JP2010042359A - Method of controlling agitated vessel equipped with high-speed rotary shearing type agitator - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method of acquiring a distribution of times of passing in an agitated vessel equipped with a high-speed rotary shearing type agitator and controlling the flowing state of a fluid in the agitated vessel by determining agitating conditions on the basis of the distribution of times of passing. <P>SOLUTION: In the agitated vessel equipped with a high-speed rotary shearing type agitator, a distribution of times of a fluid's passing through the high-speed rotary shearing type agitator in a predetermined agitation time, hereafter referred to as a distribution of times of passing, is calculated on the basis of an acquired distribution of circulation times required for the fluid to pass through the high-speed rotary shearing agitator, hereafter referred to as a distribution of circulation times. The flowing state of the fluid in the agitated vessel is controlled on the basis of the distribution of times of passing. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to a method for controlling a fluid flow state in a stirring tank equipped with a high-speed rotary shear type stirrer.

  High speed rotary shear type agitators are widely used in the production of emulsified and suspended products. Homomixer, one of the high-speed rotating shear type agitators, generates strong shearing force in a fine gap between the turbine rotating at high speed and the stationary ring (stator), giving the fluid a fine atomizing action and pumping It also serves as a function to generate a circulating flow in the stirring tank.

  In order to promote mixing in the entire area of the stirring tank, there is also a composite stirring tank that is simultaneously equipped with a low-speed rotating stirrer such as an azihomixer. Such a stirring tank is widely used for liquid emulsification / dispersion treatment from low viscosity to high viscosity liquid.

Since the emulsification and suspension of the liquid is mainly performed with a high-speed rotary shearing type stirrer, the number of times that the fluid passes through the high-speed rotary shearing type stirrer within a predetermined stirring time (hereinafter referred to as the number of passes) in controlling the stirring tank. ) Is an important indicator of fluidity. For example, Patent Document 1 discloses the number of passes K (t) within a time t (s) by measuring a flow rate (discharge flow rate) Q (m ³ / s) processed by a high-speed rotary shear type stirrer. A method is described in which K (t) = Qt / V and the stirring is controlled. Here, V (m ³ ) is the volume of the liquid in the tank. However, in this method, the discharge flow rate varies depending on the viscosity characteristics of the liquid, the type of the stirrer, and the stirring conditions. Therefore, it is necessary to experiment and determine the stirring conditions.

On the other hand, if the discharge flow rate characteristic of the high-speed rotary shear type stirrer is known, the discharge flow rate can be easily estimated. The discharge flow rate Q (m ³ / s) is generally determined from the turbine rotational speed n (1 / s) and turbine diameter d (m) of the high-speed rotary shear type agitator.

Are arranged. Here, _Nq is called a discharge flow coefficient, and is a constant unique to the stirrer in a turbulent flow state. For example, in the TK homomixer S type (normal type) (Primics Co., Ltd.), the discharge flow coefficient _Nq is approximately 0.2 in a turbulent state (Non-patent Document 1). By using this discharge flow coefficient _Nq , the number of passes can be estimated without experiment.

However, this method can be used only when the discharge flow rate characteristic of the stirrer is examined and the discharge flow rate coefficient _Nq is known.

  The number of passes calculated by the above method is an average value. Actually, the liquid in the stirring tank does not pass through the high-speed rotary shearing type stirrer equally and not all of the liquid in the stirring tank takes the same number of passes. That is, the number of passes should be grasped as a distribution, not an average value. A wide pass frequency distribution means that the liquid treatment is not uniform in the stirring tank equipped with the high-speed rotary shearing type stirrer. Variation in emulsified particle size adversely affects liquid stability. Such a problem of the spread of the pass number distribution often occurs when the liquid exhibits non-Newtonian properties in which the viscosity changes according to the shear rate. Therefore, it is desirable to grasp the pass frequency distribution.

  On the other hand, estimation by fluid analysis is expected as a method for simply evaluating the flow state in the stirring tank reflecting the viscosity characteristics and tank shape of the liquid. For example, Patent Literature 2 discloses a method for predicting a fluid state in a stirring tank and a method for displaying the fluid state. Thereby, the distribution of the flow velocity, pressure, temperature and concentration in the stirring tank can be known. However, this method only provides an outline of the flow, and the evaluation of the flow state is insufficient.

  From the viewpoint of evaluating the flow state in the agitation tank by fluid analysis, an evaluation amount that is spatially averaged focusing on a shear rate component of a specific size or more, and the influence of the axial flow velocity is added to the evaluation amount. Focusing on the method of setting the polymerization tank and stirring conditions using the evaluation amount (Patent Document 3) and the maximum value of the turbulent energy dissipation rate, droplets that are not compatible with the continuous phase maintain uniform dispersion There is a method (Patent Document 4) for obtaining the condition to perform.

  However, there is generally no known method for evaluating the pass number distribution that is important in a high-speed rotary shear type stirrer using fluid analysis.

JP 2001-157831 A JP 2001-312488 JP 2004-196842 A JP 2004-51654 A Theory and Practice of Emulsification / Dispersion Practical Section (Special Machine Industries, 1997)

  As described above, in a stirring tank equipped with a high-speed rotary shear type stirrer, the number of passes is important as an evaluation index of the flow state. Moreover, the fluid processed with such a stirring tank is a non-Newtonian fluid in most cases. Therefore, it is necessary to evaluate the number of passes as a distribution instead of an average value. However, the pass frequency distribution is difficult to obtain by measurement, and no means for calculating using the fluid analysis has been established. Therefore, although the pass number distribution is an important index, only the average value has been used so far, and therefore, the stirring condition has not been examined based on the pass number distribution.

  In contrast, an object of the present invention is to provide a method of obtaining a pass number distribution in a stirring tank equipped with a high-speed rotational shearing type stirrer, and further, a stirring condition is determined based on the pass number distribution, It aims at controlling appropriately the flow state of the fluid in the stirring tank provided with the type stirrer.

  The present inventor has obtained experimentally the distribution of circulation time (hereinafter referred to as circulation time distribution) required for the fluid to pass through the high-speed rotary shear type stirrer in the stirring tank as described in Non-Patent Document 1. However, it was also found by fluid analysis, and it was found that the pass number distribution can be calculated based on the circulation time distribution.

  That is, the present invention calculates the distribution of the number of times that the fluid passes through the high-speed rotary shearing stirrer within a predetermined stirring time (hereinafter referred to as pass number distribution) in the stirring tank equipped with the high-speed rotary shearing stirrer. A method for obtaining a circulation time distribution and then calculating a pass frequency distribution based on the circulation time distribution is provided.

  The present invention also provides a flow state control method for controlling the flow state of a fluid in a stirring tank equipped with a high-speed rotary shear type stirrer based on the pass number distribution calculated by the above-described method.

  According to the present invention, the pass number distribution can be calculated in a stirring tank equipped with a high-speed rotary shear type stirrer. Therefore, the flow state is controlled by appropriately adjusting the stirring conditions of the stirrer such as the number of revolutions per unit time, the stirring time, and the physical properties such as the viscosity of the fluid, and the fluid in the stirring tank is obtained by setting the desired number of passes. It is possible to eliminate the uneven processing.

  Therefore, for example, in the scale-up from the lab scale to the actual machine scale, by controlling the flow state by the method of the present invention, for example, the dispersion of the emulsified particle size can be suppressed and the stability of the emulsified state occurs in the product. Can be prevented.

  Hereinafter, the present invention will be described in detail with reference to the drawings. In each figure, the same numerals indicate the same or equivalent components.

  FIG. 1 is a schematic diagram of a composite agitation tank 1 for calculating a pass number distribution in one embodiment of the present invention and controlling the flow state. This combined agitation tank 1 is modeled on an ad homomixer manufactured by Primix Co., Ltd., and a turbine 4 is provided at the lower part of the shaft 3 located at the center of the tank body 2, and a cylindrical stator 5 surrounds it. The turbine 4 and the stator 5 constitute a high-speed rotary shear type stirrer 6 called a homomixer. Further, in the tank body 2, a rotating paddle 7 is attached to a frame (not shown) coaxially with the homomixer 6 to constitute a low-speed rotating stirrer. In general, there are stationary paddles or reverse rotating paddles (paddles rotating in the direction opposite to the rotating paddles 7) for improving the mixing property, and scrapers for improving heat transfer efficiency in the azihomomixers generally used. These are omitted in the composite agitation tank 1.

  The turbine 4 inside the homomixer 6 normally rotates at a high speed of 1000 rpm or more, and promotes emulsification and dispersion by a strong shearing force. The homomixer 6 also has a pump function, generates a strong discharge flow as shown by an arrow A, and contributes to the entire mixing in the tank.

  On the other hand, the rotating paddle 7 rotates at 200 rpm or less, usually about 20 to 120 rpm, causes a downward flow in the circumferential direction as indicated by an arrow B, and contributes to the mixing of the entire tank.

  The azihomomicr is a typical agitation tank targeted by the present invention, but the agitation tank targeted by the present invention is not limited to this, and the present invention can be applied to various agitation tanks equipped with a high-speed rotary shear type agitator. Can be applied.

  FIG. 2 is a schematic diagram of a procedure for obtaining a circulation time distribution by a method of an embodiment of the present invention using fluid analysis and then calculating a pass number distribution. In the present invention, the circulation time distribution can be obtained experimentally or by fluid analysis. However, since there is a problem of measurement accuracy in the experiment, it is easier to calculate by the fluid analysis.

  As a method of obtaining the circulation time distribution by fluid analysis, from the viewpoint of simulation accuracy and calculation cost, first, a time-averaged flow field is first analyzed steadily, and the flow field is fixed to make the concentration advection equation unsteady. It is preferable to obtain the circulation time distribution by solving. Although the equation of flow and the advection equation of concentration can be simultaneously solved and solved unsteady at the same time, the improvement in accuracy is often small compared to the increase in calculation cost.

  Hereinafter, a method for obtaining a circulation time distribution by first performing a steady analysis of a time-average flow field and then solving an advection equation will be described in detail with reference to an embodiment when obtaining a circulation time distribution by fluid analysis.

Example 1
FIG. 3 shows a viscosity characteristic diagram of the emulsion to be used in this example. The plot in the figure is measured data by a rheometer, and the solid line is a viscosity curve modeled using a viscosity model. Viscosity varies with shear rate and is a typical non-Newtonian fluid. In modeling the viscosity curve, the Carreau model, one of the representative models of non-Newtonian fluids, was used. Carreau model

It is represented by

In the solid line in FIG.
η ₀ = 10 (Pa · s), η _∞ = 0.02 (Pa · s), λ = 240 (s), ν = 0.4
It is. The fluid density ρ is 1000 (kg / m ³ ).

  In this embodiment, in the azihomomixer with a liquid volume of 2 L in FIG. 1, as shown in FIG. 2 (1), first, a time-average flow field is regularly analyzed. FIG. 4 is a result of analyzing the flow field when the homomixer rotation speed is 7000 rpm and the paddle rotation speed is 80 rpm with respect to the viscosity characteristics of FIG. 3. The homomixer has a turbine diameter (maximum value) of 25 mm, a maximum distance between the tips of the rotating paddles of 108 mm, and a tank diameter of 150 mm.

  In this case, assuming that the flow velocity due to the driving of the homomixer 6 is very high and is hardly influenced by the flow caused by the rotating paddle 7, first, as shown in FIG. As shown in FIG. 2 (1 b), the obtained flow state is applied to a model that solves the entire flow considering the rotating paddle 7 as a boundary condition, and the analysis result of FIG. 2 (1 c) is obtained. The details of the analysis result are shown in FIG. Here, the shape of the homomixer 6 was treated as a simple cylinder ignoring its internal structure, and boundary conditions were given at positions corresponding to the openings of the upper surface 6a and the lower surface 6b of the cylinder. By giving the boundary condition in this way, the analysis of the flow field generated in the rotating paddle 7 can be a steady analysis.

  In addition to the boundary conditions normally given in the fluid analysis of the stirring tank such as the rotation axis and rotation speed of the fluid region and the rotation speed of the wall surface (for example, the tank wall), the boundary condition setting mode applied to FIG. It is preferable that the inflow condition into the tank (that is, the portion excluding the homomixer 6 from the tank body 2) is given by speed (speed boundary condition) and the outflow condition from the tank is given by pressure (pressure boundary condition). In the case of obtaining the analysis result of FIG. 4, boundary conditions were similarly set.

  The steady-state analysis of the flow field generated by the homomixer 6 and the steady-state analysis of the flow field generated by the rotating paddle 7 can be performed by conventional steady-state analysis methods. For example, in the commercial fluid analysis software FLUENT, a single reference coordinate model, A method called a multiple reference coordinate model can be used. In this example, FLUENT was used and analysis was performed using a single reference coordinate model.

  Next, the circulation time distribution is obtained under the flow field analyzed as shown in FIG. In order to obtain the circulation time distribution, first, a certain concentration is given to the outlet of the homomixer 6 (discharge portion of the homomixer upper surface 6a), and the concentration returning to the inlet of the homomixer 6 (inflow portion of the homomixer lower surface 6b) is obtained. This concentration may be measured by using a dye or the like as a tracer in an experiment and giving a predetermined concentration, or may be determined by solving advection equations with a scalar variable corresponding to the concentration as a tracer in a fluid analysis.

  As a method for obtaining the circulation time distribution experimentally or by fluid analysis, there are an impulse response method and a step response method depending on how to give the concentration.

  In the impulse response method, the concentration is released from the outlet of the homomixer upper surface 6a in an impulse manner (delta function) for a very short time. The concentration returning to the inlet of the homomixer lower surface 6b is regarded as a function with respect to time, and normalized so that the time integration becomes 1, thereby obtaining a circulation time distribution E (τ).

  The step response method is a method in which a fluid having a certain concentration is continuously discharged from the outlet of the homomixer upper surface 6a. After a sufficient amount of time, the concentration in the tank is equal to the discharge concentration at the outlet of the homomixer upper surface 6a, so that the concentration observed at the inlet of the lower surface 6b of the homomixer is also equal to the discharge concentration at the outlet of the homomixer 6. Therefore, the concentration returned to the inlet of the homomixer 6 is regarded as a function of time, and the response curve F (τ) by the step response method is normalized by normalizing the value after a sufficient time has passed to 1. obtain. By differentiating this response curve with time,

Thus, the circulation time distribution E (τ) can be obtained. That is, the response curve F (τ) is a cumulative distribution function of the circulation time distribution E (τ).

  In general, the same circulation time distribution can be obtained by applying either the impulse response method or the step response method. However, when it is experimentally determined, it is difficult to always release a constant concentration from the outlet of the homomixer 6, so it is practically preferable to obtain the circulation time distribution by giving the concentration by the impulse response method. On the other hand, when the circulation time distribution is obtained by fluid analysis, a virtual concentration is given as a calculation condition, so there are few restrictions as in the case of obtaining it experimentally, but the impulse response method has a “short” release time. It is difficult to decide. Therefore, in this embodiment, the concentration is given by the step response method in the fluid analysis, the concentration returning to the inlet of the homomixer 6 is calculated by solving the advection equation, the response curve F (τ) is obtained, and this is differentiated. Thus, the circulation time distribution of FIG. 5 was obtained.

  In the fluid analysis, the discharge concentration from the outlet of the homomixer 6 is virtually determined arbitrarily. Therefore, in this embodiment, the discharge concentration is set to 1 from the outlet of the homomixer 6. In addition, commercial fluid analysis software FLUENT was used to obtain the circulation time distribution by solving the concentration advection equation.

  From FIG. 5, it can be seen that there is a distribution in the time required for one circulation from the homomixer 6 to return to the homomixer 6 again, and not all of the liquid in the tank circulates in the same time.

  The pass number distribution is a distribution of the number of passes, which is how many times the liquid in the tank is treated by the homomixer during a certain stirring time. Since the circulation time has a distribution as shown in FIG. 5, the number of passes also has a distribution. This means that the treatment of the liquid in the tank by the homomixer is not uniform. Conversely, in order to deal with processing non-uniformity, it is necessary to know the pass number distribution and control the flow so that the pass number distribution is as sharp as possible.

  The pass number distribution can be obtained by a Monte Carlo method, an integral equation method, an approximate solution method, or the like.

  In the Monte Carlo method, first, virtual fluid particles are considered, and it is considered that the time required for one fluid particle to circulate once is stochastically determined according to the circulation time distribution. Then, by finding the time required for the first circulation and the time required for the second circulation in order, the number of times that one fluid particle circulates within a certain stirring time is obtained. By performing the processing independently on the particles, a pass number distribution is obtained.

  In order to obtain the time required for one fluid particle to circulate once, a random number according to the circulation time distribution E (τ) is generated. A method for generating random numbers according to a certain distribution is generally well known. For example, a method called an inverse function method shown below can be used.

  FIG. 6 is a schematic explanatory diagram of a random number generation method using an inverse function method. In this method, first, a uniform random number u of 0 or more and less than 1 is generated. Next, the random number u is inversely transformed using a cumulative distribution function of the circulation time distribution E (τ), that is, F (τ).

The time τ required for one circulation obtained in this way follows the circulation time distribution E (τ).

FIG. 7 shows an example of generating random numbers according to the circulation time distribution. In the figure, the smooth solid line is the circulation time distribution to be followed and is the same as in FIG. The broken line is the frequency distribution of the generated random numbers. As the number of fluid particles, N = 10 ³ , 10 ⁴ , and 10 ⁵ were shown. Variation in N = 10 ³ stands out, it can be seen that become quite the N = 10 ⁵ smoothly.

The solid line in FIG. 8 is the pass number distribution p (k, t) determined by the Monte Carlo method with N = 10 ⁵ , homomixer rotation speed 7000 rpm, paddle rotation speed 80 rpm, and stirring time 20 minutes.
Here, k represents the number of passes, t represents time, and p (k, t) is

It is standardized by.

  FIG. 8 also shows the pass number distribution obtained by numerical integration and approximate solution described later.

  Next, a method for obtaining the pass number distribution by solving the integral equation will be described. The Monte Carlo method is intuitive and easy to understand, but the method of obtaining the pass number distribution by solving the integral equation is more accurate or simpler.

  That is, the distribution function p (k, t) of the number of passes k at a certain time t is expressed by the integral equation of the following equation (1).

Follow. Since the circulation time τ corresponding to the increase in the number of passes follows the circulation time distribution E (τ), the integral equation of Equation (1) is followed as a superposition.

In Equation (1), τ _max is the upper limit value of the integral variable τ and means the maximum circulation time. The value of τ _max is determined by the value of τ at which the circulation time distribution E (τ) exceeds its peak value and is sufficiently close to 0, or the value of τ at which the cumulative circulation time distribution F (τ) is sufficiently close to 1. Therefore, the value of tau _max can vary depending on how to take the accuracy of the simulation accuracy, or experiment, but if you take tau _max as the value F (tau) is close enough 1, the value of tau _max is according to equation (1) Almost no influence on the calculation result of the pass number distribution.

  Therefore, by solving the integral equation (1), the distribution function p (k, t) of the number k of passes at an arbitrary time t can be obtained.

  As a method of solving the integral equation (1), there are various analytical methods and numerical solution methods by a computer.

Among these, as a numerical solution method, for example, the following method can be given.
First, the time t is discretized,
t = iΔt (i = 0, 1, 2,...)
And

Further, the time variable τ in the integration is discretized at the same interval Δt as t as follows.
τ = jΔt (j = 0, 1, 2,…)

  Then the integral equation (1) becomes

And is discretized.

p _{k, i} = p (k, iΔt), G _j = E (jΔt) Δt
And

It becomes. That is, the path number distribution p _{k, i} can be calculated from the above equation if the past history p _{k−1, ij} is stored. The results obtained in this way are shown by broken lines in FIG. This broken line almost overlaps with the solid line obtained by the Monte Carlo method.

  As an analytical method for solving the integral equation (1), for example, the following method can be given.

  From the statistical consideration, it can be seen that the pass frequency distribution approaches the normal distribution as the stirring time becomes longer. At this time, if the average K (t) of the pass number distribution and the standard deviation s (t) of the pass number distribution are known, the pass number distribution p (k, t) is

It is expressed.

  By using the integral equation (1), the average K (t) of the pass number distribution and the standard deviation s (t) of the pass number distribution can be obtained.

(Where, T: average circulation time, σ: standard deviation of circulation time distribution)
It becomes.

  Where T is the average of the circulation time distribution,

Or
T = V / Q (Q: discharge flow rate (m ³ / s), V: volume of liquid (m ³ ))
Can be obtained at

  σ is the standard deviation of the circulation time distribution,

Is obtained.

  The dotted line in FIG. 8 is the pass number distribution obtained by this method. It can be seen that the pass frequency distribution by this method also gives a result that is almost identical to the pass frequency distribution by other methods.

  As described above, the pass number distribution can be obtained by the Monte Carlo method, the numerical solution of the integral equation (1), or the analytical method.

  The pass frequency distribution is often close to a normal distribution and can be characterized by two parameters: mean and standard deviation. Therefore, it is desirable to set a certain standard for the spread of the distribution and to evaluate the spread of the distribution according to the standard.

  One model flow within the device is a fully mixed flow. A fully mixed flow is a flow defined as the material entering the device is instantaneously mixed in the device and the concentration in the device equals the concentration at the device outlet. A fully mixed flow is generally used as a model flow of a stirred tank, and a stirred tank in which a completely mixed flow is assumed is called a fully mixed tank.

  Even in a homomixer or an ad homomixer, the complete mixing tank can be considered as a model flow, and the pass number distribution at that time can be obtained. For the liquid in the tank, the ratio of the liquid that has been processed k times by the homomixer at time t is defined as p (k, t). When passing through the homomixer once, the number of treatments increases by 1. Therefore, according to the idea of a complete mixing tank, p (k, t) is

(Where Q: discharge flow rate (m ³ / s), V: volume of liquid (m ³ ))
Follow.

  Solving the above equation under the initial conditions p (0, 0) = 1, p (k, 0) = 0 (k = 1, 2,...)

It becomes.

  Here, the average number K (t) of passes is K (t) = Qt / V.

The pass number distribution p (k, t) obtained in the complete mixing tank is a distribution shape known as a Poisson distribution, and is close to a normal distribution when K (t) is large. Further, the average and the variance are equal to K (t). In other words, when the average of the pass number distribution is K (t) and the standard deviation of the pass number distribution is s (t), s ² (t) / K (t) = 1 in the complete mixing tank.
It becomes.

Therefore, the spread of the pass number distribution can be evaluated based on g (t) = s ² (t) / K (t) and g (t) = 1 in the case of the complete mixing tank. The number of pass distribution is sharper as s ² (t) / K (t) is smaller, and is preferably 5 or less, more preferably 2 or less, from the viewpoint of the uniformity of treatment with a liquid homomixer.

Incidentally, in the pass frequency distribution shown in FIG. 8, g (t) = 1.13.
The value of g (t) can be a value smaller than 1, and the smaller the better, the better. However, if it is at least close to 1, which is the state of the complete mixing tank, it can be said that the fluidity is good.

  Since the spread of the pass number distribution is related to the degree of variation in fluid processing in the homomixer, the agitation conditions should be determined so that the spread of the pass number distribution is as narrow as possible. Here, the pass number distribution varies depending on the stirring conditions such as the number of rotations of the homomixer, the number of rotations of the paddle, and the stirring time, and the properties such as the viscosity of the liquid. Therefore, in the flow state control method of the present invention, the flow state is controlled by appropriately changing the agitation conditions and the properties of the liquid so that the pass number distribution has a desirable sharpness.

  Next, an example in which the pass number distribution varies depending on the viscosity characteristics of liquid and the stirring conditions will be described.

Example 2
In the present embodiment, an example in which the pass number distribution varies depending on the viscosity characteristics of the liquid is shown. Here, as a stirring tank, an ad homomixer having a volume of 2 L of the liquid in FIG. 1 was assumed as in Example 1, and an emulsion having the viscosity characteristics in FIG. 9 was assumed as the target liquid. In addition, the plot of FIG. 9 is the measurement data by a rheometer, and a continuous line models a viscosity curve using a viscosity model. In modeling the viscosity curve, the Carreau model was used as in the case of FIG. 3 described above. The solid line in FIG.
η ₀ = 1.0 × 10 ⁵ (Pa · s), η _∞ = 0.02 (Pa · s), λ = 1.3 × 10 ⁵ (s), ν = 0.27
It is the time. The density ρ of the fluid is 1000 (kg / m ³ ).

  FIG. 10 shows the fluid analysis results obtained when the homomixer rotation speed is 7000 rpm and the paddle rotation speed is 80 rpm, which is obtained in the same manner as the fluid analysis of FIG.

  FIG. 11 shows the pass frequency distribution obtained in the same manner as in FIG. Here, the stirring conditions are a homomixer rotation speed of 7000 rpm, a paddle rotation speed of 80 rpm, and a stirring time of 20 minutes.

  The pass number distribution in FIG. 11 is the same as the pass number distribution in FIG. 8 and the stirring conditions are the same, and the average pass number is almost the same. However, the pass number distribution in FIG. It is significantly wider than the pass number distribution. This means that the treatment of the liquid with the homomixer is uneven. This means that if the viscosity characteristics of the liquid can be changed by changing the blending conditions, the pass number distribution can be controlled to a more desirable distribution.

Example 3
In the present embodiment, an example in which the pass number distribution varies depending on the liquid stirring condition is shown.
FIG. 12 is a distribution of the number of passes for the liquid having the viscosity characteristics shown in FIG. 9 when the stirring conditions are a homomixer rotation speed of 8500 rpm, a paddle rotation speed of 80 rpm, and a stirring time of 17 minutes. In this stirring condition, the number of rotations of the homomixer is made higher than that in the case of FIG. 11, but the stirring time is shortened so that the average number of passes substantially coincides with that in FIG. Although the pass number distribution in FIG. 12 is not as sharp as in FIG. 8, it can be seen that the number of passes is significantly sharper than that in FIG.

  Note that g (t) as an index of the spread of the pass number distribution is g (t) = 1.13 in FIG. 8, g (t) = 5.16 in FIG. 11, and g (t) in FIG. t) = 2.01.

  The analysis method of the present invention is useful as a method for controlling the flow state in a stirring tank equipped with a high-speed rotary shearing type stirrer.

It is a schematic diagram of a composite stirring tank. It is explanatory drawing of the calculation method of pass frequency distribution. FIG. 3 is a viscosity characteristic diagram of a liquid targeted in Example 1. 2 is a fluid analysis result of an azihomomicr in Example 1. FIG. It is the circulation time distribution analyzed in Example 1. It is a schematic explanatory drawing of the random number generation method by an inverse function method. It is an example of generation | occurrence | production of the random number according to circulation time distribution. FIG. 6 is a distribution diagram of the number of passes in the first embodiment. It is a viscosity characteristic view of the liquid made into object in Example 2 and Example 3. FIG. 4 is a fluid analysis result of an azihomomicr in Example 2. FIG. 10 is a distribution diagram of the number of passes in the second embodiment. FIG. 10 is a distribution diagram of the number of passes in Example 3.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Composite type stirring tank 2 Tank main body 3 Shaft 4 Turbine 5 Stator 6 High-speed rotation shearing type stirrer (homomic mixer)
6a Upper surface 6b Lower surface 7 Rotating paddle

Claims (9)

  In a stirring tank equipped with a high-speed rotary shearing stirrer, a calculation method of a distribution of the number of times a fluid passes through the high-speed rotating shearing stirrer within a predetermined stirring time (hereinafter referred to as a pass number distribution), Is a method of obtaining a circulation time distribution (hereinafter referred to as a circulation time distribution) required for passing through a high-speed rotary shear type agitator and calculating a pass number distribution based on the circulation time distribution.   The calculation method according to claim 1, wherein the stirring tank includes a low-speed rotating stirrer.   The calculation method according to claim 2, wherein the agitation tank is provided with a high-speed rotary shear type agitator and a low-speed rotation type agitator coaxially.   The calculation method according to claim 1, wherein the pass number distribution is calculated by a Monte Carlo method based on the circulation time distribution. When the fluid circulation time distribution function is E (τ), the distribution function p (k, t) of the number of passes k at time t is expressed by the following integral equation:
The calculation method according to claim 1, which is calculated by: The distribution function p (k, t) of the number of passes k at time t is expressed by the following normal distribution
(Where K (t) is the average number of passes, s (t) is the standard deviation of the pass number distribution)
And the average number of passes K (t) and standard deviation s (t) are averaged as follows:
(Where, T: average circulation time, σ: standard deviation of circulation time distribution)
The calculation method according to claim 5, which is calculated by:   The calculation method according to claim 1, wherein the circulation time distribution is obtained by solving a concentration advection equation under a flow field obtained by fluid analysis.   A flow state control method for controlling a flow state of a fluid in a stirring tank equipped with a high-speed rotary shear type stirrer based on the pass number distribution calculated by the method according to claim 1. From the average pass number K (t) and the standard deviation s (t) of the pass number distribution, the function g (t) is
The flow state control method according to claim 8, wherein the sharpness of the pass number distribution is evaluated using the value of g (t).