JP2001183200A - Flowmeter and flow-rate measuring method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a flowmeter by which a flow rate can be found with good accuracy without using a correction factor and to provide a flow-rate measuring method. SOLUTION: A flow velocity sensor 320 and a flow velocity sensor 321 are arranged in a projection cross section inside a pipe line so as to transmit ultrasonic waves toward the central point. The width of the pipe line is standardized so as to reach 1 from -1 in its up-and-down direction, and coordinates are set in the up-and-down direction. In a plurality of depths of water (z=z0, z1) which become roots (z1,...zn) of the Legendre spherical function Pn(z) with reference to the Pn(z), the width of the pipe line in the respective depths of water is standardized so as to reach 1 from -1 in the horizontal direction, and the coordinates are set in the horizontal direction. Flow velocities are measured in a plurality of points P00, P01, P10, P11 as roots (x1,...xn) of the Legendre spherical function Pn(x) with referenced to the PN(x). On the basis of the width of the pipe line in the horizontal direction in the respective depths of water and on the basis of the flow velocities in the measuring points, the Gaussion numerical value is integrated, the area of the distribution of the flow velocities in the respective depths of water is calculated, the area of the distribution of the flow velocities on the respective depths of water is integrated, and the flow rate of the pipe line as a whole is calculated.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a flow meter and a flow rate measuring method for measuring a flow rate of a fluid flowing through a pipe in a full state.

[0002]

2. Description of the Related Art Conventionally, as a flow meter of this type, a flow velocity measuring unit comprising a Doppler type ultrasonic flow velocity meter or the like for measuring a flow velocity at a fixed point near a center point or near a pipe wall in a cross section in a pipe. It is known that an average flow velocity of a cross section is obtained from a measured flow velocity obtained by a flow velocity measurement unit, and a flow rate is obtained by multiplying the average flow velocity by an area of a cross section in a pipeline. In this case, the flow velocity distribution of the fluid flowing in the pipe changes according to the Reynolds number, and the measured flow velocity measured by the flow velocity measuring unit differs from the average flow velocity. Therefore, it is necessary to correct the flow velocity distribution based on the Reynolds number to calculate the flow rate.

[0003]

However, the flow velocity correction coefficient based on the Reynolds number is calculated based on the assumption that the flow in the pipe is a fully developed flow and is axisymmetric. Therefore, the installation conditions of the flow meter need to be strict, and the flow velocity measurement position has a restriction that a sufficiently long straight pipe portion is required in front. However, even if the installation conditions are satisfied, there is a problem that an error occurs in the obtained flow meter if the symmetry of the flow velocity distribution is broken due to some influence on the upstream side. Further, since the correction coefficient must be obtained in advance, there is a problem that it takes time to determine the correction coefficient. If the position of the measurement point of the flow velocity measurement unit is changed, the correction coefficient must be obtained again.

[0004] The present invention has been made in view of such a conventional problem, and the invention according to claims 1 to 7 has a flow meter and a flow measuring method capable of accurately obtaining a flow rate without using a correction coefficient. Its purpose is to provide.

[0005]

In order to achieve the above object, a flow meter according to the present invention is a flow meter for measuring a flow rate of a fluid flowing through a pipe in a fully-filled state. In the above, when two orthogonal coordinate axes (x-axis and z-axis) are taken, the pipeline width is normalized as extending from -1 to 1 in one of the coordinate axes (z-axis), and the one coordinate axis (z-axis) ) When the coordinates are taken in the direction, the Legendre spherical function P
For n (z), the root of Pn (z) = 0 (z1,... zn)
.., Z on a plurality of one coordinate axes (z-axis)
n), the pipe width at each point (z1,..., zn) in the direction of the other coordinate axis (x-axis) is standardized as extending from -1 to 1 in the direction of the other coordinate axis (x-axis). When coordinates are taken in the (x-axis) direction,
For the spherical function Pn (x) of e, the root of Pn (x) = 0 (x
1,... Xn) and a flow rate measuring unit for measuring the flow rates at a plurality of points (z1,... Z) on the one coordinate axis (z-axis).
From n) the channel width in the direction of the other coordinate axis (x-axis) and the flow velocity at a plurality of points measured by the flow velocity measuring unit, Gaussian numerical integration is performed to calculate the area of the flow velocity distribution. Furthermore, a flow rate calculation unit that calculates the flow rate of the entire pipeline by performing Gaussian numerical integration is provided.

The above-mentioned z-coordinate can be set in the vertical direction, and the x-coordinate can be set in the horizontal direction. In the inner projection cross section, when the pipe width is normalized in the vertical direction as ranging from -1 to 1 and the coordinates are taken in the vertical direction, P is expressed as P with respect to the Legendre's spherical function Pn (z).
At a plurality of water depths at which the root of n (z) = 0 (z1,..., zn), the pipeline width at each water depth is changed from −1 to 1 in the horizontal direction.
When the coordinates are normalized in the horizontal direction and the coordinates are taken in the horizontal direction, Pn (x) with respect to Legendre's spherical function Pn (x)
(X) A flow velocity measuring unit that measures the flow velocity at a plurality of points that are roots (x1,... Xn) of 0, and the horizontal pipe width and the flow velocity at the plurality of points measured by the flow velocity measuring unit at each of the water depths. From
Perform Gaussian numerical integration to calculate the area of the flow velocity distribution at each water depth, and calculate the area of the flow velocity distribution at each water depth,
A flow rate calculation unit that calculates the flow rate of the entire pipeline by performing Gaussian numerical integration.

A flow rate measuring method according to the present invention is a flow rate measuring method for measuring a flow rate of a fluid flowing in a pipe in a full state, wherein two orthogonal coordinate axes (x-axis) are projected in a cross section projected in the pipe. , Z axis), one of the coordinate axes (z axis)
(Axis) direction, the pipe width is normalized as ranging from -1 to 1, and the coordinates are taken in the one coordinate axis (z axis) direction.
Pn for Legendre's spherical function Pn (z)
(Z) = 0 at a plurality of points (z1,... Zn) on one of the coordinate axes (z-axis) serving as a root (z1,... Zn), the other coordinate axis (x-axis) at each point (z1,. ) In the direction of the other coordinate axis (x-axis) and normalized in the direction of the other coordinate axis (x-axis), the legendre's spherical function Pn
With respect to (x), flow velocities at a plurality of points that are roots (x1,... Xn) of Pn (x) = 0 are measured, and the one coordinate axis (z
Axis), the Gaussian numerical integration is performed from the channel width in the direction of the other coordinate axis (x axis) at each point (z1,..., Zn) and the flow velocity at a plurality of points measured by the flow velocity measuring unit to determine the area of the flow velocity distribution. The flow rate of the entire pipeline is calculated by calculating the area of the flow velocity distribution and further performing Gaussian numerical integration.

The above-mentioned z-coordinate can be taken in the vertical direction, and the x-coordinate can be taken in the horizontal direction. In this case, there is provided a flow rate measuring method for measuring a flow rate of a fluid flowing through a pipe in a full state,
In the projected cross section in the pipeline, the pipeline width is
When the coordinates are normalized in the range from 1 to 1 and the coordinates are taken in the up-down direction, at a plurality of water depths that are roots (z1,... Zn) of Pn (z) = 0 with respect to the Legendre spherical function Pn (z). , The horizontal width of the pipeline at each water depth is -1
When the coordinates are taken in the horizontal direction, normalized to the range from to 1, the flow velocity of a plurality of points that are roots (x1,... Xn) of Pn (x) = 0 with respect to the Legendre spherical function Pn (x) Is measured, and from the horizontal pipe width at each water depth and the flow velocity at a plurality of points measured by the flow velocity measurement unit, Gaussian numerical integration is performed to calculate the area of the flow velocity distribution at each water depth, and the flow velocity distribution at each water depth is calculated. Calculates the flow rate of the entire pipeline by performing Gaussian numerical integration on the area of
It is characterized by the following.

A Gaussian numerical integration is an arbitrary function f
When (x) is a polynomial of degree 2n-1 or less,

[0010]

(Equation 1) And the integral of f (x) can be represented by the sum of the root of Pn (x) = 0 and the weighting factor wi derived from the root with respect to the Legendre spherical function Pn (x). is there. Here, the Legendre's spherical function is
For all polynomials Q (x) of degree n-1 or less,

[0011]

(Equation 2) Means an n-order polynomial Pn (x) that satisfies
Is

[0012]

(Equation 3) It is expressed as The roots of Pn (x) = 0 are x1, x2,.
xn, all the roots are real and single roots, -1 and 1
Between.

The weighting coefficient wi in the equation (1) is

[0014]

(Equation 4) It is represented by

Equation (1) is obtained as follows. That is, f (x), which is a polynomial of degree 2n-1 or less, is expressed as Pn
Divide by (x) and f (x) = Pn (x) Q (x) + φ
(X), both the quotient Q (x) and the remainder φ (x) are n−
Because it is less than primary

[0016]

(Equation 5) Becomes Furthermore, φ (x) is

[0017]

(Equation 6) Since φ (xi) = f (xi), equation (1) is obtained.

The above Legend when n = 2, 3, 4
The roots of the spherical function Pn (x) = 0 of re and the real values of the weighting coefficients are as shown in the following table.

[0019]

[Table 1] For the Legendre's spherical functions and Gauss's numerical integration, see "Analysis Overview" (Sadaharu Takagi, Third Edition, Light Edition, September 27, 1983, published by Iwanami Shoten Co., Ltd.,
Pp. 119-129).

Since the flow velocity distribution at a certain water depth is considered to be a 2n-1 order function of the horizontal position x,
The area of the flow velocity distribution can be easily obtained by using the Gaussian numerical integration of the equation (1).

Now, at a certain water depth zk, when the horizontal channel width W (zk) is standardized as extending from -1 to 1, and the coordinates are taken in the horizontal direction, Legendre
For the spherical function Pn (x) of Pn (x) = 0,
The flow velocity at a plurality of points x2,... xn is v _zk (x
1), v _zk (x2),... V _zk (xn). By performing the Gaussian numerical integration of the equation (1), the area Azk of the flow velocity distribution becomes

[0022]

(Equation 7) Is calculated. Normally, it is considered that the flow velocity distribution is represented by a low-order function unless the flow is turbulent. Then, when it is estimated that the flow velocity distribution is a function of the third order or less (2n-1 = 3, n = 2), the area of the flow velocity distribution becomes n =
Referring to column 2,

[0023]

(Equation 8) Thus, the area of the flow velocity distribution can be obtained very easily and accurately. However, since the formula of the area of the flow velocity distribution is a case where the pipe width is standardized as 2 (x = −1 to 1), the actual flow velocity distribution is calculated using the pipe width W (zk). Needs to be converted to the area A ′ (zk). That is,

[0024]

(Equation 9) In this manner, the area A ′ (zk) of the flow velocity distribution is obtained at a plurality of water depths.

Next, Gaussian numerical integration is performed over the entire water depth of the area of the flow velocity distribution. That is, since the area A ′ (z) of the flow velocity distribution is also considered to be a 2n−1 order function of the vertical position z, the vertical channel width is changed from −1 to 1
When the coordinates are taken in the up-down direction and standardized as extending over the range, the Legendre's spherical function Pn (z) is expressed as Pn
The flow rate can be obtained using the area of the flow velocity distribution at the water depth at a plurality of points where the root of (z) = 0 (z1,..., Zn). The flow rate Q is

[0026]

(Equation 10) Is calculated. If the area of the flow velocity distribution is also considered to be a function of water depth, it is considered to be a lower-order function.

[0027]

[Equation 11] The flow rate can be obtained very easily and accurately. However, since the above equation of flow rate is a case where the pipe width in the vertical direction is standardized as 2 (x = −1 to 1), it is converted to the actual flow rate Q using the pipe width H. There is a need. That is,

[0028]

(Equation 12) Can be obtained by

As the flow velocity measuring unit for measuring the flow velocity, any means can be used. Preferably, the ultrasonic pulse is transmitted in a direction at an angle to the flow of the fluid, and the particles flowing through the fluid are preferably used. A plurality of pulsed Doppler ultrasonic flow sensors that receive the reflected waves reflected by the sensor can be used. By setting the transmission direction of the ultrasonic pulse from each flow rate sensor to a predetermined direction and receiving a reception signal from a predetermined direction after a predetermined time has elapsed from the transmission, it is possible to measure the flow velocity at an arbitrary measurement point. . Therefore, Legendre's spherical function Pn (x) = 0
Can be measured at any point that is the root of the flow rate.

Optionally, the transmission direction of the ultrasonic pulse from each of the flow velocity sensors can be set in the direction of the center point in the cross-section projected in the conduit, and a plurality of points having a point-symmetric relationship with respect to the center point can be set. Measurement points can be measured.

Optionally, when the projected cross section in the conduit has a shape symmetrical with respect to a predetermined axis of symmetry,
The plurality of flow sensors may be arranged symmetrically with respect to the axis of symmetry or may be arranged on the axis of symmetry.

The Legendre's spherical function Pn
The plurality of points that are roots of Pn (x) = 0 with respect to (x) include not only points that exactly match the roots of Pn (x) = 0 with respect to the Legendre spherical function Pn (x). , And points in the vicinity thereof.

[0033]

Embodiments of the present invention will be described below with reference to the drawings. FIG. 1 is a block diagram illustrating a configuration of a flow meter according to the present invention.

In the figure, a flow meter 10 controls a flow velocity measuring section 14 for measuring a flow velocity at a plurality of measurement points for a fluid 42 flowing in a full state in a conduit 40, and controls the flow velocity measuring section 14. Flow rate calculation / control section 18 for measuring flow rate from output from flow rate measurement section 14, flow rate calculation / control section 18
A display unit 22 connected to the display unit for displaying the flow rate, and an input / output unit 2 connected to the flow rate calculation / control unit 18 for inputting / outputting with the outside
0, a temperature sensor 38 that measures the temperature of the fluid 42 and outputs a measurement signal to the flow rate calculation / control unit 18.

The flow rate measuring section 14 has a flow rate calculating / controlling section 18.
A transmission circuit 30 that outputs a transmission signal in response to a trigger signal for each predetermined time interval T from the transmitter, and receives a transmission signal from the transmission circuit 30 and transmits an ultrasonic pulse toward the fluid at each predetermined interval T, and after transmission, A plurality of flow rate sensors 32 comprising a transceiver for receiving the reflected wave; a multiplexer 33 for switching between the transmission signal and the reception signal and for switching the plurality of flow rate sensors 32; and a reception circuit 34 for amplifying the reception signal from the flow rate sensor 32. And a Doppler shift detection circuit 36 that samples a received signal after a lapse of a predetermined time from transmission and detects a Doppler shift frequency by performing a Fourier transform.

As shown in FIG. 2, the flow rate sensor 32
2 (3) embedded in the hole formed in the pipe wall of the pipe 40
2₀, 32₁) Is located. Now, the cross section of conduit 40
Assuming a shape close to a perfect circle, these two flow velocity
Sensor 32 (32₀, 32₁) Is relative to its symmetric axis
It is arranged symmetrically, and the super sound
Transmit the wave pulse in a predetermined direction and in a predetermined direction
It is set to receive the ultrasonic signal from. This
The predetermined directions are, as shown in FIG.
Ultrasound is emitted toward the center point in the cross section
And one of the ultrasonic sensors 32₀Super from
The direction of sound wave emission is measured point P₀₀, P₁₁Other to pass through
Ultrasonic sensor 32₁The direction of ultrasonic radiation from is the measurement point
P₀₁, P_{1 0}Is set to pass through. Measurement point P
₀₀, P₀₁, P_Ten, P₁₁Is determined as follows
You. The vertical line width of the line 40 ranges from -1 to 1.
When the z coordinate is taken in the vertical direction and standardized as
Fixed point P₀₀, P₀₁Is the water depth z = z₀= -1 / √3 = -0.
577 and its water depth z = −0.577
And the horizontal pipe width shall be from -1 to 1.
When the x coordinate is taken in the horizontal direction₀₀X
The coordinates are at the position of x = 1 / ０．５3 = 0.577, and P₀₁of
The x coordinate is the position of x = -1 / √3 = -0.577
I have. The measurement point P_Ten, P₁₁Is the water depth z = z₁= 1 /
√3 = 0.577 and its water depth z = 0.577
In the above, the width of the pipe in the horizontal direction ranges from -1 to 1.
When the x coordinate is taken in the horizontal direction and normalized as
_TenIs the position of x = 1 / √3 = 0.577,
P₁₁Is the position of x = -1 / √3 = -0.577.
Has become. Now, let the radius of the projected cross section of the conduit 40 be R,
O, P₀₀And P ₀₁To the z axis
And the intersection of the perpendicular and the z-axis is C, and the intersection of the perpendicular and the tube wall
B, the flow rate sensor 32 (32₀, 32₁) And the center point O
When the angle between the connecting line and the x-axis is θ,

[0037]

(Equation 13) Because

[0038]

[Equation 14] Becomes Assuming that BC is 1, CP ₀₀ = 1 / 、 3,

[0039]

(Equation 15) Becomes Therefore, θ is

[0040]

(Equation 16)Becomes Measurement point P₀₀, P₀₁, P_Ten, P₁₁The position of the center
It is symmetrical with respect to the point O, and point symmetrical.
Therefore, two flow velocity cells are symmetrically placed at a position that satisfies θ.
Sensor 32 (32₀, 32₁) By placing
Flow rate sensor 32 ₀At the measurement point P₀₀, P₁₁Measurement of flow velocity
The other flow sensor 32₁At the measurement point P₀₁, P_TenFlow velocity
A measurement can be made. Also, the projection traversal shown in FIG.
On the face, OP₀₀The length of

[0041]

[Equation 17] Since the, the length of the measurement point P ₀₀ from flow sensor 32 ₀ length of R {1- (√5 / 3) } , and the measuring point P ₁₁ from flow sensor 32 ₀ R {1+ (√5 / 3) It becomes｝. However, as shown in FIG. 3, when viewed in a vertical section of the conduit 40, the ultrasonic pulse is directed in a direction at a predetermined angle に 対 し て with respect to the flow of the fluid from each of the flow velocity sensors 32 (32 ₀ , 32 ₁ ). There because the transmitting and receiving surface is set to be transmitted, the length L ₀ of the measuring points P ₀₀ from flow sensors 32 _0, L ₀ = R / sinψ
· {1- (√5 / 3) }, the length L ₁ of the measuring point P ₁₁ from flow sensor 32 _{0, L 1 = R / sinψ ·} {1+ (√5 /
3) It becomes｝. Since it is symmetrical, the flow velocity sensor 32 ₁
The length of the measuring points P ₀₁ from L _0, length of the measurement point P ₁₀ from flow rate sensor 32 ₁ becomes L _1.

[0042] transmits the ultrasonic pulses from the flow sensor 32 _0, 32 _1, receives the reflected wave scattered reflected by particles in the fluid again at the same flow rate sensor 32 _0, 32 _1. Since the received reflected wave undergoes a Doppler shift, the Doppler shift detection circuit 36 Fourier-transforms the received signal to obtain the Doppler shift Δf. Doppler shift Δ
f is the flow velocity of the fluid v, the velocity of ultrasound in the fluid c, when the transmission frequency and f _0,

[0043]

(Equation 18) It is represented by In the receiving circuit 34, by taking the received signal of the flow velocity sensors 32 ₀ after approximately 2L ₀ / c and 2L ₁ / c elapsed time from the transmission of the flow sensor 32 ₀ selectively, Doppler shift Δf at each measurement point ₀₀ , Δf
_Ask for ₁₁ . Similarly, the flow rate sensor 32 ₁ has passed approximately 2L ₀ / c and 2L ₁ / c since the transmission of the flow rate sensor 32 _1.
One of the received signals is selectively taken in, and Doppler shifts Δf ₀₁ and Δf ₁₀ at the respective measurement points are obtained. Thus, the Doppler shifts Δf ₀₀ , Δf ₀₁ , Δf ₁₀ , and Δf ₁₁ of P ₀₀ , P ₀₁ , P ₁₀ , and P ₁₁ at each measurement point are obtained.

The flow rate calculation / control section 18 includes a flow rate measurement section 1
Doppler shift from Δf ₀₀ , Δf ₀₁ , Δf ₁₀ , Δ
and f _11, the data of the temperature from the temperature sensor 38 is captured. The flow rate calculation / control section 18 can be constituted by a microprocessor including a CPU and a memory, and stores these data and obtains the flow rate using these data.

The calculation procedure in the flow rate calculation / control section 18 will be described below.

First, using the equation (8), the flow rate measuring unit 14
Shifts Δf ₀₀ , Δf ₀₁ , Δf ₁₀ , Δf
₁₁ is converted into flow rates v ₀₀ , v ₀₁ , v ₁₀ , v ₁₁ . However,
In the equation (9), since the speed c of the ultrasonic wave in the fluid varies depending on the temperature, the speed c obtained by taking in the temperature from the temperature sensor 38 and correcting the temperature is used.

Next, using the above equation (3), each water depth z
_0, obtains the area of the flow velocity distribution in the z ₁ (see Figure 4 (a)).

[0048]

[Equation 19] The area of the flow velocity distribution obtained in this manner is converted into the area of the actual flow velocity distribution based on the equation (4) using the horizontal pipe width W (z) at each of the water depths z ₀ and z ₁ . I do. Pipe width W (z ₀ ) = W (z ₁ )

[0049]

(Equation 20) Because

[0050]

(Equation 21) Becomes

Further, the flow rate Q can be obtained by adding the areas of the two flow velocity distributions by using the equation (7).

[0052]

(Equation 22) (See FIG. 4B). As described above, according to this embodiment, instead of only one measurement point as in the related art,
In order to measure the flow velocity at a plurality of measurement points, even when the flow velocity distribution is not symmetric, it is possible to cope with the flow velocity distribution, and by using the Gaussian numerical integration, a large number of measurement points in the entire cross section can be obtained. There is no need to measure the flow velocity,
Just by measuring the flow velocity at a limited measurement point, with high accuracy,
And the flow rate can be easily obtained. In addition, the flow velocity sensors are arranged symmetrically, and the flow velocity at a plurality of measurement points can be measured by one flow velocity sensor.

In the above embodiment, a circular pipe is taken as an example. However, the present invention is not limited to this, and the flow rate can be measured similarly even with a non-circular pipe. In the projection cross section in the pipeline, the z axis of the two coordinate axes z and x is in the water level direction (vertical direction), and the x axis is in the pipeline width direction (horizontal direction).
However, the present invention is not limited to this, and arbitrary two-axis coordinates can be taken.

In the above embodiment, the flow velocity distribution is assumed to be a function of the third order or less of the horizontal position x, and the flow velocity at two points is obtained at each water depth. The flow rate Q was determined on the assumption that '(z) is also a function of the third or lower order of the vertical position z, but the present invention is not limited to this. Assuming that the flow velocity distribution and the area A ′ of the flow velocity distribution are functions of the fifth order or lower of x or z, as shown in FIG. 5, the water depth z = 0.775R,
At 0, -0.775R, when the horizontal channel width is normalized to range from -1 to 1, and the coordinates are taken in the horizontal direction, 0.775, 0, -0.775R
Can be measured at the nine measurement points at the position. Thereby, the flow rate can be obtained more accurately. Each of the flow rate sensors 32 is disposed so as to transmit ultrasonic waves toward the center point, and is disposed on an extension line connecting the two measurement points so that the flow velocity at at least two measurement points can be measured. It is arranged symmetrically about the axis and on the x-axis or the z-axis. However, the arrangement of the flow velocity sensor 32 is not limited to the example shown in the figure, and may be arranged so as to be symmetrical about the x-axis.

Further, as shown in FIG. 6, when the flow velocity distribution and the area A 'of the flow velocity distribution are assumed to be a function of 7 or less of x or z, the water depth z = 0.86
In 1R, 0.34R, -0.34R, and -0.861R, when the horizontal channel width is normalized as extending from -1 to 1, and the coordinates are taken in the horizontal direction,
The flow velocity at 16 measurement points at 0.861, 0.34, -0.34, and -0.861 can be measured. Thereby, the flow rate can be obtained more accurately. Each of the flow velocity sensors 32 is arranged to transmit ultrasonic waves toward the center point, and is arranged on an extension line connecting the two measurement points so that the flow velocity at at least two measurement points can be measured. They are arranged so as to be line-symmetric with respect to the coordinate axes.

As described above, it is possible to increase the number of the flow velocity sensors 32 in order to sequentially increase the order. Incidentally, the flow velocity distribution and the area A ′ of the flow velocity distribution are 2n.
Assuming that the function is a function of -1 order or less, the number of measurement points is n ² , and 2 ^{n -1} flow rate sensors may be prepared.

In each of the above embodiments, the flow rate sensor 32 is set so that its transmitting / receiving surface is directed to the center of the projected cross section in the conduit, so that the angular position θ of each flow rate sensor 32 is given by the following equation (8). Similarly, the distance from the flow velocity sensor 32 to the measurement point can be easily obtained by the geometric calculation, and the setting thereof can be simplified. Further, since each flow rate sensor 32 measures the flow rate at at least two or more measurement points, the number of the flow rate sensors can be reduced,
It can be realized at low cost.

[0058]

As described above, according to the first aspect of the present invention,
According to the inventions described in (7), since the flow rate is measured by measuring the flow velocity at discrete measurement points and performing a Gaussian numerical integration to obtain the flow rate, the flow rate distribution can be accurately measured at a small number of measurement points even if the flow velocity distribution is not symmetric. Can be calculated. Since the number of measurement points may be limited, measurement and calculation can be simplified.

According to the third aspect of the present invention, the flow velocity at an arbitrary measurement point can be measured by using the pulse Doppler ultrasonic flow velocity sensor.

According to the fourth aspect of the present invention, in order to cause the pulse Doppler type ultrasonic flow velocity sensor to transmit an ultrasonic wave toward the center point in the cross section projected in the pipeline,
The installation position can be easily determined.

According to the fifth aspect of the present invention, the number of sensors is reduced and the cost is reduced by arranging the pulse Doppler type ultrasonic flow velocity sensor symmetrically or on the axis of symmetry. be able to.

[Brief description of the drawings]

FIG. 1 is a block diagram illustrating a configuration of a flow meter according to the present invention.

FIG. 2 is an explanatory diagram showing a relationship between a flow velocity measuring point and a flow velocity sensor as viewed from a projected cross section of a pipeline.

FIG. 3 is an explanatory diagram showing flow velocity measurement points viewed from a vertical section of a pipeline.

FIG. 4A shows a flow velocity distribution at each water depth,
(B) is an explanatory view showing the area of the flow velocity distribution with respect to the water depth.

FIG. 5 is an explanatory diagram showing a relationship between a flow velocity measurement point and a flow velocity sensor as viewed from a projected cross section of a pipeline when an order (n = 3) is increased.

FIG. 6 is an explanatory diagram showing a relationship between a flow velocity measuring point and a flow velocity sensor as viewed from a projected cross section of a pipeline when an order (n = 4) is increased.

[Explanation of symbols]

 Reference Signs List 10 Flow meter 14 Flow velocity measuring section 18 Flow rate computing / controlling section (flow velocity computing section) 32 Flow velocity sensor 40 Pipe line 42 Fluid

 ────────────────────────────────────────────────── ─── Continuing on the front page (72) Inventor Masahito Sekine 2-16-46 Minami Kamata, Ota-ku, Tokyo F-term in Tokimec Co., Ltd. (Reference) 2F030 CA10 CD15 CE04 CE22 2F035 DA12

Claims (7)

[Claims] 1. A flow meter for measuring a flow rate of a fluid flowing through a pipe in a fully-filled state, wherein two orthogonal coordinate axes (x-axis,
When taking the (z-axis), the pipeline width is normalized in the direction of one coordinate axis (z-axis) as extending from -1 to 1, and the coordinates are taken in the one coordinate axis (z-axis) direction. Leg
a plurality of one coordinate axes (z-axis) that are roots (z1,... zn) of Pn (z) = 0 with respect to the spherical function Pn (z) of ndr
In the upper point (z1,... Zn), each point (z1,.
In n), the conduit width in the direction of the other coordinate axis (x-axis) is normalized as extending from -1 to 1 in the direction of the other coordinate axis (x-axis), and the coordinates are taken in the direction of the other coordinate axis (x-axis). Sometimes P for the Legendre sphere function Pn (x)
a flow velocity measurement unit that measures the flow velocity of a plurality of points that are roots (x1,..., xn) of n (x) = 0, and the other at each point (z1,... zn) on the one coordinate axis (z-axis) Gaussian numerical integration is performed from the pipe width in the coordinate axis (x-axis) direction and the flow velocity at a plurality of points measured by the flow velocity measuring unit to calculate the area of the flow velocity distribution, and the area of the flow velocity distribution is further integrated by the Gaussian numerical integration. And a flow rate calculation unit that calculates the flow rate of the entire pipeline. 2. A flow meter for measuring a flow rate of a fluid flowing through a pipe in a fully-filled state.
When the coordinates are normalized in the range from 1 to 1 and the coordinates are taken in the up-down direction, at a plurality of water depths that are roots (z1,... Zn) of Pn (z) = 0 with respect to the Legendre spherical function Pn (z). , The horizontal width of the pipeline at each water depth is -1
When the coordinates are taken in the horizontal direction, normalized to the range from to 1, the flow velocity of a plurality of points that are roots (x1,... Xn) of Pn (x) = 0 with respect to the Legendre spherical function Pn (x) Flow velocity measurement unit to measure the, from the horizontal pipeline width at each water depth and the flow velocity at a plurality of points measured by the flow velocity measurement unit, calculate the area of the flow velocity distribution at each water depth by performing Gaussian numerical integration, A flowmeter comprising: a flow rate calculation unit that calculates the flow rate of the entire pipeline by performing a Gaussian numerical integration on the area of the flow velocity distribution at the water depth. 3. The flow velocity measuring unit transmits an ultrasonic pulse in a direction at an angle to a flow of a fluid, and receives a reflected wave reflected by particles flowing in the fluid.
3. The flow meter according to claim 1, further comprising a plurality of pulse Doppler ultrasonic flow sensors. 4. Each pulse Doppler ultrasonic flow velocity sensor transmits an ultrasonic wave toward a center point in a projection cross section in a pipe, and a plurality of measurement points having a point symmetric relationship with respect to the center point. The flowmeter according to claim 3, wherein the flow rate is measured. 5. The projection cross-section in the conduit has a line-symmetric shape with respect to a predetermined axis of symmetry, and the plurality of pulse Doppler ultrasonic flow sensors are symmetrically arranged with respect to the axis of symmetry. 5. The flow meter according to claim 3, wherein the flow meter is arranged on the axis of symmetry. 6. A flow measuring method for measuring a flow rate of a fluid flowing in a full state in a pipe, wherein two orthogonal coordinate axes (x axis,
When taking the (z-axis), the pipeline width is normalized in the direction of one coordinate axis (z-axis) as extending from -1 to 1, and the coordinates are taken in the one coordinate axis (z-axis) direction. Leg
a plurality of one coordinate axes (z-axis) that are roots (z1,... zn) of Pn (z) = 0 with respect to the spherical function Pn (z) of ndr
In the upper point (z1,... Zn), each point (z1,.
In n), the conduit width in the direction of the other coordinate axis (x-axis) is normalized as extending from -1 to 1 in the direction of the other coordinate axis (x-axis), and the coordinates are taken in the direction of the other coordinate axis (x-axis). Sometimes P for the Legendre sphere function Pn (x)
The flow velocity at a plurality of points that are roots (x1,... xn) of n (x) = 0 is measured, and the other coordinate axis (x-axis) at each point (z1,... zn) on the one coordinate axis (z-axis) ) From the pipeline width in the direction and the flow velocity at multiple points measured by the flow velocity measurement part, the area of the flow velocity distribution is calculated by performing Gaussian numerical integration, and the area of the flow velocity distribution is further subjected to the Gaussian numerical integration. , Calculate the flow rate of the entire pipeline, flow rate measurement method. 7. A flow rate measuring method for measuring a flow rate of a fluid flowing in a pipe in a fully-filled state, wherein a pipe width is reduced in a vertical direction in a projected cross section in the pipe.
When the coordinates are normalized in the range from 1 to 1 and the coordinates are taken in the up-down direction, at a plurality of water depths that are roots (z1,... Zn) of Pn (z) = 0 with respect to the Legendre spherical function Pn (z). , The horizontal width of the pipeline at each water depth is -1
When the coordinates are taken in the horizontal direction, normalized to the range from to 1, the flow velocity of a plurality of points that are roots (x1,... Xn) of Pn (x) = 0 with respect to the Legendre spherical function Pn (x) From the horizontal pipe width at each water depth and the flow velocity at a plurality of points measured by the flow velocity measurement unit, calculate the area of the flow velocity distribution at each water depth by performing Gaussian numerical integration, and calculate the flow velocity distribution at each water depth. A flow rate measurement method that calculates the flow rate of the entire pipe line by further performing Gaussian numerical integration on the area of the pipe.