Abstrict A method of improving the accuracy of a variable orifice flow meter
that includes characterizing the discharge coefficient of the flow
meter orifice for different orifice openings and for different differential
pressures. The method may be particularly useful with a flow metering
and controlling device that includes a fluid flow conduit having
at least one planar inner wall and an element having a linear edge
configured to mate with the at least one planar inner wall of the
fluid flow conduit. The element is movable relative to the conduit
to define a flow orifice and vary a cross-sectional area of the
orifice. The device also includes a processor configured to calculate
the fluid flow based on the cross-sectional area of the orifice,
the differential pressure, and the discharge coefficient.
Claims We claim:
1. A method of metering fluid flow through a variable orifice,
the method comprising the steps of: determining a cross-sectional
area defined by the variable orifice; measuring a pressure differential
across the variable orifice; determining a discharge coefficient
using the determined cross-sectional area and the measured pressure
differential; and determining a fluid flow through the variable
orifice using the determined discharge coefficient; wherein determining
the discharge coefficient includes selecting a discharge coefficient
from an array of discharge coefficient values generated in a calibration
process.
2. A method of metering fluid flow through a variable orifice,
the method comprising the steps of: determining a cross-sectional
area defined by the variable orifice; measuring a pressure differential
across the variable orifice; selecting a discharge coefficient from
an array of discharge coefficient values, the discharge coefficient
being dependent on the determined cross-sectional area and the measured
pressure differential; and solving a flow equation using the selected
discharge coefficient to determine the fluid flow.
3. The method of claim 2 further comprising interpolating between
two discharge coefficient values in the array values to determine
an exact discharge coefficient.
4. The method of claim 2 wherein the variable orifice includes
a movable element, and determining the cross-sectional area of the
orifice includes determining a position of the movable element.
5. The method of claim 4 wherein the movable element includes
at least one linear surface and the variable orifice also includes
a conduit having at least one linear surface, wherein the linear
surface of the movable element and the linear surface of the conduit
are configured to mate with each other.
6. The method of claim 2 further comprising first and second pressure
sensors configured to provide respective first and second pressure
signals, and measuring the pressure differential includes subtracting
the first and second pressure signals.
7. The method of claim 2 further comprising repeating the method
steps at predetermined timed intervals.
8. A method of metering fluid flow through a variable orifice,
the method comprising the steps of: determining a cross-sectional
area of the variable orifice; measuring a pressure differential
across the variable orifice; calculating a discharge coefficient
using the determined cross-sectional area and the measured pressure
differential; and solving a flow equation using the calculated discharge
coefficient to determine the fluid flow; wherein the variable orifice
includes a movable element, the movable element including at least
one linear surface and the variable orifice also includes a conduit
having at least one linear surface, wherein the linear surface of
the movable element and the linear surface of the conduit are configured
to mate with each other, and determining the cross-sectional area
of the orifice includes determining a position of the movable element.
9. A device for metering fluid flow, of the type having a variable
orifice, comprising: a variable sized orifice defined by a fluid
flow conduit and an element moveable relative to the fluid flow
conduit to vary a size of the orifice; a pressure sensor configured
to determine a pressure differential across the orifice and generate
a pressure signal; a positioning device configured to determine
a position of the element relative to the conduit and generate a
position signal; a processor configured to determine the fluid flow
rate using the pressure signal, the position signal, and a discharge
coefficient that is dependent on the pressure signal and the position
signal; and memory and an array of discharge coefficients stored
on the memory, the processor configured to select the discharge
coefficient value from the stored array when calculating the fluid
flow rate.
10. The device of claim 9 further comprising a software program
that controls functions of the processor.
11. The device of claim 9 wherein the array of discharge coefficients
is related to a plurality of pressure signal values and position
signal values determined during a calibration of the device.
12. A method of metering fluid flow through a variable orifice,
the method comprising the steps of: determining a cross-sectional
area defined by the variable orifice; measuring a pressure differential
across the variable orifice; determining a discharge coefficient
using the determined cross-sectional area and the measured pressure
differential; and determining a fluid flow through the variable
orifice using the determined discharge coefficient; wherein determining
the discharge coefficient includes calculating a discharge coefficient
using a polynomial, the polynomial including at least one polynomial
coefficient determined in a calibration process.
13. A method of metering fluid flow through a variable orifice,
the method comprising the steps of: determining a cross-sectional
area of the variable orifice; measuring a pressure differential
across the variable orifice; calculating a discharge coefficient
using the determined cross-sectional area and the measured pressure
differential; and solving a flow equation using the calculated discharge
coefficient to determine the fluid flow; wherein calculating the
discharge coefficient includes inputting the determined cross-sectional
area and the measured pressure differential into a polynomial.
14. A device for metering fluid flow, of the type having a variable
orifice, comprising: a variable sized orifice defined by a fluid
flow conduit and an element movable relative to the fluid flow conduit
to vary a size of the orifice; a pressure sensor configured to determine
a pressure differential across the orifice and generate a pressure
signal; a positioning device configured to determine a position
of the element relative to the conduit and generate a position signal;
and a processor configured to determine the fluid flow rate using
the pressure signal, the position signal, and a discharge coefficient
that is dependent on the pressure signal and the position signal;
wherein the processor calculates the discharge coefficient using
a polynomial and the pressure and position signals.
Description BACKGROUND OF THE INVENTION
1. Technical Field
The present invention generally relates to fluid flow metering
and control devices, and more particularly relates to software related
correction methods for such flow devices.
2. Related Art
In process control industries, it is common to use small diameter
tubes to carry process fluids at low flow rates when small amounts
of fluids are required for manufacturing processes. The tubes are
almost always of a circular cross-section. Instruments used to measure
a flow rate in the tubes must interface with a fluid flowing in
the tube while minimizing disturbance to the fluid flow. To minimize
disturbance to the fluid flow, the instrument typically includes
a circular cross-section to match the cross-section of the tubes.
The flow rate for a flow meter measuring a change in pressure across
an orifice is defined by the following Equation 1:
.rho..times..times. ##EQU00001##
Where: Q=volumetric flow rate C=orifice discharge coefficient A.sub.o=cross-sectional
area of the orifice A.sub.p=cross-sectional area of the pipe P.sub.hi=upstream
pressure P.sub.lo=downstream pressure .rho.=density of the fluid
The differential pressure measurement (P.sub.hi-P.sub.lo) could
be made using two individual pressure measurements and combining
them to get the pressure difference or pressure drop or using a
single device as represented in FIG. 15.
When orifices and differential pressure measurements are used to
calculate flow through large pipes it is common for them to be discrete
devices that are bolted or otherwise attached to the pipe. There
are also devices available for measuring the flow in small tubes
that have the orifice and pressure sensors integrated into the same
housing. In almost all cases, the measuring device orifices are
of a fixed size for measuring flow over a fixed flow range. The
flow characteristic or "discharge coefficient" of the
orifice is measured, or determined by design, by the manufacturer.
For discrete systems, the end user may calculate the flow based
upon the parameters in Equation 1 including a manufacturer provided
discharge coefficient. In integrated systems, the discharge coefficient
can simply be accounted for as part of a total device calibration
performed by the manufacturer.
Differential pressure orifice flow metering is most accurate when
the flow rate is near the upper end of the flow range that the meter
is designed for; that is, where the pressure change is relatively
large for a given change in flow rate. As the flow rate decreases,
the accuracy of the device decreases because there is a relatively
small pressure change for a given change in flow rate. This phenomena
can also be described as a decrease in the differential pressure
to flow rate ratio, which ratio is shown in the graph of FIG. 16.
Since the pressure differential must be accurately known to calculate
the flow rate, any error in the differential pressure measurement
causes an error in the flow calculation. As the slope of the curve
gets steeper at low flow rates (see FIG. 16), any pressure measurement
error causes a larger flow calculation error.
In order to make more accurate flow measurements over a larger
range of flow rates using an orifice and differential pressure measurement,
it may be advantageous to use a variable-sized orifice. A variable-sized
orifice can be used to improve the flow measurement accuracy over
the range of orifice openings by providing a relatively high pressure
differential for each flow rate. However, even though computational
fluid dynamics (CFD) software can be used to optimize the design
of a variable-sized orifice, there is still a small change in the
discharge coefficient as the size of the orifice is varied. This
change is due to the range of flows that the device is designed
to measure, and the physical factors that contribute to the discharge
coefficient of an orifice.
Some variable-sized orifice devices are designed to cover flow
ranges that begin in the laminar flow region and end in the turbulent
flow region, which make it likely that the discharge coefficient
will vary in the different flow ranges. Also, it is known that the
discharge coefficient of an orifice is comprised of a combination
of physical effects relating to the fluid and the shape of the orifice.
When the orifice is set for a very small opening, the surface area
of the walls of the flow path are large relative to the cross-sectional
area of the flow path. This is because a "slit" type opening
results. In a slit type opening, the viscous force of the liquid
against the walls in the orifice region of the flow path becomes
much more significant than when a larger opening is present. A larger
ratio of the wall surface area to the flow path cross-sectional
area has the effect of lowering the discharge coefficient of the
orifice.
Although a variable orifice flow meter may have the advantage of
extending the range of a flow meter by as much as a factor of 10
it may have the inherent drawback of decreased accuracy due to slight
changes in the discharge coefficient at different openings, and
for different flow rates at any given opening size.
In addition to the above noted disadvantages related to discharge
coefficients, known variable orifice devices are ineffective for
several other reasons. First, known variable orifice devices typically
use circular or curved members that are moved with respect to the
fluid flow to change the size of the orifice. Because of the curved
nature of these members, the shape of the orifice changes as the
size of the orifice changes, which results in significant errors
when calculating the fluid flow over a range of orifice sizes. Second,
the changed shape of the orifice leads to non-ideal orifice shapes
for at least a portion of the flow range. This leads to inconsistent
flow characteristics for any given opening as flow rate changes,
again leading to errors in the calculation of fluid flow.
A flow device that addresses these and other shortcomings of known
flow control and metering devices would be an important advance
in the art.
SUMMARY OF THE INVENTION
The present invention generally relates to software related correction
methods for flow devices such as differential pressure flow metering
and controlling devices. One aspect of the invention relates to
a method of metering fluid flow through a variable orifice. The
method includes determining a cross-sectional area of the orifice,
measuring a pressure differential across the orifice, and selecting
a discharge coefficient from an array of discharge coefficient values.
The discharge coefficient is dependent on the determined cross-sectional
area and the measured pressure differential. The method may also
include solving a flow equation using the discharge coefficient
to determine the fluid flow.
Another aspect of the invention relates to a method of metering
fluid flow through a variable orifice. This method includes determining
a cross-sectional area of the orifice, measuring a pressure differential
across the orifice, calculating a discharge coefficient using the
determined cross-sectional area and the measured pressure differential,
and solving a flow equation using the calculated discharge coefficient
to determine the fluid flow. These method steps may be repeated
at predetermined time intervals for at least the purposes of updating
the metered values or validating previous measurements.
A further aspect of the invention relates to a device for metering
fluid flow, wherein the device is of the type having a variable
orifice. The device includes a variable sized orifice defined by
a fluid flow conduit and an element movable relative to the fluid
flow conduit to vary a size of the orifice, a pressure sensor configured
to determine a pressure differential across the orifice and generate
a pressure signal, a positioning device configured to determine
a position of the element relative to the conduit and generate a
position signal, and a processor configured to determine the fluid
flow rate using the pressure signal, the position signal, and a
discharge coefficient that is dependent on the pressure signal and
the position signal.
Another device according to principles of the present invention
is a device for measuring and controlling fluid flow. The device
includes a conduit having a variable orifice defined by a movable
element adapted and configured to engage a surface of the conduit
and to control fluid flow in the conduit, a pressure sensor configured
to measure pressure in the conduit, a position device configured
to determine a position of the movable element relative to the conduit
surface, and a processor configured to calculate a discharge coefficient
based on the position of the movable element and the measured pressure
and to calculate a fluid flow through the conduit. The processor
may also be configured to compare the calculated fluid flow to a
desired fluid flow and adjust the position of the variable orifice
to increase or decrease fluid flow as required.
These and further objects of the present invention will become
clearer in light of the following detailed description of illustrative
embodiments of this invention. described in connection with the
drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
The illustrative embodiments may best be described by reference
to the accompanying drawings where:
FIG. 1 is a top perspective view of a flow device according to
principles of the invention;
FIG. 2 is a top plan view of the flow device shown in FIG. 1;
FIG. 3 is a cross-sectional view of one example configuration of
the flow device shown in FIG. 2 taken along cross-section indicators
3--3;
FIG. 4 is a cross-sectional view of the example flow device shown
in FIG. 3 taken along cross-section indicators 4--4;
FIG. 5 is an enlarged view of the orifice and movable element portion
of the device shown in FIG. 3;
FIG. 6 is a cross-sectional view of the example flow device shown
in FIG. 2 taken along cross-section indicators 6--6;
FIG. 7 is a cross-sectional view of the example flow device shown
in FIG. 2 taken along cross-section indicators 7--7 the example
device having a rectangular inlet to the orifice;
FIG. 8 is a cross-sectional view of the example flow device shown
in FIG. 2 taken along cross-section indicators 8--8;
FIG. 9 is a cross-sectional view of an alternative embodiment of
the example flow device shown in FIG. 2 taken along cross-section
indicators 9--9 the example device having a circular inlet to the
orifice;
FIG. 10 is schematic process diagram of an example flow device
according to principles of the present invention;:
FIG. 11 is an example array of discharge coefficients based on
orifice size and pressure differential for an example variable orifice
flow device according to principles of the present invention;
FIG. 12 is a schematic representation of a fluid flow control device;
FIG. 13 is a flow diagram representing an example method of determining
fluid flow through a flow device according to principles of the
present invention;
FIG. 14 is a flow diagram representing another example method of
determining fluid flow through a flow device according to principles
of the present invention;
FIG. 15 is a schematic representation of a pressure differential
measuring device configured to measure a pressure differential across
an orifice;
FIG. 16 is a chart representing flow rate verses pressure differential
for an example flow device having a fixed orifice size;
FIG. 17 is a chart representing discharge coefficient verses an
orifice size for a simulated flow device;
FIG. 18 is a chart representing discharge coefficient verses flow
rate for a simulated flow device having a fixed orifice size; and
FIG. 19 is a graph representing known values of flow coefficient
verses Reynolds number for an orifice.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT
The invention generally relates to fluid flow metering and control
devices, and more particularly relates to variable-sized orifice
flow devices and software related correction methods for such flow
devices. The variable-sized orifice may be particularly suited for
use in a differential pressure flow meter as will be described herein
with reference to the several drawings, although such an application
is only exemplary of the many applications to which principles of
the present invention may be applied.
The software related correction methods may utilize a matrix or
array of stored discharge coefficients that correlate to specific
pressure differential and orifice size characteristics of the flow
device. Other software related correction methods may utilize equations
or algorithms to calculate an exact discharge coefficient for each
determined pressure differential and orifice size of the flow device.
The arrays of discharge coefficients and the equations/algorithms
used to calculate discharge coefficients may be stored in memory
and used by a controller, such as a processor, to determined fluid
flow.
I. Example Flow Device
An example flow device 10 constructed in accordance with the principles
of the present invention for controlling and metering fluid flow
is shown in FIGS. 1 9. The device includes a housing 12 a moveable
element 14 first and second pressure sensors 16 18 and inlet
and outlet conduit connectors 22 20. A conduit 30 is formed through
the housing and includes first, second and third segments 50 52
54. The housing also includes first and second sensor bores 36
38 that intersect with the conduit 30 in a direction transverse
to the conduit 30 and an element bore 40 that also intersects with
conduit 30 in a direction transverse to conduit 30. In this example,
element bore 40 and sensor bores 36 38 extend parallel to each
other, but may be aligned perpendicular to each other in other embodiments.
Housing 12 may be divided into separate pieces or halves 13 15
(see FIG. 1) to facilitate precise formation of intricate features
within the housing, or may be integrally formed as a single piece.
Moveable element 14 includes a base 42 and a contact member 44
and is positioned in element bore 40 so as to extend into second
segment 52 of the conduit 30. Contact member 44 includes a leading
edge 46 a tapered trailing edge 48 and a planar contact surface
49 (see FIG. 5) configured to mate with a planar surface (for example,
fixed wall 90 described below and shown in FIG. 5) of second segment
52. The movable element 14 is moveably adjustable along a linear
axis through a range of positions between an open (retracted) position
and a closed position, with movement of the movable element 14 being
limited to the linear axis. The open position allows a maximum fluid
flow through the conduit 30. The fluid flow through the conduit
30 decreases as the movable element 14 is moved toward the closed
position due to contact with the fluid. Adjustment of the movable
element 14 in element bore 40 may be performed using, for example,
a linear actuator, a stepper motor, a hydraulic or pneumatic actuator,
a solenoid, a servo motor, or a manual device such as a threaded
shaft with a thumb turn button. The position of the movable element
14 may be determined using, for example, a device or sensor 15 such
as a Hall effect sensor, magnetostrictive devices, linear variable
differential transformers (LVDTs), optical encoder, and other position
determining technologies.
Limiting movement of element 14 to linear motion within element
bore 40 may simplify positioning of movable element 14. Other methods
may "infer" a position of the moveable element 14 based
on incremental movement related to the moveable element. In one
example method, the movable element 14 may be moveable a certain
number of steps from a reference position such as a fully open or
fully closed position. Software controlling the device 10 may be
programmed to convert the number of steps traveled into the distance
traveled. An independent position measuring device would not be
needed in such a configuration, which may reduce the amount and
complexity of hardware used for device 10. A possible drawback of
this method is the potential for inaccurate position measurements
if the element becomes locked in a single position and the processor
thinks that the element is moving a certain number of steps when
the element is actually stationary. An encoder used with a stepper
motor or with a linear actuator, or other devices that "infer"
a linear position from related incremental movement may have similar
issues of potential inaccuracy.
Second segment 52 includes an inlet portion 60 an outlet portion
62 and an orifice portion 64 positioned between the inlet and outlet
portions 60 62. The inlet portion 60 is in fluid communication
with sensor chamber 32 at one end, and includes a plurality of tapered
surfaces at a second end adjacent to the orifice portion 64. Similarly,
outlet portion 62 is in fluid communication with sensor chamber
34 at one end, and includes a plurality of tapered surfaces at an
opposing end adjacent to orifice portion 64.
The inlet and outlet portions of the orifice segment of the device
include a plurality of fixed sidewalls that define a noncircular
cross-section in this embodiment. Other embodiments may include
inlet and outlet portions of the orifice segment that have a circular
cross-section (see example cross-section of inlet portion 160 in
FIG. 9), which configuration may be preferred in some instances.
The example first and third portions 60 62 include four fixed walls
substantially in the shape of a square (see example cross-section
of inlet portion 60 in FIG. 7). As used throughout this document,
rectangular is defined as a four-walled shape and a square is defined
as a rectangle that has four walls of the same length. The walls
of a rectangle are substantially flat or linear and the intersection
of two walls provides an angle of about 90.degree.. In some applications,
the corners of the rectangle may be tapered slightly with a round,
fillet, chamfer or like feature as a result of manufacturing limitations.
Further, a portion of one or more of the walls may be slanted or
chamfered slightly to create sealing points or to meet other design
goals and/or address manufacturing limitations. In embodiments that
include a combination of linear and curved walls (not shown), the
intersection of these walls may also include features such as rounds,
fillets, chamfers, etc. Finally, a portion of one or more of the
walls may be formed by the exposed face of a gasket or seal.
Tapers 70 72 74 76 are formed in the sidewalls of inlet portion
60 to reduce the cross-sectional area at the point where inlet portion
60 abuts to orifice portion 64. The tapers 70 72 74 76 are aligned
at a single axial position so as to create a reduction in cross-sectional
area of portion 60 in a single step (see FIG. 3 5). Outlet portion
62 also includes a square shaped cross-section with tapered surfaces
78 80 (see FIG. 4) on opposing sidewalls so as to reduce the cross-sectional
area of outlet portion 62 at the transition point between orifice
portion 64 and outlet portion 62.
Orifice portion 64 includes three fixed walls 90 92 94 with fixed
wall 90 including a tapered trailing edge 96 and a leading edge
98 (see FIG. 5). As a result, the cross-sectional area of orifice
portion 64 tapers out to the larger cross-sectional area of portion
62 in two steps with sets of tapers 96 48 and 78 80. As shown
in the cross-sectional view of FIG. 8 orifice portion 64 has a
relatively small cross-sectional area as compared to the cross-sectional
area of inlet portion 60 shown in FIG. 7.
The leading edges 46 98 and trailing edges 96 48 of respective
moving element 44 in orifice portion 64 provide consistent flow
characteristics into and out of the orifice portion 64. A cross-sectional
size of the orifice portion 64 is determined by the location of
the movable element 14 in relation to the fixed walls 90 92 94
of the orifice portion 64. The orifice portion 64 is void of sensor
openings and dead volume spaces to avoid disruptions to the fluid
flow and potential accumulation of process material or sediment.
A linear actuator (not shown) such as those discussed above (e.g.,
stepper motor, servo motor, etc.) may be used to affect movement
of the movable element 14. By moving along a single linear axis,
the movable element 14 linearly changes the cross-sectional size
of the orifice portion 64 while maintaining a generally uniform
shape to provide a relatively consistent set of flow characteristics
through the range of movable element positions. The cross-sectional
shape of orifice portion 64 allows repeatable regulation of the
fluid flow in accordance with the position in the range of positions
of the movable element 14. In one example wherein the uniform shape
is a rectangle, the height of the cross-sectional area of the orifice
portion 64 is reduced in size as the movable element 14 moves between
the open and closed positions. Maintaining a rectangular shape,
or at least a shape having at least one planar or linear sidewall,
minimizes variations in flow characteristics (variable "C"
in the flow rate equation in the Background section), thus reducing
errors when determining the flow rate for each orifice size.
In use, fluid first enters flow device 10 (which example will be
used for the remainder of the description of various aspects of
the invention) through first segment 50 of conduit 30. The flow
through segment 50 has flow characteristics that match the circular
cross-section of first segment 50. The flow then enters the open
sensor chamber 32 where a transition volume is provided prior to
the fluid flow entering the non-circular inlet portion 60 of second
segment 52. The flow is then reduced in cross-sectional area by
the several tapers formed in inlet portion 60 just before orifice
portion 64. As mentioned above, a higher pressure is generated at
the inlet to orifice portion 64 due to the very small cross-sectional
area of orifice portion 64 and the wall-like structure created by
leading edges 46 98. The cross-sectional area of orifice portion
64 is dependent on the position of moveable element 14 in the direction
A. Each position along the direction A corresponds to a different
cross-sectional area of the orifice portion 64 for use in determining
the volumetric flow through the flow device 10.
As the fluid exits orifice portion 64 the cross-sectional area
of the fluid flow increases due to tapers 78 and 80 and trailing
edges 48 and 96 of the moveable element 14 and orifice portion 64
as the flow enters portion 62. The cross-sectional area of outlet
portion 62 preferably has the same size and shape as the cross-section
of inlet portion 60 (which is a square cross-section in the example
flow device in flow device 10--see FIG. 10). Flow exiting outlet
portion 62 enters sensor chamber 34 where another transition volume
is provided before the fluid flow enters the third segment 54 and
takes on a flow pattern for the circular cross-section of third
segment 54.
The first and second pressure sensors 16 18 are positioned at
opposing sides of orifice portion 64 so as to be able to determine
a difference in pressure at the inlet and outlet sides of second
segment 52 of conduit 30. The first and second pressure sensors
16 18 may be mounted proximate the process liquid to minimize the
amount of dead volume of the fluid and reduce crystallization and
particle buildup between the first and second pressure sensors 16
18 and the fluid in conduit 30. In other aspects of the present
invention, a single differential pressure sensor may be used to
communicate with both the first and second sensor chambers 32 34
to determine the pressure difference. Furthermore, only a single
pressure sensor may be required in applications where one of the
first or second sensor chamber 32 34 has a fixed pressure. For
example, if the second sensor chamber 34 is downstream of the orifice
and empties into an open tank at atmospheric pressure, a downstream
pressure measurement is not required and the pressure measurement
from the first sensor 16 may be used singly with atmospheric pressure
to determine the pressure differential. Likewise, if the first sensor
chamber 32 is upstream of the orifice portion 64 and is accepting
liquid from a pressurized tank where pressure is tightly controlled
to a fixed value, an upstream pressure is not required and the pressure
measurement from the second sensor 18 may be used singly with the
fixed upstream pressure value to determine the pressure differential.
Other example embodiments may use a single differential pressure
sensor that takes pressure readings from the inlet and outlet sides
of the orifice portion of the device and determines a differential
pressure across the orifice portion. This and other types of sensors
do not necessarily have to be mounted in a sensor bore, nor does
the sensor bore being used require a larger cross-sectional area
than the cross-sectional area of the conduit. For example, a sensor
may be configured to obtain pressure readings using a small probe
that requires a very small entrance opening into the conduit relative
to the conduit size, and the sensor can be mounted at a different
location within or adjacent to the device housing.
Yet further embodiments may not include any sensors associated
directly with the device, but may be configured to use pressure
signals provided by outside sources. Such pressure readings from
an outside source may include, for example, a pressure reading from
a pressure sensor positioned up or down stream from the device,
or a pressure signal representative of a know static pressure condition
for the system either up or down stream of the device. Thus, although
the device does not require a pressure sensor, the device is preferable
configured to use a pressure signal for purposes of metering and
controlling fluid flowing through the device.
A pressure signal representing a pressure differential across an
orifice may be used with the cross-sectional area of the orifice,
the cross-sectional area of the inlet and outlet portions just before
and after the orifice, and the density of the fluid to determine
the volumetric flow rate (discussed in the Background section above).
An advantage of the present invention is that the pressure signal
(.DELTA.P) may be optimized at each flow rate by varying the orifice
size. For example, the pressure signal may be set at a minimum value
for a given flow rate by varying the orifice size. Furthermore,
the pressure signal may be optimized for every desired flow rate
and inlet pressure available by varying the orifice size.
Furthermore, although the cross-sections of the inlet, outlet and
orifice portions 60 62 64 of second segment 52 are shown having
a rectangular shape, it may be appreciated that the cross-sections
may be cross-sections of different shapes, such as, but not limited
to, rectangles, isosceles triangles or the like. Furthermore, different
portions of the second segment 52 may have dissimilar cross-sectional
shapes and sizes, and may have varying shapes or sizes along a length
of each portion of the second segment 52. Additionally, although
the orifice portion 64 has a rectangular cross-section, the leading
and trailing portions of the orifice portion 64 defined by the leading
and trailing edges 44 46 of the movable element 14 and the leading
and trailing edges 98 96 of the fixed walls 90 92 94 may be of
different sizes, shapes and orientations than those shown in the
Figures.
Other example flow devices and further aspects of the flow device
10 are shown and described in U.S. patent application Ser. No. 10/728594
filed on Dec. 3 2003 and entitled APPARATUS FOR CONTROLLING AND
METERING FLUID FLOW, which patent application is incorporated by
reference herein in its entirety
Features of the preferred embodiment flow device 10 shown in FIGS.
1 9 are shown schematically as part of a flow device assembly 100
in FIG. 10. Assembly 100 includes a microcontroller 102 that controls
and communicates with most of the other assembly features. Assembly
100 includes a actuator drive circuit 104 a linear actuator 106
a position sensor reference 108 a position sensor 110 and an analog-to-digital
converter (ADC) 112 that relate to the flow device variable sized
orifice, and a switch 114 regulator 116 regulator 150 and linear
regulator 118 that control power to the features 106 108 110
112. Microprocessor 102 may be any suitable processor or controller
such as, for example, the HD64F3062 16-bit microprocessor manufactured
by RENESAS of San Jose, Calif.
The assembly 100 also includes a pressure sensor reference 120
a high pressure sensor 122 a low pressure sensor 124 and difference
amplifiers 126 128 and an ADC 129 that together are used to determine
a pressure differential in the flow device. Different memory devices
such as RAM 130 NVROM 132 and program memory 134 may be used by
the microprocessor 102 to store data, such as the example array
of FIG. 11 (and/or the polynomial equations below), instructions,
code, algorithms, etc.
The microprocessor 102 may receive inputs in the form of current
signals having a magnitude of, for example, 4 20 mA that are converted
to digital signals using ADC 136 and may communicate with direct
digital signals through a UART 138 and a digital interface 140.
Microprocessor 102 may also generate output signals that are converted
to analog signals with the voltage reference 142 digital-to-analog
converter (DAC) 144 and an output circuit 146 that generates signals
having a magnitude of, for example, 4 20 mA. Assembly 100 may use
a power source that includes a negative regulator 148 and the switching
regulator 150 for powering various features of the assembly 100.
II. Software Correction Methods
A variable orifice flow meter has an inherent drawback of losing
some accuracy due to slight changes in the discharge coefficient
at different orifice openings, and for different flow rates at any
given opening. The example flow metering and controlling devices
disclosed herein provides a means of overcoming these two drawbacks
using software correction for the discharge coefficient. Rather
than using a single discharge coefficient for the device for all
flow calculations, a discharge coefficient that is dependent upon
the orifice opening and the differential pressure measured may be
used in each flow calculation. An array (see example array in FIG.
11) of discharge coefficient values for the range of differential
pressures and orifice openings to be used may be stored in memory
of the flow meter and the appropriate value can be accessed and
used by the flow meter for each individual flow calculation.
As discussed above, a Hall effect sensor may be used to measure
a linear position of a magnet contained in the movable element of
the flow device that varies the orifice opening of the flow device.
Since the orifice opening in the flow device 10 shown in FIGS. 1
9 has at least one planar wall, the orifice cross-sectional area
is linearly proportional to the position of this sliding element.
By monitoring the Hall effect sensor output, the microprocessor
102 in flow meter assembly can determine the orifice opening area,
which is one index of the example array shown in FIG. 11. The microprocessor
102 is configured to read the pressure sensors 122 124 each time
it performs a flow calculation. By reading the pressure sensors
122 124 and calculating the differential pressure, the microprocessor
102 determines the pressure value for the second index of the array
shown in FIG. 11. For values between the differential pressure and
position points listed on the array, simple linear interpolation
can be used to determine an exact discharge coefficient value between
values in the array.
The two dimensional array of values for discharge coefficient shown
in FIG. 11 may be determined by design and stored in the program
memory 134 of each flow meter. The discharge coefficient values
in the array may also be determined by testing for each individual
flow meter manufactured, which would provide a unique and more accurate
array for each flow meter. Array values may be stored in the nonvolatile
memory (NVROM) 132 or other memory associated with the flow meter
assembly 100. Other embodiments may include arrays having indices
that extend in range beyond the range shown in FIG. 11 and may
include more or less resolution depending upon the level of accuracy
desired. Also, since the change in discharge coefficient versus
orifice opening and flow rate is not linear (see simulated results
of FIGS. 17 and 18), the values on each axis of the array need not
be linear. In this way, the array can be kept as small as possible
to reduce memory requirements while maintaining the desired accuracy.
Further, although the position of the orifice is linearly proportional
to the cross-sectional area of the orifice in the flow device 10
other embodiments may not include a linear relationship between
the area and linear position of the movable element. In such embodiments,
the index of the array could be either a position of the movable
element or the cross-sectional area of the orifice.
FIG. 19 further illustrates the relationship between discharge
coefficient and flow rate as a plot of know values that is presented
in the technical book: JOHN A. ROBERSON AND LAYTON T. CROWE, ENGINEERING
FLUID MECHANICS, at 612 (1993). FIG. 19 plots the flow coefficient
(K) as the y-axis and the Reynolds Number (Re) as the x-axis, wherein
the flow coefficient and Reynolds Number relate to the discharge
coefficient (C) and the flow rate (Q), respectively, as follows
in Equations 2 and 3:
.times..times..times..pi..times..times..times..times..rho..times..times.
##EQU00002## FIG. 19 also plots across the top axis a relationship
between the Reynolds Number and flow coefficient as follows in Equation
4:
.times..times..times..DELTA..times..times..times..times..DELTA..times..tim-
es..rho..times..times. ##EQU00003## Where:
Re.sub.d=Reynolds Number in the orifice section
D=diameter of the pipe
d=diameter of the orifice (rectangle orifice related to d using
hydraulic radius)
v=kinematic viscosity of the fluid
.rho.=density of the fluid
For fixed values of the orifice diameter and the kinematic viscosity,
the Reynolds Number changes only with a change in flow rate. The
coefficient relationships provided in equations 2 4 result in FIG.
19 essentially representing the change in discharge coefficient
versus flow rate.
The individual curves shown in FIG. 19 illustrate the significant
changes in discharge coefficient that result as flow rate (represented
as Reynolds Number) increases from low flow rates to high flow rates
for a given orifice-to-pipe size ratio. The difference from one
curve to the next in FIG. 19 represents the change in discharge
coefficient that occurs when the size of the orifice is changed
with respect to the pipe size.
The flow chart in FIG. 13 illustrates the steps involved in determining
an optimum discharge coefficient for a given flow device. These
steps may be implemented in programming stored in local memory (e.g.,
program memory 134) or may be downloaded or transmitted to the microcontroller
102. The process may begin by reading a position sensor to determine
a position of the flow meter movable element thereby determining
an area of the variable orifice. Reading the pressure sensors may
be performed before, after, or concurrently with reading the position
sensor. The pressure and position readings are used as indices to
look up a discharge coefficient in a stored array of discharge coefficients.
The discharge coefficient is interpolated if necessary to determine
an exact discharge coefficient value. The discharge coefficient
is then input into a flow equation and a fluid flow is calculated
from the flow equation. The analog and digital output variables
can then be updated using the fluid flow and sensor readings. If
there are no changes in the orifice position or any interrupts to
service of the flow device, the cycle repeats with a new pressure
reading. If there are interrupts to service or a change in the position
sensor, the cycle repeats from the beginning.
The two dimensional array of discharge coefficient values shown
in FIG. 11 may also be determined by the microprocessor 102 using
a polynomial that inputs the orifice opening size and the differential
pressure as variables. An example polynomial is listed below as
Equation 5. C=A(P.sub.hi-P.sub.lo).sup.2+B(P.sub.hi-P.sub.lo)+D(A.sub.o).sup.2+E(A.su-
b.o)+F Equation 5
Where: A, B, D, E and F=constants C=orifice discharge coefficient
A.sub.o=cross-sectional area of the orifice P.sub.hi=upstream pressure
P.sub.lo=downstream pressure The constants A, B, D, E and F are
typically determined during manufacture when characterizing differential
pressure and the discharge coefficient versus orifice opening. The
constants and discharge coefficient rather than array values may
be stored in the memory of the flow meter assembly 100. The polynomial
coefficients could be determined by design and be the same for each
flow meter manufactured and stored in program memory 134 or the
coefficients could be determined by calibration and be unique for
each flow meter manufactured and then stored in nonvolatile memory
132.
The flow chart in FIG. 14 illustrates the steps for determining
an optimum discharge coefficient and performing a flow calculation
using a polynomial. The process may begin by reading a position
sensor to determine a position of the flow meter movable element
thereby determining an area of the variable orifice. Reading the
pressure sensors may be performed before, after, or concurrently
with reading the position sensor. The pressure and position readings
are input into a polynomial and an exact discharge coefficient is
calculated. The calculated discharge coefficient is input into a
flow equation and a fluid flow is calculated from the flow equation.
The analog and digital output variables can then be updated using
the fluid flow and sensor readings. If there are no changes in the
orifice position or any interrupts to service of the flow device,
the cycle repeats by taking new pressure sensor readings. If there
are interrupts to service or a change in the position sensor reading,
the cycle repeats from the beginning.
Principles of the present invention also encompass a device that
can function either as a variable orifice flow meter or as a flow
controller. The electrical hardware for a variable orifice flow
meter and a flow controller may be similar. One difference between
a flow metering and a flow control device involves additional software
functionality required for the flow controller. FIG. 12 is a block
diagram showing the basic features of a flow device 200. Device
200 includes a controller 210 a control valve 212 and a flow meter
214. The controller 210 may include software that compares the desired
flow set point to a measured flow rate measured by the flow meter
214. The controller 210 then sends a signal to the control valve
212 to vary an orifice opening to increase or decrease flow rate
as required to meet the flow set point. Flow metering is performed
in the same or a similar way for the flow controller as performed
for the variable orifice flow meter 10 described above. Therefore,
the two-dimensional correction for the discharge coefficient of
the orifice via the array (e.g., see FIG. 11) or a polynomial (e.g.,
Equation 5) can be used both in the variable orifice flow meter
10 and in the flow meter function in the flow controller 200.
III. Conclusion
This example flow devices and software correction systems described
herein are exemplary of apparatuses and methods for improving the
accuracy of a variable orifice flow meter. The method includes simultaneously
characterizing the discharge coefficient of the orifice for different
orifice openings and for different differential pressures (flow
rates). By characterizing the discharge coefficient of the orifice
for these two parameters and correcting for them in the flow calculation,
the flow meter is able to maintain flow measurement accuracy over
a broad range of flow rates. In this way, the flow meter may be
useful for flow ranges of up to 10 times the flow range of conventional
differential pressure flow meters and perform accurately over that
entire flow range.
The above specification, examples and data provide a complete description
of the manufacture and use of the composition of the invention.
Since many embodiments of the invention may be made without departing
from the spirit and scope of the invention, the invention resides
in the claims hereinafter appended. |