WO2020196612A1 - Non-contact type rheological material property measurement device, system, program and method - Google Patents
Non-contact type rheological material property measurement device, system, program and method Download PDFInfo
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- WO2020196612A1 WO2020196612A1 PCT/JP2020/013299 JP2020013299W WO2020196612A1 WO 2020196612 A1 WO2020196612 A1 WO 2020196612A1 JP 2020013299 W JP2020013299 W JP 2020013299W WO 2020196612 A1 WO2020196612 A1 WO 2020196612A1
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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
- G01N11/02—Investigating flow properties of materials, e.g. viscosity, plasticity; Analysing materials by determining flow properties by measuring flow of the material
- G01N11/04—Investigating flow properties of materials, e.g. viscosity, plasticity; Analysing materials by determining flow properties by measuring flow of the material through a restricted passage, e.g. tube, aperture
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N29/00—Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
- G01N29/02—Analysing fluids
Definitions
- the present invention relates to a non-contact rheological property measuring device, system, program and method for measuring the rheological property of a fluid flowing in a pipe.
- milk sold in stores is sterilized from raw milk milked from cows, and components such as milk fat are adjusted. It is difficult to keep the proportion of milk fat contained in raw milk constant because it depends on the feed given to the cow, the physical condition of the cow, the weather, and the individual cow. Therefore, until now, instead of constantly managing the milk fat content by measuring it, a method has been adopted in which the milk fat content is adjusted by adding an excess amount so that the milk fat content is always contained in a predetermined ratio or more. There is.
- Non-Patent Document 1 a method for measuring the rheological properties of the fluid in the pipe by using an ultrasonic flow velocity measuring device capable of measuring the flow velocity distribution in the pipe and a differential pressure gauge has been proposed so far (Non-Patent Document 1).
- This method uses the flow velocity distribution obtained by assuming the flow in the pipe as a unidirectional steady flow and combining the flow equations based on the model equation (rheological model) that describes the rheological properties, and the ultrasonic flow velocity measuring device. By comparing with the obtained flow velocity distribution, the constants of rheological properties included in the model equation are determined.
- Non-Patent Document 1 there is a problem that the accuracy cannot be guaranteed in principle of measurement unless the flow in the pipe is a steady flow. That is, the above method assumes that the flow in the pipe is a one-way steady flow, but the flow in the pipe in a general production process is always due to the whirlpool generated by the pump for producing the flow, the shape of the pipe, and the like. Since it is pulsating (fluctuation), an error due to the pulsation occurs.
- the flow equation based on the rheology model includes the pressure gradient that drives the fluid. Therefore, it is necessary to substitute the pressure value in the pipe to calculate the rheological properties.
- the measurement accuracy of the pressure sensor itself has a great influence on the calculation result of the rheological physical properties, and the selection of the pressure sensor and the selection of the installation location of the pressure sensor and the like are restricted.
- the present invention has been made to solve the above problems, and is a non-contact type rheological property measuring device capable of measuring rheological properties in a non-contact manner by utilizing pulsation in the flow in a pipe. , Systems, programs and methods are intended to be provided.
- the non-contact rheological physical property measuring device and the non-contact rheological physical property measuring program according to the present invention utilize the pulsation in the flow in the pipe, and the rheological physical properties are non-contact without measuring the pressure in the pipe by a pressure gauge or the like.
- a non-contact type rheological property measuring device that non-contactly measures the rheological physical properties of the fluid flowing in the pipe in order to solve the problem of measuring the number of rheological properties from the ultrasonic flow velocity measuring device along the irradiation direction of ultrasonic waves.
- the peak frequency showing the maximum amplitude value from the pulsation frequency in the fluid can be obtained.
- the peak frequency to be detected and the flow velocity data at a plurality of measurement points are added to the following equation (1) obtained by Fourier transforming the motion equation of the fluid flowing in the tube based on the rheology model with respect to time. It has a numerical solution calculation unit that calculates a numerical solution from a plurality of functional expressions obtained by substitution, and a rheological physical property determination unit that determines a rheological physical property value based on the numerical solution calculated by the numerical solution calculation unit.
- ⁇ are the shear stresses related using the rheological model
- A, B, C, ... are the rheological properties in the rheological model
- ⁇ is the pressure gradient
- ⁇ is the density of the fluid
- ⁇ is the angular frequency of the pulsation in the fluid.
- omega 0 is the peak frequency
- r n is the measuring point
- u is the spatial velocity distribution when the tube ⁇ denotes the Fourier transform of a function
- subscript m is the measurement result, respectively.
- the numerical solution calculation unit may be used.
- the numerical solution may be calculated by minimizing the cost function shown in the following equation (2). [Number 2]
- the numerical solution calculation unit substitutes the data.
- the flow velocity data a function approximation value of the flow velocity data at three or more consecutively adjacent measurement points may be used.
- the numerical solution calculation unit has numerical values based on a plurality of types of rheological models. It may have a rheology model determination unit that calculates the solution and determines the rheology model that is the smallest numerical solution by comparing the numerical solutions as the rheological model of the fluid.
- the peak frequency detection unit uses the viscosity of the fluid and the above.
- the peak frequency showing the maximum amplitude value may be detected from the frequencies in which the viscous layer thickness represented by the ratio of the frequencies of the pulsations in the fluid satisfies the range of the following equation (3).
- ( ⁇ / k ⁇ ) 1/2 is the thickness of the viscous layer
- ⁇ r is the distance between the measurement points
- ⁇ is the viscosity coefficient (kinematic viscosity) of the fluid
- k ⁇ is the detected frequency
- D is the inner diameter of the pipe. Means each.
- the non-contact type rheological physical property measurement system solves the problem of non-contact measurement of rheological physical properties by utilizing the pulsation in the flow in the pipe without measuring the pressure in the pipe with a pressure gauge or the like. Therefore, the flow velocity at a plurality of measurement points along the irradiation direction of the ultrasonic wave is received by irradiating the ultrasonic wave from the outside of the tube toward the inside of the tube and receiving the ultrasonic wave reflected from the inside of the tube toward the outside of the tube. It has an ultrasonic flow velocity measuring device that measures in time series, and the non-contact type rheological physical property measuring device that acquires flow velocity data of each measurement point from the ultrasonic flow velocity measuring device and determines the rheological physical properties of the fluid.
- the non-contact rheological physical property measuring method solves the problem of non-contact measuring rheological physical properties by utilizing the pulsation in the flow in the pipe without measuring the pressure in the pipe with a pressure gauge or the like. Therefore, it is a non-contact rheological property measurement method that measures the rheological property of the fluid flowing in the pipe in a non-contact manner, and acquires flow velocity data at a plurality of measurement points along the irradiation direction of the ultrasonic wave from the ultrasonic flow velocity measuring device.
- a rheology acquisition step to be performed a peak frequency detection step to detect a peak frequency showing the maximum amplitude value from the pulsation frequency in the fluid by frequency analysis of the flow velocity data of each measurement point acquired by this flow velocity acquisition step.
- a plurality of functions obtained by substituting the peak frequency and the flow velocity data at a plurality of measurement points into the above equation (1) obtained by Fourier transforming the motion equation of the fluid flowing in the tube based on the rheology model with respect to time. It has a numerical solution calculation step for calculating a numerical solution from an equation, and a rheological physical property determination step for determining a rheological physical property value based on the numerical solution calculated by this numerical solution calculation step.
- the rheological properties can be measured in a non-contact manner by utilizing the pulsation in the flow in the pipe.
- FIG. 1 It is a block diagram which shows one Embodiment of the non-contact type rheology physical property measurement system which concerns on this invention. It is a flow chart which shows the flow of the rheological physical property measurement processing by the non-contact type rheological physical property measurement system of this embodiment. It is a contour figure which shows the calculation result of the flow velocity data of the in-pipe flow with pulsation calculated in Example 1.
- FIG. 1 is a graph showing the measurement accuracy of the frequency f viscosity coefficient calculated for o mu and pressure gradient alpha.
- FIG. 6 is a graph showing the measurement accuracy of the viscosity coefficient ⁇ and the pressure gradient ⁇ calculated for the amplitude U 1 in the first embodiment.
- It is a schematic diagram which shows the experimental apparatus used in Example 2. It is a schematic diagram which shows the installation state of the ultrasonic transducer in the experimental apparatus of this Example 2. It is a contour diagram which shows the velocity distribution in the in-pipe flow with pulsation of Example 2 and the measurement result which used the test fluid as Newtonian fluid. It is a figure which shows the calculation result of the cost function by the random search method when the test fluid is Newtonian fluid in Example 2.
- FIG. It is a figure which shows the measurement result of the viscosity and the pressure amplitude when the test fluid is a Newtonian fluid in Example 2.
- FIG. It is a three-dimensional graph diagram which shows the calculation result of the cost function by the random search method when the test fluid is a non-Newtonian fluid in Example 2.
- the non-contact rheological property measurement system 1 of the present embodiment is a non-contact rheological property measurement device 2 that measures the flow velocities at a plurality of measurement points in time series, and the ultrasonic flow velocity measurement device 2 It has a non-contact rheological property measuring device 3 that acquires flow velocity data at a measurement point and determines the rheological property of the fluid.
- a non-contact rheological property measuring device 3 that acquires flow velocity data at a measurement point and determines the rheological property of the fluid.
- the ultrasonic flow velocity measuring device 2 irradiates ultrasonic waves from outside the tube toward the inside of the tube, receives ultrasonic waves reflected from the inside of the tube toward the outside of the tube, and receives a plurality of ultrasonic waves along the irradiation direction of the ultrasonic waves.
- the flow velocity at the measurement point of is measured in time series. That is, the ultrasonic flow velocity measuring device 2 can measure the spatiotemporal flow velocity distribution u (r, t) in the pipe in a non-contact and non-invasive manner (without disturbing the flow).
- the technique disclosed in Japanese Patent Application Laid-Open No. 2003-344131 can be used.
- the non-contact type rheological physical property measuring device 3 acquires the flow velocity data of each measurement point from the ultrasonic flow velocity measuring device 2 to determine the rheological physical property of the fluid.
- the non-contact type rheology physical property measuring device 3 in the present embodiment is composed of a computer, and as shown in FIG. 1, mainly includes a display input means 4 for displaying various display screens and inputting various data.
- the storage means 5 that stores various data and functions as a working area when the arithmetic processing means 6 performs arithmetic processing, and the non-contact type rheology physical property measurement program 3a installed in the storage means 5, various types are stored. It has an arithmetic processing means 6 that executes the arithmetic processing of the above and functions as each component described later.
- the display input means 4 is a user interface having an input function and a display function, and in the present embodiment, it is configured by a display having a touch panel function.
- the configuration of the display input means 4 is not limited to that of a touch panel type display, and the display means having only a display function and the input means having only an input function such as a keyboard and a mouse are separated from each other. You may have it in.
- the storage means 5 is composed of a hard disk, ROM (Read Only Memory), RAM (Random Access Memory), flash memory, etc., and is used as a program storage unit 51 for storing the non-contact rheology physical property measurement program 31a and a rheology model. It has a rheology model expression storage unit 52 that stores an equation obtained by Fourier transforming a motion equation of a fluid flowing in a pipe based on time with respect to time, and a threshold storage unit 53 that stores various threshold values.
- the non-contact rheological property measurement program 3a for controlling the non-contact rheological property measurement device 3 of the present embodiment is installed in the program storage unit 51. Then, the arithmetic processing means 6 reads out and executes the non-contact rheological property measuring program 3a, so that the computer functions as each component in the non-contact rheological property measuring device 3.
- the usage pattern of the non-contact rheological property measurement program 3a is not limited to the above configuration.
- the non-contact rheological property measurement program 3a is stored in a non-temporary recording medium that can be read by a computer, such as a CD-ROM or a USB memory, and directly read from the recording medium and executed. Good. Further, it may be used by a cloud computing method, an ASP (Application Service Provider) method, or the like from an external server or the like.
- ASP Application Service Provider
- the rheology model formula storage unit 52 stores the formula obtained by Fourier transforming the equation of motion of the fluid flowing in the tube based on the rheology model with respect to time.
- the equation derived from the rheology model based on the following equation (1) is stored. [Number 1] here, , , , , ⁇ is the shear stress, which is related using a rheological model. A, B, C, ...
- ⁇ is the pressure gradient
- ⁇ is the density of the fluid
- ⁇ is the angular frequency of the pulsation in the fluid
- ⁇ 0 is the peak frequency
- r n is the measurement point
- u is the spatiotemporal flow velocity distribution in the pipe
- the subscript m means the measurement result.
- the number of rheological properties A, B, C, ... Changes depending on the rheological model. For example, the number of rheological properties is 1 when the rheological model suitable for the measurement target is a Newtonian fluid, and the number of rheological properties is 2 or more when the rheological model is a non-Newtonian fluid.
- the term representing the pressure gradient ⁇ is a function of the angular frequency ⁇ in the flow by Fourier transforming with time. Therefore, if the angular frequency ⁇ is specified, the pressure gradient ⁇ can be treated as an unknown constant.
- the angular frequency ⁇ can be obtained from the spatiotemporal flow velocity distribution u (r, t) in the tube. That is, in the equation (1), it is not necessary to measure using a pressure sensor, a pressure gauge, or the like in order to obtain the value of the pressure gradient ⁇ .
- the ultrasonic flow velocity measuring device 2 can measure the spatiotemporal flow velocity distribution u (r, t) in the pipe in a non-contact and non-invasive manner. That is, the non-contact type rheological property measurement system 1 of the present embodiment is a system capable of measuring the rheological property of the fluid flowing in the pipe by non-contact in principle of measurement.
- the angular frequency ⁇ of the pulsation in the fluid is included.
- the flow in a pipe in a production process is constantly pulsating (fluctuating) due to the vortex flow generated by the pump for producing the flow, the shape of the pipe, etc., and therefore the rheological properties of the fluid flowing in such a pipe. Can be used for measurement of. Therefore, the applicable range is wider than that of the conventional system in which only the in-pipe flow that can assume a steady flow can be applied.
- the rheology model includes a Newtonian fluid model in which the shear stress of the flow and the velocity gradient of the flow are proportional (linear) and a non-Newtonian fluid in which the shear stress and the velocity gradient are not proportional (non-linear). It is roughly divided into models.
- the non-Newtonian fluid model include a plastic (Bingham) fluid model, a quasi (pseudo) viscous fluid model, a quasi (pseudo) plastic fluid model, and a dilatant fluid model.
- the threshold value storage unit 53 stores various threshold values.
- the following equation (3) used for detecting the peak frequency ⁇ 0 based on the thickness of the viscous layer and each value associated therewith are stored.
- ( ⁇ / k ⁇ ) 1/2 is the thickness of the viscous layer
- ⁇ r is the distance between measurement points
- ⁇ is the kinematic viscosity coefficient of the fluid
- k ⁇ is the detected frequency
- D means the inner diameter of the pipe, respectively.
- the arithmetic processing means 6 is composed of a CPU (Central Processing Unit) or the like, and by executing the non-contact rheological physical property measurement program 3a installed in the storage means 5, the ultrasonic flow velocity is as shown in FIG.
- a flow velocity acquisition unit 61 that acquires flow velocity data from the measuring device 2
- a peak frequency detection unit 62 that detects a peak frequency ⁇ 0 that indicates the maximum amplitude value from the frequency of the pulsation in the fluid, a peak frequency ⁇ 0, and a plurality of measurement points.
- a numerical solution calculation unit 63 that calculates a numerical solution from a plurality of functional expressions obtained by substituting the flow velocity data in the above, and a rheology model determination unit 64 that determines a rheology model when the rheology model is unknown or changes. It functions as a rheological physical property determination unit 65 that determines a rheological physical property value based on the numerical solution calculated by the numerical solution calculation unit 63.
- the flow velocity acquisition unit 61 acquires flow velocity data at a plurality of measurement points along the ultrasonic irradiation direction from the ultrasonic flow velocity measuring device 2.
- the flow velocity data is discrete data measured at each time interval based on the measurement limit of the ultrasonic flow velocity measuring device 2, but it is higher than the frequency of pulsation in a fluid of several milliseconds to several tens of milliseconds. Since it can be measured at sufficiently short time intervals, it can be treated as time-continuous data.
- the flow velocity acquisition unit 61 in the present embodiment acquires the distance ⁇ r between the measurement points determined based on the measurement limit from the ultrasonic flow velocity measurement device 2, and obtains a threshold value. It is designed to be stored in the storage unit 53.
- the peak frequency detection unit 62 detects the peak frequency ⁇ 0 , which indicates the maximum amplitude value, from the frequency of the pulsation in the fluid by frequency analysis of the flow velocity data of each measurement point.
- Frequency analysis is also called spectrum analysis or waveform analysis.
- Fourier transform, wavelet transform and the like are exemplified.
- the peak frequency ⁇ 0 is detected by using the Fourier transform.
- the peak frequency ⁇ 0 is sometimes called a dominant frequency or a dominant frequency.
- the peak frequency detection unit 62 in the present embodiment has a function of detecting the peak frequency based on the thickness of the viscous layer. Specifically, the frequency showing the maximum amplitude value is detected as the peak frequency ⁇ 0 from the frequencies satisfying the above equation (3).
- 3 ⁇ r which is the minimum value of the equation (3), has at least three or more unknown constants determined by the rheology model selected for calculating the numerical solution by the numerical solution calculation unit 63, and among them.
- the number of functional expressions required to calculate an unknown constant is 3 or more, and the flow velocity data and rheology are used to suppress the deterioration of the measurement accuracy of the rheological properties due to the measurement error of the ultrasonic flow velocity measuring device 2.
- the maximum value D / 2 means the radius of the pipe, and is based on the fact that the viscous layer thickness does not become thicker in the axisymmetric in-pipe flow.
- the numerical solution calculation unit 63 calculates a numerical solution from a plurality of functional equations obtained by substituting the peak frequency ⁇ 0 and the flow velocity data at a plurality of measurement points into the above equation (1).
- the numerical solution calculation unit 63 in the present embodiment calculates the numerical solution by minimizing the cost function shown in the following equation (2).
- a program that minimizes the cost function is created, and the numerical solution is calculated by executing the created program.
- the algorithm for minimizing the cost function is not particularly limited, and examples thereof include a random search method and a gradient descent method. [Number 2]
- the numerical solution calculation unit 63 in the present embodiment uses the function approximation value of the flow velocity data at three or more consecutively adjacent measurement points as the flow velocity data to be substituted. This is to suppress the calculation error of the rheological physical property value caused by the measurement error of the flow velocity data obtained by the ultrasonic flow velocity measuring device 2.
- the method of calculating the function approximation value is not particularly limited, but examples thereof include a Bessel function and a Chebyshev series.
- the numerical solution calculation unit 63 in the present embodiment has a plurality of types of rheology when the rheology model of the fluid flowing in the pipe is unknown or when the rheology model changes from moment to moment due to a change in temperature or various component ratios. Calculate a numerical solution based on the model. Specifically, the numerical solution calculation unit 63 uses an equation obtained by Fourier transforming the equations of motion of the fluid flowing in the pipe based on a plurality of types of rheological models from the rheological model formula storage unit 52 with respect to time. Is calculated.
- the rheology model determination unit 64 determines the rheology model after the numerical solution calculation unit 63 calculates numerical solutions based on a plurality of types of rheology models when the rheology model is unknown.
- the rheology model determination unit 64 in the present embodiment compares a plurality of numerical solutions calculated by the numerical solution calculation unit 63 with each other, and determines the rheology model having the smallest numerical solution as the rheology model of the fluid.
- the method of determining the rheology model when the rheology model suitable for the measurement target is unknown is limited to the method of comparing a plurality of numerical solutions calculated by the numerical solution calculation unit 63 as in the present embodiment. Instead, for example, it is determined whether or not the numerical solution calculated by the numerical solution calculation unit 63 is below a predetermined threshold value, and if it is below the threshold value, the rheology model for which the numerical solution is calculated is measured. If it is larger than the threshold value, the rheological model is changed to a rheological model based on another rheological model stored in the rheological model formula storage unit 52, and a numerical solution is calculated. May be repeated until the rheology model is determined when is equal to or less than the threshold value.
- the rheology physical property determination unit 65 determines the rheological physical property value based on the numerical solution calculated by the numerical solution calculation unit 63.
- the rheological physical property determination unit 65 in the present embodiment determines the rheological physical property values such as the viscosity coefficient ⁇ and the kinematic viscosity coefficient ⁇ of the fluid in the pipe to be measured from the calculated numerical solution. Further, the determined kinematic viscosity coefficient ⁇ is stored in the threshold value storage unit 53 because it is used as the kinematic viscosity coefficient ⁇ when calculating the equation (3) calculated by the peak frequency detection unit 62.
- the threshold value storage unit 53 may be stored in chronological order or rewritten (overwritten) each time it is calculated.
- the component ratio is determined together with the rheological physical property value or by changing to the rheological physical property value. You may try to do it.
- the ultrasonic flow velocity measuring device 2 transmits and receives ultrasonic waves to the fluid flowing in the tube from outside the tube, and analyzes the received ultrasonic waves to obtain a flow velocity at a plurality of measurement points along the irradiation direction of the ultrasonic waves. Is measured in chronological order.
- the flow velocity acquisition unit 61 in the present embodiment acquires the flow velocity data from the ultrasonic flow velocity measuring device 2 and the distance ⁇ r between the measurement points determined at the time of calculating the flow velocity data, and stores the distance ⁇ r in the threshold value storage unit 53. Let me.
- the peak frequency detection unit 62 frequency-analyzes the flow velocity data of each measurement point acquired by the flow velocity acquisition unit 61, and detects the peak frequency ⁇ 0 showing the maximum amplitude value from the pulsation frequency in the fluid (S2). : Peak frequency detection step).
- the frequency analysis using the following spatiotemporal flow velocity distribution u (r i, t j) and equation (4) performing the Fourier transform of the equation (5) below which represents the amplitude value at each frequency (spectrum Analysis) is performed to detect the peak frequency ⁇ 0 .
- u r i, t j
- equation (4) performing the Fourier transform of the equation (5) below which represents the amplitude value at each frequency (spectrum Analysis) is performed to detect the peak frequency ⁇ 0 .
- the peak frequency detection unit 62 determines whether or not the calculated peak frequency ⁇ 0 satisfies the condition within the range of the equation (3) (S3).
- the distance ⁇ r between the measurement points in the equation (3), the kinematic viscosity coefficient ⁇ of the fluid, and the inner diameter D of the pipe are obtained from the threshold value storage unit 63. If the peak frequency ⁇ 0 calculated in step S2 is not within the range of equation (3) (S3: NO), the process returns to step S2 to detect the next largest peak frequency ⁇ 0 and equation (3). ) Is repeated until the requirements are met. Then, when the calculated peak frequency ⁇ 0 is within the range of the equation (3) (S3: YES), the frequency is determined to be the peak frequency ⁇ 0 . In this way, the peak frequency detection unit 62 in the present embodiment detects the maximum amplitude value from the frequencies satisfying the requirement of the equation (3) as the peak frequency ⁇ 0 .
- the numerical solution calculation unit 63 calculates a function approximation value of the flow velocity data in order to suppress the influence of the measurement error in the ultrasonic flow velocity measuring device 2 with respect to the flow velocity data to be substituted in the equation (1) (S4). ..
- the approximate value of the quintic function is calculated using the following equation (6), and the value is used. [Number 6]
- Equation (2) a numerical solution is calculated from a plurality of functional equations obtained by substituting the peak frequency ⁇ 0 and the flow velocity data at the plurality of measurement points based on the equation (1) (S5: numerical solution calculation step).
- the cost function shown in Eq. (2) is used to calculate the numerical solution.
- equation (2) can be rewritten as shown in equations (7) and (8) below. [Number 7] [Number 8]
- ⁇ (t i) denotes the time variation of the pressure gradient.
- the numerical solution is calculated by minimizing this cost function by using a random search method, a gradient descent method, or the like.
- a random search method a gradient descent method, or the like.
- the peak frequency ⁇ 0 detected by the peak frequency detection unit 62 and the flow velocity data acquired by the flow velocity acquisition unit 61 are substituted into each equation, and the pressure data in the pipe is unnecessary.
- the calculation load for calculating the numerical solution is suppressed.
- it depends on the type of algorithm for minimizing the cost function and the processing capacity of the arithmetic processing means it is possible to calculate a numerical solution at intervals of about several seconds to several tens of seconds for one calculation.
- step S5 in order to cope with the case where the rheology model is unknown or the shear stress ⁇ changes according to the temperature, the component ratio, etc. and the rheology model needs to be changed, a plurality of rheology models are used. Calculate the numerical solution. Specifically, the numerical solution calculation unit 63 obtains a plurality of equations obtained by Fourier transforming the equations of motion of the fluid flowing in the pipe based on the plurality of types of rheology models stored in the rheology model equation storage unit 52 with respect to time. Read out and calculate a numerical solution for each equation.
- the rheology model determination unit 64 compares a plurality of numerical solutions with each other and determines the rheology model having the smallest numerical solution as the rheology model of the fluid (S6: rheology model determination step).
- the calculation of the numerical solution for a plurality of types of rheology models in step S4 and the processing of the rheology model determination step in step S5 may be omitted. Further, if there is no change in the rheology model (the shear stress ⁇ is almost unchanged) after the unknown rheology model is determined in step S6, in the subsequent processing, the other rheology model in step 5 is used. The processing of the calculation step S5 of the numerical solution based on the numerical solution and the rheology model determination step S6 can be omitted.
- the rheology physical property determination unit 65 determines the rheological physical property value of the fluid based on the numerical solution obtained by the numerical solution calculation unit 63 (S7: rheological physical property determination step). If the component ratio or the like based on the rheological physical property value can be determined, the component ratio is also determined together with the rheological physical property value.
- Rheological physical property values and component ratios are determined by calculating numerical solutions. That is, the rheological property value can be determined at intervals of about several seconds to several tens of seconds as in the numerical solution. Therefore, fluctuations in rheological physical property values and changes in component ratios can be measured in almost real time.
- the system 1, the program 3a and the method of the present embodiment as described above, the following effects can be obtained.
- 1. By acquiring the flow velocity data that can measure the flow velocity of the fluid flowing in the pipe in a non-contact and non-invasive manner, the rheological properties of the fluid can be measured without measuring the pressure in the pipe or the like. 2.
- 2. Since it utilizes the pulsation in the flow in the pipe, it has a wide range of application and can be applied to various fluids flowing in the pipe.
- 3. 3 Since the processing load required for calculation can be reduced by using a cost function or the like, fluctuations in rheological physical property values and changes in component ratios can be measured in real time. 4.
- the peak frequency detection unit 62 can secure the accuracy in the measurement principle by detecting the peak frequency based on the thickness of the viscous layer.
- Example 1 the non-contact rheological property measurement program according to the present invention is used as flow velocity data obtained by assuming that an in-pipe flow with pulsation is numerically created and the created flow is measured by an ultrasonic flow velocity measuring device. The rheological property value was calculated by. In addition, the exact solution in the pipe flow was compared with the numerical solution obtained by the non-contact rheological property measurement program according to the present invention, and the measurement accuracy was examined.
- R is the radius of the tube
- U 0 is the maximum value of the Hagen-Poiseuille flow
- U 1 is the velocity fluctuation of the pulsation (magnitude of amplitude)
- ⁇ is the pulsation frequency (angular frequency)
- ⁇ means the kinematic viscosity coefficient
- ⁇ means the density of the fluid J 0 and J 1 means the Bessel function, respectively.
- n 10 mm 2 / s
- n 50 mm 2 / s
- n 100 mm 2 /.
- FIG. 3 shows the calculation results in the pipe with pulsation calculated based on each condition.
- the vertical axis represents the position in the pipe.
- the horizontal axis represents the passage of time. Specifically, it is dimensionless as tf o.
- the flow velocity distribution in the pipe for each hour is represented by shades of color. The darker the color, the closer the speed is to zero, and the whiter the color, the faster the speed. Specifically, it is dimensionless as u / U 0 .
- the flow velocity at the central position is high at each time, and the speed becomes slower as it approaches the pipe wall.
- the speed of the central position repeatedly increases and decreases with the passage of time. Therefore, it can be confirmed that the in-pipe flow with pulsation is calculated by the equation (17).
- the calculation result shown in FIG. 3 is an exact solution of the flow velocity distribution in which the in-pipe flow with pulsation is calculated.
- the obtained flow velocity data includes a measurement error (measurement noise).
- measurement error measurement noise
- the flow velocity distribution including the measurement error (measurement noise) in consideration of the measurement accuracy with respect to the flow velocity distribution of the in-pipe flow with pulsation calculated based on the equation (17) is calculated by the following equation (18).
- n (ave, std) is the noise function
- the noise function is represented by a normal distribution with the true value as the median, as shown in FIG.
- the flow velocity data u (r, t) is substituted for the case where the noise level a is 1.0, 5.0, 10.0 and 15.0, and the flow velocity data u'(including the error) ( r, t) was calculated.
- FIG. 5 is a calculation result. As shown in FIG. 5, as the noise level increases, the shape of the obtained flow velocity distribution becomes less smooth. That is, this flow velocity distribution can be seen as flow velocity data including measurement errors.
- the flow velocity data calculated as a true value in this way is given noise as a measurement error to obtain the flow velocity data including the measurement error by the ultrasonic flow velocity measuring device.
- the calculation result is shown in FIG.
- the left side of the figure is the calculation result of the real value Re in the equation (7), and the right side is the calculation result of the imaginary value Im.
- the spread range becomes substantially constant value real value at the center of the tube as the frequency f o (the angular frequency omega) is gradually faster.
- FIG. 7 shows the result when the cost function is minimized.
- the height direction of FIG. 7 represents the calculated viscosity coefficient ⁇
- the lower surface represents the calculated real value Re ( ⁇ a ) and imaginary value Im ( ⁇ b ).
- Each point represents a combination of viscosity coefficient ⁇ , real value and imaginary value when numerical values are randomly entered by the random search method.
- the color of each point indicates the magnitude of the cost function, and the cost function becomes smaller as the color approaches black.
- the value of the cost function calculated by the random search method concentrates on one point on the graph. This concentrated point is the minimized cost function. Then, the value in the height direction of the minimized point of the cost function can be determined as the viscosity coefficient ⁇ .
- the rheological property value obtained from the calculation result of the numerical solution was compared with the rheological property value used for the calculation of the in-pipe flow corresponding to the true value. Further, in the present invention, the pressure gradient can be calculated together with the rheological property value. Therefore, the pressure gradient obtained from the calculation result of the numerical solution was also compared with the pressure gradient used for the calculation of the in-pipe flow corresponding to the true value.
- the noise level is shown on the horizontal axis.
- the vertical axis shows ⁇ , which is the ratio of the viscosity coefficient ⁇ obtained from the calculation result of the numerical solution to the true viscosity coefficient ⁇ true , the pressure gradient ⁇ obtained from the calculation result of the numerical solution, and the true pressure. It represents ⁇ , which is the ratio to the gradient ⁇ true .
- the average value of three points consecutive in space (r direction) is used. Since the vertical axis is the ratio to the true value, the closer it is to 1, the closer to the rheological property value and the true value obtained from the calculation result of the numerical solution.
- the horizontal axis is the kinematic viscosity coefficient ⁇
- the vertical axis is ⁇ and ⁇ .
- the accuracy drops in the range where the kinematic viscosity coefficient ⁇ is high. It is considered that this is because the pressure gradient is constant, so that the speed fluctuation becomes weak, and as a result, the noise becomes relatively large.
- the kinematic viscosity coefficient ⁇ was 100 mm 2 / s or less, it almost matched the true value and the accuracy was high.
- the frequency f o (angular frequency ⁇ ) of pulsation.
- the results are shown in FIG.
- the horizontal axis is the frequency f o
- the vertical axis represents the ⁇ and lambda.
- the frequency f o is less accurate in low range. This is because it a pressure gradient constant, the amplitude decreases as the frequency f o is lower, presumably because the noise as a result is relatively large.
- the frequency f o is in the above 1.0 Hz, higher accuracy and substantially coincides with the true value.
- the rheological property of the fluid accompanied by pulsation flowing in the pipe is measured accurately without contact. It was possible to confirm that it can be done by numerical experiments.
- Example 2 an experimental device for creating an in-pipe flow accompanied by pulsation was created, and the rheological property values of the Newtonian fluid and the non-Newtonian fluid were measured by the non-contact rheological property measurement system according to the present invention according to the present invention. Further, the measurement accuracy was examined by comparing the values measured by the catalog value or a commercially available rotary rheometer with the measured values obtained by the non-contact rheological property measurement system according to the present invention.
- the pipe to be measured includes a straight stainless steel pipe and a replaceable acrylic pipe.
- a stainless steel tube having a length of 3000 mm or more, an outer diameter of 50.8 mm (2 inches), and an inner diameter of 40.8 mm was used.
- the acrylic pipe was installed on the wake side of the stainless steel pipe.
- Example 2 the one having an inner diameter of about 48 mm and the one having an inner diameter of about 22 mm were used.
- a point separated from the entrance of the stainless steel pipe by about 3000 mm or more was set as the measurement position.
- a storage tank for storing the test fluid was connected to the upstream side of the pipe to be measured.
- a rotary pump for flowing the test fluid was connected to the downstream side.
- a sanitary pump mainly used in the manufacturing process of foods, pharmaceuticals, cosmetics, etc. was used as the rotary pump.
- the rotary pump is connected to a personal computer so that the frequency of the test fluid flowing in the pipe can be controlled.
- a pipe connected to the storage tank was provided at the outlet of the rotary pump. Therefore, by operating the rotary pump, the test fluid is circulated in the laboratory equipment.
- an ultrasonic transducer which is one configuration of the ultrasonic flow velocity measuring device and a holding jig for holding the ultrasonic transducer at an angle ⁇ 1 are installed.
- an ultrasonic gel was filled between the ultrasonic transducer and the tube to enhance the transmission of ultrasonic waves.
- the ultrasonic flow velocity measuring device is connected to a personal computer configured as the non-contact rheological property measuring device according to the present invention, and a non-contact rheological property measuring system is constructed.
- ⁇ Test fluid used as Newtonian fluid silicone oil having a kinematic viscosity of 10 cSt (viscosity (viscosity coefficient): 9.35 ⁇ 10 -3 [Ps / s]) was used.
- the silicone oil contained tracer particles that promote the reflection of ultrasonic waves.
- the rotary pump was controlled so that a vibration flow of 0.1 Hz was generated, and the rheological property value of the Newtonian fluid (silicone oil) was measured.
- the ultrasonic flow velocity measuring device transmits and receives ultrasonic waves via the ultrasonic transducer, and analyzes the received ultrasonic waves to measure the flow velocity distribution of the in-tube flow accompanied by pulsation.
- the installation angle ⁇ 1 of the ultrasonic transducer and the angle ⁇ 2 in the propagation direction of ultrasonic waves are different due to the difference in the refractive index between the tube and the test fluid, but in the second embodiment, this angle is different. The difference is reflected in the measurement result of the flow velocity distribution.
- FIG. 15 shows the result of measuring the flow velocity distribution in the pipe with the ultrasonic flow velocity measuring device.
- the flow velocity distribution is represented by shades of contour-like color. The whiter the color, the closer the speed is to zero, and the darker the color, the faster the speed.
- the numerical solution was calculated from the functional formula obtained by the formula (1) as in the first embodiment. Since the test fluid is a Newtonian fluid, the rheology model is also a Newtonian fluid. Therefore, a program for minimizing the cost function was created using equations (7) and (8) representing the cost function of the in-pipe flow accompanied by pulsation in the Newtonian fluid, and a numerical solution was calculated by the program. The random search method was used as the algorithm for calculating the cost function.
- Figure 16 shows the calculation result of the cost function.
- the vertical axis shows the viscosity ⁇
- the horizontal axis shows the pressure amplitude.
- the pressure amplitude is the norm value of the real part and the imaginary part of the pressure.
- the value of the cost function is represented by shades of contour-like color. The whiter the color, the smaller the value, and the darker the color, the larger the value.
- the value of the cost function calculated by the random search method is concentrated on one point on the graph. This concentrated point is the minimized cost function. Then, the value in the height direction of the minimized point of the cost function can be determined as the viscosity coefficient ⁇ .
- FIG. 17 shows data of viscosity (Viscosity) and pressure amplitude (Pressure amplitude) measured at intervals of 10 seconds for about 1000 seconds.
- the broken line in the figure is the catalog value of the viscosity of the silicone oil used as the test fluid, 9.35 ⁇ 10 -3 [Ps / s].
- the measured viscosity (Viscosity) values were aggregated into values in the vicinity of 9.35 ⁇ 10 -3 [Ps / s], which is a catalog value.
- Example 2 the non-contact rheological property measurement system of Example 2 can measure the rheological property of the Newtonian fluid with sufficient accuracy.
- CMC aqueous solution As the non-Newtonian fluid, an aqueous solution of carboxymethyl cellulose (hereinafter referred to as "CMC aqueous solution") was used. In Example 2, the concentration of the CMC aqueous solution was 0.5 wt. %. Carboxymethyl cellulose (CMC) is commonly used as a thickener in processed products containing foods.
- the CMC aqueous solution is a pseudo-plastic fluid whose viscosity decreases as the shear rate increases, and in Example 2, a fluid having a viscosity of about 100 to 400 [mPa ⁇ s] was used.
- the left side of FIG. 18 is the result of measuring the flow velocity distribution in the pipe by the ultrasonic flow velocity measuring device.
- the vertical axis represents the dimensionless position in the pipe as r / R
- the horizontal axis represents the passage of time that has been dimensionless as tf, and shows data for about two cycles.
- 19 and 20 are the results of calculating the cost function by the random search method. Similar to FIG. 16 as a result of measuring the Newtonian fluid, the value of the cost function calculated by the random search method is concentrated on one point on the graph. Then, the value in the height direction of the minimized point of the cost function can be determined as the viscosity coefficient ⁇ .
- FIG. 21 shows the value of the shear stress ⁇ according to the strain rate ⁇
- the round plot is the measured value by a commercially available rheometer
- the triangular plot is measured by the non-contact rheological property measurement system according to the present invention. It is a measured value.
- an MCR102 manufactured by Anton Paar was used as a commercially available rheometer.
- the increase in shear stress ⁇ with respect to the strain rate ⁇ showed a similar value when compared with the value of a commercially available rheometer.
- FIG. 22 shows the value of the shear stress ⁇ according to the strain rate ⁇ as in FIG. 21, and the round plot is the measured value by a commercially available rheometer. Further, the triangular plot is the measured value measured by the non-contact rheological property measuring system according to the present invention when the inner diameter of about 48 mm is used, and the cross-shaped plot is the measured value when the inner diameter of about 22 mm is used. As shown in FIG. 22, measurement results corresponding to the entire range that could be measured with a commercially available rheometer were obtained. Moreover, the same value was shown in the whole range as compared with the measurement result of the commercially available rheometer.
- FIG. 23 shows the measurement results for the viscosity ⁇ [Pa ⁇ s] according to the strain rate ⁇ .
- the round plots are measured by a commercially available rheometer.
- the triangular plot is the measured value measured by the non-contact rheological property measuring system according to the present invention when the inner diameter of about 48 mm is used, and the cross-shaped plot is the measured value when the inner diameter of about 22 mm is used.
- the viscosity ⁇ decreases as the strain rate ⁇ measured by a commercially available rheometer increases, indicating the characteristics of the pseudoplastic fluid.
- the rheological property of the fluid accompanied by pulsation flowing in the pipe is measured accurately without contact. It was possible to confirm that it was possible with an actual experimental device.
- non-contact rheological property measuring device, system, program and method according to the present invention are not limited to the above-described embodiments, and can be changed as appropriate.
- the peak frequency detection unit 62 performs frequency analysis only in the frequency range that satisfies the condition within the range of the equation (3), and processes the one showing the largest amplitude to determine the peak frequency ⁇ 0. You may.
- Non-contact type rheology physical property measurement system 1
- Ultrasonic flow velocity measurement device 3
- Non-contact type rheology physical property measurement device 3a
- Non-contact type rheology physical property measurement program 4
- Display input means 5
- Storage means 6
- Arithmetic processing means 51
- Program storage unit 52
- Rheology model type memory Unit 53
- Threshold storage unit 61
- Flow velocity acquisition unit 62
- Peak frequency detection unit 64
- Numerical solution calculation unit 64
- Rheology model determination unit 65
- Rheology physical property determination unit 64
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Abstract
[Problem] To provide a device, a system, a program and a method for non-contact type rheological material property measurement which can measure a rheological material property with no contact, by using pulsation in the flow inside a pipe. [Solution] The present invention includes: a flow rate acquisition unit 61 that acquires flow rate data from an ultrasonic flow rate measurement device 2; a peak frequency detection unit 62 that detects a peak frequency for a fluid by performing frequency analysis of the flow rate data; a numerical solution calculation unit 63 that calculates a numerical solution from a plurality of function expressions obtained by substituting the peak frequency and flow rate data at a plurality of measurement points into an equation obtained by a Fourier transformation, with respect to time, of a motion equation of the fluid flowing inside a pipe based on a rheological model; and a rheological material property determination unit 65 that determines a rheological material property value on the basis of the numerical solution calculated by the numerical solution calculation unit 63.
Description
本発明は、管内を流れる流体のレオロジー物性を計測するための、非接触型レオロジー物性計測装置、システム、プログラムおよび方法に関するものである。
The present invention relates to a non-contact rheological property measuring device, system, program and method for measuring the rheological property of a fluid flowing in a pipe.
食品・材料・化学工学などの分野では、製品の品質管理、生産プロセスの最適化、工場プラントの保守点検等において、管内の流体のレオロジー物性を計測するニーズがある。
In fields such as food, materials, and chemical engineering, there is a need to measure the rheological properties of fluid in pipes in product quality control, production process optimization, factory plant maintenance and inspection, etc.
例えば、店頭で販売されている牛乳は、牛から搾乳された生乳を殺菌処理するとともに、乳脂肪分などの成分が調整されている。生乳に含まれている乳脂肪分等の割合は、牛に与えた飼料、牛の体調、天候、および個々の牛によって異なるため一定に保つことは難しい。そこで、これまでは、乳脂肪分を計測等して常に管理するのではなく、必ず所定割合以上の乳脂肪分が含まれるように過剰に乳脂肪分を添加して調整する方法が採られている。
For example, milk sold in stores is sterilized from raw milk milked from cows, and components such as milk fat are adjusted. It is difficult to keep the proportion of milk fat contained in raw milk constant because it depends on the feed given to the cow, the physical condition of the cow, the weather, and the individual cow. Therefore, until now, instead of constantly managing the milk fat content by measuring it, a method has been adopted in which the milk fat content is adjusted by adding an excess amount so that the milk fat content is always contained in a predetermined ratio or more. There is.
しかし、過剰な乳脂肪分を添加したことによる費用コストが高くなることが問題となっている。そこで、管内を流れる牛乳のレオロジー物性を計測することで乳脂肪分の割合を見積もり、時々刻々と変化する成分をリアルタイムで調整したいというニーズが生まれている。
However, the problem is that the cost of adding excess milk fat is high. Therefore, there is a need to estimate the proportion of milk fat by measuring the rheological properties of milk flowing in the pipe and to adjust the components that change from moment to moment in real time.
そこで、これまでに管内の流れの流速分布を計測することのできる超音波流速計測装置と差圧計とにより、管内の流体のレオロジー物性を計測する手法が提案されている(非特許文献1)。この手法は、管内の流れを一方向定常流れとして仮定するとともにレオロジー物性を記述するモデル式(レオロジーモデル)に基づく流れの式を連立することにより得られる流速分布と、前記超音波流速計測装置により得られる流速分布とを比較することで、モデル式に含まれるレオロジー物性の定数を決定するものである。
Therefore, a method for measuring the rheological properties of the fluid in the pipe by using an ultrasonic flow velocity measuring device capable of measuring the flow velocity distribution in the pipe and a differential pressure gauge has been proposed so far (Non-Patent Document 1). This method uses the flow velocity distribution obtained by assuming the flow in the pipe as a unidirectional steady flow and combining the flow equations based on the model equation (rheological model) that describes the rheological properties, and the ultrasonic flow velocity measuring device. By comparing with the obtained flow velocity distribution, the constants of rheological properties included in the model equation are determined.
しかしながら、非特許文献1に記載された手法においては、管内流れが定常な流れでなければ計測原理上、精度を保証することができないという問題がある。つまり、前記手法は、管内の流れを一方向定常流れと仮定しているが、一般的な生産プロセスにおける管内の流れは、その流れを生み出すためのポンプや配管形状等によって発生する渦流等により常に脈動(変動)しているため、前記脈動による誤差が生じてしまう。
However, in the method described in Non-Patent Document 1, there is a problem that the accuracy cannot be guaranteed in principle of measurement unless the flow in the pipe is a steady flow. That is, the above method assumes that the flow in the pipe is a one-way steady flow, but the flow in the pipe in a general production process is always due to the whirlpool generated by the pump for producing the flow, the shape of the pipe, and the like. Since it is pulsating (fluctuation), an error due to the pulsation occurs.
また、レオロジーモデルに基づく流れの式には、流体を駆動する圧力勾配が含まれる。そのため、レオロジー物性を算出するには管内の圧力値を代入する必要がある。しかし、管内の圧力を計測するには、管内に圧力センサーを設けたり、管壁に孔を空けて圧力計に接続したりして、圧力センサーや圧力計を流体に接触させる必要がある。このため、例えば、衛生面が重要視される食品等では、常に圧力センサー等を清潔な状態に保たなければならない。流体によっては、圧力センサー等が直接触れること自体が不可のものがあり、適用対象が限られるという問題もある。また、圧力センサー等自体の計測精度がレオロジー物性の算出結果に与える影響も大きく、圧力センサー等の選定や当該圧力センサー等の設置箇所の選択も制限される。
In addition, the flow equation based on the rheology model includes the pressure gradient that drives the fluid. Therefore, it is necessary to substitute the pressure value in the pipe to calculate the rheological properties. However, in order to measure the pressure inside the pipe, it is necessary to provide a pressure sensor in the pipe or to make a hole in the pipe wall and connect it to the pressure gauge so that the pressure sensor or the pressure gauge comes into contact with the fluid. For this reason, for example, in foods and the like where hygiene is important, the pressure sensor and the like must always be kept clean. Depending on the fluid, there is a problem that the pressure sensor or the like cannot be directly touched, and the application target is limited. In addition, the measurement accuracy of the pressure sensor itself has a great influence on the calculation result of the rheological physical properties, and the selection of the pressure sensor and the selection of the installation location of the pressure sensor and the like are restricted.
本発明は、以上のような問題点を解決するためになされたものであって、管内の流れにおける脈動を利用して非接触でレオロジー物性を計測することのできる、非接触型レオロジー物性計測装置、システム、プログラムおよび方法を提供することを目的としている。
The present invention has been made to solve the above problems, and is a non-contact type rheological property measuring device capable of measuring rheological properties in a non-contact manner by utilizing pulsation in the flow in a pipe. , Systems, programs and methods are intended to be provided.
本発明に係る非接触型レオロジー物性計測装置および非接触型レオロジー物性計測プログラムは、管内の流れにおける脈動を利用することで、圧力計などによって管内の圧力を計測することなく、非接触でレオロジー物性を計測するという課題を解決するために、管内を流れる流体のレオロジー物性を非接触で計測する非接触型レオロジー物性計測装置であって、超音波流速計測装置から超音波の照射方向に沿った複数の計測点における流速データを取得する流速取得部と、この流速取得部によって取得された各計測点の流速データを周波数解析することにより前記流体における脈動の周波数から最大の振幅値を示すピーク周波数を検出するピーク周波数検出部と、レオロジーモデルに基づく管内を流れる流体の運動方程式を時間に対してフーリエ変換して得られる下記式(1)に、前記ピーク周波数と複数の計測点における流速データとを代入して得られる複数の関数式から数値解を算出する数値解算出部と、この数値解算出部により算出された数値解に基づきレオロジー物性値を決定するレオロジー物性決定部とを有する。
[数1]
ここで、
、
、
、
、τはレオロジーモデルを用いて関係づけられるせん断応力、A,B,C,・・・はレオロジーモデルにおけるレオロジー物性、αは圧力勾配、ρは流体の密度、ωは流体における脈動の角周波数、ω0はピーク周波数、rnは計測点、uは管内の時空間流速分布、^は関数のフーリエ変換、添え字のmは計測結果、をそれぞれ意味する。 The non-contact rheological physical property measuring device and the non-contact rheological physical property measuring program according to the present invention utilize the pulsation in the flow in the pipe, and the rheological physical properties are non-contact without measuring the pressure in the pipe by a pressure gauge or the like. A non-contact type rheological property measuring device that non-contactly measures the rheological physical properties of the fluid flowing in the pipe in order to solve the problem of measuring the number of rheological properties from the ultrasonic flow velocity measuring device along the irradiation direction of ultrasonic waves. By frequency-analyzing the flow velocity acquisition unit that acquires the flow velocity data at the measurement points of and the flow velocity data of each measurement point acquired by this flow velocity acquisition unit, the peak frequency showing the maximum amplitude value from the pulsation frequency in the fluid can be obtained. The peak frequency to be detected and the flow velocity data at a plurality of measurement points are added to the following equation (1) obtained by Fourier transforming the motion equation of the fluid flowing in the tube based on the rheology model with respect to time. It has a numerical solution calculation unit that calculates a numerical solution from a plurality of functional expressions obtained by substitution, and a rheological physical property determination unit that determines a rheological physical property value based on the numerical solution calculated by the numerical solution calculation unit.
[Number 1]
here,
,
,
,
, Τ are the shear stresses related using the rheological model, A, B, C, ... are the rheological properties in the rheological model, α is the pressure gradient, ρ is the density of the fluid, and ω is the angular frequency of the pulsation in the fluid. omega 0 is the peak frequency, r n is the measuring point, u is the spatial velocity distribution when the tube ^ denotes the Fourier transform of a function, subscript m is the measurement result, respectively.
[数1]
ここで、
、
、
、
、τはレオロジーモデルを用いて関係づけられるせん断応力、A,B,C,・・・はレオロジーモデルにおけるレオロジー物性、αは圧力勾配、ρは流体の密度、ωは流体における脈動の角周波数、ω0はピーク周波数、rnは計測点、uは管内の時空間流速分布、^は関数のフーリエ変換、添え字のmは計測結果、をそれぞれ意味する。 The non-contact rheological physical property measuring device and the non-contact rheological physical property measuring program according to the present invention utilize the pulsation in the flow in the pipe, and the rheological physical properties are non-contact without measuring the pressure in the pipe by a pressure gauge or the like. A non-contact type rheological property measuring device that non-contactly measures the rheological physical properties of the fluid flowing in the pipe in order to solve the problem of measuring the number of rheological properties from the ultrasonic flow velocity measuring device along the irradiation direction of ultrasonic waves. By frequency-analyzing the flow velocity acquisition unit that acquires the flow velocity data at the measurement points of and the flow velocity data of each measurement point acquired by this flow velocity acquisition unit, the peak frequency showing the maximum amplitude value from the pulsation frequency in the fluid can be obtained. The peak frequency to be detected and the flow velocity data at a plurality of measurement points are added to the following equation (1) obtained by Fourier transforming the motion equation of the fluid flowing in the tube based on the rheology model with respect to time. It has a numerical solution calculation unit that calculates a numerical solution from a plurality of functional expressions obtained by substitution, and a rheological physical property determination unit that determines a rheological physical property value based on the numerical solution calculated by the numerical solution calculation unit.
[Number 1]
here,
,
,
,
, Τ are the shear stresses related using the rheological model, A, B, C, ... are the rheological properties in the rheological model, α is the pressure gradient, ρ is the density of the fluid, and ω is the angular frequency of the pulsation in the fluid. omega 0 is the peak frequency, r n is the measuring point, u is the spatial velocity distribution when the tube ^ denotes the Fourier transform of a function, subscript m is the measurement result, respectively.
また、本発明の一態様として、数値解算出部による数値解の算出処理に係る負荷を軽減してリアルタイムなレオロジー物性の計測を可能にするという課題を解決するために、前記数値解算出部では、下記式(2)に示す費用関数の最小化により数値解を算出するようにしてもよい。
[数2]
Further, as one aspect of the present invention, in order to solve the problem of reducing the load related to the numerical solution calculation process by the numerical solution calculation unit and enabling real-time measurement of rheological physical properties, the numerical solution calculation unit may be used. , The numerical solution may be calculated by minimizing the cost function shown in the following equation (2).
[Number 2]
[数2]
Further, as one aspect of the present invention, in order to solve the problem of reducing the load related to the numerical solution calculation process by the numerical solution calculation unit and enabling real-time measurement of rheological physical properties, the numerical solution calculation unit may be used. , The numerical solution may be calculated by minimizing the cost function shown in the following equation (2).
[Number 2]
さらに、本発明の一態様として、超音波流速計測装置により得られる流速データの計測誤差により生じるレオロジー物性値の算出誤差を抑制するという課題を解決するために、前記数値解算出部では、代入する流速データとして、連続して隣り合う3点以上の計測点における前記流速データの関数近似値を用いるようにしてもよい。
Further, as one aspect of the present invention, in order to solve the problem of suppressing the calculation error of the rheological property value caused by the measurement error of the flow velocity data obtained by the ultrasonic flow velocity measuring device, the numerical solution calculation unit substitutes the data. As the flow velocity data, a function approximation value of the flow velocity data at three or more consecutively adjacent measurement points may be used.
また、本発明の一態様として、管内を流れる流体のレオロジーモデルが不明の状態で計測をすることができるという課題を解決するために、前記数値解算出部では、複数種のレオロジーモデルに基づく数値解を算出するとともに、当該数値解同士を比較して最も小さい数値解となる前記レオロジーモデルを前記流体のレオロジーモデルとして決定するレオロジーモデル決定部を有するようにしてもよい。
Further, as one aspect of the present invention, in order to solve the problem that the rheological model of the fluid flowing in the pipe can be measured in an unknown state, the numerical solution calculation unit has numerical values based on a plurality of types of rheological models. It may have a rheology model determination unit that calculates the solution and determines the rheology model that is the smallest numerical solution by comparing the numerical solutions as the rheological model of the fluid.
さらに、本発明の一態様として、計測精度を担保するために十分に厚い粘性層厚さとなるピーク周波数を検出するという課題を解決するために、前記ピーク周波数検出部では、前記流体の粘性と前記流体における脈動の周波数の比により表される粘性層厚さが、下記式(3)の範囲を満たす周波数の中から最大の振幅値を示すピーク周波数を検出するようにしてもよい。
[数3]
ここで、(ν/kΔω)1/2は粘性層厚さ、Δrは計測点同士の距離、νは流体の粘性係数(動粘度)、kΔωは検出された周波数、Dは管の内径、をそれぞれ意味する。 Further, as one aspect of the present invention, in order to solve the problem of detecting a peak frequency having a viscous layer thickness sufficiently thick to ensure measurement accuracy, the peak frequency detection unit uses the viscosity of the fluid and the above. The peak frequency showing the maximum amplitude value may be detected from the frequencies in which the viscous layer thickness represented by the ratio of the frequencies of the pulsations in the fluid satisfies the range of the following equation (3).
[Number 3]
Here, (ν / kΔω) 1/2 is the thickness of the viscous layer, Δr is the distance between the measurement points, ν is the viscosity coefficient (kinematic viscosity) of the fluid, kΔω is the detected frequency, and D is the inner diameter of the pipe. Means each.
[数3]
ここで、(ν/kΔω)1/2は粘性層厚さ、Δrは計測点同士の距離、νは流体の粘性係数(動粘度)、kΔωは検出された周波数、Dは管の内径、をそれぞれ意味する。 Further, as one aspect of the present invention, in order to solve the problem of detecting a peak frequency having a viscous layer thickness sufficiently thick to ensure measurement accuracy, the peak frequency detection unit uses the viscosity of the fluid and the above. The peak frequency showing the maximum amplitude value may be detected from the frequencies in which the viscous layer thickness represented by the ratio of the frequencies of the pulsations in the fluid satisfies the range of the following equation (3).
[Number 3]
Here, (ν / kΔω) 1/2 is the thickness of the viscous layer, Δr is the distance between the measurement points, ν is the viscosity coefficient (kinematic viscosity) of the fluid, kΔω is the detected frequency, and D is the inner diameter of the pipe. Means each.
本発明に係る非接触型レオロジー物性計測システムは、管内の流れにおける脈動を利用することで、圧力計などによって管内の圧力を計測することなく、非接触でレオロジー物性を計測するという課題を解決するために、管外から管内に向けて超音波を照射するとともに前記管内から前記管外に向けて反射される超音波を受信して、前記超音波の照射方向に沿った複数の計測点における流速を時系列で計測する超音波流速計測装置と、この超音波流速計測装置から各計測点の流速データを取得して流体のレオロジー物性を決定する前記非接触型レオロジー物性計測装置とを有する。
The non-contact type rheological physical property measurement system according to the present invention solves the problem of non-contact measurement of rheological physical properties by utilizing the pulsation in the flow in the pipe without measuring the pressure in the pipe with a pressure gauge or the like. Therefore, the flow velocity at a plurality of measurement points along the irradiation direction of the ultrasonic wave is received by irradiating the ultrasonic wave from the outside of the tube toward the inside of the tube and receiving the ultrasonic wave reflected from the inside of the tube toward the outside of the tube. It has an ultrasonic flow velocity measuring device that measures in time series, and the non-contact type rheological physical property measuring device that acquires flow velocity data of each measurement point from the ultrasonic flow velocity measuring device and determines the rheological physical properties of the fluid.
本発明に係る非接触型レオロジー物性計測方法は、管内の流れにおける脈動を利用することで、圧力計などによって管内の圧力を計測することなく、非接触でレオロジー物性を計測するという課題を解決するために、管内を流れる流体のレオロジー物性を非接触で計測する非接触型レオロジー物性計測方法であって、超音波流速計測装置から超音波の照射方向に沿った複数の計測点における流速データを取得する流速取得ステップと、この流速取得ステップによって取得された各計測点の流速データを周波数解析することにより前記流体における脈動の周波数から最大の振幅値を示すピーク周波数を検出するピーク周波数検出ステップと、レオロジーモデルに基づく管内を流れる流体の運動方程式を時間に対してフーリエ変換して得られる上記式(1)に、前記ピーク周波数と複数の計測点における流速データとを代入して得られる複数の関数式から数値解を算出する数値解算出ステップと、この数値解算出ステップにより算出された数値解に基づきレオロジー物性値を決定するレオロジー物性決定ステップとを有する。
The non-contact rheological physical property measuring method according to the present invention solves the problem of non-contact measuring rheological physical properties by utilizing the pulsation in the flow in the pipe without measuring the pressure in the pipe with a pressure gauge or the like. Therefore, it is a non-contact rheological property measurement method that measures the rheological property of the fluid flowing in the pipe in a non-contact manner, and acquires flow velocity data at a plurality of measurement points along the irradiation direction of the ultrasonic wave from the ultrasonic flow velocity measuring device. A rheology acquisition step to be performed, a peak frequency detection step to detect a peak frequency showing the maximum amplitude value from the pulsation frequency in the fluid by frequency analysis of the flow velocity data of each measurement point acquired by this flow velocity acquisition step. A plurality of functions obtained by substituting the peak frequency and the flow velocity data at a plurality of measurement points into the above equation (1) obtained by Fourier transforming the motion equation of the fluid flowing in the tube based on the rheology model with respect to time. It has a numerical solution calculation step for calculating a numerical solution from an equation, and a rheological physical property determination step for determining a rheological physical property value based on the numerical solution calculated by this numerical solution calculation step.
本発明によれば、管内の流れにおける脈動を利用して非接触でレオロジー物性を計測することができる。
According to the present invention, the rheological properties can be measured in a non-contact manner by utilizing the pulsation in the flow in the pipe.
以下、本発明に係る非接触型レオロジー物性計測装置、システム、プログラムおよび方法の一実施形態について図面を用いて説明する。
Hereinafter, an embodiment of the non-contact rheological property measuring device, system, program and method according to the present invention will be described with reference to the drawings.
本実施形態の非接触型レオロジー物性計測システム1は、図1に示すように、複数の計測点における流速を時系列で計測する超音波流速計測装置2と、この超音波流速計測装置2から各計測点の流速データを取得して流体のレオロジー物性を決定する非接触型レオロジー物性計測装置3とを有する。以下、各構成について詳細に説明する。
As shown in FIG. 1, the non-contact rheological property measurement system 1 of the present embodiment is a non-contact rheological property measurement device 2 that measures the flow velocities at a plurality of measurement points in time series, and the ultrasonic flow velocity measurement device 2 It has a non-contact rheological property measuring device 3 that acquires flow velocity data at a measurement point and determines the rheological property of the fluid. Hereinafter, each configuration will be described in detail.
超音波流速計測装置2は、管外から管内に向けて超音波を照射するとともに前記管内から前記管外に向けて反射される超音波を受信して、前記超音波の照射方向に沿った複数の計測点における流速を時系列で計測するものである。つまり、超音波流速計測装置2は、管内の時空間流速分布u(r,t)を非接触かつ非侵襲(流れを乱さず)に計測することができる。例えば、特開2003-344131号公報に開示されている技術を用いることができる。
The ultrasonic flow velocity measuring device 2 irradiates ultrasonic waves from outside the tube toward the inside of the tube, receives ultrasonic waves reflected from the inside of the tube toward the outside of the tube, and receives a plurality of ultrasonic waves along the irradiation direction of the ultrasonic waves. The flow velocity at the measurement point of is measured in time series. That is, the ultrasonic flow velocity measuring device 2 can measure the spatiotemporal flow velocity distribution u (r, t) in the pipe in a non-contact and non-invasive manner (without disturbing the flow). For example, the technique disclosed in Japanese Patent Application Laid-Open No. 2003-344131 can be used.
非接触型レオロジー物性計測装置3は、超音波流速計測装置2から各計測点の流速データを取得して流体のレオロジー物性を決定するものである。本実施形態における非接触型レオロジー物性計測装置3は、コンピュータによって構成されており、図1に示すように、主として、各種の表示画面を表示するとともに各種のデータを入力する表示入力手段4と、各種のデータを記憶するとともに演算処理手段6が演算処理を行う際のワーキングエリアとして機能する記憶手段5と、記憶手段5にインストールされた非接触型レオロジー物性計測プログラム3aを実行することにより、各種の演算処理を実行し後述する各構成部として機能する演算処理手段6とを有する。
The non-contact type rheological physical property measuring device 3 acquires the flow velocity data of each measurement point from the ultrasonic flow velocity measuring device 2 to determine the rheological physical property of the fluid. The non-contact type rheology physical property measuring device 3 in the present embodiment is composed of a computer, and as shown in FIG. 1, mainly includes a display input means 4 for displaying various display screens and inputting various data. By executing the storage means 5 that stores various data and functions as a working area when the arithmetic processing means 6 performs arithmetic processing, and the non-contact type rheology physical property measurement program 3a installed in the storage means 5, various types are stored. It has an arithmetic processing means 6 that executes the arithmetic processing of the above and functions as each component described later.
表示入力手段4は、入力機能と表示機能とを有するユーザインターフェースであり、本実施形態では、タッチパネル機能を備えたディスプレイによって構成されている。なお、表示入力手段4の構成は、タッチパネル式のディスプレイによるものに限定されるものではなく、表示機能のみを備えた表示手段、およびキーボードやマウスなどの入力機能のみを備えた入力手段をそれぞれ別個に有していてもよい。
The display input means 4 is a user interface having an input function and a display function, and in the present embodiment, it is configured by a display having a touch panel function. The configuration of the display input means 4 is not limited to that of a touch panel type display, and the display means having only a display function and the input means having only an input function such as a keyboard and a mouse are separated from each other. You may have it in.
記憶手段5は、ハードディスク、ROM(Read Only Memory)、RAM(Random Access Memory)、フラッシュメモリ等で構成されており、非接触型レオロジー物性計測プログラム31aを記憶するプログラム記憶部51と、レオロジーモデルに基づく管内を流れる流体の運動方程式を時間に対してフーリエ変換して得られる式を記憶するレオロジーモデル式記憶部52と、各種のしきい値を記憶するしきい値記憶部53とを有する。
The storage means 5 is composed of a hard disk, ROM (Read Only Memory), RAM (Random Access Memory), flash memory, etc., and is used as a program storage unit 51 for storing the non-contact rheology physical property measurement program 31a and a rheology model. It has a rheology model expression storage unit 52 that stores an equation obtained by Fourier transforming a motion equation of a fluid flowing in a pipe based on time with respect to time, and a threshold storage unit 53 that stores various threshold values.
プログラム記憶部51には、本実施形態の非接触型レオロジー物性計測装置3を制御するための非接触型レオロジー物性計測プログラム3aがインストールされている。そして、演算処理手段6が、当該非接触型レオロジー物性計測プログラム3aを読み出して実行することにより、コンピュータを非接触型レオロジー物性計測装置3における各構成部として機能させるようになっている。
The non-contact rheological property measurement program 3a for controlling the non-contact rheological property measurement device 3 of the present embodiment is installed in the program storage unit 51. Then, the arithmetic processing means 6 reads out and executes the non-contact rheological property measuring program 3a, so that the computer functions as each component in the non-contact rheological property measuring device 3.
なお、非接触型レオロジー物性計測プログラム3aの利用形態は、上記構成に限られるものではない。例えば、CD-ROMやUSBメモリ等のように、コンピュータで読み取り可能な非一時的な記録媒体に非接触型レオロジー物性計測プログラム3aを記憶させておき、当該記録媒体から直接読み出して実行してもよい。また、外部サーバ等からクラウドコンピューティング方式やASP(Application Service Provider)方式等で利用してもよい。
The usage pattern of the non-contact rheological property measurement program 3a is not limited to the above configuration. For example, even if the non-contact rheological property measurement program 3a is stored in a non-temporary recording medium that can be read by a computer, such as a CD-ROM or a USB memory, and directly read from the recording medium and executed. Good. Further, it may be used by a cloud computing method, an ASP (Application Service Provider) method, or the like from an external server or the like.
レオロジーモデル式記憶部52は、レオロジーモデルに基づく管内を流れる流体の運動方程式を時間に対してフーリエ変換して得られる式を記憶するものである。本実施形態では、下記式(1)に基づきレオロジーモデルに導き出された式が記憶されている。
[数1]
ここで、
、
、
、
、
τはレオロジーモデルを用いて関係づけられるせん断応力、
A,B,C,・・・はレオロジーモデルにおけるレオロジー物性、
αは圧力勾配、
ρは流体の密度、
ωは流体における脈動の角周波数、
ω0はピーク周波数、
rnは計測点、
uは管内の時空間流速分布、
^は関数のフーリエ変換、
添え字のmは計測結果、をそれぞれ意味する。なお、レオロジー物性のA,B,C,・・・はレオロジーモデルに応じてその数が変わるものである。例えば、測定対象に適したレオロジーモデルがニュートン流体である場合のレオロジー物性の数は1であり、非ニュートン流体の場合のレオロジー物性の数は2以上である。 The rheology modelformula storage unit 52 stores the formula obtained by Fourier transforming the equation of motion of the fluid flowing in the tube based on the rheology model with respect to time. In this embodiment, the equation derived from the rheology model based on the following equation (1) is stored.
[Number 1]
here,
,
,
,
,
τ is the shear stress, which is related using a rheological model.
A, B, C, ... are rheological properties in the rheological model,
α is the pressure gradient,
ρ is the density of the fluid,
ω is the angular frequency of the pulsation in the fluid,
ω 0 is the peak frequency,
r n is the measurement point,
u is the spatiotemporal flow velocity distribution in the pipe,
^ Is the Fourier transform of the function,
The subscript m means the measurement result. The number of rheological properties A, B, C, ... Changes depending on the rheological model. For example, the number of rheological properties is 1 when the rheological model suitable for the measurement target is a Newtonian fluid, and the number of rheological properties is 2 or more when the rheological model is a non-Newtonian fluid.
[数1]
ここで、
、
、
、
、
τはレオロジーモデルを用いて関係づけられるせん断応力、
A,B,C,・・・はレオロジーモデルにおけるレオロジー物性、
αは圧力勾配、
ρは流体の密度、
ωは流体における脈動の角周波数、
ω0はピーク周波数、
rnは計測点、
uは管内の時空間流速分布、
^は関数のフーリエ変換、
添え字のmは計測結果、をそれぞれ意味する。なお、レオロジー物性のA,B,C,・・・はレオロジーモデルに応じてその数が変わるものである。例えば、測定対象に適したレオロジーモデルがニュートン流体である場合のレオロジー物性の数は1であり、非ニュートン流体の場合のレオロジー物性の数は2以上である。 The rheology model
[Number 1]
here,
,
,
,
,
τ is the shear stress, which is related using a rheological model.
A, B, C, ... are rheological properties in the rheological model,
α is the pressure gradient,
ρ is the density of the fluid,
ω is the angular frequency of the pulsation in the fluid,
ω 0 is the peak frequency,
r n is the measurement point,
u is the spatiotemporal flow velocity distribution in the pipe,
^ Is the Fourier transform of the function,
The subscript m means the measurement result. The number of rheological properties A, B, C, ... Changes depending on the rheological model. For example, the number of rheological properties is 1 when the rheological model suitable for the measurement target is a Newtonian fluid, and the number of rheological properties is 2 or more when the rheological model is a non-Newtonian fluid.
式(1)において圧力勾配αを表す項は時間によってフーリエ変換することにより流れにおける角周波数ωの関数となっている。このため、前記角周波数ωを特定すれば圧力勾配αは未知の定数として扱うことができる。ここで、前記角周波数ωは管内の時空間流速分布u(r,t)によって得ることができる。つまり、式(1)では、圧力勾配αの値を得るために、圧力センサーや圧力計などを用いて計測する必要がない。また、上述のとおり超音波流速計測装置2は、非接触かつ非侵襲で管内の時空間流速分布u(r,t)を計測することができる。つまり、本実施形態の非接触型レオロジー物性計測システム1は、計測原理的に非接触により管内を流れる流体のレオロジー物性を計測することができるシステムである。
In equation (1), the term representing the pressure gradient α is a function of the angular frequency ω in the flow by Fourier transforming with time. Therefore, if the angular frequency ω is specified, the pressure gradient α can be treated as an unknown constant. Here, the angular frequency ω can be obtained from the spatiotemporal flow velocity distribution u (r, t) in the tube. That is, in the equation (1), it is not necessary to measure using a pressure sensor, a pressure gauge, or the like in order to obtain the value of the pressure gradient α. Further, as described above, the ultrasonic flow velocity measuring device 2 can measure the spatiotemporal flow velocity distribution u (r, t) in the pipe in a non-contact and non-invasive manner. That is, the non-contact type rheological property measurement system 1 of the present embodiment is a system capable of measuring the rheological property of the fluid flowing in the pipe by non-contact in principle of measurement.
また、式(1)では、流体における脈動の角周波数ωが含まれる。一般的に、生産プロセスにおける管内の流れは、その流れを生み出すためのポンプや配管形状等によって発生する渦流等により常に脈動(変動)していることから、そのような管内を流れる流体のレオロジー物性の計測に使用することができる。よって、従来の定常流を仮定できる管内流れしか適用できないシステムに比べて、適用対象となる範囲は広い。
Further, in the equation (1), the angular frequency ω of the pulsation in the fluid is included. In general, the flow in a pipe in a production process is constantly pulsating (fluctuating) due to the vortex flow generated by the pump for producing the flow, the shape of the pipe, etc., and therefore the rheological properties of the fluid flowing in such a pipe. Can be used for measurement of. Therefore, the applicable range is wider than that of the conventional system in which only the in-pipe flow that can assume a steady flow can be applied.
なお、レオロジーモデルは、流れのせん断応力と流れの速度勾配とが比例する性質(線形)があるニュートン流体モデルと、前記せん断応力と前記速度勾配とが比例しない性質(非線形)がある非ニュートン流体モデルとに大別される。また、非ニュートン流体モデルには、塑性(ビンガム)流体モデル、準(擬)粘性流体モデル、準(擬)塑性流体モデル、ダイラタント流体モデル等が例示される。
The rheology model includes a Newtonian fluid model in which the shear stress of the flow and the velocity gradient of the flow are proportional (linear) and a non-Newtonian fluid in which the shear stress and the velocity gradient are not proportional (non-linear). It is roughly divided into models. Examples of the non-Newtonian fluid model include a plastic (Bingham) fluid model, a quasi (pseudo) viscous fluid model, a quasi (pseudo) plastic fluid model, and a dilatant fluid model.
しきい値記憶部53は、各種のしきい値を記憶するものである。本実施形態では、粘性層厚さを基準にピーク周波数ω0を検出するために用いられる下記式(3)およびそれに伴う各値が記憶されている。
[数3]
ここで、
(ν/kΔω)1/2は粘性層厚さ、
Δrは計測点同士の距離、
νは流体の動粘性係数、
kΔωは検出された周波数、
Dは管の内径、をそれぞれ意味する。 The thresholdvalue storage unit 53 stores various threshold values. In this embodiment, the following equation (3) used for detecting the peak frequency ω 0 based on the thickness of the viscous layer and each value associated therewith are stored.
[Number 3]
here,
(Ν / kΔω) 1/2 is the thickness of the viscous layer,
Δr is the distance between measurement points,
ν is the kinematic viscosity coefficient of the fluid,
kΔω is the detected frequency,
D means the inner diameter of the pipe, respectively.
[数3]
ここで、
(ν/kΔω)1/2は粘性層厚さ、
Δrは計測点同士の距離、
νは流体の動粘性係数、
kΔωは検出された周波数、
Dは管の内径、をそれぞれ意味する。 The threshold
[Number 3]
here,
(Ν / kΔω) 1/2 is the thickness of the viscous layer,
Δr is the distance between measurement points,
ν is the kinematic viscosity coefficient of the fluid,
kΔω is the detected frequency,
D means the inner diameter of the pipe, respectively.
つぎに、演算処理手段6について説明する。演算処理手段6は、CPU(Central Processing Unit)等によって構成されており、記憶手段5にインストールされた非接触型レオロジー物性計測プログラム3aを実行することにより、図1に示すように、超音波流速計測装置2から流速データを取得する流速取得部61と、流体における脈動の周波数から最大の振幅値を示すピーク周波数ω0を検出するピーク周波数検出部62と、ピーク周波数ω0と複数の計測点における流速データとを代入して得られる複数の関数式から数値解を算出する数値解算出部63と、レオロジーモデルが不明の場合や変化する場合にレオロジーモデルを決定するレオロジーモデル決定部64と、前記数値解算出部63により算出された数値解に基づきレオロジー物性値を決定するレオロジー物性決定部65として機能するようになっている。
Next, the arithmetic processing means 6 will be described. The arithmetic processing means 6 is composed of a CPU (Central Processing Unit) or the like, and by executing the non-contact rheological physical property measurement program 3a installed in the storage means 5, the ultrasonic flow velocity is as shown in FIG. A flow velocity acquisition unit 61 that acquires flow velocity data from the measuring device 2, a peak frequency detection unit 62 that detects a peak frequency ω 0 that indicates the maximum amplitude value from the frequency of the pulsation in the fluid, a peak frequency ω 0, and a plurality of measurement points. A numerical solution calculation unit 63 that calculates a numerical solution from a plurality of functional expressions obtained by substituting the flow velocity data in the above, and a rheology model determination unit 64 that determines a rheology model when the rheology model is unknown or changes. It functions as a rheological physical property determination unit 65 that determines a rheological physical property value based on the numerical solution calculated by the numerical solution calculation unit 63.
流速取得部61は、超音波流速計測装置2から超音波の照射方向に沿った複数の計測点における流速データを取得するものである。流速データは、厳密には超音波流速計測装置2の測定限界に基づく時間間隔毎に計測される離散的なデータであるが、数ミリ秒~数十ミリ秒程度の流体における脈動の周波数よりも充分に短い時間間隔で計測できるため時間的に連続したデータとして扱うことができる。また、式(3)の計算に用いるため、本実施形態における流速取得部61は、前記超音波流速計測装置2から測定限界に基づき決定される計測点同士の距離Δrを取得し、しきい値記憶部53に記憶させるようになっている。
The flow velocity acquisition unit 61 acquires flow velocity data at a plurality of measurement points along the ultrasonic irradiation direction from the ultrasonic flow velocity measuring device 2. Strictly speaking, the flow velocity data is discrete data measured at each time interval based on the measurement limit of the ultrasonic flow velocity measuring device 2, but it is higher than the frequency of pulsation in a fluid of several milliseconds to several tens of milliseconds. Since it can be measured at sufficiently short time intervals, it can be treated as time-continuous data. Further, for use in the calculation of the equation (3), the flow velocity acquisition unit 61 in the present embodiment acquires the distance Δr between the measurement points determined based on the measurement limit from the ultrasonic flow velocity measurement device 2, and obtains a threshold value. It is designed to be stored in the storage unit 53.
ピーク周波数検出部62は、各計測点の流速データを周波数解析することにより前記流体における脈動の周波数から最大の振幅値を示すピーク周波数ω0を検出するものである。周波数解析は、スペクトル解析や波形分析ともいう。例えば、フーリエ変換やウェーブレット変換等が例示される。本実施形態では、フーリエ変換を用いてピーク周波数ω0を検出している。なお、ピーク周波数ω0は、優位周波数や卓越周波数と呼ばれることもある。
The peak frequency detection unit 62 detects the peak frequency ω 0 , which indicates the maximum amplitude value, from the frequency of the pulsation in the fluid by frequency analysis of the flow velocity data of each measurement point. Frequency analysis is also called spectrum analysis or waveform analysis. For example, Fourier transform, wavelet transform and the like are exemplified. In this embodiment, the peak frequency ω 0 is detected by using the Fourier transform. The peak frequency ω 0 is sometimes called a dominant frequency or a dominant frequency.
また、本実施形態におけるピーク周波数検出部62は、粘性層厚さを基準にピーク周波数を検出する機能を有する。具体的には、上記の式(3)を満たす周波数の中から最大の振幅値を示す周波数をピーク周波数ω0として検出する。ここで式(3)の最低値である3Δrは、数値解算出部63において数値解を算出する上で、選択されるレオロジーモデルによって定められる未知の定数の数が少なくとも3つ以上あり、それらの未知の定数を算出するために必要となる関数式の数が3本以上であること、また超音波流速計測装置2の計測誤差によるレオロジー物性の計測精度の低下を抑制するために流速データやレオロジー物性値の算出結果を空間差分や多項式近似するために必要なデータ点数(計測点の数)が3点以上であることに基づく。よって、粘性層厚さがこれよりも薄いと精度の高い数値解が得られない。また、最大値のD/2は管の半径を意味しており、軸対称となる管内流れにおいて粘性層厚さがこれ以上厚くなることがないことに基づく。
Further, the peak frequency detection unit 62 in the present embodiment has a function of detecting the peak frequency based on the thickness of the viscous layer. Specifically, the frequency showing the maximum amplitude value is detected as the peak frequency ω 0 from the frequencies satisfying the above equation (3). Here, 3Δr, which is the minimum value of the equation (3), has at least three or more unknown constants determined by the rheology model selected for calculating the numerical solution by the numerical solution calculation unit 63, and among them. The number of functional expressions required to calculate an unknown constant is 3 or more, and the flow velocity data and rheology are used to suppress the deterioration of the measurement accuracy of the rheological properties due to the measurement error of the ultrasonic flow velocity measuring device 2. It is based on the fact that the number of data points (number of measurement points) required for spatial difference or polynomial approximation of the calculation result of the physical property value is 3 points or more. Therefore, if the viscous layer thickness is thinner than this, a highly accurate numerical solution cannot be obtained. Further, the maximum value D / 2 means the radius of the pipe, and is based on the fact that the viscous layer thickness does not become thicker in the axisymmetric in-pipe flow.
数値解算出部63は、上記の式(1)にピーク周波数ω0と複数の計測点における流速データとを代入して得られる複数の関数式から数値解を算出するものである。本実施形態における数値解算出部63は、下記式(2)に示す費用関数の最小化により数値解を算出する。本実施形態では、費用関数を最小化するプログラムを作成し、その作成プログラムを実行することで数値解を算出している。費用関数を最小化するアルゴリズムは、特に限定されるものではないが、例えばランダムサーチ法や勾配降下法などが例示される。
[数2]
The numericalsolution calculation unit 63 calculates a numerical solution from a plurality of functional equations obtained by substituting the peak frequency ω 0 and the flow velocity data at a plurality of measurement points into the above equation (1). The numerical solution calculation unit 63 in the present embodiment calculates the numerical solution by minimizing the cost function shown in the following equation (2). In this embodiment, a program that minimizes the cost function is created, and the numerical solution is calculated by executing the created program. The algorithm for minimizing the cost function is not particularly limited, and examples thereof include a random search method and a gradient descent method.
[Number 2]
[数2]
The numerical
[Number 2]
また、本実施形態における数値解算出部63は、代入する流速データとして、連続して隣り合う3点以上の計測点における前記流速データの関数近似値を用いる。これは、超音波流速計測装置2により得られる流速データの計測誤差により生じるレオロジー物性値の算出誤差を抑制するためである。関数近似値の算出方法は、特に限定されるものではないが、ベッセル関数やチェビシェフ級数などが例示される。
Further, the numerical solution calculation unit 63 in the present embodiment uses the function approximation value of the flow velocity data at three or more consecutively adjacent measurement points as the flow velocity data to be substituted. This is to suppress the calculation error of the rheological physical property value caused by the measurement error of the flow velocity data obtained by the ultrasonic flow velocity measuring device 2. The method of calculating the function approximation value is not particularly limited, but examples thereof include a Bessel function and a Chebyshev series.
また、本実施形態における数値解算出部63は、管内を流れる流体のレオロジーモデルが不明な場合や、温度または各種成分割合の変化によってレオロジーモデルが時々刻々と変化する場合には、複数種のレオロジーモデルに基づく数値解を算出する。具体的には、数値解算出部63が、レオロジーモデル式記憶部52から複数種のレオロジーモデルに基づく管内を流れる流体の運動方程式を時間に対してフーリエ変換して得られる式を用いて数値解を算出する。
Further, the numerical solution calculation unit 63 in the present embodiment has a plurality of types of rheology when the rheology model of the fluid flowing in the pipe is unknown or when the rheology model changes from moment to moment due to a change in temperature or various component ratios. Calculate a numerical solution based on the model. Specifically, the numerical solution calculation unit 63 uses an equation obtained by Fourier transforming the equations of motion of the fluid flowing in the pipe based on a plurality of types of rheological models from the rheological model formula storage unit 52 with respect to time. Is calculated.
レオロジーモデル決定部64は、レオロジーモデルが不明な場合などにおいて数値解算出部63が複数種のレオロジーモデルに基づく数値解を算出した上で、レオロジーモデルを決定するものである。本実施形態におけるレオロジーモデル決定部64は、数値解算出部63が算出した複数の数値解同士を比較して最も小さい数値解となる前記レオロジーモデルを前記流体のレオロジーモデルとして決定する。
The rheology model determination unit 64 determines the rheology model after the numerical solution calculation unit 63 calculates numerical solutions based on a plurality of types of rheology models when the rheology model is unknown. The rheology model determination unit 64 in the present embodiment compares a plurality of numerical solutions calculated by the numerical solution calculation unit 63 with each other, and determines the rheology model having the smallest numerical solution as the rheology model of the fluid.
なお、測定対象に適したレオロジーモデルが不明な場合のレオロジーモデルを決定する方法は、本実施形態のように数値解算出部63により算出した複数の数値解同士を比較する方法に限定されるものではなく、例えば、数値解算出部63により算出された数値解が所定のしきい値以下か否かを判別し、前記しきい値以下の場合には当該数値解を算出したレオロジーモデルを計測対象の流体のレオロジーモデルと決定し、前記しきい値より大きい場合には、レオロジーモデル式記憶部52に記憶された他のレオロジーモデルに基づく式に変更した上で数値解を算出し、当該数値解が前記しきい値以下となってレオロジーモデルが決定されるまで当該判別処理を繰り返すようにしてもよい。
The method of determining the rheology model when the rheology model suitable for the measurement target is unknown is limited to the method of comparing a plurality of numerical solutions calculated by the numerical solution calculation unit 63 as in the present embodiment. Instead, for example, it is determined whether or not the numerical solution calculated by the numerical solution calculation unit 63 is below a predetermined threshold value, and if it is below the threshold value, the rheology model for which the numerical solution is calculated is measured. If it is larger than the threshold value, the rheological model is changed to a rheological model based on another rheological model stored in the rheological model formula storage unit 52, and a numerical solution is calculated. May be repeated until the rheology model is determined when is equal to or less than the threshold value.
レオロジー物性決定部65は、数値解算出部63により算出された数値解に基づきレオロジー物性値を決定するものである。本実施形態におけるレオロジー物性決定部65は、算出された数値解から計測対象としている管内の流体の粘性係数μや動粘性係数νなどのレオロジー物性値を決定するようになっている。また、決定された動粘性係数νは、ピーク周波数検出部62で算出される式(3)を算出する場合の動粘性係数νとして用いるため、しきい値記憶部53に記憶される。ここで動粘性係数νが時々刻々と変化する場合は、前記しきい値記憶部53に時系列で並べて記憶させるか、算出されるごとに書き換え(上書き)するようにしてもよい。
The rheology physical property determination unit 65 determines the rheological physical property value based on the numerical solution calculated by the numerical solution calculation unit 63. The rheological physical property determination unit 65 in the present embodiment determines the rheological physical property values such as the viscosity coefficient μ and the kinematic viscosity coefficient ν of the fluid in the pipe to be measured from the calculated numerical solution. Further, the determined kinematic viscosity coefficient ν is stored in the threshold value storage unit 53 because it is used as the kinematic viscosity coefficient ν when calculating the equation (3) calculated by the peak frequency detection unit 62. Here, when the kinematic viscosity coefficient ν changes from moment to moment, the threshold value storage unit 53 may be stored in chronological order or rewritten (overwritten) each time it is calculated.
なお、前記レオロジー物性値と、流体に含まれる特定成分の割合との間に相関などの関係性がある場合には、前記レオロジー物性値とともに、または前記レオロジー物性値に変えて当該成分割合を決定するようにしてもよい。
When there is a correlation or the like between the rheological physical property value and the ratio of the specific component contained in the fluid, the component ratio is determined together with the rheological physical property value or by changing to the rheological physical property value. You may try to do it.
つぎに、本実施形態の非接触型レオロジー物性計測装置3、システム1およびプログラム3aにおける各構成の作用について、非接触型レオロジー物性計測方法とともに説明する。
Next, the action of each configuration in the non-contact rheological property measuring device 3, the system 1 and the program 3a of the present embodiment will be described together with the non-contact rheological property measuring method.
超音波流速計測装置2が、管内を流れる流体に対して管外から超音波の送受信を行い、受信した超音波を解析することにより、前記超音波の照射方向に沿った複数の計測点における流速を時系列に計測する。
The ultrasonic flow velocity measuring device 2 transmits and receives ultrasonic waves to the fluid flowing in the tube from outside the tube, and analyzes the received ultrasonic waves to obtain a flow velocity at a plurality of measurement points along the irradiation direction of the ultrasonic waves. Is measured in chronological order.
図2に示すように、非接触型レオロジー物性計測装置3では、流速取得部61が、超音波流速計測装置2によって計測された流速データ、具体的には時空間流速分布u(ri,tj)、(i=1,2,・・・,N、j=1,2,・・・,M)を取得する(S1:流速取得ステップ)。本実施形態における流速取得部61は、前記超音波流速計測装置2から流速データとともに、当該流速データを算出する時に定められた計測点同士の距離Δrを取得し、しきい値記憶部53に記憶させる。
As shown in FIG. 2, the non-contact type rheology properties measuring device 3, the flow velocity acquiring unit 61, an ultrasonic flow rate measuring device flow rate data measured by the 2, specifically when the spatial velocity distribution u (r i, t j ), (i = 1,2, ···, N, j = 1,2, ···, M) are acquired (S1: Flow velocity acquisition step). The flow velocity acquisition unit 61 in the present embodiment acquires the flow velocity data from the ultrasonic flow velocity measuring device 2 and the distance Δr between the measurement points determined at the time of calculating the flow velocity data, and stores the distance Δr in the threshold value storage unit 53. Let me.
次に、ピーク周波数検出部62が、流速取得部61によって取得された各計測点の流速データを周波数解析し、流体における脈動の周波数から最大の振幅値を示すピーク周波数ω0を検出する(S2:ピーク周波数検出ステップ)。本実施形態では、下記時空間流速分布u(ri,tj)のフーリエ変換を行った式(4)と、各周波数における振幅値を示す下記の式(5)を用いて周波数解析(スペクトル解析)を行いピーク周波数ω0を検出する。
[数4]
[数5]
Next, the peakfrequency detection unit 62 frequency-analyzes the flow velocity data of each measurement point acquired by the flow velocity acquisition unit 61, and detects the peak frequency ω 0 showing the maximum amplitude value from the pulsation frequency in the fluid (S2). : Peak frequency detection step). In the present embodiment, the frequency analysis using the following spatiotemporal flow velocity distribution u (r i, t j) and equation (4) performing the Fourier transform of the equation (5) below which represents the amplitude value at each frequency (spectrum Analysis) is performed to detect the peak frequency ω 0 .
[Number 4]
[Number 5]
[数4]
[数5]
Next, the peak
[Number 4]
[Number 5]
また、ピーク周波数検出部62が、算出されたピーク周波数ω0が式(3)の範囲内の条件を満たすか否かを判別する(S3)。当該式(3)における計測点同士の距離Δr、流体の動粘性係数νおよび管の内径Dはしきい値記憶部63から取得する。もし、ステップS2で算出されたピーク周波数ω0が式(3)の範囲内にない場合には(S3:NO)、ステップS2に戻って次に大きいピーク周波数ω0を検出し、式(3)の要件が満たすまでこの処理を繰り返す。そして、算出されたピーク周波数ω0が式(3)の範囲内である場合には(S3:YES)、その周波数をピーク周波数ω0に決定する。本実施形態におけるピーク周波数検出部62では、このようにして式(3)の要件を満たす周波数の中から最大の振幅値をピーク周波数ω0として検出する。
Further, the peak frequency detection unit 62 determines whether or not the calculated peak frequency ω 0 satisfies the condition within the range of the equation (3) (S3). The distance Δr between the measurement points in the equation (3), the kinematic viscosity coefficient ν of the fluid, and the inner diameter D of the pipe are obtained from the threshold value storage unit 63. If the peak frequency ω 0 calculated in step S2 is not within the range of equation (3) (S3: NO), the process returns to step S2 to detect the next largest peak frequency ω 0 and equation (3). ) Is repeated until the requirements are met. Then, when the calculated peak frequency ω 0 is within the range of the equation (3) (S3: YES), the frequency is determined to be the peak frequency ω 0 . In this way, the peak frequency detection unit 62 in the present embodiment detects the maximum amplitude value from the frequencies satisfying the requirement of the equation (3) as the peak frequency ω 0 .
次に、数値解算出部63が、式(1)に代入する流速データについて、超音波流速計測装置2における計測誤差の影響を抑制するために、流速データの関数近似値を算出する(S4)。本実施形態では、下記の式(6)を用いて5次関数近似値を計算しその値を用いる。
[数6]
Next, the numericalsolution calculation unit 63 calculates a function approximation value of the flow velocity data in order to suppress the influence of the measurement error in the ultrasonic flow velocity measuring device 2 with respect to the flow velocity data to be substituted in the equation (1) (S4). .. In this embodiment, the approximate value of the quintic function is calculated using the following equation (6), and the value is used.
[Number 6]
[数6]
Next, the numerical
[Number 6]
そして、式(1)に基づきピーク周波数ω0と複数の計測点における流速データとを代入して得られる複数の関数式から数値解を算出する(S5:数値解算出ステップ)。本実施形態では、数値解を算出するために式(2)に示す費用関数を用いる。レオロジーモデルがニュートン流体の場合、式(2)は、下記の式(7)および式(8)に示すように書き換えることができる。
[数7]
[数8]
ここで、α(ti)は圧力勾配の時間変動を意味する。 Then, a numerical solution is calculated from a plurality of functional equations obtained by substituting the peak frequency ω 0 and the flow velocity data at the plurality of measurement points based on the equation (1) (S5: numerical solution calculation step). In this embodiment, the cost function shown in Eq. (2) is used to calculate the numerical solution. When the rheology model is a Newtonian fluid, equation (2) can be rewritten as shown in equations (7) and (8) below.
[Number 7]
[Number 8]
Here, α (t i) denotes the time variation of the pressure gradient.
[数7]
[数8]
ここで、α(ti)は圧力勾配の時間変動を意味する。 Then, a numerical solution is calculated from a plurality of functional equations obtained by substituting the peak frequency ω 0 and the flow velocity data at the plurality of measurement points based on the equation (1) (S5: numerical solution calculation step). In this embodiment, the cost function shown in Eq. (2) is used to calculate the numerical solution. When the rheology model is a Newtonian fluid, equation (2) can be rewritten as shown in equations (7) and (8) below.
[Number 7]
[Number 8]
Here, α (t i) denotes the time variation of the pressure gradient.
また、レオロジーモデルが非ニュートン流体であり、レオロジーモデルを用いて関係づけられるせん断応力τを下記の式(9)で表した場合、式(2)は、下記の式(10)ないし式(12)に示すように書き換えることができる。
[数9]
[数10]
[数11]
[数12]
ここで、Π1, Π2, Π3, ・・・は、非ニュートン流体におけるレオロジー物性を意味する。なお、式(11)は上記式(8)と同じ式であり、α(ti)は圧力勾配の時間変動を意味する。 Further, when the rheology model is a non-Newtonian fluid and the shear stress τ associated with the rheology model is expressed by the following equation (9), the equation (2) is expressed by the following equations (10) to (12). ) Can be rewritten.
[Number 9]
[Number 10]
[Number 11]
[Number 12]
Here, Π 1 , Π 2 , Π 3 , ... Means rheological properties in non-Newtonian fluids. Incidentally, formula (11) is the same formula as the equation (8), alpha (t i) denotes the time variation of the pressure gradient.
[数9]
[数10]
[数11]
[数12]
ここで、Π1, Π2, Π3, ・・・は、非ニュートン流体におけるレオロジー物性を意味する。なお、式(11)は上記式(8)と同じ式であり、α(ti)は圧力勾配の時間変動を意味する。 Further, when the rheology model is a non-Newtonian fluid and the shear stress τ associated with the rheology model is expressed by the following equation (9), the equation (2) is expressed by the following equations (10) to (12). ) Can be rewritten.
[Number 9]
[Number 10]
[Number 11]
[Number 12]
Here, Π 1 , Π 2 , Π 3 , ... Means rheological properties in non-Newtonian fluids. Incidentally, formula (11) is the same formula as the equation (8), alpha (t i) denotes the time variation of the pressure gradient.
そして、この費用関数を、ランダムサーチ法や勾配降下法などを用いて最小化することで数値解を算出する。このとき、各式に代入されるのは前記ピーク周波数検出部62により検出されたピーク周波数ω0や流速取得部61により取得された流速データのみであり、管内の圧力データは不要である。また、費用関数を用いることで、数値解を算出するための計算負荷が抑制される。費用関数の最小化するためのアルゴリズムの種類や演算処理手段の処理能力に依存するが、1回の算出に対しおよそ数秒から数十秒間隔で数値解の算出が可能である。
Then, the numerical solution is calculated by minimizing this cost function by using a random search method, a gradient descent method, or the like. At this time, only the peak frequency ω 0 detected by the peak frequency detection unit 62 and the flow velocity data acquired by the flow velocity acquisition unit 61 are substituted into each equation, and the pressure data in the pipe is unnecessary. Moreover, by using the cost function, the calculation load for calculating the numerical solution is suppressed. Although it depends on the type of algorithm for minimizing the cost function and the processing capacity of the arithmetic processing means, it is possible to calculate a numerical solution at intervals of about several seconds to several tens of seconds for one calculation.
本実施形態では、ステップS5において、レオロジーモデルが不明な場合や温度や成分割合などに応じてせん断応力τが変化しレオロジーモデルの変更が必要な場合に対応するため、複数のレオロジーモデルを用いて数値解を算出する。具体的には、数値解算出部63がレオロジーモデル式記憶部52に記憶された複数種のレオロジーモデルに基づく管内を流れる流体の運動方程式を時間に対してフーリエ変換して得られる複数の式を読み出し、それぞれの式に対して数値解を算出する。
In the present embodiment, in step S5, in order to cope with the case where the rheology model is unknown or the shear stress τ changes according to the temperature, the component ratio, etc. and the rheology model needs to be changed, a plurality of rheology models are used. Calculate the numerical solution. Specifically, the numerical solution calculation unit 63 obtains a plurality of equations obtained by Fourier transforming the equations of motion of the fluid flowing in the pipe based on the plurality of types of rheology models stored in the rheology model equation storage unit 52 with respect to time. Read out and calculate a numerical solution for each equation.
そして、レオロジーモデル決定部64では、複数の数値解同士を比較して最も小さい数値解となる前記レオロジーモデルを前記流体のレオロジーモデルとして決定する(S6:レオロジーモデル決定ステップ)。
Then, the rheology model determination unit 64 compares a plurality of numerical solutions with each other and determines the rheology model having the smallest numerical solution as the rheology model of the fluid (S6: rheology model determination step).
なお、ニュートン流体など、レオロジーモデルが予め判っている場合は、ステップS4における複数種のレオロジーモデルを対象にした数値解の算出やステップS5のレオロジーモデル決定ステップの処理を省略してもよい。また、不明であったレオロジーモデルがステップS6において決定された後、レオロジーモデルに変更がない(せん断応力τに殆ど変化がない)場合には、その後の処理において、ステップ5における他のレオロジーモデルに基づく数値解の算出ステップS5やレオロジーモデル決定ステップS6の処理を省略することができる。
If the rheology model such as Newtonian fluid is known in advance, the calculation of the numerical solution for a plurality of types of rheology models in step S4 and the processing of the rheology model determination step in step S5 may be omitted. Further, if there is no change in the rheology model (the shear stress τ is almost unchanged) after the unknown rheology model is determined in step S6, in the subsequent processing, the other rheology model in step 5 is used. The processing of the calculation step S5 of the numerical solution based on the numerical solution and the rheology model determination step S6 can be omitted.
そして、レオロジー物性決定部65が、数値解算出部63によって得られた数値解に基づき流体のレオロジー物性値を決定する(S7:レオロジー物性決定ステップ)。もし、レオロジー物性値に基づく成分割合等が決定できる場合は、レオロジー物性値とともに成分割合も決定する。レオロジー物性値や成分割合などは、数値解を算出することで決定される。つまり、前記数値解と同様におよそ数秒から数十秒間隔でレオロジー物性値を決定することができる。よって、レオロジー物性値の変動や成分割合の変化などをほぼリアルタイムに計測することができる。
Then, the rheology physical property determination unit 65 determines the rheological physical property value of the fluid based on the numerical solution obtained by the numerical solution calculation unit 63 (S7: rheological physical property determination step). If the component ratio or the like based on the rheological physical property value can be determined, the component ratio is also determined together with the rheological physical property value. Rheological physical property values and component ratios are determined by calculating numerical solutions. That is, the rheological property value can be determined at intervals of about several seconds to several tens of seconds as in the numerical solution. Therefore, fluctuations in rheological physical property values and changes in component ratios can be measured in almost real time.
以上のような本実施形態の非接触型レオロジー物性計測装置3、システム1、プログラム3aおよび方法によれば、以下の効果を奏することができる。
1.管内を流れる流体の流速を非接触かつ非侵襲によって計測することのできる流速データを取得することによって、管内の圧力などを計測することなく、前記流体のレオロジー物性を計測することができる。
2.管内の流れにおける脈動を利用するため、適用範囲が広く、様々な管内を流れる流体に適用することができる。
3.費用関数などを用いることで計算にかかる処理負荷を軽くすることができるため、レオロジー物性値の変動や成分割合の変化などをリアルタイムに計測することができる。
4.流速データの関数近似値を用いることで、超音波流速計測装置2により計測される前記流速データの計測誤差に基づくレオロジー物性値等の計測誤差を抑制することができる。
5.ピーク周波数検出部62では、粘性層厚さに基づきピーク周波数を検出することで、計測原理上の精度を確保することができる。 According to the non-contact rheologicalproperty measuring device 3, the system 1, the program 3a and the method of the present embodiment as described above, the following effects can be obtained.
1. 1. By acquiring the flow velocity data that can measure the flow velocity of the fluid flowing in the pipe in a non-contact and non-invasive manner, the rheological properties of the fluid can be measured without measuring the pressure in the pipe or the like.
2. 2. Since it utilizes the pulsation in the flow in the pipe, it has a wide range of application and can be applied to various fluids flowing in the pipe.
3. 3. Since the processing load required for calculation can be reduced by using a cost function or the like, fluctuations in rheological physical property values and changes in component ratios can be measured in real time.
4. By using the function approximation value of the flow velocity data, it is possible to suppress a measurement error such as a rheological physical property value based on the measurement error of the flow velocity data measured by the ultrasonic flowvelocity measuring device 2.
5. The peakfrequency detection unit 62 can secure the accuracy in the measurement principle by detecting the peak frequency based on the thickness of the viscous layer.
1.管内を流れる流体の流速を非接触かつ非侵襲によって計測することのできる流速データを取得することによって、管内の圧力などを計測することなく、前記流体のレオロジー物性を計測することができる。
2.管内の流れにおける脈動を利用するため、適用範囲が広く、様々な管内を流れる流体に適用することができる。
3.費用関数などを用いることで計算にかかる処理負荷を軽くすることができるため、レオロジー物性値の変動や成分割合の変化などをリアルタイムに計測することができる。
4.流速データの関数近似値を用いることで、超音波流速計測装置2により計測される前記流速データの計測誤差に基づくレオロジー物性値等の計測誤差を抑制することができる。
5.ピーク周波数検出部62では、粘性層厚さに基づきピーク周波数を検出することで、計測原理上の精度を確保することができる。 According to the non-contact rheological
1. 1. By acquiring the flow velocity data that can measure the flow velocity of the fluid flowing in the pipe in a non-contact and non-invasive manner, the rheological properties of the fluid can be measured without measuring the pressure in the pipe or the like.
2. 2. Since it utilizes the pulsation in the flow in the pipe, it has a wide range of application and can be applied to various fluids flowing in the pipe.
3. 3. Since the processing load required for calculation can be reduced by using a cost function or the like, fluctuations in rheological physical property values and changes in component ratios can be measured in real time.
4. By using the function approximation value of the flow velocity data, it is possible to suppress a measurement error such as a rheological physical property value based on the measurement error of the flow velocity data measured by the ultrasonic flow
5. The peak
次に、本発明に係る非接触型レオロジー物性計測装置、システム、プログラムおよび方法の具体的な実施例について説明する。なお、本発明の技術的範囲は、以下の実施例によって示される特徴に限定されるものではない。
Next, specific examples of the non-contact rheological property measuring device, system, program and method according to the present invention will be described. The technical scope of the present invention is not limited to the features shown in the following examples.
実施例1では、数値的に脈動を伴う管内流れを作り出し、作り出された流れを超音波流速計測装置で計測したと仮定して得られる流速データとして、本発明に係る非接触型レオロジー物性計測プログラムによるレオロジー物性値の算出を行った。また、管内流れにおける厳密解と、本発明に係る非接触型レオロジー物性計測プログラムで得られる数値解とを比較し、計測精度の検討を行った。
In Example 1, the non-contact rheological property measurement program according to the present invention is used as flow velocity data obtained by assuming that an in-pipe flow with pulsation is numerically created and the created flow is measured by an ultrasonic flow velocity measuring device. The rheological property value was calculated by. In addition, the exact solution in the pipe flow was compared with the numerical solution obtained by the non-contact rheological property measurement program according to the present invention, and the measurement accuracy was examined.
<脈動を伴う管内流れの数値計算について>
ニュートン流体において一方向に流れる管内定常流れはハーゲン・ポアズイユ流れと呼ばれ、以下の支配方程式(13)および式(14)で表すことができる。
[数13]
[数14]
また、脈動する管内流れは、以下の支配方程式(15)および式(16)で表すことができる。
[数15]
[数16]
そして、脈動を伴う管内流れは、式(12)~式(16)により、以下の式(17)として得られる。
[数17]
ここで、
R は管の半径
U0 はハーゲン・ポアズイユ流れの最大値
U1は脈動の速度変動(振幅の大きさ)
ωは脈動の周波数(角周波数)
νは動粘性係数
ρは流体の密度
J0およびJ1はベッセル関数、をそれぞれ意味する。 <Numerical calculation of in-pipe flow with pulsation>
The steady flow in a pipe that flows in one direction in a Newtonian fluid is called the Hagen-Poiseuille flow, and can be expressed by the following governing equations (13) and (14).
[Number 13]
[Number 14]
Further, the pulsating in-pipe flow can be expressed by the following governing equations (15) and (16).
[Number 15]
[Number 16]
Then, the in-pipe flow accompanied by pulsation is obtained as the following equation (17) by the equations (12) to (16).
[Number 17]
here,
R is the radius of the tube U 0 is the maximum value of the Hagen-Poiseuille flow U 1 is the velocity fluctuation of the pulsation (magnitude of amplitude)
ω is the pulsation frequency (angular frequency)
ν means the kinematic viscosity coefficient ρ means the density of the fluid J 0 and J 1 means the Bessel function, respectively.
ニュートン流体において一方向に流れる管内定常流れはハーゲン・ポアズイユ流れと呼ばれ、以下の支配方程式(13)および式(14)で表すことができる。
[数13]
[数14]
また、脈動する管内流れは、以下の支配方程式(15)および式(16)で表すことができる。
[数15]
[数16]
そして、脈動を伴う管内流れは、式(12)~式(16)により、以下の式(17)として得られる。
[数17]
ここで、
R は管の半径
U0 はハーゲン・ポアズイユ流れの最大値
U1は脈動の速度変動(振幅の大きさ)
ωは脈動の周波数(角周波数)
νは動粘性係数
ρは流体の密度
J0およびJ1はベッセル関数、をそれぞれ意味する。 <Numerical calculation of in-pipe flow with pulsation>
The steady flow in a pipe that flows in one direction in a Newtonian fluid is called the Hagen-Poiseuille flow, and can be expressed by the following governing equations (13) and (14).
[Number 13]
[Number 14]
Further, the pulsating in-pipe flow can be expressed by the following governing equations (15) and (16).
[Number 15]
[Number 16]
Then, the in-pipe flow accompanied by pulsation is obtained as the following equation (17) by the equations (12) to (16).
[Number 17]
here,
R is the radius of the tube U 0 is the maximum value of the Hagen-Poiseuille flow U 1 is the velocity fluctuation of the pulsation (magnitude of amplitude)
ω is the pulsation frequency (angular frequency)
ν means the kinematic viscosity coefficient ρ means the density of the fluid J 0 and J 1 means the Bessel function, respectively.
<脈動を伴う管内の計算条件および計算結果>
ここで、式(17)により脈動を伴う管内流れを計算する際の計算条件としてU0 = 0.2 m/s、U1 = 0.1 m/s、r = 1000 kg/m3、R = 25.4 mm、Dt = 10 ms、Dr = 0.1 mmとした。 <Calculation conditions and calculation results in the pipe with pulsation>
Here, U 0 = 0.2 m / s, U 1 = 0.1 m / s, r = 1000 kg / m 3 , R = 25.4 mm, as calculation conditions when calculating the in-pipe flow with pulsation by Eq. (17). Dt = 10 ms and Dr = 0.1 mm.
ここで、式(17)により脈動を伴う管内流れを計算する際の計算条件としてU0 = 0.2 m/s、U1 = 0.1 m/s、r = 1000 kg/m3、R = 25.4 mm、Dt = 10 ms、Dr = 0.1 mmとした。 <Calculation conditions and calculation results in the pipe with pulsation>
Here, U 0 = 0.2 m / s, U 1 = 0.1 m / s, r = 1000 kg / m 3 , R = 25.4 mm, as calculation conditions when calculating the in-pipe flow with pulsation by Eq. (17). Dt = 10 ms and Dr = 0.1 mm.
また、異なる粘性(レオロジー物性)を有する流体の流れを解析対象とするため、動粘性係数νの条件は、n = 10 mm2/s、n = 50 mm2/s、n = 100 mm2/sなどの複数の条件とした。
In addition, since the flow of fluids with different viscosities (rheological properties) is analyzed, the conditions for the kinematic viscosity coefficient ν are n = 10 mm 2 / s, n = 50 mm 2 / s, n = 100 mm 2 /. Multiple conditions such as s were used.
さらに、周波数ω、つまり脈動の速さの違いによる計算精度の影響について検討するためにfo (=ω/2π) =0.5 Hz、fo(=ω/2π)=1.0 Hzなどの複数の条件とした。
Furthermore, the frequency omega, i.e. f o (= ω / 2π) = 0.5 Hz in order to examine the influence of calculation accuracy due to the difference in speed of the pulsation, the plurality of conditions, such as f o (= ω / 2π) = 1.0 Hz And said.
各条件に基づき計算された脈動を伴う管内の計算結果を図3に示す。各図において、縦軸が管内の位置を表している。縦軸の中央が管の中心位置を表しており、上下の両端が管壁の位置を表している。具体的には、r/Rとして無次元化されており、管の中心位置である縦軸の中央がr/R=0、管壁に相当する値がr/R=1またはr/R=-1である。横軸は、時間の経過を表している。具体的には、tfo として無次元化されている。また、時間毎の管内の流速分布は色の濃淡で表している。色が黒いほど速度はゼロに近づき、色が白いほど速度は速くなる。具体的には、u/U0として無次元化されている。
FIG. 3 shows the calculation results in the pipe with pulsation calculated based on each condition. In each figure, the vertical axis represents the position in the pipe. The center of the vertical axis represents the center position of the pipe, and the upper and lower ends represent the position of the pipe wall. Specifically, it is dimensionless as r / R, the center of the vertical axis, which is the center position of the pipe, is r / R = 0, and the value corresponding to the pipe wall is r / R = 1 or r / R = It is -1. The horizontal axis represents the passage of time. Specifically, it is dimensionless as tf o. In addition, the flow velocity distribution in the pipe for each hour is represented by shades of color. The darker the color, the closer the speed is to zero, and the whiter the color, the faster the speed. Specifically, it is dimensionless as u / U 0 .
図3に示すように、各時間において中央位置の流速が早く、管壁に近づくにつれ速度が遅くなっている。これは、ハーゲン・ポアズイユ流れのように軸対象となる管内の流速分布を示している。また、例えば、中心位置は時間の経過とともに速度が速くなったり遅くなったりを繰りかえしている。よって、式(17)により脈動を伴う管内流れを計算されていることが確認できる。
As shown in FIG. 3, the flow velocity at the central position is high at each time, and the speed becomes slower as it approaches the pipe wall. This shows the flow velocity distribution in the pipe that is the axial target like the Hagen-Poiseuille flow. Further, for example, the speed of the central position repeatedly increases and decreases with the passage of time. Therefore, it can be confirmed that the in-pipe flow with pulsation is calculated by the equation (17).
<超音波流速計測装置による計測シミュレーション>
図3に示す計算結果は、脈動を伴う管内流れを計算した流速分布の厳密解である。一方、管内の流れを超音波流速計測装置を用いて非接触で計測する場合、得られる流速データには計測誤差(計測ノイズ)が含まれる。計測誤差の要因は様々であるが、例えば、流体に含まれており超音波を反射させる固形物の密度や流体内や管壁内における超音波の乱反射などによる影響が考えられる。 <Measurement simulation with ultrasonic flow velocity measuring device>
The calculation result shown in FIG. 3 is an exact solution of the flow velocity distribution in which the in-pipe flow with pulsation is calculated. On the other hand, when the flow in the pipe is measured in a non-contact manner using an ultrasonic flow velocity measuring device, the obtained flow velocity data includes a measurement error (measurement noise). There are various factors of measurement error, but for example, the influence of the density of solids contained in the fluid and reflecting ultrasonic waves and the diffuse reflection of ultrasonic waves in the fluid and the pipe wall can be considered.
図3に示す計算結果は、脈動を伴う管内流れを計算した流速分布の厳密解である。一方、管内の流れを超音波流速計測装置を用いて非接触で計測する場合、得られる流速データには計測誤差(計測ノイズ)が含まれる。計測誤差の要因は様々であるが、例えば、流体に含まれており超音波を反射させる固形物の密度や流体内や管壁内における超音波の乱反射などによる影響が考えられる。 <Measurement simulation with ultrasonic flow velocity measuring device>
The calculation result shown in FIG. 3 is an exact solution of the flow velocity distribution in which the in-pipe flow with pulsation is calculated. On the other hand, when the flow in the pipe is measured in a non-contact manner using an ultrasonic flow velocity measuring device, the obtained flow velocity data includes a measurement error (measurement noise). There are various factors of measurement error, but for example, the influence of the density of solids contained in the fluid and reflecting ultrasonic waves and the diffuse reflection of ultrasonic waves in the fluid and the pipe wall can be considered.
そこで、本実施例1では、式(17)に基づき計算された脈動を伴う管内流れの流速分布に対し計測精度を考慮した計測誤差(計測ノイズ)の含まれる流速分布を下記の式(18)と定義した。
[数18]
ここで、
n(ave, std)はノイズ関数、
aはノイズレベル、をそれぞれ意味する。 Therefore, in the first embodiment, the flow velocity distribution including the measurement error (measurement noise) in consideration of the measurement accuracy with respect to the flow velocity distribution of the in-pipe flow with pulsation calculated based on the equation (17) is calculated by the following equation (18). Was defined as.
[Number 18]
here,
n (ave, std) is the noise function,
a means the noise level, respectively.
[数18]
ここで、
n(ave, std)はノイズ関数、
aはノイズレベル、をそれぞれ意味する。 Therefore, in the first embodiment, the flow velocity distribution including the measurement error (measurement noise) in consideration of the measurement accuracy with respect to the flow velocity distribution of the in-pipe flow with pulsation calculated based on the equation (17) is calculated by the following equation (18). Was defined as.
[Number 18]
here,
n (ave, std) is the noise function,
a means the noise level, respectively.
例えば、ノイズレベルa = 5.0とすると、ノイズ関数は、図4に示すよう、真の値を中央値とした正規分布で表される。本実施例1では、この式(18)を用いて、ノイズレベルaが1.0、5.0、10.0および15.0の場合について、流速データu(r,t)を代入して誤差を含む流速データu'(r,t)を計算した。図5は計算結果である。図5に示すように、ノイズレベルが大きくなるに従い、得られる流速分布の形状の滑らかさがなくなる。つまり、この流速分布は、計測誤差が含まれた流速データと見ることができる。本実施例1では、このように真の値として算出された流速データを計測誤差としてノイズを与えることで、超音波流速計測装置による計測誤差を含む流速データとした。
For example, assuming that the noise level is a = 5.0, the noise function is represented by a normal distribution with the true value as the median, as shown in FIG. In the first embodiment, using this equation (18), the flow velocity data u (r, t) is substituted for the case where the noise level a is 1.0, 5.0, 10.0 and 15.0, and the flow velocity data u'(including the error) ( r, t) was calculated. FIG. 5 is a calculation result. As shown in FIG. 5, as the noise level increases, the shape of the obtained flow velocity distribution becomes less smooth. That is, this flow velocity distribution can be seen as flow velocity data including measurement errors. In the first embodiment, the flow velocity data calculated as a true value in this way is given noise as a measurement error to obtain the flow velocity data including the measurement error by the ultrasonic flow velocity measuring device.
<本発明により得られる関数式の数値解について>
次に、式(17)および式(18)によって算出された流速データを用いて式(1)により得られる関数式から数値解を算出した。レオロジーモデルは、ニュートン流体とした。そこで、ニュートン流体における脈動を伴う管内流れの費用関数を表す式(7)および式(8)を用いて、前記費用関数が最小化させるプログラムを作成し、当該プログラムにより数値解を算出した。費用関数を算出するアルゴリズムにはランダムサーチ法を用いた。 <About the numerical solution of the functional expression obtained by the present invention>
Next, a numerical solution was calculated from the functional equation obtained by the equation (1) using the flow velocity data calculated by the equations (17) and (18). The rheology model was Newtonian fluid. Therefore, using equations (7) and (8) representing the cost function of the in-pipe flow accompanied by pulsation in the Newtonian fluid, a program for minimizing the cost function was created, and a numerical solution was calculated by the program. The random search method was used as the algorithm for calculating the cost function.
次に、式(17)および式(18)によって算出された流速データを用いて式(1)により得られる関数式から数値解を算出した。レオロジーモデルは、ニュートン流体とした。そこで、ニュートン流体における脈動を伴う管内流れの費用関数を表す式(7)および式(8)を用いて、前記費用関数が最小化させるプログラムを作成し、当該プログラムにより数値解を算出した。費用関数を算出するアルゴリズムにはランダムサーチ法を用いた。 <About the numerical solution of the functional expression obtained by the present invention>
Next, a numerical solution was calculated from the functional equation obtained by the equation (1) using the flow velocity data calculated by the equations (17) and (18). The rheology model was Newtonian fluid. Therefore, using equations (7) and (8) representing the cost function of the in-pipe flow accompanied by pulsation in the Newtonian fluid, a program for minimizing the cost function was created, and a numerical solution was calculated by the program. The random search method was used as the algorithm for calculating the cost function.
本実施例1では、脈動の周波数fo(角周波数ω)が数値解に与える影響について検討するため、周波数fo [Hz]を0.1、0.2、0.5、1.0、2.0、4.0のそれぞれの場合について計算した。
In the first embodiment, in order to examine the influence of the pulsation frequency f o (the angular frequency omega) has on the numerical solution for each case of 0.1,0.2,0.5,1.0,2.0,4.0 frequency f o [Hz] Calculated.
図6に算出結果を示す。図の左側が式(7)における実数値Re、右側が虚数値Imの計算結果である。また、上側は動粘性係数n = 100 mm2/sの場合であり、下側は動粘性係数の値がそれよりも1/10である動粘性係数n = 10 mm2/sの場合である。なお、n = 100 mm2/sは食用油程度の粘性であり、n = 10 mm2/sは水よりもやや高い粘性である。
The calculation result is shown in FIG. The left side of the figure is the calculation result of the real value Re in the equation (7), and the right side is the calculation result of the imaginary value Im. The upper side is the case where the kinematic viscosity coefficient n = 100 mm 2 / s, and the lower side is the case where the kinematic viscosity coefficient n = 10 mm 2 / s, which is 1/10 of the value of the kinematic viscosity coefficient. .. Note that n = 100 mm 2 / s is as viscous as cooking oil, and n = 10 mm 2 / s is slightly higher in viscosity than water.
まずは、粘性の影響について検討する。図6の左側の実数値について、周波数fo =0.1[Hz]の場合に着目すると、上側の粘性が高い場合は、その大きさが管壁(r/R=1.0)の近傍から管の中央(r/R=0.0)に至るまでなだらかに実数値Reが増加している。これは、粘性が管の中央まで影響していることを示す。一方、下側の粘性が高い場合、管の中央(r/R=0.0)からr/R=0.25までの範囲はほぼ一定値である。つまり、管の中央では粘性の影響が弱いことを意味している。
First, the effect of viscosity will be examined. The real value of the left side of FIG. 6, when attention is paid to the case of the frequency f o = 0.1 [Hz], if the upper viscosity is high, the center from the vicinity of the tube of the size of the tube wall (r / R = 1.0) The real value Re gradually increases until (r / R = 0.0). This indicates that the viscosity affects the center of the tube. On the other hand, when the viscosity on the lower side is high, the range from the center of the pipe (r / R = 0.0) to r / R = 0.25 is almost a constant value. In other words, it means that the influence of viscosity is weak in the center of the pipe.
図6の右側の虚数値Imについても、周波数fo =0.1[Hz]の場合に着目すると、上側の粘性が高い場合は、実数値Reと同様、管壁(r/R=1.0)の近傍から管の中央(r/R=0.0)に至るまでなだらかに増加している。一方、下側の粘性が低い場合は、管の中央(r/R=0.0)からr/R=0.7までの範囲はほぼ一定値である。
For even right imaginary value Im of FIG. 6, when attention is paid to the case of the frequency f o = 0.1 [Hz], if the upper viscosity is high, near the same real value Re, the tube wall (r / R = 1.0) It gradually increases from to the center of the pipe (r / R = 0.0). On the other hand, when the viscosity on the lower side is low, the range from the center of the pipe (r / R = 0.0) to r / R = 0.7 is almost a constant value.
ここで、式(3)における粘性層厚さ(ν/kΔω)1/2を検討してみると、粘性の高い動粘性係数n = 100 mm2/sの場合、粘性層厚さは約12.6mmである。管の半径R = 25.4 mmであることから粘性層厚さは管壁(r/R=1.0)からr/R=0.5の範囲(管の半径の1/2)程度であった。一方、粘性の低い(さらさらしている)動粘性係数n = 10 mm2/sの場合、粘性層厚さは約4.0mmである。よって、粘性層厚さは管壁(r/R=1.0)からr/R=0.85程度であった。
Here, when the viscous layer thickness (ν / kΔω) 1/2 in the equation (3) is examined, the viscous layer thickness is about 12.6 when the highly viscous kinematic viscosity coefficient n = 100 mm 2 / s. mm. Since the radius of the pipe was R = 25.4 mm, the thickness of the viscous layer was in the range from the pipe wall (r / R = 1.0) to r / R = 0.5 (1/2 of the radius of the pipe). On the other hand, when the kinematic viscosity coefficient n = 10 mm 2 / s with low viscosity (free-flowing), the thickness of the viscous layer is about 4.0 mm. Therefore, the thickness of the viscous layer was about r / R = 0.85 from the pipe wall (r / R = 1.0).
なお、粘性層厚さは約4.0mmの場合、本実施例1において式(3)における超音波流速計測装置における計測点同士の距離Δrが0.1mmであることから、粘性層厚さはΔrの40倍程度あり、3Δrより大きい。よって、粘性の影響の大きい管壁(r/R=1.0)からr/R=0.85の範囲内にある約40点ある計測点のうち3点以上の流速データを用いれば式(1)に基づき十分に精度の良い数値解を算出することができる。
When the viscous layer thickness is about 4.0 mm, the distance Δr between the measurement points in the ultrasonic flow velocity measuring device in the equation (3) in the first embodiment is 0.1 mm, so that the viscous layer thickness is Δr. It is about 40 times larger than 3Δr. Therefore, if the flow velocity data of 3 or more of the approximately 40 measurement points within the range of r / R = 0.85 from the tube wall (r / R = 1.0), which is greatly affected by viscosity, is used, it is based on equation (1). It is possible to calculate a numerical solution with sufficiently high accuracy.
次に、脈動の周波数fo(角周波数ω)の影響について検討する。図6の上側の実数値Reについて注目すると、比較的ゆっくりと振動している周波数fo(角周波数ω)が0.1や0.2の場合には、実数値Reは管壁(r/R=1.0)の近傍から管の中央(r/R=0.0)に至るまでなだらかに増加している。しかし、周波数fo(角周波数ω)が段々早くなるにつれて管の中央における実数値がほぼ一定値となる範囲が広がる。つまり、周波数fo(角周波数ω)が速くなると粘性の影響が管壁(r/R=1.0)から離れるに従って伝わりにくくなっている。
Next, consider the influence of the pulsation of frequency f o (angular frequency ω). Paying attention to real values Re of the upper side of FIG. 6, a relatively slow vibration to which the frequency f o in the case (the angular frequency omega) is 0.1 or 0.2, the real value Re tube wall (r / R = 1.0) It gradually increases from the vicinity of to the center of the pipe (r / R = 0.0). However, spread range becomes substantially constant value real value at the center of the tube as the frequency f o (the angular frequency omega) is gradually faster. In other words, when the frequency f o (angular frequency ω) is increased influence of viscosity is less likely to be transmitted as the distance from the tube wall (r / R = 1.0).
また、図6の上側の虚数値Imについても、同様に、比較的ゆっくりと振動している場合に数値解である実数値Reおよび虚数値Imは管壁(r/R=1.0)の近傍から管の中央(r/R=0.0)に至るまでなだらかに増加している。そして、周波数fo(角周波数ω)が段々早くなるにつれて管の中央における実数値がほぼ一定値となる範囲が広がる。
Similarly, for the imaginary value Im on the upper side of FIG. 6, the real value Re and the imaginary value Im, which are numerical solutions when vibrating relatively slowly, are from the vicinity of the pipe wall (r / R = 1.0). It gradually increases to the center of the pipe (r / R = 0.0). The spread range becomes substantially constant value real value at the center of the tube as the frequency f o (the angular frequency omega) is gradually faster.
さらに、粘性の低い図6の下側の実数値Reおよび虚数値Imについても、比較的ゆっくりと振動している場合には、管壁(r/R=1.0)の近傍から管の中央(r/R=0.0)に向けて比較的、解析値が変化しており、粘性の影響が現れているが、周波数fo(角周波数ω)が速くなると、管壁(r/R=1.0)の近傍に粘性の影響が現れている。
Furthermore, when the real value Re and the imaginary value Im on the lower side of FIG. 6 having low viscosity are vibrating relatively slowly, the vicinity of the pipe wall (r / R = 1.0) to the center of the pipe (r). relatively towards the /R=0.0), analysis value has changed, but the influence of the viscosity has appeared, when the frequency f o (angular frequency ω) becomes faster, the tube wall of (r / R = 1.0) The effect of viscosity appears in the vicinity.
<レオロジー物性の算出結果について>
次に、本発明により得られる関数式の数値解に基づきレオロジー物性値を決定する。図7は、費用関数の最小化を行ったときの結果である。図7の高さ方向は算出された粘性係数μ、下の面は算出された実数値Re(αa)および虚数値Im(αb)を表している。そして、各点はランダムサーチ法によりランダムに数値を入れたときの粘性係数μ、実数値および虚数値の組合せを表している。また、各点の色は費用関数の大きさを示しており、色が黒に近づくにつれて費用関数が小さくなっていく。 <About the calculation result of rheological properties>
Next, the rheological property value is determined based on the numerical solution of the functional formula obtained by the present invention. FIG. 7 shows the result when the cost function is minimized. The height direction of FIG. 7 represents the calculated viscosity coefficient μ, and the lower surface represents the calculated real value Re (α a ) and imaginary value Im (α b ). Each point represents a combination of viscosity coefficient μ, real value and imaginary value when numerical values are randomly entered by the random search method. In addition, the color of each point indicates the magnitude of the cost function, and the cost function becomes smaller as the color approaches black.
次に、本発明により得られる関数式の数値解に基づきレオロジー物性値を決定する。図7は、費用関数の最小化を行ったときの結果である。図7の高さ方向は算出された粘性係数μ、下の面は算出された実数値Re(αa)および虚数値Im(αb)を表している。そして、各点はランダムサーチ法によりランダムに数値を入れたときの粘性係数μ、実数値および虚数値の組合せを表している。また、各点の色は費用関数の大きさを示しており、色が黒に近づくにつれて費用関数が小さくなっていく。 <About the calculation result of rheological properties>
Next, the rheological property value is determined based on the numerical solution of the functional formula obtained by the present invention. FIG. 7 shows the result when the cost function is minimized. The height direction of FIG. 7 represents the calculated viscosity coefficient μ, and the lower surface represents the calculated real value Re (α a ) and imaginary value Im (α b ). Each point represents a combination of viscosity coefficient μ, real value and imaginary value when numerical values are randomly entered by the random search method. In addition, the color of each point indicates the magnitude of the cost function, and the cost function becomes smaller as the color approaches black.
図7に示すように、ランダムサーチ法により算出された費用関数の値はグラフ上の一点に集中していく。この集中されている点が最小化された費用関数となる。そして、費用関数の最小化された点の高さ方向の値が粘性係数μとして決定することができる。
As shown in FIG. 7, the value of the cost function calculated by the random search method concentrates on one point on the graph. This concentrated point is the minimized cost function. Then, the value in the height direction of the minimized point of the cost function can be determined as the viscosity coefficient μ.
<数値解の算出精度について>
次に、数値解の算出結果から得られるレオロジー物性値と、真の値に相当する管内流れの計算に用いたレオロジー物性値との比較を行った。また、本発明では、レオロジー物性値とともに圧力勾配も算出することができる。そこで、数値解の算出結果から得られる圧力勾配と、真の値に相当する管内流れの計算に用いた圧力勾配との比較も行った。 <Accuracy of calculation of numerical solution>
Next, the rheological property value obtained from the calculation result of the numerical solution was compared with the rheological property value used for the calculation of the in-pipe flow corresponding to the true value. Further, in the present invention, the pressure gradient can be calculated together with the rheological property value. Therefore, the pressure gradient obtained from the calculation result of the numerical solution was also compared with the pressure gradient used for the calculation of the in-pipe flow corresponding to the true value.
次に、数値解の算出結果から得られるレオロジー物性値と、真の値に相当する管内流れの計算に用いたレオロジー物性値との比較を行った。また、本発明では、レオロジー物性値とともに圧力勾配も算出することができる。そこで、数値解の算出結果から得られる圧力勾配と、真の値に相当する管内流れの計算に用いた圧力勾配との比較も行った。 <Accuracy of calculation of numerical solution>
Next, the rheological property value obtained from the calculation result of the numerical solution was compared with the rheological property value used for the calculation of the in-pipe flow corresponding to the true value. Further, in the present invention, the pressure gradient can be calculated together with the rheological property value. Therefore, the pressure gradient obtained from the calculation result of the numerical solution was also compared with the pressure gradient used for the calculation of the in-pipe flow corresponding to the true value.
図8は、横軸にノイズレベルを示している。そして、縦軸には、数値解の算出結果から得られる粘性係数μと、真の粘性係数μtrueとの比であるηと、数値解の算出結果から得られる圧力勾配αと、真の圧力勾配αtrueとの比であるλを表している。また、数値解の算出結果から得られる粘性係数μおよび圧力勾配αについては空間的(r方向)に連続する3点の平均値を用いている。縦軸は真の値との比であるため1に近いほど数値解の算出結果から得られるレオロジー物性値および真の値に近いことになる。
In FIG. 8, the noise level is shown on the horizontal axis. The vertical axis shows η, which is the ratio of the viscosity coefficient μ obtained from the calculation result of the numerical solution to the true viscosity coefficient μ true , the pressure gradient α obtained from the calculation result of the numerical solution, and the true pressure. It represents λ, which is the ratio to the gradient α true . Further, for the viscosity coefficient μ and the pressure gradient α obtained from the calculation result of the numerical solution, the average value of three points consecutive in space (r direction) is used. Since the vertical axis is the ratio to the true value, the closer it is to 1, the closer to the rheological property value and the true value obtained from the calculation result of the numerical solution.
図8に示すようにノイズレベルが5以下の場合には、数値解の算出結果から得られる結果は、ほぼ真の値と同じ値を示した。一方、ノイズレベルが10では、η(粘性係数の比)が真の値に対してやや小さい値を示し、ノイズレベルが15の場合にはさらに真の値からは離れる結果となった。また、λ(圧力勾配の比)については、ノイズレベル15においてもほぼ真の値と同じ値を示し非常に高い精度であった。
As shown in FIG. 8, when the noise level was 5 or less, the result obtained from the calculation result of the numerical solution showed almost the same value as the true value. On the other hand, when the noise level was 10, η (ratio of viscosity coefficients) showed a value slightly smaller than the true value, and when the noise level was 15, the result was that the value was further separated from the true value. Further, regarding λ (ratio of pressure gradient), even at the noise level 15, the value was almost the same as the true value, and the accuracy was very high.
よって、本発明に係る非接触型レオロジー物性計測装置、システム、プログラムおよび方法において、超音波流速計測装置による計測精度を保つことで、非常に精度の高い結果が得られることが示された。
Therefore, it was shown that in the non-contact rheological property measuring device, system, program and method according to the present invention, extremely high accuracy results can be obtained by maintaining the measurement accuracy by the ultrasonic flow velocity measuring device.
次に、脈動の周期(半周期内)に対する精度の違いについて確認した。結果を図9に示す。横軸は脈動の周期であり、縦軸はηおよびλである。その結果、ηおよびλはいずれも1に近似しており、周期の違いによる精度には影響は確認できなかった。よって、本発明に係る非接触型レオロジー物性計測装置、システム、プログラムおよび方法では、脈動を伴う管内流れに対してどのタイミングで計測を行っても精度に大きな違いは生じないことがわかった。
Next, we confirmed the difference in accuracy with respect to the pulsation cycle (within half a cycle). The results are shown in FIG. The horizontal axis is the period of pulsation, and the vertical axis is η and λ. As a result, both η and λ were close to 1, and no effect could be confirmed on the accuracy due to the difference in period. Therefore, it was found that in the non-contact rheological property measuring device, system, program and method according to the present invention, there is no significant difference in accuracy regardless of the timing of measurement of the in-pipe flow accompanied by pulsation.
次に、動粘性係数νに対する精度の違いについて確認した。結果を図10に示す。横軸は動粘性係数νであり、縦軸はηおよびλである。図10に示すように、動粘性係数νが高い範囲では精度が落ちている。これは、圧力勾配を一定にしているため、速度変動が弱くなり、結果としてノイズが相対的に大きくなるためと考えられる。一方、動粘性係数νが100 mm2/s 以下においては、真の値とほぼ一致しており精度が高かった。
Next, the difference in accuracy with respect to the kinematic viscosity coefficient ν was confirmed. The results are shown in FIG. The horizontal axis is the kinematic viscosity coefficient ν, and the vertical axis is η and λ. As shown in FIG. 10, the accuracy drops in the range where the kinematic viscosity coefficient ν is high. It is considered that this is because the pressure gradient is constant, so that the speed fluctuation becomes weak, and as a result, the noise becomes relatively large. On the other hand, when the kinematic viscosity coefficient ν was 100 mm 2 / s or less, it almost matched the true value and the accuracy was high.
次に、脈動の周波数fo(角周波数ω)に対する精度の違いについて確認した。結果を図11に示す。横軸は周波数foであり、縦軸はηおよびλである。図11に示すように、周波数foが低い範囲で精度が落ちている。これは、圧力勾配を一定にしているため、周波数foが低くなると振幅が小さくなり、結果としてノイズが相対的に大きくなるためと考えられる。一方、周波数foが1.0Hz以上においては、真の値とほぼ一致しており精度が高かった。
Next, it was checked for accuracy differences in respect to the frequency f o (angular frequency ω) of pulsation. The results are shown in FIG. The horizontal axis is the frequency f o, the vertical axis represents the η and lambda. As shown in FIG. 11, the frequency f o is less accurate in low range. This is because it a pressure gradient constant, the amplitude decreases as the frequency f o is lower, presumably because the noise as a result is relatively large. On the other hand, the frequency f o is in the above 1.0 Hz, higher accuracy and substantially coincides with the true value.
次に、脈動の振幅U1に対する精度の違いについて確認した。結果を図12に示す。横軸は振幅U1であり、縦軸はηおよびλである。図12に示すように、振幅U1が低いと精度が落ちている。これは、脈動の周波数fo(角周波数ω)のときと同様に振幅が小さくなり、結果としてノイズが相対的に大きくなるためと考えられる。一方、振幅U1が0.1m/s以上においては、真の値とほぼ一致しており精度が高かった。
Next, we confirmed the difference in accuracy with respect to the pulsation amplitude U 1 . The results are shown in FIG. The horizontal axis is the amplitude U 1 and the vertical axis is η and λ. As shown in FIG. 12, the accuracy drops when the amplitude U 1 is low. This amplitude as in the case of pulsating frequency f o (the angular frequency omega) is reduced, presumably because the noise as a result is relatively large. On the other hand, when the amplitude U 1 was 0.1 m / s or more, it almost matched the true value and the accuracy was high.
以上より、本実施例1では、本発明に係る非接触型レオロジー物性計測装置、システム、プログラムおよび方法を用いることで、管内を流れる脈動を伴う流体のレオロジー物性を、非接触で精度よく計測することができることを数値実験により確かめることができた。
From the above, in the first embodiment, by using the non-contact rheological property measuring device, system, program and method according to the present invention, the rheological property of the fluid accompanied by pulsation flowing in the pipe is measured accurately without contact. It was possible to confirm that it can be done by numerical experiments.
実施例2では、脈動を伴う管内流れを作り出す実験装置を作成し、本発明に係る本発明に係る非接触型レオロジー物性計測システムによってニュートン流体および非ニュートン流体のレオロジー物性値の計測を行った。また、カタログ値や市販されている回転式のレオメータによる計測値と、本発明に係る非接触型レオロジー物性計測システムで得られる計測値とを比較し、計測精度の検討を行った。
In Example 2, an experimental device for creating an in-pipe flow accompanied by pulsation was created, and the rheological property values of the Newtonian fluid and the non-Newtonian fluid were measured by the non-contact rheological property measurement system according to the present invention according to the present invention. Further, the measurement accuracy was examined by comparing the values measured by the catalog value or a commercially available rotary rheometer with the measured values obtained by the non-contact rheological property measurement system according to the present invention.
<脈動を伴う管内流れを作り出す実験装置について>
本実施例2では、図13に示すように脈動を伴う管内流を作り出す実験装置を作成した。計測対象となる管は、直線状のステンレス管と、交換可能に設置されるアクリル管とを有する。ステンレス管には、長さは3000mm以上、外径50.8mm(2インチ)、内径40.8mmのものを用いた。アクリル管は、ステンレス管の後流側に設置した。本実施例2では、内径約48mmのものと、内径約22mmのものを用いた。また、管内の流れを安定させるためステンレス管の入り口から約3000mm以上離れた地点を計測位置とした。 <Experimental equipment that creates pulsating intraductal flow>
In the second embodiment, as shown in FIG. 13, an experimental device for creating an in-pipe flow accompanied by pulsation was created. The pipe to be measured includes a straight stainless steel pipe and a replaceable acrylic pipe. As the stainless steel tube, a stainless steel tube having a length of 3000 mm or more, an outer diameter of 50.8 mm (2 inches), and an inner diameter of 40.8 mm was used. The acrylic pipe was installed on the wake side of the stainless steel pipe. In Example 2, the one having an inner diameter of about 48 mm and the one having an inner diameter of about 22 mm were used. Further, in order to stabilize the flow in the pipe, a point separated from the entrance of the stainless steel pipe by about 3000 mm or more was set as the measurement position.
本実施例2では、図13に示すように脈動を伴う管内流を作り出す実験装置を作成した。計測対象となる管は、直線状のステンレス管と、交換可能に設置されるアクリル管とを有する。ステンレス管には、長さは3000mm以上、外径50.8mm(2インチ)、内径40.8mmのものを用いた。アクリル管は、ステンレス管の後流側に設置した。本実施例2では、内径約48mmのものと、内径約22mmのものを用いた。また、管内の流れを安定させるためステンレス管の入り口から約3000mm以上離れた地点を計測位置とした。 <Experimental equipment that creates pulsating intraductal flow>
In the second embodiment, as shown in FIG. 13, an experimental device for creating an in-pipe flow accompanied by pulsation was created. The pipe to be measured includes a straight stainless steel pipe and a replaceable acrylic pipe. As the stainless steel tube, a stainless steel tube having a length of 3000 mm or more, an outer diameter of 50.8 mm (2 inches), and an inner diameter of 40.8 mm was used. The acrylic pipe was installed on the wake side of the stainless steel pipe. In Example 2, the one having an inner diameter of about 48 mm and the one having an inner diameter of about 22 mm were used. Further, in order to stabilize the flow in the pipe, a point separated from the entrance of the stainless steel pipe by about 3000 mm or more was set as the measurement position.
測定対象となる管の上流側には試験流体を貯留する貯留タンクを接続した。また、下流側には試験流体を流すためのロータリーポンプを接続した。本実施例2では、ロータリーポンプとして、主に食品や医薬品、化粧品などの製造工程で使用されるサニタリーポンプを用いた。また、前記ロータリーポンプはパソコンに接続されており、管内を流れる試験流体の振動数を制御できるようになっている。ロータリーポンプの排出口には貯留タンクに連結された管を設けた。よって、ロータリーポンプを作動させることで、試験流体は実験装置内で循環するようになっている。
A storage tank for storing the test fluid was connected to the upstream side of the pipe to be measured. In addition, a rotary pump for flowing the test fluid was connected to the downstream side. In the second embodiment, a sanitary pump mainly used in the manufacturing process of foods, pharmaceuticals, cosmetics, etc. was used as the rotary pump. Further, the rotary pump is connected to a personal computer so that the frequency of the test fluid flowing in the pipe can be controlled. A pipe connected to the storage tank was provided at the outlet of the rotary pump. Therefore, by operating the rotary pump, the test fluid is circulated in the laboratory equipment.
また、計測位置には、図14に示すように、超音波流速計測装置の一構成である超音波トランスデューサと、この超音波トランスデューサを角度θ1で保持する保持治具とが設置されている。また、超音波トランスデューサと管と間には、超音波の伝達性を高めるための超音波ジェルを充填させた。
Further, as shown in FIG. 14, at the measurement position, an ultrasonic transducer which is one configuration of the ultrasonic flow velocity measuring device and a holding jig for holding the ultrasonic transducer at an angle θ 1 are installed. In addition, an ultrasonic gel was filled between the ultrasonic transducer and the tube to enhance the transmission of ultrasonic waves.
超音波流速計測装置は、本発明に係る非接触型レオロジー物性計測装置として構成されるパソコンに接続されており、非接触型レオロジー物性計測システムを構築している。
The ultrasonic flow velocity measuring device is connected to a personal computer configured as the non-contact rheological property measuring device according to the present invention, and a non-contact rheological property measuring system is constructed.
<ニュートン流体として用いる試験流体について>
ニュートン流体には、動粘度10cStのシリコーンオイル(粘度(粘性係数):9.35×10-3[Ps/s])を用いた。本実施例2においては、シリコーンオイル内に超音波の反射を促すトレーサ粒子を含有させた。 <Test fluid used as Newtonian fluid>
As the Newtonian fluid, silicone oil having a kinematic viscosity of 10 cSt (viscosity (viscosity coefficient): 9.35 × 10 -3 [Ps / s]) was used. In Example 2, the silicone oil contained tracer particles that promote the reflection of ultrasonic waves.
ニュートン流体には、動粘度10cStのシリコーンオイル(粘度(粘性係数):9.35×10-3[Ps/s])を用いた。本実施例2においては、シリコーンオイル内に超音波の反射を促すトレーサ粒子を含有させた。 <Test fluid used as Newtonian fluid>
As the Newtonian fluid, silicone oil having a kinematic viscosity of 10 cSt (viscosity (viscosity coefficient): 9.35 × 10 -3 [Ps / s]) was used. In Example 2, the silicone oil contained tracer particles that promote the reflection of ultrasonic waves.
<ニュートン流体の物性値の計測について>
本実施例2では、0.1Hzの振動流が発生するようにロータリーポンプを制御し、ニュートン流体(シリコーンオイル)のレオロジー物性値の計測を行った。まず、超音波流速計測装置が、前記超音波トランスデューサを介して超音波の送信および受信を行い、受信した超音波を解析することで脈動を伴う管内流の流速分布を計測した。なお、図14に示すように、管と試験流体との屈折率の違いから超音波トランスデューサの設置角度θ1と超音波の伝播方向の角度θ2とは異なるが、本実施例2ではこの角度の違いを流速分布の計測結果に反映させている。 <Measurement of physical property values of Newtonian fluid>
In the second embodiment, the rotary pump was controlled so that a vibration flow of 0.1 Hz was generated, and the rheological property value of the Newtonian fluid (silicone oil) was measured. First, the ultrasonic flow velocity measuring device transmits and receives ultrasonic waves via the ultrasonic transducer, and analyzes the received ultrasonic waves to measure the flow velocity distribution of the in-tube flow accompanied by pulsation. As shown in FIG. 14, the installation angle θ 1 of the ultrasonic transducer and the angle θ 2 in the propagation direction of ultrasonic waves are different due to the difference in the refractive index between the tube and the test fluid, but in the second embodiment, this angle is different. The difference is reflected in the measurement result of the flow velocity distribution.
本実施例2では、0.1Hzの振動流が発生するようにロータリーポンプを制御し、ニュートン流体(シリコーンオイル)のレオロジー物性値の計測を行った。まず、超音波流速計測装置が、前記超音波トランスデューサを介して超音波の送信および受信を行い、受信した超音波を解析することで脈動を伴う管内流の流速分布を計測した。なお、図14に示すように、管と試験流体との屈折率の違いから超音波トランスデューサの設置角度θ1と超音波の伝播方向の角度θ2とは異なるが、本実施例2ではこの角度の違いを流速分布の計測結果に反映させている。 <Measurement of physical property values of Newtonian fluid>
In the second embodiment, the rotary pump was controlled so that a vibration flow of 0.1 Hz was generated, and the rheological property value of the Newtonian fluid (silicone oil) was measured. First, the ultrasonic flow velocity measuring device transmits and receives ultrasonic waves via the ultrasonic transducer, and analyzes the received ultrasonic waves to measure the flow velocity distribution of the in-tube flow accompanied by pulsation. As shown in FIG. 14, the installation angle θ 1 of the ultrasonic transducer and the angle θ 2 in the propagation direction of ultrasonic waves are different due to the difference in the refractive index between the tube and the test fluid, but in the second embodiment, this angle is different. The difference is reflected in the measurement result of the flow velocity distribution.
図15は、超音波流速計測装置により管内の流速分布を計測した結果である。縦軸が管内の位置を表しており、ξ=0mmが超音波トランスデューサを設置した管の内壁に相当している。流速分布はコンター(等高線)状の色の濃淡で表している。色が白いほど速度はゼロに近づき、色が黒いほど速度は速い。横軸は、時間であり約10秒間のデータを示している。略中心地点(ξ=約28mm)の流速を時間に沿って見ていくと、この約10秒間で約1周期の変動をしており、0.1Hzの振動流が計測されていることがわかる。
FIG. 15 shows the result of measuring the flow velocity distribution in the pipe with the ultrasonic flow velocity measuring device. The vertical axis represents the position in the tube, and ξ = 0 mm corresponds to the inner wall of the tube in which the ultrasonic transducer is installed. The flow velocity distribution is represented by shades of contour-like color. The whiter the color, the closer the speed is to zero, and the darker the color, the faster the speed. The horizontal axis is time and shows data for about 10 seconds. Looking at the flow velocity at the substantially central point (ξ = about 28 mm) over time, it can be seen that the fluctuation is about one cycle in about 10 seconds, and the vibration flow of 0.1 Hz is measured. ..
本実施例2では、実施例1と同様に、式(1)により得られる関数式から数値解を算出した。試験流体は、ニュートン流体であるためレオロジーモデルもニュートン流体とした。よって、ニュートン流体における脈動を伴う管内流れの費用関数を表す式(7)および式(8)を用いて、前記費用関数が最小化させるプログラムを作成し、当該プログラムにより数値解を算出した。費用関数を算出するアルゴリズムにはランダムサーチ法を用いた。
In the second embodiment, the numerical solution was calculated from the functional formula obtained by the formula (1) as in the first embodiment. Since the test fluid is a Newtonian fluid, the rheology model is also a Newtonian fluid. Therefore, a program for minimizing the cost function was created using equations (7) and (8) representing the cost function of the in-pipe flow accompanied by pulsation in the Newtonian fluid, and a numerical solution was calculated by the program. The random search method was used as the algorithm for calculating the cost function.
図16に費用関数の算出結果を示す。縦軸は粘度μを、横軸は圧力振幅(Pressure amplitude)を示す。ここで圧力振幅(Pressure amplitude)は、圧力の実部と虚部のノルム値である。費用関数の値はコンター(等高線)状の色の濃淡で表している。色が白いほど値が小さく、色が黒いほど値は大きい。図16に示すように、ランダムサーチ法により算出された費用関数の値はグラフ上の一点に集中していく。この集中されている点が最小化された費用関数となる。そして、費用関数の最小化された点の高さ方向の値が粘性係数μとして決定することができる。
Figure 16 shows the calculation result of the cost function. The vertical axis shows the viscosity μ, and the horizontal axis shows the pressure amplitude. Here, the pressure amplitude is the norm value of the real part and the imaginary part of the pressure. The value of the cost function is represented by shades of contour-like color. The whiter the color, the smaller the value, and the darker the color, the larger the value. As shown in FIG. 16, the value of the cost function calculated by the random search method is concentrated on one point on the graph. This concentrated point is the minimized cost function. Then, the value in the height direction of the minimized point of the cost function can be determined as the viscosity coefficient μ.
図17は、10秒間隔で計測した粘度(Viscosity)および圧力振幅(Pressure amplitude)の約1000秒間のデータを示すものである。また、図中の破線は、試験流体として用いたシリコーンオイルの粘度のカタログ値9.35×10-3[Ps/s]である。図17に示すように、計測した粘度(Viscosity)の値はカタログ値である9.35×10-3[Ps/s]近辺の値に集約された。
FIG. 17 shows data of viscosity (Viscosity) and pressure amplitude (Pressure amplitude) measured at intervals of 10 seconds for about 1000 seconds. The broken line in the figure is the catalog value of the viscosity of the silicone oil used as the test fluid, 9.35 × 10 -3 [Ps / s]. As shown in FIG. 17, the measured viscosity (Viscosity) values were aggregated into values in the vicinity of 9.35 × 10 -3 [Ps / s], which is a catalog value.
よって、本実施例2の非接触型レオロジー物性計測システムは、充分な精度でニュートン流体のレオロジー物性を計測できることが実証できた。
Therefore, it was demonstrated that the non-contact rheological property measurement system of Example 2 can measure the rheological property of the Newtonian fluid with sufficient accuracy.
<非ニュートン流体の物性値の計測について>
次に、非ニュートン流体の物性値についての計測を行った。 <Measurement of physical properties of non-Newtonian fluids>
Next, the physical property values of the non-Newtonian fluid were measured.
次に、非ニュートン流体の物性値についての計測を行った。 <Measurement of physical properties of non-Newtonian fluids>
Next, the physical property values of the non-Newtonian fluid were measured.
<非ニュートン流体として用いる試験流体について>
非ニュートン流体には、カルボキシメチルセルロースの水溶液(以下、「CMC水溶液」という。)を用いた。本実施例2ではCMC水溶液の濃度を0.5wt.%とした。カルボキシメチルセルロース(CMC)は、一般に増粘剤として食品を含む加工製品に使用されるものである。CMC水溶液は、せん断速度が大きくなると粘度が低下する擬塑性流体であって、本実施例2では粘度は約100~400[mPa・s]のものを使用した。 <Test fluid used as a non-Newtonian fluid>
As the non-Newtonian fluid, an aqueous solution of carboxymethyl cellulose (hereinafter referred to as "CMC aqueous solution") was used. In Example 2, the concentration of the CMC aqueous solution was 0.5 wt. %. Carboxymethyl cellulose (CMC) is commonly used as a thickener in processed products containing foods. The CMC aqueous solution is a pseudo-plastic fluid whose viscosity decreases as the shear rate increases, and in Example 2, a fluid having a viscosity of about 100 to 400 [mPa · s] was used.
非ニュートン流体には、カルボキシメチルセルロースの水溶液(以下、「CMC水溶液」という。)を用いた。本実施例2ではCMC水溶液の濃度を0.5wt.%とした。カルボキシメチルセルロース(CMC)は、一般に増粘剤として食品を含む加工製品に使用されるものである。CMC水溶液は、せん断速度が大きくなると粘度が低下する擬塑性流体であって、本実施例2では粘度は約100~400[mPa・s]のものを使用した。 <Test fluid used as a non-Newtonian fluid>
As the non-Newtonian fluid, an aqueous solution of carboxymethyl cellulose (hereinafter referred to as "CMC aqueous solution") was used. In Example 2, the concentration of the CMC aqueous solution was 0.5 wt. %. Carboxymethyl cellulose (CMC) is commonly used as a thickener in processed products containing foods. The CMC aqueous solution is a pseudo-plastic fluid whose viscosity decreases as the shear rate increases, and in Example 2, a fluid having a viscosity of about 100 to 400 [mPa · s] was used.
<非ニュートン流体の物性値の計測について>
図18の左側は、超音波流速計測装置により管内の流速分布を計測した結果である。ここでは、図3と同様、縦軸がr/Rとして無次元化された管内の位置であり、r/R=0が管の中心位置を表している。横軸は、tf として無次元化された時間の経過を表しており、約2周期分のデータを示している。流速分布はコンター(等高線)状の色の濃淡で表しており、色が白いほど速度はゼロに近づき、色が黒いほど速度は速い。略中心地点(r/R=0)の流速を時間に沿って見ていくと、約1周期毎に変動をしており振動流が計測されていることがわかる。 <Measurement of physical properties of non-Newtonian fluids>
The left side of FIG. 18 is the result of measuring the flow velocity distribution in the pipe by the ultrasonic flow velocity measuring device. Here, as in FIG. 3, the vertical axis represents the dimensionless position in the pipe as r / R, and r / R = 0 represents the center position of the pipe. The horizontal axis represents the passage of time that has been dimensionless as tf, and shows data for about two cycles. The flow velocity distribution is represented by shades of contour-like color. The whiter the color, the closer the velocity approaches zero, and the darker the color, the faster the velocity. Looking at the flow velocity at the substantially central point (r / R = 0) over time, it can be seen that the flow velocity fluctuates approximately every cycle and the oscillating flow is measured.
図18の左側は、超音波流速計測装置により管内の流速分布を計測した結果である。ここでは、図3と同様、縦軸がr/Rとして無次元化された管内の位置であり、r/R=0が管の中心位置を表している。横軸は、tf として無次元化された時間の経過を表しており、約2周期分のデータを示している。流速分布はコンター(等高線)状の色の濃淡で表しており、色が白いほど速度はゼロに近づき、色が黒いほど速度は速い。略中心地点(r/R=0)の流速を時間に沿って見ていくと、約1周期毎に変動をしており振動流が計測されていることがわかる。 <Measurement of physical properties of non-Newtonian fluids>
The left side of FIG. 18 is the result of measuring the flow velocity distribution in the pipe by the ultrasonic flow velocity measuring device. Here, as in FIG. 3, the vertical axis represents the dimensionless position in the pipe as r / R, and r / R = 0 represents the center position of the pipe. The horizontal axis represents the passage of time that has been dimensionless as tf, and shows data for about two cycles. The flow velocity distribution is represented by shades of contour-like color. The whiter the color, the closer the velocity approaches zero, and the darker the color, the faster the velocity. Looking at the flow velocity at the substantially central point (r / R = 0) over time, it can be seen that the flow velocity fluctuates approximately every cycle and the oscillating flow is measured.
次に、式(9)ないし式(12)を用いて非ニュートン流体における脈動を伴う管内流れの費用関数を表す前記費用関数が最小化させるプログラムを作成し、当該プログラムにより数値解を算出した。図18の右側は、r/Rが0~0.6の範囲の流速分布を用いて式(10)により算出された実数値Reと虚数値Imの計算結果である。実数値Reおよび虚数値Imは、中心位置に近づくにつれてなだらかに増加しており、0~0.6の全範囲において粘性の影響が現れているものと考えられる。
Next, using equations (9) to (12), a program was created that minimizes the cost function of the in-pipe flow with pulsation in the non-Newtonian fluid, and the numerical solution was calculated by the program. The right side of FIG. 18 shows the calculation results of the real value Re and the imaginary value Im calculated by the equation (10) using the flow velocity distribution in the range of r / R of 0 to 0.6. The real value Re and the imaginary value Im gradually increase as they approach the center position, and it is considered that the influence of viscosity appears in the entire range of 0 to 0.6.
図19および図20は、ランダムサーチ法により費用関数を算出した結果である。ニュートン流体を計測した結果の図16と同様に、ランダムサーチ法により算出された費用関数の値はグラフ上の一点に集中していく。そして、費用関数の最小化された点の高さ方向の値が粘性係数μとして決定することができる。
19 and 20 are the results of calculating the cost function by the random search method. Similar to FIG. 16 as a result of measuring the Newtonian fluid, the value of the cost function calculated by the random search method is concentrated on one point on the graph. Then, the value in the height direction of the minimized point of the cost function can be determined as the viscosity coefficient μ.
図21は、ひずみ速度γに応じたせん断応力τの値を示すものであり、丸形のプロットは市販のレオメータによる計測値、三角形のプロットが本発明に係る非接触型レオロジー物性計測システムで計測された計測値である。本実施例2では、市販のレオメータとしてAnton Paar社製のMCR102を用いた。
FIG. 21 shows the value of the shear stress τ according to the strain rate γ, the round plot is the measured value by a commercially available rheometer, and the triangular plot is measured by the non-contact rheological property measurement system according to the present invention. It is a measured value. In Example 2, an MCR102 manufactured by Anton Paar was used as a commercially available rheometer.
図21に示すように、本実施例2で使用したCMC水溶液は、市販のレオメータで計測するとひずみ速度γが増加するにつれてせん断応力τも増加している。このときせん断応力τの増加は、ひずみ速度γが大きくなるにつれてやや鈍化するように増加している。せん断応力τとひずみ速度γとの関係がτ=Kγnのべき乗則で表されると仮定した場合、γがAからBの範囲においては、K=0.569[Pa・s]、n=0.9751であった。
As shown in FIG. 21, in the CMC aqueous solution used in Example 2, the shear stress τ increases as the strain rate γ increases when measured with a commercially available rheometer. At this time, the increase in shear stress τ increases so as to become slightly slower as the strain rate γ increases. Assuming that the relationship between the shear stress τ and the strain rate γ is expressed by the power law of τ = Kγ n , K = 0.569 [Pa · s], n = in the range of γ from A to B. It was 0.9751.
これに対し、本発明に係る非接触型レオロジー物性計測システムで計測された計測値は、γがAからBの範囲においてK=0.467[Pa・s]、n=0.9981であった。市販のレオメータの値と比較すると、ひずみ速度γに対するせん断応力τの増加も同様な値を示した。
On the other hand, the measured values measured by the non-contact rheological property measurement system according to the present invention were K = 0.467 [Pa · s] and n = 0.9981 in the range of γ from A to B. .. The increase in shear stress τ with respect to the strain rate γ showed a similar value when compared with the value of a commercially available rheometer.
<アクリル管による追加実験について>
本実施例2では、ステンレス管の後流側に設置した交換式のアクリル管を用いて、流速を早めることでよりひずみ速度γの範囲を広範囲にした計測を行った。具体的には、上述するように内径約48mmのアクリル管と、内径約22mmのアクリル管を用いた。内径約48mmのアクリル管を用いた場合のおおよその最大流速は0.12[m/s]であったのに対し、内径約22mmのアクリル管を用いた場合のおおよその最大流速は0.5[m/s]であった。そしてr/Rが約0~0.6の範囲の流速分布を用いてレオロジー物性値を算出した。 <About additional experiments with acrylic tubes>
In the second embodiment, a replaceable acrylic pipe installed on the wake side of the stainless steel pipe was used, and the measurement was performed in a wider range of the strain rate γ by increasing the flow velocity. Specifically, as described above, an acrylic tube having an inner diameter of about 48 mm and an acrylic tube having an inner diameter of about 22 mm were used. The approximate maximum flow velocity when using an acrylic tube with an inner diameter of about 48 mm was 0.12 [m / s], whereas the approximate maximum flow velocity when using an acrylic tube with an inner diameter of about 22 mm was 0.5. It was [m / s]. Then, the rheological property value was calculated using the flow velocity distribution in the range of r / R of about 0 to 0.6.
本実施例2では、ステンレス管の後流側に設置した交換式のアクリル管を用いて、流速を早めることでよりひずみ速度γの範囲を広範囲にした計測を行った。具体的には、上述するように内径約48mmのアクリル管と、内径約22mmのアクリル管を用いた。内径約48mmのアクリル管を用いた場合のおおよその最大流速は0.12[m/s]であったのに対し、内径約22mmのアクリル管を用いた場合のおおよその最大流速は0.5[m/s]であった。そしてr/Rが約0~0.6の範囲の流速分布を用いてレオロジー物性値を算出した。 <About additional experiments with acrylic tubes>
In the second embodiment, a replaceable acrylic pipe installed on the wake side of the stainless steel pipe was used, and the measurement was performed in a wider range of the strain rate γ by increasing the flow velocity. Specifically, as described above, an acrylic tube having an inner diameter of about 48 mm and an acrylic tube having an inner diameter of about 22 mm were used. The approximate maximum flow velocity when using an acrylic tube with an inner diameter of about 48 mm was 0.12 [m / s], whereas the approximate maximum flow velocity when using an acrylic tube with an inner diameter of about 22 mm was 0.5. It was [m / s]. Then, the rheological property value was calculated using the flow velocity distribution in the range of r / R of about 0 to 0.6.
図22は、図21と同様、ひずみ速度γに応じたせん断応力τの値を示すものであり、丸形のプロットは市販のレオメータによる計測値である。また、三角形のプロットは内径約48mmを用いた場合、およびバツ形のプロットは内径約22mmを用いた場合の本発明に係る非接触型レオロジー物性計測システムで計測された計測値である。図22に示すように、市販のレオメータで計測できた全範囲に対応する計測結果が得られた。また、市販のレオメータの計測結果と比較して、全範囲で同様な値を示した。
FIG. 22 shows the value of the shear stress τ according to the strain rate γ as in FIG. 21, and the round plot is the measured value by a commercially available rheometer. Further, the triangular plot is the measured value measured by the non-contact rheological property measuring system according to the present invention when the inner diameter of about 48 mm is used, and the cross-shaped plot is the measured value when the inner diameter of about 22 mm is used. As shown in FIG. 22, measurement results corresponding to the entire range that could be measured with a commercially available rheometer were obtained. Moreover, the same value was shown in the whole range as compared with the measurement result of the commercially available rheometer.
また、図23に、ひずみ速度γに応じた粘度μ[Pa・s]についての計測結果を示す。丸形のプロットは市販のレオメータによる計測値である。また、三角形のプロットは内径約48mmを用いた場合、およびバツ形のプロットは内径約22mmを用いた場合の本発明に係る非接触型レオロジー物性計測システムで計測された計測値である。図23に示すように、市販のレオメータで計測されたひずみ速度γが増加するにつれて粘度μは低下しており、擬塑性流体の特徴を示している。同様に、非接触型レオロジー物性計測システムで計測された計測値についても、ひずみ速度γに対して粘度μは低下傾向にある。粘度μとひずみ速度γとの関係をμ=Kγn-1のべき乗則で表されると仮定した場合、図24に示すように、K=0.559[Pa・s]、n=0.89となり擬塑性流体の特徴を示す値が計測されることが実証できた。
Further, FIG. 23 shows the measurement results for the viscosity μ [Pa · s] according to the strain rate γ. The round plots are measured by a commercially available rheometer. Further, the triangular plot is the measured value measured by the non-contact rheological property measuring system according to the present invention when the inner diameter of about 48 mm is used, and the cross-shaped plot is the measured value when the inner diameter of about 22 mm is used. As shown in FIG. 23, the viscosity μ decreases as the strain rate γ measured by a commercially available rheometer increases, indicating the characteristics of the pseudoplastic fluid. Similarly, with respect to the measured values measured by the non-contact rheological property measurement system, the viscosity μ tends to decrease with respect to the strain rate γ. Assuming that the relationship between the viscosity μ and the strain rate γ is expressed by the power law of μ = Kγ n-1 , as shown in FIG. 24, K = 0.559 [Pa · s], n = 0. It was 89, and it was proved that the value indicating the characteristics of the pseudoplastic fluid was measured.
以上より、本実施例2では、本発明に係る非接触型レオロジー物性計測装置、システム、プログラムおよび方法を用いることで、管内を流れる脈動を伴う流体のレオロジー物性を、非接触で精度よく計測することができることを実際の実験装置により確かめることができた。
From the above, in the second embodiment, by using the non-contact type rheological property measuring device, system, program and method according to the present invention, the rheological property of the fluid accompanied by pulsation flowing in the pipe is measured accurately without contact. It was possible to confirm that it was possible with an actual experimental device.
なお、本発明に係る非接触型レオロジー物性計測装置、システム、プログラムおよび方法は、前述した実施形態に限定されるものではなく、適宜変更することができる。
The non-contact rheological property measuring device, system, program and method according to the present invention are not limited to the above-described embodiments, and can be changed as appropriate.
例えば、ピーク周波数検出部62が、式(3)の範囲内の条件を満たす周波数の範囲のみ周波数解析を行い、その中から最も大きい振幅を示すものをピーク周波数ω0と決定するように処理してもよい。
For example, the peak frequency detection unit 62 performs frequency analysis only in the frequency range that satisfies the condition within the range of the equation (3), and processes the one showing the largest amplitude to determine the peak frequency ω 0. You may.
1 非接触型レオロジー物性計測システム
2 超音波流速計測装置
3 非接触型レオロジー物性計測装置
3a 非接触型レオロジー物性計測プログラム
4 表示入力手段
5 記憶手段
6 演算処理手段
51 プログラム記憶部
52 レオロジーモデル式記憶部
53 しきい値記憶部
61 流速取得部
62 ピーク周波数検出部
63 数値解算出部
64 レオロジーモデル決定部
65 レオロジー物性決定部 1 Non-contact type rheology physicalproperty measurement system 2 Ultrasonic flow velocity measurement device 3 Non-contact type rheology physical property measurement device 3a Non-contact type rheology physical property measurement program 4 Display input means 5 Storage means 6 Arithmetic processing means 51 Program storage unit 52 Rheology model type memory Unit 53 Threshold storage unit 61 Flow velocity acquisition unit 62 Peak frequency detection unit 63 Numerical solution calculation unit 64 Rheology model determination unit 65 Rheology physical property determination unit
2 超音波流速計測装置
3 非接触型レオロジー物性計測装置
3a 非接触型レオロジー物性計測プログラム
4 表示入力手段
5 記憶手段
6 演算処理手段
51 プログラム記憶部
52 レオロジーモデル式記憶部
53 しきい値記憶部
61 流速取得部
62 ピーク周波数検出部
63 数値解算出部
64 レオロジーモデル決定部
65 レオロジー物性決定部 1 Non-contact type rheology physical
Claims (12)
- 管内を流れる流体のレオロジー物性を非接触で計測する非接触型レオロジー物性計測装置であって、
超音波流速計測装置から超音波の照射方向に沿った複数の計測点における流速データを取得する流速取得部と、
この流速取得部によって取得された各計測点の流速データを周波数解析することにより前記流体における脈動の周波数から最大の振幅値を示すピーク周波数を検出するピーク周波数検出部と、
レオロジーモデルに基づく管内を流れる流体の運動方程式を時間に対してフーリエ変換して得られる下記式(1)に、前記ピーク周波数と複数の計測点における流速データとを代入して得られる複数の関数式から数値解を算出する数値解算出部と、
この数値解算出部により算出された数値解に基づきレオロジー物性値を決定するレオロジー物性決定部と
を有する、前記非接触型レオロジー物性計測装置。
[数1]
ここで、
、
、
、
、
τはレオロジーモデルを用いて関係づけられるせん断応力、
A,B,C,・・・はレオロジーモデルにおけるレオロジー物性、
αは圧力勾配、
ρは流体の密度、
ωは流体における脈動の角周波数、
ω0はピーク周波数、
rnは計測点、
uは管内の時空間流速分布、
^は関数のフーリエ変換、
添え字のmは計測結果、をそれぞれ意味する。 A non-contact rheological property measuring device that non-contactly measures the rheological properties of the fluid flowing in the pipe.
A flow velocity acquisition unit that acquires flow velocity data at multiple measurement points along the ultrasonic irradiation direction from an ultrasonic flow velocity measuring device,
A peak frequency detection unit that detects the peak frequency showing the maximum amplitude value from the pulsation frequency in the fluid by frequency analysis of the flow velocity data of each measurement point acquired by the flow velocity acquisition unit.
A plurality of functions obtained by substituting the peak frequency and the flow velocity data at a plurality of measurement points into the following equation (1) obtained by Fourier transforming the equation of motion of the fluid flowing in the tube based on the rheology model with respect to time. A numerical solution calculation unit that calculates a numerical solution from an equation,
The non-contact type rheological property measuring device having a rheological property determining unit that determines a rheological property value based on a numerical solution calculated by the numerical solution calculating unit.
[Number 1]
here,
,
,
,
,
τ is the shear stress, which is related using a rheological model.
A, B, C, ... are rheological properties in the rheological model,
α is the pressure gradient,
ρ is the density of the fluid,
ω is the angular frequency of the pulsation in the fluid,
ω 0 is the peak frequency,
r n is the measurement point,
u is the spatiotemporal flow velocity distribution in the pipe,
^ Is the Fourier transform of the function,
The subscript m means the measurement result. - 前記数値解算出部では、下記式(2)に示す費用関数の最小化により数値解を算出する、請求項1に記載の非接触型レオロジー物性計測装置。
[数2]
The non-contact rheological property measuring device according to claim 1, wherein the numerical solution calculation unit calculates a numerical solution by minimizing the cost function shown in the following equation (2).
[Number 2]
- 前記数値解算出部では、代入する流速データとして、連続して隣り合う3点以上の計測点における前記流速データの関数近似値を用いる、請求項1または請求項2に記載の非接触型レオロジー物性計測装置。 The non-contact rheological property according to claim 1 or 2, wherein the numerical solution calculation unit uses a function approximation value of the flow velocity data at three or more consecutively adjacent measurement points as the flow velocity data to be substituted. Measuring device.
- 前記数値解算出部では、複数種のレオロジーモデルに基づく数値解を算出するとともに、
当該数値解同士を比較して最も小さい数値解となる前記レオロジーモデルを前記流体のレオロジーモデルとして決定するレオロジーモデル決定部を有する、請求項1から請求項3のいずれかに記載の非接触型レオロジー物性計測装置。 The numerical solution calculation unit calculates numerical solutions based on a plurality of types of rheological models, and also calculates numerical solutions.
The non-contact rheology according to any one of claims 1 to 3, further comprising a rheology model determining unit that determines the rheology model that is the smallest numerical solution by comparing the numerical solutions as the rheological model of the fluid. Rheological measuring device. - 前記ピーク周波数検出部では、前記流体の粘性と前記流体における脈動の周波数の比により表される粘性層厚さが、下記式(3)の範囲を満たす周波数の中から最大の振幅値を示すピーク周波数を検出する、請求項1から請求項4のいずれかに記載の非接触型レオロジー物性計測装置。
[数3]
ここで、
(ν/kΔω)1/2は粘性層厚さ、
Δrは計測点同士の距離、
νは流体の動粘性係数(動粘度)、
kΔωは検出された周波数、
Dは管の内径、をそれぞれ意味する。 In the peak frequency detection unit, the viscous layer thickness represented by the ratio of the viscosity of the fluid to the frequency of the pulsation in the fluid is the peak showing the maximum amplitude value from the frequencies satisfying the range of the following equation (3). The non-contact rheological property measuring device according to any one of claims 1 to 4, which detects a frequency.
[Number 3]
here,
(Ν / kΔω) 1/2 is the thickness of the viscous layer,
Δr is the distance between measurement points,
ν is the kinematic viscosity coefficient (kinematic viscosity) of the fluid,
kΔω is the detected frequency,
D means the inner diameter of the pipe, respectively. - 管外から管内に向けて超音波を照射するとともに前記管内から前記管外に向けて反射される超音波を受信して、前記超音波の照射方向に沿った複数の計測点における流速を時系列で計測する超音波流速計測装置と、
この超音波流速計測装置から各計測点の流速データを取得して流体のレオロジー物性を決定する請求項1から請求項5のいずれかに記載の非接触型レオロジー物性計測装置と
を有する、非接触型レオロジー物性計測システム。 The ultrasonic waves are radiated from the outside of the tube to the inside of the tube, and the ultrasonic waves reflected from the inside of the tube to the outside of the tube are received, and the flow velocity at a plurality of measurement points along the irradiation direction of the ultrasonic waves is measured in time series. Ultrasonic flow velocity measuring device to measure with
The non-contact type rheological property measuring device according to any one of claims 1 to 5, which acquires flow velocity data of each measurement point from this ultrasonic flow velocity measuring device and determines the rheological property of the fluid. Type rheology physical property measurement system. - 管内を流れる流体のレオロジー物性を非接触で計測する非接触型レオロジー物性計測プログラムであって、
超音波流速計測装置から超音波の照射方向に沿った複数の計測点における流速データを取得する流速取得部と、
この流速取得部によって取得された各計測点の流速データを周波数解析することにより前記流体における脈動の周波数から最大の振幅値を示すピーク周波数を検出するピーク周波数検出部と、
レオロジーモデルに基づく管内を流れる流体の運動方程式を時間に対してフーリエ変換して得られる下記式(1)に、前記ピーク周波数と複数の計測点における流速データとを代入して得られる複数の関数式から数値解を算出する数値解算出部と、
この数値解算出部により算出された数値解に基づきレオロジー物性値を決定するレオロジー物性決定部と
してコンピュータを機能させる、前記非接触型レオロジー物性計測プログラム。
[数1]
ここで、
、
、
、
、
τはレオロジーモデルを用いて関係づけられるせん断応力、
A,B,C,・・・はレオロジーモデルにおけるレオロジー物性、
αは圧力勾配、
ρは流体の密度、
ωは流体における脈動の角周波数、
ω0はピーク周波数、
rnは計測点、
uは管内の時空間流速分布、
^は関数のフーリエ変換、
添え字のmは計測結果、をそれぞれ意味する。 A non-contact rheological property measurement program that measures the rheological properties of the fluid flowing in the pipe in a non-contact manner.
A flow velocity acquisition unit that acquires flow velocity data at multiple measurement points along the ultrasonic irradiation direction from an ultrasonic flow velocity measuring device,
A peak frequency detection unit that detects the peak frequency showing the maximum amplitude value from the pulsation frequency in the fluid by frequency analysis of the flow velocity data of each measurement point acquired by the flow velocity acquisition unit.
A plurality of functions obtained by substituting the peak frequency and the flow velocity data at a plurality of measurement points into the following equation (1) obtained by Fourier transforming the equation of motion of the fluid flowing in the tube based on the rheology model with respect to time. A numerical solution calculation unit that calculates a numerical solution from an equation,
The non-contact type rheological property measurement program that operates a computer as a rheological property determination unit that determines a rheological property value based on a numerical solution calculated by the numerical solution calculation unit.
[Number 1]
here,
,
,
,
,
τ is the shear stress, which is related using a rheological model.
A, B, C, ... are rheological properties in the rheological model,
α is the pressure gradient,
ρ is the density of the fluid,
ω is the angular frequency of the pulsation in the fluid,
ω 0 is the peak frequency,
r n is the measurement point,
u is the spatiotemporal flow velocity distribution in the pipe,
^ Is the Fourier transform of the function,
The subscript m means the measurement result. - 前記数値解算出部では、下記式(2)に示す費用関数の最小化により数値解を算出する、請求項7に記載の非接触型レオロジー物性計測プログラム。
[数2]
The non-contact rheological property measurement program according to claim 7, wherein the numerical solution calculation unit calculates a numerical solution by minimizing the cost function shown in the following equation (2).
[Number 2]
- 前記数値解算出部では、代入する流速データとして、連続して隣り合う3点以上の計測点における前記流速データの関数近似値を用いる、請求項7または請求項8に記載の非接触型レオロジー物性計測プログラム。 The non-contact rheological property according to claim 7 or 8, wherein the numerical solution calculation unit uses a function approximation value of the flow velocity data at three or more consecutively adjacent measurement points as the flow velocity data to be substituted. Measurement program.
- 前記数値解算出部では、複数種のレオロジーモデルに基づく数値解を算出するとともに、
当該数値解同士を比較して最も小さい数値解となる前記レオロジーモデルを前記流体のレオロジーモデルとして決定するレオロジーモデル決定部を有する、請求項7から請求項9のいずれかに記載の非接触型レオロジー物性計測プログラム。 The numerical solution calculation unit calculates numerical solutions based on a plurality of types of rheological models, and also calculates numerical solutions.
The non-contact rheology according to any one of claims 7 to 9, further comprising a rheology model determining unit that determines the rheology model that is the smallest numerical solution by comparing the numerical solutions as the rheological model of the fluid. Rheological measurement program. - 前記ピーク周波数検出部では、前記流体の粘性と前記流体における脈動の周波数の比により表される粘性層厚さが、下記式(3)の範囲を満たす周波数の中から最大の振幅値を示すピーク周波数を検出する、請求項7から請求項10のいずれかに記載の非接触型レオロジー物性計測プログラム。
[数3]
ここで、
(ν/kΔω)1/2は粘性層厚さ、
Δrは計測点同士の距離、
νは流体の動粘性係数(動粘度)、
kΔωは検出された周波数、
Dは管の内径、をそれぞれ意味する。 In the peak frequency detection unit, the viscous layer thickness represented by the ratio of the viscosity of the fluid to the frequency of the pulsation in the fluid is the peak showing the maximum amplitude value from the frequencies satisfying the range of the following equation (3). The non-contact rheological property measurement program according to any one of claims 7 to 10, which detects a frequency.
[Number 3]
here,
(Ν / kΔω) 1/2 is the thickness of the viscous layer,
Δr is the distance between measurement points,
ν is the kinematic viscosity coefficient (kinematic viscosity) of the fluid,
kΔω is the detected frequency,
D means the inner diameter of the pipe, respectively. - 管内を流れる流体のレオロジー物性を非接触で計測する非接触型レオロジー物性計測方法であって、
超音波流速計測装置から超音波の照射方向に沿った複数の計測点における流速データを取得する流速取得ステップと、
この流速取得ステップによって取得された各計測点の流速データを周波数解析することにより前記流体における脈動の周波数から最大の振幅値を示すピーク周波数を検出するピーク周波数検出ステップと、
レオロジーモデルに基づく管内を流れる流体の運動方程式を時間に対してフーリエ変換して得られる下記式(1)に、前記ピーク周波数と複数の計測点における流速データとを代入して得られる複数の関数式から数値解を算出する数値解算出ステップと、
この数値解算出ステップにより算出された数値解に基づきレオロジー物性値を決定するレオロジー物性決定ステップと
を有する、前記非接触型レオロジー物性計測方法。
[数1]
ここで、
、
、
、
、
τはレオロジーモデルを用いて関係づけられるせん断応力、
A,B,C,・・・はレオロジーモデルにおけるレオロジー物性、
αは圧力勾配、
ρは流体の密度、
ωは流体における脈動の角周波数、
ω0はピーク周波数、
rnは計測点、
uは管内の時空間流速分布、
^は関数のフーリエ変換、
添え字のmは計測結果、をそれぞれ意味する。 It is a non-contact rheological property measurement method that measures the rheological properties of the fluid flowing in the pipe in a non-contact manner.
A flow velocity acquisition step for acquiring flow velocity data at a plurality of measurement points along the ultrasonic irradiation direction from an ultrasonic flow velocity measuring device, and
A peak frequency detection step that detects a peak frequency showing the maximum amplitude value from the pulsation frequency in the fluid by frequency analysis of the flow velocity data of each measurement point acquired by this flow velocity acquisition step.
A plurality of functions obtained by substituting the peak frequency and the flow velocity data at a plurality of measurement points into the following equation (1) obtained by Fourier transforming the equation of motion of the fluid flowing in the tube based on the rheology model with respect to time. Numerical solution calculation step to calculate the numerical solution from the equation and
The non-contact type rheological physical property measurement method including a rheological physical property determination step for determining a rheological physical property value based on a numerical solution calculated by this numerical solution calculation step.
[Number 1]
here,
,
,
,
,
τ is the shear stress, which is related using a rheological model.
A, B, C, ... are rheological properties in the rheological model,
α is the pressure gradient,
ρ is the density of the fluid,
ω is the angular frequency of the pulsation in the fluid,
ω 0 is the peak frequency,
r n is the measurement point,
u is the spatiotemporal flow velocity distribution in the pipe,
^ Is the Fourier transform of the function,
The subscript m means the measurement result.
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Title |
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BIRKHOFER BEAT ET AL.: "IN -LINE RHEOMETRY BASED ON ULTRASONIC VELOCITY PROFILES: COMPARISON OF DATA PROCESSING METHODS", APPLIED RHEOLOGY, vol. 22, no. 4, 2012, pages 44701 - 1 - 44701-9, XP055743841 * |
YUJI TASAKA; TAIKI YOSHIDA; YUICHI MURAI: "Rheological Evaluations of Complex Fluids by Ultrasonic Velocity Profiling", NAGARE, vol. 38, no. 4, August 2019 (2019-08-01), pages 283 - 290, XP009523719, ISSN: 0286-3154 * |
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