Based on work done from 1972 to 1976 to which access was initially restricted for commercail reasons. Presented in Seoul, Korea 1993, supported by the UK's Royal Institution.




A brief description is given of the ultrasonic correlation flowmeter together with an outline of its advantages and disadvantages. There is a short account of previously published results relating to the design constraints of the basic instrument and reasons given for doing the work. The paper presents results showing the various effects of high-pass filtering flow signals before correlation which includes strong evidence that, contrary to some indications, filtering does not improve the flow meter's performance. Comparison of direct repeatability measurements with those calculated using Burdic's equation, relating repeatability to signal bandwidth and signal to noise ratio, demonstrates that the equation is useful for estimating repeatabilities if the signals are unfiltered but of little use if the signals are filtered.


Bx = bandwidth of signal x
Bxy = correlatable bandwidth between signals x and y
Cxy = cross-correlation between signals x and y
d = flow disturbance flight time over distance L
fc = cut-off frequency
L = sensor spacing in direction of flow meter head axis
r = flow meter repeatability
s = signal to noise ratio
T = correlator integration time
v = mean flow velocity
x = upstream flow related signal to correlator
y = downstream flow related signal to correlator


Fig.1 illustrates the basic features of an ultrasonic, correlation flowmeter. It includes two flow turbulence signal detecting channels, each of which has an oscillator, typically operating at a quasi-constant frequency between 0.3 and 3 MHz., an ultrasonic transmitting transducer, an ultrasonic receiving transducer and a demodulator. The demodulator supplied from the upstream transducer feeds a flow turbulence related electrical signal x to one channel of the cross-correlator and the downstream transducer feeds a flow turbulence related electrical signal y to the second channel of the cross-correlator.

The correlator cross-correlates the two signals to produce, or effectively produce, a correlation 'peak', as shown in Fig. 4, delayed by a delay time d. As the flow rate changes, d changes and the correlator translates this linearly into a flow rate related output signal. In essence the flow velocity v is determined from the relationship v = L / d. In the case of the correlator used for the experiments described in this paper, the flow related output signal was an electrical sinusoid derived directly from the oscillator driving the correlator's delay line shift register.


Superficially the ultrasonic correlation flowmeter is extremely attractive. It offers a method of non-invasive flow measurement and as such has no incremental pressure loss, nor parts that can be corroded or abraded by the flow. It works with clean or two phase fluids and can be in a form which clamps onto the outside of an existing pipe, thus making it extremely portable and easy to install on an established process.

The correlation flowmeter's disadvantages are that it; requires electrical power, is only able to detect limited turbulent bandwidth, which slows its dynamic response and reduces repeatability to an extent which can easily be a problem, and suffers acoustic difficulties which promote vibration sensitivity, poor reliability and further degrade repeatability. In clamp on versions of the instrument the degradation in performance caused by acoustic difficulties are severe.

Even made as a spool piece the gas version of the instrument is very susceptible to the commonest form of vibration found in process plants, periodic vibration. However, if used on a gas solids mixture, as in a pneumatic conveyer, the flow signal can be sufficiently strong to swamp small vibration signals and thus make the instrument viable for some applications. The instrument is better suited for the more restricted field of a spool-piece flowmeter for use on liquid flow. This is particularly the case for liquid flow carrying a second phase since, as for the pneumatic version of the instrument, the presents of a second phase greatly decreases relative sensitivity to vibration. Never the less, the large, and hence economically attractive, flowmeter market is for clean flow liquid measurement.

Given the more restricted application described above the flowmeter's major economic restriction is caused by limited flow signal bandwidth. If the flowmeter could 'see' higher frequency components it would be both quicker to respond to flow rate changes and have a better repeatability. Since visible bandwidth falls with increasing flowmeter size, larger instruments suffer more than smaller ones, and this to the extent that the instrument seems impractical for most applications at sizes larger than about 200 mm diameter.

The strong sensitivity of the flowmeter's repeatability to bandwidth is conveyed in Burdic's equation :

r = [100 / d] . [0.23 / Bxy3 . T . s] 0.5

This equation was originally derived in connection with radar signal analysis but later claimed, and to some extent tested by bench simulation, to be applicable to correlation flow measurement, (1 , 2). An area of some uncertainty has been that for both derivation and bench testing the signals were assumed, for simplicity, to have a triangular frequency spectrum, rather than the distribution typical of real flow turbulence, see Fig.2. One usefulness of the equation is that it allows the determination of the flowmeter's repeatability from terms on the right hand side of the equation. These terms are much more accessible than direct measurement of repeatability itself. Another usefulness is that with data that has since been discovered the equation also allows a prediction of the performance of correlation flowmeter's of various sizes. It has been shown (3) that the signal strength and bandwidth vary linearly with flow velocity, the bandwidth decreases approximately linearly with increasing flowmeter size and the normalized cross correlation depends to some extent on flowmeter head geometry, but generally takes the form indicated by the curve marked, "no filter" in Fig. 8.

It is perhaps worth noting that viewed in terms of the correlation "peak" Fig. 4, used either directly, or indirectly, to determine flow rate, good flowmeter performance is facilitated if the peak is narrow in relation to its delay (a reflection of high signal bandwidth), is clearly defined and smooth (a reflection of good signal to noise ratio), is unskewed (the result
of zero net relative phase difference between the two correlated signals) and is without minor maxima (a consequence, at least in part, of no coherent periodic component between the two signals).


The flowmeter's apparent size limit of about 200 mm diameter has led to interest in investigating possibilities to raise it. One of these possibilities is to high-pass filter the flow signals x and y from the demodulators, Fig.1, with the aim of seemingly presenting the correlator with higher bandwidth signals. Although this has direct impact on both the flowmeter's repeatability and response to flow rate changes, results showing exactly what the effects of filtering are, have not previously been published.

The work described in this paper concentrates on the way filtering effects repeatability. It does so because for a correlation flowmeter, repeatability is a general description of overall performance which is particularly useful for comparing behaviour under different flow conditions, or for comparing different versions of the instrument. In contrast there are so many possibilities for developing various electronic tracking circuits to considerably effect the flowmeter's response to flow changes, that any work in that area must inevitably be very particular, (2, 4). It is almost essential to reliably establish repeatability as a base measurement for comparing different flow tracking circuits.

The principle aim of the work was to highlight the ramifications of high pass filtering a correlation flowmeter's signals to demonstrate if its repeatability is improved. A second objective was to test Burdic's equation with real flow signals, in a real industrial version of the flowmeter incorporating typical features such as relay correlation and automatic, correlation peak balancing and tracking circuits (2). By doing this it was hoped to so validate the equation that a user wishing to know a particular flowmeter's repeatability could reliably use it to calculate repeatabilities from the easily measurable quantities of signal bandwidth and signal to noise ratio, rather than have to pursue the lengthy, and difficult task of making direct measurements.


All tests involving filtering were done using either a single, eight pole high pass filter or a carefully matched pair of double pole, high pass filters. They were used on signals x and y, between the demodulator outputs and the correlator inputs, Fig. 1.

Figs 2 and 3 helps give some overall impression of the effects of filtering. Fig. 2 shows the auto-correlation and spectra of unfiltered flow signals for high and low flow rates. The broken lines of Fig. 3 show the effect on the auto-correlation and spectrum of using the eight pole, high pass filter with cut-off frequencies of 50 Hz and 100 Hz.

Fig. 4 shows cross-correlation peaks produced with no filtering. Fig. 5 shows cross-correlation peaks obtained when the signals x and y to the correlator's inputs were each passed through a two pole, 50 Hz, high pass filter. Both Figs 4 and 5 were obtained with the same "high" and "low" flow rates. Of note is the lower amplitude of the peaks produced by the filtered signals and larger relative difference in peak heights, 6.7 : 1, as compared to 2.8 : 1, obtained from filtered signals as opposed to unfiltered signals. Filtering approximately halved the relative width of the cross-correlation peaks, W/D = 0.4 for the unfiltered signals, and 0.2 for the filtered signals. Also of note is that, as for the auto-correlations, Fig. 5, filtering produced ringing at the base of the cross-correlation peaks.

The narrowing of the cross-correlation peaks would seem to benefit the flowmeter's performance by offering the possibility of greater resolution, but the greater difference in correlation peak heights would not benefit performance because it requires the system which identifies and tracks the correlation peak to be able to work over a far larger amplitude range. The 'ringing' at the peaks extremities could be undesirable for some versions of the instrument because it might cause the flow rate change tracking system to lock onto the top of one of the 'rings' rather than the major, flow produced correlation peak, (2, 3).

In pursuance of a less illustrative but more quantitative approach, Fig. 6 shows the variation of r.m.s. signal voltage obtained from one of the flowmeter's demodulators. The conditions for each curve are marked. Note the lower signal voltages produced as the filter's cut-off frequency fc is increased so that less of the total available signal is used. Compare this with Fig. 2. Note also the shape of the curve produced by, for example, the 100 Hz filter. At a velocity of 5 m.s-1 the signal is about 45% that produced if no filter were used. At 1 m.s-1 the signal is only about 10% that obtained if no filter were used. Although this reduction is not catastrophic it is undesirable because the correlator's input, automatic gain control (a.g.c.) needs a larger dynamic range to cope and, in any case, the flowmeter's performance is degraded because signal to noise ratio is decreased. Using half peak power as a measure of bandwidth it is clearly evident from Fig. 5 that bandwidth is increased by high pass filtering. How it varies with flow rate is shown in Fig. 7, and this can be compared on the same graph with the result obtained with unfiltered signals (fc = 0). The improvement in bandwidth is substantial and such that it is relatively greater at low flow rates, a desirable feature.

Fig. 8 shows signal filtering causes lower normalised cross-correlation at low flow rates than occurs in the absence of filters. An undesirable consequence of this is that a correlator's system for detecting correlation peaks requires a greater dynamic range.


A difficulty in establishing the range of application of Burdic's equation in connection with signal filtering was that the equation incorporates a term T for a fixed, flow signal integration time, whereas an industrial correlation flowmeter uses a correlator which continuously updates the correlation estimate with new information while rejecting old (2, 3). In the correlator used for the tests, data was moved through a shift register at a rate determined by an oscillator which automatically adjusted its frequency to keep the correlation peak at a set position in the delay line. At equilibrium, the delay of the correlation peak was inversely proportional to the clocking frequency and hence the clocking frequency was proportional to the flow rate. Clocking frequency was thus the flowmeter's basic flow rate related output signal and the capacitor which stabilised the frequency control voltage, equivalent to the integration time of a fixed term integrator.

An important step in testing the relationship was to measure the repeatability directly. The obvious way to do this was to fix the flow rate through the instrument, then note repeatability from a sufficiently large number of flowmeter indicated flow rates. Unfortunately this method was handicapped by the fact that the flowmeter's calibration was very sensitively dependent on the temperature of the flowing water. A factor not accounted for in Burdic's equation, and therefore in need of isolation for the equation to be tested. Fractions of a degree change in water temperature so modified the acoustic standing wave pattern that the flowmeter's calibration would be changed by more than the range of the 'random' flow readings resulting from the pure flow signal. Although, in general, pumping the water tended to cause a temperature rise of about 2 degrees Celsius per hour, this was variable, so drift could not be simply 'off-set'. What was needed was that a fairly large number of flowmeter output readings were obtained at a rate which was slow in relation to correlator produced variations in repeatability, yet fast in relation to temperature produced variations in calibration. Unfortunately, one such gathering of data did not give results to provide a reliable measure of repeatability, so many sets were obtained at different flow rates, each set comprising 23 rapidly recorded, individual readings.

The root mean squared (r.m.s.) of each set was calculated and plotted against the largest percentage error from the mean of the set. This allowed the drawing of a straight line graph, through data which was only moderately scattered, to average the total of all readings to obtain a fixed term empirical relationship between repeatability and the quickly and easily measured r.m.s. of any sample of only 23 readings.


Fig. 9 shows the directly measure variation of the flowmeter's repeatability with flow rate for unfiltered signals using three different correlator integration capacitors. The capacitors were nominally 47 nF (actually 41.0 nF), 220 nF (actually 231 nF) and 1 mF (actually 0.946 mF). Results fall into quite distinct groups as the continuous curves sketched in Fig. 9 emphasise. The curvature results from the self tracking correlator's inability to maintain constant repeatability with flow rate as falling flow rate caused excessive drop in signal bandwidth and correlation, Figs. 7 and 8. The loss of repeatability with reduction in the correlator's integration capacitor is for the reasons given above concerning the correlator's internal oscillator.

Fig. 10 shows the very good agreement between the direct measurements of repeatability as presented in Fig. 9, and the predictions of repeatability based on Burdic's equation using measurements of signal bandwidth as presented in Fig. 7, signal to noise ratio, as determined from Fig. 8, and the delay time of the correlation peak, as calculated from the known flow rate and continuous dimensions of the transducer head. The lines of Fig. 10 have been traced directly from Fig. 9, the broken lines plotted using Burdic's equation.

Fig. 11 shows the result of experimentally measuring the flowmeter's repeatability in the same way as described in connection with Fig. 9 but with each of the signals from the transducers to the correlator being passed through a high pass filter with a 50 Hz cut-off frequency. As can be seen from Figs. 2 through 8 the filters produced quite a significant modification to the nature of the signals used for the correlation, but Fig. 11 shows that filtering did not cause any significant overall modification to the flowmeter's repeatability. The apparent gain in flow signal bandwidth is offset by the decrease in flow signal to noise ratio. The flow range over which results were obtained did not exceed the dynamic range of a.g.c. circuits to cope with the wider range of signal amplitudes produced by filtering, Fig. 6. Had they done, the repeatability would have been much further degraded at the extremities of the flow range.

If Burdic's equation and the relevant data relating to fc = 50 Hz in Fig. 7 and 8 are used, the flowmeter's expected repeatabilities can be calculated for the filtered signals. For the 47 nF, 220 nF and 1 mF capacitors the repeatabilities for a flow velocity of 4 m.s-1 work out to be 1.96%, 0.83% and 0.41% respectively. These are under half what was actually measured in each case and cannot be accounted for by the scatter of experimental results, Fig. 11. The result shows Burdic's equation to be of little use in connection with high pass filtered signals.


Because a correlation flowmeter's correlator integrates over a period of time which is typically fairly long compared to the time interval over which large changes in flow rate can occur, its correlator needs a correlogram peak 'search' feature to find the peak if it moves rapidly out of the current, accurate measurement range. Flowmeters therefore have typically two modes of operation; a 'tracking' mode in which they lock onto the correlation peak to fine tune output signal to match the delay, and a search mode in which they scan their full adjustable range to find a peak, (2, 3, 4). Provided flow rate excursions are not too rapid, flowmeters can track them over their full adjustable range without leaving the tracking mode. Wide signal bandwidth facilitates fast operation of both search and track modes of operation.

Fig.12 shows the step response of the flowmeter used for the tests and clearly illustrates the operation of its separate search and track modes. The numbers against different traces indicate successive step changes in flow rate. As can be seen there could be considerable variation in response, depending on whether the correlator managed to stay in the tracking mode or locked quickly, or more slowly, into the search mode. The erratic nature of the response resulted from the fundamentally random nature of the turbulent flow data on which the flowmeter worked and hence its chance of adopting one path or another. All four traces shown in Fig. 12 were produced without the use of filters. Their randomness illustrates the very limited benefit that might be achieved attempting to compare such results with comparable information produced with the use of filters.


Fig. 13 shows the basic flowmeter's gravimetric calibration without any signal filtering. The basic flowmeter always read slightly high, progressively so as flow rate dropped. The cause of this was its weighted sensitivity to flow along the centre line and the flow's more 'peaky' flow profile at lower flow rates (3).


The results presented in this paper show that high pass filtering a correlation flowmeter's flow signals does not circumvent previously reported design constraints, (3). When high pass filtering is used the benefits to be gained by relatively more powerful high frequency components in the signal are offset by degraded signal to noise ratio. The wider range of signal strengths reaching the correlator tend to curtail flow range because of the inability of a.g.c circuits to cope. The greater range of cross-correlation peak heights require greater rangeability of the system for their detection. Limited bandwidth at the cut-off, low frequency end of the spectrum results in 'ringing' of the correlograms which cause tracking problems for some forms of the flowmeter (2). Inaccuracy can also be caused by phase differences between imperfectly matched filters (3) and these can appear as poorer repeatability if dependent on some unpredictable influence such as temperature.

Results here confirm (3) that Burdic's equation provides a fairly accurate description of a correlation flowmeter's flow signal limited component of overall repeatability if flow signals are unfiltered. However, they also show the equation wrongly predicts much better performance than achievable if applied to a flowmeter in which flow signals are high pass filtered.

In the past it has been argued that if limited signal bandwidth prevents sufficiently repeatable correlations being physically established in a given interval of time, then repeatability can be improved by combining the results of several simultaneously implemented correlation processes based on multi-channel data collection. This increases the instrument's cost and power consumption but development in this direction seems to be fruitful (4).

There is always scope for reducing a correlation flowmeter's sensitivity to periodic vibration. A possible way to do this is to negatively feedback signals generated by the vibration's action on transducer inertia.

Fig. 12 shows room for improving the flowmeter's step response by advancing correlator design to enable it to lock into and cope more efficiently in the search mode, (2).

The very smooth curve shown in Fig. 13 suggests it should be easy to linearize the flowmeter's calibration by electronic means. Much of the scatter of data points shown in Fig. 13 was found to be caused by temperature dependent acoustic phase differences between the two measurement channels, and not limitations of bandwidth, signal to noise ratio or the correlation process. The results of Fig. 13 were achieved after careful, manual adjustment of acoustic transmission frequencies to minimise unbalanced phase shifts caused by temperature dependent changes in acoustic path length. If this was not done the flowmeter could exhibit less linearity and worse repeatability. Such manual adjustment is not appropriate for an industrial instrument because it would not necessarily only be a requirement at commissioning and regular maintenance.

Although in latter years development has tended to concentrate on correlator design (4), it is very evident that an equally necessary area to address is that of unbalanced sensitivity to temperature changes. In the flowmeter used for the tests, a step to achieve this had already been implemented by using heavily damped transducers. Whatever further improvements are possible it is likely to be desirable for primary electronics to incorporate a scanning feature to automatically adjust acoustic transmission frequencies to minimize such sensitivity.


1. Burdic W.S., "Radar Signal Analysis", Prentice Hall Inc., 1968.

2. Hayes A.M., "Cross Correlator Design for Flow Measurement", Ph.D.Thesis, Univ. Bradford, UK 1975.

3. Battye J.S., "The Industrial Correlation Flowmeter and its Design Constraints", Flowmeko '85, Conference on Flow Measurement, Melbourne, Australia, 1985.

4. Keech and Couthard, J., "Advances in Cross-Correlation Flow Measurement and its Application", Flowmeko '85, Conference on Flow Measurement, Melbourne, Australia, 1985.