WO2018190585A2

WO2018190585A2 - Method and system for measuring viscosity in continuous flow field, and method and system for predicting flow rate or pressure drop of non-newtonian fluid in continuous flow field

Info

Publication number: WO2018190585A2
Application number: PCT/KR2018/004117
Authority: WO
Inventors: 황욱렬; 장혜경
Original assignee: 경상대학교산학협력단
Priority date: 2017-04-13
Filing date: 2018-04-09
Publication date: 2018-10-18
Also published as: WO2018190585A3

Abstract

One embodiment of the present invention can provide a method and/or a system which can easily measure viscosity behavior of a fluid by measuring only a flow rate and a pressure drop by preparing a flow number in an arbitrary continuous flow field. Another embodiment of the present invention can provide a method and/or a system which can easily measure a pressure drop or a flow rate in a flow field by only preparing a flow number in an arbitrary continuous flow field and viscosity behavior of a non-Newton fluid flowing in the flow field.

Description

Methods and systems for measuring viscosity in continuous flow fields, methods and systems for predicting flow or pressure drop of non-Newtonian fluids in continuous flow fields

One embodiment of the invention relates to a method and system for measuring viscosity in any continuous flow field, and another embodiment of the invention relates to a method and system for predicting the flow rate or pressure drop of a non-Newtonian fluid in a continuous flow field.

Rheologically complex fluids, such as polymer melts and solutions, particle suspensions, slurries, and droplet systems, have complex viscosities such as shear thinning and yield stress due to microstructure and hydrodynamic interactions. It is applied to various processes such as chemical process, polymer processing, electronic materials (display and secondary battery), food, cosmetics, paint, water treatment, oil drilling.

Conventional methods for measuring the viscosity of such complex fluids basically take one of the following methods by taking a sample of the fluid. (i) It is possible to measure the viscosity through the relationship between the two by placing a fluid between the plates and giving a shear force to one plate to measure the shear rate. (ii) Viscosity can be measured using the relationship between pressure difference and flow rate by flowing a fluid through a simple circular cross section or a thin rectangular microtube.

However, since both methods are derived from the principle of momentum conservation (force balance), it may be applicable only to very simple shapes (circular flat plate, circular cross-sectional microtube, rectangular microtube).

On the other hand, there is Metzner-Otto technique, which is an energy dissipation rate-based flow quantification technique that is applied to scaling concept and empirical approach only in existing limited agitator flow. Metzner-Otto assumed that there was an average shear rate representative of the total flow field in the stirring system, and defined a correlation that the average shear rate is proportional to the velocity of the impeller, and that the equality of the energy dissipation rate between Newtonian fluid and non-Newtonian fluid is defined. The effective shear rate and effective viscosity of the flow in the non-Newtonian fluid stirrer are defined. The present invention has been developed to apply similar energy dissipation-based quantification techniques to all continuous flow fields with inlets and outlets.

An example of the prior art is US Pat. No. 6,412,337. This prior art extends the concept of Metzner-Otto to implement viscosity measurements in static mixers. The concept using the equality of energy dissipation is the same, but suppose that the viscosity model of the fluid is a power-law fluid, and to find two coefficients (consistency index and power-law index) of the power-supply fluid, “two static mixers ) To measure the pressure drop and flow rate, respectively. On the other hand, the present invention is different from the prior art and can be applied to a wider range because the viscosity can be measured immediately by measuring only one pressure drop and flow rate in any flow field without predetermine a viscosity model. The wide range of applications means that the fluid viscosity models can be varied and can be applied to general flow fields of any shape other than a static stirrer.

On the other hand, in the continuous flow field, the relationship between the flow rate and the pressure drop on the properties of the non-Newtonian fluids is very different. In the related art, the flow rate and the pressure drop for each fluid have to be determined separately through flow analysis or experiment, which is very cumbersome. There was this.

For example, the flow rate and pressure drop relations, called die characteristics of extrusion dies used in polymer processing, are very important information in determining process conditions.The relationship between flow rate and pressure drop is the type of polymer used. And all appeared different depending on the temperature, there was a need to obtain through separate experiments and analysis for each fluid used.

The present invention is to provide a method that can easily measure the viscosity behavior of the fluid by obtaining the flow number (flow number) of the flow field in any continuous flow field and using only the flow rate and pressure drop.

It is also to provide a method for measuring the viscosity of a fluid in-situ in an actual system on-site in an arbitrary form of continuous flow field with an inlet and an outlet.

In addition, the present invention is to provide a method and system that can easily predict the pressure drop or flow rate of the non-Newtonian fluid by preparing only the flow characteristics of the flow field and the viscosity behavior of the non-Newtonian fluid in any continuous flow field.

Viscosity measurement method in a continuous flow field according to an embodiment of the present invention, a method for measuring the viscosity in a continuous flow field of a specific shape having an inlet and an outlet, comprising the steps of preparing the flow water in the flow field; Measuring the flow rate and pressure drop of the fluid in the flow field; And calculating an average energy dissipation rate using the flow rate and the pressure drop, and deriving a viscosity of the fluid according to the effective shear rate based on the flow water in the flow field and the average energy dissipation rate.

Here, in the derivation of the viscosity of the fluid, the viscosity of the fluid according to the effective shear rate may be derived using

Equations

1 and 2 below.

[Equation 1]

[Equation 2]

here,

Is the average energy dissipation rate of the flow field and is a function of the flow rate, the pressure drop and the volume of the flow field,

Is the effective shear rate of the flow field,

Is the viscosity of the fluid,

Is the apparent shear rate of the flow field, K _p Is the energy dissipation factor and K _s is the effective shear factor.

Here, the continuous flow field has a plurality of inlets and a single outlet, the step of deriving the viscosity of the fluid to calculate the total energy dissipation rate using the following equation A, the total energy dissipation rate and the volume of the flow field Based on the average energy dissipation rate can be calculated.

Equation A

Where n is the quantity of the inlet,

Is the pressure drop of the fluid between each inlet and single outlet,

Is the flow rate of the fluid at each inlet.

Here, the continuous flow field has a single inlet and a plurality of outlets, the step of deriving the viscosity of the fluid to calculate the total energy dissipation rate using the following equation B, the total energy dissipation rate and the volume of the flow field Based on the average energy dissipation rate can be calculated.

Equation B

Where n is the quantity of exits,

Is the pressure drop of the fluid between a single inlet and each outlet,

Is the flow rate of the fluid at each outlet.

Here, the flow water in the flow field includes an energy dissipation factor K _p , and preparing the flow water in the flow field includes obtaining the energy energy dissipation factor K _p in advance, and the energy dissipation rate Acquiring a coefficient K _p in advance includes injecting a Newtonian fluid of known viscosity into the flow field; Measuring the flow rate and pressure drop of the Newtonian fluid in the flow field; Obtaining an average energy dissipation rate of the Newtonian fluid using the flow rate and the pressure drop of the Newtonian fluid; Obtaining Reynolds number and power number using the density, average velocity and viscosity of the Newtonian fluid, the characteristic length of the flow field, the apparent shear rate of the Newtonian fluid, and the average energy dissipation rate of the Newtonian fluid; And it may include the step of obtaining the energy dissipation rate coefficient K _p using the relationship between the Reynolds number, the number of power and the energy dissipation rate coefficient K _p.

Here, the flow water in the flow field includes an energy dissipation factor K _p , and preparing the flow water in the flow field includes obtaining the energy energy dissipation factor K _p in advance, and the energy dissipation rate Obtaining a coefficient K _p in advance comprises: obtaining a velocity field of the flow field using Newtonian fluid; Obtaining a local energy dissipation rate by multiplying the viscosity of the Newtonian fluid by the square of the shear rate at the minute point of the flow field; Integrating the local energy dissipation rate over the entire flow field to obtain a total energy dissipation rate; Dividing the total energy dissipation rate by the volume of the flow field to obtain an average energy dissipation rate of the Newtonian fluid; Obtaining Reynolds number and power number using the density, average velocity and viscosity of the Newtonian fluid, the characteristic length of the flow field, the apparent shear rate of the Newtonian fluid, and the average energy dissipation rate of the Newtonian fluid; And it may include the step of obtaining the energy dissipation rate coefficient K _p using the relationship between the Reynolds number, the number of power and the energy dissipation rate coefficient K _p.

Here, the flow water in the flow field includes an effective shear rate coefficient K _s , and preparing the flow water in the flow field includes obtaining the effective shear rate coefficient K _s in advance, and the effective shear rate coefficient Acquiring K _s in advance includes injecting a non-Newtonian fluid having a known viscosity behavior into the flow field; Measuring the flow rate and pressure drop of the non-Newtonian fluid in the flow field; Obtaining an average energy dissipation rate and a power number of the non-Newtonian fluid using the flow rate and the pressure drop of the non-Newtonian fluid; Finding a Reynolds number of the Newtonian fluid corresponding to the power number of the Newtonian fluid having the same value as the number of powers of the non-Newtonian fluid, and considering the Reynolds number of the Newtonian fluid as an effective Reynolds number; Calculating the viscosity of the non-Newtonian fluid using the effective Reynolds number, the density of the non-Newtonian fluid, the average velocity, and the characteristic length of the flow field, and considering the viscosity as the effective viscosity; Obtaining an effective shear rate of the flow field using the effective viscosity and the viscosity behavior; And calculating the effective shear rate coefficient K _s using the relationship between the effective shear rate and the apparent shear rate.

Here, the flow water in the flow field includes an effective shear rate coefficient K _s , and preparing the flow water in the flow field includes obtaining the effective shear rate coefficient K _s in advance, and the effective shear rate coefficient Acquiring K _s in advance may include performing a flow analysis using a non-Newtonian fluid having a known viscosity behavior; Obtaining a local energy dissipation rate by multiplying the viscosity of the non-Newtonian fluid by the square of the shear rate at the minute point of the flow field; Integrating the local energy dissipation rate over the entire flow field to obtain a total energy dissipation rate; Dividing the total energy dissipation rate by the volume of the flow field to obtain an average energy dissipation rate of the non-Newtonian fluid; Obtaining a power number using the density, average speed, apparent shear rate, and average energy dissipation rate of the non-Newtonian fluid; Finding a Reynolds number of the Newtonian fluid corresponding to the power number of the Newtonian fluid having the same value as the number of powers of the non-Newtonian fluid, and considering the Reynolds number of the Newtonian fluid as an effective Reynolds number; Calculating the viscosity of the non-Newtonian fluid using the effective Reynolds number, the density of the non-Newtonian fluid, the average velocity, and the characteristic length of the flow field, and considering the viscosity as the effective viscosity; Obtaining an effective shear rate of the flow field using the effective viscosity and the viscosity behavior; And calculating the effective shear rate coefficient K _s using the relationship between the effective shear rate and the apparent shear rate.

Viscosity measurement system in a continuous flow field according to another aspect of the present invention is a system for measuring the viscosity in a continuous flow field of a specific shape having an inlet and an outlet, the flow water storage unit for storing the flow water in the flow field ; A flow rate measuring unit measuring a flow rate of the fluid in the flow field; A pressure measuring unit for calculating a pressure drop in the flow field; And a derivation unit for calculating an average energy dissipation rate using the measured flow rate and pressure drop, and deriving a viscosity of the fluid according to the effective shear rate based on the flow water in the flow field and the average energy dissipation rate. Can be.

Here, the derivation unit may derive the viscosity of the fluid according to the effective shear rate by using

Equations

1 and 2 below.

[Equation 1]

*

[Equation 2]

here,

Is the effective shear rate of the flow field,

Is the viscosity of the fluid,

Here, the continuous flow field has a plurality of inlets and a single outlet, the derivation unit calculates the total energy dissipation rate using the following equation A, the average energy dissipation based on the total energy dissipation rate and the volume of the flow field The rate can be calculated.

Equation A

*

Where n is the quantity of the inlet,

Is the pressure drop of the fluid between each inlet and single outlet,

Is the flow rate of the fluid at each inlet.

Equation B

Where n is the quantity of exits,

Is the pressure drop of the fluid between a single inlet and each outlet,

Is the flow rate of the fluid at each outlet.

According to another aspect of the present invention, a method for predicting a flow rate or a pressure drop of a non-Newtonian fluid is to predict a flow rate or pressure drop of a non-Newtonian fluid flowing in a continuous flow field of a specific shape having an inlet and an outlet. A method, comprising: preparing a flow of water in the flow field; Preparing viscosity behavior information of the non-Newtonian fluid; And deriving the other information from any one of flow rate and pressure drop of the non-Newtonian fluid in the flow field based on the flow water and the viscosity behavior information in the flow field.

Here, the deriving of the other information may use at least one of

Equations

6, 7 and 8 below.

[Equation 6]

[Equation 7]

[Equation 8]

Where N _p Is the number of powers, P is the total power according to the stress, the product of the flow rate and the pressure drop,

Is the apparent shear rate of the flow field,

Is the effective shear rate of the flow field, Re is the Reynolds number, K _p is the energy dissipation factor, and K _s is the effective shear factor.

Here, the flow water in the flow field is the energy dissipation factor K _p The extracting of the other information may include: obtaining an effective shear rate of the flow field using a relationship between an apparent shear rate and an effective shear rate coefficient K _s of the flow field; Obtaining an effective viscosity using the effective shear rate and the viscosity behavior of the flow field; Obtaining an effective Reynolds number using the relationship between the average velocity, the density and the viscosity of the fluid, the characteristic length of the flow field and the effective viscosity; Calculating a power number using the effective shear rate coefficient K _s and the effective Reynolds number; and an overall velocity depending on the stress using the average velocity, density, apparent shear rate, fluid volume in the flow field, and the power number. Comprising a step of obtaining a power, and the relationship between the flow rate and the pressure drop of the non-Newtonian fluid in the flow field through the step of obtaining the total power according to the stress.

The deriving of the other information may include the flow rate information of the non-Newtonian fluid in the flow field, and the apparent shear rate and the flow rate of the fluid through the flow rate information of the non-Newtonian fluid in the flow field. The method may further include obtaining at least one of average speeds.

A prediction system for predicting the flow rate or pressure drop of a non-Newtonian fluid according to another aspect of the present invention may predict the flow rate or pressure drop of the non-Newtonian fluid flowing in a continuous flow field of a specific shape having an inlet and an outlet. A system capable of: a flow water storage unit for storing the flow water in the flow field; A viscosity behavior information storage unit for storing the viscosity behavior information of the non-Newtonian fluid; And a derivation unit for deriving the other information from any one of the flow rate and the pressure drop of the non-Newtonian fluid in the flow field based on the flow water and the viscosity behavior information in the flow field.

Here, the derivation unit may use at least one of

Equations

6, 7 and 8 below.

[Equation 6]

[Equation 7]

[Equation 8]

The apparent shear rate,

Is effective shear rate, Re is Reynolds number, K _p is energy dissipation factor, K _s Is the effective shear factor.

Here, the flow water in the flow field includes the energy dissipation rate K _p , the effective shear rate coefficient K _s , and the derivation unit, the effective shear rate to obtain the effective shear rate using the relationship between the apparent shear rate and the effective shear rate coefficient K _s A rate calculator; An effective viscosity calculation unit for obtaining an effective viscosity using the effective shear rate and the viscosity behavior; An effective Reynolds number calculation unit for obtaining an effective Reynolds number using the relationship between the average velocity of the fluid, the density and the viscosity, the characteristic length of the flow field and the effective viscosity; A power number calculation unit for calculating a power number using the effective shear rate coefficient K _s and the effective Reynolds number; and a stress using the average velocity, density, apparent shear rate, fluid volume in the flow field, and the power number And a total power calculation unit for calculating a total power according to the above, wherein the total power calculation unit may obtain a relationship between the flow rate and the pressure drop of the non-Newtonian fluid in the flow field based on the total power according to the obtained stress.

Here, the any one of the information is the flow rate information of the non-Newtonian fluid in the flow field, the derivation unit flow rate for obtaining at least one of the apparent shear rate and the average speed of the fluid through the flow rate information of the non-Newtonian fluid in the flow field The information usage unit may further include.

According to one embodiment of the present invention, a method and / or system that can easily measure the viscosity behavior of a fluid by measuring only the flow rate and pressure drop by using the flow number of the flow field in any continuous flow field Can be provided.

It is also possible to provide a method and / or system capable of measuring the viscosity of a fluid on-site in an actual system in-situ in any form of continuous flow field with an inlet and an outlet.

According to another embodiment of the present invention, it is possible to easily predict the pressure drop or the flow rate in the flow field if only the viscosity behavior according to the flow rate of the flow field and the shear rate of the non-Newtonian fluid flowing in the flow field is known in any continuous field flow field. Methods and / or systems may be provided.

1 is a graph showing the relationship between the shear rate and the viscosity of a rheological complex fluid.

2 is a conceptual diagram schematically showing an example of a flow field having a single inlet and a single outlet.

3 is a conceptual diagram schematically showing an example of a flow field having a plurality of inlets and a single outlet.

4 is a conceptual diagram schematically showing an example of a flow field having a single inlet and a plurality of outlets.

5 is a conceptual diagram schematically showing the configuration of a fluid viscosity measurement system according to another aspect of an embodiment of the present invention.

FIG. 6 shows the results obtained by calculating the viscosity according to the shear rate for the flow of a given Carbopol 981 aqueous solution in various ratios of the enlarged / reduced circular pipe, and the flow rate and the effective shear rate coefficient based on the previously obtained energy dissipation factor and effective shear rate coefficient. This is a result plot showing that the results of viscosity measurements using only the pressure drop information coincide.

7A is a schematic diagram of a die of a particular shape.

FIG. 7B is a flow rate and pressure based on the results obtained by calculating the viscosity according to the shear rate through the simulation of two non-Newtonian fluid models in the die shown in FIG. 7A, and the energy dissipation factor and the effective shear rate coefficient. This figure shows that all the results obtained from the viscosity using only the drop information agree.

FIG. 8 is a conceptual block diagram illustrating a configuration of a system for predicting a flow rate or a pressure drop of a non-Newtonian fluid according to another aspect of the present disclosure.

FIG. 9 is a flow simulation of a corresponding pressure drop for an arbitrary flow rate for an enlarged / reduced circular pipe flow, and predicts a flow rate or pressure drop of a non-Newtonian fluid according to another aspect of the present invention. The results show that the pressure drop corresponding to any flow rate using the method and / or the system is almost identical.

FIG. 10 is a flow simulation of a corresponding pressure drop for an arbitrary flow rate for a "Kenics static mixer" flow, and predicts a flow rate or pressure drop of a non-Newtonian fluid according to another aspect of the present invention. The results show that the pressure drop corresponding to any flow rate using the method and / or the system is almost identical.

FIG. 11 is a flow simulation of a pressure drop corresponding to an arbitrary flow rate for a flow in a “body-centered cubic (BCC) porous medium”, and a ratio according to one aspect of another embodiment of the present invention. This figure shows that the results of estimating the pressure drop corresponding to an arbitrary flow rate using a method and / or a system for estimating the flow rate or pressure drop of a Newtonian fluid are almost identical.

Hereinafter, specific embodiments will be described in detail with reference to the accompanying drawings. In addition, when it is determined that the detailed description of the related known configuration or known function may obscure the gist of the embodiments, the detailed description thereof will be omitted.

On the other hand, the singular expression includes the plural expression unless the context clearly indicates the singular. And when a particular part is said to "include" a particular configuration, this means that unless specifically stated otherwise said particular portion may further include said other configuration, not to exclude other configurations than said specific configuration.

How to measure fluid viscosity

Hereinafter will be described in detail a fluid viscosity measurement method according to an aspect of an embodiment of the present invention. Fluid viscosity measurement method according to one aspect of the present embodiment is to prepare the flow water quantified the flow characteristics of the unspecified multiple fluids flowing in a continuous flow field of a specific shape with an inlet and an outlet, such as a pipe, the actual flow in the flow field A method of measuring the viscosity behavior (viscosity, effective shear rate and their relationship) of a fluid, in particular a non-Newtonian fluid, by measuring only the flow rate and pressure drop of the fluid.

Such a method of measuring fluid viscosity includes preparing a flow water in a flow field, measuring a flow rate and a pressure drop of the fluid in the flow field, and calculating an average energy dissipation rate using the flow rate and the pressure drop, Deriving the viscosity of the fluid according to the effective shear rate based on the flow rate and the average energy dissipation rate.

On the other hand, the flow characteristics of the unspecified complex fluids flowing in a specific shape of the flow field may be a quantified flow rate, that is, a non-dimensionalized number regardless of the types of fluids, and the flow water in such a flow field is the coefficient of energy dissipation rate) K _p and / or the coefficient of effective shear rate K _s . The flow water in such a flow field is a non-dimensionalized number N _p that can represent energy dissipation for a particular shape of the flow field. And the relationship between Reynolds number Re and the step of preparing the flow water in the flow field will be described later.

In the step of measuring the flow rate and pressure drop of the fluid in the flow field, the flow rate may be measured using a flow meter, and the pressure drop may be measured using a pressure gauge. The pressure drop can be calculated by comparing each pressure at the start and end points of the viscosity measurement section.

Deriving the viscosity according to the effective shear rate of the fluid, the effective shear rate

And the corresponding viscosity μ may be derived using

Equations

1 and 2 below. Effective Shear Rate of Fluid

The relationship between and viscosity μ may be equal to the relationship between the shear rate and the viscosity of the rheological complex fluid shown in FIG. 1.

[Equation 1]

[Equation 2]

here,

Is the average energy dissipation rate of the flow field,

Is the effective shear rate of the flow field,

Is the viscosity of the fluid,

Is the apparent shear rate of the flow field, K _p Is the coefficient of energy dissipation rate, K _s May mean a coefficient of effective shear rate.

Average energy dissipation rate

Can be expressed as the total energy dissipation rate divided by the volume of the flow field, and the total energy dissipation rate can be calculated based on the flow rate and pressure drop of the fluid in the laminar flow region.

Can be a function of the flow rate, the pressure drop, and the volume of the flow field.

Apparent shear rate

Can be defined differently for each flow field and chosen by the researcher. For example, in a round section pipe with an inlet radius of R, the apparent shear rate is

It can be defined as. That is, the apparent shear rate may also be a function of the flow rate of the fluid.

Effective Shear Rate

Is K _p , which is one of the flows determined according to the shape of a specific flow field according to Equation 2 And apparent shear rate

Therefore, once the flow field is determined, it can be treated as a function of the flow rate of the fluid.

In the case of a flow field having a single inlet and a single outlet as shown in FIG. 2, the flow rate is measured at at least one of the inlet and the outlet, and the measured value is obtained as the flow rate value of the fluid and measured at the inlet. The difference between the pressure and the pressure measured at the outlet is obtained, and the difference is obtained as the pressure drop of the fluid.The average energy dissipation rate is obtained by dividing the product (total energy dissipation rate) of the obtained flow rate and the pressure drop by the volume of the flow field.

Can be calculated.

In the case of a flow field having a plurality of inlets and a single outlet as shown in FIG. 3, the flow rate is measured at the plurality of inlets, and the measured value is determined by the flow rate value of the fluid at each inlet (

, In the case of the flow field of FIG.

,

) And compare the pressure measured at each outlet with the pressure measured at the outlet and compare the difference between the pressure drop values of the fluid between each inlet and single outlet (

, In the case of the flow field of FIG.

,

) And the flow rate value of the fluid at each inlet (

) And the pressure drop value of the fluid between each inlet and single outlet (

The total energy dissipation rate can be calculated using Equation A below.

Equation A

Where n is the quantity of the inlet,

Is the pressure drop of the fluid between each inlet and single outlet,

May refer to the flow rate of the fluid at each inlet.

And, dividing the calculated total energy dissipation rate by the volume of the flow field, the average energy dissipation rate

Can be calculated.

In the case of a flow field as shown in FIG. 3, the apparent shear rate

Is the flow rate at a single outlet (

) Can be defined as the value divided by the cross-sectional area at a single outlet.

In the case of a flow field having a plurality of inlets and a single outlet as shown in FIG. 4, the flow rate is measured at the plurality of outlets and the measured value is determined by the flow rate value of the fluid at each outlet (

In the case of the flow field of FIG.

,

) And compare each of the pressures measured at a single inlet with the pressures measured at the plurality of outlets and compare the difference between the pressure drop values of the fluid between the single inlet and each outlet (

, In the case of the flow field of FIG.

,

) And the flow rate value of the fluid at each outlet (

) And the pressure drop value of the fluid between a single inlet and each outlet (

The total energy dissipation rate can be calculated using Equation B below.

Equation B

Where n is the quantity of exits,

Is the pressure drop of the fluid between a single inlet and each outlet,

Is the flow rate of the fluid at each outlet.

And, if the calculated total energy dissipation rate is divided by the volume of the flow field, the average energy dissipation rate

Can be calculated.

In the case of a flow field as shown in FIG. 4, the apparent shear rate

Is the flow rate at a single inlet (

) Can be defined as the value divided by the cross-sectional area at a single inlet.

Hereinafter, the steps of preparing the flow water in the flow field will be described.

Preparing the flow water in the flow field includes obtaining the energy dissipation factor K _p in advance, so that the energy dissipation factor K _p can be obtained in advance for the flow field. For example, the energy dissipation factor K _p can be found by experimental techniques.

First, a Newtonian fluid having a known viscosity can be injected into a corresponding flow field system, that is, a flow field having a specific shape, and the flow rate and pressure drop in the laminar flow region can be measured. For reference, the flow rate can be measured using a flow meter, the pressure drop can be measured using a pressure gauge. The pressure drop can be calculated by comparing each pressure at the start and end points of a particular section.

The average energy dissipation rate can be calculated from the flow rate, the pressure drop value, and the volume of the flow field in the laminar flow region. For example, average energy dissipation rate in a flow field with a single inlet and a single outlet as shown in FIG.

Can be expressed as the product of the flow rate and pressure drop in the laminar flow divided by the volume.

Then, two dimensional numbers (Reynolds number Re and power number N _p ) are used to quantify the energy dissipation rate-based flow characteristics.The density, average velocity and viscosity of the Newtonian fluid, the characteristic length of the flow field, the apparent shear rate, and Newton It can be calculated using the average energy dissipation rate of the fluid. For example, it can be obtained as shown in Equations 3 and 4 below.

[Equation 3]

Where ρ is the density of the fluid,

Is the average velocity of the fluid, L is the characteristic length of the flow field system, and μ is the viscosity of the fluid.

Specifically, the physical density of the Newtonian fluid injected into the system may be used as the density ρ and the viscosity μ of the fluid in Equation 3 above. Average speed in Equation 3

May be the flow rate divided by the cross-sectional area, and the characteristic length of the system may vary depending on the shape of the flow field.

[Equation 4]

here,

Is the average energy dissipation rate of the flow field,

May refer to the apparent shear rate of the flow field.

Specifically, the average energy dissipation rate of the flow field in Equation 4

Is the value calculated based on the flow rate and pressure drop in the laminar flow region of Newtonian fluid injected into the system, and the volume of the flow field.

May be a value calculated based on the flow rate of Newtonian fluid injected into the system.

In Equations 3 and 4, since the values on the right side are already known or can be measured using a related device such as a speed sensor, the Reynolds number Re and the power number N _P can be obtained using the values.

The energy dissipation factor K _P can be obtained by using Equation 5 below indicating the relationship between the Reynolds number Re, the power number N _P, and the energy dissipation factor K _P. Can be calculated. Equation 5 may refer to a relationship between two dimensionless numbers established in a laminar flow having a small Reynolds number.

[Equation 5]

In the above, the energy dissipation factor K _P Calculate the energy dissipation factor K _P Can also be obtained through numerical analysis. For example, the Newtonian fluid used in the experimental technique can be used to find the velocity field in a given flow field. The local energy dissipation rate μγ ² can be obtained by multiplying the viscosity of the Newtonian fluid and the shear rate at the micro point of the flow field, and the total energy dissipation rate can be obtained by integrating it over the entire flow field. The total energy dissipation rate obtained as above may be divided by the volume of the flow field to obtain the average energy dissipation rate, and then may be obtained using the same. After obtaining the average energy dissipation rate, the same method as the experimental method described above can be used. That is, Reynolds number and power number are calculated by using information including average energy dissipation rate, Reynolds number, power number and energy dissipation factor K _P The energy dissipation factor K _P can be found using the relationship between.

Preparing the flow water in the flow field includes obtaining the effective shear rate coefficient K _s in advance, so that the effective shear coefficient K _s can also be obtained in advance for the flow field system. For example, the effective shear modulus K _s can be found by experimental techniques.

First, a non-Newtonian fluid (such as an Xanthan gum aqueous solution) having a known viscosity behavior (viscosity-effective shear rate relationship) can be injected into the system, i.e., a flow field having a specific shape, and the flow rate and pressure drop can be measured. The viscosity behavior (viscosity-effective shear rate relationship) of the non-Newtonian fluid can be, for example, as shown in FIG.

And the average energy dissipation rate of the non-Newtonian fluid from the flow rate and pressure drop in the laminar flow region

And the power number N _p can be calculated.

Specifically, the average energy dissipation rate of non-Newtonian fluids

Can be calculated based on the flow rate and pressure drop in the laminar flow region of the non-Newtonian fluid injected into the system and the volume of the flow field. In addition, the power number N _p is the average energy dissipation rate of the non-Newtonian fluid calculated based on the density ρ of the non-Newtonian fluid injected into the system and the flow rate in the laminar flow region of the non-Newtonian fluid.

, Apparent shear rate

And average speed

By using Equation 4 on the basis of can be calculated.

[Equation 4]

Then, the power number N _p calculated as above The number of power-Newtonian fluid has the same value N _p Find the Reynolds number corresponding to. The Reynolds number at this time may be the effective Reynolds number Re _eff of the complex fluid. Where the power number N _p of the Newtonian fluid The relation between Reynolds number Re and the corresponding Reynolds number Re may be defined by the energy dissipation rate K _P and Equation 5 previously calculated.

And the effective Reynolds number Re _eff The viscosity can be calculated using the density of the non-Newtonian fluid, the average speed, and the characteristic length of the flow field. For example, Equation 3 described above may be used. The viscosity thus calculated may be the effective viscosity μ _eff of the complex fluid.

[Equation 3]

Where ρ is the density of the fluid,

Specifically, the Reynolds number Re is used as the effective Reynolds number Re _eff , and the density ρ of the fluid may be the density of the non-Newtonian fluid injected into the system. Average speed

And the effective shear rate through the viscosity behavior (viscosity-effective shear rate relationship) of the complex fluid from the effective viscosity.

You can find

Finally, the effective shear rate coefficient K _s can be found using the relationship between the effective shear rate and the apparent shear rate, that is, Equation 2 described above.

[Equation 2]

here,

Is the average energy dissipation rate of the flow field,

Is the effective shear rate of the flow field,

Is the viscosity of the fluid,

On the other hand, the effective shear rate coefficient K _s Can also be obtained through numerical techniques. For example, first, the flow analysis in the flow field may be performed using the non-Newtonian fluid having known viscosity behavior. The local energy dissipation rate μγ ² is obtained by multiplying the viscosity of the non-Newtonian fluid by the shear rate at the micro point of the flow field, and the total energy dissipation rate can be obtained by integrating the total energy dissipation rate over the entire flow field. The total energy dissipation rate obtained as described above is divided by the volume of the flow field to obtain the average energy dissipation rate, and the power number can also be obtained through Equation 4.

[Equation 4]

Where ρ is the density of the fluid,

Is the average velocity of the fluid,

Is the average energy dissipation rate of the flow field,

May refer to the apparent shear rate of the flow field. Specifically, the density ρ of the fluid in Equation 4 is the density of the non-Newtonian fluid is used, the average velocity of the fluid

And apparent shear rate

The results obtained by using information such as flow rate and pressure drop that can be obtained through flow analysis using simulation can be used.

After obtaining the average energy dissipation rate and the number of power, the same method as the experimental method described above can be used. That is, the Reynolds number corresponding to the power number N _P of the Newtonian fluid having the same value as the obtained power number N _P can be found. Reynolds number effective Reynolds number of complex fluid Re _eff Can be. And the viscosity can be calculated using the effective Reynolds number and equation (3).

[Equation 3]

Where ρ is the density of the fluid,

Is the average velocity of the fluid, L is the characteristic length of the flow field system, and μ is the viscosity of the fluid. Specifically, the density ρ of the fluid in Equation 3 is the density of the non-Newtonian fluid is used, the average velocity of the fluid

The viscosity thus calculated may be the effective viscosity μ _eff of the complex fluid. And the effective shear rate through the viscosity behavior (viscosity-effective shear rate relationship) of the complex fluid from the effective viscosity.

You can find Finally, the effective shear rate coefficient K _s can be found using Equation 2.

The energy dissipation factor K _p and the effective shear modulus K _s described above may be a kind of flow number that does not have much relation with the rheological properties of the fluid but only with respect to the type of system (flow field). Therefore, if the energy dissipation factor and the effective shear modulus are obtained only once for a specific type of flow field, the flow characteristics of various complex fluids can be quantified thereafter.

유체 점도 측정 시스템Fluid viscosity measuring system

Hereinafter will be described a fluid viscosity measurement system according to another aspect of an embodiment of the present invention. When the fluid viscosity measuring system 100 prepares the flow water quantifying the flow characteristics of a plurality of unspecified fluids flowing in a continuous flow field (F) of a specific shape having an inlet and an outlet, the flow rate of the fluid flowing in the flow field (F) Only the overpressure drop can be measured to determine the viscosity behavior (viscosity, effective shear rate, and their relationship) of fluids, especially non-Newtonian fluids. The fluid viscosity measuring system 100 may be used as the fluid viscosity measuring method described above.

Referring to FIG. 5, the fluid viscosity measuring system 100 is a system for measuring viscosity in a continuous flow field F having a specific shape having an inlet and an outlet, and includes a flow water storage unit for storing the flow water in the flow field F ( 110); A flow rate measuring unit 120 measuring a flow rate of the fluid in the flow field F; A pressure measuring unit 130 for calculating a pressure drop in the flow field F; And a derivation unit 140 for calculating an average energy dissipation rate using the measured flow rate and pressure drop, and deriving a viscosity of the fluid according to the effective shear rate based on the flow water and the average energy dissipation rate in the flow field F; It may include.

In FIG. 5, the fluid viscosity measuring system 100 is shown as an example of applying the continuous inlet flow field F having a single inlet and a single outlet as shown in FIG. 2, but the fluid viscosity measuring system 100 may be applied. The shape of the continuous flow field is not limited to this. That is, the fluid viscosity measurement system 100 may include a continuous flow field having a plurality of inlets and a single outlet as shown in FIGS. 3 and 4, a continuous flow field having a single inlet and a plurality of outlets, and a plurality of inlets and multiple outlets, although not shown in the drawings. Branches can also be applied to continuous flow fields. In addition, the fluid viscosity measuring system 100 may be applied to a continuous flow field having a complex cross-sectional shape in addition to a simple cross-sectional shape such as a circular cross section.

For convenience of explanation, hereinafter, the description will focus on the application of the fluid viscosity measuring system 100 to a continuous flow field F having a single inlet and a single outlet as shown in FIG. 2.

The flow water storage unit 110 may store flow water information that quantifies the flow characteristics of the unspecified multiple fluids flowing in a specific shape of the flow field (for example, a pipe of a circular cross section) having an inlet and an outlet. The fluid storage unit 110 may be implemented as a nonvolatile memory, a volatile memory, a flash-memory, a hard disk drive (HDD), or a solid state drive (SSD) capable of storing various data. Here, the flow water of the flow field may include an energy dissipation rate K _p and / or an effective shear rate coefficient K _s for the flow field system, and may be prepared by preparing the flow water in the fluid viscosity measurement method. Since preparing the flow water in the fluid viscosity measurement method has been described above, a detailed description thereof will be omitted.

The flow rate measuring unit 120 may measure the flow rate of the fluid in the flow field (F) that is the information for calculating the average energy dissipation rate. The flow rate measuring unit 120 may include a flow meter disposed at at least one position of the inlet or the outlet to measure the flow rate of the fluid in the flow field F through the flow meter.

The pressure measuring unit 130 may measure the pressure at the inlet and / or outlet of the flow field F to calculate the pressure drop in the flow field F, which is the information for calculating the average energy dissipation rate. . The pressure drop of the flow field F may be calculated by obtaining the difference between the respective pressures at the inlet and the outlet of the flow field F measured by the pressure measuring unit 130.

The pressure measuring unit 130 may include at least a first pressure sensor 131 disposed at the inlet. When a die installed in an extruder or an injection molding machine used for processing a polymer such as plastic is used as a continuous flow field to be subjected to viscosity measurement, the outlet of the die is atmospheric pressure, so the pressure drop in the flow field F is reduced to the first. The pressure at the inlet measured by the pressure sensor 131 may be calculated by comparing the pressure at the outlet, which is preliminary atmospheric pressure information.

When the pressure at the outlet is not the atmospheric pressure, the pressure measuring unit 130 may further include a second pressure sensor 132 disposed at the outlet. The pressure drop of the flow field F may be calculated by comparing the pressure at the inlet measured by the first pressure sensor 131 with the pressure at the outlet measured by the second pressure sensor 132.

Derivation unit 140 calculates the average energy dissipation rate by using and processing the flow rate measured by the flow rate measuring unit 120 and the pressure drop information that can be calculated through the pressure measuring unit 130, the flow water storage unit 110 The viscosity of the fluid according to the effective shear rate can be derived by using and processing the information of the flow water in the flow field (F). The derivation unit 140 includes an operation algorithm for generating new data by using and processing the various information stored in the flow water storage unit 110 and the various measuring bells measured in the flow measurement unit 120 and / or the pressure measurement. It may be a program module or software.

The derivation unit 140 may derive the viscosity according to the effective shear rate of the fluid by deriving the viscosity according to the effective shear rate of the fluid in the method of measuring the viscosity of the fluid. That is, the step of deriving the viscosity according to the effective shear rate of the fluid can be derived using Equation 1 and Equation 2, and as described above, a detailed description thereof will be omitted.

FIG. 6 shows the results obtained by calculating the viscosity according to the shear rate for the flow of a given Carbopol 981 aqueous solution in various ratios of the enlarged / reduced circular pipe, and the flow rate and the effective shear rate coefficient based on the previously obtained energy dissipation factor and effective shear rate coefficient. This is a result plot showing that the results of viscosity measurements using only the pressure drop information coincide. In particular, the graph on the right shows the actual viscosity behavior of Carbopol 981 0.2wt% aqueous solution and the viscosity predicted by the method of the present disclosure, and even if the ratio of enlargement / reduction is different, the energy dissipation factor is calculated to predict the viscosity. It was confirmed that the actual viscosity behavior can be accurately predicted. For reference, Carbopol 981 aqueous solution is a representative non-Newtonian fluid having both yield stress and shear thinning.

FIG. 7A is a schematic diagram of a die of a specific shape, and FIG. 7B is a result of obtaining a viscosity according to a shear rate through simulation for two non-Newtonian fluid models in a die shown in FIG. Based on the dissipation factor and effective shear modulus, the results show that the results of viscosity measurements using only flow rate and pressure drop information are consistent. Specifically, FIG. 7A shows a die of a particular shape with a single inlet and outlet. In addition, in FIG. 7B, the results of obtaining the viscosity according to the simulation permit shear rate through a finite element method (FEM) based program for two non-Newtonian fluid models (Carreau) are represented by solid lines. Based on the energy dissipation factor and the effective shear modulus obtained in advance for the die, the viscosity was calculated according to the shear rate using only the flow rate and pressure drop information. It can be seen from FIG. 7B that the results obtained by obtaining the viscosity according to the shear rate derived by the simulation and the results obtained by obtaining the viscosity according to the shear rate derived according to an embodiment of the present invention are consistent.

유체 유량 또는 압력강하 예측 방법How to predict fluid flow or pressure drop

Hereinafter, a method of predicting a flow rate or a pressure drop of a non-Newtonian fluid according to another aspect of the present invention will be described in detail. According to another aspect of the present invention, a method for estimating the flow rate or pressure drop of a non-Newtonian fluid may include: By preparing in advance the viscosity behavior (viscosity, effective shear rate and their relationship) of a Newtonian fluid, the present invention relates to a method for predicting the flow rate or pressure drop of a non-Newtonian fluid actually flowing in the flow field.

The method for estimating the flow rate or pressure drop of the non-Newtonian fluid may include preparing the flow water in the flow field, preparing the viscosity behavior information of the non-Newtonian fluid, and the viscosity behavior information of the flow water and the non-Newtonian fluid in the flow field. And deriving the other information from the information of any one of the flow rate and the pressure drop of the non-Newtonian fluid in the flow field based on the following (hereinafter referred to as 'derivating another information'). have. In detail, when the flow rate of the non-Newtonian fluid is determined, the pressure drop corresponding to the flow rate may be predicted, or when the pressure drop of the non-Newtonian fluid is determined, the flow rate corresponding to the pressure drop may be predicted.

On the other hand, the flow characteristics of the unspecified complex fluids flowing in a specific shape of the flow field may be a quantified flow rate, that is, a non-dimensionalized number regardless of the types of fluids, and the flow water in such a flow field is the coefficient of energy dissipation rate) K _p and / or the coefficient of effective shear rate K _s . The flow water in such a flow field is a non-dimensionalized number N _p that can represent energy dissipation for a particular shape of the flow field. And the relationship between Reynolds number Re and the step of preparing the flow water in the flow field is substantially the same as the step of preparing the flow water in the flow field in the above-described method for measuring the viscosity of the fluid, and thus the detailed description is omitted. Let's do it.

Preparing the viscosity behavior information of the non-Newtonian fluid may be to prepare a viscosity behavior curve as shown in Figure 1 showing the viscosity-effective shear rate relationship. This viscosity behavior curve can be obtained through a viscosity measuring instrument.

Deriving the other information may use at least one of the following

Equations

6, 7 and 8 below. Equations described after Equation 6 may be the same as Equations previously described, but are described as new equations for convenience of description.

[Equation 6]

[Equation 7]

[Equation 8]

Is the apparent shear rate of the flow field,

Is the effective shear rate of the flow field, Re is Reynolds number, K _p is the energy dissipation rate coefficient, K _s may mean the effective shear rate coefficient.

Extracting this other piece of information first involves the apparent shear rate

The effective shear rate can be obtained by using the relationship between the effective shear rate coefficient K _s derived from the flow characteristics of the flow field. Where apparent shear rate

May be a function of the flow rate of the non-Newtonian fluid flowing in the flow field. Apparent shear rate

The relationship between and the effective shear rate coefficient K _s can be defined by Equation 8, the effective shear rate through Equation 8

Can be derived. Where effective shear rate

Apparent apparent shear rate

Similarly, it can be derived as a function of the flow rate of the non-Newtonian fluid.

In addition, the effective viscosity can be obtained using the derived effective shear rate and the viscosity behavior (viscosity-effective shear rate relationship, viscosity behavior curve) of the non-Newtonian fluid prepared in advance. Here, the effective viscosity can be expressed by μ _eff . Effective viscosity μ _eff degree Effective shear rate

Likewise, it may mean a function of the flow rate of the non-Newtonian fluid.

The effective Reynolds number can then be determined using the relationship between the average velocity, density and viscosity of the fluid, the characteristic length of the flow field and the derived effective viscosity. Here, the relationship between the average velocity, density and viscosity of the fluid, and the characteristic length of the flow field can be defined by Equation 9.

[Equation 9]

Where ρ is the density of the fluid,

Is the average velocity of the fluid, L is the characteristic length of the flow field system, and μ is the viscosity of the fluid. Average velocity of fluid

May be the flow rate of the fluid divided by the cross-sectional area, and the characteristic length of the flow field system may vary depending on the shape of the flow field.

The density ρ of the fluid in Equation 9 is determined by the type of non-Newtonian fluid, the characteristic length L of the flow field is determined by the shape of the flow field, and the average velocity of the fluid

The effective viscosity μ _eff as the viscosity μ of the fluid can mean a function of the flow rate of the fluid, so the effective Reynolds number Re _eff derived as Reynolds number Re It may also mean a function of the flow rate of the fluid.

The power number can be obtained using the effective shear rate coefficient K _s and the effective Reynolds number Re _eff derived in advance. In detail, the number of powers may be derived using Equation (7).

Since the effective Reynolds number Re _eff derived above can be used for Reynolds number Re in Equation 7, power number N _p derived using the same may also mean a function of the flow rate of the fluid.

Thereafter, the average power, density, apparent shear rate of the fluid, the fluid volume in the flow field, and the derived power number can be used to find the total power according to the stress. In detail, Equation 6 may be used.

The density ρ of the fluid in Equation 6 is determined by the type of non-Newtonian fluid, the volume of the fluid may be determined by the shape of the flow field, the average velocity of the fluid

Apparent shear rate

, Power N _p Since may be a function of the flow rate of the fluid as mentioned above, the total power P for the stress derived by Equation 6 may also mean a function of the flow rate of the fluid.

On the other hand, the total power P for stress can be expressed as the product of the pressure drop and the flow rate of the fluid, as shown in Equation 10.

[Equation 10]

Here, P may mean the total power according to the stress, Δp is the pressure drop of the fluid, Q may mean the flow rate of the fluid.

Therefore, if we establish an equation that equals the total power P for the stress derived from Equation 6 and the total power P for the stress according to Equation 10, the equation is the shape of the flow field, the flow characteristics in the flow field, and the non-Newtonian. It may be arranged in a form including a constant (Constant Number) determined by the viscosity behavior of the fluid, and a variable (Variable Number) such as the pressure drop and the flow rate of the fluid. That is, the relationship between the pressure drop and the flow rate of a particular non-Newtonian fluid in the flow field can be derived.

For example, in a general flow field system having characteristic length L and total volume V, the relationship between the pressure drop and the flow rate of the flowing non-Newtonian fluid can be derived as in Equation 11 below.

[Equation 11]

Where Δp is the pressure drop of the fluid, Q is the flow rate of the fluid, K _p Is the energy dissipation factor, V is the volume of the flow field, L is the characteristic length of the flow field,

Is the average velocity of the fluid,

Is the apparent shear rate, μ _eff may mean the effective viscosity.

Therefore, when the flow rate of the non-Newtonian fluid is determined in the flow field system, the pressure drop of the non-Newtonian fluid corresponding to the flow rate may be derived.

Conversely, if the pressure drop of the non-Newtonian fluid is determined in the flow field system, the flow rate of the non-Newtonian fluid corresponding to the pressure drop can be derived. However, Equation 11 is derived based on the flow function of the non-Newtonian fluid, and since the variables on the right side include many variables related to the flow function of the non-Newtonian fluid, it is possible to find a flow solution related to each variable. It is desirable to use computing devices, software, and numerical analysis tools that include algorithms. In addition to using such a tool, using Equation 11, the arbitrary flow rates of the non-Newtonian fluid and the pressure drops corresponding to the flow rates are organized into table data, and the specific pressure drop information of the non-Newtonian fluid is based on the summarized data. The flow rate of the non-Newtonian fluid may also be derived by searching for corresponding flow rate information.

On the other hand, based on Equation 11, the relationship between the pressure drop and the flow rate in a simple circular pipe flow field having a radius R and the total volume V can be derived by Equation 12.

[Equation 12]

Fluid flow rate or pressure drop prediction system

In another embodiment of the present invention, a system for predicting the flow rate or pressure drop of a non-Newtonian fluid according to another aspect (hereinafter referred to as a 'prediction system') is provided in a specific shape of a flow field having an inlet and an outlet, such as a pipe. Preliminary preparation of the flow water quantifying the flow characteristics of the unspecified multiple fluids and the viscosity behavior (viscosity, effective shear rate, and their relationship) of the non-Newtonian fluid can predict the flow rate or pressure drop of the non-Newtonian fluid flowing in the flow field. It is about a system that can.

Such a prediction system may be a system using a method for predicting a flow rate or a pressure drop of a non-Newtonian fluid according to an aspect of the present invention described above. For the convenience of description, the role played by the configuration included in the prediction system may correspond to the technical contents of various steps including the method of estimating the flow rate or the pressure drop of the non-Newtonian fluid according to one embodiment of the present invention. Therefore, detailed description thereof will be omitted.

The prediction system 200 includes a flow water storage unit 210 for storing the flow water in the flow field, a viscosity behavior information storage unit 220 for storing the viscosity behavior information of the non-Newtonian fluid, and the flow water in the flow field and the Based on the viscosity behavior information, may include a derivation unit 230 for deriving the other information from any one of the information of the flow rate and pressure drop of the non-Newtonian fluid in the flow field. Here, the flow water storage unit 210 and the viscosity behavior information storage unit 220 is a nonvolatile memory, a volatile memory, a flash memory (flash-memory), a hard disk drive (HDD), or a solid state drive capable of storing various data. SSD) and the like. Here, the derivation unit 230 may be a program module or software including an operation algorithm for generating new data by using and processing various data stored in the flow water storage unit 210 and the viscosity behavior information storage unit 220.

The flow water storage unit 210 may store the energy dissipation rate K _p and the effective shear rate coefficient K _s obtained in advance for the flow field system. Since the method for calculating the energy dissipation rate K _p and the effective shear rate coefficient K _s has been described above, a detailed description thereof will be omitted.

Viscosity behavior information storage unit 220 may store the viscosity-effective shear rate coordinate information of the viscosity behavior curve to the clay behavior curve as shown in Figure 1 showing the viscosity-effective shear rate relationship of the non-Newtonian fluid to be predicted.

The derivation unit 230 calculates a pressure drop corresponding to the flow rate of the non-Newtonian fluid by using at least one of

Equations

6, 7, and 8 described above, or calculates a flow rate corresponding to the pressure drop of the non-Newtonian fluid. Can be calculated.

The derivation unit 230 represents a functional relationship including variables that can be derived based on the flow rate of the non-Newtonian fluid in the flow field and a pressure drop variable or a flow rate information-pressure drop information relationship of the non-Newtonian fluid in the flow field. Using the table data, the pressure drop information corresponding to the flow rate information of the non-Newtonian fluid may be derived, or the flow rate information corresponding to the pressure drop information of the non-Newtonian fluid may be derived.

The derivation unit 230 calculates an effective shear rate using the relationship between the apparent shear rate and the effective shear rate coefficient K _s , and calculates an effective viscosity using the effective shear rate and the viscosity behavior. An effective Reynolds number calculation unit 233 for calculating an effective Reynolds number using the relationship between the effective viscosity calculation unit 232 to obtain the average velocity, density and viscosity of the fluid, the characteristic length of the flow field and the effective viscosity; A power number calculation unit 2134 for calculating the power number using the effective shear rate coefficient K _s and the effective Reynolds number, and using the average velocity, density, apparent shear rate, fluid volume in the flow field, and the power number The total power calculation unit 235 for obtaining the total power according to the stress; may include.

The total power calculator 235 may calculate a relationship between the flow rate and the pressure drop of the non-Newtonian fluid in the flow field based on the total power according to the obtained stress.

The derivation unit 230 may further include a flow rate information using unit 236 for obtaining at least one of an apparent shear rate and an average speed of the fluid through the flow rate information of the non-Newtonian fluid in the flow field.

At least one of the effective shear rate calculator 231, the effective Reynolds number calculator 233, and the total power calculator 235 may use information derived from the flow rate information utilization unit 236.

Energy Dissipation Factor K _p and Effective Shear Factor K _s May be a kind of flow number that does not have much to do with the rheological properties of the fluid and only depends on the type of system (flow field). Therefore, once the energy dissipation factor and effective shear modulus are obtained once for a particular type of flow field, the flow characteristics such as the relationship between pressure drop and flow rate for various complex fluids, especially non-Newtonian fluids, are Can be quantified.

This makes it easy to quantify the relationship between the pressure drop and the flow rate for a particular non-Newtonian fluid for a particular type of flow field, so that the pressure drop and flow rate, referred to as the die characteristics of the extrusion die used in polymer processing Using the quantified information of the advantage that can be easily derived the optimal process.

Here, the non-Newtonian fluid models used are three kinds, such as a power-law model, a Carreau model, and a modified H-B model.

Flow information of the enlarged / reduced circular pipe flow of FIG. 9 is as follows.

Energy dissipation factor K _p = 86, effective shear modulus K _p = 0.71

FIG. 10 is a flow simulation of a corresponding pressure drop for an arbitrary flow rate for a "Kenics static mixer" flow, and predicts a flow rate or pressure drop of a non-Newtonian fluid according to another aspect of the present invention. The results of predicting the pressure drop corresponding to an arbitrary flow rate using a method and / or a system show that the result is almost identical.

Flow information of the "Kenics static mixer" flow according to FIG. 10 is as follows.

Energy dissipation factor K _p = 16.13, effective shear modulus K _p = 1.77

Here, the non-Newtonian fluid model used is a power-law model.

Flow information of the flow corresponding to each volume fraction vf in the "porous medium of the body-centered cubic (BCC) structure" according to FIG. 11 is as follows.

Vf = 0.1: Energy dissipation factor K _p = 2.34, effective shear rate coefficient K _p = 1.29

Vf = 0.3: Energy dissipation factor K _p = 5.78, effective shear rate coefficient K _p = 1.05

Vf = 0.5: energy dissipation factor K _p = 9.94, effective shear rate coefficient K _p = 0.9

Vf = 0.65: Energy dissipation factor K _p = 13.58, effective shear rate coefficient K _p = 0.83

The embodiments described above are merely illustrative of some examples of the present invention, and the scope of the present invention is not limited to the described embodiments, and various changes, modifications or substitutions may be made by those skilled in the art. Can be. For example, the components or features described together in a particular embodiment may be implemented in a distributed manner, and the components or features described in each of the different embodiments may be implemented in a combined form. Likewise, the elements or features described in each claim may be practiced in a distributed manner or in combination with one another. And all such implementations should be seen as falling within the scope of the present invention.

Claims

A method of measuring the viscosity in a continuous flow field of a particular shape having an inlet and an outlet,

Preparing flow water in the flow field;

Measuring the flow rate and pressure drop of the fluid in the flow field; And

Calculating an average energy dissipation rate using the flow rate and the pressure drop, and deriving a viscosity of the fluid according to the effective shear rate based on the flow water in the flow field and the average energy dissipation rate. Method for measuring the viscosity of.
The method of claim 1,

Deriving the viscosity of the fluid is a method of measuring the viscosity in a continuous flow field to derive the viscosity of the fluid according to the effective shear rate using the following equation (1) and (2):

[Equation 1]

[Equation 2]

here,
Is the average energy dissipation rate of the flow field and is a function of the flow rate, the pressure drop and the volume of the flow field,
Is the effective shear rate of the flow field,
Is the viscosity of the fluid,
Is the apparent shear rate of the flow field, K p Is the energy dissipation factor and K s is the effective shear factor.
The method of claim 1,

The continuous flow field has a plurality of inlets and a single outlet,

Deriving the viscosity of the fluid is calculated in the total energy dissipation rate using the following equation A, the average energy dissipation rate based on the total energy dissipation rate and the volume of the flow field, viscosity in a continuous flow field How to measure:

Equation A

Where n is the quantity of the inlet,
Is the pressure drop of the fluid between each inlet and single outlet,
Is the flow rate of the fluid at each inlet.
The method of claim 1,

The continuous flow field has a single inlet and a plurality of outlets,

Deriving the viscosity of the fluid is calculated in the total energy dissipation rate using the following equation B, the average energy dissipation rate based on the total energy dissipation rate and the volume of the flow field, viscosity in a continuous flow field How to measure:

Equation B

Where n is the quantity of exits,
Is the pressure drop of the fluid between a single inlet and each outlet,
Is the flow rate of the fluid at each outlet.
The method of claim 1,

The flow water in the flow field includes an energy dissipation factor K p ,

Preparing the flow water in the flow field includes obtaining the energy dissipation factor K p in advance,

Acquiring the energy dissipation rate coefficient K p in advance,

Injecting Newtonian fluid with known viscosity into the flow field;

Measuring the flow rate and pressure drop of the Newtonian fluid in the flow field;

Obtaining an average energy dissipation rate of the Newtonian fluid using the flow rate and the pressure drop of the Newtonian fluid;

Obtaining Reynolds number and power number using the density, average velocity and viscosity of the Newtonian fluid, the characteristic length of the flow field, the apparent shear rate of the Newtonian fluid, and the average energy dissipation rate of the Newtonian fluid; And

The energy dissipation factor K p using the relationship between the Reynolds number, the power number and the energy dissipation factor K p Method for measuring the viscosity in a continuous flow field comprising the step of obtaining.
The method of claim 1,

The flow water in the flow field includes an energy dissipation factor K p ,

Preparing the flow water in the flow field includes obtaining the energy dissipation factor K p in advance,

Acquiring the energy dissipation rate coefficient K p in advance,

Obtaining a velocity field of the flow field using a Newtonian fluid;

Obtaining a local energy dissipation rate by multiplying the viscosity of the Newtonian fluid by the square of the shear rate at the minute point of the flow field;

Integrating the local energy dissipation rate over the entire flow field to obtain a total energy dissipation rate;

Dividing the total energy dissipation rate by the volume of the flow field to obtain an average energy dissipation rate of the Newtonian fluid;

Obtaining Reynolds number and power number using the density, average velocity and viscosity of the Newtonian fluid, the characteristic length of the flow field, the apparent shear rate of the Newtonian fluid, and the average energy dissipation rate of the Newtonian fluid; And

The energy dissipation factor K p using the relationship between the Reynolds number, the power number and the energy dissipation factor K p Method for measuring the viscosity in a continuous flow field comprising the step of obtaining.
The method of claim 1,

The flow water in the flow field includes the effective shear rate coefficient K s ,

Preparing the flow water in the flow field includes acquiring the effective shear rate coefficient K s in advance,

Acquiring the effective shear rate coefficient K s in advance,

Injecting a non-Newtonian fluid having a known viscosity behavior into the flow field;

Measuring the flow rate and pressure drop of the non-Newtonian fluid in the flow field;

Obtaining an average energy dissipation rate and a power number of the non-Newtonian fluid using the flow rate and the pressure drop of the non-Newtonian fluid;

Finding a Reynolds number of the Newtonian fluid corresponding to the power number of the Newtonian fluid having the same value as the number of powers of the non-Newtonian fluid, and considering the Reynolds number of the Newtonian fluid as an effective Reynolds number;

Calculating the viscosity of the non-Newtonian fluid using the effective Reynolds number, the density of the non-Newtonian fluid, the average velocity, and the characteristic length of the flow field, and considering the viscosity as the effective viscosity;

Obtaining an effective shear rate of the flow field using the effective viscosity and the viscosity behavior; And

Determining the effective shear rate coefficient K s using the relationship between the effective shear rate and the apparent shear rate.
The method of claim 1,

The flow water in the flow field includes the effective shear rate coefficient K s ,

Preparing the flow water in the flow field includes acquiring the effective shear rate coefficient K s in advance,

Acquiring the effective shear rate coefficient K s in advance,

Performing a flow analysis using a non-Newtonian fluid having a known viscosity behavior;

Obtaining a local energy dissipation rate by multiplying the viscosity of the non-Newtonian fluid by the square of the shear rate at the minute point of the flow field;

Integrating the local energy dissipation rate over the entire flow field to obtain a total energy dissipation rate;

Dividing the total energy dissipation rate by the volume of the flow field to obtain an average energy dissipation rate of the non-Newtonian fluid;

Obtaining a power number using the density, average speed, apparent shear rate, and average energy dissipation rate of the non-Newtonian fluid;

Finding a Reynolds number of the Newtonian fluid corresponding to the power number of the Newtonian fluid having the same value as the number of powers of the non-Newtonian fluid, and considering the Reynolds number of the Newtonian fluid as an effective Reynolds number;

Calculating the viscosity of the non-Newtonian fluid using the effective Reynolds number, the density of the non-Newtonian fluid, the average velocity, and the characteristic length of the flow field, and considering the viscosity as the effective viscosity;

Obtaining an effective shear rate of the flow field using the effective viscosity and the viscosity behavior; And

Determining the effective shear rate coefficient K s using the relationship between the effective shear rate and the apparent shear rate.
A system for measuring the viscosity in a continuous flow field of a specific shape having an inlet and an outlet,

A flow water storage unit for storing the flow water in the flow field;

A flow rate measuring unit measuring a flow rate of the fluid in the flow field;

A pressure measuring unit for calculating a pressure drop in the flow field; And

A derivation unit for calculating an average energy dissipation rate using the measured flow rate and pressure drop, and deriving a viscosity of the fluid according to the effective shear rate based on the flow water in the flow field and the average energy dissipation rate; Viscosity Measurement System in Continuous Flow Field.
The method of claim 9,

The derivation unit uses the following equations (1) and (2) to derive the viscosity of the fluid according to the effective shear rate, viscosity measurement system in a continuous flow field:

[Equation 1]

[Equation 2]

here,
Is the average energy dissipation rate of the flow field and is a function of the flow rate, the pressure drop and the volume of the flow field,
Is the effective shear rate of the flow field,
Is the viscosity of the fluid,
Is the apparent shear rate of the flow field, K p Is the energy dissipation factor and K s is the effective shear factor.
The method of claim 9,

The continuous flow field has a plurality of inlets and a single outlet,

The derivation unit calculates the total energy dissipation rate using the following equation A, and calculates an average energy dissipation rate based on the total energy dissipation rate and the volume of the flow field, viscosity measuring system in a continuous flow field:

Equation A

Where n is the quantity of the inlet,
Is the pressure drop of the fluid between each inlet and single outlet,
Is the flow rate of the fluid at each inlet.
The method of claim 9,

The continuous flow field has a single inlet and a plurality of outlets,

The derivation unit calculates the total energy dissipation rate using the following equation B, and calculates the average energy dissipation rate based on the total energy dissipation rate and the volume of the flow field, viscosity measuring system in a continuous flow field:

Equation B

Where n is the quantity of exits,
Is the pressure drop of the fluid between a single inlet and each outlet,
Is the flow rate of the fluid at each outlet.
A method of predicting the flow rate or pressure drop of a non-Newtonian fluid flowing in a continuous flow field of a specific shape having an inlet and an outlet,

Preparing flow water in the flow field;

Preparing viscosity behavior information of the non-Newtonian fluid; And

Deriving the other information from any one of the flow rate and the pressure drop of the non-Newtonian fluid in the flow field based on the flow water and the viscosity behavior information in the flow field. How to predict the descent.
The method of claim 13,

The deriving of the other information may include predicting the flow rate or pressure drop of the non-Newtonian fluid in the continuous flow field using at least one of the following Equations 6, 7 and 8.

[Equation 6]

[Equation 7]

[Equation 8]

Where N p Is the number of powers, P is the total power according to the stress, the product of the flow rate and the pressure drop,
Is the apparent shear rate of the flow field,
Is the effective shear rate of the flow field, Re is the Reynolds number, K p is the energy dissipation factor, and K s is the effective shear factor.
The method of claim 14,

The flow water in the flow field is energy dissipation rate K p , effective shear rate coefficient K s Including;

Extracting the other information,

Apparent shear rate and effective shear rate coefficient K s of the flow field Obtaining the effective shear rate of the flow field using the relationship between

Obtaining an effective viscosity using the effective shear rate and the viscosity behavior of the flow field;

Obtaining an effective Reynolds number using the relationship between the average velocity, the density and the viscosity of the fluid, the characteristic length of the flow field and the effective viscosity;

The effective shear rate coefficient K s And calculating the number of powers using the effective Reynolds number; and

Calculating the total power according to the stress using the average velocity, density, apparent shear rate of the fluid, fluid volume in the flow field and the number of powers;

Obtaining a total power according to the stress, wherein the relationship between the flow rate and the pressure drop of the non-Newtonian fluid in the flow field can be obtained.
The method of claim 15,

Deriving the other information,

Wherein the information is the flow rate information of the non-Newtonian fluid in the flow field, and further comprising the step of obtaining at least one of the apparent shear rate and the average velocity of the fluid through the flow rate information of the non-Newtonian fluid in the flow field, A method of predicting the flow rate or pressure drop of a non-Newtonian fluid.
A system for predicting the flow rate or pressure drop of a non-Newtonian fluid flowing in a continuous flow field of a specific shape having an inlet and an outlet,

A flow water storage unit for storing the flow water in the flow field;

A viscosity behavior information storage unit for storing the viscosity behavior information of the non-Newtonian fluid; And

A flow rate of the non-Newtonian fluid, including a derivation unit for deriving the other information from any one of the non-Newtonian flow rate and the pressure drop in the flow field based on the flow rate and the viscosity behavior information in the flow field. Prediction system to predict pressure drop.
The method of claim 17,

The derivation unit predicts the flow rate or the pressure drop of the non-Newtonian fluid using at least one of the following Equations 6, 7 and 8:

[Equation 6]

[Equation 7]

[Equation 8]

Where N p Is the number of powers, P is the total power according to the stress, the product of the flow rate and the pressure drop,
The apparent shear rate,
Is the effective shear rate, Re is the Reynolds number, K p Is the energy dissipation factor and K s is the effective shear factor.
The method of claim 18,

The flow water in the flow field is energy dissipation rate K p , effective shear rate coefficient K s Including;

The derivation unit,

An effective shear rate calculation unit for calculating an effective shear rate using a relationship between the apparent shear rate and the effective shear rate coefficient K s ;

An effective viscosity calculation unit for obtaining an effective viscosity using the effective shear rate and the viscosity behavior;

An effective Reynolds number calculation unit for obtaining an effective Reynolds number using the relationship between the average velocity of the fluid, the density and the viscosity, the characteristic length of the flow field and the effective viscosity;

The effective shear rate coefficient K s And a power number calculation unit for calculating a power number using the effective Reynolds number; and

And a total power calculation unit for calculating the total power according to the stress using the average velocity of the fluid, the density, the apparent shear rate, the fluid volume in the flow field, and the number of powers.

The total power calculation unit predicts the flow rate or pressure drop of the non-Newtonian fluid, which obtains a relationship between the flow rate and the pressure drop of the non-Newtonian fluid in the flow field based on the total power according to the obtained stress.
The method of claim 19,

Wherein any one of the information is the flow rate information of the non-Newtonian fluid in the flow field,

The derivation unit further includes a flow rate information using unit for obtaining at least one of the apparent shear rate and the average velocity of the fluid through the flow rate information of the non-Newtonian fluid in the flow field, the prediction system for predicting the flow rate or pressure drop of the non-Newtonian fluid. .