JP2010044611A - Analysis method of flow state of fluid in composite stirring tank - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method for precisely executing a fluid analysis, in a short period of time, of a composite stirring tank having a high speed rotation stirrer and a low speed rotation stirrer. <P>SOLUTION: An analysis method of a flow state of fluid in a composite stirring tank 1 having a high speed rotation stirrer (homo mixer 6) and a low speed rotation stirrer (rotation paddle 7) firstly applies steady analysis to a flow state caused by the driving of the high speed rotation stirrer 6, and secondly, by using the analysis result as boundary conditions, applies steady analysis to a flow state caused by the driving of the low speed rotation stirrer 7, and then, analyzes a flow state when driving the stirrers 6, 7 at the same time. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to a method for analyzing the flow state of a fluid in a combined stirring tank provided with a high-speed rotating stirrer and a low-speed rotating stirrer.

  In the fluid analysis of the agitation tank, usually, a region around the rotating object such as a stirring blade (rotating region) and a stationary region are defined separately, and the calculation mesh is moved together with the rotating object in the rotating region. At that time, physical quantities such as flow velocity and pressure are exchanged between the regions by re-creating a mesh between the regions or defining an interface surface between the regions. (Non-Patent Documents 1 and 3)

  This method is highly accurate as a method for calculating a flow field including a rotating object, but is inevitably an unsteady analysis in order to move the mesh over time. In transient analysis, fluid analysis is performed in small time steps. Since this time step needs to be sufficiently small compared to the time scale corresponding to the rotation speed of the rotating object, a high-speed rotation is required in a combined stirring tank equipped with a high-speed rotating stirrer and a low-speed rotating stirrer, such as the Ad homomixer. It is necessary to take very small time steps corresponding to the mold agitator. On the other hand, since a low-speed rotating stirrer exists, it takes time for the flow to stabilize as an actual phenomenon. Therefore, the unsteady analysis of the composite stirring tank has a problem that a long time must be analyzed with very small time steps.

  In order to reduce the time required for fluid analysis in unsteady analysis, Patent Document 1 attempts to reduce the calculation time by simultaneously taking a continuous equation and a Navier-Stokes equation so that a large time step can be taken. However, even with this method, the time step cannot be made shorter than the time scale inherent to the rotating object, which is insufficient for fluid analysis of the composite stirred tank.

  In Patent Document 2, calculation time is shortened by using an explicit method for time integration. The explicit method requires less calculation time for each time step than the commonly used implicit method, but it is required to make the time step very small so that non-physical numerical vibration specific to the explicit method does not appear. Although Patent Document 2 introduces a damping term to suppress numerical vibration, it is not easy to ensure that this method does not affect the solution that should be obtained originally.

  There are other ways to increase the speed of fluid analysis in unsteady analysis, but the upper limit of the time step size is determined in the combined stirring tank analysis in correspondence with the high-speed rotating stirrer. As long as analysis is adopted, no significant improvement in calculation time can be expected.

  On the other hand, in practice, it is often sufficient if a time-average flow field is known. In fact, even if the fluid analysis is unsteady, the data is often organized by taking a time average to understand the characteristics of the flow field.

  In the conventional example in which the fluid analysis of the agitation tank is performed by steady analysis, when considering the agitation tank in which only one agitator is incorporated, if the shape of the tank excluding the agitator is rotationally symmetric, it is synchronized with the rotation of the agitator. By establishing the equation of motion in the rotating coordinate system, a strict flow field can be obtained as a steady solution in the rotating coordinate system. This technique is called a single reference coordinate model in, for example, FLUENT, which is commercial fluid analysis software. In addition, the solution obtained by this method is a solution that fluctuates periodically with the rotation of the stirrer when viewed from the stationary coordinate system (Non-Patent Document 2).

  However, if a baffle (baffle plate) or the like is present in the agitation tank, the shape of the tank is not rotationally symmetric, and therefore a single reference coordinate model cannot be applied.

  On the other hand, when the region is divided into a rotating region and a stationary region, there is a method of obtaining an approximately time-averaged flow field when it can be considered that the flow is sufficiently mixed between them. This method is a method of defining a separate coordinate system for a rotation region and a stationary region and guaranteeing continuity of physical quantities between the regions and performing steady state analysis. In FLUENT, this method is called a multiple reference coordinate model (non-patent document). Reference 2).

  Even in a combined stirring tank having a high-speed rotating stirrer and a low-speed rotating stirrer, two coordinate systems having different rotational speeds can be defined. Therefore, it is conceivable to apply a plurality of reference coordinate models also in the fluid analysis of the composite stirring tank. However, in the combined stirring tank, the flow interaction between the flow field corresponding to the high-speed rotating stirrer and the flow field corresponding to the low-speed rotating stirrer is strong. I can't.

JP-A-3-229156 Japanese Patent Laid-Open No. 2001-34605 Chemical Engineering Society, Recent Chemical Engineering 57 (Chemical Industry, 2007) FLUENT 6.3 User ’s Guide (Chapter 10) FLUENT 6.3 User ’s Guide (Chapter 11)

  As described above, it is difficult to perform a fluid analysis in a short time in a composite agitation tank equipped with a high-speed rotating stirrer and a low-speed rotating stirrer such as an azihomomixer, and the flow state is simulated. Absent.

  Therefore, an object of the present invention is to perform fluid analysis of a composite stirring tank with high accuracy in a short time and to enable simulation of a flow state.

  The inventor of the present invention has a very high fluid flow rate by driving a high-speed rotating stirrer in a combined stirring tank equipped with a high-speed rotating stirrer and a low-speed rotating stirrer. In contrast to the fact that the flow field is almost unaffected, the flow rate of the fluid by driving the low-speed rotating stirrer is greatly influenced by the flow field by driving the high-speed rotating stirrer. The steady flow analysis of the flow field due to the drive of the machine, and the steady flow analysis of the flow field due to the drive of the low-speed rotating stirrer using the obtained flow state as a boundary condition, It was found that it is required in a short time with high accuracy.

  That is, the present invention is a method for analyzing the flow state of a fluid in a combined stirring tank equipped with a high-speed rotating stirrer and a low-speed rotating stirrer. When the high-speed rotating stirrer and the low-speed rotating stirrer are driven at the same time by performing steady-state analysis and then analyzing the flow state due to the driving of the low-speed rotating stirrer using the analysis result as a boundary condition A method for analyzing the flow state is provided.

  ADVANTAGE OF THE INVENTION According to this invention, the flow state of the composite stirring tank provided with the high speed rotation type stirrer and the low speed rotation type stirrer can be analyzed accurately in a short time. Therefore, in the present invention, the number of passes of the fluid in the composite agitation tank (the number of times the fluid passes through the high-speed agitator), the mixing time, the temperature distribution, etc. necessary for evaluating the temperature distribution, etc. are included in the present invention. Therefore, it is possible to calculate in a short time, and it is possible to simulate the flow state.

  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 stirring tank 1 to be analyzed in one embodiment of the present invention. This composite 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 the periphery thereof is fixed as a cylindrical fixing member. Ring 5 surrounds. The stationary ring 5 is generally called a stator, and the turbine 4 and the stator 5 constitute a high-speed rotating stirrer 6 called a homomixer. Moreover, in the tank main body 2, the rotation paddle 7 is attached to a flame | frame (not shown), and comprises the low speed rotation type stirrer. In general, there are stationary paddles or reverse rotating paddles (paddles rotating in the opposite direction to the rotating paddles 7) that improve mixing properties, and scrapers that improve heat transfer efficiency in the azihomomixers that are generally used. In the mold stirring tank 1, these are omitted.

  The turbine 4 normally rotates at a high speed of 1000 rpm or more, and promotes emulsification and dispersion inside the homomixer 6 by a strong shearing force. Further, since the turbine 4 is surrounded by the stator 5, a strong discharge flow is generated outside the homomixer 6 as indicated by an arrow A, so that the homomixer 6 also has a function of a pump and contributes to the mixing in the entire 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.

  In the composite agitation tank 1, the flow speed generated by the homomixer 6 (high-speed rotary stirrer) is very high and is hardly affected by the flow of the rotary paddle 7 (low-speed rotary stirrer). That is, the influence on the flow is one-way from the high-speed rotating stirrer to the low-speed rotating stirrer.

  Therefore, in this embodiment, as shown in FIG. 2 (a), first, the flow field generated in the homomixer 6 is first subjected to steady analysis, and then the obtained flow state is converted into boundary conditions as shown in FIG. 2 (b). And applied to a model considering the rotating paddle 7. In this case, the shape of the homomixer 6 is treated as a simple cylinder ignoring its internal structure, and boundary conditions are 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 boundary condition to 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 boundary condition from the tank is given by pressure (pressure boundary condition). In many cases, in the fluid analysis, only the differential pressure is important as the pressure. Therefore, the pressure value given in the pressure boundary condition may be zero.

  Moreover, the steady analysis of the flow field generated in the homomixer 6 in FIG. 2A and the steady analysis of the flow field generated in the rotating paddle 7 in FIG. 2B can be performed by the conventional steady analysis methods, respectively. For example, a single reference coordinate model, a multiple reference coordinate model, or the like can be used.

  A fluid analysis method using a single reference coordinate model will be described with reference to FIG. FIG. 3 is a schematic diagram of a cross section at the position of the homomixer 6 of the model of the composite stirring tank 1 of FIG. In the figure, the center circle represents the homomixer 6, and two rotating paddles 7 are provided around the homomixer 6. Now, the turbine in the homomixer 6 is not considered, that is, the homomixer 6 is a mere stationary cylinder having no internal structure. The outer circle is the tank wall 2a of the tank body 2, and the inner lattice schematically represents a calculation mesh.

  The basic equations for fluid analysis are the continuity equation and the Navier-Stokes equation.

It is expressed. Where t is the time, ρ is the density of the fluid, v is the velocity vector, p is the pressure, and F is the volume force vector such as gravity. Also, τ is the viscous stress tensor, using viscosity μ

It is expressed.

Consider a coordinate system (rotating coordinate system) that rotates in accordance with the rotation of the fluid in the arrow direction by the rotating paddle 7. When viewed from the rotating coordinate system, the rotating paddle 7 is stationary, and the tank wall 2a rotates in the opposite direction. The speed v _r seen from the rotating coordinate system is

It is expressed. Here, Ω is an angular velocity vector, and r is a position vector. The direction of the angular velocity vector Ω is downward along the shaft 3 in the case of the rotational direction as shown in FIG. 3, and the magnitude is the angular velocity of the rotating coordinate system (that is, the angular velocity of the rotating paddle 7 as viewed from the stationary coordinate system).

  In the rotating coordinate system, the continuity equation and the Navier-Stokes equation are

It becomes.

In FIG. 3, only the tank wall 2a and the homomixer 6 move relative to the rotating coordinate system, and have a rotationally symmetric shape. In such a case, the flow field is strictly steady as viewed from the rotating coordinate system. Thus, equation (4), (5) you can drop the time derivative term of the left-hand side the first term, a set of converged solution p as the time stationary solution, v _r is only to be obtained. For this reason, the calculation time is greatly reduced.

  FIG. 4 is a conceptual diagram in the case where the above-described composite stirring tank 1 is subjected to steady analysis using a plurality of reference coordinate models. The homomixer 6 and the rotating paddle 7 are also shown in the tank wall 2a in the same figure, but this time there is a turbine in the homomixer 6 and it is assumed that analysis is performed in consideration of the rotation of the turbine (in the schematic diagram of FIG. 4). The description of the shape of the turbine and the mesh in the homomixer is omitted). The rotating paddle 7 rotates at a different speed when viewed from a coordinate system rotating with the turbine in the homomixer 6, and the rotating paddle 7 is not rotationally symmetric. Therefore, it cannot be solved with a single reference coordinate model. Therefore, the area is divided into two around the homomixer 6 and the rotating paddle 7, and the area 1 is described with a coordinate system that rotates at high speed and the area 2 is described with a coordinate system that rotates at low speed. A steady solution is obtained approximately by guaranteeing. This method assumes that the flow interaction between the two regions is weak. However, since the interaction between the homomixer 6 (or the turbine) and the rotating paddle 7 is strong, it is difficult to obtain an appropriate steady solution by this method. Therefore, in the analysis method of the composite agitation tank 1 of the present invention, since it is a rigorous technique and the reliability of the obtained solution is high, it is usually simplified to the extent that the characteristics of the shape of the composite agitation tank are not impaired. Preferably, a single reference coordinate model is used, and non-stationary analysis is used as needed.

  For example, in the analysis of FIG. 2B, in addition to the rotating paddle 7, a stationary paddle (or reverse rotating paddle) is included in the analysis shape, and the interaction between the rotating paddle 7 and the stationary paddle (or reverse rotating paddle) is known. If desired, a multi-reference coordinate model can be used. Furthermore, when it is desired to know the unsteady state in more detail with respect to the interaction, the unsteady analysis described below may be used instead of the steady analysis.

  FIG. 5 is a conceptual diagram of unsteady analysis in which a high-speed rotation region and a low-speed rotation region are separated. The calculation mesh in the region around the homomixer 6 is a high-speed rotation region that moves with the turbine in the homomixer 6, and the calculation mesh in the region around the rotation paddle 7 is a low-speed rotation region that moves with the rotation paddle 7. In this example, the calculation meshes in the high speed rotation area and the low speed rotation area are discontinuous between the areas. Therefore, physical quantities such as flow velocity and pressure are exchanged by defining interface surfaces between regions in accordance with commercial fluid analysis software FLUENT or the like.

  The analysis method of the present invention can be applied to a case where a homomixer (homomixer), a disperser mixer or the like is used as a high-speed rotation type agitator, and a paddle blade, an anchor blade or the like is used as a low-speed rotation type agitator. Can be widely applied to fluid analysis in a composite stirring tank in which an arbitrary number is combined. In particular, the present invention is based on the fact that the flow interaction is unidirectional from the flow by the high-speed rotating stirrer to the flow by the low-speed rotating stirrer. It can be preferably applied to those having a rotation speed of 1000 rpm or more and a low-speed rotating stirrer of 200 rpm or less.

  When the high-speed rotating stirrer is surrounded by a stator like a homomixer, the flow inside the homomixer is hardly affected from the outside, and therefore the present invention can be applied more suitably. Further, the homomixer has an advantage that the boundary condition can be easily set because the fluid discharge portion and the inflow portion are determined by the shape of the opening of the stator.

  Hereinafter, the present invention will be specifically described with typical calculation examples.

In the composite agitation tank model of FIG. 1, assuming a Newtonian fluid with a viscosity of 1 Pa · s and a density of 1000 kg / m ^{3 as} a fluid, using the analysis method of the example and the moving mesh of the comparative example under the following operating conditions: According to the unsteady analysis method, the following analyzes (1) to (3) were performed.

  In this case, in the analysis method of the embodiment, as the boundary condition of the flow field analysis by the rotating paddle, the velocity boundary condition is used in the inflow condition to the tank (that is, the outflow condition from the homomixer), and the outflow condition from the tank (that is, In the condition of inflow to the homomixer, the pressure boundary condition was zero pressure. For these analyses, both the steady analysis and the non-steady analysis were used by ANSYS FLUENT.

[Operation conditions]
Homomixer speed: 6000rpm
Homomixer turbine diameter (maximum value): 25 mm
Rotation paddle speed: 60rpm
Maximum distance between rotating paddle tips: 108 mm
Tank diameter: 150mm
Fluid volume: 2L

(1) Velocity distribution at the discharge portion S1 from the homomixer The velocity distribution at the discharge portion S1 from the homomixer, which is considered to be hardly affected by the rotating paddle, is a steady analysis in the homomixer that is first performed by the analysis method of the embodiment. The comparison was made with the unsteady analysis using the moving mesh of the comparative example (the unsteady analysis was at 2 seconds after the start of rotation). FIG. 6 shows the position of the discharge portion S1, and FIG. 7 shows the result. FIG. 7 is a plot of the flow velocity at the discharge portion S1 with respect to the r, θ, and z components, where z is the vertical direction (axial direction), the radial direction of the cross section perpendicular to z is r, and the circumferential direction is θ. It is.

  From FIG. 7, it can be confirmed that the analysis result by the example and the analysis result by the comparative example are in good agreement. Thus, it can be seen that the assumption of the present invention holds that the discharge flow by the homomixer is hardly affected by the rotating paddle.

(2) Velocity distribution at three locations S2, S3, and S4 in the tank Velocity distribution at three locations S2, S3, and S4 in the tank, which are considered to be affected by both the homomixer and rotating paddle. Comparison was made between the method and the unsteady analysis using the moving mesh of the comparative example (the unsteady analysis was at 2 seconds after the start of rotation). In this case, in the analysis of the example, the velocity distribution obtained in FIG. 7 was used as the velocity boundary condition constituting the inflow condition to the tank (that is, the outflow condition from the homomixer).

  FIG. 8 shows the positions S2, S3, and S4 to be analyzed, and FIG. 9 shows the analysis results. From FIG. 9, it can be seen that the analysis result by the example and the analysis result by the comparative example coincide with each other in the entire tank. In the method of the comparative example, there is a jump in the plot around r = 24 (mm) and r = 54 (mm) in the analysis results of the positions S2 and S3. This is a mesh between the rotation region and the stationary region. Is supposed to be smoothly connected.

(3) Analysis of velocity distribution in tank FIG. 10 (a) shows the analysis result of the velocity distribution in the tank at 2 seconds after the start of rotation by the unsteady analysis of the comparative example, and FIG. The analysis result of the velocity distribution in a tank by the analysis method of an Example is shown.

  10 (a) and 10 (b), even in the unsteady analysis of the comparative example, the flow is almost stable at t = 2 (s) and becomes a steady state, and the velocity distribution is the same as the result of the steady analysis of the embodiment. You can see that

  On the other hand, in the example, it took about 4 hours as the calculation time to obtain this analysis result, and about 2.5 days in the comparative example. The computer used was a Windows (registered trademark) PC with Core2Duo 2.66 GHz as the CPU.

  In this example and the comparative example, a Newtonian fluid having a viscosity of 1 Pa · s is assumed. However, in a non-Newtonian fluid whose viscosity depends on the shear rate, it generally takes time until the flow becomes stable. Calculation time is required.

  As described above, according to the present invention, it is understood that the flow state can be analyzed with high accuracy in a very short time as compared with the method of the conventional comparative example.

  The analysis method of the present invention is useful as a fluid analysis in a combined stirring tank equipped with a high-speed rotating stirrer and a low-speed rotating stirrer, and is also useful as a basis for analyzing the number of passes, mixing time, temperature distribution, etc. It is.

It is a schematic diagram of a composite stirring tank. It is a schematic diagram of the analysis method which analyzes the flow field by a homomixer (high-speed rotating stirrer) and then analyzes the flow field by a rotating paddle (low-speed rotating stirrer). It is a conceptual diagram of the fluid analysis by a single reference coordinate model. It is a conceptual diagram of the fluid analysis by a multiple reference coordinate model. It is a conceptual diagram of unsteady analysis. It is the figure which showed the comparison position of the velocity distribution in an Example and a comparative example. It is a velocity distribution map of the fluid in the discharge part from a homomixer by an Example and a comparative example. It is the figure which showed the analysis position of the velocity distribution in an Example and a comparative example. It is a velocity distribution map of the fluid by an Example and a comparative example. It is an analysis figure of the velocity distribution of the fluid in the tank by an Example and a comparative example.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Composite type | mold stirring tank 2 Tank main body 2a Tank wall 3 Shaft 4 Turbine 5 Fixed ring (stator)
6 High-speed rotating stirrer (Homomixer)
6a Upper surface 6b Lower surface 7 Rotating paddle

Claims (3)

  A method for analyzing the flow state of a fluid in a combined stirring tank equipped with a high-speed rotating stirrer and a low-speed rotating stirrer. , Analyzing the flow state when a high-speed rotating stirrer and a low-speed rotating stirrer are driven simultaneously by steady-state analysis of the flow state due to the driving of the low-speed rotating stirrer using the analysis result as a boundary condition .   The analysis method according to claim 1, wherein a velocity boundary condition is used as an inflow boundary condition to the tank and a pressure boundary condition is used as an outflow boundary condition from the tank as the boundary condition.   The analysis method according to claim 1 or 2, wherein the high-speed rotating stirrer is surrounded by a stationary ring.