JP7412786B2 - Non-contact rheological property measuring device, system, program and method - Google Patents

Description

The present invention relates to a non-contact rheological property measuring device, system, program, and method for measuring the rheological properties 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 fluids in pipes for product quality control, production process optimization, factory plant maintenance and inspection, etc.

For example, milk sold in stores is made by pasteurizing raw milk from cows and adjusting components such as milk fat. It is difficult to keep the proportion of milk fat contained in raw milk constant because it varies depending on the feed given to the cow, the cow's physical condition, the weather, and the individual cow. Therefore, in the past, instead of constantly controlling the milk fat content by measuring it, the method of adjusting the milk fat content by adding excess milk fat content was adopted to ensure that the milk fat content exceeded a predetermined percentage. There is.

However, the problem is that the cost increases due to the addition of excessive milk fat. Therefore, there is a need to estimate the percentage of milk fat by measuring the rheological properties of milk flowing through the tube, and to adjust the ever-changing components in real time.

Therefore, a method has been proposed to measure the rheological properties of a fluid in a pipe using an ultrasonic flow velocity measuring device and a differential pressure gauge that can measure the flow velocity distribution of the flow in the pipe (Non-Patent Document 1). This method assumes that the flow in the pipe is a steady flow in one direction, and uses the flow velocity distribution obtained by simultaneously creating a flow equation based on a model equation (rheology model) that describes rheological properties, and the ultrasonic flow velocity measuring device. By comparing the obtained flow velocity distribution, the constants of the rheological properties included in the model equation are determined.

Ouriev, B., and E. J. Windhab, "Rheological study of concentrated suspensions in pressure-driven shear flow using novel in-line ultrasound Doppler method", Exp. Fluids 32, 204-211 (2002).

However, the method described in Non-Patent Document 1 has a problem in that accuracy cannot be guaranteed due to the principle of measurement unless the flow in the pipe is a steady flow. In other words, the above method assumes that the flow inside the pipe is a steady flow in one direction, but the flow inside the pipe in a general production process is always due to vortices, etc. generated by the pump or piping shape used to generate the flow. Since it pulsates (varies), errors occur due to the pulsation.

Flow equations based on rheological models also include pressure gradients that drive the fluid. Therefore, in order to calculate the rheological properties, it is necessary to substitute the pressure value inside the pipe. However, in order to measure the pressure inside a pipe, it is necessary to place a pressure sensor inside the pipe or make a hole in the pipe wall and connect it to a pressure gauge so that the pressure sensor or pressure gauge comes into contact with the fluid. For this reason, for example, in foods where hygiene is important, pressure sensors and the like must be kept clean at all times. Depending on the fluid, there are some fluids that cannot be directly touched by a pressure sensor or the like, and there is also the problem that the scope of application is limited. Furthermore, the measurement accuracy of the pressure sensor, etc. itself has a large influence on the calculation results of rheological properties, which limits the selection of the pressure sensor, etc., and the selection of the installation location of the pressure sensor, etc.

The present invention has been made to solve the above-mentioned problems, and is a non-contact rheological property measuring device that can measure rheological properties in a non-contact manner using pulsations in the flow inside a pipe. , systems, programs and methods.

The non-contact rheological property measuring device and the non-contact rheological property measuring program according to the present invention utilize pulsations in the flow inside the pipe to measure the rheological property in a non-contact manner without measuring the pressure inside the pipe with a pressure gauge or the like. In order to solve the problem of measuring the rheological properties of a fluid flowing inside a pipe, we have developed a non-contact rheological property measuring device that non-contactly measures the rheological properties of a fluid flowing inside a pipe. A flow velocity acquisition unit acquires flow velocity data at measurement points, and a peak frequency indicating the maximum amplitude value is determined from the frequency of pulsation in the fluid by frequency analysis of the flow velocity data at each measurement point acquired by this flow velocity acquisition unit. The peak frequency to be detected and the flow velocity data at a plurality of measurement points are combined into the following equation (1) obtained by Fourier transforming the equation of motion of the fluid flowing in the pipe 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 property determination unit that determines rheological property values based on the numerical solution calculated by the numerical solution calculation unit.
[Number 1]
here,
,
,
,
, τ is the shear stress 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, ω is the angular frequency of pulsation in the fluid, ω ₀ means the peak frequency, r _n means the measurement point, u means the spatiotemporal flow velocity distribution in the pipe, ^ means the Fourier transform of the function, and the subscript m means the measurement result.

Further, as an aspect of the present invention, in order to solve the problem of reducing the load related to numerical solution calculation processing by the numerical solution calculation unit and enabling real-time measurement of rheological properties, the numerical solution calculation unit , the numerical solution may be calculated by minimizing the cost function shown in equation (2) below.
[Number 2]

Furthermore, as one aspect of the present invention, in order to solve the problem of suppressing calculation errors in rheological property values caused by measurement errors in flow velocity data obtained by an ultrasonic flow velocity measurement device, the numerical solution calculation unit may substitute 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 an aspect of the present invention, in order to solve the problem that measurement can be performed in a state where the rheological model of the fluid flowing in the pipe is unknown, the numerical solution calculating section calculates numerical values based on multiple types of rheological models. It may also include a rheology model determination unit that calculates the solution, compares the numerical solutions, and determines the rheology model that is the smallest numerical solution as the rheology model of the fluid.

Furthermore, as one aspect of the present invention, in order to solve the problem of detecting a peak frequency at which the thickness of the viscous layer is sufficiently thick to ensure measurement accuracy, the peak frequency detection section detects the viscosity of the fluid and the peak frequency of the viscous layer. The viscous layer thickness expressed by the frequency ratio of pulsations in the fluid may detect a peak frequency at which the maximum amplitude value is found from among frequencies that satisfy the range of formula (3) below.
[Number 3]
Here, (ν/kΔω) ^1/2 is the viscous layer thickness, Δr is the distance between measurement points, ν is the viscosity coefficient of the fluid (kinetic viscosity), kΔω is the detected frequency, and D is the inner diameter of the pipe. each meaning.

The non-contact rheological property measurement system according to the present invention solves the problem of measuring rheological properties in a non-contact manner by utilizing pulsations in the flow inside the pipe, without measuring the pressure inside the pipe with a pressure gauge or the like. In order to measure the flow velocity at a plurality of measurement points along the irradiation direction of the ultrasonic waves, ultrasonic waves are irradiated from outside the tube to the inside of the tube, and the ultrasonic waves reflected from the inside of the tube toward the outside of the tube are received. The present invention includes an ultrasonic flow velocity measurement device that measures the flow rate in time series, and the non-contact rheology property measurement device that obtains flow velocity data at each measurement point from the ultrasonic flow velocity measurement device to determine the rheology properties of the fluid.

The non-contact rheological property measuring method according to the present invention solves the problem of measuring rheological properties in a non-contact manner by utilizing pulsations in the flow inside the pipe, without measuring the pressure inside the pipe with a pressure gauge or the like. This is a non-contact rheological property measurement method that non-contactly measures the rheological properties of a fluid flowing inside a pipe, and it acquires flow velocity data at multiple measurement points along the ultrasound irradiation direction from an ultrasonic flow velocity measuring device. a peak frequency detection step of detecting a peak frequency indicating the maximum amplitude value from the frequency of pulsation in the fluid by frequency-analyzing the flow velocity data at each measurement point acquired by the flow velocity acquisition step; A plurality of functions obtained by substituting the peak frequency and flow velocity data at a plurality of measurement points into the above equation (1) obtained by Fourier transforming the equation of motion of a fluid flowing in a pipe based on a rheological model with respect to time. The method includes a numerical solution calculation step of calculating a numerical solution from an equation, and a rheological property determination step of determining a rheological property value based on the numerical solution calculated by the numerical solution calculation step.

According to the present invention, rheological properties can be measured in a non-contact manner using pulsations in the flow within a pipe.

1 is a block diagram showing an embodiment of a non-contact rheological property measurement system according to the present invention. FIG. 2 is a flowchart showing the flow of rheological property measurement processing by the non-contact rheological property measurement system of the present embodiment. 3 is a contour diagram showing calculation results of flow velocity data of a flow in a pipe with pulsation calculated in Example 1. FIG. 3 is a graph showing the probability density distribution of the noise speed at the noise level a=5.0 defined by equation (18) in the first embodiment. FIG. 3 is a contour diagram showing noise-added flow velocity data calculated using equation (18) in Example 1. FIG. 7 is a graph showing the real value Re and the imaginary value Im calculated by Equation (7) in Example 1. FIG. 3 is a three-dimensional graph diagram showing calculation results of a cost function using a random search method in Example 1. FIG. 3 is a graph showing the measurement accuracy of the calculated viscosity coefficient μ and pressure gradient α with respect to the measurement error (noise level) in Example 1. FIG. 3 is a graph showing the measurement accuracy of the calculated viscosity coefficient μ and pressure gradient α at different periods in Example 1. FIG. 3 is a graph showing the measurement accuracy of the calculated viscosity coefficient μ and pressure gradient α with respect to the kinematic viscosity coefficient ν in Example 1. 3 is a graph showing the measurement accuracy of the calculated viscosity coefficient μ and pressure gradient α with respect to frequency _fo in Example 1. FIG. 3 is a graph showing the measurement accuracy of the calculated viscosity coefficient μ and pressure gradient α with respect to the amplitude U ₁ in Example 1. FIG. FIG. 2 is a schematic diagram showing an experimental apparatus used in Example 2. FIG. 7 is a schematic diagram showing the installation state of an ultrasonic transducer in the experimental apparatus of Example 2. FIG. 7 is a contour diagram showing the velocity distribution in a flow in a pipe accompanied by pulsation in Example 2, and the measurement results using a Newtonian fluid as the test fluid. FIG. 7 is a diagram showing calculation results of a cost function by a random search method when a Newtonian fluid is used as a test fluid in Example 2. 7 is a diagram showing measurement results of viscosity and pressure amplitude when the test fluid is Newtonian fluid in Example 2. FIG. 2 is a graph showing the contour diagram of the measurement results of the velocity distribution in the flow in the pipe with pulsation in Example 2, where the test fluid is a non-Newtonian fluid, and the real value Re and the imaginary value Im calculated by equation (10). . FIG. 7 is a diagram showing calculation results of a cost function of the root sum of squares of viscosity and pressure (real part/imaginary part) by a random search method when the test fluid is a non-Newtonian fluid in Example 2. FIG. 3 is a three-dimensional graph diagram showing the calculation results of a cost function by a random search method when the test fluid is a non-Newtonian fluid in Example 2. FIG. 3 is a graph showing shear stress and strain rate measured when the test fluid is a non-Newtonian fluid in Example 2. FIG. 3 is a graph showing shear stress for a wide range of strain rates measured in an experiment in which the test fluid of Example 2 was a non-Newtonian fluid. 23 is a graph showing viscosity and strain rate measured in an experiment using a non-Newtonian fluid as a test fluid corresponding to FIG. 22. FIG. 24 is a graph showing the result of an approximate solution calculated based on a power law for the experimental results corresponding to FIG. 23. FIG.

DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of a non-contact rheological property measuring device, system, program, and method according to the present invention will be described below with reference to the drawings.

As shown in FIG. 1, the non-contact rheological property measurement system 1 of this embodiment includes an ultrasonic flow velocity measurement device 2 that measures flow velocity at a plurality of measurement points in time series, and a It has a non-contact rheological property measuring device 3 that acquires flow velocity data at measurement points and determines the rheological properties of the fluid. Each configuration will be explained in detail below.

The ultrasonic flow velocity measuring device 2 irradiates ultrasonic waves from outside the tube into the inside of the tube, receives ultrasonic waves reflected from inside the tube toward the outside of the tube, and detects a plurality of ultrasonic waves along the irradiation direction of the ultrasonic waves. This method measures the flow velocity at measurement points in time series. In other words, the ultrasonic flow velocity measuring device 2 can measure the spatiotemporal flow velocity distribution u(r,t) within the pipe in a non-contact and non-invasive manner (without disturbing the flow). For example, the technique disclosed in Japanese Patent Application Publication No. 2003-344131 can be used.

The non-contact rheological property measuring device 3 acquires flow velocity data at each measurement point from the ultrasonic flow velocity measuring device 2 and determines the rheological properties of the fluid. The non-contact rheological property measuring device 3 in this embodiment is constituted by 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 storing various data and functioning as a working area when the arithmetic processing means 6 performs arithmetic processing, and by executing the non-contact rheological property measurement program 3a installed in the storage means 5, various data can be stored. It has an arithmetic processing means 6 that executes arithmetic processing 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 this embodiment, it is configured by a display equipped with a touch panel function. Note that the configuration of the display input means 4 is not limited to a touch panel display, and may include separate display means with only a display function and input means with only an input function such as a keyboard or mouse. may have.

The storage means 5 is composed of a hard disk, a ROM (Read Only Memory), a RAM (Random Access Memory), a flash memory, etc., and includes a program storage section 51 that stores a non-contact rheological property measurement program 31a, and a rheology model. It has a rheology model equation storage section 52 that stores equations obtained by Fourier transforming the equation of motion of a fluid flowing in a pipe based on time, and a threshold storage section 53 that stores various threshold values.

A non-contact rheological property measuring program 3a for controlling the non-contact rheological property measuring device 3 of this embodiment is installed in the program storage unit 51. The arithmetic processing means 6 reads out and executes the non-contact rheological property measurement program 3a, thereby causing the computer to function as each component in the non-contact rheological property measurement apparatus 3.

Note that the usage form of the non-contact rheological property measurement program 3a is not limited to the above configuration. For example, the non-contact rheology physical property measurement program 3a may be stored in a computer-readable non-temporary recording medium such as a CD-ROM or a USB memory, and then read directly from the recording medium and executed. good. Furthermore, it may be used in a cloud computing method, an ASP (Application Service Provider) method, etc. from an external server or the like.

The rheology model equation storage unit 52 stores an equation obtained by Fourier transforming an equation of motion of a fluid flowing in a pipe based on a rheology model with respect to time. In this embodiment, an equation derived from the rheology model based on the following equation (1) is stored.
[Number 1]
here,
,
,
,
,
τ is the shear stress 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 pulsations 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. Note that the number of rheological properties A, B, C, . . . changes depending on the rheological model. For example, when the rheology model suitable for the object to be measured is a Newtonian fluid, the number of rheological properties is 1, and when the rheology model is a non-Newtonian fluid, the number of rheological properties is 2 or more.

In equation (1), the term representing the pressure gradient α becomes a function of the angular frequency ω in the flow by performing Fourier transformation over 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) within the pipe. That is, in Equation (1), there is no need to measure using a pressure sensor, a pressure gauge, etc. 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 a pipe in a non-contact and non-invasive manner. In other words, the non-contact type rheological property measurement system 1 of this embodiment is a system that can measure the rheological properties of a fluid flowing in a pipe in a non-contact manner based on the measurement principle.

Furthermore, equation (1) includes the angular frequency ω of pulsation in the fluid. In general, the flow inside a pipe in a production process is constantly pulsating (fluctuations) due to vortices generated by the pump or piping shape used to generate the flow, so the rheological properties of the fluid flowing inside such a pipe are important. It can be used for measurement. Therefore, the range of application is wider than conventional systems that can only be applied to pipe flow where a steady flow can be assumed.

Note that rheology models include a Newtonian fluid model in which the shear stress of the flow is proportional to the velocity gradient of the flow (linear), and a non-Newtonian fluid model in which the shear stress and the velocity gradient are not proportional (nonlinear). It is broadly divided into models. Examples of non-Newtonian fluid models 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 storage unit 53 stores various thresholds. In this embodiment, the following formula (3) used to detect the peak frequency ω ₀ based on the viscous layer thickness and each value associated therewith are stored.
[Number 3]
here,
(ν/kΔω) ^1/2 is the viscous layer thickness,
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 tube.

Next, the arithmetic processing means 6 will be explained. The arithmetic processing means 6 is constituted by a CPU (Central Processing Unit), etc., and by executing the non-contact rheological property measurement program 3a installed in the storage means 5, the ultrasonic flow velocity is calculated 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 indicating the maximum amplitude value from the frequency of pulsation in the fluid, and 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 equations obtained by substituting the flow velocity data in , 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 property determination unit 65 that determines rheological property values 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 measurement device 2, but it is higher than the frequency of pulsation in the fluid of several milliseconds to tens of milliseconds. Since it can be measured at sufficiently short time intervals, it can be treated as temporally continuous data. Further, in order to use it for calculation of equation (3), the flow velocity acquisition unit 61 in this embodiment acquires the distance Δr between measurement points determined based on the measurement limit from the ultrasonic flow velocity measurement device 2, and The information is stored in the storage unit 53.

The peak frequency detection unit 62 detects a peak frequency ω ₀ indicating the maximum amplitude value from the frequency of pulsation in the fluid by frequency-analyzing the flow velocity data at each measurement point. Frequency analysis is also called spectrum analysis or waveform analysis. For example, Fourier transform, wavelet transform, etc. are exemplified. In this embodiment, the peak frequency ω ₀ is detected using Fourier transform. Note that the peak frequency ω ₀ is sometimes called a dominant frequency or dominant frequency.

Furthermore, the peak frequency detection section 62 in this embodiment has a function of detecting a peak frequency based on the viscous layer thickness. Specifically, the frequency exhibiting the maximum amplitude value is detected as the peak frequency ω ₀ from among the frequencies that satisfy the above equation (3). Here, 3Δr, which is the lowest value of equation (3), is determined by the fact that there are at least three or more unknown constants defined by the selected rheology model when calculating the numerical solution in the numerical solution calculation unit 63. The number of function equations required to calculate the unknown constant is three or more, and the flow velocity data and rheology are This is based on the fact that the number of data points (number of measurement points) required to perform spatial difference or polynomial approximation of the calculation results of physical property values is 3 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 tube, and is based on the fact that the viscous layer thickness does not increase any further in an axially symmetrical flow in the tube.

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 flow velocity data at a plurality of measurement points into the above equation (1). The numerical solution calculation unit 63 in this embodiment calculates a numerical solution by minimizing the cost function shown in equation (2) below. In this embodiment, a program for minimizing the cost function is created, and a numerical solution is calculated by executing the created program. Although the algorithm for minimizing the cost function is not particularly limited, examples include a random search method and a gradient descent method.
[Number 2]

Further, the numerical solution calculation unit 63 in this embodiment 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. This is to suppress calculation errors in the rheological property values caused by measurement errors in 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 include Bessel function and Chebyshev series.

In addition, in the case where the rheological model of the fluid flowing in the pipe is unknown, or when the rheological model changes from time to time due to changes in temperature or the proportions of various components, the numerical solution calculation unit 63 in this embodiment uses multiple types of rheology. Compute a numerical solution based on the model. Specifically, the numerical solution calculation unit 63 calculates a numerical solution using an equation obtained by Fourier transforming the equation of motion of the fluid flowing in the pipe based on multiple types of rheology models from the rheology model equation storage unit 52 with respect to time. Calculate.

The rheology model determination unit 64 determines a rheology model after the numerical solution calculation unit 63 calculates numerical solutions based on a plurality of types of rheology models, such as when the rheology model is unknown. The rheology model determination unit 64 in this embodiment compares the plurality of numerical solutions calculated by the numerical solution calculation unit 63 and determines the rheology model that is the smallest numerical solution as the rheology model of the fluid.

Note that the method for determining a 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 this embodiment. Instead, for example, it is determined whether the numerical solution calculated by the numerical solution calculation unit 63 is below a predetermined threshold, and if it is below the threshold, the rheology model that calculated the numerical solution is set as the measurement target. is determined to be the fluid rheology model of The discrimination process may be repeated until the rheology model is determined when the rheology model becomes less than or equal to the threshold value.

The rheological property determining unit 65 determines rheological property values based on the numerical solution calculated by the numerical solution calculating unit 63. The rheological property determination unit 65 in this embodiment is configured to determine rheological 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 storage unit 53 in order to be used as the kinematic viscosity coefficient ν when calculating equation (3) calculated by the peak frequency detection unit 62. If the kinematic viscosity coefficient ν changes from moment to moment, it may be stored in the threshold storage unit 53 in chronological order, or it may be rewritten (overwritten) each time it is calculated.

In addition, if there is a relationship such as a correlation between the rheological property value and the proportion of a specific component contained in the fluid, the proportion of the component is determined together with or in place of the rheological property value. You may also do so.

Next, the operation of each component in the non-contact rheological property measuring device 3, system 1, and program 3a of this embodiment will be explained together with the non-contact rheological property measuring method.

The ultrasonic flow velocity measurement device 2 transmits and receives ultrasonic waves to the fluid flowing inside the pipe from outside the pipe, and analyzes the received ultrasonic waves to determine the flow velocity at a plurality of measurement points along the irradiation direction of the ultrasonic waves. measured over time.

As shown in FIG. 2, in the non-contact rheological property measuring device 3, the flow velocity acquisition unit 61 collects the flow velocity data measured by the ultrasonic flow velocity measuring device 2, specifically, the spatio-temporal flow 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 this embodiment acquires the flow velocity data from the ultrasonic flow velocity measurement device 2 as well as the distance Δr between the measurement points determined when calculating the flow velocity data, and stores it in the threshold storage unit 53. let

Next, the peak frequency detection unit 62 performs frequency analysis on the flow velocity data at each measurement point acquired by the flow velocity acquisition unit 61, and detects a peak frequency ω ₀ indicating the maximum amplitude value from the frequency of pulsation in the fluid (S2 : peak frequency detection step). In this embodiment, frequency analysis _{( spectrum} analysis) to detect the peak frequency ω ₀ .
[Number 4]
[Number 5]

Furthermore, the peak frequency detection unit 62 determines whether the calculated peak frequency ω ₀ satisfies the condition within the range of 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 acquired from the threshold storage unit 63. If the peak frequency ω ₀ calculated in step S2 is not within the range of formula (3) (S3: NO), the process returns to step S2 to detect the next highest peak frequency ω ₀ and ) Repeat this process until the requirements are met. Then, if the calculated peak frequency ω ₀ is within the range of equation (3) (S3: YES), that frequency is determined as the peak frequency ω ₀ . The peak frequency detection unit 62 in this embodiment thus detects the maximum amplitude value from among the frequencies that satisfy the requirements of equation (3) as the peak frequency ω ₀ .

Next, the numerical solution calculation unit 63 calculates a function approximation value for the flow velocity data to be substituted into equation (1) in order to suppress the influence of measurement errors in the ultrasonic flow velocity measuring device 2 (S4). . In this embodiment, a quintic function approximation value is calculated using the following equation (6), and that value is used.
[Number 6]

Then, based on equation (1), a numerical solution is calculated from a plurality of functional equations obtained by substituting the peak frequency ω ₀ and flow velocity data at a plurality of measurement points (S5: numerical solution calculation step). In this embodiment, the cost function shown in equation (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 ) means the time variation of the pressure gradient.

Furthermore, when the rheological model is a non-Newtonian fluid and the shear stress τ related using the rheological model is expressed by the following equation (9), the equation (2) is changed from the following equation (10) to equation (12). ) can be rewritten as shown.
[Number 9]
[Number 10]
[Number 11]
[Number 12]
Here, Π ₁ , Π ₂ , Π ₃ , ... mean rheological properties in a non-Newtonian fluid. Note that equation (11) is the same equation as equation (8) above, and α(t _i ) means the time variation of the pressure gradient.

A numerical solution is then calculated by minimizing this cost function using a random search method, gradient descent method, or the like. At this time, only the peak frequency ω ₀ detected by the peak frequency detection section 62 and the flow velocity data acquired by the flow velocity acquisition section 61 are substituted into each equation, and the pressure data inside the pipe is not necessary. Furthermore, by using the cost function, the computational load for calculating the numerical solution is suppressed. Although it depends on the type of algorithm for minimizing the cost function and the processing power of the arithmetic processing means, numerical solutions can be calculated at intervals of approximately several seconds to several tens of seconds for one calculation.

In this embodiment, in step S5, multiple rheology models are used to cope with cases where the rheology model is unknown or where the shear stress τ changes depending on temperature, component ratio, etc. and the rheology model needs to be changed. Calculate the numerical solution. Specifically, the numerical solution calculation unit 63 calculates a plurality of equations obtained by performing Fourier transformation of the equation of motion of a fluid flowing in a pipe based on a plurality of types of rheology models stored in the rheology model equation storage unit 52 with respect to time. Read and calculate numerical solutions for each equation.

Then, the rheology model determination unit 64 compares the plurality of numerical solutions and determines the rheology model that is the smallest numerical solution as the rheology model of the fluid (S6: rheology model determination step).

Note that if the rheology model, such as a Newtonian fluid, is known in advance, the calculation of numerical solutions for multiple types of rheology models in step S4 and the rheology model determination step in step S5 may be omitted. Further, after the unknown rheology model is determined in step S6, if there is no change in the rheology model (there is almost no change in the shear stress τ), in the subsequent processing, other rheology models in step S6 are changed. It is possible to omit the calculation step S5 of calculating a numerical solution based on this and the rheology model determination step S6.

Then, the rheological property determining unit 65 determines the rheological property value of the fluid based on the numerical solution obtained by the numerical solution calculating unit 63 (S7: rheological property determining step). If the component ratio etc. can be determined based on the rheological property value, the component ratio is determined together with the rheological property value. Rheological property values, component ratios, etc. are determined by calculating numerical solutions. In other words, similar to the numerical solution described above, rheological property values can be determined at intervals of approximately several seconds to several tens of seconds. Therefore, fluctuations in rheological property values, changes in component ratios, etc. can be measured almost in real time.

According to the non-contact rheological property measuring device 3, system 1, program 3a, and method of this embodiment as described above, the following effects can be achieved.
1. By acquiring flow velocity data that allows non-contact and non-invasive measurement of the flow velocity of the fluid flowing inside the pipe, the rheological properties of the fluid can be measured without measuring the pressure inside the pipe.
2. Since it utilizes pulsations in the flow within the pipe, it has a wide range of applicability and can be applied to fluids flowing in various pipes.
3. By using cost functions, etc., the processing load required for calculations can be reduced, making it possible to measure changes in rheological properties, changes in component ratios, etc. in real time.
4. By using the function approximation value of the flow velocity data, it is possible to suppress measurement errors such as rheological property values based on measurement errors of the flow velocity data measured by the ultrasonic flow velocity measuring device 2.
5. The peak frequency detection section 62 detects the peak frequency based on the viscous layer thickness, thereby ensuring accuracy based on the measurement principle.

Next, specific examples of the non-contact rheological property measuring device, system, program, and method according to the present invention will be described. Note that the technical scope of the present invention is not limited to the features shown in the following examples.

In Example 1, the non-contact rheology physical property measurement program according to the present invention is used as flow velocity data obtained by assuming that a numerically pulsating flow in a pipe is created and the created flow is measured with an ultrasonic flow velocity measurement device. The rheological properties were calculated using the following method. Furthermore, the exact solution for the flow in the pipe 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.

［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
Ｊ_０およびＪ_１はベッセル関数、をそれぞれ意味する。<Numerical calculation of flow in a pipe with pulsation>
A steady flow in a pipe in a Newtonian fluid that flows in one direction is called a Hagen-Poiseuille flow, and can be expressed by the following governing equation (13) and equation (14).
[Number 13]

[Number 14]

Further, the pulsating flow in the pipe can be expressed by the following governing equation (15) and equation (16).
[Number 15]

[Number 16]

Then, the flow in the pipe accompanied by pulsation is obtained as the following equation (17) using equations (12) to (16).
[Number 17]

here,
R is the radius of the tube
U ₀ is the maximum value of Hagen-Poiseuille flow
U ₁ is the speed fluctuation of pulsation (size of amplitude)
ω is the frequency of pulsation (angular frequency)
ν is the kinematic viscosity coefficient, ρ is the density of the fluid, and J ₀ and J ₁ are Bessel functions, respectively.

<Calculation conditions and results for inside a pipe with pulsation>
Here, the calculation conditions when calculating the flow in the pipe with pulsation using equation (17) are U ₀ = 0.2 m/s, U ₁ = 0.1 m/s, r = 1000 kg/m ³ , R = 25.4 mm, Dt = 10 ms, Dr = 0.1 mm.

In addition, since the analysis target is the flow of fluids with different viscosities (rheological properties), 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 were used, such as s.

Furthermore, in order to examine the effect of differences in frequency ω, that is, pulsation speed, on calculation accuracy, multiple conditions such as f _o (=ω/2π) =0.5 Hz and f _o (=ω/2π) = 1.0 Hz were set. And so.

Figure 3 shows the calculation results for the inside of the tube with pulsation calculated based on each condition. In each figure, the vertical axis represents the position within the tube. The center of the vertical axis represents the center position of the tube, and the upper and lower ends represent the positions of the tube walls. Specifically, it is nondimensionalized as r/R, and the center of the vertical axis, which is the center position of the tube, is r/R=0, and the value corresponding to the tube wall is r/R=1 or r/R= -1. The horizontal axis represents the passage of time. Specifically, it is nondimensionalized as tf _o . In addition, the flow velocity distribution within the pipe over time is expressed by color shading. The darker the color, the closer the speed is to zero, and the whiter the color, the faster the speed. Specifically, it is made dimensionless as u/U ₀ .

As shown in FIG. 3, the flow velocity at the central position is high at each time, and the velocity becomes slower as it approaches the pipe wall. This shows a flow velocity distribution in the pipe that is axially symmetrical like the Hagen-Poiseuille flow. Furthermore, for example, the speed of the center position repeatedly increases and decreases over time. Therefore, it can be confirmed that the flow in the pipe accompanied by pulsation is calculated using equation (17).

<Measurement simulation using ultrasonic flow velocity measuring device>
The calculation results shown in FIG. 3 are exact solutions of the flow velocity distribution calculated for the flow in the pipe accompanied by pulsation. On the other hand, when the flow in a pipe is measured in a non-contact manner using an ultrasonic flow velocity measurement device, the obtained flow velocity data includes measurement errors (measurement noise). There are various factors contributing to measurement errors, but for example, the influence of the density of solid objects contained in the fluid that reflect ultrasound waves, and the diffuse reflection of ultrasound waves within the fluid or pipe walls can be considered.

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 this Example 1, the flow velocity distribution including measurement error (measurement noise) in consideration of measurement accuracy is calculated using the following equation (18) with respect to the flow velocity distribution of the flow in the pipe with pulsation calculated based on the equation (17). It was defined as
[Number 18]

here,
n(ave, std) is the noise function,
a means the noise level, respectively.

For example, when the noise level a = 5.0, the noise function is expressed by a normal distribution with the true value as the median, as shown in FIG. In Example 1, using this equation (18), flow velocity data u(r,t) is substituted for noise levels a of 1.0, 5.0, 10.0, and 15.0, and flow velocity data u'( r,t) was calculated. Figure 5 shows the calculation results. As shown in FIG. 5, as the noise level increases, the shape of the obtained flow velocity distribution becomes less smooth. In other words, this flow velocity distribution can be viewed as flow velocity data that includes measurement errors. In Example 1, noise is added as a measurement error to the flow velocity data calculated as the true value in this way, thereby creating flow velocity data that includes measurement errors by the ultrasonic flow velocity measuring device.

<About numerical solutions of functional expressions obtained by the present invention>
Next, a numerical solution was calculated from the functional equation obtained by equation (1) using the flow velocity data calculated by equation (17) and equation (18). The rheology model was a Newtonian fluid. Therefore, a program was created to minimize the cost function using equations (7) and (8) representing the cost function of a flow in a pipe with pulsation in a Newtonian fluid, and a numerical solution was calculated using the program. A random search method was used as the algorithm to calculate the cost function.

In Example 1, in order to examine the influence of the pulsation frequency f _o (angular frequency ω) on the numerical solution, we will examine the cases where the frequency f _o [Hz] is 0.1, 0.2, 0.5, 1.0, 2.0, and 4.0. I calculated it.

Figure 6 shows the calculation results. The left side of the figure is the calculation result of the real value Re in equation (7), and the right side is the calculation result of the imaginary value Im. Also, 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 is 1/10 of that value, which is the kinematic viscosity coefficient n = 10 mm ² /s. . Note that n = 100 mm ² /s has a viscosity similar to that of cooking oil, and n = 10 mm ² /s has a viscosity slightly higher than that of water.

First, let's consider the influence of viscosity. Regarding the real values on the left side of Figure 6, focusing on the case of frequency f _o =0.1 [Hz], when the upper viscosity is high, the size varies from near the pipe wall (r/R = 1.0) to the center of the pipe. The real value Re increases gradually until it reaches (r/R=0.0). This shows that the viscosity affects the middle of the tube. On the other hand, when the lower viscosity is high, the value is almost constant in the range from the center of the tube (r/R=0.0) to r/R=0.25. This means that the influence of viscosity is weak in the center of the tube.

Regarding the imaginary value Im on the right side of _FIG . It increases gently from to the center of the tube (r/R=0.0). On the other hand, when the lower viscosity is low, the value is almost constant in the range from the center of the tube (r/R=0.0) to r/R=0.7.

Now, when considering the viscous layer thickness (ν/kΔω) ^1/2 in equation (3), when the kinematic viscosity coefficient of high viscosity n = 100 mm ² /s, the viscous layer thickness is approximately 12.6 mm. Since the radius of the tube was R = 25.4 mm, the thickness of the viscous layer ranged from the tube wall (r/R = 1.0) to r/R = 0.5 (1/2 of the radius of the tube). On the other hand, when the kinematic viscosity coefficient n = 10 mm ² /s with low viscosity (flowing), the viscous layer thickness is about 4.0 mm. Therefore, the viscous layer thickness was about r/R=0.85 from the tube wall (r/R=1.0).

Note that when the viscous layer thickness is approximately 4.0 mm, the distance Δr between the measurement points in the ultrasonic flow velocity measuring device in equation (3) in Example 1 is 0.1 mm, so the viscous layer thickness is approximately 4.0 mm. It is about 40 times larger than 3Δr. Therefore, if we use the flow velocity data from 3 or more of the approximately 40 measurement points within the range of r/R = 0.85 from the pipe wall (r/R = 1.0), where the influence of viscosity is large, based on equation (1), Numerical solutions with sufficient accuracy can be calculated.

Next, the influence of the pulsation frequency _fo (angular frequency ω) will be considered. If we pay attention to the real value Re on the upper side of Figure 6, if the relatively slowly vibrating frequency f _o (angular frequency ω) is 0.1 or 0.2, the real value Re will be the pipe wall (r/R = 1.0). It increases gently from the vicinity to the center of the tube (r/R=0.0). However, as the frequency f _o (angular frequency ω) becomes progressively faster, the range in which the real value at the center of the tube is approximately constant becomes wider. In other words, as the frequency f _o (angular frequency ω) increases, the effect of viscosity becomes more difficult to propagate as the distance from the pipe wall (r/R=1.0) increases.

Similarly, regarding the imaginary value Im on the upper side of FIG. It increases gently up to the center of the tube (r/R=0.0). As the frequency f _o (angular frequency ω) becomes progressively faster, the range in which the real value at the center of the tube is approximately constant becomes wider.

Furthermore, regarding the real value Re and imaginary value Im on the lower side of Fig. 6, which have low viscosity, if they vibrate relatively slowly, it is possible to move from the vicinity of the pipe wall (r/R = 1.0) to the center of the pipe (r /R=0.0), and the influence of viscosity appears, but as the frequency f _o (angular frequency ω) increases, the pipe wall (r/R=1.0) The influence of viscosity appears in the vicinity.

<About the calculation results of rheological properties>
Next, rheological property values are determined based on the numerical solution of the functional equation obtained by the present invention. FIG. 7 shows the results when minimizing the cost function. 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 entered at random using a random search method. Furthermore, the color of each point indicates the size of the cost function, and as the color approaches black, the cost function becomes smaller.

As shown in FIG. 7, the values of the cost function calculated by the random search method concentrate at one point on the graph. This concentrated point becomes the minimized cost function. Then, the value in the height direction at the point where the cost function is minimized can be determined as the viscosity coefficient μ.

<About the calculation accuracy of numerical solutions>
Next, we compared the rheological property values obtained from the calculation results of the numerical solution with the rheological property values used to calculate the flow in the pipe, which correspond to the true values. Furthermore, in the present invention, pressure gradients can be calculated as well as rheological property values. Therefore, we also compared the pressure gradient obtained from the calculation results of the numerical solution with the pressure gradient used to calculate the flow in the pipe, which corresponds to the true value.

FIG. 8 shows the noise level on the horizontal axis. The vertical axis shows η, which is the ratio between the viscosity coefficient μ obtained from the calculation result of the numerical solution and 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 of the gradient α _true . Furthermore, for the viscosity coefficient μ and pressure gradient α obtained from the calculation results of the numerical solution, the average value of three spatially (r-direction) consecutive points is used. Since the vertical axis is the ratio to the true value, the closer it is to 1, the closer it is 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 results obtained from the calculation results 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 it was even further away from the true value. Further, regarding λ (ratio of pressure gradients), even at a noise level of 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, very highly accurate results can be obtained by maintaining the measurement accuracy of the ultrasonic flow velocity measuring device.

Next, we confirmed the difference in accuracy with respect to the period of pulsation (within half a period). 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 approximated to 1, and no influence on accuracy due to the difference in period could be confirmed. Therefore, it has been 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 no matter what timing the measurement is performed on a pulsating pipe flow.

Next, we confirmed the difference in accuracy with respect to the kinematic viscosity coefficient ν. 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 decreases in a range where the kinematic viscosity coefficient ν is high. This is thought to be because, since the pressure gradient is kept constant, velocity fluctuations become weaker, and as a result, 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, we confirmed the difference in accuracy with respect to the pulsation frequency _fo (angular frequency ω). The results are shown in FIG. The horizontal axis is the frequency _fo , and the vertical axes are η and λ. As shown in FIG. 11, the accuracy decreases in the range where the frequency _fo is low. This is thought to be because the pressure gradient is kept constant, so as the frequency _fo becomes lower, the amplitude becomes smaller, and as a result, the noise becomes relatively larger. On the other hand, when the frequency f _o was 1.0 Hz or higher, the accuracy was high as it almost matched the true value.

Next, we confirmed the difference in accuracy with respect to the pulsation amplitude _U1 . The results are shown in FIG. The horizontal axis is the amplitude U ₁ and the vertical axes are η and λ. As shown in FIG. 12, the accuracy decreases when the amplitude U ₁ is low. This is considered to be because the amplitude becomes small, as in the case of the pulsation frequency _fo (angular frequency ω), and as a result, the noise becomes relatively large. On the other hand, when the amplitude U ₁ was 0.1 m/s or more, the accuracy was high as it almost matched the true value.

As described above, in Example 1, by using the non-contact type rheological property measuring device, system, program, and method according to the present invention, the rheological properties of a pulsating fluid flowing in a pipe can be accurately measured in a non-contact manner. We were able to confirm through numerical experiments that this is possible.

In Example 2, an experimental device that creates a pulsating flow in a pipe was created, and the rheological property values of a Newtonian fluid and a non-Newtonian fluid were measured using a non-contact rheological property measurement system according to the present invention. In addition, measurement accuracy was examined by comparing catalog values and measurement values using a commercially available rotary rheometer with measurement values obtained by the non-contact rheology physical property measurement system according to the present invention.

<About the experimental device that creates a pulsating flow in the pipe>
In Example 2, an experimental device was created that produces a pulsating flow in a pipe as shown in FIG. 13. The tubes to be measured include a straight stainless steel tube and an acrylic tube that is installed to be replaceable. The stainless steel tube used had a length of 3000 mm or more, an outer diameter of 50.8 mm (2 inches), and an inner diameter of 40.8 mm. The acrylic tube was installed on the downstream side of the stainless steel tube. In Example 2, one with an inner diameter of about 48 mm and one with an inner diameter of about 22 mm were used. In addition, in order to stabilize the flow inside the pipe, the measurement position was set at a point approximately 3000 mm or more away from the entrance of the stainless steel pipe.

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 was connected to the downstream side to flow the test fluid. In Example 2, a sanitary pump mainly used in the manufacturing process of foods, medicines, cosmetics, etc. was used as the rotary pump. Furthermore, the rotary pump is connected to a personal computer so that the frequency of the test fluid flowing inside the pipe can be controlled. A pipe connected to a storage tank was provided at the outlet of the rotary pump. Therefore, by operating the rotary pump, the test fluid is circulated within the experimental apparatus.

Furthermore, as shown in FIG. 14, at the measurement position, an ultrasonic transducer, which is one component of the ultrasonic flow rate measuring device, and a holding jig that holds the ultrasonic transducer at an angle _θ1 are installed. In addition, an ultrasonic gel was filled between the ultrasonic transducer and the tube to improve the transmittance of ultrasonic waves.

The ultrasonic flow rate measuring device is connected to a personal computer configured as a non-contact rheological property measuring device according to the present invention, thereby constructing a non-contact rheological property measuring system.

<About the test fluid used as Newtonian fluid>
As the Newtonian fluid, silicone oil with a kinematic viscosity of 10 cSt (viscosity (viscosity coefficient): 9.35×10 ⁻³ [Ps/s]) was used. In Example 2, tracer particles that promote reflection of ultrasonic waves were contained in silicone oil.

<About measurement of physical property values of Newtonian fluid>
In Example 2, the rotary pump was controlled to generate an oscillating flow of 0.1 Hz, and the rheological properties of a Newtonian fluid (silicone oil) were measured. First, an ultrasonic flow velocity measurement device transmitted and received ultrasonic waves via the ultrasonic transducer, and analyzed the received ultrasonic waves to measure the flow velocity distribution of the pulsating flow in the pipe. As shown in FIG. 14, the installation angle θ ₁ of the ultrasonic transducer and the angle θ ₂ of the ultrasonic propagation direction are different due to the difference in refractive index between the tube and the test fluid. This difference is reflected in the measurement results of flow velocity distribution.

FIG. 15 shows the results of measuring the flow velocity distribution in the pipe using an ultrasonic flow velocity measuring device. The vertical axis represents the position within the tube, and ξ=0 mm corresponds to the inner wall of the tube where the ultrasonic transducer is installed. The flow velocity distribution is represented by contour-like color shading. 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. If we look at the flow velocity at the approximate center point (ξ = about 28 mm) over time, we can see that it fluctuates about one cycle in about 10 seconds, and an oscillating flow of 0.1 Hz is measured. .

In Example 2, as in Example 1, a numerical solution was calculated from the functional expression obtained by equation (1). Since the test fluid was a Newtonian fluid, the rheology model was also a Newtonian fluid. Therefore, a program was created to minimize the cost function using equations (7) and (8) representing the cost function of a flow in a pipe with pulsation in a Newtonian fluid, and a numerical solution was calculated using the program. A random search method was used as the algorithm to calculate the cost function.

FIG. 16 shows the calculation results 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 imaginary part of pressure. The value of the cost function is expressed as a contour (contour line) with different shades of color. The whiter the color, the smaller the value, and the darker the color, the larger the value. As shown in FIG. 16, the values of the cost function calculated by the random search method concentrate at one point on the graph. This concentrated point becomes the minimized cost function. Then, the value in the height direction at the point where the cost function is minimized can be determined as the viscosity coefficient μ.

FIG. 17 shows data of viscosity and pressure amplitude measured at 10 second intervals for about 1000 seconds. Furthermore, 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 values were concentrated around the catalog value of 9.35×10 ⁻³ [Ps/s].

Therefore, it was demonstrated that the non-contact rheological property measuring system of Example 2 can measure the rheological properties of Newtonian fluid with sufficient accuracy.

<About measurement of physical property values of non-Newtonian fluids>
Next, we measured the physical properties of the non-Newtonian fluid.

<About the test fluid used as a non-Newtonian fluid>
An aqueous solution of carboxymethylcellulose (hereinafter referred to as "CMC aqueous solution") was used as the non-Newtonian fluid. In this Example 2, the concentration of the CMC aqueous solution was set to 0.5wt. %. Carboxymethylcellulose (CMC) is commonly used as a thickener in processed products, including foods. The CMC aqueous solution is a pseudoplastic fluid whose viscosity decreases as the shear rate increases, and in Example 2, one with a viscosity of about 100 to 400 [mPa·s] was used.

<About measurement of physical property values of non-Newtonian fluids>
The left side of FIG. 18 shows the results of measuring the flow velocity distribution in the pipe using an ultrasonic flow velocity measuring device. Here, as in FIG. 3, the vertical axis is the position within the pipe rendered dimensionless as r/R, and r/R=0 represents the center position of the pipe. The horizontal axis represents the passage of time rendered dimensionless as tf, and shows data for about two cycles. The flow velocity distribution is represented by contour-like color shading; the whiter the color, the closer the velocity is to zero, and the darker the color, the faster the velocity. If we look at the flow velocity at the approximate center point (r/R=0) over time, we can see that it fluctuates approximately every cycle, indicating that an oscillating flow is being measured.

Next, a program was created using Equations (9) to (12) to minimize the cost function of a flow in a pipe with pulsation in a non-Newtonian fluid, and a numerical solution was calculated using the program. The right side of FIG. 18 shows the calculation results of the real value Re and the imaginary value Im calculated by equation (10) using a flow velocity distribution in which r/R is in the range 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 from 0 to 0.6.

19 and 20 show the results of calculating the cost function using the random search method. Similar to the measurement result of Newtonian fluid shown in FIG. 16, the value of the cost function calculated by the random search method concentrates on one point on the graph. Then, the value in the height direction at the point where the cost function is minimized can be determined as the viscosity coefficient μ.

FIG. 21 shows the value of shear stress τ according to the strain rate γ, where the round plots are the values measured by a commercially available rheometer, and the triangular plots are the values measured by the non-contact rheological property measurement system according to the present invention. This is the measured value. In Example 2, MCR102 manufactured by Anton Paar was used as a commercially available rheometer.

As shown in FIG. 21, when the CMC aqueous solution used in Example 2 is measured with a commercially available rheometer, the shear stress τ increases as the strain rate γ increases. At this time, the increase in shear stress τ slows down somewhat as the strain rate γ increases. Assuming that the relationship between shear stress τ and strain rate γ is expressed by a power law of τ=Kγ ⁿ , in the range of γ from A to B, K=0.569 [Pa・s], n= 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. . When compared with the values of a commercially available rheometer, the increase in shear stress τ with respect to strain rate γ also showed similar values.

<About additional experiments using acrylic tubes>
In Example 2, an exchangeable acrylic tube installed on the downstream side of the stainless steel tube was used to increase the flow rate, thereby making the range of strain rate γ wider. Specifically, as described above, an acrylic tube with an inner diameter of about 48 mm and an acrylic tube with 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 [m/s]. Then, rheological property values were calculated using a flow velocity distribution in which r/R was in the range of approximately 0 to 0.6.

Similar to FIG. 21, FIG. 22 shows the value of shear stress τ depending on the strain rate γ, and the circular plots are measured values using a commercially available rheometer. Furthermore, the triangular plots are the measured values measured by the non-contact rheological property measuring system according to the present invention when an inner diameter of about 48 mm is used, and the cross-shaped plots are when the inner diameter is about 22 mm. As shown in FIG. 22, measurement results corresponding to the entire range that could be measured with a commercially available rheometer were obtained. Furthermore, when compared with the measurement results of a commercially available rheometer, similar values were shown over the entire range.

Further, FIG. 23 shows measurement results regarding the viscosity μ [Pa·s] according to the strain rate γ. The circular plots are measured values using a commercially available rheometer. Furthermore, the triangular plots are the measured values measured by the non-contact rheological property measuring system according to the present invention when an inner diameter of about 48 mm is used, and the cross-shaped plots are when the inner diameter is about 22 mm. As shown in FIG. 23, as the strain rate γ increases as measured by a commercially available rheometer, the viscosity μ decreases, indicating the characteristics of a pseudoplastic fluid. Similarly, the viscosity μ tends to decrease with respect to the strain rate γ with respect to the measured values measured by the non-contact rheology physical property measurement system. Assuming that the relationship between viscosity μ and strain rate γ is expressed by a power law of μ=Kγ ^n-1 , as shown in FIG. 24, K=0.559 [Pa·s], n=0. 89, and it was verified that a value indicating the characteristics of a pseudoplastic fluid was measured.

As described above, in this Example 2, by using the non-contact type rheological property measuring device, system, program, and method according to the present invention, the rheological properties of a pulsating fluid flowing in a pipe can be accurately measured in a non-contact manner. We were able to confirm that this is possible using actual experimental equipment.

Note that the non-contact rheological property measuring device, system, program, and method according to the present invention are not limited to the embodiments described above, and can be modified as appropriate.

For example, the peak frequency detection unit 62 performs frequency analysis only on the frequency range that satisfies the condition within the range of equation (3), and processes the frequency analysis to determine the peak frequency ω ₀ that exhibits the largest amplitude. It's okay.

1 Non-contact rheological property measuring system 2 Ultrasonic current velocity measuring device 3 Non-contact rheological property measuring device 3a Non-contact rheological property measuring program 4 Display input means 5 Storage means 6 Arithmetic processing means 51 Program storage unit 52 Rheological model formula storage Section 53 Threshold storage section 61 Flow velocity acquisition section 62 Peak frequency detection section 63 Numerical solution calculation section 64 Rheology model determination section 65 Rheology physical property determination section

Claims (12)

A non-contact rheological property measuring device that non-contactly measures the rheological properties of a fluid flowing inside a pipe,
a flow velocity acquisition unit that acquires flow velocity data at a plurality of measurement points along the ultrasonic irradiation direction from the ultrasonic flow velocity measuring device;
a peak frequency detection unit that detects a peak frequency indicating the maximum amplitude value from the frequency of pulsation in the fluid by frequency-analyzing the flow velocity data at each measurement point acquired by the flow velocity acquisition unit;
Multiple functions obtained by substituting the peak frequency and flow velocity data at multiple measurement points into the following equation (1) obtained by Fourier transforming the equation of motion of the fluid flowing in the pipe based on the rheology model with respect to time. a numerical solution calculation unit that calculates a numerical solution from the equation;
The non-contact rheological property measuring device, comprising: a rheological property determining unit that determines a rheological property value based on the numerical solution calculated by the numerical solution calculating unit.
[Number 1]
here,
,
,
,
,
τ is the shear stress 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 pulsations 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 rheology physical property measuring device according to claim 1, wherein the numerical solution calculation unit calculates the numerical solution by minimizing a cost function shown in equation (2) below.
[Number 2]
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 consecutive measurement points as the flow velocity data to be substituted. Measuring device. The numerical solution calculation unit calculates numerical solutions based on multiple types of rheological models, and
The non-contact rheology according to any one of claims 1 to 3, further comprising a rheology model determining unit that compares the numerical solutions and determines the rheology model that is the smallest numerical solution as the rheology model of the fluid. Physical property measuring device. In the peak frequency detection section, the viscous layer thickness, which is expressed by the ratio of the viscosity of the fluid to the frequency of pulsation in the fluid, detects a peak at which the viscous layer thickness exhibits the maximum amplitude value from among the frequencies that satisfy the range of formula (3) below. 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 viscous layer thickness,
Δr is the distance between measurement points,
ν is the kinematic viscosity coefficient (kinetic viscosity) of the fluid,
kΔω is the detected frequency,
D means the inner diameter of the tube. Ultrasonic waves are emitted from the outside of the tube toward the inside of the tube, and the ultrasonic waves reflected from the inside of the tube toward 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. An ultrasonic flow velocity measurement device that measures
and a non-contact rheological property measuring device according to any one of claims 1 to 5, which acquires flow velocity data at each measurement point from the ultrasonic flow velocity measuring device to determine the rheological properties of the fluid. Mold rheology physical property measurement system. A non-contact rheological property measurement program that non-contactly measures the rheological properties of fluid flowing inside a pipe,
a flow velocity acquisition unit that acquires flow velocity data at a plurality of measurement points along the ultrasonic irradiation direction from the ultrasonic flow velocity measuring device;
a peak frequency detection unit that detects a peak frequency indicating the maximum amplitude value from the frequency of pulsation in the fluid by frequency-analyzing the flow velocity data at each measurement point acquired by the flow velocity acquisition unit;
Multiple functions obtained by substituting the peak frequency and flow velocity data at multiple measurement points into the following equation (1) obtained by Fourier transforming the equation of motion of the fluid flowing in the pipe based on the rheology model with respect to time. a numerical solution calculation unit that calculates a numerical solution from the equation;
The non-contact rheological property measuring program causes a computer to function as a rheological property determining unit that determines rheological property values based on the numerical solution calculated by the numerical solution calculating unit.
[Number 1]
here,
,
,
,
,
τ is the shear stress 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 pulsations 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 physical property measurement program according to claim 7, wherein the numerical solution calculating section calculates a numerical solution by minimizing a cost function shown in equation (2) below.
[Number 2]
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 consecutive measurement points as the flow velocity data to be substituted. Measurement program. The numerical solution calculation unit calculates numerical solutions based on multiple types of rheological models, and
Non-contact rheology according to any one of claims 7 to 9, further comprising a rheology model determining unit that compares the numerical solutions and determines the rheology model that is the smallest numerical solution as the rheology model of the fluid. Physical property measurement program. In the peak frequency detection section, the viscous layer thickness, which is expressed by the ratio of the viscosity of the fluid to the frequency of pulsation in the fluid, detects a peak at which the viscous layer thickness exhibits the maximum amplitude value from among the frequencies that satisfy the range of formula (3) below. 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 viscous layer thickness,
Δr is the distance between measurement points,
ν is the kinematic viscosity coefficient (kinetic viscosity) of the fluid,
kΔω is the detected frequency,
D means the inner diameter of the tube. A non-contact rheological property measuring method for non-contactly measuring the rheological properties of a fluid flowing inside a pipe,
a flow velocity acquisition step of acquiring flow velocity data at a plurality of measurement points along the ultrasonic irradiation direction from the ultrasonic flow velocity measuring device;
a peak frequency detection step of detecting a peak frequency indicating the maximum amplitude value from the frequency of pulsation in the fluid by frequency-analyzing the flow velocity data of each measurement point acquired in this flow velocity acquisition step;
Multiple functions obtained by substituting the peak frequency and flow velocity data at multiple measurement points into the following equation (1) obtained by Fourier transforming the equation of motion of the fluid flowing in the pipe based on the rheology model with respect to time. a numerical solution calculation step of calculating a numerical solution from the equation;
The non-contact rheological property measuring method, comprising: a rheological property determining step of determining a rheological property value based on the numerical solution calculated by the numerical solution calculating step.
[Number 1]
here,
,
,
,
,
τ is the shear stress 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 pulsations 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.

Images