Flow measurement systems and methods for gas and liquid applications
View Patent ↗A system for measuring the superposition of a plurality of sound waves propagating within a conduit containing a fluid having a plurality of transducers positioned substantially parallel to the flow direction along the wall of the conduit. The system includes means for modeling the superposition of a plurality of sound waves as they propagate within the conduit.
1. A system for measuring the superposition of a plurality of sound waves propagating within a conduit containing a fluid, the conduit having a longitudinal length, wherein the fluid flows through the conduit in a flow direction, and wherein at least one sound wave of the plurality of sound waves is generated by the fluid flowing through the conduit, the system comprising:
a plurality of transducers positioned substantially parallel to the flow direction along at least a portion of the longitudinal length of the conduit, wherein each transducer of the plurality of transducers comprises means for sensing the velocity of fluid flow through the conduit in the flow direction, wherein each transducer of the plurality of transducers further comprises means for sensing the speed at which the plurality of sound waves are propagating through the fluid, and wherein each transducer of the plurality of transducers is positioned in a spaced position relative to a predetermined reference point on the conduit, the spaced position corresponding to the longitudinal distance between the transducer and reference point;
means for modeling the superposition of the plurality of sound waves as they propagate within the conduit, wherein the means for modeling the superposition is in communication with each transducer of the plurality of transducers, and wherein the means for modeling the superposition is configured to:
receive a time domain signal from each transducer;
assign a position value to the time domain signal indicative of the spaced position of the transducer which generated the time domain signal; and
store an array of time domain signals and their corresponding position values,
wherein, upon storage of a selected number of time domain signals, the means for modeling the superposition is configured to process the array of time domain signals to produce a model of the phases of the plurality of sound waves as they propagate therein the conduit, and
wherein the superposition of the plurality of sound waves is modeled using the wave equations
Ψ
RL
(
r
,
z
,
t
)
=
NJ
0
(
M
cal
2
π
r
w
(
f
c
-
k
)
)
ⅇ
2
π
i
(
ft
+
kz
)
,
and
Ψ
LR
(
r
,
z
,
t
)
=
NJ
0
(
M
cal
2
π
r
w
(
f
c
-
k
)
)
ⅇ
2
π
i
(
ft
-
kz
)
where:
Ψ=the phase of the wave moving right-to-left (RL) or left-to-right (LR) through the conduit,
r w =the radius of the conduit,
z=the horizontal position of the wave measured relative to the direction of fluid flow within the conduit,
t=elapsed time since generation of the wave,
N=amplitude of the sound wave,
J 0 =cylindrical Bessel function of the first kind,
M cal =calibration coefficient,
f=frequency of the sound waves,
c=speed of the sound waves within the conduit, and
k=the wavenumber associated with the sound waves, and
wherein the means for modeling the superposition of the plurality of sound waves as they propagate within the conduit further generating correlation information from the model to display features of the fluid flowing through the conduit.
2. The system of claim 1 , wherein the means for modeling the superposition is configured to:
generate a frequency domain signal associated with each transducer;
form a two-dimensional time- and space-domain matrix for the plurality of transducers comprising the time- and frequency-domain signals associated with each respective transducer;
perform a two-dimensional fast Fourier transform (2DFFT) on the two-dimensional time- and space-domain matrix; and
correlate the results of the 2DFFT with the results modeled by the wave equations.
3. The system of claim 2 , wherein the means for modeling the superposition is configured to identify the maximum correlation between the results of the 2DFFT and the results modeled by the wave equations.
4. The system of claim 3 , wherein, based upon the maximum correlation between the results of the 2DFFT and the results modeled by the wave equations, the means for modeling the superposition is configured to calculate the sound propagation in the direction of fluid flow and the sound propagation against the direction of fluid flow within the conduit.
5. The system of claim 4 , wherein, based upon the calculated sound propagation within the conduit, the means for modeling the superposition is configured to calculate at least one of the velocity of fluid flow and the speed of sound within the conduit.
6. The system of claim 1 , wherein the time domain signal associated with each transducer is indicative of the sensed velocity of fluid flow through the conduit in the flow direction and the sensed speed at which the sound waves are propagating through the fluid.
7. The system of claim 2 , wherein the means for modeling the superposition is further configured to:
perform a one-dimensional fast Fourier transform (1DFFT) on the time domain signal acquired from each respective transducer; and
generate a normalized time domain signal for each respective transducer,
wherein the normalized time domain signal is included in the two-dimensional time- and space-domain matrix.
8. The system of claim 1 , wherein plurality of sound waves comprises a first sound wave and a second sound wave.
9. The system of claim 1 , wherein the plurality of transducers comprises 2 transducers.
10. The system of claim 1 , wherein the plurality of transducers comprises at least 64 transducers.
11. The system of claim 1 , wherein the plurality of transducers comprises at least 128 transducers.
12. The system of claim 1 , wherein each transducer of the plurality of transducers is longitudinally spaced from adjacent transducers by a separation length.
13. The system of claim 12 , wherein the separation length ranges from about 0.5 inches to about 3.5 inches.
14. The system of claim 12 , wherein the separation length ranges from about 1.0 inches to about 3.0 inches.
15. The system of claim 12 , wherein the separation length ranges from about 1.5 inches to about 2.5 inches.
16. The system of claim 1 , wherein the means for modeling the superposition of the plurality of sound waves comprises a computer having a processor.
17. The system of claim 16 , wherein the processor comprises an analog-to-digital converter for processing the data sets received from the plurality of transducers, and wherein the analog-to-digital converter processes the data sets at a sample rate.
18. The system of claim 1 , wherein the conduit comprises an external surface, and wherein the plurality of transducers are detachably mountable on the external surface of the conduit.
19. The system of claim 18 , wherein the plurality of transducers are interconnected to form a substantially linear array of transducers.
20. A method for measuring the superposition of a plurality of sound waves propagating within a conduit containing a fluid, wherein the fluid flows through the conduit in a flow direction, and wherein at least one sound wave of the plurality of sound waves is generated by the fluid flowing through the conduit, the method comprising:
providing a plurality of transducers positioned substantially parallel to the flow direction along at least a portion of a longitudinal length of the conduit, wherein each transducer of the plurality of transducers comprises means for sensing the velocity of fluid flow through the conduit in the flow direction, wherein each transducer of the plurality of transducers further comprises means for sensing the speed at which the plurality of sound waves are propagating through the fluid, and wherein each transducer of the plurality of transducers is positioned in a spaced position relative to a predetermined reference point on the conduit, the spaced position corresponding to the longitudinal distance between the transducer and reference point;
receiving a time domain signal each respective transducer;
assigning a position value to the time domain signal indicative of the spaced position of the transducer which generated the time domain signal;
storing an array of time domain signals and their corresponding position values; and
processing the array of data sets to produce a model of the superposition of the plurality of sound waves as they propagate therein the conduit,
wherein the superposition of the plurality of sound waves is modeled using the wave equations
Ψ
RL
(
r
,
z
,
t
)
=
NJ
0
(
M
cal
2
π
r
w
(
f
c
-
k
)
)
ⅇ
2
π
i
(
ft
+
kz
)
,
and
Ψ
LR
(
r
,
z
,
t
)
=
NJ
0
(
M
cal
2
π
r
w
(
f
c
-
k
)
)
ⅇ
2
π
i
(
ft
-
kz
)
where:
Ψ=the phase of the wave moving right-to-left (RL) or left-to-right (LR) through the conduit,
r w =the radius of the conduit,
z=the horizontal position of the wave measured relative to the direction of fluid flow within the conduit,
t=elapsed time since generation of the wave,
N=amplitude of the sound wave,
J 0 =cylindrical Bessel function of the first kind,
M cal =calibration coefficient,
f=frequency of the sound waves,
c=speed of the sound waves within the conduit, and
k=the wavenumber associated with the sound waves, and
wherein the means for modeling the superposition of the plurality of sound waves as they propagate within the conduit further generating correlation information from the model to display features of the fluid flowing through the conduit.