Abstrict The present invention relates to a method of setting a flow coefficient
used in a flow meter for measuring a flow rate of a fluid, and a
flow meter having the flow coefficient which is set by the flow
coefficient setting method. An object of the present invention is
to provide a method for efficiently providing an optimal approximate
line represented by a lowdegree function such that flow coefficients
including a number of data sets are within a predetermined error,
and to provide a flow meter with a reduced error. In order to achieve
the object, the present invention includes the steps of: obtaining
an optimal approximate line using a number n of consecutive sets
of data points (Xi, Yi); increasing or decreasing the number n so
that the n sets of data points are all within a predetermined error
Er with respect to the optimal approximate line; and setting a region.
Thus, it is possible to easily and automatically set a flow coefficient
using a personal computer, or the like, with high efficiency and
good reproducibility.
Claims What is claimed is:
1. A method of setting a flow coefficient, comprising the steps
of: obtaining an optimal approximate line of a relationship between
the flow velocity of the fluid and the flow coefficient using a
number n of consecutive sets of data points (Xi, Yi) of all flow
velocity data points stored in a flow velocity data memory section
for storing flow velocity data measured by a flow velocity measurement
section, and reference data stored in a reference data memory section;
increasing or decreasing the number n so that the n sets of data
points are all within a predetermined error Er with respect to the
optimal approximate line; performing a calculation operation for
setting a region by a flow coefficient calculation section; and
storing an obtained flow coefficient in a flow coefficient memory
section.
2. A method of setting a flow coefficient according to claim 1
wherein a linear function is used to represent the optimal approximate
line if the n sets of data points (Xi, Yi) are distributed on both
sides of the optimal approximate line in a middle portion of the
optimal approximate line.
3. A method of setting a flow coefficient according to claim 1
wherein a guadric function is used to represent the optimal approximate
line if the n sets of data points (Xi, Yi) are distributed on one
side of the optimal approximate line in a middle portion of the
optimal approximate line.
4. A method of setting a flow coefficient, comprising the steps
of: obtaining an optimal approximate curve of a relationship between
the flow velocity of the fluid and the flow coefficient using a
plurality of sets of data points (Xi, Yi) of all flow velocity data
points stored in a flow velocity data memory section for storing
flow velocity data measured by a flow velocity measurement section,
and reference data stored in a reference data memory section; dividing
the optimal approximate curve into a number m regions; performing
a calculation operation for approximating each region with an optimal
approximate straight line by a flow coefficient calculation section;
and storing an obtained flow coefficient in a flow coefficient memory
section.
5. A method of setting a flow coefficient according to claim 4
wherein the optimal approximate curve is equally divided into the
number m of regions along a yaxis direction.
6. A method of setting a flow coefficient according to claim 4
wherein the optimal approximate curve is equally divided into the
number m of regions along an xaxis direction.
7. A method of setting a flow coefficient according to claim 4
wherein the optimal approximate curve is divided into the number
m of regions along an xaxis direction such that a width of each
region is inversely proportional to a gradient of the optimal approximate
straight line for the region.
8. A method of setting a flow coefficient according to claim 4
wherein the optimal, approximate curve is represented by Y=a.times.Log(X)+b.
9. A method of setting a flow coefficient according to claim 4
wherein the optimal approximate curve is represented by Y=(ab)/[1+exp(c.times.X)]+b.
10. A method of setting a flow coefficient according to claim 1
or 4 wherein the flow velocity measurement section comprises a
thermal type flow sensor.
11. A method of setting a flow coefficient according to claim 1
or 4 wherein the flow velocity measurement section comprises an
ultrasonic flow meter.
12. A method of setting a flow coefficient according to claim 1
or 4 wherein the optimal approximate line is represented by a lowdegree
function which is a linear function or a quadric function.
13. A method of setting a flow coefficient according to claim 1
or 4 wherein a data point which is included by two adjacent regions
is set to belong to one of the two adjacent regions in which an
error Er calculated based on the optimal approximate line is smaller.
14. A method of setting a flow coefficient according to claim 1
or 4 wherein an intersection between two optimal approximate lines
for two adjacent regions is used as a boundary point between the
two regions.
15. A method of setting a flow coefficient according to claim 1
or 4 wherein the error Er is gradually increased until an entire
data range required can be divided into a predetermined number of
regions.
16. A method of setting a flow coefficient according to claim 1
or 4 wherein when a type of a fluid changes from a first fluid
to a second fluid, an xaxis value of a flow coefficient is multiplied
by a fluidtypedependent constant so as to convert the flow coefficient
to a new flow coefficient.
17. A method of setting a flow coefficient according to claim 16
wherein the constant is a new flow Velocity (Vm.times.Vg/m) which
is obtained by multiplying a flow velocity ratio (Vg/Vm) to a flow
velocity (Vm) of the first fluid, where Vg is a flow velocity, of
the second fluid for any flow coefficient value (Ko).
18. A method of setting a flow coefficient according to claim 1
or 4 wherein when a temperature of a fluid changes from a first
temperature to a second temperature, an xaxis value of a flow coefficient
is multiplied by a temperaturedependent function value so as to
convert the flow coefficient to a new flow coefficient.
19. A method of setting a flow coefficient according to claim 18
wherein the function value used for obtaining the new flow coefficient
is calculated by the following expression:
where Ts denotes the first temperature, Ti denotes the second temperature,
Vi denotes a flow velocity of the fluid measured at Ti, and p denotes
an exponent.
20. A method of setting a flow coefficient according to claim 19
wherein an absolute temperature (Tm) of the fluid is determined
from an ultrasonic wave propagation time from an ultrasonic flow
meter.
21. A method of setting a flow coefficient according to claim 18
wherein an absolute temperature (Tm) of the fluid is determined
from a temperaturesensitive resistor of a thermal type flow sensor.
22. A flow meter, comprising: a flow velocity measurement section
for measuring a flow velocity of a fluid; a flow coefficient memory
section for storing a flow coefficient which is set by a method
of setting a flow coefficient according to claim 1 or 4; and a flow
rate calculation section for calculating a flow rate of the fluid
from the measured flow velocity using the flow coefficient stored
in the flow coefficient memory section.
23. A flow meter according to claim 22 wherein the flow velocity
measurement section comprises a thermal type flow sensor.
24. A flow meter according to claim 22 wherein the flow velocity
measurement section comprises an ultrasonic flow meter.
Description TECHNICAL FIELD
The present invention relates to a method of setting a flow coefficient
used in a flow meter for measuring a flow rate of a fluid.
BACKGROUND ART
A conventional flow meter will be described with reference to FIG.
21. A flow velocity measurement device 2 for measuring a flow velocity
of a fluid, such as a thermal type flow sensor, is provided at a
point in a fluid pipe 1 where a fluid passes therethrough. The flow
velocity (Vm) obtained by the flow velocity measurement device 2
is multiplied by a crosssectional area (S) of the fluid pipe 1
and a flow coefficient (K), so as to calculate a flow rate (Qm).
The flow velocity measurement device 2 obtains the flow velocity
(Vm) of the fluid by measuring the flow velocity of only a portion
of the fluid in the vicinity of the flow velocity measurement device
2. Therefore, an average flow velocity for the entire area of the
fluid pipe 1 needs to be calculated as follows. A reference flow
rate setting section capable of setting a reference flow rate is
connected to the fluid pipe 1 so as to pass a fluid at an appropriate
reference flow rate through the fluid pipe 1 and obtain an average
flow rate (Qa). Then, the relationship (K=Va/Vm; "flow coefficient")
between an average flow velocity (Va), which is calculated from
the average flow rate value and the flow velocity (Vm) measured
by the flow velocity measurement device is obtained. This relationship
is measured for various reference flow rates so as to obtain a number
of data Bets each including the flow velocity (Vm) and the flow
coefficient (K) of the fluid.
Next, the flow velocity (Vm) of the fluid measured by the flow
velocity measurement device 2 is multiplied by the flow coefficient
(K) and the crosssectional area (S) of the fluid pipe 1 thereby
obtaining a measured flow rate (Qm). In other words, the measured
flow rate (Qm) is obtained by calculating Qm=K.multidot.S.multidot.Vm.
In FIG. 21 an arrow 3 denotes the direction of the fluid flow.
FIG. 22 illustrates a relationship between the flow velocity (Vm)
and the flow coefficient (K) which are obtained as described above.
In FIG. 22 the horizontal axis represents the flow velocity (Vm)
measured by the flow velocity measurement device, and the vertical
axis represents the flow coefficient (K). For example, if the flow
velocity (Vm) of the fluid measured by the flow velocity measurement
device 2 is about 2 m/s, the flow coefficient (K) can be read from
FIG. 22 to be about 0.89. Therefore, if the crosssectional area
(S) of the fluid pipe 1 is about 0.3.times.10.sup.3 m.sup.2 the
measured flow rate (Qm) is: ##EQU1##
The conventional flow meter has the following problems. That is,
using a number of sets of data (see FIG. 22) each including the
flow velocity (Vm) and the flow coefficient (K) measured by the
flow velocity measurement device, the flow velocity range is appropriately
divided into regions by visual observation so as to set an optimal
approximate line for each region which optimally approximates a
group of data sets (flow coefficients) within the region, thereby
obtaining a kinked line which optimally approximates the group of
data sets (flow coefficients) across all regions.
It is time consuming and labor intensive to set such an optimal
approximate straight line by repeatedly performing complicated calculations.
Moreover, because the setting operation is based on a visual observation,
it has a poor reproducibility, and the obtained optimal approximate
straight line may vary each time it is set. Although the optimal
flow coefficient may be approximated by a highdegree curve, a lowdegree
approximation such as a linear or quadric approximation is preferred
when the calculation is done by a microcomputer, or the like, because
of the limitations associated with the use of a microcomputer such
as the calculation time and the number of significant digits.
When the type of a fluid is changed from that used when measuring
the reference flow rate and setting the flow coefficient, it is
necessary to remeasure the average flow rate (Qa) and the flow
velocity (Vm) of the new fluid so as to reset a new flow coefficient
(K).
When the temperature of the fluid changes, the characteristics
of the fluid may also change, thereby changing the flow coefficient
and deteriorating the flow rate measurement precision.
DISCLOSURE OF THE INVENTION
The present invention has been made to solve the abovedescribed
problems and provides a method of setting a flow coefficient, including
the steps of: obtaining an optimal approximate line using a number
n of consecutive sets of data points (Xi, Yi) of all flow velocity
data points measured by a flow velocity measurement section, and
reference data stored in a reference data memory section; increasing
or decreasing the number n so that the n sets of data points are
all within a predetermined error Er with respect to the optimal
approximate liner performing a calculation operation for setting
a region by a flow coefficient calculation section; and storing
an obtained flow coefficient in a flow coefficient memory section.
With such a structure, according to the flow coefficient setting
method of the present invention having such a structure, it is possible
to easily and automatically set a flow coefficient using a personal
computer, or the like, with good reproducibility, while suppressing
the flow rate value within a predetermined error.
Another method of setting a flow coefficient of the present invention
includes the steps of: obtaining an optimal approximate curve using
a plurality of sets of data points (Xi, Yi) of all flow velocity
data points measured by a flow velocity measurement section, and
reference data stored in a reference data memory section, dividing
the optimal approximate curve into a number m of regions; performing
a calculation operation for approximating each region with an optimal
approximate straight line by a flow coefficient calculation section;
and storing an obtained flow coefficient in a flow coefficient memory
section.
With such a structure, even if the number of data points available
is limited, it is possible to select an optimal curve so that a
flow coefficient can be set with a reduced error over a wider range,
in a more efficient manner and within a shorter period of time.
A flow meter of the present invention includes: a flow velocity
measurement section for measuring a flow velocity of a fluid; a
flow coefficient memory section for storing a flow coefficient which
is set by the abovedescribed method of setting a flow coefficient;
and a flow rate calculation section for calculating a flow rate
of the fluid from the measured flow velocity using the flow coefficient
stored in the flow coefficient memory section.
With such a structure, it is possible to provide a flow meter with
a reduced error over a wide flow rate range.
Various embodiments of the present invention will be described
below.
A method of setting a flow coefficient according to one embodiment
of the present invention includes the steps of: obtaining an optimal
approximate line using a number n of consecutive sets of data points
(Xi, Yi) of all flow velocity data points measured by a flow velocity
measurement section, and reference data stored in a reference data
memory section; increasing or decreasing the number n so that the
n sets of data points are all within a predetermined error Er with
respect to the optimal approximate line; performing a calculation
operation for setting a region by a flow coefficient calculation
section; and storing an obtained flow coefficient in a flow coefficient
memory section.
With such a structure, according to the flow coefficient setting
method of the present invention having such a structure, it is possible
to easily and automatically set a flow coefficient using a personal
computer, or the like, with good reproducibility, while suppressing
the flow rate value within a predetermined error.
In a method of setting a flow coefficient according to one embodiment
of the present invention, a linear function is used to represent
the optimal approximate line if the n sets of data points (Xi, Yi)
are distributed on both sides of the optimal approximate line in
a middle portion of the optimal approximate line.
With such a structure, it is possible to set a flow coefficient
with a simple linear function and thus to obtain a flow rate value
with a reduced error by a a simple calculation.
In a method of setting a flow coefficient according to one embodiment
of the present invention, a quadric function is used to represent
the optimal approximate line if the n sets of data points (Xi, Yi)
are distributed on one side of the optimal approximate line in a
middle portion of the optimal approximate line.
With such a structure, it is possible to approximate a wider range,
as compared with when using a linear function, using a curve with
a reduced error.
A method of setting a flow coefficient according to one embodiment
of the present invention includes the steps of: obtaining an optimal
approximate curve using a plurality of sets of data points (Xi,
Yi) of all flow velocity data points measured by a flow velocity
measurement section, and reference data stored in a reference data
memory section; dividing the optimal approximate curve into a number
m of regions; performing a calculation operation for approximating
each region with an optimal approximate straight line by a flow
coefficient calculation section; and storing an obtained flow coefficient
in a flow coefficient memory section.
With such a structure, even if the number of data points available
is limited, it is possible to select an optimal curve so that a
flow coefficient can be set with a reduced error over a wider range,
in a more efficient manner and within a shorter period of time.
In a method of setting a flow coefficient according to one embodiment
of the present invention, the optimal approximate curve is equally
divided into the number m of regions along a yaxis direction.
With such a structure, it is possible to divide a data range into
m regions along a yaxis direction within a shorter period of time,
thereby efficiently setting a flow coefficient.
In a method of setting a flow coefficient according to one embodiment
of the present invention, the optimal approximate curve is equally
divided into the number m of regions along an xaxis direction.
With such a structure, it is possible to divide a data range into
m regions along an xaxis direction within a shorter period of time,
thereby efficiently setting a flow coefficient.
In a method of setting a flow coefficient according to one embodiment
of the present invention, the optimal approximate curve is divided
into the number m of regions along an xaxis direction such that
a width of each region is inversely proportional to a gradient of
the optimal approximate straight line for the region.
With such a structure, it is possible to divide a data range into
m regions within a shorter period of time, while efficiently setting
a flow coefficient so that the errors of the respective regions
are close to one another.
In a method of setting a flow coefficient according to one embodiment
of the present invention, the optimal approximate curve is represented
by Y=a.times.Log(X)+b.
With such a structure, it is possible to divide a setting range
into m regions to linearly approximate each region with as few as
two data points.
In a method of setting a flow coefficient according to one embodiment
of the present invention, the optimal approximate curve is represented
by Y=(ab)/[1+exp(c.times.X)]+b.
With such a structure, it is possible to divide a wide setting
range into n regions to linearly approximate each region with a
small number of data points.
In a method of setting a flow coefficient according to one embodiment
of the present invention, the flow velocity measurement section
includes a thermal type flow sensor.
With such a structure, it is possible to set a flow coefficient
with a reduced error and a good reproducibility particularly in
a low flow rate region.
In a method of setting a flow coefficient according to one embodiment
of the present invention, the flow velocity measurement section
includes an ultrasonic flow meter.
With such a structure, it is possible to set a flow coefficient
with a reduced error and a good reproducibility over a wide flow
rate range.
In a method of setting a flow coefficient according to one embodiment
of the present invention, the optimal approximate line is represented
by a lowdegree function which is a linear function or a quadric
function.
With such a structure, it is possible to obtain a flow rate value
with a reduced error by a simple calculation.
In a method of setting a flow coefficient according to one embodiment
of the present invention, a data point which is included by two
adjacent regions is set to belong to one of the two adjacent regions
in which an error Er calculated based on the optimal approximate
line is smaller.
With such a structure, it is possible to reduce the error for a
boundary value.
In a method of setting a flow coefficient according to one embodiment
of the present invention, an intersection between two optimal approximate
lines for two adjacent regions is used as a boundary point between
the two regions.
With such a structure, it is possible to smoothly connect the region
boundary points to one another.
In a method of setting a flow coefficient according to one embodiment
of the present invention, the error Er is gradually increased until
an entire data range required can be divided into a predetermined
number of regions.
With such a structure, even when the number of regions is prescribed,
it is possible to divide a data range into the prescribed number
of regions while setting a flow coefficient with a minimum error.
In a method of setting a flow coefficient according to one embodiment
of the present invention, when a type of a fluid changes from a
first fluid to a second fluid, an xaxis value of a flow coefficient
is multiplied by a fluidtypedependent constant so as to convert
the flow coefficient to a new flow coefficient.
With such a structure, even when the type of a fluid changes from
that used when setting a flow coefficient, the flow coefficient
can easily be converted to a new flow coefficient for the new fluid,
thereby suppressing an error which may be caused by such a change
in the type of a fluid.
In a method of setting a flow coefficient according to one embodiment
of the present invention, the constant is a new flow velocity (Vm.times.Vg/Vm)
which is obtained by multiplying a flow velocity ratio (Vg/Vm) to
a flow velocity (Vm) of the first fluid, where Vg is a flow velocity
of the second fluid for any flow coefficient value (Kc).
With such a structure, even when there is a change in the type
of a fluid, it is possible to update the flow coefficient using
only one data point according to the type a of the fluid, thereby
eliminating the need to remeasure the flow coefficient.
In a method of setting a flow coefficient according to one embodiment
of the present invention, when a temperature of a fluid changes
from a first temperature to a second temperature, an xaxis value
of a flow coefficient is multiplied by a temperaturedependent function
value so as to convert the flow coefficient to a new flow coefficient.
With such a structure, even when the temperature of the fluid changes
from that when setting a flow coefficient, the flow coefficient
can easily be converted to a new flow coefficient for the new temperature,
thereby suppressing an error which may be caused by such a change
in the temperature of the fluid.
In a method of setting a flow coefficient according to one embodiment
of the present invention, the function value used for obtaining
the new flow coefficient is calculated by the following expression:
where Ts denotes the first temperature, Ti denotes the second temperature,
Vi denotes a flow velocity of the fluid measured at Ti, and p denotes
an exponent.
With such a structure, even when there is a change in the temperature
of a fluid, it is possible to obtain a flow coefficient for the
new temperature, thereby suppressing an error which may be caused
by such a change in the temperature of the fluid.
In a method of setting a flow coefficient according to one embodiment
of the present invention, an absolute temperature (Tm) of the fluid
is determined from a temperaturesensitive resistor of a thermal
type flow sensor.
With such a structure, it is not necessary to separately provide
a temperature sensor, thereby realizing an efficient setting method.
In a method of setting a flow coefficient according to one embodiment
of the present invention, an absolute temperature (Tm) of the fluid
is determined from an ultrasonic wave propagation time from an ultrasonic
flow meter.
With such a structure, it is not necessary to separately provide
a temperature sensor, while realizing an accurate hydraulic temperature
measurement utilizing the characteristics of a fluid.
A flow meter according to one embodiment of the present invention
includes: a flow velocity measurement section for measuring a flow
velocity of a fluid; a flow coefficient memory section for storing
a flow coefficient which is set by the abovedescribed method of
setting a flow coefficient; and a flow rate calculation section
for calculating a flow rate of the fluid from the measured flow
velocity using the flow coefficient stored in the flow coefficient
memory section.
With such a structure, it is possible to provide a flow meter with
a reduced error over a wide flow rate range.
In a flow meter according to one embodiment of the present invention,
the flow velocity measurement section includes a thermal type flow
sensor.
With such a structure, it is possible to provide a flow meter with
a reduced error and with good reproducibility particularly in a
low flow rate region.
In a flow meter according to one embodiment of the present invention,
the flow velocity measurement section includes an ultrasonic flow
meter.
With such a structure, it is possible to provide a flow meter with
a reduced error and with good reproducibility over a wide flow rate
range.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a conceptual diagram of a flow meter for illustrating
Embodiment 1 of the present invention;
FIG. 2 shows a flow velocity measurement section including a thermal
type flow sensor according to Embodiment 1 of the present invention;
FIG. 3 is a flow velocity measurement section including ultrasonic
transceivers according to Embodiment 1 of the present invention:
FIG. 4 is a characteristic diagram showing a flow coefficient for
illustrating Embodiment 1 of the present invention;
FIG. 5 is a characteristic diagram showing a flow coefficient for
illustrating Embodiment 1 of the present invention;
FIG. 6 is a characteristic diagram showing a flow coefficient for
illustrating Embodiment 1 of the present invention;
FIG. 7 is a characteristic diagram showing a flow coefficient for
illustrating Embodiment 1 of the prevent invention;
FIG. 8 is a characteristic diagram showing a flow coefficient for
illustrating Embodiment 2 of the present invention;
FIG. 9 is a characteristic diagram showing a flow coefficient for
illustrating Embodiment 3 of the present invention;
FIG. 10 is a characteristic diagram showing a flow coefficient
for illustrating Embodiment 4 of the present invention;
FIG. 11 is a characteristic diagram showing a flow coefficient
for illustrating Embodiment 5 of the present invention;
FIG. 12 is a characteristic diagram showing a flow coefficient
for illustrating Embodiment 6 of the present invention;
FIG. 13 is a characteristic diagram showing a flow coefficient
for illustrating Embodiment 7 of the present invention;
FIG. 14 is a characteristic diagram showing a flow is coefficient
for illustrating Embodiment 8 of the present invention;
FIG. 15 is a characteristic diagram showing a flow coefficient
for illustrating Embodiment 8 of the present invention;
FIG. 16 is a characteristic diagram showing a flow coefficient
for illustrating Embodiment 8 of the present invention;
FIG. 17 is a characteristic diagram showing a flow coefficient
for illustrating Embodiment 9 of the present invention;
FIG. 18 is a characteristic diagram showing a flow coefficient
for illustrating Embodiment 10 of the present invention;
FIG. 19 is a characteristic diagram showing a flow coefficient
for illustrating Embodiment 11 of the present invention;
FIG. 20 is a diagram showing a structure of a flow meter for illustrating
Embodiment 16 of the present invention;
FIG. 21 is a diagram showing a flow velocity measurement section
for illustrating a conventional example; and
FIG. 22 is a characteristic diagram showing a flow coefficient
for illustrating a conventional example.
BEST MODE FOR CARRYING OUT THE INVENTION
(Embodiment 1)
FIG. 1 is a conceptual diagram showing a flow meter for illustrating
a method of setting a flow coefficient according to Embodiment 1
of the present invention. Referring to FIG. 1 the flow meter includes:
a flow velocity measurement section 4 including a thermal type flow
sensor or an ultrasonic transceiver; a reference data memory section
5 for storing a reference flow rate of a fluid; a flow velocity
data memory section 6 for storing flow velocity data measured by
the flow velocity measurement section 4; a flow coefficient calculation
section 7 for calculating a flow coefficient; and a flow coefficient
memory section 8 for storing a calculated flow coefficient.
Reference flow rate data of a fluid flowing through the flow velocity
measurement section 4 is stored in the reference flow rate data
memory section 5. A measured flow velocity of the fluid flowing
through the flow velocity measurement section 4 is stored in the
flow velocity data memory section 6. The flow coefficient calculation
section 7 calculates a flow coefficient using the reference flow
rate data stored in the reference flow rate data memory section
5 and the flow velocity data of the fluid stored in the flow velocity
data memory section 6. The calculation results are stored in the
flow coefficient memory section 8.
FIG. 2 shows a flow velocity measurement section which includes
a thermal type flow sensor as a flow velocity measurement device.
FIG. 3 shows another flow velocity measurement section which includes
ultrasonic transceivers as a flow velocity measurement device.
Referring to FIG. 2 a thermal type flow sensor 10 is provided
at a point in a fluid pipe 9 as a flow velocity measurement device.
The thermal type flow sensor 10 includes a temperaturesensitive
resistor and a heater element. An electric power is momentarily
provided from an external unit to the heater element. Then, the
thermal equilibrium between the heating of the temperaturesensitive
resistor by the heater element and the cooling of the temperaturesensitive
resistor by the fluid is measured as a resistance value of the temperaturesensitive
resistor, and converted to the flow velocity of the fluid. In this
case, the flow velocity (Vm) of the fluid measured by the flow velocity
measurement device represents the flow velocity of a portion of
the fluid in the vicinity of the flow velocity measurement device.
If the temperaturesensitive resistor is appropriately calibrated
in advance, it is possible to measure the temperature of the fluid
from the change in the resistance value.
Referring to FIG. 3 ultrasonic transceivers 12 and 13 as a flow
velocity measurement device are provided along a fluid pipe 11 respectively
on the upstream side and the downstream side with respect to each
other. An ultrasonic wave is transmitted from the upstream ultrasonic
transceiver 12 to the downstream ultrasonic transceiver 13 and
vice versa, so as to measure the propagation time of the ultrasonic
wave for each direction. The flow velocity of the fluid is measured
by the difference between the respective propagation times. In FIG.
3 a broken line 14 denotes the propagation direction of the ultrasonic
waves, and a one dot chain line 15 and an arrow 16 both denote the
direction of the fluid flow. Reference numeral 17 (.theta.) denotes
an angle between the propagation direction of the ultrasonic waves
and the direction of the fluid flow. In this case, the ultrasonic
transceivers as a flow velocity measurement device measure the flow
velocity (Vm) as an average flow velocity of the fluid along the
propagation direction 14 of the ultrasonic waves.
The abovedescribed operation can be mathematically expressed as
follows:
and
where: Tud denotes the time required for an ultrasonic wave transmitted
from the upstream ultrasonic transceiver 12 to be received by the
downstream ultrasonic transceiver 13; Tdu denotes the time required
for an ultrasonic wave transmitted from the downstream ultrasonic
transceiver 13 to be received by the upstream ultrasonic transceiver
12; L denotes the distance between the ultrasonic transceivers 12
and 13; Vs denotes the sound velocity; and Vm denotes the flow velocity
of the fluid.
Thus,
and
The sum of the two expressions and the difference therebetween
are respectively as follows:
and
Thus,
and
As can be seen from the above, the sound velocity Vs can be calculated
based on the distance L between the ultrasonic transceivers and
the sum of the respective inverse numbers of the propagation times
Tud and Tdu. The flow velocity Vm can be calculated based on the
distance, L between the ultrasonic transceivers and the difference
between the respective inverse numbers of the propagation times
Tud and Tdu.
FIG. 4 shows a relationship between the flow velocity (Vm) of the
fluid and the flow coefficient (K) measured as described above,
for a number of data sets (Vm, K). These sets of data are stored
in the reference data memory section 5 and the flow velocity data
memory section 6.
FIG. 4 shows the flow velocity (Vm) of the fluid measured by the
flow velocity measurement device along the horizontal axis, and
the flow coefficient (K) along the vertical axis. As described above,
the flow coefficient (K) can be calculated as X=Va/Vm. Herein, the
average flow velocity (Va) can be calculated as Va=Qa/S (where,
Qa denotes the reference flow rate, and S denotes the crosssectional
area of the fluid pipe), Thus, the reference flow rate (Qa) can
be expressed as Qa=S.times.Va=S.times.K.times.Vm.
Next, a method of setting the flow coefficient (K) used in the
flow coefficient calculation section 7 according to the present
invention will be described. First, any number (e.g., five) of consecutive
sets of data (Vm, K) (17 18 19 20 and 21 in FIG. 4) are selected.
Then, an optimal approximate straight line 22 which gives the flow
rate conversion coefficient (K), is calculated by a method such
as a least square method.
The optimal approximate straight line 22 is a straight line which
gives a flow coefficient for a flow velocity value (Vm) measured
by the flow velocity measurement device. The optimal approximate
straight line 22 can be expressed by the following expression:
where A and B denote the gradient and the intercept of the line,
respectively.
An error of each of the selected five data sets with respect to
the optimal approximate straight line 22 is calculated, and it is
determined whether the error is within a predetermined range of
error Er, e.g., 0.5%. In particular, the measured flow velocity
Vm is applied to the optimal approximate straight line 22 (Kc=A.times.Vm+B)
so as to calculate an approximated flow coefficient (Kc). The calculated
flow coefficient (Kc) is compared with the measured flow coefficient
(K) so as to obtain the error therebetween.
If all of the data sets (the five data sets in this example) are
within the error Er (0.5%), a new data set 23 is added thereto,
as illustrated in FIG. 5 thereby increasing the number of data
sets to six. In the same manner as described above, another optimal
approximate straight line 24 which gives the flow coefficient (K),
is obtained by a least square method using these six sets of data.
It is determined whether all of the six data sets are within the
error Er with respect to the optimal approximate straight line 24.
In the illustrated example, one of the six data sets (e.g., the
data set 20) has an error greater than Er. Thus, in this example,
the highest possible number of consecutive data sets within the
predetermined error Er is five. Thus, a first region including the
five data sets 17 18 19 20 and 21 is set.
Next, starting from the last data set 21 in the first region, any
number of data sets (21 23 25 26 . . . ) are selected. Then,
as described above, an optimal approximate straight line is calculated
by a least square method, and it is determined whether the data
sets are within the error Er. Thus, in the manner as described above,
a second region is set which satisfies the error Er. For example,
if six, and no mote, data sets 21 23 25 26 27 and 28 are within
the error Er, the second region is determined to include the six
data sets, thereby obtaining another optimal approximate straight
line 29. This is shown in FIG. 6. In this case, the data set 21
is a boundary point between the two regions. Thereafter, further
regions are set in this manner. When the setting operation is complete,
a flow coefficient given by the optimal approximate straight line
is within the predetermined error Er in each region.
FIG. 7 illustrates the obtained optimal approximate straight line
including a plurality of regions. The optimal approximate line including
a plurality of regions 3039 which gives the flow coefficient,
is stored in the flow coefficient memory section. The first region
30 includes five data sets and the optimal approximate straight
line therefor is denoted by reference numeral 22. The second region
31 includes six data sets and the optimal approximate straight line
therefor is denoted by reference numeral 32. The third region 33
includes seven data sets and the optimal approximate straight line
therefor is denoted by reference numeral 34. The fourth region 35
includes four data sets and the optimal approximate straight line
therefor is denoted by reference numeral 36. The fifth region 37
includes four data sets and the optimal approximate straight line
therefor is denoted by reference numeral 38. The sixth region 39
includes six data sets and the optimal approximate straight line
therefor is denoted by reference numeral 40.
When using the abovedescribed method by applying it to a part
of the regions, an upper limit value or a lower limit value can
be set, so that the setting operation can be performed in one direction
toward the upper limit value or toward the lower limit value from
one data set. In such a case, it is possible to perform the setting
operation more efficiently and thus to save time.
(Embodiment 2)
FIG. 8 shows a relationship between the flow velocity (Vm) and
the flow coefficient (K) for one region stored in the flow coefficient
memory section. In FIG. 8 reference numeral 40 denotes an optimal
approximate line, 41 denotes another optimal approximate line 0.5%
higher than the optimal approximate line 40 42 denotes another
optimal approximate line 0.5% lower than the optimal approximate
line 40 43 denotes the upper limit of the region, and 44 denotes
the lower limit of the region. In this case, the relationship between
the measured flow velocity (Vm) and the flow coefficient (K) is
distributed within a range of .+.0.5% with respect to the optimal
approximate line 40 represented by a linear function. Thus, an optimal
approximate line represented by a linear function is sufficient
for approximating the obtained data points.
(Embodiment 3)
FIG. 9 shows a relationship between the flow velocity (Vm) and
the flow coefficient (K) for another region stored in the flow coefficient
memory section. In FIG. 9 reference numeral 45 denotes an optimal
approximate line, 46 denotes another optimal approximate line 0.5%
higher than the optimal approximate line 45 47 denotes another
optimal approximate line 0.5% lower than the optimal approximate
line 45 48 denotes the upper limit of the region, and 49 denotes
the lower limit of the region. In this case, the relationship between
the measured flow velocity (Vm) and the flow coefficient (K) is
distributed in a bell curvelike pattern. In particular, data points
in the middle portion of the region represented by a linear function
(between 48 and 49), are shifted toward the upper side of the optimal
approximate line 45. On the other hand, data points near the upper
limit 48 and those near the lower limit 49 are shifted toward the
lower side of the optimal approximate line 45. In this case, if
an optimal approximate line is represented by a bellshaped quadric
curve 50 the data points are more closely approximated by the optimal
approximate quadric curve.
Thus, where the data sets in the middle portion of the region are
shifted to one side of the optimal approximate straight line, it
is more effective to represent the optimal approximate line by a
quadric function rather than a linear function, so that the error
can be reduced and/or a greater range can be set as one region,
thereby making the setting operation efficient.
(Embodiment 4)
Next, another method of setting a flow coefficient will be described.
FIG. 10 shows a relationship between the measured flow velocity
(Vm) and the flow coefficient (K), for a number of data sets (Vm,
K). These sets of data are stored in the reference data memory section
5 and the flow velocity data memory section 6.
First, using all of the data sets (Vm, K) in FIG. 10 the flow
coefficient calculation section 7 calculates by a least square method,
or the like, an optimal approximate function which gives the flow
coefficient K. The optimal approximate function may be, for example,
a fifth degree curve: Y=a.sub.5.times.X.sup.5 +a.sub.4.times.X.sup.4
+a.sub.3.times.X.sup.3 +a.sub.2.times.X.sup.2 +a.sub.1.times.X.sup.1
+a.sub.0.times.X.sup.0. The optimal approximate curve is denoted
by a solid line 51 in FIG. 10. A predetermined flow velocity range
is divided into a predetermined number n of regions. Each region
is linearly approximated by using a value along the obtained solid
line 51 as a flow coefficient true value. In this way, even at a
point between two measured data points, where there in no measured
value, the flow coefficient (K) can be calculated from a flow velocity
(Vm) using the fifth degree curve 51. Thus, it is possible to more
accurately obtain an approximate straight line.
The optimal approximate line calculated as described above is stored
in the flow coefficient memory section 8.
As can be seen from the above fifth degree expression, obtaining
a fifth degree curve requires only six data points (or six unknowns
was, "a.sub.5 a.sub.4 a.sub.3 a.sub.2 a.sub.1 and a.sub.0
"). Accordingly, obtaining a quartic curve requires five data
points, and obtaining a cubic curve requires four data points. Thus,
in the manner as described above, a wide range can be covered with
a small number of data points. Moreover, if a tendency is known
in advance, the flow coefficient can be set more efficiently by
determining the relationship between the flow velocity (Vm) and
the flow coefficient (K) according to the degree of the optimal
approximate line.
(Embodiment 5)
Next, a method of dividing a given flow velocity range into n regions
will be described. FIG. 11 shows a case where the flow velocity
(Vm) range is divided into five regions. More specifically, the
flow velocity (Vm) range is divided into the following five regions:
01.3 1.32.6 2.63.9 3.95.2 and 5.26.5. For each of the boundary
Vm values, the flow coefficient (K) is calculated by using the fifth
degree curve 51. The calculated boundary points are linked to one
another by straight lines. The straight lines (denoted by five solid
lines 52 53 54 55 and 56 respectively, in FIG. 11) are used
as flow coefficient approximate straight lines. For the solid line
52 for example, the data sets at the opposite ends thereof are
calculated from the fifth degree curve 51 shown in FIG. 10 thereby
obtaining two data sets (Vm, K): (0 0.65) and (1.3 0.87). Then,
the flow coefficient (K) can be expressed by the following expression:
K=0.16.times.Vm+0.65. As described above, even a point where there
is no measured data can easily be calculated. Thus, an approximate
straight line can easily be set.
(Embodiment 6)
Next, another ndivision method will be described. FIG. 12 shows
a case where the flow coefficient (K) range is divided into three
regions. More specifically, the flow coefficient (K) range to divided
into the following three regions: 0.650.77 0.770.88 and 0.880.95.
For each of the boundary flow coefficients (K), a data set corresponding
to the boundary point is calculated. The calculated data points
are linked to one another by straight lines. The straight lines
(denoted by three solid lines 57 58 and 59 respectively, in FIG.
12) are used as flow coefficient approximate straight lines for
the respective regions.
As in Embodiment 5 even a point where there is no measured data
can easily be calculated. Thus, an approximate straight line can
easily be set. The set approximate straight lines for calculating
the flow coefficient (K) are stored in the flow coefficient memory
section.
In the setting method of Embodiment 5 an upper limit value or
a lower limit value is preferably provided for the flow velocity
(Vm) (or for the flow coefficient (K) for Embodiment 6), so that
the setting operation can be performed more efficiently. In this
way, the setting operation can be performed more efficiently within
a shorter period of time, particularly when applying the present
invention to a flow meter, or the like, where the required range,
the flow velocity range or the flow coefficient range is often prescribed.
(Embodiment 7)
Next, still another ndivision method will be described. In this
Embodiment, the width of each region (the width along the x axis)
is set to be inversely proportional to the gradient of the approximate
line so as to improve the proximity to the flow coefficient (K).
In this way, the width along the x axis is smaller for a region
where the gradient is larger, and the width along the x axis is
larger for a region where the gradient is smaller. As a result,
the proximity of the approximate straight line which depends upon
the gradient becomes more uniform across all regions. FIG. 13 shows
a case where a data range is divided into five regions in such a
manner. More specifically, the data range is divided into the following
five regions: 0.650.73 0.730.83 0.830.88 0.880.93 and 0.930.98
in terms of the flow coefficient (K). In the figure, the respective
approximate straight lines are denoted by five solid lines 60 61
62 63 and 64. As described above, even for a point where there
is no measured data, a data set corresponding to a boundary value
can easily be calculated using, the fifthdegree curve. Thus, an
approximate straight line can easily be set. The set approximate
straight lines for calculating the flow coefficient (K) are stored
in the flow coefficient memory section.
(Embodiment 8)
Next, referring to FIG. 14 a further ndivision method will be
described in which the proximity to the flow coefficient is further
improved so an to better suppress the error within the predetermined
error Er. FIG. 14 shows a fifth degree curve 51 obtained by measured
data sets (Vm, K). More particularly, FIG. 14 shows a case where
the setting operation starts from an upper limit value 65 (indicated
by the symbol ".smallcircle."), using the fifth degree
curve 51 as a flow coefficient true value with the error Er being
predetermined to be 2%, for example. Any point, e.g., a point 66
(also indicated by the symbol ".smallcircle."), is selected
along the fifth degree curve 51 at a flow velocity (Vm) smaller
than that at the point 65. Referring to an enlarged view shown in
FIG. 15 the points 65 and 66 are linked to each other by a straight
line (indicated by a broken line 67). The straight line 67 is assumed
to be an approximate straight line which gives the flow coefficient
(K). Since the straight line 67 passes through the two points 65
and 66 along the fifth degree curve 51 the coordinates (Vm, K)
of the two points 65 and 66 can easily be calculated using the fifth
degree expression shown above. Accordingly, the expression which
represents the straight line 67 passing through the two points 65
and 66 can also be calculated easily.
Then, for a selected flow velocity Vm between the points 65 and
66 the flow coefficient (K) is calculated. In particular, the true
value of the flow coefficient (K) is calculated using the fifth
degree curve 51. Moreover, for the flow velocity Vm, an approximate
value (Kc) of the flow coefficient is also calculated using the
straight line 67. The calculated approximate value (Kc) is compared
with the true value (K) so as to calculate the error therebetween.
If the error is within the predetermined error Er (2%), the point
66 is slightly moved to a smaller flow velocity (Vm) (i.e., to the
left in FIG. 15), and the abovedescribed operation is repeated.
If the calculated error is greater than the predetermined error
Er (2%), the point 66 is slightly moved to a larger flow velocity
(Vm) (i.e., to the right in FIG. 25), and the abovedescribed operation
is repeated. The amount by which the point 66 is moved each time
is dependent upon the required precision. In the present Embodiment,
the amount is set to 0.001.
FIG. 16 shows the results of the operation as described above Referring
to FIG. 16 five approximate straight lines (indicated by broken
lines 67 68 69 70 and 71) are set starting from the upper limit
value 65 (indicated by the symbol ".smallcircle."), wherein
the error is within the error Er (2% for each of the approximate
straight lines. Thus, the predetermined flow velocity (Vm) range
is divided into five regions. The obtained results show that any
point along the fifth degree curve 51 has an error within 2% as
calculated using these approximate straight lines. The set approximate
straight lines for calculating the flow coefficient (K) are stored
in the flow coefficient memory section.
(Embodiment 9)
Still another ndivision method will be described, which is similar
to Embodiment 8 but is more suitable where the maximum number of
regions, i.e., the maximum number of approximate straight lines,
is limited. For example, the maximum number of approximate straight
lines (regions) is assumed to be three. The setting operation as
shown in Embodiment 8 is performed with the error Er being predetermined
to be 2%, thereby resulting in five approximate straight lines (regions).
Since this is over the maximum number of regions available (i.e.,
three), the predetermined error Er is gradually increased, e.g.,
to 2.5%, 3.0%, and so forth, and the setting operation as shown
in Embodiment 8 is repeated. In this manner, three approximate straight
lines (regions) with an optimal error distribution across all regions
can be obtained.
When the maximum number of approximate straight lines is as large
as ten, on the other hand, the predetermined error Er can be gradually
decreased, e.g., to 1.5%, 0.5%, and so forth, thereby obtaining
ten approximate straight lines (regions) with an optimal error distribution
across all regions. For the data shown in FIGS. 14 to 16 the number
of approximate straight lines is nine with the error Er being 0.5%.
In this way, an optimal error distribution can be obtained for any
particular number of approximate straight lines. The set approximate
straight lines for calculating the flow coefficient (K) are stored
in the flow coefficient memory section.
(Embodiment 10)
Next, a function form other than the fifth degree curve which can
be used as a true value of the flow coefficient (K) will be described.
It has been found that with the arrangement of the flow velocity
measurement section as illustrated in FIGS. 2 and 3 the following
function form exhibits a higher proximity than a fifth degree function.
where X denotes the flow velocity (Vm), and Y denotes the flow
coefficient (K).
FIG. 17 shows a solid line 72 obtained by the above expression
where a=0.067 and b=0.299. It can be seen from FIG. 17 that the
solid line 72 is a good approximate curve in the wide range of flow
velocity (Vm) from 0.2 to 6.0. In this case, since there are only
two unknowns (a and b), the above expression can be calculated only
with two measured data points so as to calculate an approximate
curve over a wide range. Thus, it is also possible to calculate
an approximate straight line by calculating the above expression
from two data sets (Vm, K) and using the calculated value as a flow
coefficient true value. Thus, the operation efficiency is considerably
improved. In Embodiment 10 the abovedescribed function form is
applied to all of the regions. Alternatively, the setting operation
can efficiently be performed by partially applying it to some of
the regions.
(Embodiment 11)
Next, still another function form will be described. It has been
found that with the arrangement of the flow velocity measurement
section as illustrated in FIGS. 2 and 3 if a rectification section
is provided along the pipe upstream of the flow velocity measurement
section, the flow coefficient (K) tends to approach a constant value
in a low flow velocity region and in a high flow velocity region.
In such a case, the function form represented by the following expression
exhibits a higher proximity than that described in Embodiment 10.
where X denotes the flow velocity (Vm), Y denotes the flow coefficient
(K), and a, b and c are unknowns,
Herein, the unknown b denotes a constant value in the low flow
velocity region, i.e., a lower limit value of the flow coefficient.
The unknown a denotes a constant value in the high flow velocity
region, i.e., an upper limit value of the flow coefficient. FIG.
18 shows the measured flow coefficient values measured with the
rectification section provided on the upstream side, and the calculation
result of the above expression where a=0.920 b=0.385 and c=1.50.
In FIG. 18 each symbol ".diamond." represents a measured
value, and a solid line 73 is a curve obtained based on the above
expression. It can be seen that the above function including the
three unknowns a, b and c exhibits a good proximity over a very
wide range. The above expression can be calculated with as few as
three data sets (Vm, K). Using the obtained value as a true value
of the flow coefficient (K), it is possible to easily set an approximate
straight line to the flow coefficient (K) without having to measure
many data points.
Again, the set approximate straight lines for calculating the flow
coefficient (K) are stored in the flow coefficient memory section.
It has also been confirmed that where the flow coefficient (K) exhibits
an upward slant to the right in the high flow velocity region (i.e.,
where the flow coefficient (K) increases in proportion to the flow
velocity), the constant a in the above function form can be substituted
with d.times.X+e to obtain a good proximity to the measured values.
In such a case, however, there is one additional unknown d. In Embodiment
11 the abovedescribed function form is applied to all of the regions.
Alternatively, the setting operation can efficiently be performed
by partially applying it to some of the regions.
(Embodiment 12)
Next, how to handle a boundary point between two adjacent regions
will be discussed. The flow coefficients and the regions are set
while using successive data sets. As a result, a data set corresponding
to the boundary between two regions belongs to both of the regions.
If the flow velocity of the fluid measured by the flow velocity
measurement section coincides with a boundary flow velocity value,
it is necessary to determine whether the flow coefficient of one
region or that of the other region is to be used for the measured
flow velocity. According to Embodiment 12 a boundary value between
two adjacent regions is net so that it belongs to one of the regions
that gives a flow coefficient with a smaller error. As a result,
it is possible to reduce the error for a boundary value.
(Embodiment 13)
Next, a method of setting a boundary value will be described. An
intersection between two lowdegree optimal approximate lines which
are set for two adjacent regions is used as the boundary value therebetween.
This method reduces a gap which may occur between two adjacent
optimal approximate lines, thereby more smoothly connecting the
optimal approximate lines with one another. Moreover, with this
method, it is possible to uniquely determine the boundary between
two adjacent regions, and to realize at onetoone correspondence
between the measured flow velocity (Vm) and the flow coefficient
(K).
(Embodiment 14)
Another method of setting a flow coefficient suitable when a type
of a fluid whose flow rate is to be measured changes after setting
a flow coefficient (K). For example, assume a case where the flow
coefficient (K) of air is first measured, thereby obtaining measured
values (each denoted by the symbol ".diamond." in FIG.
18) and setting a flow coefficient (represented by the solid line
73 in FIG. 18), after which the measured fluid is changed to nitrogen,
methane, propane, etc. Referring to FIG. 18 for example, the change
in the flow coefficient (K) for air for the flow velocity range
of 07 m/s is about 0.65 to about 0.98. The mid value between the
flow coefficient values 0.65 and 0.98 is about K=0.80. Then, the
flow velocity of the new fluid for K=0.80 is measured by a flow
velocity measurement device, so as to calculate the flow velocity
ratio Rv therebetween by the following expression:
where Vm(Gas, 0.80) denotes the flow velocity of the new fluid
for K=0.80 and Vm(Air, 0.80) denotes the flow velocity of air measured
for K=0.80.
Then, the measured flow velocity Vm(Air), which can be obtained
from FIG. 18 is multiplied by the flow velocity ratio Rv so as
to obtain a new flow velocity. FIG. 19 shows the results by a two
dot chain line 74. In the illustrated example, the flow velocity
ratio Rv is about 2 to about 3. The two dot chain line 74 obtained
as described above denotes the converted flow coefficient (K) for
the new fluid (Gas). The solid line 73 in FIG. 19 denotes the flow
coefficient (K) for air.
In this manner, the flow coefficient (K) can easily be recalculated
even when the measured fluid changes. Thus, it is possible to easily
obtain the flow coefficient for a new fluid (Gas) without having
to newly measure the flow coefficient (K) for the new fluid (Gas).
In other words, it is possible to obtain a flow coefficient for
a different fluid by changing (rescaling, in this case) the flow
velocity (Vm) according to the type of the fluid. As described above,
any change in the measured fluid can be accommodated simply by multiplying
a constant, which depends upon the type of the fluid (i.e., the
flow velocity ratio Rv) to the horizontal axis value (Vm) of the
flow coefficient (K) graph.
(Embodiment 15)
A method of setting a flow coefficient for a fluid suitable when
the temperature of the fluid, whose flow rate is to be measured,
changes after setting the flow coefficient (K) for a certain fluid
at a certain temperature will be described below. When the temperature
of a fluid changes, the characteristics of the fluid may also change,
thereby causing an error in the measured flow rate value. The method
of Embodiment 15 can provide a flow rate value with a reduced error
even when the temperature of the fluid changes.
For example, assume that the flow coefficient (K) as shown in FIG.
18 is first set at a temperature Ts (e.g., 20.degree. C., 293.15
K, reference temperature). When the temperature of the fluid changes
(e.g., due to a change in the ambient temperature) to a new temperature
Ti before the flow rate of the fluid is measured, some error may
occur if the predetermined flow coefficient (K) is used with the
new temperature. It has been experimentally confirmed that it is
possible to suppress the error to a level which is practically not
problematic (e.g., about 1.5% or less), as follows. First, the flow
velocity Vi is measured at the new temperature Ti. Then, the flow
velocity Vi is converted to a new flow velocity Vi.sub.2 by the
following expression:
where Ts denotes the temperature of the fluid when setting the
flow coefficient (K), Ti denotes the temperature of the fluid when
measuring the flow rate of the fluid, Vi denotes the flow velocity
of the fluid measured at the new temperature Ti, and p denotes an
exponent to be described below. Herein, the temperatures Ts and
Ti are both absolutetemperatures [K].
Then, a flow coefficient Ki at the new temperature Ti obtained
from FIG. 18 as a flow coefficient value for the converted flow
velocity Vi.sub.2. Finally, the flow rate of the fluid is calculated
based on the obtained flow coefficient Ki.
Regarding the exponent p, it has been confirmed that the exponent
p should preferably be about 1.5 to about 3.0 and more preferably
about 2.5 the value which exhibited the best conformity to the
experimental values.
For example, assume a case where a flow coefficient (K) is met
when the temperature Ts of the fluid is 20.degree. C. (293 K), after
which the flow velocity Vi of the same fluid is measured to be 2
m/s when the temperature Ti of the fluid is 0.degree. C. (273 K).
At 20.degree. C.; the flow coefficient (K) for the flow velocity
of 2 m/s can be read from FIG. 12 to be about 0.89. However, the
flow coefficient (K) should instead be obtained as follows since
the temperature has changed to 0.degree. C. First, by using the
above expression, the measured flow velocity Vi is converted to
Vi.sub.2 as follows:
Then, the flow coefficient (Ki) for the fluid temperature of 0.degree.
C. can be read from FIG. 18 to be about 0.91 (corresponding to Vm=2.38
m/sec).
Thus, even when the temperature of the fluid changes, the flow
coefficient value for the new temperature can be obtained by converting
the solid line 73 in FIG. 18 i.e., the flow coefficient for the
first temperature (20.degree. C.), to another flow coefficient for
the now temperature, thereby eliminating the need to newly measure
the flow coefficient for the new temperature and thus making the
setting operation very efficient. In other words, since the approximate
straight line to the flow coefficient is set while using an optimal
function, it is possible, even when the temperature of the fluid
changes, to calculate a new flow coefficient for the new temperature
by a simple coordinate conversion, i.e., by multiplying a temperaturedependent
function value (e.g., the temperature ratio as in this case) to
the xaxis value (flow velocity).
To measure the temperature of the fluid, a temperature sensor may
be separately provided in the fluid pipe. However, it may not be
necessary according to the present invention. For example, when
the flow velocity of the fluid is measured by a thermal type flow
sensor, since a thermal type flow sensor includes a temperaturesensitive
resistor, the temperature of the fluid can easily be obtained by
measuring the resistance value thereof.
Also when the flow velocity of the fluid is measured by a pair
of ultrasonic transceivers which are provided along the fluid pipe
respectively on the upstream side and the downstream side with respect
to each other), it is not necessary to separately provide a temperature
sensor for the following reason.
The distance L between the upstream ultrasonic transceiver and
the downstream ultrasonic transceiver is constant and known. Therefore,
based on the average propagation time between the ultrasonic transceivers
(i.e., the sum of the inverse number of the propagation time from
the upstream side to the downstream side and the inverse number
of the propagation time from the downstream side to the upstream
side), the sound velocity Vs through the measured fluid can be obtained
by the following expression:
As can be seen, the sound velocity expression contains no term
for the flow velocity of the fluid. This means that the sound velocity
Vs through the measured fluid can be known independently of the
flow velocity of the fluid.
Since the velocity of sound propagating through a fluid is strongly
dependent upon the temperature of the fluid, it is possible to obtain
the temperature of the fluid based on the sound velocity. As is
commonly known, the sound velocity through air V(Air) m/s can be
expressed as follows by a linear function:
or
V(Air)=331.5+0.6.times.(Tabs273.15)
where t denotes a temperature in Celsius (.degree.C.), and Tabs
denotes an absolute temperature (K).
Since the temperature t of the fluid can easily be obtained from
the sound velocity V(Air), as described above, it is not necessary
in the present invention to separately provide the temperature sensor
for measuring the temperature of the fluid.
In Embodiment 15 described above, the temperature ratio of the
fluid (in absolute temperature) is used when converting the flow
coefficient to accommodate a change in the temperature of the fluid.
However, a sound velocity ratio of the fluid may alternatively be
used instead of the temperature ratio because the temperature of
a fluid and the sound velocity through the fluid are strongly correlated
with each other, as described above. In such a case, however, the
exponent p may be slightly different from that shown above.
(Embodiment 16)
A flow meter which uses a flow coefficient (K) obtained by the
flow coefficient setting method of the present invention will be
described with reference to FIG. 20. Referring to FIG. 20 the flow
meter includes: a flow velocity measurement section 4 for measuring
the flow velocity of a fluid; a flow coefficient memory section
8 for storing a flow coefficient which is set as described above
according to the present invention; a flow rate calculation section
75 for calculating the flow rate of the fluid using the flow velocity
(Vm) measured by the flow velocity measurement section 4 and the
flow coefficient (K) stored in the flow coefficient memory section
8; and an output section 76 for outputting the calculated flow rate
value (Qcal). When the flow velocity measurement section 4 measures
the flow velocity of the fluid to be Vm, a flow coefficient (K)
corresponding to the flow velocity Vm is obtained from the flow
coefficient memory section 8. Then, the flow rate calculation section
75 performs a calculation Qcal=S.times.Vm.times.K, thereby obtaining
the flow rate (Qcal) of the fluid. The calculation result is output
to the output section 76 which includes a liquid crystal display,
or the like.
As described above, the flow meter of the present invention includes
the flow coefficient memory section 8 for storing the flow coefficient
which is set based on the flow coefficient setting method as described
above in detail. Thus, the flow meter of the present invention is
capable of outputting a flow rate value with a reduced error. Even
when the type of a fluid changes from that used when setting the
flow coefficient, the flow coefficient can easily be converted as
described above, whereby the flow meter of the present invention
is still capable of outputting a flow rate value with a reduced
error. Moreover, also when the temperature of the fluid changes,
the flow coefficient can easily be converted as described above,
whereby the flow meter of the present invention is still capable
of outputting a flow rate value with a reduced error.
(Embodiment 17)
A flow meter of Embodiment 17 is similar to that described above
in Embodiment 16 but the flow velocity measurement section 4 in
Embodiment 17 employs a thermal type flow sensor. In other words,
the flow velocity measurement section 4 has a structure as illustrated
in FIG. 2. With such a structure, it is possible to provide a flow
meter having a reduced error particularly in a low flow rate region.
Moreover, the temperature of the fluid can be directly measured
from the temperaturesensitive resistor of the thermal type flow
sensor. Thus, the flow meter can be provided in a simpler structure
without having to separately provide a temperature sensor for measuring
the temperature of the fluid.
(Embodiment 18)
A flow meter of Embodiment 18 is similar to that described above
in Embodiment 16 but the flow velocity measurement section 4 in
Embodiment 18 employs a pair of ultrasonic transceivers which are
provided along the fluid pipe respectively on the upstream side
and the downstream side with respect to the flow velocity measurement
section. In other words, the flow velocity measurement section 4
has a structure as illustrated in FIG. 3. With such a structure,
it is possible to provide a flow meter having a particularly reduced
error over a wide flow rate range. Moreover, the temperature of
the fluid can be directly measured based on the sound velocity.
Thus, the flow meter can be provided in a simpler structure without
having to separately provide a temperature sensor for measuring
the temperature of the fluid.
INDUSTRIAL APPLICABILITY
As is apparent from the above description, the flow coefficient
setting method of the present invention first obtains a lowdegree
optimal approximate line using an arbitrarily selected number of
consecutive data sets, and then selects (or adjusts) the number
of data sets so as to select a highest possible number of data sets
all within a predetermined error Er, thereby efficiently setting
the optimal approximate line.
Alternatively, a highdegree function representing an optimal approximate
curve may be obtained by using a number of data sets over a wide
range, after which a lowdegree function representing an optimal
approximate line to flow coefficients is obtained based on the optimal
approximate curve. In such a case, it is possible to quickly and
efficiently calculate the flow coefficients over a wide range using
a limited number of data sets.
An alternative flow coefficient setting method of the present invention
converts a flow coefficient for one type of a fluid to a new flow
coefficient for another type of a fluid by multiplying a fluidtypedependent
constant to an xaxis value. Thus, even when the type of a fluid
changes from that used when setting a flow coefficient, the flow
coefficient can easily be converted to a new flow coefficient for
the new fluid, thereby realizing a flow coefficient with a reduced
error even when there is a change in the type of a fluid.
An alternative flow coefficient setting method of the present invention
converts a flow coefficient for one temperature to a new flow coefficient
for another temperature by multiplying a temperaturedependent function
value to an xaxis value. Thus, even when the temperature of the
fluid changes from that when setting a flow coefficient, the flow
coefficient can easily be converted to a new flow coefficient for
the new temperature, thereby realizing a flow coefficient with a
reduced error even when there is a change in the temperature of
a fluid.
A flow meter using such a flow coefficient setting method can measure
the flow rate of a fluid with a reduced error over a wide range
of flow rates.
