Based on work done between 1972 and 1976 to which access was initially restricted for commercial reasons. Published in Elsevier's magazine, 'Sensors and Actuators -- A', 2001.

See :



an outline :


A brief description is give of the ultrasonic correlation flowmeter together and its advantages and disadvantages. By summarising past acoustic difficulties and solutions in developing its features, a short account is given of the flow meter’s history to explain its present day electronic design and acoustic limitations. Previously unpublished design details, results and theories provide insight into intricacies of the flowmeter’s acoustic nature and point the way for future developments.

Keywords : flow meter, correlation, ultrasonics, interface electronics


In the earliest forms of the flow meter acoustic problems so dominated performance that it failed to work without the most delicate and repeated laboratory adjustment. Because results were easier to obtain on slurry flows research concentrated on these, but the greatest commercial attraction was for an instrument to meter clean liquids. Research focused on this lead to a better understanding of the detection mechanism which lead to vast improvements in the flowmeter’s design. Means were discovered to control previously inhibiting acoustic aspects, so that the flowmeter’s performance limitations became dominated by flow signal bandwidth and integration time. Now improvements in signal handling [5, 8] have refined the instrument to the extent that the acoustic weaknesses are again among its major handicaps, although of much smaller scale than before.

This paper relates to the metering of clean liquids, specifically water, although most that is said generally applies almost equally to clean gases, and two phase flows, e.g. slurries. The few differences should be evident if it is remembered that ultrasonic waves travel more slowly through gases than liquids, ultrasonic transducers for use with gases are more sharply resonant than those for use with liquids, and a second phase produces much stronger modulation of an ultrasonic beam than does the transverse velocity fluctuations of a clean fluid [7].

This paper describes the novel signal handling electronics that overcame the major acoustic problem and turned the instrument from being an appealing laboratory toy into an industrial flowmeter with presentable fluid dynamic characteristics [7]. That improvement opened the door for meaningful advances in correlator design [5, 8] although it has been shown that their is limited scope for this because of unavoidably curtailed flow signal bandwidth [9].


Some of the earliest work on the ultrasonic correlation flowmeter was done by Couthard [3]. Amongst his findings were that correlation peaks, Fig. 2, that might have been expected to be similar to those produced by other detection methods [1, 2], could be greatly skewed. He correctly attributed this phenomenon to gross phase differences between the signals x(t) and y(t), Figs 1 and 3.

Fig.1 Typical cross-collrelation peak produced by fully developed fluid flow in a pipe.

Fig.3 Theoretically calculated idealised, crossocorrelation peaks for one flow rate, but different relative phase shifts between signals x(t) and y(t).

At that time there was controversy as to whether the mean flow rate of a single phase fluid through an ultrasonic correlation flowmeter was better related to dg or dm, [1, 3]. The difference, then judged to be less than 5%, was expected to vary slightly with flow rate in such a way as to effect the instrument’s linearity and absolute accuracy, but not its repeatability. However, the discovery of highly skewed correlation peaks made such controversy academic because the phenomenon caused practical instruments working on slurry flows to have repeatability’s of up to +/- 30%. At that time it was so difficult to obtain any signals from single phase fluids that it was uncertain as to whether they could be metered by the ultrasonic correlation technique, for it was suspected that when any signals were produced, they originated from the presents of some dirt, i.e. second phase, in the flow. In addition an automatic system could not be devised to ensure identification of severally skewed correlation peaks so that flow rate related output signal was unavoidably intermittent. In effect the flowmeter’s ‘availability’ was limited to less than 20% for two phase flows and was effectively nil for single phase fluids. As such it was useless as an industria iinstrument.

Flemons, of the Canadian General Electric Company, recognised the acoustic nature of the problem, and devised a system for its alleviation, [6]. In doing so he solved a lesser difficulty associated with insufficient signal strength at the receiving transducers. Earlier work [3] had shown the ability of amplitude, frequency and phase demodulation to produce flow related signals, x(t) and y(t), Fig. 1, but without any great leaning as to which was the best. Flemons, working on much larger pipe sizes than others, suffered more severely from weak acoustic signals at the receiving transducers and so chose to use phase demodulation to ensure that even very weak signals arriving at the receiving transducers underwent sufficient amplification for convenient manipulation. Coupled with this he divided the received signal electronically into four quadrature components, the relative amplitudes of which were sensed by a logic system which only allowed passage of the one with positive phase/voltage conversion characteristic. The basic electronic system of one channel of this system is shown in Fig. 4, in which the four quadrature components; S5, S6, S7, and S8 are marked. Their phase relationship is represented in Fig.5.

Fig.4 Electronics used to give a positive gradient, quasi-linear phase/voltasge transfer characteristic.

Fig.5 Experimentally plotted illustration of the Fig.4 demodultor's use of quadrature signals to give a positive gradient, quasi-linear phase/voltage transfer chgaracteristic (bench test without acoustics).

Because of the logic controlled, automatic signal switching, Fig. 4, the demodulator’s overall, phase / voltage conversion characteristic was effectively a continuos repetition of the segment CDE, of Fig. 5. The net effect was that illustrated by the segments CDEFGHIJ in Fig.5.

In use the oscillator frequency of each channel was adjusted until, as observed on an oscilloscope, the received carrier amplitude was of good strength and then the equipment left to, ‘look after itself’. If conditions drifted slightly to produce a change in the mean phase difference between the electronic signal reference path, S1, to the demodulator, and the Fig.5 characteristic, the output signal x(t) to the correlator changed. Fig. 5 is the experimentally measured demodulator quadrature signal showing the positive gradient, quasi linear phase/voltage transfer characteristic x(t) resulting from a bench test of the electronics without acoustics. The automatic quadrature signal selection system ensured minor flow turbulence originating phase variations only produced electrical output signals x(t) and y(t) by way of a positive gradient segment of phase/voltage conversion characteristic, Fig. 5. The result was a demodulator system that never produced inverted correlation peaks, and the peaks it did produce always seemed, by casual observation, to be unskewed. As a result when used with the special flow metering correlator, that had already been built by that time [5], the flow meter produced an output signal that was fairly closely related to the true mean flow rate. As an industrial instrument it could be roughly said that the flowmeter’s availability had been raised to about 80 % and long integration time repeatability reduced to about +/- 10 % when used on a single phase liquid, water, the fluid in which his company was interested. Later tests by others, [7] confirmed, as expected, that this availability and roughly this repeatability also applied to a two phase water flow.

The reason the availability of the flowmeter using Flemon’s demodulators was not higher than approximately 80 % was that when the flow produced phase excursions beyond the range of sections such as CD, or EF, or GH, or the like, rapid transitions occurred along the sections such as DE, or FG, or HI, as the phase selection mechanism switched between the different quadrature components when signal excursions exceeded the allowed range of any one segment. When these conditions prevailed the result was an enormous amount of signal noise, resulting from the switching mechanism, which degenerated the quality of the correlation peak to the extent that the correlator could not make use of it. It also became apparent that if, for a given pipe size, the carrier frequency was increased to effectively increase the phase to output voltage gain of the system [7], the effect was not to achieve a desirable, proportionate increase in signal to noise ratio, but rather to cause a vast decrease in signal to noise ratio, because of phase selection switching, and hence decrease in the flowmeter’s availability. It was also evident that at least part of the rather poor, +/- 10%, repeatability was caused by the fact that the four quadrature segments were only approximately linear, being in fact parts of a sine function between +/- 90 degrees.

By controlling the net phase shifts throughout the system, the arrangement of Fig. 6, designed by the author, gave the flowmeter 100 % availability and reduced long integration time repeatability to about +/- 2.5 %. The true linearity of this characteristic is evident from the empirical result illustrated in Fig. 7B. With this arrangement, in which there was strong control of phase shifts, it was possible to concentrate on investigating the flow meter’s basic design rules [7] and what was then its basic weakness, limited flow signal bandwidth [9]. During the course of this work the nature of the flowmeter’s acoustic characteristics and weaknesses became more apparent, as are now described.

Fig. 7B Experimentally measured phse/voltage transfer characterisitc of the Fig 6 electronics (bench test without acoutics).


Fig. 8 is a photograph obtained using a single transmitter/receiver pair of transducers on the flow meter head, Fig. 1, applying a linear sweep oscillator of constant output amplitude to the transmitting transducer and connecting an oscilloscope to the receiving transducer. The photograph is of the oscilloscope screen and shows the variation of received carrier amplitude with frequency in the region of the transducer’s, the active component being a piezoelectric ceramic, fundamental thickness resonance. It can be seen that the strength of received carrier amplitude is strongly dependent on how close it is to that thickness resonance, (in this case 709.21 kHz., based on physical dimensions) and it can be easily demonstrated that it is otherwise strongly dependent on how close it is to allowing an integral number of half wavelengths in the fluid between the transmitting and receiving transducers.

For normal operation the transmitting frequency of the oscillator for each channel is set near the combined thickness resonance frequency of the transducer pair, both transmitting and receiving transducers having the same nominal resonance, to optimise carrier signal path to the receiving electronics. For amplitude demodulation this would be expected to have a direct baring on the flow signal amplitude, i.e. on the gain of the system. For frequency demodulation and phase demodulation this might not be so expected because such communication merely ensures coupling via the fluid route, after which limiting amplifiers in the first stage of frequency and phase demodulators effectively remove any amplitude information conveyed by the carrier signal itself, Fig.6.

Since the ‘fine structure’ in Fig. 8 results from the acoustic standing waves in the beam through the water between transmitting and receiving transducers, Fig.1, it can be easily appreciated that if whatever modulates the beam causes phase shifts of many hundreds, or thousands, of degrees then an amplitude demodulated output signal would appear as a series of pulses as the ‘fine structure’ swept past the receiving transducer. This did not happen in the earliest experiments because of the fortuitous combination of fairly low carrier frequencies and small pipes resulted in maximum levels of modulation far less than even 90 degrees. By contrast, for the large pipe sizes Flemons was using there was considerable potential for such an undesirable performance.

The gross phase distortions that Couthard reported [3] were therefore predominantly acoustic in origin and resulted from the demodulators of the two different channels operating at different points on the standing wave pattern. If one channel operated at a point of positive gradient, i.e. one for which increasing phase shift caused increased received carrier amplitude, then a flow disturbance that caused an effective shortening of the acoustic path caused a rising demodulator output voltage. If the other demodulator operated at a point of negative gradient, the same flow disturbance caused a falling voltage. Thus a given flow disturbance produce demodulated signals x(t) and y(t) of opposite sign and the resulting correlogram would be inverted. In general all possibilities could occur between; both channels operating at completely equivalent points, to both channels operating at completely ‘opposite’, or 180 degree phase shifted points, and all possible correlogram distortions could ensue.

Although the above is described in relation to amplitude modulation it also generally relates to both frequency and phase demodulation, as will be understood by reference to Fig. 5. The benefit of the switching mechanism incorporated into the circuitry of Fig. 4 is that correlogram distortions are limited to those reflective of only +/- 45 degree phase difference between the two transducer channels. The benefit of the circuit of Fig. 6 is that it seems to avoid the introduction of all phase distortions.


Evidence that all is not quite what it might seem is illustrated by the results of Fig. 9 which were obtained using one channel of the flow meter with the demodulator circuitry if Fig. 6, less the connection between the integrator output and the oscillator ---- to avoid automatic carrier frequency adjustment forcing operation at point ‘A’, Fig.7A. As can be seen neither amplitude, nor phase (hence frequency), demodulated signals are greatest when the carrier amplitude is greatest, but they do pass through a maximum. Amplifier limiting prevented the production of signals beyond approximately ?/10.

Fig. 9 Experimentally measured variations of amplitude and phase demodulated signals x(t) with respect to carrier amplitude.

Other interesting results, illustrated in Figs. 10, were obtained with a flow meter using two channels of Fig. 6 circuitry, operating normally to measuring a constant flow rate based on dm (ref. Fig.1). The lower pair of traces in Fig.10 show variation of the flowmeter’s meter factor for the two channels working at a range of different operating points, i.e. different carrier frequencies, in the region of their transducer’s thickness resonances. All the operating points shown are zero crossing points such as A, A’, shown in Fig. 7A, obtained by manually ‘jumping’ the lock frequency from one point on the fine structure standing wave pattern to another, Fig. 8. While adjusting the frequency for channel X the frequency of channel Y was kept constant, and while adjusting the frequency of channel Y the frequency of channel X was kept constant. The upper pair of traces in Fig. 10 show, for information, the amplitude envelopes of the transducer pairs in the two channels. The transducers had a fundamental thickness resonance of about 2 MHz. The curves are comparable to Fig.8 but the individual points in the upper traces of Fig.11 are those of the locking frequencies, and the curve between them merely drawn to aid visualisation. The variations in meter factor shown in the lower traces of Fig.11 are the direct consequence of correlation peak skew, Fig.3. The reason that even a symmetrical correlation peak results in the flow meter indicating a flow rate higher than true, reflected by the meter factor of approximately 1.12 rather than 1.00, is simply understood and easily resolvable in a practical instrument [7].

Of concern here is that the meter factor varies by about +/- 2.5 % depending on to exactly which cycle of the fine structure each of the two channels lock, Fig.8. This amounts in up to 2.5 % uncertainty in flow reading which is quite independent of all those contributory factors, including the basic correlation between the flow disturbances at the two measuring locations, the bandwidth of signals x(t) and y(t) and correlator integration time, as all discussed in references [7, 8, 9].

....... .............................. etc


1. Shell Flow Meter Engineering Handbook, McGraw-Hill, New York 1985.

2. M.J. Fisher, POAL Davis, Correlation measurement in a non-frozen pattern of turbulence, J. Fluid Mech, 18 (1964) 97-116.

3. M.S. Beck, J Drane, A Plaskowski, N. Wainwright, Particle velocity and mass flow measurement in pneumatic conveyors, Powder Flow Technology, Vol. 2, 1968-1969, pp269-227.

4. J. Couthard, Flow measurement by cross correlation fo ultrasonic waves, PhD thesis, University of Bradford, 1973.

5. A.M. Hayes, G. Musgrave, Correlator design for flow measuemttn, Radio Electron. Eng. 43 (6) (1973) 363-368.

6. R.S. Flemons, An acouic cross-correlation flow meter for heavy water plant use, Canadian General Electric Co. Ltd.,Report No. R74CAP11.

7. J.S. Battye, The industrial correlation flowmeter and its design constaints, Flowmeko '85, University of Melbourne, Australia 1985, pp.187-194.

8. R.P. Keech, J.Couthard, Advances in cross-correlation flow measurement and its application, Flowmeko '85 Conference, University of Melbourne, Australia, 1985, pp. 195-202.

9. J.S. Battye, The correlation flowmeter --- a detailed investigation of an attempt to improve its performance, Flowmeko '93 Conference, Seoul, Korea, 1993, pp.597-604.

10. C Jun, K.Matti, T. Esko, T. Jouni, Flow measurement of medium consistancy pulp suspension by cross correlation flowmeter, Flowmeko '93 Concerence, Seoul, Korea, 1993, pp.590-596.

11. J.S. Battye, Experimental development of ultrasonic transducers, Eurosensors XII Conference, University of Southampton, UK, 1998, pp.113-116.


For full details refer to Elsevier's 'Sensors and Actuators' A 88 (2001) 29-40.

See :

The paper is cited in such as: :