## Abstrict Two-wire transmitters are described in which the required voltage
that a control room must supply to the transmitter is lower at high
current than at low current, thus freeing up more voltage for other
uses, and in which a constant set of operating voltages may be maintained.
A corrected pressure in a vortex flow meter may be determined that
reflects the mass flow rate. Thus, the mass flow rate may be determined
based on the corrected pressure reading and a measured volumetric
flow rate. Density may be determined from pressure and temperature
using a table containing error values based on a standard density
determination and a relatively simple approximation. During operation
of a flow meter, the stored error values may be linearly interpolated
and the approximation may be computed to determine the density from
the stored error value.
## Claims What is claimed is:
1. A method of specifying a transmitter, the transmitter for regulating
an amplitude of a supplied current to encode a parameter, the method
comprising providing a set of data to a customer, wherein the set
of data represents a maximum allowable load at one or more supply
voltage levels, and the set of data has a first segment operable
only for a lower range of currents below a transition current and
has a second segment operable only for a higher range of currents
above the transition current.
2. The method of claim 1 wherein: the first segment results from
the transmitter multiplying a regulated current by a first non-unitary
factor when the regulated current is within the lower range of currents,
and the second segment results from the transmitter multiplying
the regulated current by a second non-unitary factor when the regulated
current is within the higher range of currents.
3. The method of claim 2 wherein the first segment approximates
a first line having a first slope, the second segment approximates
a second line having a second slope, and the first slope is at least
twice as large as the second slope.
4. A method of controlling a current signal, the method comprising:
receiving a current with a variable amplitude over a line, the amplitude
being regulated; multiplying the regulated amplitude by a first
non-unitary factor when the regulated amplitude is below a first
level; multiplying the regulated amplitude by a second non-unitary
factor when the regulated amplitude is above a second level; maintaining
a constant set of operating voltages whether the regulated amplitude
is multiplied by the first non-unitary factor or the second non-unitary
factor; and providing the multiplied amplitude and the constant
set of operating voltages to circuitry.
5. The method of claim 4 wherein: receiving the variable current
comprises receiving the current at a transmitter, and the amplitude
is regulated by the transmitter to communicate an output parameter
by encoding a value of the output parameter on the current.
6. The method of claim 4 wherein maintaining a constant set of
operating voltages comprises using a reversible power transformation.
7. The method of claim 6 wherein: multiplying by the first non-unitary
factor comprises injecting the regulated current into an input of
a first multiplier and coupling an output of the first multiplier
to an input of a second multiplier, multiplying by the second non-unitary
factor comprises injecting the regulated current into the input
of the second multiplier and into the output of the first multiplier,
and maintaining the constant set of operating voltages comprises
using a reversible multiplier for the first multiplier, allowing
regulated current that is coupled to the output of the first multiplier
to produce a current emanating from the input to the first multiplier
and having an amplitude approximately equal to the regulated current
divided by the first non-unitary factor.
8. The method of claim 7 wherein maintaining the constant set of
operating voltages further comprises regulating a voltage at the
input of the first multiplier, providing the same voltage whether
the regulated current is injected into the input of the first multiplier
or the input of the second multiplier.
9. The method of claim 4 wherein the transmitter receives power
from a supply over the line.
10. The method of claim 9 wherein the regulated current extends
over a range of about 4 milliamps to 20 milliamps.
11. The method of claim 5 wherein the output parameter is a vortex
frequency, a linear flow rate, or a volumetric flow rate.
12. The method of claim 4 wherein: receiving the variable current
comprises receiving the current at a transmitter, and the amplitude
is regulated before being received by the transmitter.
13. A transmitter comprising: a switching circuit configured to
couple a regulated current to either a first output or a second
output based on an amplitude of the regulated current; a first non-unitary
current multiplier having an input and an output, with the input
of the first non-unitary multiplier being coupled to the first output
of the switching circuit, the first non-unitary multiplier operable
in a forward direction as a current multiplier and in a backward
direction as a current divider; and a second non-unitary multiplier
having an input and an output, with the input of the second non-unitary
multiplier coupled to both the second output of the switching circuit
and the output of the first non-unitary multiplier.
14. The transmitter of claim 13 further comprising a current regulator
coupled to an input of the switching circuit and configured to regulate
the amplitude of the current to encode a value of an output parameter
on the current.
15. The transmitter of claim 14 wherein the current regulator is
configured to receive the current over a line in a two-wire system.
16. The transmitter of claim 15 wherein the current regulator is
configured to regulate the amplitude over a range extending at least
from 4 milliamps to 20 milliamps.
17. The transmitter of claim 14 wherein the current regulator is
configured as part of a vortex flow meter system and is configured
to encode a value of a vortex frequency, a linear flow rate, or
a volumetric flow rate.
18. A transmitter comprising: switching means, having a first output
and a second output, for coupling a regulated current to either
the first output or the second output based on an amplitude of the
regulated current; first means for multiplying current by a non-unitary
number, the first means having an input and an output, with the
input of the first means being coupled to the first output of the
switching means, the first means being operable in a forward direction
as a current multiplier and in a backward direction as a current
divider; and second means for multiplying current by a non-unitary
number, the second means having an input and an output, with the
input of the second means being coupled to both the second output
of the switching means and the output of the first means.
19. The transmitter of claim 18 further comprising regulating means
coupled to the switching means for regulating the amplitude of the
current to encode a value of an output parameter on the current.
20. A method of determining a pressure, the method comprising:
measuring a pressure of a fluid flowing through a system; measuring
a temperature of the flowing fluid; determining a velocity of the
flowing fluid; and determining a corrected pressure for the flowing
fluid based on the pressure, the temperature, and the velocity,
the corrected pressure corresponding to a density reflective of
the velocity and a mass flow rate.
21. The method of claim 20 further comprising determining a density
based on the pressure and the temperature, and wherein determining
the corrected pressure comprises using the following formula: 19
P c P p s + 1 2 .times. k diff .times. p s .times. V VOR 2 .
22. The method of claim 21 wherein the constant k.sub.diff is determined
during a calibration procedure for a portion of the pressurized
system, during which the mass flow rate is known.
23. The method of claim 22 wherein the calibration procedure comprises:
measuring a calibration pressure; measuring a calibration temperature;
determining a calibration density based on the calibration pressure
and the calibration temperature; determining a calibration velocity;
determining a calibration volumetric flow rate; determining the
corrected pressure using the known mass flow rate, the calibration
temperature, and the calibration volumetric flow rate; and determining
the constant k.sub.diff by using the following formula: 20 k diff
= 2 .times. ( P c - P p s ) p s .times. V VOR 2 .
24. The method of claim 22 wherein the calibration procedure comprises:
measuring a calibration pressure; measuring a calibration temperature;
determining a calibration density based on the calibration pressure
and the calibration temperature; determining a calibration velocity;
determining a volumetric flow-rate; and determining the constant
k.sub.diff by using the following formula: 21 k diff = 2 .times.
( c V VOR ) 2 .times. ( Q m p s .times. Q v - 1 ) .
25. The method of claim 20 further comprising: determining a volumetric
flow rate from the velocity; determining the density; and determining
a mass flow rate from the volumetric flow rate and the density.
26. The method of claim 20 wherein determining the velocity comprises:
using a vortex flow meter to determine a vortex frequency; and determining
the velocity based on the vortex frequency.
27. A device comprising a storage medium having instructions stored
thereon that when executed result in at least the following: measuring
a pressure of a fluid flowing through a system; measuring a temperature
of the flowing fluid; determining a velocity of the flowing fluid;
and determining a corrected pressure for the flowing fluid based
on the pressure, the temperature, and the velocity, the corrected
pressure corresponding to a density reflective of the velocity and
a mass flow rate.
28. The device of claim 27 further comprising a controller that
is part of a transmitter in a vortex flow meter system, the controller
being operable to execute the instructions.
29. The device of claim 27 wherein the device comprises a compact
diskette.
30. A method of calibrating a device, the method comprising: measuring
a pressure of a fluid flowing in a system; measuring a temperature
of the flowing fluid; determining a density of the flowing fluid
based on the pressure and the temperature; determining a velocity
of the flowing fluid; determining a volumetric flow rate of the
flowing fluid; determining a corrected pressure using a mass flow
rate, the determined volumetric flow rate, and the measured temperature,
wherein the corrected pressure corresponds to a corrected density
reflective of the determined velocity and the mass flow rate; and
determining a calibration constant k.sub.diff according to the following
equation: 22 k diff = 2 .times. ( P c - P p s ) p s .times. V VOR
2 .
31. The method of claim 30 wherein the calibration constant k.sub.diff
can be used to determine another corrected pressure during operation
with a second mass flow rate according to the following equation:
23 P c P p s + 1 2 .times. k diff .times. p s .times. V VOR 2 .
32. The method of claim 30 wherein: the device comprises a vortex
flow meter, the method further comprises using the vortex flow meter
to measure a vortex frequency of the flowing fluid, and the velocity
is determined based on the measured vortex frequency.
33. A device comprising a storage medium having instructions stored
thereon that when executed result in at least the following: measuring
a pressure of a fluid flowing in a system; measuring a temperature
of the flowing fluid; determining a density of the flowing fluid
based on the pressure and the temperature; determining a velocity
of the flowing fluid; determining a volumetric flow rate of the
flowing fluid; determining a corrected pressure using a mass flow
rate, the determined volumetric flow rate, and the measured temperature,
wherein the corrected pressure corresponds to a corrected density
reflective of the determined velocity and the mass flow rate; and
determining a calibration constant k.sub.diff according to the following
equation: 24 k diff = 2 .times. ( P c - P p s ) p s .times. V VOR
2 .
34. The device of claim 33 further comprising a controller that
is part of a transmitter in a vortex flow meter system, the controller
being operable to execute the instructions.
35. A method of calibrating a device, the method comprising: measuring
a pressure of a fluid flowing in a system; measuring a temperature
of the flowing fluid; determining a density of the flowing fluid
based on the pressure and the temperature; determining a velocity
of the flowing fluid; determining a volumetric flow rate of the
flowing fluid; and determining a calibration constant, using a known
speed of sound in the flowing fluid and a mass flow rate, according
to the following equation: 25 k diff = 2 .times. ( c V VOR ) 2 .times.
( Q m p s .times. Q v - 1 ) .
36. The method of claim 35 wherein: the calibration constant k.sub.diff
can be used to determine a corrected pressure during operation with
a second mass flow rate according to the following equation: 26
P c P p s + 1 2 .times. k diff .times. p s .times. V VOR 2 andthe
corrected pressure corresponds to a corrected density reflective
of the determined velocity and the second mass flow rate.
37. The method of claim 35 wherein: the device comprises a vortex
flow meter, the method further comprises using the vortex flow meter
to measure a vortex frequency of the flowing fluid, and the velocity
and the volumetric flow rate of the flowing fluid are determined
based on the vortex frequency.
38. A device comprising a storage medium having instructions stored
thereon that when executed result in at least the following: measuring
a pressure of a fluid flowing in a system; measuring a temperature
of the flowing fluid; determining a density of the flowing fluid
based on the pressure and the temperature; determining a velocity
of the flowing fluid; determining a volumetric flow rate of the
flowing fluid; and determining a calibration constant, using a known
speed of sound in the flowing fluid and a mass flow rate, according
to the following equation: 27 k diff = 2 .times. ( c V VOR ) 2 .times.
( Q m p s .times. Q v - 1 ) .
39. The device of claim 38 further comprising a controller that
is part of a transmitter in a vortex flow meter system, the controller
being operable to execute the instructions.
40. A method of computing density, the method comprising: accessing
a pressure input and a temperature input; determining a density
error for the pressure input and temperature input based on one
or more stored density errors, wherein the one or more stored density
errors each reflect error between a density approximation and a
standard density value for a different pressure input and temperature
input; determining a density approximation for the pressure input
and temperature input; and determining a density value for the pressure
input and temperature input based on the density error for the pressure
input and temperature input and the density approximation for the
pressure input and temperature input.
41. The method of claim 40 wherein determining the density error
for the pressure input and temperature input comprises interpolating
between at least two stored density errors.
42. The method of claim 41 wherein interpolating comprises linear
interpolating.
43. The method of claim 40 wherein the one or more stored density
errors comprises multiple stored density errors and the multiple
stored density errors represent density errors for different pressure
and temperature inputs that are not equally spaced in at least one
of pressure or temperature.
44. The method of claim 43 wherein the spacing of at least one
of pressure and temperature is closer for a first pressure and temperature
range than for a second pressure and temperature range, and density
changes more rapidly within the first range than the second range.
45. The method of claim 40 wherein the one or more stored density
errors comprises multiple stored density errors and the multiple
stored density errors have each been scaled.
46. The method of claim 40 wherein error between a given density
approximation and a given standard density value is expressed as
a ratio involving the given density approximation and the given
standard density value.
47. The method of claim 40 wherein the one or more stored density
errors comprises stored density errors for pressure and temperature
inputs on both a first side and a second side of a saturation line,
and stored density errors for pressure and temperature inputs on
the second side are based on an extrapolation of standard density
values for pressure and temperature inputs on the first side.
48. The method of claim 40 wherein: determining the density approximation
for the pressure input and temperature input comprises using an
approximation equation that is a third order, or lower order, equation,
and an error between the determined density value and a standard
density value for the pressure input and temperature input is 0.1%
or less.
49. The method of claim 40 wherein determining the density approximation
for the pressure input and temperature input comprises using a virial
equation.
50. The method of claim 40 wherein determining the density approximation
for the pressure input and temperature input comprises using an
approximation equation that has been tailored to a range of densities
needed.
51. The method of claim 50 wherein the approximation equation comprises
a virial equation having coefficients that have been tailored to
the range of densities needed.
52. A device comprising a storage medium having instructions stored
thereon that when executed result in at least the following: accessing
a pressure input and a temperature input; determining a density
error for the pressure input and temperature input pair based on
one or more stored density errors, wherein the one or more stored
density errors each reflect error between a density approximation
and a standard density value for a different pressure input and
temperature input; determining a density approximation for the pressure
input and temperature input; and determining a density value for
the pressure input and temperature input based on the density error
for the pressure input and temperature input and the density approximation
for the pressure input and temperature input.
53. The device of claim 52 further comprising a controller that
is part of a transmitter in a vortex flow meter, the controller
being operable to execute the instructions.
54. A device comprising a storage medium having stored thereon
density errors computed using at least the following operations:
determine a standard density value for each of multiple pressure
and temperature input pairs; determine a density approximation for
each of the multiple pressure and temperature input pairs; and determine
a density error, based on the standard density value and the density
approximation, for each of the multiple pressure and temperature
input pairs.
55. The device of claim 54 wherein the multiple pressure and temperature
input pairs are not equally spaced in at least one of pressure or
temperature.
56. The device of claim 55 wherein the spacing of at least one
of pressure and temperature is closer for a first pressure and temperature
range than for a second pressure and temperature range, and density
changes more rapidly within the first range than the second range.
57. The device of claim 54 wherein the multiple determined density
errors are scaled before being stored on the storage medium.
58. The device of claim 54 wherein determining the density error
for each of the multiple pressure and temperature input pairs comprises
determining a ratio involving the standard density value and the
density approximation for each of the pressure and temperature input
pairs.
59. The device of claim 54 wherein: the multiple pressure and temperature
input pairs include pairs on both a first side and a second side
of a saturation line, and determining a standard density value for
pressure and temperature input pairs on the second side is based
on an extrapolation of standard density values for pressure and
temperature input pairs on the first side.
60. The device of claim 54 wherein determining the density approximation
for each of the multiple pressure and temperature input pairs comprises
using an approximation equation that is a third order, or lower
order, equation.
61. The device of claim 54 wherein determining the density approximation
for each of the multiple pressure and temperature input pairs comprises
using a virial equation.
62. The device of claim 54 wherein determining the density approximation
for each of the multiple pressure and temperature input pairs comprises
using an approximation equation that has been tailored to a range
of the determined standard density values.
63. The device of claim 54 wherein determining the density approximation
for each of the multiple pressure and temperature input pairs comprises
using a virial equation having coefficients that have been tailored
to the range of the determined standard density values.
## Description TECHNICAL FIELD
[0001] Certain implementations relate generally to processing and
transmitting data, and more particularly to power reduction and
data processing in a vortex flow meter.
BACKGROUND
[0002] Flow meters may measure the rate of flow of a fluid in a
pipe or other pathway. The fluid may be, for example, a gas or a
liquid, and may be compressible or incompressible. One type of flow
meter is a vortex flow meter which measures parameters including,
for example, flow rate based on the principle of vortex shedding.
Vortex shedding refers to a natural process in which a fluid passing
a bluff body causes a boundary layer of slowly moving fluid to be
formed along the surface of the bluff body. A low pressure area
is created behind the bluff body and causes the boundary layer to
roll up, which generates vortices in succession on opposite sides
of the bluff body. The vortices induce pressure variations that
may be sensed by a pressure sensor. The vortex-shedding pressure
variations have a frequency that is related to the flow rate. Accordingly,
by measuring the frequency of the pressure variations, the flow
rate may be determined.
[0003] Vortex flow meters provide vortex frequency data that in
conjunction with flow calibration factors determine the velocity
and volumetric flow rate of the fluid passing through the meter.
With inputted fluid density values, the mass flow rate can also
be computed. These measurements, and others, can be transmitted
to a control room or other receiver over a communication line, such
as, for example, a standard two-wire 4-20 milliamp ("mA")
transmission line.
SUMMARY
[0004] Certain implementations described below provide a two-wire
transmitter in which the required voltage that a control room must
supply to the transmitter is lower at high current than at low current,
thus freeing up more voltage for other uses. The transmission line
and any other resistive elements in the line generally consume more
voltage at high current. Accordingly, the maximum load resistance
of the transmission system, excluding the transmitter, is generally
dictated by the transmitter's required voltage at high current.
By lowering the transmitter's required voltage at high current,
therefore, it is possible to design the rest of the system with
a higher resistive load. The lower required voltage and the higher
allowable load can be specified to a customer, allowing the customer
to design a system to those specifications.
[0005] The required voltage can be lowered in these implementations
because at high current the majority of the transmitter's current
requirements can be met by doubling the current, rather than multiplying
it by four. By merely doubling the current, the voltage is only
divided by two, rather than by four. Thus, the required starting
voltage, to achieve a given divided voltage, is also cut in half.
[0006] Certain implementations of a two-wire transmitter multiply
the current by injecting the controlled current amplitude into either
a first or a second of two current doublers coupled in series. If
the current is low and needs to be multiplied by four, then the
controlled current is injected into the first doubler. If, however,
the current is high and only needs to be multiplied by two, then
the controlled current is injected into the second doubler.
[0007] Certain of these implementations use a reverse power transformation
for the first current doubler. In this way, when current is injected
into the second current doubler, the current is also injected into
the output of the first current doubler. The first current doubler
then operates in reverse and divides the controlled current by two.
The first current doubler, operating in reverse, also multiplies
the voltage by two. Thus, even though the required voltage has been
lowered, a higher voltage is still available to power circuitry
needing the higher voltage. In this way, a constant set of operating
voltages is maintained whether the received current is high or low.
[0008] Certain implementations of a transmitter described below
determine a corrected pressure, based on a pressure reading and
a velocity determination. The corrected pressure value along with
a temperature measurement are used to determine the correct density
value which in conjunction with the volumetric flow measurement
allow the calculation of mass flow rate, for example.
[0009] Certain implementations calculate the density, using the
corrected pressure and a measured temperature, by performing a table
look-up of stored density errors. The stored density errors are
linearly interpolated to provide a density error corresponding to
the desired pressure and temperature. The interpolated density error
reflects an estimate of an error between a standard density value
and an approximated density. The approximated density is computed
for the desired pressure and temperature, and combined with the
interpolated density error to yield the estimate of the actual density
value. In this way, instead of computing the actual density value
in real time, the approximated density is computed in real time.
Because the actual density calculation is generally a time consuming
calculation, and because the density approximation can be selected
to be comparatively fast, the estimate of the density is determined
quickly in real time.
[0010] According to a general aspect, specifying a transmitter
for regulating an amplitude of a supplied current to encode a parameter
includes providing a set of data to a customer. The set of data
represents a maximum allowable load at one or more supply voltage
levels. The set of data has a first segment used only for a lower
range of currents below a transition current, and a second segment
used only for a higher range of currents above the transition current.
[0011] The first segment may result from the transmitter multiplying
a regulated current by a first non-unitary factor when the regulated
current is within the lower range of currents. The second segment
may result from the transmitter multiplying the regulated current
by a second non-unitary factor when the regulated current is within
the higher range of currents. The first segment may approximate
a first line having a first slope. The second segment may approximate
a second line having a second slope. The first slope may be at least
twice as large as the second slope.
[0012] According to another general aspect, controlling a current
signal includes receiving a current with a variable amplitude over
a line, wherein the amplitude is regulated. The regulated amplitude
is multiplied by a first non-unitary factor when the regulated amplitude
is below a first level. The regulated amplitude is multiplied by
a second non-unitary factor when the regulated amplitude is above
a second level. A constant set of operating voltages is maintained
whether the regulated amplitude is multiplied by the first non-unitary
factor or the second non-unitary factor. The multiplied amplitude
and the constant set of operating voltages are provided to circuitry.
[0013] Receiving the variable current may include receiving the
current at a transmitter. The amplitude may be regulated by the
transmitter to communicate an output parameter by encoding a value
of the output parameter on the current. Maintaining a constant set
of operating voltages may include using a reversible power transformation.
Multiplying by the first non-unitary factor may include injecting
the regulated current into an input of a first multiplier and coupling
an output of the first multiplier to an input of a second multiplier.
Multiplying the second non-unitary factor may include injecting
the regulated current into the input of the second multiplier and
into the output of the first multiplier. Maintaining the constant
set of operating voltages may include using a reversible multiplier
for the first multiplier, allowing regulated current that is coupled
to the output of the first multiplier to produce a current emanating
from the input to the first multiplier and having an amplitude approximately
equal to the regulated current divided by the first non-unitary
factor. Maintaining the constant set of operating voltages may further
include regulating a voltage at the input of the first multiplier,
providing the same voltage whether the regulated current is injected
into the input of the first multiplier or the input of the second
multiplier.
[0014] The transmitter may receive power from a supply over the
line. The regulated current may extend over a range of about 4 milliamps
to 20 milliamps. The output parameter may be a vortex frequency,
a linear flow rate, or a volumetric flow rate. Receiving the variable
current may include receiving the current at a transmitter, and
the amplitude may be regulated before being received by the transmitter.
[0015] According to another general aspect, a transmitter includes
a switching circuit configured to couple a regulated current to
either a first output or a second output based on the amplitude
of the regulated current. The transmitter includes a first non-unitary
current multiplier having an input and an output, with the input
of the first non-unitary multiplier being coupled to the first output
of the switching circuit, wherein the first non-unitary multiplier
is configured to operate in a forward direction as a current multiplier
and in a backward direction as a current divider. The transmitter
includes a second non-unitary multiplier having an input and an
output, with the input of the second non-unitary multiplier being
coupled to both the second output of the switching circuit and the
output of the first non-unitary multiplier.
[0016] The transmitter may include a current regulator coupled
to an input of the switching circuit and configured to regulate
an amplitude of the current to encode a value of an output parameter
on the current. The current regulator may be configured to receive
the current over a line in a two-wire system. The current regulator
may be configured to regulate the amplitude over a range extending
at least from 4 milliamps to 20 milliamps. The current regulator
may be configured as part of a vortex flow meter system and be configured
to encode a value of a vortex frequency, a linear flow rate, or
a volumetric flow rate.
[0017] According to another general aspect, a transmitter includes
a switching mechanism having a first output and a second output,
for coupling a regulated current to either the first output or the
second output based on the amplitude of the regulated current. The
transmitter includes a first mechanism for multiplying current by
a non-unitary number, the first mechanism having an input and an
output, with the input of the first mechanism being coupled to the
first output of the switching mechanism, wherein the first mechanism
is configured to operate in a forward direction as a current multiplier
and in a backward direction as a current divider. The transmitter
includes a second mechanism for multiplying current by a non-unitary
number, the second mechanism having an input and an output, with
the input of the second mechanism being coupled to both the second
output of the switching mechanism and the output of the first mechanism.
[0018] The transmitter may further include a regulating mechanism
coupled to the switching mechanism for regulating the amplitude
of the current to encode a value of an output parameter on the current.
[0019] According to another general aspect, determining a pressure
includes (i) measuring a pressure of a fluid flowing through a system,
(ii) measuring a temperature of the flowing fluid, (iii) determining
a velocity of the flowing fluid, and (iv) determining a corrected
pressure for the flowing fluid based on the pressure, the temperature,
and the velocity, wherein the corrected pressure corresponds to
a density reflective of the velocity and a mass flow rate.
[0020] Determining a pressure may include determining a density
based on the pressure and the temperature, and determining the corrected
pressure may include using the following formula: 1 P c P p s +
1 2 .times. k diff .times. p s .times. V VOR 2 .
[0021] The constant k.sub.diff may be determined during a calibration
procedure for a portion of the system, during which the mass flow
rate is known. The calibration procedure may include (i) measuring
a calibration pressure, (ii) measuring a calibration temperature,
(iii) determining a calibration density based on the calibration
pressure and the calibration temperature, (iv) determining a calibration
velocity, (v) determining a calibration volumetric flow rate, (vi)
determining the corrected pressure using the known mass flow rate,
the calibration temperature, and the calibration volumetric flow
rate, and (vii) determining the constant k.sub.diff by using the
following formula: 2 k diff = 2 .times. ( P c - P p s ) p s .times.
V VOR 2 .
[0022] The calibration procedure may include (i) measuring a calibration
pressure, (ii) measuring a calibration temperature, (iii) determining
a calibration density based on the calibration pressure and the
calibration temperature, (iv) determining a calibration velocity,
(v) determining a volumetric flow-rate, and (vi) determining the
constant k.sub.diff by using the following formula: 3 k diff = 2
.times. ( c V VOR ) 2 .times. ( Q m p s .times. Q v - 1 ) .
[0023] Determining a pressure may further include (i) determining
a volumetric flow rate from the velocity, (ii) determining the density,
and (iii) determining a mass flow rate from the volumetric flow
rate and the density. Determining the velocity may include using
a vortex flow meter to determine a vortex frequency, and determining
the velocity based on the vortex frequency.
[0024] A device may include a storage medium having instructions
stored thereon that when executed result in at least the following:
(i) measuring a pressure of a fluid flowing through a system, (ii)
measuring a temperature of the flowing fluid, (iii) determining
a velocity of the flowing fluid, and (iv) determining a corrected
pressure for the flowing fluid based on the pressure, the temperature,
and the velocity, the corrected pressure corresponding to a density
reflective of the velocity and a mass flow rate. The device may
further include a controller that is part of a transmitter in a
vortex flow meter system, the controller being operable to execute
the instructions. The device may include a compact diskette.
[0025] According to another general aspect, calibrating a device
includes (i) measuring a pressure of a fluid flowing in a system,
(ii) measuring a temperature of the flowing fluid, (iii) determining
a density of the flowing fluid based on the pressure and the temperature,
(iv) determining a velocity of the flowing fluid, (v) determining
a volumetric flow rate of the flowing fluid, (vi) determining a
corrected pressure using a mass flow rate, the determined volumetric
flow rate, and the measured temperature, wherein the corrected pressure
corresponds to a corrected density reflective of the determined
velocity and the mass flow rate, and (vii) determining a calibration
constant k.sub.diff according to the following equation: 4 k diff
= 2 .times. ( P c - P p s ) p s .times. V VOR 2 .
[0026] The calibration constant k.sub.diff may be used to determine
another corrected pressure during operation with a second mass flow
rate according to the following equation: 5 P c P p s + 1 2 .times.
k diff .times. p s .times. V VOR 2 .
[0027] The device may include a vortex flow meter, the vortex flow
meter may be used to measure a vortex frequency of the flowing fluid,
and the velocity may be determined based on the measured vortex
frequency.
[0028] A device may include a storage medium having instructions
stored thereon that when executed result in at least the following:
(i) measuring a pressure of a fluid flowing in a system, (ii) measuring
a temperature of the flowing fluid, (iii) determining a density
of the flowing fluid based on the pressure and the temperature,
(iv) determining a velocity of the flowing fluid, (v) determining
a volumetric flow rate of the flowing fluid, (vi) determining a
corrected pressure using a mass flow rate, the determined volumetric
flow rate, and the measured temperature, wherein the corrected pressure
corresponds to a corrected density reflective of the determined
velocity and the mass flow rate, and (vii) determining a calibration
constant k.sub.diff according to the following equation: 6 k diff
= 2 .times. ( P c - P p s ) p s .times. V VOR 2 .
[0029] The device may include a controller that is part of a transmitter
in a vortex flow meter system, the controller being operable to
execute the instructions.
[0030] According to another general aspect, calibrating a device
includes (i) measuring a pressure of a fluid flowing in a system,
(ii) measuring a temperature of the flowing fluid, (iii) determining
a density of the flowing fluid based on the pressure and the temperature,
(iv) determining a velocity of the flowing fluid, (v) determining
a volumetric flow rate of the flowing fluid, and (vi) determining
a calibration constant, using a known speed of sound in the flowing
fluid and a mass flow rate, according to the following equation:
7 k diff = 2 .times. ( c V VOR ) 2 .times. ( Q m p s .times. Q v
- 1 ) .
[0031] The calibration constant k.sub.diff may be used to determine
a corrected pressure during operation with a second mass flow rate
according to the following equation: 8 P c P p s + 1 2 .times. k
diff .times. p s .times. V VOR 2 and
[0032] the corrected pressure may correspond to a corrected density
reflective of the determined velocity and the second mass flow rate.
The device may include a vortex flow meter, calibrating the device
may further include using the vortex flow meter to measure a vortex
frequency of the flowing fluid, and the velocity and the volumetric
flow rate of the flowing fluid may be determined based on the vortex
frequency.
[0033] A device may include a storage medium having instructions
stored thereon that when executed result in at least the following:
(i) measuring a pressure of a fluid flowing in a system, (ii) measuring
a temperature of the flowing fluid, (iii) determining a density
of the flowing fluid based on the pressure and the temperature,
(iv) determining a velocity of the flowing fluid, (v) determining
a volumetric flow rate of the flowing fluid, and (vi) determining
a calibration constant, using a known speed of sound in the flowing
fluid and a mass flow rate, according to the following equation:
9 k diff = 2 .times. ( c V VOR ) 2 .times. ( Q m p s .times. Q v
- 1 ) .
[0034] The device may further include a controller that is part
of a transmitter in a vortex flow meter system, the controller being
operable to execute the instructions.
[0035] According to another general aspect, computing density includes
(i) accessing a pressure input and a temperature input, (ii) determining
a density error for the pressure input and temperature input based
on one or more stored density errors, wherein the one or more stored
density errors each reflect error between a density approximation
and a standard density value for a different pressure input and
temperature input, (iii) determining a density approximation for
the pressure input and temperature input, and (iv) determining a
density value for the pressure input and temperature input based
on the density error for the pressure input and temperature input
and the density approximation for the pressure input and temperature
input.
[0036] Determining the density error for the pressure input and
temperature input may include interpolating between at least two
stored density errors. Interpolating may include linear interpolating.
The one or more stored density errors may include multiple stored
density errors and the multiple stored density errors may represent
density errors for different pressure and temperature inputs that
are not equally spaced in at least one of pressure or temperature.
The spacing of at least one of pressure and temperature may be closer
for a first pressure and temperature range than for a second pressure
and temperature range, and density may change more rapidly within
the first range than the second range.
[0037] The one or more stored density errors may include multiple
stored density errors and the multiple stored density errors may
each have been scaled. Error between a given density approximation
and a given standard density value may be expressed as a ratio involving
the given density approximation and the given standard density value.
The one or more stored density errors may include stored density
errors for pressure and temperature inputs on both a first side
and a second side of a saturation line, and stored density errors
for pressure and temperature inputs on the second side may be based
on an extrapolation of standard density values for pressure and
temperature inputs on the first side.
[0038] Determining the density approximation for the pressure input
and temperature input may include using an approximation equation
that is a third order, or lower order, equation, and an error between
the determined density value and a standard density value for the
pressure input and temperature input may be 0.1% or less. Determining
the density approximation for the pressure input and temperature
input may include using a virial equation. Determining the density
approximation for the pressure input and temperature input may include
using an approximation equation that has been tailored to a range
of densities needed. The approximation equation may include a virial
equation having coefficients that have been tailored to the range
of densities needed.
[0039] A device may include a storage medium having instructions
stored thereon that when executed result in at least the following:
(i) accessing a pressure input and a temperature input, (ii) determining
a density error for the pressure input and temperature input based
on one or more stored density errors, wherein the one or more stored
density errors each reflect error between a density approximation
and a standard density value for a different pressure input and
temperature input, (iii) determining a density approximation for
the pressure input and temperature input, and (iv) determining a
density value for the pressure input and temperature input based
on the density error for the pressure input and temperature input
and the density approximation for the pressure input and temperature
input. The device may further include a controller that is part
of a transmitter in a vortex flow meter, the controller being operable
to execute the instructions.
[0040] According to another general aspect, a device includes a
storage medium having stored thereon density errors computed using
at least the following operations: (i) determine a standard density
value for each of multiple pressure and temperature input pairs,
(ii) determine a density approximation for each of the multiple
pressure and temperature input pairs, and (iii) determine a density
error, based on the standard density value and the density approximation,
for each of the multiple pressure and temperature input pairs.
[0041] The multiple pressure and temperature input pairs need not
be equally spaced in at least one of pressure or temperature. The
spacing of at least one of pressure and temperature may be closer
for a first pressure and temperature range than for a second pressure
and temperature range, and density may change more rapidly within
the first range than the second range. The multiple determined density
errors may be scaled before being stored on the storage medium.
Determining the density error for each of the multiple pressure
and temperature input pairs may include determining a ratio involving
the standard density value and the density approximation for each
of the pressure and temperature input pairs.
[0042] The multiple pressure and temperature input pairs may include
pairs on both a first side and a second side of a saturation line,
and determining a standard density value for pressure and temperature
input pairs on the second side may be based on an extrapolation
of standard density values for pressure and temperature input pairs
on the first side. Determining the density approximation for each
of the multiple pressure and temperature input pairs may include
using an approximation equation that is a third order, or lower
order, equation.
[0043] Determining the density approximation for each of the multiple
pressure and temperature input pairs may include using a virial
equation. Determining the density approximation for each of the
multiple pressure and temperature input pairs may include using
an approximation equation that has been tailored to a range of the
determined standard density values. Determining the density approximation
for each of the multiple pressure and temperature input pairs may
include using a virial equation having coefficients that have been
tailored to the range of the determined standard density values.
[0044] The details of one or more implementations are set forth
in the accompanying drawings and the description below. Other features
will be apparent from the description, the drawings, and the claims.
DESCRIPTION OF DRAWINGS
[0045] FIG. 1 shows one implementation of a system including a
vortex flow meter.
[0046] FIG. 2 shows an exemplary implementation of the transmitter
from FIG. 1.
[0047] FIG. 3 is a graph of compliance voltage versus current for
the transmitter of FIG. 2.
[0048] FIG. 4 is a graph of output load versus supply voltage for
the transmitter of FIG. 2.
[0049] FIG. 5 is a graph of output load versus supply voltage for
another implementation of a transmitter.
[0050] FIG. 6 shows a first calibration process to determine the
term k.sub.diff.
[0051] FIG. 7 shows a second calibration process to determine the
term k.sub.diff.
[0052] FIG. 8 shows a process for creating a table of density errors.
[0053] FIG. 9 shows temperature, pressure pairs on two sides of
a saturation line.
[0054] FIG. 10 shows a process for using a table created with the
process of FIG. 8.
DETAILED DESCRIPTION
[0055] General Description and Power Control
[0056] Referring to FIG. 1 a system 100 includes a pipe 10 through
which a fluid is flowing in the direction indicated by an arrow
120. Fluid flows past a bluff body 130 that generates vortices in
succession on opposite sides of the bluff body 130. The vortices
induce pressure variations that are sensed by a vortex pressure
sensor (not shown) and converted to an electrical signal that is
provided to a transmitter 140 over a set of communication lines
150. The transmitter 140 also receives signals over the communication
lines 150 from a pressure sensor 160 and a temperature sensor 170
that measure the pressure and temperature, respectively, of the
fluid away from the bluff body 130 vortices. The transmitter 140
is coupled to a control room 180 over a two-wire transmission line
190. The control room 180 provides power to the transmitter 140
over the line 190 by providing current at a specific voltage. The
amount of current supplied is controlled by the transmitter 140
and is used to communicate the value of an output parameter. The
output parameter may be, for example, fluid velocity, volumetric
flow rate, or mass flow rate. In the case where the line 190 is
part of a 4-20 mA transmission system, the transmitter varies the
current between approximately 4 mA and 20 mA depending on the level
of the output parameter. In practice, 4-20 mA systems have an actual
current that may fluctuate between, for example, 3.6 mA and 22 mA.
[0057] Referring to FIG. 2 the transmitter 140 receives power
over an input line 292. The input power has a voltage determined
by the control room 180 and is received by a current controller
240. The current controller 240 determines the amount of current
that is drawn by the transmitter 140 and supplies the current to
a switch 241. The current controller 240 controls the switch 241
using a control line 242. If the current is low, then the control
line 242 directs the switch 241 to inject the current out of an
output 243 (labeled "L") that is shunt regulated at V.sub.0
volts. If the current is high, then the control line 242 directs
the switch 241 to inject the current out of an output 244 (labeled
"H") that is shunt regulated at V.sub.0/2 volts.
[0058] The output 243 is coupled to a load 245 and a voltage divider
246. The load 245 represents circuitry operating at a voltage of
V.sub.0 volts. The voltage divider 246 is a divide-by-two circuit,
and also has the effect of doubling the current. Thus the voltage
divider 246 can equivalently be referred to as a current multiplier.
The voltage divider 246 is also a reversible power transformer,
meaning that it can be operated in the reverse direction as explained
below.
[0059] The output 244 is coupled to a voltage divider 247 that
divides the voltage by two and multiplies the current by two, providing
the output signal to a load 248. The load 248 represents circuitry
operating at V.sub.0/4 volts. In one implementation having V.sub.0
set to 14 volts, V.sub.0/4 is 3.5 volts and most of the circuitry
for processing the fluid flow information operates at V.sub.0/4.
The load 248 receives the communication lines 150 that include signals
representing the vortex pressure signal as well as the pressure
and temperature at a point away from the vortices. The load 248
supplies a control signal 249 to the current controller 240 indicating
how much current the transmitter 140 should draw to properly encode
the output parameter. The indication may be, for example, the level
of the output parameter or the level of the current that should
be drawn.
[0060] The output 244 is also coupled to the "output"
of the voltage divider 246. Because the voltage divider 246 is reversible,
the controlled current is divided by two (and the voltage is doubled)
by the voltage divider operating in reverse, and the resulting signal
appears at the output 243 of the switch 241. Using a reversible
power transformation, such as the voltage divider 246 allows the
transmitter 140 to maintain a constant set of operating voltages
irrespective of whether a low current or a high current is being
drawn. Although the operating voltages are maintained, the amount
of current at each of those voltages varies.
[0061] Referring to FIG. 3 a graph 300 shows compliance voltage
versus current for the transmitter 140 where compliance voltage
is the voltage required by the transmitter. As the graph 300 indicates,
at high current the required voltage is lower than at low current.
The discussion of FIG. 2 above stated that the switch 241 provided
current on the output 243 for low current and on the output 244
for high current. As the graph 300 suggests, "low" generally
refers to current below 8 mA and "high" generally refers
to current above 9 mA. The graph 300 also shows that hysteresis
is built into the current controller 240 so that it does not oscillate
around a switch point.
[0062] At low current, the circuitry of one implementation of the
transmitter 140 requires 15.8 volts plus the voltage drop across
a 50 Ohm load. At 4 ma, the voltage drop across 50 Ohms is 0.20
volts and the total required voltage is 16.0 volts, as indicated
in the graph 300. At 9 ma, the voltage drop across 50 Ohms is 0.45
volts and the total required voltage is 16.25 volts, as indicated
in the graph 300. These voltages reflect a shunt regulated V.sub.0
equal to 13.75 volts. After 9 ma, as indicated in FIG. 2 the controlled
current is injected at a voltage of V.sub.0/2 which is 6.875 volts.
The required voltage does not drop by V.sub.0/2 due to the presence
of additional circuitry (not shown in FIG. 2), but the required
voltage does drop to 9.625 volts (a drop of 6.175 volts) plus the
voltage drop across a 94 Ohm load which reflects an additional 44
Ohm resistor (not shown in FIG. 2). At 9 ma, the voltage drop across
94 Ohms is 0.846 volts and the total required voltage is 10.47 volts.
At 22 ma, the voltage drop across 94 Ohms is 2.068 volts and the
total required voltage is 11.69 volts.
[0063] Referring to FIG. 4 a graph 400 shows the impact on allowed
load from reducing the required voltage at high current. The voltage
supplied by the control room 180 shown on the x-axis of the graph
400 is expended in the various components of a transmission loop.
Those components may include, for example, the transmitter 140
the transmission line 190 various other components including a
sense resistor used by the control room 180 to sense the current,
and an intrinsic safety ("IS") barrier having a resistance.
A system designer is generally interested in knowing the maximum
output load that can be used with a given transmitter. That information
can be supplied by the graph 400 for the transmitter 140. For example,
a line A shows that with a 24 volt power supply, the transmission
loop can have an output load of 559 Ohms. If a sense resistor having
250 Ohms is used, and IS barrier resistance is 273 Ohms, then 36
Ohms is available for line drop. Using 24 American Wire Gauge ("AWG")
wire, 36 Ohms allows for a loop of 697 feet each way, for a round
trip of 2*697 feet.
[0064] The line A reflects the output load allowable when the transmitter
is drawing a high current. The data points in the line A assume
that 22 mA is being drawn, which leaves the least amount of voltage
remaining for the rest of the transmission system. Because the required
voltage at 22 mA is 11.69 volts ("V"), there is approximately
12.3 V (24-11.69) available. This allows a resistance of 559 Ohms
(12.3 V/22 mA). A line B reflects the output load allowable when
the transmitter is drawing a low current. The data points in the
line B assume that 9 mA is being drawn, because that is the highest
"low" current. Thus, data points on the line B have a
resistance of (supply voltage -16.25 V)/9 mA. If the line B were
shown for 24 V, it would provide an allowable resistance of 861
Ohms (7.75 V/9 mA). As indicated in the preceding examples, the
data points on each of the lines A and B assume that all supplied
voltage except for the required compliance voltage is available
and Ohm's Law (V=I*R) is used to determine the allowable output
load at the maximum current. The maximum output load allowable for
a system is the lower of the two values provided by the lines A
and B for a given voltage supply. By lowering the required voltage
at high currents, the transmitter 140 is making additional power
available to the rest of the system when the system needs it most.
[0065] A line C reflects the output load line for a transmitter
with a compliance voltage of approximately 12.5 volts, for all current
values. As can be seen, the implementation of the lines A and B,
having a variable compliance voltage, allows a higher load resistance
than the implementation of the line C for all supply voltages higher
than approximately 19 V. The implementation of the lines A and B
draws a power equal to (4 mA)*(16.25 V), or 65 milliwatts. The implementation
of the line C, however, draws only (4 mA)*(12.5 V), or 50 milliwatts.
Thus, for supply voltages of 19 V or more, the implementation of
the lines A and B draws 30% more power than the implementation of
the line C and allows a load that is at least as large.
[0066] The allowable output load can be increased by moving the
switching point and by lowering the required voltage at either high
or low current. For example, if the switching point were lowered
from 9 mA to a lower value, then the line B would maintain the same
allowable resistance of zero Ohms at approximately 16.25 volts,
but would rotate counterclockwise about that point (slope is 1/I).
When the injection point is moved and the switching point is lowered,
the minimum required power needs to be maintained. Thus, in the
implementation of FIG. 2 when the injection point is moved to the
junction between the voltage dividers 246 247 the switching point
is not lowered below 8 mA and the minimum required power is maintained.
For example, power of at least V.sub.0 volts*4 mA is maintained
at the output 243 of the switch 241 regardless of the value of the
regulated current. Additionally, if the required voltage at high
current (or low current) were lowered, then the line A (or the line
B) would shift to the left.
[0067] As explained earlier, the implementation of FIGS. 2-4 uses
two current multipliers (voltage dividers) 246 247. The use of
two non-unitary multipliers (that is, multipliers that multiply
by a number other one) to achieve the desired low-current multiplication
allows one of the multipliers (the voltage divider 246) to be switched
out at high-current while the other multiplier (the voltage divider
247) remains in the circuit. Switching out only one of the voltage
dividers allows the switching point to be lower than if all of the
voltage dividers were switched out, as further explained below with
respect to FIG. 5. This results in a steeper low-current line segment
in a corresponding load curve, and allows more load points to be
characterized by the high-current line, which also shifts left by
a lower amount because of the lower transition point.
[0068] Referring to FIG. 5 for an example, if the implementation
of FIG. 2 is modified so that the two voltage dividers 246 247
are combined into a divide-by-four, then the switching point would
not be until approximately 16 mA (ignoring any hysteresis), instead
of 8 mA. This is because at least 16 mA are provided to the load
248. That would result in a low-current load curve having a line
B' (corresponding to the line B) with a slope of 1/0.016 rather
than 1/0.009. Additionally, because both voltage dividers are switched
out at 16 mA in this example, the required high-current voltage
would further drop by approximately V.sub.0/4 (approximately 3.5
volts), resulting in a line A' (corresponding to the line A) shifted
left by an additional 3.5 volts. A customer with a supply voltage
of 24 volts would now only be allowed to insert approximately 484
Ohms into the transmission loop. Note that 484 Ohms is given by
the line B' (24-16.25 V/16 mA) rather than the line A' which yields
approximately 719 Ohms (24-(11.69-3.5) V/22 mA). The new load figure
of 484 Ohms is less than that provided by the implementation of
FIG. 2 which is 559 Ohms.
[0069] An examination of the slopes of the various lines is instructive.
The line A has a slope of approximately 45.5 (1/0.022), whereas
the line B has a slope of approximately 111.1 (1/0.009), which is
more than twice that of the line A. The line A' also has a slope
of approximately 45 but the line B' has a slope of only approximately
62.5 (1/0.016).
[0070] Implementations of the transmitter 140 may switch at different
current values and at multiple current values. Different schemes
may be used to divide or multiply the voltage or current, including,
for example, a divide-by-three circuit. More than one divider/multiplier
may be reversible and different sets of operating voltages may be
used. Further, the set of operating voltages need not be maintained
for all current values. Different transmission schemes may also
be used, such as, for example, a three-wire system with separate
power and signal lines and a common ground. Even if appreciable
operating power is not being drawn off of the same line on which
the signal is encoded, implementations of the transmitter 140 can
be used to lower the power consumed by a transmitter off of the
signal line, thereby allowing the control room to be designed to
provide a signal line having less power and improving the transmitter's
cooling requirements. Implementations of the transmitter 140 are
not restricted to vortex meter applications or to metering applications
generally, and may be used in other applications in which a parameter
is being communicated between two points.
[0071] Data Processing
[0072] Referring again to FIG. 2 implementations of the load 248
or some other component, may be used to process fluid data in a
variety of ways. One processing task common in vortex flow meters
is to convert the vortex pressure signal into a vortex frequency
and then to determine the velocity and/or the volumetric flow rate
from the vortex frequency. The relationship between a vortex frequency
and fluid velocity is linear. A factor may be computed using calibration
procedures for each flow meter. The factor is a constant that relates
vortex shedding frequency to volumetric flow rate for the specific
flow meter.
[0073] Another processing task involves converting a volumetric
flow rate into a mass flow rate. Mass flow rate is equal to the
product of volumetric flow rate multiplied by density. For compressible
fluids, the density can vary considerably from point to point in
the flow meter. It is desirable to determine an appropriate pressure
value, referred to as a corrected pressure, that leads to a density
that can be multiplied by the measured volumetric flow rate (determined
by a vortex flow meter or otherwise) to yield the correct mass flow
rate. Because temperature can be taken to be constant throughout
the flow meter in certain implementations, density can be determined
from pressure and temperature using the standard relation of density=(universal
gas constant)*(temperature)/(pressure).
[0074] By analyzing collected data it has been determined that
the pressure measured downstream of a bluff body, relative to the
pressure at the input to a flow meter, can be given by equation
1 below: 10 P p s P o - 1 2 .times. k p s .times. p s .times. V
VOR 2 ( 1 )
[0075] where,
[0076] P.sub.ps=pressure measured at the pressure sensor location,
[0077] P.sub.o=reference pressure at the input to the flow meter,
[0078] k.sub.ps=constant related to location of the pressure sensor,
[0079] .rho..sub.ps=density determined at the measured pressure
and temperature, and
[0080] V.sub.VOR=flow velocity calculated from the vortex shedding
frequency.
[0081] It has further been determined that the corrected pressure
can be given by equation 2 below: 11 P c P o - 1 2 .times. k c .times.
p s .times. V VOR 2 ( 2 )
[0082] where,
[0083] P.sub.c=corrected pressure as defined above, and
[0084] k.sub.c=constant related to the unknown location of the
corrected pressure.
[0085] Subtracting equation (1) from equation (2) yields equation
3 below for the corrected pressure: 12 P c P p s + 1 2 .times. k
diff .times. p s .times. V VOR 2 where , - k diff k p s - k c ,
- V VOR = 4 .times. f VOR .times. d 2 .times. K COR , - f VOR =
vortex frequency , - K COR = constant relating f VOR to Q V ( volumetric
flow rate ) , corrected for conditions such as temperature , upstream
effects , and the thickness of mating pipe , and - d = diameter
of flow meter at bluff body . ( 3 )
[0086] The term k.sub.diff is a constant for a given flow meter
line size, and can be determined by a mass flow calibration without
having to determine the term k.sub.c. Two procedures are now described,
both of which include measuring or otherwise determining the mass
flow rate through the flow meter.
[0087] Referring to FIG. 6 a first calibration process 600 determines
k.sub.diff by solving equation 3 for k.sub.diff and determining
a calibration value for the corrected pressure. The process 600
includes determining the mass flow rate of the fluid through the
flow meter (610). This may be done, for example, at a calibration
facility that monitors or controls the mass flow. With the mass
flow rate of the standard (calibration facility) being known, and
the vortex volumetric flow rate and fluid temperature being known,
the factor by which the measured pressure must be adjusted to compute
the density and corresponding mass flow rate can be determined.
This factor is k.sub.diff and will be a constant for each line size
vortex flow meter due to the fact that the measured pressure value
is taken at a precise position in the flow tube.
[0088] The process 600 includes determining the volumetric flow
rate and the velocity (620). In a vortex flow meter implementation,
the volumetric flow rate may be determined by, for example, determining
the vortex frequency and multiplying that frequency by K.sub.COR.
The velocity can be determined, for example, from the volumetric
flow rate by dividing by the cross-sectional area of the flow.
[0089] The process 600 includes determining the corrected density
(630). This may be done, for example, by dividing the mass flow
rate by the volumetric flow rate, as shown in the following equation
4: 13 c = Q m Q v = Q m .times. K COR f VOR ( 4 )
[0090] As equation 4 shows, the volumetric flow rate need not be
determined explicitly in operation 620 because the vortex frequency
and K.sub.COR are sufficient.
[0091] The process 600 includes determining the temperature at
a temperature sensor (640). Because the temperature does not change
appreciably within the flow meter, the temperature at the temperature
sensor may be assumed to be the same at other points within the
flow meter, including the unknown location of the corrected pressure
and density.
[0092] The process 600 includes determining the corrected pressure
(650). This may be done, for example, by using the corrected density,
the temperature, and existing algorithms for determining pressure
from density and temperature.
[0093] The process 600 includes measuring the pressure at a pressure
sensor (660) and determining the density at the pressure sensor
(670). The density may be determined, for example, using the previously
measured temperature which is assumed to be the same at the temperature
sensor and the pressure sensor, and using existing algorithms for
determining density from pressure and temperature.
[0094] The process 600 includes determining k.sub.diff using the
following equation 5 by plugging in the previously determined or
measured terms (680): 14 k diff = 2 .times. ( P c - P p s ) p s
.times. V VOR 2 ( 5 )
[0095] Equation 5 is the same as equation 3 after solving for k.sub.diff.
[0096] Referring to FIG. 7 a second calibration process 700 determines
k.sub.diff by utilizing another relationship between density and
pressure. It has been determined that the following equation 6 relates
the change in density between two points in a flow meter to the
change in pressure between those two points. 15 = P c 2 ( 6 )
[0097] where c is the velocity of sound in the gas.
[0098] Equation 4 can be rearranged and expanded to yield equation
7 below:
Q.sub.m=.rho..sub.c.times.Q.sub.v=(.rho..sub.ps+.DELTA..rho.).times.Q.sub.-
v (7)
[0099] Incorporating equation 6 into equation 7 yields equation
8 below: 16 Q m = ( p s + P c 2 ) .times. Q v = ( s + P c - P p
s c 2 ) .times. Q v ( 8 )
[0100] Solving equation 5 for the term (P.sub.c-P.sub.ps) and substituting
the result into equation 8 results in equation 9 below: 17 Q m =
p s .times. [ 1 + k diff 2 .times. ( V VOR c ) 2 ] .times. Q v (
9 )
[0101] Solving for k.sub.diff leads to the result shown in equation
10 below, 18 k diff = 2 .times. ( c V VOR ) 2 .times. ( Q m p s
.times. Q v - 1 ) , ( 10 )
[0102] The process 700 includes determining the mass flow rate
of the fluid through the flow meter (710), and determining the volumetric
flow rate and the velocity of the fluid through the flow meter (720).
These operations are analogous to operations 610 and 620 respectively.
[0103] The process 700 includes measuring the temperature at a
temperature sensor (730), measuring the pressure at a pressure sensor
(740), and determining the density at the pressure sensor (750).
These operations are analogous to operations 640 660 and 670
respectively.
[0104] The process 700 includes determining the speed of sound
in the fluid (760). The speed is determined at the measured temperature
and pressure. Calibration tests may be performed in air to take
advantage of the fact that the speed of sound in air as a function
of temperature and pressure is well known.
[0105] The process 700 includes determining k.sub.diff based on
equation 10 (770). The determined value of k.sub.diff can then be
used during operation of the flow meter to determine corrected pressure.
[0106] As discussed above, the corrected pressure is that pressure
that leads to a density that can be multiplied by the measured volumetric
flow rate (determined by a vortex flow meter or otherwise) to yield
the correct mass flow rate. Many techniques for determining the
density corresponding to the corrected pressure (and the assumed
constant temperature) involve lengthy computations and iterative
algorithms. Such techniques introduce delays into the real-time
determination of density.
[0107] An implementation discussed below determines density, as
a function of temperature and pressure, by accessing pre-computed
values reflective of the density and interpolating between the accessed
values. This implementation can be used, for example, to determine
the density at the pressure sensor (670 750) and to determine the
corrected density during non-calibration operations.
[0108] In this implementation, the pre-computed values are stored
in a table so that the values can be accessed. The stored values
are not density, however, because density can vary by several orders
of magnitude, which can make it difficult to use a simple interpolation
algorithm between two or more points. Instead, an error term reflective
of the difference between the density and a standard approximation
is stored. The error term has a smaller range, allowing a simpler
interpolation algorithm. Further, the error term may be scaled to
a supported range to provide better precision in calculations. The
stored values are computed according to the following equation 11:
TableValue=ScaleFactor*(standard density)/(approximated density)
(11)
[0109] In operation, when a density is needed, the appropriate
table values are accessed and interpolated to provide a TableValue
corresponding to the pressure and temperature pair. To determine
the density, the approximated density is calculated, multiplied
by the interpolated TableValue, and divided by the known and constant
ScaleFactor. Both the processes of creating one or more tables,
and using those tables are now described in more detail with respect
to a particular implementation.
[0110] Referring to FIG. 8 a process 800 for creating a table
includes selecting a standard for determining density values (810).
An equation for density as a function of temperature and pressure
can be selected from, for example, one of several available sources/standards.
Examples of sources/standards include (i) the steam equation from
the American Society of Mechanical Engineers ("ASME"),
(ii) the America Gas Association Report No 8 for Natural Gas ("AGA8"),
(iii) the America Gas Association Report No 4 for Natural Gas ("AGA4"),
(iv) the America Gas Association NX-19 Gas Supercompressibility
("NX19"), and (v) Thermodynamic Properties in SI, by William.
C. Reynolds, copyright 1979 ("Reynolds").
[0111] The process 800 includes determining temperature and pressure
pairs of interest (820). This may include, for example, determining
the actual pairs of interest or determining a range of pairs of
interest. The temperature, pressure pairs need not be evenly spaced
apart in either temperature or pressure. This allows one or more
areas of greater change in the density, for example, to have pairs
that are more closely spaced (higher sampling) than areas of lesser
change. By spacing pairs more closely when the density is changing
more rapidly, the range of the error term will be reduced and a
simpler interpolation algorithm may be used.
[0112] The process 800 includes selecting a density approximation
(830). In one implementation, the Virial Equation, provided by the
American Institute of Chemical Engineers ("AIChE"), is
used. The implementation does not simply compute the Virial Equation
density approximation and store that figure in a table as the density
because the Virial Equation density approximation may have up to
several percent error. The Virial Equation is given by equation
12 below:
B(T)=a+b/T+c/T.sup.3+d/T.sup.8+e/T.sup.9 (12)
[0113] where,
[0114] B(T) is the molar density expressed in units of m.sup.3/kg*mol,
[0115] T is the temperature in degrees Kelvin, and
[0116] a-e are constant coefficients.
[0117] The AIChE provides the coefficients a-e. B(T) does not represent
an approximation to the standard volumetric density, but can be
converted to a standard volumetric density with the following equation
13:
VEDensity=(Mol. Wt.)/(UGC*T/P+B(T)) (13)
[0118] where,
[0119] VEDensity is the density based on the Virial Equation, expressed
in kg/m3
[0120] Mol. Wt. is the molecular weight, a constant for a particular
material, expressed in kg/kg*mol,
[0121] UGC is the Universal Gas Constant, expressed in Joule/(g*mol*deg
Kelvin), and
[0122] P is the absolute pressure, expressed in PAA.
[0123] The process 800 includes modifying the density approximation
(840). This operation is optional, as are various other operations
even if not explicitly noted. In one implementation, the Virial
Equation is modified by both using a lower order approximation of
the Virial Equation and by tailoring the Virial Equation to the
specific density values of interest.
[0124] It has been determined the first three terms of the Virial
Equation provide a reasonable approximation to the Virial Equation
while also reducing the computational requirements. Equation 14
shows this approximation:
Ba(T)-a+b/T+c/T.sup.3 (14)
[0125] where Ba(T) is an approximation to B(T), expressed in m.sup.3/kg*mol.
[0126] Although the coefficients for the Virial Equation are provided
by AIChE, a better approximation is possible in one implementation
by tailoring the coefficients to the density values of interest.
The coefficients can be tailored by fitting the standard density
values into the form of the Virial Equation (or the form of the
approximation to the Virial Equation). Solving equation 13 for B(T),
and substituting the standard density for the VEDensity yields equation
15 below:
Bvalue=(Mol. Wt./StdDensity(T,P))-(UGC*T/P) (15)
[0127] A table of Bvalues can be created for various T,P pairs
of interest as shown in TABLE 1 below, and the table represents
the desired values of B(T):
1 TABLE 1 P T Bvalue P0 T0 Bvalue(0)(0) P0 . . . . . . P0 Tm Bvalue(0)(m)
. . . . . . . . . . . . . . . . . . Pn T0 Bvalue(n)(0) Pn . . .
. . . Pn Tm Bvalue(n)(m)
[0128] The data can be fit to the form of the Virial Equation (or
an approximation) using a least squares method, for example. The
equation to be solved would take the form of equation 16 below:
Bvalue=a+b/T+c/(T).sup.3+d/(T).sup.8+e/(T).sup.9 (16)
[0129] Because the change in density is proportional to the change
in 1/T, we substitute iT=1/Tm, which yields equation 17 below:
Bvalue=a+b*iT+c*(iT).sup.3+d*(iT).sup.8+e*(iT).sup.9 (17)
[0130] Solving equation 17 yields the coefficients a-e. The process
800 includes determining the standard density for the temperature,
pressure pairs of interest that are on one side of the saturation
line (850). The standard density is determined, for example, using
the standard selected in operation 810. To determine whether a temperature,
pressure pair has crossed over the saturation line, one implementation
uses a standard equation for the saturation line. The process 800
includes extrapolating the standard density values across the saturation
line for all temperature, pressure pairs of interest on the other
side of the saturation line (860). An extrapolated density value
is used instead of the actual density value because the density
can be very non-linear at, and near, the saturation line. Extrapolating
standard density values across the saturation line (for example,
from gas to liquid, or from liquid to gas), and storing a related
point in the table, allows the table to be interpolated for a temperature,
pressure point arbitrarily close to the saturation line using the
same interpolation algorithm that is used with the rest of the table.
Rather than storing extrapolated density values from the other side
of the saturation line, other implementations may detect when a
temperature, pressure pair is close to the saturation line and then
use a different technique to determine the density. Implementations
may also interpolate/extrapolate needed density values from existing
table points on the same side of the saturation line; however, providing
one or more extrapolated points can improve the accuracy of the
interpolation.
[0131] Referring to FIG. 9 a graph 900 shows three temperature,
pressure points 910 920 930 on the gas side a saturation line
940 and a temperature, pressure point 950 on the liquid side of
the saturation line 940. All four points 910 920 930 950 correspond
to temperature, pressure pairs having a corresponding entry in a
density error table.
[0132] In one implementation, extrapolated points are needed on
the liquid side of the saturation line. Density values are computed
for 300-400 temperature, pressure pairs near the needed point, but
on the gas side of the saturation line, using a standard density
algorithm. These density values are then fit to equation 18 below,
which is a second-order equation that will be relatively simple
to extrapolate:
D=c0+c1*P+c2*P.sup.2+(c3+c4*P+c5*P.sup.2)*T+(c6+c7*P)*T.sup.2 (18)
[0133] After the coefficients c0-c7 are determined, equation 18
can be used to compute the extrapolated standard density for temperature,
pressure pairs of interest.
[0134] The process 800 includes determining the density approximation
for each temperature, pressure pair of interest (870). This may
be done, for example, using equation 13 above for the density based
on the Virial Equation. If the approximation breaks down over the
saturation line, then an extrapolation may be used.
[0135] The process 800 includes determining an error term for each
of the temperature, pressure points in the table (880). In one implementation,
the error term is the ratio of the standard density value to the
approximated density value, as indicated in equation 11 above. Other
implementations may use, for example, the inverse ratio (approximated
density/standard density, or a difference between the approximated
density and the standard density.
[0136] The process 800 includes scaling the error term and storing
the scaled error term in the table (890). The range of error terms
computed may be scaled, but scaling is optional in the process 800.
Scaling may provide various advantages. For example, scaling may
lower the required processor time if the table can be implemented
with integers and the errors are still acceptable.
[0137] If non-even spacing is used, as indicated in operation 820
one or more variable-arrays can be created to index into the density
error table. In one implementation, a temperature array and a pressure
array are created that store each of the temperature and pressure
values represented in the density error table. TABLE 2 below shows
a pressure array (columns one and two) and a temperature array (columns
three and four) for such an implementation. In TABLE 2 the pressure
and temperature are listed that correspond to each of the indices,
Pindex and Tindex, into the density error table. For example, the
density error value in the second row and second column of the density
error table corresponds to a pressure of 100000 PAA and a temperature
of 315 degrees Kelvin.
2 TABLE 2 Pressure (PAA) Pindex Temperature (K.) Tindex 0 1 300
1 100000 2 315 2 200000 3 318 3 . . . . . . . . . . . . 1000000
N-1 500 M-1 10000000 N 600 M
[0138] Other mechanisms may be used to index into the density table.
Examples include arrays, tables, equations, and programs statements,
such as, for example, "case" statements from C.
[0139] Referring to FIG. 10 a process 1000 for using a table such
as that created with the process 800 includes determining the temperature
and pressure for which the density is desired (1010). These values
may be supplied, for example, from sensors and/or from a pressure
value that has been corrected, as described earlier.
[0140] The process 1000 includes determining the Tindex, Pindex
pairs surrounding the temperature and pressure of interest (1020).
This may be done, for example, using a table such as TABLE 2 above.
In one implementation, 2.times.2 linear interpolation is used and,
therefore, four surrounding pairs are determined unless the temperature
or the pressure is the same as that of one of the indices.
[0141] The process 1000 includes accessing table values for each
of the surrounding Tindex, Pindex pairs (1030), and interpolating
between these pairs (1040). TABLE 3 below shows, for one implementation,
the four pairs of surrounding Tindex, Pindex pairs and the associated
table values that are accessed.
3TABLE 3 Y1 (TindexStart + 1) Tbl2 Tbl3 Y0 (TindexStart) Tbl0 Tbl1
X0 (PindexStart) X1 (PindexStart + 1)
[0142] The four table values can be interpolated, in one implementation,
by solving the following set of four equations 19.1-19.4:
4 Tbl0 = A + B * X0 + C * Y0 + D * X0 * Y0 (19.1) Tbl1 = A + B
* X1 + C * Y0 + D * X1 * Y0 (19.2) Tbl2 = A + B * X0 + C * Y1 +
D * X0 * Y1 (19.3) Tbl3 = A + B * X1 + C * Y1 + D * X1 * Y1 (19.4)
[0143] where,
[0144] X0 and X1 are the pressure at the corresponding index, expressed
in PAA,
[0145] Y0 and Y1 are 1/temperature at the corresponding index,
expressed in 1/degrees K, and
[0146] Tb10-Tb13 are the table values, which are unitless.
[0147] Equations 19.1-19.4 can be solved for the coefficients A-D
with the pseudo-code in TABLE 4 below:
5TABLE 4 dX10 = X1 - X0 dY01 = Y0 - Y1 dTbl10 = Tbl1 - Tbl0 D =
(tbl2 - tbl3 + dTbl10) / (dX10 * dY01) dX0 = -D * X0 C = ((tbl0
- tbl2) / dY01) + dX0 B = dTbl10 / dX10 - D * Y0 A = tbl0 - B *
X0 - C * Y0 + dX0 * Y0
[0148] After the values for the coefficients A-D are determined
by solving equations 19.1-19.4 the interpolated table value can
be determined as follows in equation 20:
InterpolatedTblVal=A+B*X+C*Y+D*X*Y (20)
[0149] where,
[0150] X is the pressure value of interest, expressed in PAA,
[0151] Y is the inverse of the temperature value of interest, expressed
in 1/degrees K, and
[0152] InterpolatedTblVal is the interpolated value of the table,
which is unitless.
[0153] The process 1000 includes determining a density approximation
for the temperature and pressure of interest (1050). In one implementation,
a density approximation is calculated according to equation 13
using the virial equation as described in either equation 12 or
equation 14.
[0154] The process 1000 includes estimating the standard density
for the temperature and pressure of interest (1060). In one implementation,
the standard density is estimated according to equation 11 by solving
for "standard density" and substituting "InterpolatedTblVal"
for "TableValue," yielding equation 21 below:
Est.D=InterpolatedTblVal*(Approx. Density)/ScaleFactor (21)
[0155] where,
[0156] Est.D is the estimate of the standard density, and
[0157] Approx. Density is the approximated density.
[0158] For temperature, pressure pairs that correspond to density
error table entries, the estimate will be the same as the standard
density value, assuming no precision is lost in the calculations.
The term estimating is used as a subset of the term determining.
[0159] The process 1000 may be used with multiple tables. In one
implementation, density tables are created for a variety of materials
and for different states for each of the materials, with one table
per state per material. The process 1000 is informed of the table
to use by, for example, providing the process 1000 information on
the material and state or providing the process 1000 an address
or other pointer to the appropriate table. In this implementation,
the process 1000 uses the same interpolation process or technique
and the same equation for determining approximated density for each
of the states and materials. It is not necessary, however, in this
implementation, to use the same standard for each of the states
and materials. Other implementations of the process 1000 use different
interpolation processes or techniques and/or different equations
for approximated density for the various supported states and materials,
and provide information to the process 1000 indicating which process
or technique and/or equations to use.
[0160] The processes 800 and 1000 can be combined in an implementation
that produces density determinations within 0.1% of the standard
density value, while at the same time requiring relatively minimal
calculations by the end device. This may be advantageous for end
devices, such as, for example, vortex flow meters, other metering
devices, and other devices used to process data. Many end devices
include controllers having limited random access memory ("RAM")
and clock rates. Controllers include, for example, processors, controller
chips and chip sets, application specific integrated circuits ("ASICS"),
programmable logic devices ("PLDs"), digital signal processors
("DSPs"), and other devices capable of executing instructions.
[0161] Additional Variations
[0162] Referring again to FIG. 2 the current controller 240 may
be implemented, at least in part, using a set point voltage and
feedback control. The switch 241 may be implemented, at least in
part, using a set point comparator controlling a transistor switch.
The voltage dividers 246 247 may be implemented, at least in part,
using a switched capacitor charge transfer circuit. The voltage
may be shunt regulated at V.sub.0 and V.sub.0/2 at least in part,
using a set point comparator and a load dumping switch.
[0163] The processes and systems described above for determining
and using corrected pressure and/or the corrected density can be
used in a variety of applications that require density, including,
for example, tank level calculations, steam quality determinations,
and energy content determinations.
[0164] The components and operations described in the various implementations
above may generally be interchanged, supplemented, or omitted. For
example, a circuit component such as, for example, a resistor, a
capacitor, an inductor, a transformer, an isolator, an operational
amplifier, or a filter may be desired in one or more locations of
an implementation. The terms "coupled" and "injected,"
and their cognates, are understood to allow for other components
to be disposed between two coupled components or between a switch
and an injection point, for example.
[0165] As indicated earlier, the transmitter may communicate over
other communication lines, including, for example, 2-wire, 3-wire,
cable, and free space. The implementations disclosed may be used
with devices, such as, for example, transmitters, that do not regulate
a received current amplitude. For example, a device may receive
a variable current from a supply and may use the power management
concepts disclosed herein to reduce the voltage required by the
device when a high current is being received. The current regulation,
control, or varying, may be done by another device, such as, for
example, a control room or a supply. Additionally, the varying current
need not encode information. The disclosed implementations for data
processing may be used with a variety of communication systems including,
but not limited to, a 4-20 mA system. Other communication systems,
standards, techniques, and protocols, including, for example, Foundation
fieldbus by the Fieldbus Foundation of Austin, Tex., the HART standard,
and other digital, analog, or hybrid analog/digital techniques.
The various concepts disclosed herein can be used independently
and need not be combined.
[0166] Various of the processes, algorithms, and techniques disclosed
may be implemented in instructions that can be stored on a storage
medium, such as, for example, a floppy diskette, a compact diskette,
a hard disk, random access memory ("RAM"), or read only
memory ("ROM"). A storage medium may be included in a
device, such as, for example, a controller.
[0167] A number of implementations have been described. Nevertheless,
it will be understood that various modifications may be made. Accordingly,
other implementations are within the scope of the following claims. |