Abstrict A method and apparatus are provided for calibrating a flow meter
having an array of sensors arranged in relation to a pipe that measures
a flow rate of a fluid flowing in the pipe. The method features
the step of calibrating the flow rate using a calibration correction
function based on one or more parameters that characterize either
the array of sensors, the pipe, the fluid flowing in the pipe, or
some combination thereof. The calibration correction function depends
on either a ratio t/D of the pipe wall thickness (t) and the pipe
inner diameter (D); a ratio t/.lambda. of the pipe wall thickness
(t) and the eddie wavelength (X) of the fluid; a Reynolds number
(.rho.UD/.mu.) that characterizes the fluid flow in the pipe; a
ratio .DELTA.x/D of the sensor spacing (.DELTA.x) and the pipe inner
diameter (D); a ratio f.DELTA.x/U.sub.meas of usable frequencies
in relation to the sensor spacing (.DELTA.x) and the raw flow rate
(U.sub.meas); or some combination thereof. The apparatus takes the
form of a flow meter having a calibration correction function module
performing the aforementioned functionality.
Claims 1. A method for calibrating a flow meter having an array of sensors
arranged in relation to a pipe that measures a flow rate of a fluid
flowing in the pipe, characterized in that the method comprises
the step of: calibrating the flow rate using a calibration correction
function based on one or more parameters that characterize either
the array of sensors, the pipe, the fluid flowing in the pipe, or
some combination thereof.
2. A method according to claim 1 wherein the calibration correction
function depends on either a ratio t/D of the pipe wall thickness
(t) and the pipe inner diameter (D); a Reynolds number (.rho.UD/.mu.)
that characterizes the fluid flow in the pipe; a ratio .DELTA.x/D
of the sensor spacing (Ax) and the pipe inner diameter (D); a ratio
f.DELTA.x/U.sub.meas of usable frequencies in relation to the sensor
spacing (.DELTA.x) and the raw flow rate (U.sub.meas); or some combination
thereof.
3. A method according to claim 2 wherein the flow rate is a volumetric
flow rate (Q) and the method includes the step of determining the
volumetric flow rate (Q) based on the equation: Q=A*U.sub.av, where
a is a cross sectional area of the pipe's inner diameter and U.sub.av
is an average flow velocity:.
4. A method according to claim 3 wherein the method includes the
step of determining the average flow velocity (U.sub.av) based on
the equation: U.sub.av=the calibration correction function*U.sub.meas,
where U.sub.meas is a measured flow rate.
5. A method according to claim 3 wherein the Reynolds number .rho.UD/.mu.
is defined by a ratio of the fluid density (.rho.), the volumetrically
averaged flow velocity (U) and the pipe inner diameter (D) in relation
to the dynamic viscosity of the fluid (.mu.).
6. A method according to claim 1 wherein the flow rate includes
the velocity of flow.
7. A method according to claim 6 wherein the velocity of flow
is determined by using a K-.omega. plot.
8. A method according to claim 1 wherein the array of sensors
includes an array of pressure sensors.
9. A method according to claim 1 wherein the array of sensors
includes an array of strain or temperature sensors.
10. A method according to claim 1 wherein the method includes
the step of receiving as inputs the one or more parameters.
11. A flow meter having an array of sensors arranged in relation
to a pipe that measures a flow rate of a fluid flowing in the pipe,
characterized in that the flow meter comprises a calibration correction
function module that calibrates the flow rate using a calibration
correction function based on one or more parameters that characterize
either the array of sensors, the pipe, the fluid flowing in the
pipe, or some combination thereof.
12. A flow meter according to claim 1 wherein the calibration
correction function depends on either a ratio t/D of the pipe wall
thickness (t) and the pipe inner diameter (D); a Reynolds number
(.rho.UD/.mu.) that characterizes the fluid flow in the pipe; a
ratio .DELTA.x/D of the sensor spacing (Ax) and the pipe inner diameter
(D); a ratio f.DELTA.X/U.sub.meas of usable frequencies in relation
to the sensor spacing (.DELTA.x) and the raw flow rate (U.sub.meas);
or some combination thereof.
13. A flow meter according to claim 12 wherein the flow rate is
a volumetric flow rate (Q) and the calibration correction function
module determines the volumetric flow rate (Q) based on the equation:
Q=A*.sub.Uav, where A is a cross sectional area of the pipe's inner
diameter and U.sub.av is an average flow velocity.
14. A flow meter according to claim 13 wherein the calibration
correction function module determines the average flow velocity
(U.sub.av) based on the equation: U.sub.av=the calibration correction
function*U.sub.meas, where U.sub.meas is a measured flow rate.
15. A flow meter according to claim 13 wherein the Reynolds number
.rho.UD/.mu. is defined by a ratio of the fluid density (.rho.),
the volumetrically averaged flow velocity (U) and the pipe inner
diameter (D) in relation to the dynamic viscosity of the fluid (.mu.).
16. A flow meter according to claim 11 wherein the flow rate includes
the velocity of flow.
17. A flow meter according to claim 16 wherein the velocity of
flow is determined by using a K-.omega. plot.
18. A flow meter according to claim 11 wherein the array of sensors
includes an array of pressure sensors.
19. A flow meter according to claim 11 wherein the array of sensors
includes an array of strain or temperature sensors.
20. A flow meter according to claim 11 wherein the method includes
the step of receiving as inputs the one or more parameters.
Description CROSS-REFERENCE TO RELATED PATENT APPLICATIONS
[0001] This application claims benefit to U.S. provisional patent
application serial No. 60/428312 filed Nov. 22 2002 (CC-0556);
U.S. provisional patent application serial No. 60/510765 filed
Oct. 9 2003 (CC-0662); and U.S. provisional patent application
serial No. 60/511399 filed Oct. 13 2003 (CC-0665), which are
all hereby incorporated by reference in their entirety.
BACKGROUND OF THE INVENTION
[0002] 1. Field of the Invention
[0003] The present invention relates to flow meters; and more particularly
to a method and apparatus for calibrating a flow meter having an
array of sensors arranged in relation to a pipe that measures a
flow rate of a fluid flowing in the pipe.
[0004] 2. Description of the Related Art
[0005] Volumetric flow measurement plays a critical role in process
optimization and control of most industrial processes. The current
industrial flow measurement market is often segmented into two broad
technology categories: old technology and new technology flow meters.
Old technology flow meters include flow measurement technologies
that have been in used for greater than 70 years and include turbine
meters, orifice plates and variable area flow meters. The new technology
flow meters have emerged over the last 30.about.50 years and offer
advantages over the old technologies in performance, functionality,
and reliability. The major types of new technology flow meters include
ultrasonic meters, electromagnetic flow meters, vortex flow meters,
and coriolis flow meters. Each type has evolved to serve various
aspects of the diverse range of applications within the industrial
flow meter landscape. For example, the electromagnetic flow meter
has emerged as the dominate type of flow meter used in the paper
and pulp industry.
[0006] In particular, flow meters having an array of sensors arranged
in relation to a pipe that measure a flow rate of a fluid flowing
in the pipe are known in the art. For example, U.S. Pat. No. 6609069
which is incorporated by reference, discloses a method and apparatus
for determining the flow velocity of fluid within a pipe, such as
an oil pipe.
[0007] One problem with flow meters in the art is that, despite
the fact that they are calibrated to measure a flow rate of a given
fluid(s) flowing in a given pipe(s), this calibration may not be
correct when the flow meter is used in the field to measure different
types of fluids flowing, for example, in different types of pipes
than those in which the flow meter was originally calibrated to
measure fluid flow. For example, the original calibration is likely
to provide an incorrect measurement when the flow meter is used
in relation to a fluid having a different density or viscosity than
it was originally calibrated, or when the flow meter is used in
relation to a pipe having a different wall thickness or inner diameter
than it was originally calibrated, or when the array of sensors
are spaced differently in relation to the pipe than it was originally
calibrated. In view of this, the known flow meters are likely to
have an error in their measurement, for which no correction is made.
Moreover, the known flow meters are not designed to correct the
original calibration based on one or more parameters that characterize
either the array of sensors, the pipe, the fluid flowing in the
pipe, or some combination thereof.
[0008] There is a need in the prior art for a flow meter that can
be calibrated in the field based on receiving such parameters.
SUMMARY OF THE INVENTION
[0009] The present invention provides a new and unique method and
apparatus for calibrating a flow meter having an array of sensors
arranged in relation to a pipe that measures a flow rate of a fluid
flowing in the pipe. The method features the step of calibrating
the flow rate using a calibration correction function based on one
or more parameters that characterize either the array of sensors,
the pipe, the fluid flowing in the pipe, or some combination thereof.
The calibration correction function depends on either a ratio t/D
of the pipe wall thickness (t) and the pipe inner diameter (D);
a Reynolds number (.rho.UD/.mu.) that characterizes the fluid flow
in the pipe; a ratio .DELTA.x/D of the sensor spacing (.DELTA.x)
and the pipe inner diameter (D); a ratio f.DELTA.x/U.sub.meas of
usable frequencies in relation to the sensor spacing (.DELTA.x)
and the raw flow rate (U.sub.meas); or some combination thereof.
The apparatus takes the form of a flow meter having a calibration
correction function module performing the aforementioned functionality.
[0010] The Reynolds number (Re), based on pipe diameter (D), characterizes
many of the engineering properties of the flow. The Reynolds number
is a non-dimensional ratio representing the relative importance
of inertial forces to viscous forces within a flow: 1 Re = inertial
viscous forces = u u x 2 u y 2 = UD v
[0011] Where .rho. is the fluid density, .mu. is the dynamic viscosity,
U is the volumetrically averaged flow velocity and v (=.mu./.pi.)
is the kinematic viscosity. The critical Reynolds number for pipe
flows, above which flows are considered turbulent, is .about.2300.
Most flows in the paper and pulp industry have Reynolds number ranging
from one hundred thousand to several million, well within the turbulent
regime. In addition to demarcating a boundary between laminar and
turbulent flow regimes, the Reynolds number is a similarity parameter
for pipe flows, i.e. flows in geometrically similar pipes with the
same Reynolds number are dynamically similar.
[0012] The flow rate being calibrated may include a volumetric
flow rate (Q) or a velocity of flow. In operation, the volumetric
flow rate (Q) is determined based on the equation:
Q=A*U.sub.av,
[0013] where A is a cross sectional area of the pipe's inner diameter
and U.sub.av is an average flow velocity.
[0014] The average flow velocity (U.sub.av) is determined based
on the equation:
U.sub.av=the calibration correction function*U.sub.meas,
[0015] where U.sub.meas is a measured flow rate.
[0016] The velocity of flow is determined by using a K-.omega.
plot. The array of sensors includes an array of pressure sensors,
as well as an array of strain or temperature sensors.
[0017] One advantage of the present invention is that the flow
meter according to the present invention can be calibrated in the
field based on receiving the one or more parameters that characterize
either the array of sensors, the pipe, the fluid flowing in the
pipe, or some combination thereof.
[0018] Another advantage of the present invention is that the flow
meter according to the present invention provides a more accurate
measurement after being calibrated in the field.
[0019] Still another advantage of the present invention is that
the flow meter according to the present invention can be designed
and used in relation to a class of pipes, such as Sch 10 or 40
and calibrated in the field based on a family of calibration curves.
[0020] In one particular application of the present invention relates
to providing a new flow measurement technology well-suited for the
paper and pulp industry. The present invention provides robust,
high-accuracy, volumetric flow rate measurement for a broad range
of single and multiphase flows. The present invention can be implemented
with ported pressure transducers or with non-intrusive sensors clamped-on
to existing process piping. This first-principles flow measurement
methodology utilizes an array of sensors to listen to the unsteady
pressure field within standard process flow lines. Sonar array processing
techniques are employed to track the speed at which coherent structures,
inherent within the turbulent pipe flow of the process fluid, convect
past the sensor array. The present invention results in a meter
performance on paper and pulp slurries ranging from 0-5% pulp. Results
from a single phase calibration facility are also presented demonstrating
0.5% accuracy for pipes ranging from 3 to 16 inches in diameter.
BRIEF DESCRIPTION OF THE DRAWINGS
[0021] FIG. 1 is a block diagram of a flow meter having an array
of sensors disposed axially along a pipe for measuring the volumetric
flow of the process flow flowing in the pipe, in accordance with
the present invention.
[0022] FIG. 2 is a cross-sectional view of a pipe with fluid flowing
therein having an array of pressure sensors disposed axially along
the pipe, in accordance with the present invention.
[0023] FIG. 3 is a flow chart illustrative of the algorithm of
the signal processor, in accordance with the present invention.
[0024] FIG. 4 is a k-w plot showing a convective ridge illustrative
of the convective flow within the pipe, in accordance with the present
invention.
[0025] FIG. 5 is a graph of an attenuation profile showing a dependence
of a ratio of the pipe wall thickness (t) in relation to the pipe
inner diameter (D).
[0026] FIG. 6 is a graph showing a dependence of the Reynolds number
(Re) in relation to an offset (%) of the flow velocity.
[0027] FIG. 7 is a graph of the Reynolds number (Re) in relation
to an offset (%) of the flow velocity showing a dependence of the
sensor spacing and inner pipe diameter.
[0028] FIG. 8 including FIGS. 8a, 8b, 8c, show . . . .
[0029] FIG. 9 is a graph of the Reynolds number (Re) in relation
to an offset (%) of the flow velocity in the form of a family of
calibration curves.
BEST MODE FOR CARRYING OUT THE INVENTION
[0030] FIGS. 1 and 2 show a flow meter generally shown as 10 that
measures the flow rate, including the volumetric flow rate and flow
velocity, of a single phase fluid 12 (e.g., gas and liquid) and/or
a multi-phase mixture 12 (e.g., process flow) flowing through a
pipe 14 shown in FIG. 2. The multi-phase mixture may be a two-phase
liquid/vapor mixture, a solid/vapor mixture or a solid/liquid mixture,
gas entrained liquid or a three-phase mixture. The scope of the
invention is not intended to be limited to the type or kind of fluid,
flow, media or mixture being measured by the flow meter 10 or the
type or kind of the pipe 14 in which the fluid, flow, media or mixture
is flowing.
[0031] The flow meter 10 includes a sensing device 16 comprising
an array of pressure sensors (or transducers) 18-21 spaced axially
along the outer surface 22 of the pipe 14 (FIG. 2), having a process
flow 12 propagating therein. The pressure sensors 18-21 measure
the unsteady pressures produced by vortical disturbances 118 (FIG.
2) within the pipe 14 which are indicative of the velocity of the
process flow 12. The output signals (P.sub.1(t)-P.sub.N(t)) may
be conditioned in one or more ways, including amplified and/or converted
in an analog-to-digital (A/D) converter, although the scope of the
invention is not intended to be limited to any such conditioning.
[0032] The output signals (P.sub.1(t)-P.sub.N(t)) of the pressure
sensors 18-21 are then provided to a processor 24 which processes
the pressure measurement data to determine the volumetric flow rate
and flow velocity. The measurements are derive by the processor
24 by interpreting the unsteady pressure field within the process
piping using multiple transducers/sensors displaced axially over
about 2 diameters in length. The processor 24 including the modules
and functionality described herein, may be implemented using hardware,
software or a combination thereof. One software embodiment envisioned
comprises, among other things, a microprocessor based architecture
having a microprocessor, memory, input/output devices and address
and data bus coupling the same. A person skilled in the art would
be able to implement the processor 24 without undue experimentation.
The flow measurements can be performed using ported pressure transducers
or clamp-on, strain-based sensors.
[0033] The flow meter 10 measures the volumetric flow rate by determining
the velocity of vortical disturbances or "eddies" 118
(FIG. 2) propagating through the flow 12 using the array of pressure
sensors 18-21. Similar to that shown in U.S. patent application
Ser. No. 10/007736 filed Nov. 8 2001 (CiDRA Corporation Docket
No. CC-0122A). The flow meter 10 measures the velocities associated
with unsteady flow fields and/or pressure disturbances created by
the vortical disturbances or "eddies" 118 to determine
the velocity of the flow 12. The pressure sensors 18-21 measure
the unsteady pressures P.sub.1(t)-P.sub.N(t) created by the vortical
disturbances 118 as these disturbances convect within the flow 12
through the pipe 14 in a known manner. Therefore, the velocity of
these vortical disturbances 118 is related to the velocity of the
flow 12 and hence the volumetric flow rate may be determined, as
will be described in greater detail hereinafter.
The Pressure Sensors 18-21
[0034] In FIG. 1 each of the pressure sensors 18-21 may include
a piezoelectric film sensor to measure the unsteady pressures of
the flow 12. The piezoelectric film sensors include a piezoelectric
material or film to generate an electrical signal proportional to
the degree that the material is mechanically deformed or stressed.
The piezoelectric sensing element is typically conformed to allow
complete or nearly complete circumferential measurement of induced
strain to provide a circumferential-averaged pressure signal. The
sensors can be formed from PVDF films, co-polymer films, or flexible
PZT sensors, similar to that described in "Piezo Film Sensors
Technical Manual" provided by Measurement Specialties, Inc.,
which is incorporated herein by reference. A piezoelectric film
sensor that may be used for the present invention is part number
1-1002405-0 LDT4-028K, manufactured by Measurement Specialties,
Inc.
[0035] Piezoelectric film ("piezofilm"), like piezoelectric
material, is a dynamic material that develops an electrical charge
proportional to a change in mechanical stress. Consequently, the
piezoelectric material measures the strain induced within the pipe
14 due to unsteady pressure variations (e.g., vortical disturbances)
within the process flow 12. Strain within the pipe is transduced
to an output voltage or current by the attached piezoelectric sensor.
The piezoelectrical material or film may be formed of a polymer,
such as polarized fluoropolymer, polyvinylidene fluoride (PVDF).
The piezoelectric film sensors are similar to that described in
U.S. patent application Ser. No. ______ (Express Mail No. EV 286
928 210 US) (CiDRA Docket No. CC-0676), which is incorporated herein
by reference.
[0036] The scope of the invention is not intended to be limited
to the kind or type of pressure sensors 18-21.
The Measurement of Volumetric Flow
[0037] To measure volumetric flow, the flow meter 10 characterizes
the velocity at which the coherent vortical structures 118 convect
past the axial array of sensors 18-21. Coherent structures 118 are
an inherent feature of turbulent boundary layers present in all
turbulent flows. Unlike conventional vortex shedding meters, no
internal geometry is required to generate these structures.
[0038] The overwhelming majority of industrial process flows involve
turbulent flow 12. Turbulent fluctuations within the process flow
govern many of the flow properties of practical interest including
the pressure drop, heat transfer, and mixing. For engineering applications,
considering only the time-averaged properties of turbulent flows
is often sufficient for design purposes. For sonar based array processing
flow metering technology, understanding the time-averaged velocity
profile in turbulent flow 12 provides a means to interpret the relationship
between speed at which the coherent structures 118 convect and the
volumetrically averaged flow rate.
[0039] Turbulent pipe flows 12 are highly complex flows. Predicting
the details of any turbulent flow is problematic, however, much
is known regarding the statistical properties of the flow. The maximum
length scale of the eddies 118 is set by the diameter of the pipe
14. These structures 118 remain coherent for several pipe diameters
downstream, eventually breaking down into progressively smaller
eddies until the energy is dissipated by viscous effects.
[0040] Experimental investigations have established that eddies
generated within turbulent boundary layers convect at roughly 80%
of maximum flow velocity. For pipe flows, this implies that turbulent
eddies will convect at approximately the volumetrically averaged
flow velocity within the pipe 14. The precise relationship between
the convection speed of the turbulent eddies 118 and the flow rate
for each class of meters can be calibrated empirically as described
below.
[0041] In FIG. 2 the relevant flow features of the turbulent pipe
flow 12 are illustrated along with the axial array of sensors 18-21.
As shown, the time-averaged axial velocity is a function of radial
position, from zero at the wall to a maximum at the centerline of
the pipe. The flow 12 near the wall is characterized by steep velocity
gradients and transitions to relatively uniform core flow near the
center of the pipe 14. Vortical structures 118 are superimposed
over time averaged velocity profile. These coherent structures contain
temporally and spatially random fluctuations with magnitudes typically
less than 10% percent of the mean flow velocity and are carried
along with the mean flow. Experimental investigations have established
that the eddies 118 generated within turbulent boundary layers remain
coherent for several pipe diameters and convect at roughly 80% of
maximum flow velocity.
[0042] From a volumetric flow measurement perspective, the volumetrically
averaged flow velocity is of interest. The volumetrically averaged
flow velocity, defined as the total volumetric flow rate, Q, divided
by the cross sectional area of the conduit, A, is a useful, but
arbitrarily defined property of the flow. In fact, given the velocity
profile within the pipe, little flow is actually moving at this
speed. The precise relationship between the convection speed of
turbulent eddies and the flow rate is determined experimentally
through calibration for each.
The Calibration Correction Module 38
[0043] The processor 24 includes a calibration correction function
module 38 for calibrating the flow rate using a calibration correction
function based on one or more parameters that characterize either
the array of sensors 18-21 the pipe 14 the fluid 12 flowing in
the pipe 14 or some combination thereof. The calibration correction
function depends on either a ratio t/D of the pipe wall thickness
(t) and the pipe inner diameter (D); a Reynolds number (.rho.UD/.mu.)
that characterizes the fluid flow in the pipe; a ratio .DELTA.x/D
of the sensor spacing (.DELTA.x) and the pipe inner diameter (D);
a ratio f.DELTA.x/U.sub.meas of usable frequencies in relation to
the sensor spacing (.DELTA.x) and the raw flow rate (U.sub.meas);
or some combination thereof.
[0044] The Reynolds number, based on pipe diameter, characterizes
many of the engineering properties of the flow. The Reynolds number
is a non-dimensional ratio representing the relative importance
of inertial forces to viscous forces within a flow: 2 Re = inertial
viscous forces = u u x 2 u y 2 = UD v
[0045] Where .rho. is the fluid density, .mu. is the dynamic viscosity,
U is the volumetrically averaged flow velocity and v (=.mu./.rho.)
is the kinematic viscosity. Pipe flows with Reynolds numbers exceeding
a critical value, typically .about.2300 are turbulent. Those with
Reynolds numbers below this value are laminar.
[0046] The calibration correction function module 38 may be implemented
using hardware, software or a combination thereof. One software
embodiment envisioned comprises, among other things, a microprocessor
based architecture having a microprocessor, memory, input/output
devices and address and data bus coupling the same. A person skilled
in the art would be able to implement the calibration correction
function module 38 without undue experimentation.
[0047] The flow rate includes a volumetric flow rate (Q) and the
calibration correction function module 38 determines the volumetric
flow rate (Q) indicated as 40' based on the equation:
Q=A*U.sub.av,
[0048] where A is a cross sectional area of the pipe's inner diameter
and U.sub.av is an average flow velocity. The average flow velocity
(U.sub.av) is determined based on the equation:
U.sub.av=the calibration correction function.multidot.U.sub.meas,
[0049] where U.sub.meas is a measured flow rate.
[0050] The Reynolds number .rho.UD/.mu. is defined by a ratio of
the fluid density (.SIGMA.), the volumetrically averaged flow velocity
(U) and the pipe inner diameter (D) in relation to the dynamic viscosity
of the fluid (.mu.).
[0051] The calibration correction function module 38 also may receive
as inputs one or more parameters via line 38a, consistent with that
discussed below.
FIG. 3: The Basic Steps
[0052] FIG. 3 shows the basic steps generally indicated as 46 performed
by the processor 24 in FIG. 1 including a step 48 for performing
an FFT of pressure signals P.sub.1(t)-P.sub.N(t); a step 50 for
determining power of the pressure signals in a K-.omega. plane;
a step 52 for determining a convective ridge in the K-.omega. plane;
a step 54 for calculating velocity of flow (Vc(t)) and/or volumetric
flow (VF); and a step 62 for calibrating the velocity of flow (Vc(t)
and/or volumetric flow (VF). The step 48 is performed by the FFT
modules 30-33; the steps 50 52 54 are performed by the array processor
36 and the step 62 is performed by the calibration correction function
module 38.
[0053] In FIG. 1 the flow meter 10 has an array of at least three
acoustic pressure sensors 18-21 located at three locations x.sub.1x.sub.2x.sub.3
axially along the pipe 14. One will appreciate that the sensor array
may include more than three pressure sensors as depicted by pressure
sensor 21 at location x.sub.N. The pressure generated by the vortical
disturbances 118 may be measured through pressure sensors 18-21.
The pressure sensors provide pressure time-varying signals P.sub.1(t),P.sub.2(t),P.sub.3(t),P.sub.N(t)
to a signal processor 24 to known Fast Fourier Transform (FFT) logics
30-33 respectively. The FFT logics 30-33 calculate the Fourier
transform of the time-based input signals P.sub.1(t)-P.sub.N(t)
and provide complex frequency domain (or frequency based) signals
P.sub.1(.omega.),P.sub.2(.o- mega.),P.sub.3(.omega.)),P.sub.N(.omega.)
indicative of the frequency content of the input signals. Instead
of FFT's, any other technique for obtaining the frequency domain
characteristics of the signals P.sub.1(t)-P.sub.N(t) may be used.
[0054] The frequency signals P.sub.1(.omega.)-P.sub.N(.omega.)
are fed to an array processor 36 which provides a flow signal 40
indicative of the volumetric flow rate of the process flow 12 and
a velocity signal 42 indicative of the velocity of the process flow.
[0055] One technique of determining the convection velocity of
the vortical disturbances 118 within the process flow 12 is by characterizing
the convective ridge of the vortical disturbances using an array
of unsteady pressure sensors or other beam forming techniques, similar
to that shown in U.S. Pat. No. 6609069 entitled "Method
and Apparatus for Determining the Flow Velocity Within a Pipe",
which is incorporated herein by reference.
[0056] The flow metering methodology uses the convection velocity
of coherent structure with turbulent pipe flows 12 to determine
the volumetric flow rate. The convection velocity of these eddies
118 is determined by applying arraying processing techniques to
determine the speed at which the eddies convect past an axial array
of unsteady pressure measurements distributed along the pipe 14
similar to that used in the radar and sonar fields.
[0057] The array processing algorithms determine the speed of the
eddies 118 by characterizing both the temporal and spatially frequency
characteristics of the flow field. For a series of coherent eddies
convecting past a fixed array of sensors, the temporal and spatial
frequency content of pressure fluctuations are related through the
following relationship: 3 k = U convect
[0058] Here k is the wave number, defined as k=2.pi./.lambda. and
has units of l/length, .omega. is the temporal frequency in rad/sec,
and U.sub.convect is the convection velocity. Thus, the shorter
the wavelength (larger k) is, the higher the temporal frequency.
[0059] In array processing, the spatial/temporal frequency content
of time stationary sound fields are often displayed using "k-.omega.
plots". K-.omega. plots are essentially three-dimensional power
spectra in which the power of a sound field is decomposed into bins
corresponding to specific spatial wave numbers and temporal frequencies.
On a K-.omega. plot, the power associated with a pressure field
convecting with the flow is distributed in regions, which satisfies
the dispersion relationship developed above. This region is termed
"the convective ridge" and the slope of this ridge on
a K-.omega. plot indicates the convective velocity of the pressure
field. This suggests that the convective velocity of turbulent eddies,
and hence flow rate within a pipe, can be determined from the output
of a phased array of sensor and identifying the slope of the convective
ridge within the K-.omega. plane.
FIG. 4: The K-.omega. plot
[0060] FIG. 4 shows an example of a K-.omega. plot generated from
a phased array of pressure sensors 18-21. The power contours show
a well-defined convective ridge. A parametric optimization method
was used to determine the "best" line representing the
slope of the convective ridge 200. For this case, a slope of 14.2
ft/sec was determined. The intermediate result of the optimization
procedure is displayed in the insert, showing that optimized value
is a unique and well-defined optima.
[0061] The K-.omega. plot shown in FIG. 4 illustrates the fundamental
principle behind sonar based flow measure, namely that axial arrays
of sensors can be used in conjunction with sonar array processing
techniques to determine the speed at which naturally occurring turbulent
eddies convect within a pipe.
The Volumetric Flow Rate
[0062] The volumetric flow rate for a given pipe is defined as
follows:
Q=A.multidot.U.sub.av
[0063] Where:
[0064] A=Cross sectional area of the pipe's inner diameter
[0065] U.sub.av=Average velocity of the flow profile within the
pipe As described herein before, the average velocity is defined
as follows: 4 U av = f { t D ; UD ; x D ; f x U meas } U meas
[0066] Where:
[0067] U.sub.meas=raw flow rate as determined by the algorithm
[0068] f { }=calibration correction function 5 U meas = raw flow
rate as determined by the algorithm f { } = calibration correction
function t D = ratio of pipe wall thickness ( t ) and pipe inner
diameter ( D ) UD = Reynolds Number x D = dependence on the ration
of sensor spacing ( x ) and the inner diameter of the pipe ( D )
f x U meas = dependence on the useable frequencies ( f ) within
the array response
[0069] FIGS. 5-7 provide graphs of empirical testing that has been
conducted to determine the correction function dependence on each
of the contributing parameters.
FIG. 5: The Pipe Wall Thickness (t) to Pipe Inner Diameter (D)
Dependence
[0070] FIG. 5 shows a graph indicating an attenuation profile in
relation to the dependence of the pipe wall thickness (t) to pipe
inner diameter (D). In effect, the unsteady pressure fluctuations
created by the convecting field of eddies strain the pipe at a corresponding
set of frequencies. These are proportional to the wavelength of
the eddies. The pipe wall acts as an attenuator and will decrease
the signal power as a function of the wall thickness and frequency.
The Attenuation Characteristics
[0071] The attenuation characteristics of the pipe wall change
as a function of the ratio of the wall thickness to the inner diameter.
FIG. 6: The Reynolds Number Dependence
[0072] FIG. 6 shows the measured velocity of the flow is a function
of the Reynolds Number. The graph provides a set of empirical data
demonstrating this effect: The Reynolds Number effects the velocity
profile and therefore the distribution of the velocity across the
diameter of the pipe.
FIG. 7: The Sensor Spacing to Pipe Inner Diameter (D) Dependence
[0073] FIG. 7 is a graph of empirical data showing the dependence
between the sensor spacing (.DELTA.x) and pipe inner diameter (D).
In effect, the sensor spacing (.DELTA.x) defines the wavelength,
or alternatively the wave number, of the signals to be measured
through the dispersion relationship. This establishes the size of
the vortical signals that can be measured. The convective velocity
of this set of vorticals has a unique relationship to the average
volumetric flow rate.
The Dependence of Usable Frequencies Within the Array Response
[0074] The sensor spacing .DELTA.x defines the wavelength, or alternatively
the wave number, of the
[0075] signals to be measured through the dispersion relationship.
The 6 f x U meas
[0076] ratio defines which of the measurable wavelengths should
be used at a given flow rate. For the previously described empirical
testing, the minimum and maximum values were set to 0.3 and 0.7
respectively.
[0077] FIG. 8a shows a dimensional K-.omega. plot; FIG. 8b shows
an array gain; and FIG. 8c shows a non-dimensional K-.omega. plot.
[0078] Using the parameter f.DELTA.x/U where f is the frequency
in Hz (f=.omega./(2.pi.) where .omega. is the frequency in rad/sec)
enables the k-.omega. plot to be non-dimensionalized. This results
in the ability to use the same region of the array gain function
regardless of the velocity. This same region is preferably centered
about the point of maximum array response (.pi./.DELTA.x) of the
array gain function. (For example, per the attached figure the maximum
array response occurs at k=.pi./.DELTA.x. Keeping in mind the dispersion
relationship k=.omega./u=2.pi./u the maximum array response will
occur at different frequencies for different velocities. That is,
for an array with .DELTA.x=0.2 feet at 3 ft/sec velocity the maximum
array response will occur at 3.pi./.DELTA.x=47.1 rad/sec where at
10 ft/sec velocity the maximum response will occur 10.pi./.DELTA.x=157
rad/sec. If the frequency is non-dimensionalized in this manner,
the maximum array response will always occur at f.DELTA.x/u=0.5
regardless of the velocity. The advantage of this non-dimensionalization
is that regardless of the velocity, the section of the k-.omega.
plot that yields the maximum array response can be identified and
used.
[0079] Referring to step 62 of FIG. 3 knowing the calibration
function and the relationship of each of the factors in the calibration
function, the measured velocity of the flow Uc(t) and measured volumetric
flow (VF) signals may be calibrated knowing the actual or empirical
relationship of each of the relationships of the calibration function
to provide a more accurate flow velocity Uc(t) and volumetric flow
(VF).
FIG. 9
[0080] FIG. 9 illustrates empirical data representative of a family
of calibration curves for a plurality of classes of flow meter of
the present invention, described herein before, used to calibrate
each respective class of meter. Each class of meter is represented
or defined by the pipe that the flow meter is measuring. For example,
one class is represented by a 4 inch ID, schedule 10 that is represented
by the calibration curve 100. Each calibration curve using empirical
data collected for a particular class of flow meters is defined
by the equation C.sub.0+C.sub.1/Re{circumflex over ( )}C.sub.2 (Correction
Function), wherein each class have a unique value for each of the
coefficients C0 C1 and C2. Re is the Reynolds number of the flow
propagating through the pipe. The Calibration Curves are defined
by Percent Error or Offset versus the Reynolds number of the fluid,
which is related to the velocity of the fluid flow as shown in FIG.
9. For example, V.sub.corrected=V.sub.measured/(Offset+1), the Offset=C.sub.0+C.sub.1/RE{circumflex
over ( )}C.sub.2 and Re=0.00774.times..rho..times.V.times.ID/.mu.,
where 0.007742=Combined conversion factor V (ft/s to m/s) and ID(in
to m).
[0081] Each calibration curve includes all the factors or terms
of the calibration correction function described hereinbefore. All
meters within the same class are calibrated using the same calibration
curve, defined by the correction function.
[0082] As shown in FIG. 9 the measured velocity is corrected in
accordance with the corresponding calibration curve. For example,
the measured output velocity for a meter mounted to a 4 inch ID,
40 schedule pipe having a flow with a Reynolds number of 5.0E+05
is corrected for a 4.50% offset.
[0083] Each sensor head includes 3 numbers representative of each
of the three coefficients C0 C1 and C2 of the "Correction
Function". These calibration numbers are pre-programmed, or
entered into the processor 24 via line 38a, for example, to calibrate
the flow meter 10. This enables any sensor head 16 of a different
classes to be used with any processor 24. Therefore the processor
24 are independent of the pipes being measured.
[0084] The pressure sensors 18-21 of FIG. 1 described herein may
be any type of pressure sensor, capable of measuring the unsteady
(or ac or dynamic) pressures within a pipe 14 such as piezoelectric,
optical, capacitive, resistive (e.g., Wheatstone bridge), accelerometers
(or geophones), velocity measuring devices, displacement measuring
devices, etc. If optical pressure sensors are used, the sensors
18-21 may be Bragg grating based pressure sensors, such as that
described in U.S. patent application Ser. No. 08/925598 entitled
"High Sensitivity Fiber Optic Pressure Sensor For Use In Harsh
Environments", filed Sep. 8 1997 now U.S. Pat. No. 6016702
and in U.S. patent application Ser. No. 10/224821 entitled "Non-Intrusive
Fiber Optic Pressure Sensor for Measuring Unsteady Pressures within
a Pipe", which are incorporated herein by reference. In an
embodiment of the present invention that utilizes fiber optics as
the pressure sensors 14 they may be connected individually or may
be multiplexed along one or more optical fibers using wavelength
division multiplexing (WDM), time division multiplexing (TDM), or
any other optical multiplexing techniques.
[0085] In certain embodiments of the present invention, a piezo-electronic
pressure transducer may be used as one or more of the pressure sensors
15-18 and it may measure the unsteady (or dynamic or ac) pressure
variations inside the pipe 14 by measuring the pressure levels inside
of the pipe. These sensors may be ported within the pipe to make
direct contact with the process flow 12. In an embodiment of the
present invention, the sensors comprise pressure sensors manufactured
by PCB Piezotronics. In one pressure sensor there are integrated
circuit piezoelectric voltage mode-type sensors that feature built-in
microelectronic amplifiers, and convert the high-impedance charge
into a low-impedance voltage output. Specifically, a Model 106B
manufactured by PCB Piezotronics is used which is a high sensitivity,
acceleration compensated integrated circuit piezoelectric quartz
pressure sensor suitable for measuring low pressure acoustic phenomena
in hydraulic and pneumatic systems.
[0086] It is also within the scope of the present invention that
any strain sensing technique may be used to measure the variations
in strain in the pipe, such as highly sensitive piezoelectric, electronic
or electric, strain gages and piezo-resistive strain gages attached
to the pipe 14. Other strain gages include resistive foil type gages
having a race track configuration similar to that disclosed U.S.
patent application Ser. No. 09/344094 filed Jun. 25 1999 now
U.S. Pat. No. 6354147 which is incorporated herein by reference.
The invention also contemplates strain gages being disposed about
a predetermined portion of the circumference of pipe 14. The axial
placement of and separation distance .DELTA.X.sub.1 .DELTA.X.sub.2
between the strain sensors are determined as described herein above.
[0087] It is also within the scope of the present invention that
any other strain sensing technique may be used to measure the variations
in strain in the pipe, such as highly sensitive piezoelectric, electronic
or electric, strain gages attached to or embedded in the pipe 14.
[0088] The scope of the invention is intended to include using
other types or kinds of sensors including ultrasonic sensors similar
to that disclosed in CC-0680 (Express Mail No. EV 286 928 152 US)
and U.S. patent application serial No. 60/439715 (CiDRA Docket
No. CC-0530) filed Jan. 13 2003. The other types or kinds of sensors
may sense or measure any parameter that converts within a flow.
For example, any inhomogeneities, including temperature, particles,
turbulence eddies, acoustic variations or disturbances.
Scope of the Invention
[0089] The dimensions and/or geometries for any of the embodiments
described herein are merely for illustrative purposes and, as such,
any other dimensions and/or geometries may be used if desired, depending
on the application, size, performance, manufacturing requirements,
or other factors, in view of the teachings herein.
[0090] It should be understood that, unless stated otherwise herein,
any of the features, characteristics, alternatives or modifications
described regarding a particular embodiment herein may also be applied,
used, or incorporated with any other embodiment described herein.
Also, the drawings herein are not drawn to scale.
[0091] Although the invention has been described and illustrated
with respect to exemplary embodiments thereof, the foregoing and
various other additions and omissions may be made therein and thereto
without departing from the spirit and scope of the present invention.
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