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DESCRIPTION JP2006030041

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DESCRIPTION JP2006030041
The present invention provides an ultrasonic flow velocity distribution meter capable of
measuring the flow velocity and flow rate of a fluid with high accuracy by appropriately selecting
the transmission frequency of ultrasonic waves and the incident angle to a pipe. SOLUTION: An
ultrasonic wave is incident on a fluid to be measured in a pipe from an ultrasonic transducer
installed outside the pipe, and the frequency of the ultrasonic wave reflected by a reflector
present in the fluid to be measured changes by the Doppler effect A clamp-on type Doppler
ultrasonic flow velocity distribution meter that measures the flow velocity distribution of the
fluid to be measured by using the ultrasonic flow velocity generated by interposing an acoustic
wave propagating wedge between the ultrasonic transducer and the tube body It relates to a
distribution meter. The critical angle is the refraction angle in piping of each mode of Lamb wave,
which is calculated from the incident angle of ultrasonic waves incident on the pipe from the
weir and the speed of sound at the weir, the speed of sound of transverse and longitudinal waves
in the pipe, and the plate thickness of the pipe. Avoid the frequency and select the ultrasound
transmission frequency. [Selected figure] Figure 5
Clamp-on type Doppler ultrasonic flowmeter
[0001]
The present invention is a clamp-on in which ultrasonic waves are incident on a fluid to be
measured inside a pipe from an ultrasonic transducer installed outside the pipe, and the flow
velocity distribution of the fluid to be measured is measured without contact using the Doppler
effect. Type Doppler ultrasonic flow velocity distribution meter.
[0002]
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1
As is well known, the clamp-on type Doppler ultrasonic flow velocity distribution meter assumes
that floating particles and bubbles contained in the fluid to be measured in the pipe move at the
same speed as the fluid, so that the moving velocity of the floating particles etc. The flow velocity
distribution and flow rate of the fluid to be measured are measured.
That is, as shown in FIG. 14, the ultrasonic transducer 11 is fixed to the outer peripheral surface
of the pipe 21 through the sound wave transmitting wedge 31 so as to be inclined with respect
to the pipe 21. When a pulse is transmitted, the frequency of the echo wave reflected by the
reflector 23 such as floating particles changes according to the moving velocity (flow velocity of
the fluid) of the reflector 23 by the Doppler effect. The Doppler shift frequency fd of the echo
wave in this case is expressed by Equation 1. [Formula 1] fd = (2Vfsin θff0) / Cf where Vf is the
flow velocity of fluid 22, θf is the refraction angle of ultrasonic waves at the interface between
pipe 21 and fluid 22, and Cf is fluid 22 It is the speed of sound.
[0003]
Therefore, the flow velocity Vf of the fluid 22 can be obtained by Equation 2. Since the flow
velocity Vf and the Doppler shift frequency fd are functions of the position x along the radial
direction of the pipe 21, they are represented as Vf (x) and fd (x), respectively. Vf (x) = (Cf · fd (x))
/ (2 · sin θf · f0) FIG. 15 illustrates the main part of FIG. 14 and the flow velocity distribution
according to the position x in the pipe 21. FIG. The flow velocity Vf on the measurement line ML
of the ultrasonic pulse is measured at predetermined intervals by the above equation 2 to obtain
the flow velocity distribution, and this is integrated with respect to the cross sectional area A of
the pipe 21 as shown in equation 3 to obtain The flow rate Q is determined. [Equation 3] Q =
∫Vf · dA
[0004]
Next, FIG. 16 is a diagram showing the entire configuration of the clamp-on type Doppler
ultrasonic flow velocity distribution meter (the internal configuration of the ultrasonic transducer
11 and the transducer 18 connected thereto). For example, Patent Document 1 described later It
is substantially identical to the Doppler ultrasonic flowmeter described in. In FIG. 16, a
transmission / reception timing control unit 12 controls transmission / reception timings of
ultrasonic pulses and echo waves, and a transmission pulse 13 generates an ultrasonic pulse
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2
which is activated by the transmission / reception timing control unit 12 and transmitted from
the ultrasonic transducer 11. 14 is a received signal amplification control unit for amplifying an
echo wave received by the ultrasonic transducer 11, 15 is an A / D conversion unit for
performing analog / digital conversion according to the sampling clock from the transmission /
reception timing control unit 12, and 16 is the aforementioned A flow velocity distribution
calculating unit for obtaining a flow velocity distribution by the calculation of Equation 2 and a
flow rate calculating unit 17 for calculating the flow volume by the calculation of Equation 3
described above.
[0005]
Unexamined-Japanese-Patent No. 2000-97742 (FIG. 1)
[0006]
Now, according to the principle described above, it is possible to accurately obtain the flow
velocity Vf and the flow rate Q of the fluid 22 without depending on the transmission frequency
f0 of the ultrasonic pulse by the calculation of Equation 2 and Equation 3. .
However, the inventor found that the flow velocity Vf and the flow rate Q change when the
transmission frequency f0 of the ultrasonic waves is different, and particularly when the pipe 21
is made of thin metal, this frequency dependency becomes remarkable, and the plastic We found
that in piping, the frequency dependency was small.
[0007]
The applicant of the present invention, as Japanese Patent Application No. 2003-396755, when
the sound velocity of the shear wave of the ultrasonic wave propagating in the pipe is equal to or
higher than the sound velocity of the longitudinal wave at the weir (when mainly metal pipe is
used), The ultrasonic transducer is inclined and fixed to the crucible so that only the transverse
wave propagates in the piping with the incident angle of the ultrasonic wave incident on the
piping from the crucible above the critical angle of the longitudinal wave in the piping and below
the critical angle of the transverse wave. We have already filed an application for sound velocity
distribution. According to this flow velocity distribution meter, the echo wave from the reflector
in the fluid to be measured is only due to the transverse wave in the pipe, and the ultrasonic
transducer does not receive the echo wave due to the longitudinal wave, and the acoustic noise is
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3
reduced. However, the frequency dependence of the flow velocity Vf and the flow rate Q
described above is still unsolved.
[0008]
Therefore, the problem to be solved by the present invention is a clamp-on type in which the
frequency dependency is small and the flow velocity and flow rate of the fluid can be measured
with high accuracy by appropriately selecting the transmission frequency of ultrasonic waves
and the incident angle to piping. An object of the present invention is to provide a Doppler
ultrasonic flow velocity distribution meter.
[0009]
In order to solve the above-mentioned subject, in the invention described in Claim 1, an
ultrasonic wave is entered from the ultrasonic transducer installed in the outside of piping to the
fluid to be measured inside piping, and it reflects by the reflector which exists in the fluid to be
measured A clamp-on type Doppler ultrasonic flow velocity distribution meter that measures the
flow velocity distribution of a fluid to be measured by using the change in the frequency of the
ultrasonic waves due to the Doppler effect, and between the ultrasonic transducer and the tube
body In a clamp-on type Doppler ultrasonic flow velocity distribution meter having a sound wave
propagating wedge, the incident angle of ultrasonic waves entering the pipe from the weir and
the speed of sound at the weir, the speed of sound of the transverse wave and the longitudinal
wave in the pipe, and the plate of the pipe The transmission frequency of the ultrasonic wave is
selected by avoiding the frequency at which the refraction angle in piping of each mode of the
Lamb wave is calculated from the thickness and the critical angle.
[0010]
The invention according to claim 2 is the clamp-on type Doppler ultrasonic flow velocity
distribution meter, wherein the incident angle of the ultrasonic wave incident on the pipe from
the weir and the speed of sound in the weir, the speed of sound of the transverse and
longitudinal waves in the pipe and the thickness of the pipe The transmission frequency of the
ultrasonic wave is selected from the intermediate frequency of the two frequencies at which the
refraction angle in the two continuous mode piping of the Lamb wave becomes a critical angle,
calculated from and.
[0011]
The invention according to claim 3 is the clamp-on type Doppler ultrasonic flow velocity
distribution meter, wherein the incident angle of the ultrasonic wave incident on the pipe from
the weir and the speed of sound in the weir, the speed of sound of transverse and longitudinal
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4
waves in the pipe and the thickness of the pipe The transmission frequency of the ultrasonic
wave is selected from frequencies lower than the frequency at which the angle of refraction in
the piping of the primary mode of the antisymmetric Lamb wave is calculated from
[0012]
The invention described in claim 4 is a clamp-on type Doppler ultrasonic flow velocity
distribution meter, which is calculated from the transmission frequency of ultrasonic waves and
the speed of sound in a weir, the speed of sound of transverse and longitudinal waves in piping,
and the thickness of piping. An ultrasonic wave is made to enter the pipe from the crucible at an
incident angle larger than the incident angle at which the refraction angle in the piping of the
first-order mode of the antisymmetric Lamb wave is a critical angle.
[0013]
The invention according to claim 5 is the clamp-on type Doppler ultrasonic flow velocity
distribution meter, which selects the transmission frequency of the ultrasonic wave from
frequencies lower than the cutoff frequency of the first-order mode of the antisymmetric Lamb
wave determined from the dispersion curve. It is a thing.
[0014]
The invention described in claim 6 uses the asymptotic solution in any one of claims 1 to 5 as a
phase velocity of a Lamb wave for determining a transmission frequency or an incident angle.
[0015]
In the invention described in claim 7, the ultrasonic transducer is attached to the reference pipe
in any one of claims 1 to 6, and the reference flow rate of the fluid flowing through the reference
pipe is measured without using the ultrasonic transducer; The ratio of the flow rate according to
the flow velocity distribution measured using an ultrasonic transducer to the reference flow rate
is used as an actual flow calibration constant, and the flow measurement value is calibrated using
this actual flow calibration constant.
[0016]
The invention described in claim 8 is the one according to claim 7, wherein the actual flow
calibration constant is held as a calibration constant for each ultrasonic transducer.
[0017]
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The invention described in claim 9 is that, in any one of claims 1 to 8, the measurement error
due to the Lamb wave is calculated, and the measurement value is corrected based on the
calculation result.
[0018]
According to the present invention, by appropriately selecting the transmission frequency of
ultrasonic waves and the incident angle to the pipe, the frequency dependency of the
measurement value caused by the Lamb wave is reduced, and the clamp on with a measurement
error near the minimum value. Type Doppler ultrasonic flow velocity distribution meter can be
realized.
In addition, real-flow calibration of ultrasonic transducers can cancel offset errors and ensure
mutual compatibility of the transducers, and can maintain high accuracy even when the
combination with transducers is changed.
[0019]
Hereinafter, embodiments of the present invention will be described with reference to the
drawings.
First, according to the study of the inventors, the above-described frequency dependency occurs
because a dispersion phenomenon (a phenomenon in which the speed of sound changes with
frequency) occurs in the pipe, and this dispersion phenomenon is the same as the pipe When
considered as a plate having a thickness, it is considered that the plate is caused by a plate wave
propagating as a waveguide.
Here, a plate wave refers to a sound wave propagating along a flat plate having a finite thickness
which has a specific frequency and wavelength satisfying a boundary condition and which
extends infinitely, and the generation thereof depends on the material and thickness of the plate.
Dependent.
[0020]
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6
There are SH-waves (horizontally-polarized shear waves) and lamb waves in plate waves.
Here, as well known, Lamb waves mean waves in which vertically-polarized shear waves of
vertical waves and shear waves are coupled to each other while performing mode conversion on
the upper surface of a flat plate.
Of the plate waves, SH waves are considered not to propagate in the fluid because they do not
excite longitudinal waves at the interface with the liquid.
Therefore, it is the Lamb wave that causes the dispersion phenomenon, and the behavior of this
Lamb wave is considered to be the cause of the above-described frequency dependence.
[0021]
1 and 2 show dispersion models of Lamb waves when ultrasonic waves are obliquely incident on
a plate (pipe), and FIG. 1 shows that the incident angle θw to the pipe is θw ≦ (the longitudinal
wave in the pipe In the case of the critical angle), FIG. 2 shows the case of (critical angle of
longitudinal wave in piping) ≦ θw ≦ (critical angle of transverse wave in piping).
According to the inventor's examination, when ultrasonic waves enter the pipe from the weir, due
to the difference in phase velocity (= ω / k, ω: angular frequency, k: wave number), a plurality of
pipes in the pipe with a constant frequency It is considered that Lamb waves are excited, and as
shown in FIG. 1, if θw ≦ (critical angle of longitudinal waves in piping), wavelengths determined
by eigen equations described later besides L waves (longitudinal waves) and SV waves One of the
antisymmetric Lamb wave mode Am and the symmetric Lamb wave mode Sm (m is a continuous
order or mode according to the difference in wavelength, m = 0, 1, 2,...) The part enters the fluid.
Also, as shown in FIG. 2, if (critical angle of longitudinal wave in the pipe) ≦ θw ≦ (critical
angle of transverse wave in the pipe), modes Am and Sm are similarly excited in addition to the
SV wave and one of them is The part will be incident on the fluid.
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7
[0022]
Here, according to Reference 1 ("Ultrasonic Handbook", edited by the Ultrasonic Handbook
Editing Committee, published by Maruzen Co., Ltd., p. 63 to p. 65), the Eigen equation (frequency
equation) of Lamb waves is Formula 7 is expressed.
[Formula 4] β1 <2> = (− β2) <2> = (ω / Vl) <2> −k <2> [Formula 5] β3 <2> = (− β4) <2> =
(ω / Vs) <2> -k <2> [Formula 6] tan (β1d / 2) / tan (β3d / 2) = − (k <2> −β3 <2>) <2> / (4k
<2> β1β3 ): In the case of symmetric mode [Formula 7] tan (β3d / 2) / tan (β1d / 2) = − (k
<2> −β3 <2>) <2> / (4k <2> β1β3): antisymmetric In the case of mode, in Equations 4 to 7,
β1 to β4 are propagation constants in the plate thickness direction, d is the plate thickness, ω
is the angular frequency, V1 is the velocity of longitudinal waves, Vs is the velocity of shear
waves, and k is the wave number.
[0023]
With the above-mentioned eigen equation, the relationship between the frequency and the
wavelength can be calculated for each mode m (mth order) of the symmetric Lamb wave and the
antisymmetric Lamb wave.
Further, the phase velocity Vp and the group velocity Vg (generally Vg ≠ Vp, which is the actual
propagation velocity of the wave packet, and Vg = Vp if there is no dispersion phenomenon) can
be obtained by Equations 8 and 9. Vp = ω / k Equation 9 Vg = ∂ω / ∂k Further, from the
above-mentioned phase velocity Vp and Snell's law, it is possible to calculate the refraction angle
θp in piping of each mode of Lamb wave.
[0024]
FIG. 3 is an example of a Lamb wave dispersion curve (ω-k dispersion curve) obtained by solving
the above-mentioned characteristic equation. The solid line is the dispersion curve of the
antisymmetric Lamb wave mode Am, and the broken line is the dispersion curve of the
symmetric Lamb wave mode Sm. The horizontal axis in FIG. 3 corresponds to the wave number
of the ultrasonic wave, and the vertical axis corresponds to the transmission frequency of the
ultrasonic wave, and the mode of the Lamb wave generated at a certain transmission frequency,
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8
pipe thickness and pipe sound speed is the corresponding vertical axis The mode of the
dispersion curve intersects the horizontal line orthogonal to the value of. However, the mode
actually generated is limited to the case where the critical angle determined by the sound
velocity in the pipe and the phase velocity of each mode is larger than the incident angle θw to
the pipe.
[0025]
The exact solution of the frequency and wavelength of each mode of Lamb wave can be obtained
by solving the above-mentioned eigen equation, but when the product kd of wave number and
plate thickness is large, it is practically substituted by asymptotic solution This can simplify the
calculation. That is, with respect to the phase velocity Vp, in the case of the zero-order mode (m =
0), the phase velocity Vp of the Rayleigh wave (Rayleigh wave) is asymptotically approximated as
shown in Equation 10, and the higher order modes (m = 1, 2,. In the case of ...), it is
asymptotically close to the solution (the velocity of sound Vs of the transverse wave) of the eigen
equation of the transverse wave of the corresponding mode as shown in Formula 11. [Equation
10] Vp <(A0)> = Vp <(S0)> = VR (m = 0) [Equation 11] Vp <(Am)> = ω / {(ω / Vs) <2>-(2mπ / d)
<2>} <1/2> Vp <(Sm)> = ω / {(ω / Vs) <2>-((2m + 1) π / d) <2>} <1/2> (m = 1, 2, ......) In
Equation 11, superscript Am and Sm respectively indicate the mode m of the antisymmetric
Lamb wave and the symmetric Lamb wave.
[0026]
Further, since there is an approximate solution for the phase velocity of the Rayleigh wave, when
applying the above equation 10, it is possible to simplify the calculation practically by
substituting the approximate solution. In Reference 2 (Natsushi, K. et al., “Ultrasonic
Technology”, published by The University of Tokyo Press, pp. 173 to p. 174), the exact solution
of the phase velocity VR of the Rayleigh wave is given by L = {1- (VR) It is described that it can be
determined as a solution of Expression 12 by setting / Vl) <2>} <1/2>, S = {1- (VR / Vs) <2>}
<1/2>, and further It is described that an approximate solution is expressed by Equation 13 when
the Poisson's ratio is σ. [Expression 12] 4 LS− (1 + S <2>) <2> = 0 [Expression 13] VR = Vs
(0.87 + 1.12σ) / (1 + σ)
[0027]
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9
Next, in the structure including the ultrasonic transducer 11, the crucible 31 and the stainless
steel pipe 21 as shown in FIG. 4, the critical angle of the shear wave is larger than the critical
angle of the longitudinal wave in the pipe 21. The relationship between the transmission
frequency of the ultrasonic wave and the refraction angle θp in the pipe 21 in each mode of the
lamb wave when it is set as follows (corresponding to the above-mentioned FIG. 2) is asymptotic
of the phase velocity shown in Equations 10 and 11. It calculated by Numerical formula 14 and
15 using a solution and Snell's law. [Equation 14] θp <(Am)> = sin <−1> (Vp <(Am)> / Cw · sin
θw) θp <(Sm)> = sin <−1> (Vp <(Sm)> / Cw · sin θw) In Equation 14, Cw is the speed of sound
at 楔 31. FIG. 5 is a graph showing the relationship between the transmission frequency and the
refraction angle θp according to the above calculation.
[0028]
Further, the same pipe 21 was used to measure the relationship between the transmission
frequency and the flow rate measurement error. The results are shown in FIG. According to FIG.
5 and FIG. 6, the frequency fcritical near the frequency at which the refraction angle θp of the
mode with a Lamb wave (eg A2, S1) reaches the critical angle (θp <(Am)>, θp <(Sm)> = 90 &
deg;) It can be seen that the measurement error is at a maximum. Here, the frequency fcritical
can be obtained by the following equation 15. This equation 15 substitutes θp <(Am)>, θp
<(Sm)> = 90 & deg., And Vp <(Am)>, Vp <(Sm)> in equation 11 into Eq. It is the one I understood
about). Fcritical <(Am)> = m / {(1 / Vs) <2> − (sin θw / Cw) <2>} <1/2> / d (m = 1, 2,...) Fcritical
<(Sm)> = (2m + 1) / {(1 / Vs) <2>-(sin θw / Cw) <2>} <1/2> / d / 2 (m = 1, 2,...)
[0029]
Therefore, it is possible to prevent the measurement error of the flow rate from becoming near
the maximum by selecting the transmission frequency of the ultrasonic wave avoiding the abovementioned frequency fcritical. The selection frequency (Set frequency) in FIGS. 5 and 6 indicates
the middle of the frequency at which the refraction angle θp of the Lamb waves A2 and S1
reaches the critical angle. Since there is a frequency at which the measurement error is near the
minimum between the frequency at which the refraction angle θp of two successive modes A2
and S1 of the Lamb wave reaches the critical angle in this way, select this frequency as the
transmission frequency By this, it is possible to make the measurement error be near the local
minimum while avoiding the local maximum.
[0030]
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10
In each mode of the Lamb wave, there is a difference in time τ for propagating through the pipe
due to the difference in the refraction angle θp in the pipe and the difference in the group
velocity Vg due to the difference in the phase velocity. Here, the group velocity Vg according to
the asymptotic solution of each mode of Lamb waves is shown in Expression 16. Further, the
propagation time τ of the Lamb wave in the pipe differs depending on the group velocity Vg as
shown in Formula 17. [Expression 16] Vg <(A0)> = Vg <(S0)> = VR Vg <(Am)> = Vs <2> / Vp
<(Am)> Vg <(Sm)> = Vs <2> / Vp <(Sm)> [Expression 17] τ <(Am)> = d / cos θp <(Am)> / Vg
<(Am)> τ <(Sm)> = d / cos θp <(Sm)> / Vg <( Sm)>
[0031]
For this reason, the flow velocity distribution by the other Lamb waves (interference waves)
overlaps the flow velocity distribution obtained by the ultrasonic wave (for example, the SV wave
of the transverse wave or the L wave of the longitudinal wave) in the original principle formula.
Therefore, this causes a flow measurement error. Formula 18 shows propagation time T in the
fluid of Lamb waves (under water), and D is an inner diameter of piping. Due to the propagation
time T and the propagation time τ in the pipe, a positional deviation along the radial direction is
generated as shown in Formula 19. [Expression 18] T = D / cos θf / Vf [Expression 19] r <(Am)>
/ R = 2 (τ <(Am)> − τ <(Vs)>) / T r <(Sm)> / R Where R is the radius (= D / 2) of the inner
diameter D of the pipe, and r is the distance from the center along the radius R (= 2 (τ <(Sm)>-τ
<(Vs)>) / T It is r <= R).
[0032]
FIG. 7 shows the velocity profile of the measured water flow velocity for each of the Lamb wave
modes A0 to A2, S0, S1 and the shear wave SV (Vs), and the horizontal axis represents the radial
direction of the pipe. The position is shown, and the vertical axis shows the measured value of
the flow velocity. In addition, the average flow velocity of water is 2 m / s. According to FIG. 7,
the velocity profile differs depending on each of the modes A0 to A2, S0 and S1, and a positional
deviation in the radial direction occurs for the same flow velocity, which causes the measurement
error. Recognize. Further, FIG. 8 is a result of calculating the flow rate error using the same
model, and the error is maximized near the frequency fcritical of the critical angle (about 1.4
MHz and about 1.9 MHz). Equation 20 is a equation for calculating the turbulent velocity
distribution for obtaining the velocity profile of FIG. 7, and Equation 21 is an equation for
obtaining the flow rate error of FIG. Here, FIG. 8 is a simple average of errors of all modes of
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11
Lamb waves. [Equation 20] V (r) = Vmax {1- (r−r <(Am)>) / R} <1 / n> or V (r) = Vmax {1− (r−r
<(Sm) ()>) / R} <1 / n> n = 2.1logRe−1.9 Re = VavD / ν (Re: Reynolds number, Vmax: maximum
flow velocity, Vav: average flow velocity, :: kinematic viscosity coefficient) [Expression 21] ΔQ
<(Am)> / Q0 = {(2n + 1) / n)} {2r <(Am)> / R− (r <(Am)> / R) <1 + 1 / n>} + (1−r < (Am)> / R) <2
+ 1 / n>-(r <(Am)> / R) <2 + 1 / n> -1 ΔQ <(Sm)> / Q0 = {(2n + 1) / n)} {2r < (Sm)> / R- (r <(Sm)>
/ R) <1 + 1 / n>} + (1-r <(Sm)> / R) <2 + 1 / n>-(r <(Sm)> / R) <2 + 1 / n> -1 ΔQ / Q0 = Σ (ΔQ
<(Am)> + ΔQ <(Sm)>) / Q0 / N (N: number of modes)
[0033]
Also, by using three types of stainless steel pipes having different thicknesses, as in the modes
A1 and S1 of the above-described lamb waves, substantially the frequencies at which the
refraction angles θp of the lamb waves of two continuous modes reach a critical angle An
intermediate frequency was selected as the transmission frequency, and the relationship between
the plate thickness and the flow rate error was measured. The results are shown in FIG. In FIG. 9,
1.9 MHz, 1.6 MHz and 1.8 MHz are selected transmission frequencies, which correspond to the
board thicknesses d1, d2 and d3, respectively. According to FIG. 9, it is possible to suppress the
measurement error to a small value regardless of the plate thickness of the pipe.
[0034]
In addition to the above, as another method of suppressing the frequency dependency, there is a
method of setting the transmission frequency smaller than the frequency at which the refraction
angle θp of the first-order mode A1 of the antisymmetric Lamb wave reaches the critical angle.
This frequency is a frequency at which the refraction angle θp reaches 90 & deg; (critical angle),
and the mode A1 does not occur below this frequency, and only the zero-order modes A0 and S0
of the SV wave and the Lamb wave occur. The frequency dependence can be significantly
reduced.
[0035]
FIG. 10 is an example in which the frequency at which the refraction angle θp of the Lamb wave
reaches the critical angle when the plate thickness of the pipe is variously changed is calculated
as asymptotic solutions for each mode. As the Lamb wave mode m becomes larger, the frequency
becomes higher, so it can be seen that all modes higher than the first order are not generated if
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the transmission frequency is made smaller than the frequency at which the refraction angle θp
of mode A1 reaches the critical angle. .
[0036]
Further, as another method of suppressing the frequency dependency, the incident angle of the
ultrasonic wave to the pipe may be made larger than the critical angle of the first-order mode A1
of the antisymmetric lamb wave. The phase velocity of the Lamb wave is higher at higher order
and the critical angle is lower at higher order. Therefore, if an ultrasonic wave is incident at an
incident angle larger than the critical angle of the antisymmetric mode A1, the higher order is
The mode does not occur and the frequency dependency can be significantly suppressed.
[0037]
Furthermore, a method is also conceivable in which the transmission frequency is smaller than
the cutoff frequency of the antisymmetric Lamb wave in the first order mode A1. This cutoff
frequency is a frequency at which the phase velocity is infinite and the group velocity is 0 (value
at kd = 0 in FIG. 3, ie, the contact on the vertical axis), and below this frequency, regardless of the
incident angle θw. No, that mode of Lamb wave does not occur. Since the cutoff frequency
becomes higher as the higher order mode, higher order modes are not generated below the
cutoff frequency of mode A1, and the frequency dependency can be largely suppressed
regardless of the incident angle θw.
[0038]
Now, as shown in FIG. 6 and FIG. 8 described above, even when the intermediate frequency of the
frequency at which the refraction angle θp of the two successive modes of Lamb waves reaches
the critical angle is set as the selected frequency, as shown in FIG. Offset error occurs, but this
offset error is canceled by performing an actual flow calibration of the ultrasonic transducer with
the reference piping as described in Japanese Patent Application No. 2004-50998, which is the
prior application of the present applicant. can do. The actual flow calibration described in this
prior application is proposed for the purpose of suppressing the variation of θw and Cw.
[0039]
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FIG. 11 is a block diagram of the actual flow calibration facility in the above prior application,
and FIG. 12 is an explanatory view of the action. This actual flow calibration facility includes a
reference pipe 21A, a reference flow meter 41, a flow control valve 42, and a reference converter
51. , And the reference converter 51 is constituted by the blocks 12 to 17 in FIG. 16 described
above. The reference pipe 21A has an inner peripheral surface machined to have an accurate
cross-sectional area A, and the fluid flowing through the inside is axisymmetric flow fully
developed, so that the straight pipe length is sufficiently smooth. It is finished. Further, the outer
peripheral surface of the reference pipe 21A is smoothed to be parallel to the inner peripheral
surface.
[0040]
Then, by adjusting the opening degree of the flow control valve 42 while observing with the
reference flow meter 41, the flow rate of the fluid flowing inside the reference pipe 21A can be
precisely set or controlled. As the precise control of the fluid flow rate, the reference tank 43 is
used instead of the reference flow meter 41, and the amount of fluid stored per unit time in the
reference tank 43 via the reference flow meter 41 is precisely measured. A method may be used.
[0041]
The ultrasonic transducer 11 is attached to and fixed to the reference pipe 21A, and the
reference converter 51 is connected, and the fluid at a known (true) flow rate Qs precisely set by
the reference flow meter 41 and the flow control valve 42 Flow distribution and flow rate
measurement with the ultrasonic transducer 11 and the reference converter 51, and the actual
flow calibration constant of the ultrasonic transducer 11 based on the flow rate Qf measured at
that time and the known Qs. The measured flow rate is corrected by calculating α = Qs / Qf and
storing the calibration constant α as a constant unique to the transducer 11 in the ultrasonic
flowmeter using the transducer 11. According to this prior application, θf and Cf of the abovementioned equation 2 are replaced by the incident angle θw to the pipe and the sound velocity
Cw of に 従 い according to the Snell's law of equation 22 to become the equation 23.
[Expression 22] Cf / sin θf = Cp / sin θp = Cw / sin θw [Expression 23] Vf (x) = (Cw · fd (x)) / (2
· sin θw · f0)
[0042]
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In the prior application invention described in Japanese Patent Application No. 2004-50998, θw
and Cw are corrected by actual flow calibration in order to make Vf (x) in Expression 23 highly
accurate. On the other hand, in the present invention, not only θw and Cw but also the offset
error described above is corrected by actual flow calibration. Also in the present invention, the
actual flow calibration is performed by comparison with the high-accuracy measurement flow
rate by the reference flow meter 41 (or reference tank 43), and the measurement flow rate by
the reference flow meter 41 is measured by the ultrasonic transducer 11 using Qs. The ratio to
the flow rate Qf based on the calculated flow rate distribution is taken as an actual flow
calibration constant α. At this time, Qs is expressed by Formula 24. [Expression 24] Qs = α · Qf
= C {α (Cw · fd (x)) / (2 · sin θw · f0)} · dA
[0043]
That is, in FIG. 13, the flow rate Qf measured using the ultrasonic transducer 11 and the
transducer 18 is multiplied by the actual flow calibration constant α to obtain the same
measurement value as the flow rate measured with high accuracy by the reference flowmeter 41.
it can. Therefore, even if θw and Cw and the offset errors are not measured one by one,
correction can be performed simultaneously using only one calibration constant α. If this
calibration constant α is attached to the nameplate of each transducer as a constant unique to
the ultrasonic transducer 11, the calibration constant α specific to the transducer 11 is
measured even when the combination of the transducer 11 and the transducer 18 is changed
Since the flow rate of high accuracy can be obtained by multiplying by, the transducers are
compatible with each other.
[0044]
Further, as another correction method of the offset error, the offset error may be corrected with
or without the actual flow calibration using the calculated value of the error shown in FIG.
Furthermore, the difference in the offset error in the case of using a pipe of different material
and thickness from the case of using the reference pipe 21A may be calculated and corrected.
[0045]
In the present invention, as in the prior application Japanese Patent Application No. 2003396755, when the sound velocity of the shear wave of the ultrasonic wave propagating in the
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15
pipe is equal to or higher than the sound velocity of the longitudinal wave in the weir, it enters
the pipe from the weir An ultrasonic flow velocity distribution meter with an ultrasonic
transducer inclined and fixed to a weir so that only the shear wave propagates in the pipe with
the incident angle of the ultrasonic wave above the critical angle of the longitudinal wave in the
pipe and below the critical angle of the transverse wave. It is applicable, and it is possible to
suppress the frequency dependence of the flow velocity and flow rate resulting from Lamb
waves.
[0046]
It is a figure which shows the propagation state of an ultrasonic wave.
It is a figure which shows the propagation state of an ultrasonic wave. It is a figure which shows
the dispersion curve of a Lamb wave. It is a rough block diagram of the flow velocity distribution
meter concerning an embodiment. It is a figure which shows the relationship of the transmission
frequency and refraction angle in each mode of a Lamb wave. It is a figure which shows the
relationship between a transmission frequency and a flow measurement error. It is a figure which
shows the velocity profile in each mode of Lamb wave. It is a figure which shows the relationship
(calculation result) of a transmission frequency and a flow volume error. It is a figure which
shows the relationship between the plate | board thickness of piping, and a flow measurement
error. It is the figure which showed the frequency which reaches the critical angle in each mode
of a Lamb wave for every board thickness of piping (calculated value by asymptotic solution). It
is a block diagram of the actual flow calibration installation in a prior application. It is
explanatory drawing of an effect | action of the actual flow calibration installation in a prior
application. It is a conceptual diagram of real flow calibration in the embodiment of the present
invention. It is explanatory drawing of the principle of operation of a Doppler type ultrasonic
flow velocity distribution meter. It is a figure which shows the principal part of FIG. 14, and flow
velocity distribution. FIG. 1 is an entire configuration diagram of a clamp-on type Doppler
ultrasonic ultrasonic flow velocity distribution meter.
Explanation of sign
[0047]
11: ultrasonic transducer 12: transmission / reception timing control unit 13: transmission pulse
generation unit 14: reception signal amplification control unit 15: A / D conversion unit 16: flow
velocity distribution operation unit 17: flow operation unit 18: converter 21: piping 21A :
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16
Reference piping 22: Fluid 23: Reflector 31: 楔 41: Reference flow meter 42: Flow control valve
43: Reference tank 51: Reference converter ML: Measurement line
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17
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