WO2020196612A1 - Non-contact type rheological material property measurement device, system, program and method - Google Patents

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

Non-contact rheology physical property measuring devices, systems, programs and methods

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.

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.

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.

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.

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.

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.

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.

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. 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.

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]

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.

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.

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.

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.

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.

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.

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. It is a graph which shows the probability density distribution of the noise rate of the noise level a = 5.0 defined by the equation (18) in this Example 1. It is a contour figure which shows the flow velocity data which added the noise calculated by the equation (18) in this Example 1. It is a graph which shows the real value Re and the imaginary value Im calculated by the formula (7) in this Example 1. It is a 3D graph which shows the calculation result of the cost function by the random search method in Example 1. FIG. It is a graph which shows the measurement accuracy of the viscosity coefficient μ and the pressure gradient α calculated with respect to the measurement error (noise level) in Example 1. FIG. It is a graph which shows the measurement accuracy of the viscosity coefficient μ and the pressure gradient α calculated in the difference of the period in Example 1. FIG. It is a graph which shows the measurement accuracy of the viscosity coefficient μ and the pressure gradient α calculated with respect to the kinematic viscosity coefficient ν in this Example 1. In the present embodiment 1 is a graph showing the measurement accuracy of the frequency f viscosity coefficient calculated for _o mu and pressure gradient alpha. 6 is a graph showing the measurement accuracy of the viscosity coefficient μ and the pressure gradient α 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 velocity distribution in the in-pipe flow with pulsation of Example 2, and is a contour diagram of the measurement result using the test fluid as a non-Newtonian fluid and a graph showing the real value Re and the imaginary value Im calculated by the equation (10). .. It is a figure which shows the calculation result of the cost function of the sum of square roots of viscosity and pressure (real part / imaginary part) by the random search method when the test fluid is a non-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. It is a graph which shows the shear stress and strain rate measured when the test fluid is a non-Newtonian fluid in Example 2. It is a graph which shows the shear stress for a wide range of strain rates measured in the experiment which used the test fluid of this Example 2 as a non-Newtonian fluid. It is a graph which shows the viscosity and strain rate measured in the experiment which made the test fluid corresponding to FIG. 22 a non-Newtonian fluid. It is a graph which shows the result of the approximate solution which calculated the experimental result corresponding to FIG. 23 based on the power law.

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.

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.

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.

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.

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. 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.

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. 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.

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.

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.

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.

The threshold value 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.

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.

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.

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.

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.

The numerical solution 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]

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.

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.

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 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.

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.

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.

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.

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.

Next, 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 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]

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 .

Next, 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). .. In this embodiment, the approximate value of the quintic function is calculated using the following equation (6), and the value is used.
[Number 6]

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.

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.

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.

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.

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).

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.

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.

According to the non-contact rheological property 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 flow velocity measuring device 2.
5. 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.

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.

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.

<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.

<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.

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.

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.

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 .

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).

<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.

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.

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.

<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.

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.

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.

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.

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.

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).

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.

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).

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.

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.

<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.

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.

<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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

<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.

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.

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.

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>
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.

<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.

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. ..

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.

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.

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.

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.

<Measurement of physical properties of non-Newtonian fluids>
Next, the physical property values of the non-Newtonian fluid were measured.

<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.

<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.

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.

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.

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.

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.

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.

<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.

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.

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.

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.

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.

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 Non-contact type rheology physical property 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

Claims (12)

1. 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.
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]
   

   
3. 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.
4. 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.
5. 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.
6. 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.
7. 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.
8. 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]
   

   
9. 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.
10. 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.
11. 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.
12. 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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