Abstrict In an ultrasonic flow meter in which an ultrasonic transducer for
transmission and an ultrasonic transducer for reception are arranged
so as not to be opposite to each other, so that the flow rate is
measured from the flow rate dependency of the phase difference of
the ultrasonic wave in the fluid and the distance between said ultrasonic
transducers, (1) the ultrasonic flow meter being provided with an
oscillator wherein the frequency of the ultrasonic wave is controlled
in correspondence with said phase difference in order to make it
possible to measure when the phase difference is not smaller than
0-.pi., and (2) the ultrasonic flow meter also being provided with
an electric circuit to compensate the measurement error due to the
variance of the acoustic velocity of the ultrasonic wave in the
fluid.
Claims What is claimed is:
1. An ultrasonic flowmeter for measuring flow along a fluid flow
path having a center thereof comprising:
first ultrasonic transducer means for emitting an ultrasonic wave
for transmission in the fluid flowing in the path;
second ultrasonic transducer means for receiving said ultrasonic
wave propagated in said fluid along the path and producing a reception
signal indicative thereof, wherein a line drawn between said first
and second transducer means does not cross directly through the
center of said fluid flow path;
transmission oscillator means for generating a drive signal to
drive said first ultrasonic transducer means for transmission;
first counter means for frequency dividing said drive signal generated
by said transmission oscillator means;
second counter means synchronized with said transmission oscillator
for frequency dividing the reception signal received by said second
ultrasonic transducer means to develop an output signal thereof;
phase difference detection means for detecting the phase difference
between the drive signal generated by said transmission oscillator
means and the reception signal from said second ultrasonic transducer
means and developing an output, wherein both the signals are synchronized
and frequency divided by said first and second counter means with
the said dividing ratio;
frequency/voltage converter means for converting the output of
said phase difference detection means into an analog signal corresponding
to the flow rate of said fluid;
an oscillator oscillating with a frequency proportional to said
analog signal and producing an output;
third counter means for counting the output of said oscillator
up to a predetermined number;
monostable flip-flop means, triggered by an output signal of said
third counter means for resetting said second counter means.
2. The ultrasonic flowmeter of claim 1 further comprising monostable
flip-flop means for driving said oscillator within a predetermined
period after its triggering by the output signal of said first counter
means.
3. An ultrasonic flowmeter for measuring flow along a fluid flow
path having a center thereof comprising:
first ultrasonic transducer means driven with a transmission oscillator
for emitting an ultrasonic wave for transmission in the fluid flowing
in the path;
second ultrasonic transducer means for receiving said ultrasonic
wave propagated in said fluid along the flow and producing a reception
signal indicative thereof, wherein a line drawn between said first
and second transducer means does not cross directly through the
center of said fluid flow path;
third ultrasonic transducer means for receiving said ultrasonic
wave propagated in said fluid against the flow and producing a reception
signal indicative thereof, wherein a line drawn between said first
and third transducer means does not cross directly through the center
of said fluid flow path;
means for obtaining the phase difference between the ultrasonic
wave propagated along the flow and a driving signal of said first
ultrasonic transducer;
means for obtaining the phase difference between the ultrasonic
wave propagated against the flow and the driving signal of said
first ultrasonic transducer;
means for converting the sum of said two phase differences into
a first analog signal;
means for converting the difference of said two phase differences
into a second analog signal;
signal feed-back means for controlling the frequency of the transmission
oscillator so that the sum of said phase differences is a constant
value; and
indicator means for obtaining and indicating the flow rate from
the difference of said phase differences.
4. The ultrasonic flowmeter of claim 3 in which said means for
obtaining the phase difference is composed of an exclusive OR means
and a smoothing circuit for smoothing the output of said exclusive
OR means, wherein one input of the exclusive OR means is the output
of a series connection of the transmission oscillator for driving
said first ultrasonic transducer and a rectangular wave producing
means.
Description BACKGROUND
The present invention relates to an ultrasonic flow meter. In particular,
the invention relates to a flow meter using continuous ultrasonic
waves.
Flow meters using ultrasonic waves can be classified into two types.
That is, one is the flow meter of the ultrasonic pulse system and
the other is the flow meter of the continuous ultrasonic wave system.
In a conventional flow meter using ultrasonic pulses, the ultrasonic
pulse beam is transmitted into the fluid so that the flow rate is
obtained from the propagation time of the pulse in the fluid. In
this case, there was a drawback. That is, since the flow rate is
measured from the time difference of the pulses, which becomes short
when the flow rate is small, it was required that the clock frequency
be high (to the limit of IC at present). Thus it was difficult to
enlarge and measure small time differences.
In a flow meter using continuous ultrasonic waves, the ultrasonic
beam is transmitted into the fluid from the ultrasonic transducer
for transmission directly to the ultrasonic transducer for reception
provided at another position in the fluid, and the flow rate of
the fluid is obtained from the phase difference or another quantity
depending on the flow rate.
In the conventional ultrasonic flow meter of either one of the
above mentioned types, the ultrasonic wave was transmitted and received
as a beam. It was required that the ultrasonic transmitter and the
ultrasonic receiver are to be opposite to each other in order that
the ultrasonic wave beam is mutually transmitted and received; it
was possible to measure the flow rate only at the straight portion
of the tube in which the fluid flows.
To improve the accuracy in measurement by making the phase difference
or the time difference large, it is preferable that the angle .theta.
between the ultrasonic beam and the axis of the tube should be made
small to make the time difference long, in other words, the beam
is made parallel to the axis of the tube. Since it was also required
that the ultrasonic transmitter be opposite to the ultrasonic receiver,
the degree of design freedom was limited.
In addition, in order to make the ultrasonic beam sharp, the frequency
should be high. When the frequency becomes high, the short range
acoustic field AF (=D.sup.2 /4.lambda., wherein D is the diameter
of the ultrasonic transducer and .lambda. is the wave length) becomes
larger; the length l between the transmitter and the receiver becomes
comparable with the short range acoustic field and the side lobe
becomes larger, particularly when the diameter of the tube is small.
In other words, not only the waves propagated along the straight
line connecting the transmitter and the receiver, but also the waves
which have propagated in various directions, are received, which
increases the beam width and makes it difficult to measure the time
difference correctly. These drawbacks were present in the continuous
ultrasonic flow meter using the ultrasonic beam in accordance with
the piror art.
In order to overcome the above mentioned drawbacks, the present
inventor has invented a flow meter using a continuous ultrasonic
wave which is not in the form of an ultrasonic beam. The ultrasonic
wave is a standing wave in the cross section of the tube and a propagating
wave in the axial direction of the tube. It is characteristic that
the ultrasonic transducer for transmission and the ultrasonic transducer
for reception are arranged on the wall of the tube so as not to
be opposite to each other.
The degree of freedom is high in mounting the ultrasonic transducers
in this ultrasonic flow meter. It is also possible to measure without
disturbing the flow in the tube, because it is possible to mount
the ultrasonic transducers on the outside of the wall of the tube.
In addition, since it is not necessary to provide any member for
causing a vortex as in the Karman vortex flow meter, it is possible
to make the pressure loss zero due to the member for causing vortex.
The principle of the measurement of the flow meter in accordance
with the present invention is as follows: The ultrasonic wave does
not propagate in a form of the ultrasonic beam but propagates as
a standing wave in the tube. The propagation of the ultrasonic wave
in the fluid follows the wave equation. Since the ultrasonic wave
in tube has the limited boundary, the solution of to the equation
is different from that in free space, so that the group velocity
(acoustic velocity) C of the ultrasonic wave is different from that
in free space. The solution to this equation is obtained by a mathematical
method which is the same as that for a microwave waveguide.
When the tube has the cross section in the x, y planes and the
ultrasonic wave propagates in the z direction, a solution of the
wave equation is a standing wave in the x, y planes, being a propagating
wave in the z direction. With respect this solution, the group velocity
C of the ultrasonic wave, which is a function of the frequency f
of the ultrasonic wave, is expressed as follows: wherein f.sub.c
is the cut-off frequency. ##EQU1##
And the following formula stands.
where L is the distance between the ultrasonic transmitter and
the ultrasonic receiver, C is the group velocity of the ultrasonic
wave in the fluid, V is the relative velocity of the fluid and the
ultrasonic transmitter and T.sub.v is the time necessary for the
propagation from the ultrasonic transmitter to the ultrasonic receiver.
Therefore, the difference .DELTA.T between the propagation times
at V=0 and at V.noteq.0 is expressed as follows.
The above expression is Taylor-expanded, so as to obtain the following
expression. ##EQU2##
In case V<<C, .DELTA.T is proportional to V, .DELTA.T=LV/C.sup.2.
Thus, it is possible to obtain the flow rate V from .DELTA.T, C
and l.
It is to be noted that the time difference .DELTA.T may be obtained
from the phase difference of the ultrasonic waves. Suppose the frequency
of the ultrasonic wave is f, the phase difference .phi. which corresponds
to the time difference .DELTA.T satisfies the following relationship.
When 0.ltoreq..phi..ltoreq..pi., the following expression stands.
Thus it is possible to obtain the flow rate V by detecting the
phase difference .phi..
In obtaining the flow rate V from the time difference .DELTA.T,
the group velocity (acoustic velocity) C and the distance L, the
measurement has the following difficulties.
(i) In obtaining the flow rate V from the phase difference .DELTA..phi.,
the available phase difference range is 0-.pi.. Therefore, it is
impossible to enlarge the range of the measurable flow rate.
(ii) The variance of the acoustic velocity in the fluid is a cause
of error in measuring the flow rate, since the acoustic velocity
C of the ultrasonic wave in the fluid depends upon the temperature
of the fluid.
SUMMARY OF THE DISCLOSURE
Thus it is the first object of the present invention to provide
an ultrasonic flow meter provided with a phase difference detector
circuit which is able to freely enlarge the range of the measurable
phase difference in order to make it possible to use the meter even
if the phase difference is larger than one period of ultrasound.
It is the second object of the present invention to provide an
ultrasonic flow meter wherein the ultrasonic frequency f is varied
in correspondence with the variance of the acoustic velocity in
the fluid so as to compensate for the above mentioned temperature
dependence.
Additional objects and advantages of the invention will be best
understood from the following description of preferred embodiments
when read in connection with the accompanying drawings. The following
embodiments are presented for illustrative purposes only and not
for a limitative purpose. Various modifications can be made by those
skilled in the art without departing from the spirit and scope of
the present invention.
BRIEF DESCRIPTION OF THE DRAWINGS
FIGS. 1(A), 1(B) and 1(C) are perspective views, partially in cross
section, showing exemplary arrangements of an ultrasonic flow meter
in accordance with the present invention.
FIG. 1(A) shows the case wherein an ultrasonic transmitter T and
an ultrasonic receiver R are provided so as not to be opposite to
each other, with a distance L between them.
FIG. 1(B) shows the case wherein the ultrasonic transmitter T and
the ultrasonic receiver R are provided outside the wall of the tube
and
FIG. 1(C) shows the case wherein the tube is bent and the ultrasonic
transmitter T and the ultrasonic receiver R are arranged thereon
so as not to be opposite to each other;
FIG. 2 is a block diagram showing one embodiment of an ultrasonic
flow meter in compliance with the first object of the present invention;
FIG. 3 shows timing charts of electric signals (e)-(h) in the circuit
which is shown in FIG. 2;
FIG. 4 is a block diagram showing a preferred embodiment of an
ultrasonic flow meter in compliance with the second object of the
present invention; and
FIGS. 5(A) and 5(B) are views of experimental examples showing
the case with temperature compensation in accordance with the present
invention and the case without temperature compensation so that
they are compared with each other. FIG. 5(A) is the view showing
the variance of the measured values of the water temperature (dotted
line) and the flow rate (solid line) with the passage of time (t)
when the fluid of a constant flow rate V is measured without the
temperature compensation in accordance with the present invention.
FIG. 5(B) is the view showing the variance of the measured values
of the water temperature (dotted line) and the flow rate (solid
line) with the passage of time (t) under the same condition with
the temperature compensation in accordance with the present invention.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
First, an explanation will be given with respect to the ultrasonic
flow meter in compliance with the first object of the present invention:
the ultrasonic flow meter provided with a phase difference detector
circuit which makes it possible to measure even if the phase difference
is larger than one period, detecting the time difference .DELTA.T
as the phase difference .DELTA..phi. with the ultrasonic transducer
arrangements shown in FIGS. 1(A), 1(B), and 1(C).
For obtaining the time difference .DELTA.T from the phase difference
.DELTA..phi., the sine-wave signal generated in the continuous oscillator
is sent to the ultrasonic transmitter T to generate the ultrasonic
wave. At the same time, one portion thereof is sent directly to
a converter circuit (for example, a comparator) to convert it into
a square wave (which will be referred to as "reference signal").
The ultrasonic wave propagated in the fluid is again converted into
an electric signal by means of the ultrasonic receiver R and amplified
at an amplifier to convert it to a square wave (which will be referred
to as "reception wave") at another converter circuit (for
example, a comparator). The phase difference of the above mentioned
reference wave and reception wave is detected at the phase difference
detector circuit.
In accordance with the phase difference detector circuit, both
the transmission signal and the reception signal are subjected to
a frequency division with the same ratio, and are supplied to the
phase difference detector circuit (for example, an exclusive "OR"
circuit), thereby making it possible to obtain the time delay of
the reception signal even if the time delay is larger than one period
of the transmission wave.
The ultrasonic flow meter in compliance with the first object of
the present invention will be described with reference to FIG. 2
and FIG. 3.
An ultrasonic wave is transmitted into the fluid of a flow rate
V from the ultrasonic transducer T for transmission according to
the output signal (a) of an transmission oscillator 1. The ultrasonic
wave propagated in the fluid is converted into an electric signal
(b) at the ultrasonic transducer R for reception and amplified at
an amplifier circuit 2 to convert into a rectangular wave (c) at
a rectangular wave circuit 3. The rectangular wave (c) is subjected
to a frequency division at a counter circuit 4 and a flip-flop circuit
5 so that its period may be made long and then supplied as one input
signal (d) to a phase difference detector circuit 6. On the other
hand, one portion of the output signal (a) of the transmission oscillator
1 is converted into a signal (e) of a rectangular wave form at a
rectangular wave circuit 7 and subjected to a frequency division
at a counter circuit 8 so as to generate a signal (f) whose period
is made long. And this signal (f) is supplied as the other input
signal to the phase difference detector circuit 6. The ratio of
the frequency division at the counter circuit 8 is the same as the
product of the ratios of the frequency divisions respectively at
the counter circuit 4 and the flip-flop circuit 5. Therefore, in
case the signal (a) and the signal (b) have the same period, the
signal (f) and the signal (d) have the same period. The phase difference
of the signal (f) and the signal (d) is detected at the phase difference
detector circuit 6 which is, for example, an exclusive OR circuit.
Its output signal (h) is converted into an analog signal .phi. by
a frequency/voltage converter circuit 9 which may be, for example,
a low-pass filter circuit or the like. And the flow rate V is obtained
from .phi..
The above mentioned counter circuit 4 and flip-flop circuit 5 are
reset as follows. The output signal (f) of the counter circuit 8
branches so as to trigger a monostable flip-flop circuit 10 thereby
generating a one-shot pulse signal (i). This signal (i) is sent
to the oscillation control terminal of an oscillator circuit 11
which oscillates with the frequency which is in proportion to the
inverse number of the above mentioned signal .phi., so that the
oscillator circuit 11 generates an oscillation signal (j) during
a period of time which is determined by the monostable flip-flop
circuit 10 from the fall of the signal (f). This signal (j) is counted
by means of a counter circuit 12. An output signal (k) from the
counter circuit 12 which is generated at every pulse of a predetermined
number N (for example, N=32), triggers a monostable flip-flop circuit
13 for gating so as to generate a one-shot pulse signal l. The counter
circuit 12 is reset at the starting end of the one-shot pulse signal
(i). Thus, the starting end of the one-shot pulse signal l is delayed
by a time which is in proportion to the signal .phi. with respect
to the starting end of the signal (i). The signal l resets the counter
circuit 4. In addition, the signal l branches so as to reset the
flip-flop circuit 5 by way of a gate circuit 14. The gate circuit
14 is for example, an AND circuit being supplied with the signal
(c) of a rectangular wave and the signal l.
Since the phase difference detector circuit in accordance with
the present invention is constituted as mentioned above, it is possible
to obtain the flow rate V as an analog signal .phi. even if the
phase difference is larger than one period. Now, this will be explained
more precisely with reference to FIG. 2 and FIG. 3.
The rectangular wave (e) which is obtained from the output signal
(a) of the transmission oscillator 1 is subjected to a frequency
division at the counter circuit 8 so to make the signal (f). There
is shown the example of the signal (f) wherein the frequency division
ratio is 1/4 in the FIG. 3. In this case, it is possible to detect
the phase difference corresponding to two periods with respect to
the signal (a) or the signal (e). The one-shot pulse (i) with long
pulse length is excited at the rise end of the signal (f), and at
the same time, the oscillator circuit 11 starts to oscillate. Since
the oscillation frequency of the oscillator circuit 11 is in proportion
to the inverse number of the signal .phi., the time necessary to
count pulses up to N is in proportion to the signal .phi.. The signal
l is triggered and said signal l resets the counter circuit 4 when
the pulses are counted up to N, so that the count-starting time
of the counter circuit 4 is delayed from that of the counter circuit
8 by the time which is in proportion to the signal .phi.. The product
of ratios of the frequency divisions at the counter circuit 4 and
the flip-flop circuit 5 is equal to the ratio of the frequency division
(1/4 in the example) at the counter circuit 8.
The signal (a) is subjected to a frequency division at the counter
circuit 8 and the signal (b) is subjected to a frequency division
at the counter circuit 4 and the flip-flop circuit 5 respectively
with the same ratio. In addition, the synchronization is given by
providing a time difference proportional to the signal .phi. at
the count-starting end thereof, so that the phase relationship of
the signal (d) and the signal (f) corresponds to that of the signal
(a) and the signal (b). In other words, the signal .phi. is in proportion
to the phase difference of the signal (a) and the signal (b). Since
the synchronization is given and the signals are subjected to the
frequency division as mentioned above, the signal .phi. varies following
the flow rate V.
As the phase difference of the signal (a) and the signal (b) is
in proportion to the flow rate V, it is possible to obtain the flow
rate V from the phase difference.
Thus the ultrasonic flow meter in accordance with the present invention
is provided with the phase difference detector circuit as mentioned
above, and there is an advantage that the measurable range of the
flow rate is enlarged and the distance between both the ultrasonic
transducers can be decided freely. In addition, the measured value
is stable due to the memory effect of the flip-flop circuit. In
other words, the measured value does not vary at once even if the
ultrasonic reception signal disappears by some reason.
Now, an explanation will be given with respect to an ultrasonic
flow meter in compliance with the second object of the present invention.
The meter is provided with an electric circuit to compensate for
the temperature dependence of the group velocity (acoustic velocity)
of the ultrasonic wave in the fluid.
The ultrasonic transducer for transmission and the ultrasonic transducer
for reception are provided at the wall of the tube in which the
fluid flows so as not to be opposite to each other in this ultrasonic
flow meter. A continuous ultrasonic wave is transmitted from the
ultrasonic transducer for transmission according to the oscillation
signal from the ultrasonic oscillator. The ultrasonic wave propagated
in the fluid is detected by the ultrasonic transducer for reception
and converted into an electric signal. And the phase difference
.DELTA..phi. of the output signal is given by the phase difference
detector circuit to obtain the flow rate.
The phase difference .phi. between the output signals of both the
ultrasonic transducers may be obtained by the following formula
(1). ##EQU3## where f is the frequency of the ultrasonic wave, L
is the distance between both the ultrasonic transducers, C is the
group velocity of the ultrasonic wave and V is the flow rate.
In case V/C is small, the formula (1) is expanded as shown in the
following formula (2). ##EQU4## Suppose the value of .phi. in the
formula (2) is .phi..sub.1 in the case where the propagation direction
is along the flow, and the value of .phi. is .phi..sub.2 in the
case where the propagation direction is against the flow, the difference
thereof is given as shown in the following expression (3) ##EQU5##
Although it is possible to obtain the flow rate V from the formula
(3), the acoustic velocity C in the formula (3) depends upon the
temperature, which is one of the causes of measurement error.
In order to compensate for the temperature dependency of the acoustic
velocity, the present inventor has proposed an ultrasonic flow meter
in which the frequency is controlled in correspondence with the
acoustic velocity C so that f/C.sup.2 may become constant. In that
case, however, it was required to provide a microcomputer for the
above mentioned control. As a consequence, there was a problem in
that the ultrasonic flow meter was complicated and the cost thereof
was high.
In accordance with the present invention, 1/2 of the sum .phi..sub.1
+.phi..sub.2 of the phase differences .phi..sub.1 .phi..sub.2 is
kept so as to be equal to .pi./2 thereby providing a solution of
the problem.
The function of the ultrasonic flow meter in compliance with the
second object of the present invention wherein the temperature dependence
of the acoustic velocity is compensated will be described with reference
to FIG. 4.
An output of a transmission oscillator 15 is supplied to an ultrasonic
transducer T.sub.1 for transmission. The ultrasonic wave is transmitted
from the transducer T.sub.1 into a fluid of the flow rate V to be
received by ultrasonic transducers R.sub.1 and R.sub.2 for reception.
The output of the transducer R.sub.1 is transferred via an amplifier
circuit 16 and a delay circuit 17 to a rectangular wave circuit
18 to be converted into a rectangular wave. The output of the transducer
R.sub.2 is likewise transferred via an amplifier circuit 19 and
a delay circuit 20 to a rectangular wave circuit 21 to be converted
into a rectangular wave. In addition, one portion of the output
of said transmission oscillator 15 is also converted into a rectangular
wave at a rectangular wave circuit 22.
The phase difference of the outputs of the rectangular wave circuits
18 and 22 is detected by a phase difference detector circuit 23
(for example, an exclusive OR circuit) and a voltage signal .phi..sub.1
which is in proportion to the above phase difference with the same
reference symbol is obtained by a converter circuit 24 (for example,
a CR smoothing circuit). And a voltage signal .phi..sub.2 which
is in proportion to the phase difference with the same reference
symbol of the outputs of the rectangular wave circuits 21 and 22
is likewise obtained by a phase difference detector circuit 25 and
a converter circuit 26.
The said signals .phi..sub.1 and .phi..sub.2 are supplied as inputs
to an adding circuit 27 so as to obtain a sum signal (.phi..sub.1
+.phi..sub.2)/2. The frequency of the transmission oscillator 15
is controlled via a negative feed-back circuit 28 so that (.phi..sub.1
+.phi..sub.2)/2 may be a constant value. It is preferable that the
above constant value is .pi./2 in view of the measurable range.
On the other hand, the signals .phi..sub.1 and .phi..sub.2 are also
supplied as inputs to a subtraction circuit 29. Since the output
(.phi..sub.1 -.phi..sub.2) thereof is in proportion to the flow
rate, the output (.phi..sub.1 -.phi..sub.2) is indicated by an indicator
30 so that the flow rate is indicated. The flow rate which is obtained
from (.phi..sub.1 -.phi..sub.2) is independent of the acoustic velocity
by the control of the frequency as mentioned above.
It is also possible that the roles of the ultrasonic transducer
for transmission and the ultrasonic transducer for reception are
reversed by a transmission and reception switching circuit (not
shown).
The flow rate obtained from (.phi..sub.1 -.phi..sub.2) is not dependent
upon the temperature variance of the acoustic velocity.
Suppose the angular frequency of the oscillator is .omega., the
distance between the transducer T for transmission and the transducer
R for reception is L, the flow rate is V, the acoustic velocity
in the fluid is C and the delay time in the delay circuit is chosen
to be a proper value, the voltages .phi..sub.1 and .phi..sub.2 being
proportional to the corresponding phase differences can be expressed
by the following formulae (4) and (5), neglecting the scale factors.
##EQU6##
The flow rate V is obtained from the difference .phi. of the formula
(4) and (5). ##EQU7##
In case the acoustic velocity C in the formula (6) has the temperature
(T) dependence, the measured result may have the temperature dependence.
In order to compensate for this temperature dependence, it has been
considered to vary the frequency .omega.. The condition of .omega.
such that .phi. does not have a temperature dependence is given
as follows. ##EQU8##
Substituting the formula (6) into the formula (7), the following
formula (8) is obtained. ##EQU9##
In case V<<C, the formula (8) becomes the following formula
(9). ##EQU10##
Therefore, if the frequency .omega. is changed in accordance with
the formula (10), .phi. in the expression (6) does not have the
temperature dependency. ##EQU11##
In order to control the frequency in accordance with the expression
(10), information as to the acoustic velocity C and the frequency
.omega. is necessary; a suitable sensor or microprocessor is required.
In accordance with the ultrasonic flow meter of the present invention,
the same object is performed by keeping .phi..sub.1 +.phi..sub.2
to be a constant value.
In case V<<C, the following expression (11) is obtained from
the expression (4) and (5). ##EQU12##
Substituting .omega..sup.0 +.DELTA..omega. for .omega. and C.sub.0
+.DELTA.C for C in, the expression (11), it can be transformed into
the expression (12). ##EQU13##
In this case, since the .DELTA.C/C.sub.0 is a small value, (.phi..sub.1
+.phi..sub.2)/2 practically becomes constant by keeping the following
expression (13). The formula (13) stands by keeping (.phi..sub.1
+.phi..sub.2)/2 so as to be .pi./2 in the range for practical use.
The formula (13) and the formula (10) are of the same form of function
neglecting the constant factor. Thus to keep (.phi..sub.1 +.phi..sub.2)/2
so as to be .pi./2 means that the frequency satisfies the relation
in the formula (10) in the range for practical use accordingly.
As described hereinbefore, when the sum of the phase difference
of the ultrasonic wave propagated along the flow and that of the
ultrasonic wave propagated against the flow is kept constant, there
is compensation for the temperature dependency of the acoustic velocity
in the fluid. In other words, it is possible to substantially compensate
for the temperature dependency of the acoustic velocity in the flow,
without using any temperature sensor or microprocessors.
In general, when the water temperature fluctuates with time, the
acoustic velocity (group velocity) in the water also fluctuates
with time. In spite of this, there is shown in FIGS. 5(A) and 5(B)
that the dependence on the water temperature fluctuation (the acoustic
velocity variance) is not recognized in the measured flow rate by
means of the ultrasonic flow meter in compliance with the second
object of the present invention.
Although .phi..sub.1 and .phi..sub.2 are measured at the same time
in the embodiments described above, it is also possible, to measure
them alternately using a sample hold circuit and a transmission
and reception switching circuit. |