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WO2018190585A2 - Procédé et système pour la mesure de viscosité dans un champ d'écoulement continu, et procédé et système pour la prédiction de débit ou de chute de pression de fluide non newtonien dans un champ d'écoulement continu - Google Patents

Procédé et système pour la mesure de viscosité dans un champ d'écoulement continu, et procédé et système pour la prédiction de débit ou de chute de pression de fluide non newtonien dans un champ d'écoulement continu Download PDF

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Publication number
WO2018190585A2
WO2018190585A2 PCT/KR2018/004117 KR2018004117W WO2018190585A2 WO 2018190585 A2 WO2018190585 A2 WO 2018190585A2 KR 2018004117 W KR2018004117 W KR 2018004117W WO 2018190585 A2 WO2018190585 A2 WO 2018190585A2
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Prior art keywords
rate
flow field
flow
viscosity
fluid
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PCT/KR2018/004117
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English (en)
Korean (ko)
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WO2018190585A3 (fr
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황욱렬
장혜경
Original Assignee
경상대학교산학협력단
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Priority claimed from KR1020170154237A external-priority patent/KR102013036B1/ko
Application filed by 경상대학교산학협력단 filed Critical 경상대학교산학협력단
Priority to EP18783849.5A priority Critical patent/EP3614123B1/fr
Publication of WO2018190585A2 publication Critical patent/WO2018190585A2/fr
Publication of WO2018190585A3 publication Critical patent/WO2018190585A3/fr

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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N11/00—Investigating flow properties of materials, e.g. viscosity, plasticity; Analysing materials by determining flow properties
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N11/00—Investigating flow properties of materials, e.g. viscosity, plasticity; Analysing materials by determining flow properties
    • G01N11/02—Investigating flow properties of materials, e.g. viscosity, plasticity; Analysing materials by determining flow properties by measuring flow of the material

Definitions

  • 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.
  • Metzner-Otto technique 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.
  • the flow rate and pressure drop relations 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.
  • 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 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.
  • the viscosity of the fluid according to the effective shear rate may be derived using Equations 1 and 2 below.
  • 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.
  • n is the quantity of the inlet
  • 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.
  • n is the quantity of exits
  • 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 energy dissipation factor K p in advance
  • 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.
  • 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 energy dissipation factor K p in advance
  • 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
  • the flow water in the flow field includes an effective shear rate coefficient K s
  • preparing the flow water in the flow field includes obtaining the effective shear rate coefficient K s in advance
  • 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
  • the flow water in the flow field includes an effective shear rate coefficient K s
  • preparing the flow water in the flow field includes obtaining the effective shear rate coefficient K s in advance
  • 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
  • Viscosity measurement system in a continuous flow field 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.
  • the derivation unit may derive the viscosity of the fluid according to the effective shear rate by using Equations 1 and 2 below.
  • 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.
  • n is the quantity of the inlet
  • 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.
  • n is the quantity of exits
  • 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.
  • the deriving of the other information may use at least one of Equations 6, 7 and 8 below.
  • 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
  • Re is the Reynolds number
  • K p is the energy dissipation factor
  • K s is the effective shear factor
  • 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 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.
  • the derivation unit may use at least one of Equations 6, 7 and 8 below.
  • 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 effective shear rate, Re is Reynolds number
  • K p is energy dissipation factor
  • K s Is the effective shear factor.
  • 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
  • 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-
  • 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.
  • 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.
  • 1 is a graph showing the relationship between the shear rate and the viscosity of a rheological complex fluid.
  • FIG. 2 is a conceptual diagram schematically showing an example of a flow field having a single inlet and a single outlet.
  • FIG. 3 is a conceptual diagram schematically showing an example of a flow field having a plurality of inlets and a single outlet.
  • FIG. 4 is a conceptual diagram schematically showing an example of a flow field having a single inlet and a plurality of outlets.
  • FIG. 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.
  • BCC body-centered cubic
  • 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.
  • Fluid viscosity measurement method 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.
  • 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.
  • N p non-dimensionalized number
  • 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.
  • the effective shear rate And the corresponding viscosity ⁇ may be derived using Equations 1 and 2 below.
  • Effective Shear Rate of Fluid The relationship between and viscosity ⁇ may be equal to the relationship between the shear rate and the viscosity of the rheological complex fluid shown in FIG. 1.
  • 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.
  • 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
  • apparent shear rate Therefore, once the flow field is determined, it can be treated as a function of the flow rate of the fluid.
  • FIG. 2 is a conceptual diagram schematically showing an example of a flow field having a single inlet and a single outlet.
  • 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.
  • FIG. 3 is a conceptual diagram schematically showing an example of a flow field having a plurality of inlets and a single outlet.
  • 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.
  • n is the quantity of the inlet
  • the average energy dissipation rate Can be calculated.
  • 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.
  • FIG. 4 is a conceptual diagram schematically showing an example of a flow field having a single inlet and a plurality of outlets.
  • 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.
  • n is the quantity of exits
  • the average energy dissipation rate Can be calculated.
  • 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.
  • 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.
  • the energy dissipation factor K p can be found by experimental techniques.
  • 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.
  • 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.
  • Equations 3 and 4 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.
  • ⁇ is the density of the fluid
  • Is the average velocity of the fluid
  • L is the characteristic length of the flow field system
  • ⁇ is the viscosity of the fluid
  • the physical density of the Newtonian fluid injected into the system may be used as the density ⁇ and the viscosity ⁇ 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.
  • 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.
  • 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.
  • Equation 5 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.
  • the energy dissipation factor K P Calculate the energy dissipation factor K P Can also be obtained through numerical analysis.
  • 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 ⁇ 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.
  • 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.
  • the effective shear modulus K s can be found by experimental techniques.
  • a non-Newtonian fluid such as an Xanthan gum aqueous solution
  • a known viscosity behavior viscosity-effective shear rate relationship
  • the viscosity behavior (viscosity-effective shear rate relationship) of the non-Newtonian fluid can be, for example, as shown in FIG.
  • 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.
  • the power number N p is the average energy dissipation rate of the non-Newtonian fluid calculated based on the density ⁇ 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.
  • 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.
  • 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.
  • 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 ⁇ eff of the complex fluid.
  • ⁇ is the density of the fluid
  • Is the average velocity of the fluid
  • L is the characteristic length of the flow field system
  • ⁇ is the viscosity of the fluid
  • the Reynolds number Re is used as the effective Reynolds number Re eff
  • the density ⁇ of the fluid may be the density of the non-Newtonian fluid injected into the system.
  • Average speed 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.
  • 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.
  • 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.
  • the effective shear rate coefficient K s can also be obtained through numerical techniques.
  • the flow analysis in the flow field may be performed using the non-Newtonian fluid having known viscosity behavior.
  • the local energy dissipation rate ⁇ 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.
  • ⁇ is the density of the fluid
  • Is the average velocity of the fluid Is the average energy dissipation rate of the flow field
  • ⁇ 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 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).
  • ⁇ is the density of the fluid
  • I the average velocity of the fluid
  • L is the characteristic length of the flow field system
  • ⁇ the viscosity of the fluid.
  • the density ⁇ 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 ⁇ eff of the complex fluid.
  • 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.
  • 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.
  • FIG. 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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, so 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.
  • 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.
  • 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.
  • 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
  • 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.
  • FIG. 7A shows a die of a particular shape with a single inlet and outlet.
  • 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.
  • FEM finite element method
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • Equation 6 may be the same as Equations previously described, but are described as new equations for convenience of description.
  • 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 Reynolds number
  • K p is the energy dissipation rate coefficient
  • K s may mean the effective shear rate coefficient.
  • 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.
  • 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.
  • the effective viscosity can be expressed by ⁇ eff .
  • Effective viscosity ⁇ 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.
  • 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.
  • ⁇ is the density of the fluid
  • Is the average velocity of the fluid
  • L is the characteristic length of the flow field system
  • ⁇ 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 ⁇ 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 ⁇ eff as the viscosity ⁇ 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.
  • the number of powers may be derived using Equation (7).
  • power number N p derived using the same may also mean a function of the flow rate of the fluid.
  • Equation 6 may be used.
  • the density ⁇ 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.
  • 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.
  • P may mean the total power according to the stress
  • ⁇ p is the pressure drop of the fluid
  • Q may mean the flow rate of the fluid.
  • 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.
  • Equation 11 the relationship between the pressure drop and the flow rate of the flowing non-Newtonian fluid can be derived as in Equation 11 below.
  • ⁇ p 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
  • ⁇ eff may mean the effective viscosity
  • the pressure drop of the non-Newtonian fluid corresponding to the flow rate may be derived.
  • 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.
  • Equation 12 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.
  • Fluid flow rate or pressure drop prediction system
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • the non-Newtonian fluid models used are three kinds, such as a power-law model, a Carreau model, and a modified H-B model.
  • 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.
  • the non-Newtonian fluid models used are three kinds, such as a power-law model, a Carreau model, and a modified H-B model.
  • 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.
  • BCC body-centered cubic
  • 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.

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Abstract

Selon un mode de réalisation, la présente invention peut fournir un procédé et/ou un système qui peuvent facilement mesurer le comportement de viscosité d'un fluide par la seule mesure d'un débit et d'une chute de pression par la préparation d'un numéro de flux dans un champ d'écoulement continu arbitraire. Selon un autre mode de réalisation, la présente invention peut fournir un procédé et/ou un système qui peuvent facilement mesurer une chute de pression ou un débit dans un champ d'écoulement par la seule préparation d'un numéro de flux dans un champ d'écoulement continu arbitraire et un comportement de viscosité d'un fluide non newtonien circulant dans le champ d'écoulement.
PCT/KR2018/004117 2017-04-13 2018-04-09 Procédé et système pour la mesure de viscosité dans un champ d'écoulement continu, et procédé et système pour la prédiction de débit ou de chute de pression de fluide non newtonien dans un champ d'écoulement continu WO2018190585A2 (fr)

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US6412337B1 (en) 2000-01-28 2002-07-02 Polyvalor S.E.C. Apparatus and method for measuring the rheological properties of a power law fluid

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MX2009009656A (es) * 2007-03-14 2009-09-22 Micro Motion Inc Caudalimetro vibratorio y metodo para determinar la viscosidad en un material de fluencia.
KR101215353B1 (ko) * 2011-03-03 2012-12-26 광주과학기술원 유체 점도 측정 장치 및 점도 측정 방법
US20140005957A1 (en) * 2012-06-29 2014-01-02 Rosemount Inc. Viscometer for newtonian and non-newtonian fluids
DE102012113045B4 (de) * 2012-12-21 2023-03-23 Endress+Hauser SE+Co. KG Verfahren zur Bestimmung und oder Überwachung von zumindest einem Parameter in der Automatisierungstechnik

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US6412337B1 (en) 2000-01-28 2002-07-02 Polyvalor S.E.C. Apparatus and method for measuring the rheological properties of a power law fluid

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