Measurement Techniques, Vol. 37, No. 10, 1994
DEVELOPMENT OF ULTRASONIC FLOWMETERS UDC 621.034
B. I. Filatov
The advantages are considered of a method that eliminates the shortcomings of flow meters with alternate switching of ultrasonic signals and considerably reduces the error of flow-rate measurements. With the improvements in their metrological and technical characteristics ultrasonic flowmeters are used increasingly in industry. Turbine flowmeters will undoubtedly replace ultrasonic flowmeters in industry in this decade. Analysis has shown that ultrasonic flowmeters can be used to measure the flow rate of substances with a maximum error of measurement of _+0.1-0.2% [1]. Such a high accuracy of measurement can be obtained only if the method of measurement, flowmeter design, transducer parameters, and electronic circuit of the flowmeter are chosen correctly and the influence of reverberation and other factors are eliminated in the flowmeters built. Frequency-pulse ultrasonic flowmeters have the best metrological characteristics. The flowmeters developed have low errors of measurement (_+0.5-1.5%), the broadest relative measuring range (500-1000), and a negligible dependence of the results of measurement on the variations of the ultrasound velocity, while delivering a frequency output signal that is very convenient for obtaining information. A disadvantage is that reverberation noise arises during operation of the synchro ring circuit. Since the 1970s the overwhelming majority of frequency-pulse flowmeters have been based on a single-channel scheme with alternating switching of ultrasonic signals, directed along and counter to the flow. The frequency of autocirculation of signals along and counter to the flow is stored by circuits, using voltage-controlled generators. These memory circuits have an error of roughly _+0.5-1.5%, which is the dominant error that prevents a higher accuracy of measurement by flowmeters. Circuits for separating signals of various frequencies introduce an appreciable error into the results of the measurements. Moreover, inherent to these flowmeters are errors due to the variation of the hydrodynamic parameters of the flow under alternating switching of ultrasonic signals traveling along and counter to the flow. The disadvantages of flowmeters with alternating switching of ultrasonic signals can be eliminated and errors of flowrate measurements can be reduced substantially by the Filatov method of ultrasonic measurement of the flow rate. The highcurrent, fast-response method makes it possible to set the instrument at zero and simply determine the direction of flow. The method eliminates the error that is inherent to known flowmeters because of the design shortcomings mentioned above. The method consists in the following. Ultrasonic signals, both along and counter to the flow, autocirculate in the singlechannel transducer of the flowmeter, which has one pair of piezoelectric elements, and produce two pulse trains that propagate in opposite directions. To prevent coincidence of emission and reception of ultrasonic signals at a piezoelectric element, each pulse train undergoes a relative shift and delay. Autocirculation of pulses is accomplished with a synchro ring circuit. The frequency of the delays of a pulse train, which is directly proportional to the flow velocity, is measured. The direction of the flow is determined on the basis that the pulses traveling counter to the flow in time "catch up" to the pulses traveling along the flow. The only coincidence possible, therefore, is that of the trailing edges of the pulses counter to the flow with the trailing edges of the pulses traveling along the flow. The signal obtained from such coincidences indicates the direction of the flow. One version of this method, which this author has developed, is shown in Fig. 1. Diagrams a and d show signals propagating along and counter to the flow, respectively, with repetition periods ta and tu; diagrams b and e show expanded signals a and d, respectively, with length r~; diagrams c and f show signals of the pulse trains a and d with a delay r; and diagram g shows output signals with repetition periods ta. Let us describe the proof of the method. According to this method, the period of the frequency output signal (diagram g) is t~ = tA' + ta", where tA' and tA" are the intervals between the delays of trains of autocirculating pulses along and counter to the flow, respectively, which can be written as Translated from Izmeritel'naya Tekhnika, No. 10, pp. 37-39, October, 1994.
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0543-1972/94/3710-1152512.50
9
Plenum Publishing Corporation
t ~ = n t u - - n l a + : , where n=0, 1,2 . . . . . ; t"a=mtd=(m--1 )tu+,c , wherem=O, 1 , 2 , . . . .
Hence, ta = ( n + m ) td + r = ( n + m - - 1 ) tu + r . Solving the last equation with allowance for fd = 1/td, fu = 1/tu, Af = fu -- fd, we obtain the frequency of the output signal Fsllt~ =
M
l--xA f "
The transducer of the ultrasonic flowmeter for high-current measurements must be made as single-channel angle transducer without refraction of ultrasonic waves. When low-viscosity liquids are measured by flowmeters with angle transducers, the error of measurement can reach 0.3-0.13 % because of changes in the Reynolds number. This error is roughly five times higher in an axial transducer [2]. Many of the flowmeters made in recent years involved refraction of ultrasonic waves, with transducers mounted onto the pipe. Such transducers can be mounted easily but the flowmeters used with them have inferior metrological characteristics: the error due to variations of the ultrasound velocity in the flow and sound duct may reach 3 % or more [2]; the error due to the hydrodynamic of the flow may be several percent; the sensitivity decreases and the error of measurement increases because the emission angles are small and far from optimal; and a disruption of the acoustic coupling between the transducers and the pipe can lead to very substantial systematic errors. Flowmeters that have transducers without refraction of the ultrasonic waves do not have these errors. The emission-reception angle in the angle transducers of frequency-pulse flowmeters should be chosen to be 45 ~ to obtain maximum sensitivity. The influence of reverberation of ultrasonic waves on the results of measurements must be eliminated or substantially reduced if measurements with ultrasonic flowmeters are to be of the highest accuracy. Frequency-pulse and phase flowmeters may be affected Very much by ultrasonic signals which are reflected many times from the receiver-emitter, primarily by doubly-reflected signals which cause modulation of the calibration characteristic, i.e., a systematic error of the instrument. The effect of other kinds of reverberation, e.g., the passage of ultrasonic signals along the transducer tube, reverberation of signals in sound ducts, and so forth, can be eliminated entirely or attenuated considerably by the construction and the circuit design. The emission period in pulse-time flowmeters is increased by eliminating the influence of multiply-refected signals. Let us consider how signals reflected many times from the surfaces of piezoelectric elements or sound ducts affect the characteristics of flowmeters. The intervals AVZnd and 2Xt2nu between signals reflected 2n times and the main signals, respectively, emitted along and counter to the flow can be written as [3] Alan t =
At.~,,--
2nDvct~7 c2
2nDvct~ c"-
+2n% :
(1)
+2n%.
(2)
where D is the inside diameter of the transducer of the flowmeter; v is the flow velocity; ~ is the angle of ultrasonic-signal emission; c is the ultrasound velocity in the flow; and ~'0 is the signal delay in the electronic circuit of the instrument, sound ducts, and connecting cables. From Eqs. (1) and (2) we see that the multiply-reflected signals periodically are far from the main signal and have a period of 2r0: as the flow velocity increases the multiply-reflected signals approach the main signal along the flow and move away from the main signal counter to the flow. Assuming that the shape of the multiply-reflected signals coincides with that of main signal r s, from Eq. (1) we obtain the condition for no doubly-reflected signals, i.e., all multiply-reflected signals, to be superposed onto the main signal: ":s~<2%-
2Dvm.~ c t ~
c'
'
(3)
where Vmax is the maximum flow velocity.
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n
n
_A
I
h
fl
n
n_
t
I
n
I
,z-
hI
f
[] n_
I I
I
n
n
i
i
I
nl
n
I
I
1 t~
I
-S
t~
Fig. 1 Inequality (3) can be satisfied in frequency-pulse flowmeters because of a decrease in r s, i.e., emission of short ultrasonic signals possibly at a higher velocity, or because of an increase in the signal delay r o in the electronic circuit of the flowmeter. A considerable increase in r 0 diminishes one of the main advantages of frequency-pulse flowmeters, i.e., a dependence of the results of measurements on the ultrasound velocity c. Let us consider this in detail. The expression for the difference of the frequencies of the signal autocirculations has the form 2Dvct~a
"= (
+,
1.2..
where l is the depth of the transducer "pocket." As we see from the last expression, the dependence of the output signal on the ultrasound velocity c is responsible for the last two terms in the denominator, which have rather large values for large r 0. When inequality (3) is not satisfied or when a long harmonic signal is emitted, multiply-reflected signals are superposed onto the main signals, causing modulation of the calibration characteristic of the flowmeter by multiply-reflected signals, i.e., causing a systematic error of the measurements. Such a modulated calibration characteristic was obtained in studies of the UZRF2-150 flowmeter [4]. Upon summing the harmonic vibrations Fv(t) = A v sin(~0t + ~v), we obtain
~. Avsin(od§ k==O
where A v is the amplitude of the vibrations and Cv is the phase of the vibrations. When the main signal A s sin(cot + %) is added to the doubly-reflected signal A 1 sin(~ot + r and phase can be written as A= V
~ , As~ +A~-4-2AsA1cos(~s-%)
Ass{ncps4--Av~inqh
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the signal amplitude
(4)
Solving Eq. (5), we see that only for 'Ps = tPl does ~ = 'Ps, otherwise ,p ~ ~'s. This causes phase ultrasonic flowmeters to have a large systematic error ( ~ = ~ - - Cs/~s), which is a disadvantage of phase flowmeters that cannot be removed. In the sum signal Acsin(o~t + ~s) + Alsin(wt + ~Pl) = Asin [r + (~ - - ,ps/r + ~s] from frequency-pulse flowmeters the change of phase results in a time shift relative to the main signal, t ~ - tP--q~'s co
q~--tp,s --
2~f
'
where f is the frequency of the emitted signal. The output signal has the form Af' = 1/tu + l~(t d + td' ). The value of td' determines the systematic error of measurements caused by the phase shift; that error is 5' = ( A f - Af'/Af). The change in the signal amplitude because of the addition with a doubly-reflected signal is also a source of error of frequency-pulse flowmeters. In the flowmeter the signal generator has an operation threshold Us, which is part of the signal amplitude As, i.e., m s --- Us/A s. When the signal is added to a doubly-reflected signal the amplitude changes and another part of the sum signal, m = Us/A = msAs/A, now corresponds to the operation threshold. A time displacement t" d forms because of the steepness of the signal and the sum signal at the operation threshold level: .
1
td -- 2~/' (arc sinms--arc'sinm ). This time displacement changes the output signal frequency Af" = 1/tu -- 1/(td + td"), which leads to an error of measurement 5" = (Af -- Af"/Af). As the frequency f of the emitted signal increases the condition for no superposition of a doubly-reflected signal onto the main signal (3) is satisfied better and the errors of measurement 5' and 5" decrease. The amplitude of the doubly-reflected signal can be decreased substantially by an appropriate choice of the piezoeletric element diameter d, which should be chosen from the formula d _> L ~ , where L is the distance between the piezoelectric elements and k is the wavelength in the flow. The method presented here is employed in the flowmeters UZRF 2-150 and UER 3-70. The UZRF 2-150 [5] has an error of less than 0.5 % and a transducer diameter of 150 mm, is provided with emergency signaling that indicates when the pipe has been emptied and when the electronic circuit of the instrument has malfunctioned, and the output circuits of its electronic unit are spark-proof. The UZRF 2-150 has been used successfully to measure natural gasoline and stock-tank oil. The measurements stop automatically when a gas cushion passes through the transducer. Measurements are resumed in less than 2.5 msec after the pipe has been filled with liquid. The UFR 3-70 was developed for dynamic tests of aviation engines. The broad measuring range and the zero lag make it suitable for dynamic measurements. Such instruments were not previously known. Since the calibration characteristic is linear and depends very weakly on the Reynolds number, measurements can be made in the transitional region of the flow and very short straight lengths of pipes can be used.
REFERENCES .
2. ,
4. 5.
V. I. Filatov, "Automation and telemechanization of the oil industry," RNTS VNNIIOI~NG, No. 1, 22 (1975). V. I. Filatov, in: Process Control in Oilfield Development and Operation [in Russian], Izd. Kazan. Univ., Kazan (1974). V. I. Filatov, Izmer. Tekh, No. 3, 39 (1993). V. I. Filatov, "Automation and instrumentation in the oil refining and petrochemical industries," NRTS TsNIII~Neftexim., No. 1, 26 (1983). V. I. Filatov, Flowmeter Design and Construction [in Russian], Mashinostroenie, Leningrad (1978).
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