mesh data for performing thermal fluid analysis. (Mesh generator), and the preprocessor creates mesh data based on input data defining main parameters characterizing the inside of the mixer and the number of divisions in each of three-dimensional directions.

The heat-fluid analysis unit 2 converts all three-dimensional components of the continuous equation, the equation of motion, the energy equation, and the constitutive equation governing the heat flow into predetermined boundary conditions (wall temperature, etc.) for the generated mesh data. ) And the flow analysis to be solved based on the physical property value data of the mixture. The flow analysis is roughly divided into a flow analysis section and a temperature analysis section. Place,
The flow velocity field is repeatedly calculated until it reaches a stable state (steady state). For each grid point of the mesh, the flow velocity field (coordinates and velocity vectors), temperature field (coordinates and temperature), and stress field are discretized. (Coordinates and stress tensor) and strain field (coordinates and strain tensor) are obtained as output.

[0010] That is, the heat flow analysis referred to here means that the flow path data (mesh data) to be mixed is determined based on various conditions (boundary wall temperature, temperature of the mixture, rotation speed of the mixing rotor, etc.). The flow field, the temperature field, the stress field, and the strain field are repeatedly calculated until a convergent solution is finally obtained for a mixed system. As the method, a finite element method, a finite difference method, a finite volume method and the like are typical. However, any method other than the above may be used as long as a flow velocity field is required.

The particle tracking analysis unit 3 calculates trajectory data from the discretized flow velocity field obtained by the heat flow analysis. FIG. 3 shows an analysis flowchart in the particle tracking analysis unit 3.

That is, the mesh data created by the preprocessor 1 and the flow velocity field data obtained from the results of the heat flow analysis are read from each file (step S1).
Next, a predetermined number of virtual particles having no size and mass of the analysis region defined by the input data are initially arranged at predetermined positions in the flow path of the mixture (step S2). Then, the position coordinates of the virtual particle are detected, and the flow velocity of the virtual particle is interpolated from the flow velocity of the element including the coordinate and the surrounding elements (step S3). Based on this, the displacement after the minute unit time step dt is calculated (step S4). Then, the flow velocity at that position is calculated (from step S5, S6 to step S3), and the displacement after the next minute unit time step dt is calculated (step S4). The calculation of such flow velocity and the calculation of displacement
By repeating the process until the virtual particle reaches the coordinate value or time (Tend) specified by the input data (steps S5 and S6), for each minute unit time step dt, the time t and the coordinates (x, y, z)
Is obtained as many as the number of virtual particles in the initial arrangement (step S).
7). The analysis procedure itself of the particle tracking analysis unit 3 is as follows.
A conventional procedure that has been performed conventionally can sufficiently cope with the problem.

The mixing performance evaluation / analysis unit 4 evaluates the mixing performance of the mixing system according to the following algorithm.

As shown in FIG. 4, a spherical area (left in FIG. 4) having a predetermined radius ε is set from a point [r ₀ ^t ] on a certain trajectory line at a certain time t, and the inside of the spherical area is set. A point [r _i ^t ] (i = 1,..., M) on a certain nearby trajectory is searched for. Then, assuming that a vector connecting [r ₀ ^t ] and [r _i ^t ] is [y _i ^t ], [y _i ^t ] is given by the following equation (1).
Becomes

[0015]

(Equation 1)

[R ₀ ^t ] and [r _i ^t ] (i = 1,...)
., N) the position [r ₀ after a minute unit time step dt
^{t + dt} ], [r _i ^{t + dt} ] (i = 1,..., M), and calculates the Bertle connecting [r ₀ ^{t + dt} ] and [r _i ^{t + dt} ] to [y _i ^{t + dt} ], [y _i ^{t + dt} ] is given by the following equation (2).

[0017]

(Equation 2)

If the radius ε of the sphere and the unit time step dt are made sufficiently small, [y _i ^{t + dt} ] and [y _i ^t ] can be linearly approximated, and using a certain matrix G _i ,

[0019]

(Equation 3)

Can be expressed as Specifically G
_i is the error represented by the following equation (4)

[0021]

(Equation 4)

Is determined by the least-squares method so that is minimized. That is, when the first kl component of G _i was g _kl, minimum conditions,

[0023]

(Equation 5)

## EQU1 ## When performing the calculation in the above equation, eventually, G _i is given by the following equation.

[0025]

(Equation 6)

Where the kl components of the matrices V and C in the above equation are:

[0027]

(Equation 7)

Is as follows. In the case of the present invention, physical degeneration of [y _i ^t ] cannot occur, so in the case of three dimensions,
If n ≧ 3, uniquely G _i from the above equation can be determined.

Next, as shown in FIG. 5, until the sum of the minute unit time steps dt reaches a predetermined development time T0, the above processing [calculation of the equations (1) to (8)] is repeated. a transformation matrix G _t representing a transformation area per unit time step dt is obtained by linear approximation.

Thereafter, a matrix G _all representing the transformation of the area during the predetermined development time T0 is obtained by synthesizing the matrix G _t for each step.

The radius ε of the microsphere and the development time T0 in the above processing [calculation of the equations (1) to (8)] are parameters, and can be set to a range in which the linear approximation of the transformation matrix can be established. That is,

[0032]

(Equation 8)

## EQU1 ## Here, G _all physically represents a mapping (transformation) from a three-dimensional space to a three-dimensional space, and thus has three different eigenvalues and linearly independent eigenvectors corresponding to the three eigenvalues. Then, G obtained by the above procedure
_{For all} , the calculated eigenvalues are λ ₁ ,
Assuming that λ ₂ , λ ₃ (where λ ₁ > λ ₂ > λ ₃ ), the eigenvalues λ ₁ , λ ₂ , λ ₃ and the eigenvector have the following properties.

That is, each eigenvalue λ ₁ , λ ₂ ,
The eigenvectors corresponding to λ ₃ are e ₁ , e ₂ , e
_{Assuming 3} ,

[0035]

(Equation 9)

The following holds. e _1, e _2, e ₃ is for a linearly independent, any vector in three-dimensional space e _1,
It can be uniquely expressed by e ₂ and e ₃ . That is, for any vector R in the three-dimensional space,

[0037]

(Equation 10)

There is only one set of l, m, n that satisfies.
The mapping of R by G _all is

[0039]

[Equation 11]

Is as follows. Therefore, as shown in FIG. 6, the eigenvalues λ ₁ , λ ₂ , λ ₃ correspond to the enlargement ratio (reduction ratio) in the respective eigenvector directions of the space.

Therefore, the eigenvalue λ ₁ corresponding to the maximum stretching rate is used as the mixture index in that section.

Next, as shown in FIG. 7, the end point of the previous section is set as the starting point of the next section, and an index value (eigenvalue) λ ₁ until the next development time T0 is obtained.

For each trajectory, the above processing (calculation of equations (1) to (12)) is performed until a predetermined time which is the sum of the development times T0 is reached, or a predetermined position of the trajectory is obtained. Repeat until Then, for each flow trajectories, seek lambda ₁ for each development time T0, to evaluate the mixing performance of the entire mixing system by the average value.

FIG. 8 shows the processing performed by the mixing performance evaluation and analysis unit 4.
6 is a flowchart showing a management procedure. This floater
If you briefly explain again along with the
According to the sphere radius ε of the
At time t₀ ^t] And a spherical area with a predetermined radius
An area is set (step S11). And the spherical area
Point [r] on the nearby trajectory inside the area_i ^t]
And [r₀ ^t] And [r _i ^t] Minute unit time step
dt position [r₀ ^{t + dt}] And [r_i ^{t + dt}Calculate
(Step S12).

Then, as shown in FIGS. 4 and 5, after this minute unit time step dt, the above equations (1) to (8)
Performing formula calculation, it calculates a transformation matrix G _t representing a transformation region after time small unit step dt (step S1
3). Further, the above formulas (9) to (12) are calculated to calculate the eigenvalue λ ₁ corresponding to the maximum stretching rate after the minute unit time step dt (step S14).
In this way, until the sum of the minute unit time steps dt reaches the predetermined development time T0, the above equations (1) to (12)
The calculation of the equation is repeated (steps S15 and S16), and FIG.
As shown in ( ₁ ), a transformation matrix G _all representing the transformation of the area is calculated for each development time T0, and an index value (eigenvalue) λ ₁ corresponding to the maximum enlargement ratio is calculated.

Next, as shown in FIG. 7, the index value λ until the next development time T0 is set with the end point of the previous section as the start point of the next section.
₁ and the development time T0 is set to a predetermined time (end time Ten
Until d) is reached, the processing of steps S11 to S18 is repeated. As a result, the mixed index for one trajectories (average value of the obtained lambda ₁₎ is obtained (step S19), repeats for such process all the trajectories (step S20, S21) Then, the average value of λ ₁ obtained for each trajectory for each development time T0 is calculated (step S22). Then, the mixing performance of the entire mixing system is evaluated based on the average value.

In the present invention, the mixing performance is evaluated on the basis of the flow velocity field obtained by the heat flow analysis. Anything is fine. For example, in addition to a complete fluid such as water and alcohol, and a viscoelastic fluid such as polyvinyl chloride resin, polyethylene, and polystyrene, if the constitutive equation is known and a thermohydraulic analysis can be performed, a multiphase flow or powder It may be a flow. Next, an embodiment in which the mixing performance analysis system having the above configuration is used for evaluating the mixing performance of the crested rotor mixer shown in FIG. 9 will be described.

That is, assuming a peaked rotor shown in FIG. 9, the compression ratio B / A (ie, the ratio between the peak height B and the clearance A) at the peak defined as shown in FIG. 10 is changed. The analysis was performed, and the mixing performance (kneading performance in this case) was evaluated for each case.

FIG. 9 and Table 1 show the input parameters for the crested rotor mixer.

[0050]

[Table 1]

Here, the meaning of each variable in FIG. 9 and Table 1 is as follows. That is, for the flow path of the mixture,
Number of rotor divisions in the radial direction (NR), number of divisions in the circumferential direction (NT)
H), number of axial divisions (NZ), inner radius of barrel (RO),
Rotor outer radius (RI), rotor height (H), peak width (W), peak elevation angle (MA), peak number (NM), compression ratio (P
RA). FIG. 11 is a bird's-eye view at the time of mesh division.

The heat-fluid analysis unit 2 converts the mesh data of the flow path of the mixture to be mixed into meshes as shown in FIG. 11 into three-dimensional equations of a continuous equation governing the heat flow, a kinetic equation, an energy equation, and a constitutive equation. A flow analysis is performed in which all components are solved under predetermined boundary conditions (such as wall surface temperature) and physical property value data of the mixture. That is, the calculation is repeatedly performed until the whole reaches the stable calculation stage by the convergence calculation of the flow analysis unit and the temperature analysis unit. The temperature boundary condition sets a temperature defined by actual phenomena on the rotor wall surface and the barrel wall surface. Here, the temperature was 140 ° C. In addition, the flow boundary conditions differ depending on the coordinate system used for calculation, but in the case of analysis in the stationary coordinate system,
A boundary condition was set such that the peripheral speed defined by the rotor rotation speed of the rotor portion was 0 in the barrel portion, that is, there was no slip on the wall surface. The kneaded material has a degree of polymerization of 1
000 rigid polyvinyl chloride resin, and a viscosity model used was a power-law model (Power-law model).

Under the above conditions, the convergence calculation is repeated until both the temperature field and the flow velocity field reach a stable state (steady state), and the discretized flow velocity field (coordinates and velocity) is calculated for each grid point of the mesh. Vector) as output.

The particle tracking analysis unit 3 reads the mesh data created by the preprocessor 1 and the flow velocity field data obtained from the results of the heat flow analysis from each file, and determines the size of the analysis area defined by the input data, A predetermined number of virtual particles having no mass are initially arranged at predetermined positions in the flow path of the mixture. Then, the position coordinates of the virtual particle are detected, and the flow velocity of the virtual particle is interpolated from the flow velocity of the element including the coordinate and the surrounding elements. Thereafter, the virtual particle is moved at the flow velocity, the coordinates of the virtual particle position after the movement are obtained, and the processing of obtaining the flow velocity is repeated. This processing is repeated until the virtual particle reaches the coordinate value or time specified by the input data. Then, for each virtual particle, the coordinate data of the virtual particle at each time is output as trajectory data. In the present embodiment, a total of 15 pieces in the radial direction and 180 pieces in the circumferential direction
700 particles were initially placed.

The mixing performance evaluation analysis unit 4 reads the trajectory data of each virtual particle obtained by the particle tracking analysis unit 3 and control parameters for the mixing performance evaluation analysis. In this embodiment, the spherical radius ε = 1 (mm), the development time T0 = 5 (sec), and the end time Tend = 480.
(Sec). Next, for each trajectory, the development time T
Calculate the area conversion matrix for each 0, further obtain the maximum component of the eigenvalue of the area conversion matrix corresponding to the maximum value of the stretching rate of the unit spherical area, and use it as the local mixing index at the position of the trajectory . The above calculation is applied to the end time Ten for each trajectory
After repeating up to d, the average value of the local mixing index was obtained and used as the mixing performance evaluation index of the entire mixed system.

Table 2 shows the analysis results of evaluating the mixing performance in this way. Table 3 shows a list of parameters at the time of kneading the polyvinyl chloride resin.

[0057]

[Table 2]

[0058]

[Table 3]

In Table 2, the compression ratio (compression ratio B / A)
A value of 0 corresponds to a cylindrical rotor (rotor without ridges). In this case, only the kneading due to the shearing force occurs, and the index is 1.2, which indicates that the kneading due to the stretching is not so large. In the case of a rotor having a peak having a compression ratio of 0.4 to 0.8, in addition to kneading by shearing force, kneading by stretching is performed at the peak, so that the degree of kneading is larger than that of a cylindrical rotor. The results in Table 2 also show that the kneading performance of the crested rotor is high, and that the effect of kneading by stretching can be evaluated.

Here, as a comparative example, Table 4 shows the measurement results of the degree of disintegration of the polyvinyl chloride resin when the polyvinyl chloride resin was kneaded with a plastmill having substantially the same shape as in the above example.

[0061]

[Table 4]

The degree of disintegration indicates the rate at which the polyvinyl chloride resin having a structure in which the primary particles are agglomerated is broken by the action of kneading and the primary particles are dispersed separately. Obtained by microscopic observation. In polyvinyl chloride resin, the disintegration degree is used as one index expressing the strength of kneading. The degree of collapse is greatest when the compression ratio is 0.6, which means that the kneading degree is the strongest under these conditions. Also in the mixing performance evaluation and analysis system according to the present invention, the kneading degree was highest near the compression ratio of 0.6, which proved that the correct analysis was performed.

[0063]

According to the mixing performance analysis system of the present invention, the mixing performance is evaluated using the concept of eigenvalue based on the flow velocity data obtained from the heat flow analysis. Therefore, in the heat flow analysis, the physical property data of the mixture such as density, specific heat, viscosity, etc., various mixing conditions such as wall temperature, rotation speed, incoming flow rate, and shape parameters such as the length and number of blades of the mixer are relatively determined. Since it can be easily changed, mixing and mixing performance when various parameters are changed can be easily evaluated on a desk. Therefore, the degree of freedom in design is increased, and the design period and design cost can be reduced. In addition, since the mixing performance can be quantitatively described, the model shape, physical property data, and evaluation results thereof can be stored as a database and used when designing a new product. In addition, since the mixing is indexed for each trajectory, the mixing state of a specific portion in the entire mixing system can be quantitatively grasped, so that the design can be performed with clearer design guidelines.

[Brief description of the drawings]

FIG. 1 is an overall configuration diagram of a mixed performance evaluation / analysis system of the present invention.

FIG. 2 is a more specific configuration diagram of a model shape creation unit and a heat flow analysis unit.

FIG. 3 is a flowchart illustrating an analysis procedure in a particle tracking analysis unit.

FIG. 4 is a conceptual diagram of an area conversion matrix of a minute time step.

FIG. 5 is a conceptual diagram of a development time transformation matrix.

FIG. 6 is a conceptual diagram illustrating a relationship between a domain transformation matrix and eigenvalues.

FIG. 7 is a conceptual diagram showing how to proceed with calculation for each development time.

FIG. 8 is a flowchart illustrating an analysis procedure in a mixed performance evaluation analysis unit.

FIG. 9 is a plan view of a crested rotor.

FIG. 10 is an enlarged view of a peak portion of a peaked rotor.

FIG. 11 is a bird's-eye view showing a mesh-divided state of a kneaded material flow path.

[Description of Signs] 1 Model shape creation unit 2 Heat flow analysis unit 3 Particle tracking analysis unit 4 Mixing performance evaluation analysis unit

Claims (1)

[Claims] 1. A flow path of a mixture to be mixed is divided into three-dimensional minute regions using a polyhedral cell element for a target mixing system,
By solving all three-dimensional components of the continuous equation governing heat flow, the equation of motion, the energy equation, and the constitutive equation for the divided mesh data under predetermined boundary conditions and physical property value data of the mixture, A thermal-hydraulic analysis unit that obtains flow velocity field data consisting of its coordinates and flow velocity for each grid point of the mesh, and virtual particles having no physical size and mass are placed at predetermined positions in the flow path of the mixture. Initially arranged by a predetermined number, based on the discretized flow velocity field data obtained as a result of the heat flow analysis, by interpolating or extrapolating the flow velocity at the virtual particle position, and combining A particle tracking analysis unit that obtains trajectory data; and a trajectory line of each virtual particle obtained by the particle tracing analysis unit, a point on the trajectory line, and a near point existing within a predetermined distance from this point. Calculates the change of the vector connecting the points on the trajectory group after a predetermined time, obtains a conversion matrix representing the change in the vector by linear approximation, and calculates the area when any three-dimensional area is converted using this conversion matrix. The maximum component of the eigenvalue corresponding to the maximum value of the stretch rate in the eigenvector direction as the stretch rate of the area in that section, repeatedly determine the stretch rate every predetermined time to a predetermined position of the trajectory, A mixing performance evaluation analysis unit that indexes the mixing history along each trajectory with the average value and analyzes the performance of the mixing system with the average value of the index value data obtained for each trajectory A mixed performance analysis system.