Doppler flowmeter

A Doppler flowmeter impulses an ultrasonic fixed-frequency signal obliquely into a slurry flowing in a pipe and a reflected signal is detected after having been scattered off of the slurry particles, whereby the shift in frequencies between the signals is proportional to the slurry velocity and hence slurry flow rate. This flowmeter filters the Doppler frequency-shift signal, compares the filtered and unfiltered shift signals in a divider to obtain a ratio, and then further compares this ratio against a preset fractional ratio. The flowmeter utilizes a voltage-to-frequency convertor to generate a pulsed signal having a determinable rate of repetition precisely proportional to the divergence of the ratios. The pulsed signal serves as the input control for a frequency-controlled low-pass filter, which provides thereby that the cutoff frequency of the filtered signal is known. The flowmeter provides a feedback control by minimizing the divergence. With the cutoff frequency and preset fractional ratio known, the slurry velocity and hence flow will also be determinable.

BACKGROUND OF THE INVENTION 
Many industrial applications, such as coal conversion plants, paper mills, 
cement manufacturing plants, and sewage treatment plants have difficulty 
in reliably measuring the flow of a liquid type slurry through a pipe. 
Part of the problem is that the slurry temperature and/or pressure can be 
quite high, the slurry can be corrosive or abrasive, or the slurry can be 
of high viscosity. Conventional flowmeters requiring structure located 
inside of the pipe or having takeoff ports in the pipe walls generally 
prove inappropriate as such flowmeters tend to foul up in a very short 
time. Flowmeters that use structure located only outside of the pipe, 
including the electromagnetic flowmeter, the thermal flowmeter, and the 
sonic flowmeter, are available and have various degrees of appeal. The 
electromagnetic flowmeter however, requires that the liquid conveyed be 
electrically conductive in order to detect flow movement. In the thermal 
flowmeter, heat is applied to the moving slurry between a pair of axially 
spaced sensors, and the temperature differential is sensed. This flowmeter 
proves inappropriate where the liquid temperature itself is extremely high 
or where the heat loss from the pipe is high. The sonic flowmeter utilizes 
the possible shift in the time or location of a sonic signal through the 
slurry as a function of the slurry velocity, and the one type includes the 
Doppler flowmeter. 
An ultrasonic flowmeter of the Doppler type would have two transducer units 
bonded or mechanically held tightly against the outside walls of the pipe. 
A constant frequency ultrasonic signal (500,000 Hz, for example) from the 
one transducer unit is transmitted through the pipe wall obliquely into 
the flow stream and is scattered off the particles moving therein, and the 
scattered signal is detected by the other transducer unit. In theory, the 
detected signal will have a shift in frequency to higher or lower than 
that of the original signal, depending on whether the signal is sent out 
against or in the same direction respectively, as the direction of the 
slurry flow. The Doppler frequency shift is proportional to the operating 
frequency and to the ratio of the vector components of the slurry velocity 
in the direction of the wave propagation at a velocity. Thus 
EQU F.sub.d =2F.sub.o (V/C) cos .theta. 
where 
F.sub.d =Doppler frequency shift 
F.sub.o =Sending transducer frequency 
V=Velocity of slurry 
C=Velocity of wave 
.theta.=Angle of wave propagation relative to the axial flow. 
The use of ultrasonic waves is attractive because of the relatively low 
propagation velocity and the ability to penetrate solid pipes and opaque 
slurries. However, as there are many particles moving with the slurry, the 
detected frequency shift signal therefore is received off of many 
particles and is in the form of a broadband of many frequencies. 
Correlating the frequency shift signal to the velocity flow thus becomes 
very difficult. Moreover, inasmuch as the Doppler frequency shift is a 
function of the velocity of the slurry flow compared to the velocity of 
the ultrasonic signal in the slurry, the frequency shift is quite small, 
of the order of 0.01-1.0% of the original ultrasonic signal. 
SUMMARY OF THE INVENTION 
This invention teaches an improved Doppler flowmeter having a transmitter 
that emits a fixed frequency ultrasonic signal into a slurry flowing in a 
pipe, this signal being scattered off particles in the slurry, and the 
scattered signal being detected then by a receiver; and the Doppler shift 
signal representing the difference between these signals is determined and 
used to give the velocity of the slurry. 
The Doppler shift signal comprises a continuous broadband of different 
frequencies. For laminar flow, the frequency distribution is uniform 
ideally to correspond to the uniform distribution of slurry particles 
travelling in the pipe at the various incrementally different speeds from 
near zero up to the maximum. For turbulent flow, the frequency 
distribution is weighted more toward the maximum to correspond to the more 
uniform near maximum velocity of slurry over the central region of the 
pipe. The flowmeter determines the area under the power spectrum of the 
Doppler shift signal, which thereby corresponds to and gives slurry 
velocity and slurry flow. 
The flowmeter utilizes frequency controlled means to obtain a cutoff signal 
that is a fractional ratio of the bandwidth of the Doppler shift signal, 
further utilizes means to compare the cutoff and Doppler shift signals to 
generate a fractional ratio and an error function signal that is 
proportional to the departure of this fractional ratio from a preset fixed 
fractional ratio, further utilizes a precise voltage-to-frequency 
converter to produce a pulsed signal that is at an adjusted repetition 
rate proportional to the error function signal and to introduce this 
pulsed signal as a control input to the frequency controlled means, and 
further utilizes feedback loop means tending to minimize the error 
function, whereby the pulse rate and hence cutoff signal and hence the 
Doppler shift signal can each be determined and obtain thereby the slurry 
flow.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
FIG. 1 illustrates in schematic form a preferred embodiment of the subject 
invention. The figure shows a pipe 10 through which a liquid slurry would 
flow in the direction indicated by the arrow 12. The flowmeter would 
comprise a pair of transducer units 14 and 16 that are mounted in sound 
transmitting relationship relative to the exterior wall of the pipe. In 
order to provide isolation from the temperature of the pipe, waveguides 18 
and 20 are actually positioned between the pipe surface and the surface of 
the transducer, the waveguides being of a sound transmitting material but 
yet have sufficient thermal insulating capacity to keep the temperature of 
the transducer low as compared to that of the pipe surface. Although the 
transducers 14 and 16 are shown on opposite sides of the pipe at similar 
axial locations relative to the pipe, the actual positions of the 
transducers can be varied both angularly and axially. 
As illustrated, transducer 14 is the signal sending unit and transducer 16 
is the signal receiving unit. The transducer 14 is activated by an 
electric generator 22 via conductor 24, and the activated transducer 14 in 
turn emits a fixed frequency tone or signal that is transmitted through 
the waveguide and pipe wall obliquely into the slurry toward the pipe 
center in the direction against the slurry flow. This signal is scattered 
off many particles in the slurry, and the scattered signal is picked up by 
the receiving transducer 16. This scattered signal via conductor 25 is 
directed to amplifier 26 and the amplified signal is carried via conductor 
29 to a mixer 30. The mixer 30 in effect combines the fixed input signal 
received at conductor 31 and the scattered signal received at conductor 29 
to isolate a Doppler shift signal at conductor 32. 
The Doppler frequency shift signal, as thus isolated by mixer 30, is 
treated by the following components in order to allow for standardized 
signal analysis. As illustrated in FIG. 1, the signal at conductor 32 is 
first passed through an automatic gain control 34, to make all signals of 
approximately equal amplitude. The signal at conductor 35 is then passed 
through a high pass filter 36 which effectively stops the very low 
frequency part of the signal. Background noise, such as caused by bubbles, 
tends to clutter the low frequency range a disproportionate amount. Based 
on the severity of this noise condition compared to the total signal and 
the need for flowmeter accuracy at extremely low flow rates, the amount 
filtered out represents a compromise of sort but generally is in the 5-10% 
range of the maximum. The resultant signal at conductor 37 is then passed 
through automatic gain control 38, again to make the strength of all 
compared signals at conductor 39 of uniform amplitude. Thus, only the 
shape of the Doppler shift spectrum is of concern. 
In the circuit illustrated in FIG. 1, the alternating current Doppler shift 
signal V.sub.d on the one hand is passed by conductor 39a through a 
squaring unit 40 and an averaging unit 42 and the resultant squared, 
averaged and rectified DC signal V.sub.d.sup.2 at line 43 is admitted as 
one input to analog divider 46. This squared and average voltage signal is 
proportional then to the power of the signal. On the other hand, the 
Doppler shift signal V.sub.d is also transmitted via conductor 39b through 
an adjustable low pass filter unit 48 to exit at conductor 49 as signal 
V.sub.c, and this is passed through a squaring unit 50 and an averaging 
unit 52, and the resultant rectified DC signal V.sub.c.sup.2 at conductor 
53 is admitted as a counterpart input to the analog divider 46. This 
squared and averaged DC signal V.sub.c.sup.2 also is proportional then to 
the power of the signal. 
The analog divider 46 in effect compares the signals at conductors 53 and 
43 to obtain a fixed quotient or fractional ratio 
(V.sub.c.sup.2)/(V.sub.d.sup.2) at conductor 55. The fractional ratio from 
the divider 46 is then additively compared with a constant value "Y" in a 
summation unit 54. The output signal "Y-(V.sub.c.sup.2)/(V.sub.d.sup.2)" 
is passed via conductor 57 through an amplifier 56 which amplifies the 
signal by a large constant "C", such as on the order of 100. This 
magnified signal V.sub.o at conductor 58a then passes through an averaging 
unit 59, conductor 61 and amplifier 60 to produce at conductor 62 a DC 
output voltage V.sub.o. The voltage of course can be measured with a 
potentiometer 64 calibrated with a scale 65 to indicate the velocity 
and/or flow directly. 
The magnified signal V.sub.o further passes via conductor 58b to a precise 
voltage-to-frequency convertor 66. The convertor 66 has the 
characteristics of producing at conductor 67 a pulsed signal F.sub.p at a 
repetition rate that is proportional to the input voltage signal at 
conductor 58b. This pulsed signal F.sub.p at the line 67 is used to 
control the low pass filter 48. The low pass filter 48 is frequency 
responsive and has the characteristic to pass to conductor 49 only the 
lower frequency bandwidth of the input signal at line 39b and variably and 
adjustably cuts off the higher frequency bandwidth from the signal, 
depending on the rate of repetition of the pulsed control signal at 
conductor 67. The filter 48 further has the characteristic to maintain the 
frequency of the cut off signal at conductor 49 a fixed ratio of the 
pulsed input rate of repetition at conductor 67, or as selected herein, at 
one-one hundredth (1/100) of the pulsed rate. 
In effect, the loop circuit illustrated is an automatic servo or feedback 
control that continuingly compares the squared and averaged filtered and 
nonfiltered Doppler shift signals or voltages V.sub.c.sup.2 and 
V.sub.d.sup.2 against each other and the fractional ratio constant Y. By 
making the amplification constant C at amplifier 56 quite large, the ratio 
V.sub.c.sup.2 /V.sub.d.sup.2 will approach the preset fractional ratio 
constant Y and the error function Y-V.sub.c.sup.2 /V.sub.d.sup.2 will 
become quite small. Further the feedback loop seeks out stabilized 
readings for flow, so that if the error function were instantaneously too 
large, the voltage V.sub.o at the conductor 58b to the 
voltage-to-frequency convertor 66 would likewise be too high to provide a 
higher rate of repetition of the pulsed signal F.sub.p at line 67 than 
needed, which then would cause the controlled filter 48 to increase the 
cutoff frequency F.sub.c so that V.sub.c.sup.2 also would be increased, so 
that the larger V.sub.c.sup.2 when compared with the Doppler shift signal 
V.sub.d.sup.2 at input line 43 would automatically produce a smaller error 
function signal. 
The frequency-controlled low pass filter 48 is selected to provide that the 
output cutoff frequency F.sub.c is precisely related the pulsed control 
frequency F.sub.p, for example in the R5609, F.sub.c is 0.01 times 
F.sub.p. Thus, if pulsed frequency F.sub.p is at 35,000 Hz, the adjusted 
filtered output cutoff F.sub.c will be equal to 350 Hz. 
Knowing the cutoff frequency F.sub.c and the preset cutoff fractional ratio 
Y, the bandwidth or corner-frequency F.sub.d of the original signal can be 
inferred. The feedback circuit makes sure that F.sub.c /F.sub.d 
=V.sub.c.sup.2 /V.sub.d.sup.2 .congruent.Y. This further corresponds to 
the power level of the voltage squared signal. The departure or error 
function signal Y-V.sub.c.sup.2 /V.sub.d.sup.2 can be made small by making 
the feedback gain C large. 
As an interpretation of the fixed and scattered signals, the sending 
transducer 14 has a fixed tone at frequency F.sub.o, for example at 
500,000 Hz, and this fixed signal is scattered by the pipe wall in 
homogeneities and by the many particles in the slurry and is received as 
signal F.sub.s at the transducer receiver 16. The signal scattered off the 
pipe wall in homogeneities will be "background" and will be the same as 
the transmitted signal frequency F.sub.o. The signal scattered off the 
many slurry particles moving toward the source of the signal will be 
shifted to a slightly higher frequency than the fixed tone. Inasmuch as 
flow velocities will be very low when compared to the speed of the signal 
through the slurry, the maximum shift in frequency is very small compared 
to the fixed tone frequency, such as of the order of magnitude of 20-2000 
Hz versus 500,000 Hz. The receiving transducer 16 in turn converts the 
many frequency scattered signals into a single AC voltage, which includes 
both the background and particle scattered frequencies. 
The resulting Doppler shift signal is comprised of many separate 
alternating current impulses each at a specific frequency, being 
representative of a particle in the flow stream moving at a specific 
speed. In this regard, it is well known that under laminar flow 
conditions, the flow in a pipe is at maximum velocity at or near the pipe 
center, is at substantially zero velocity at the molecular layer on the 
pipe walls, and varies in velocity along a parabolic three dimensional 
cone from the maximum to the wall layer zero velocity. The number of 
particles flowing at each incrementally different velocity between the 
zero and maximum velocities is substantially equal. Conversely, turbulent 
flow has maximum velocity at or near the center of the pipe, little 
drop-off from this maximum velocity for most of the remaining cross 
section of the pipe moving toward the pipe walls, and a rapid dropoff in 
particle velocities across a narrow transition zone from the near maximum 
to zero velocity at the wall layer. Thus, most of the particles in 
turbulent flow are flowing at near maximum velocity. 
As a further point of interpretation, the Doppler shift signal can be 
analyzed by a Fourier analyzer, where the spectrum indicates the frequency 
distribution corresponding to the velocity distribution of the particles 
in the flow. The idealized spectra for signals obtained under turbulent 
flow and laminar flow conditions are illustrated separately in FIGS. 2 and 
3, respectively and together in FIG. 6. 
FIG. 4 illustrates representative spectra obtained at different laminar 
flows, where the Doppler shift signals were analyzed with a Fourier 
analyzer (not shown). The characteristic continuous power spectrum 
generated can be noted for each flow rate, as well as the characteristic 
corner frequency of the spectrum. FIG. 5 illustrates the calibrated 
flowmeter outputs for the actual flow of slurry in the pipe according to 
that covered in FIG. 4. 
FIG. 6 illustrates the idealized relative distribution of the particles in 
turbulent flow and in laminar flow, as compared to the mean or average 
velocity of the flow. The average velocity of the flow in either case is 
indicated at the frequency corresponding to approximately the half way 
frequency splitting the power spectrum in half. 
The corner frequency of the laminar flow spectrum is theoretically twice 
the Doppler frequency produced by the average velocity. The feedback 
circuit can measure this corner frequency. The power (or voltage squared) 
content of a broad-band spectrum signal is proportional to its bandwidth. 
The Doppler spectrum is compared to the filtered portion of it, and the 
controlled filter 48 is adjusted automatically to keep the ratio F.sub.c 
/F.sub.d constant. Thus, knowing the cutoff F.sub.c, the spectrum corner 
F.sub.d and hence flow rate can be evaluated. 
The flow rate of either laminar flow or turbulent flow is equal to the 
average flow velocity multiplied by the flow area of the pipe. The output 
signal at conductor 62 can be passed through the voltmeter 64 which could 
be calibrated with an appropriate scale 65 to indicate the velocity and/or 
flow units of the slurry. The output signal F.sub.p from line 67 can also 
be passed through a frequency activated meter 69 to indicate as on scale 
70 the repetition rate of the pulsed signal from the frequency convertor, 
and/or can be scaled to indicate the actual velocity or flow of the 
slurry. Further, an integrator (not shown) could be used in accumulating 
the successively obtained flow rates for determining the total slurry 
passed through the pipe over an extended period. 
The fractional ratio constant Y can be most any value between approximately 
0.2 and 0.99 (&lt;1) for measuring laminar flow. This is possible because the 
constant power spectrum, as provided by a Fourier analysis, has a 
generally uniform amplitude throughout the bandwidth of different 
frequencies, and the area under the spectrum is proportional to the cutoff 
frequency or to the maximum frequency (see FIG. 3). However, the power 
spectrum provided by the Fourier analyzer for turbulent flow is 
nonuniform, but more generally assumes a narrow inverted and continuous 
distribution curve only approximately one-half octave wide across the half 
power amplitude, where the peak is shifted more toward the maximum 
frequency (see FIG. 6). The average velocity will occur at the frequency 
that splits the power spectrum in two by area. This will be approximately 
where Y is equal to 0.5. Thus, by selecting Y as always equal to 0.5, the 
flowmeter can be used for either laminar or turbulent flow conditions 
without any recalibration. 
The disclosed Doppler flowmeter has all physical structure located outside 
of the pipe, and can be used on most any type of slurry. The slurry 
therefore need not be magnetic, transparent or nonviscous, parameters that 
have limited the success and accuracy of other externally located 
flowmeters. Moreover, the positioning of the transducers on adjacent sides 
of the pipes or on opposite sides of the pipe do not materially affect the 
accuracy of the flowmeter, so that the sender and receiver transducers can 
be angularly and/or axially varied somewhat relative to the pipe as 
determined for convenience. 
The advantage that all of the flowmeter apparatus can be located outside of 
the pipe however need not require that the transducers in fact be located 
there, if such positioning is not required because of the conditions of 
the flow and/or material. In other words, the transducers can be located 
inside the pipe, if such were desired, such as in special annular chambers 
accessible through windows in the pipe walls, while the improved circuit 
could be used to analyze the signal. Also, while the disclosure shows the 
signal being impulsed against the direction of the flow, the signal can 
also be sent in the same direction as the flow stream. The resulting 
scattered frequency shift however will be to a lesser frequency than the 
input signal, but the disclosed concept will allow for the same analysis 
of the signal and the resultant determination of the velocity or flow rate 
of the slurry. 
The disclosed flowmeter has been used successfully in a coal slurry plant 
where oil and 5-45% by weight solid particulates, 95% of which are sized 
through a 100 mesh screen, were flowing at 0.5 to 4.5 ft. per second at 
temperatures ranging between 175.degree.-400.degree. C. and at pressures 
of approximated 300 psi. The particular flowmeter as developed has been 
operated by the Argonne National Laboratory according to the following 
general catalog of components listed by part name and number, model 
number, and manufacturer. 
______________________________________ 
Part Name and Number 
Model Number Manufacturer 
______________________________________ 
Transducers 16, 18 
NDT type 0.5 MHz 
Parametrics 
KB - Aerotech 
Mixer Component 30 
SRA 3 Mini Circuits, Inc. 
High Pass Filter 36 
R5611 EG&G Reticon 
Squaring Circuit 
AD 534 Analog Devices 
Dividing Circuit 46 
AD 535 Analog Devices 
and Adder 54 
Voltage to Frequency 
VFL 32 Burr Brown 
Convertor 66 
Frequency Controlled 
R5609 EG&G Reticon 
Low Pass Filter 48 
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