Based on work done from 1972 to 1976 to which access was initially restricted for commercial reasons. Presented at University of Melbourne, Australia, 1985.




A brief history of the development of the correlation flowmeter is given with reasons why the version using ultrasonics to detect flow disturbances was studied with a view to its industrialization. There is an outline description of the equipment used to investigate the flowmeter's characteristics and of the resulting tests done to demonstrate the flow detecting mechanism and the presents of strong acoustic beams and standing waves between the transmitter/receiver transducer pairs. Results are presented to show how the signal strength, band width and cross-correlation of flow signals varies with ultrasonic carrier frequency, pipe diameter, transducer diameter, flow rate and the axial separation of the sensing locations, and these briefly discussed to highlight the flowmeter's resulting design constraints.


B = correlatable bandwidth between signals x and y
Cxy = cross-correlation between signals x and y
c = velocity of sound in process fluid
D = flowmeter head bore
d = time delay
df = mean flight time of flow between sensors
dm = maximum flight time of flow disturbance between sensors
dt = a finite time increment
f = frequency
G = voltage/(phase shift) gain of demodulators
i = an integer
k = a constant
L = sensor spacing
m = an integer
N = an integer
R = ratio of flowmeter head bore to sensor diameter
r = flowmeter’s repeatability
Re = Reynolds number (based on D)
S = half peak-peak voltage range of demodulator’s output
sn = signal to noise ratio
T = integration time
t = time
v = mean flow velocity in meter head
vm = max. mean flow velocity of fluid within flowmeter head
w = cross correlation peak width at half the height of crest
x = upstream signal to correlator
y = downstream signal to correlator


This paper outlines the design constraints of a flowmeter which began being investigated in the late sixties, was developed to a basic industrial prototype by the mid. seventies but, for reasons indicated here, was not launched as a complete instrument by any major instrument manufacturer. In the early days of development it was hailed as a new method of dirty, corrosive or two phase flow metering that was almost fundamental in its simple reliance on distance/time measurement. Work was carried out using a variety of different sensors ; thermal (1), capacitance (2), conductivity (3), and ultrasonic using amplitude, frequency and phase demodulation (4), but always concentrating on two phase flow and almost always exclusively on very small pipelines. Although the work was academically attractive, and of interest to some sections of the process industry, instrument manufacturer's considered it of limited significance because of the small market it represented. They, understandably, were primarily concerned with the instrument's money earning capacity and for that needed to know the size of market it might capture. Two things would very much effect this, its applicational range and production cost.

Initially the overwhelmingly expensive part of the flow meter was the correlator which, besides requiring continual manual intervention to adjust settings, produced only an industrially impractical trace on a cathode ray tube (crt), as an output. By ingenious development a special 'flowmeter' correlator was designed which could be produced at less than one hundredth the cost of the laboratory instrument, needed no manual intervention and output a flow related proportional signal (5). The use of ultrasonics to detect flow seemed to offer the greatest market potential because of the possibility of being able to produce an instrument which clamped onto the outside of a pipe. Not only could this be so cheap, relative to alternative flowmeters and installation costs, that it might capture a large market from existing products, but also might increase total market size by providing a new way of obtaining temporary measurements. As a spool piece instrument it was seen as being less attractive, but still viable, provided it had a sufficiently competitive performance metering both clean and dirty flows. Early work had shown it could be used to detect two phase flow in both liquids and gases and that transducers could be clamped onto the outside of the pipe, but highlighted several problems, didn't establish whether or not it could work on clean flows and didn't formulate industrial design rules.

This paper outlines experiments done to determine the basic mechanisms by which the ultrasonic correlation flowmeter works and identifies factors constraining its performance. A necessary part of being able to do this was identifying and overcomming previous problem areas which resulted in the development of much improved flow sensors, sensor electronics and correlator. The paper only describes work done with clean water using spool piece flowmeters, i.e. flowmeters with the ultrasonic transducers in direct contact with the fluid, because tests were confined to this arrangement and application in order to minimize experimental complications caused by acoustics. The more easily identified fluiddynamic design constrains of this version of the instrument are of relevance to all forms of the ultrasonic flowmeter, whether using clamp-on or wetted transducers, whether working on liquid or gas service.


Fig.1 illustrates the basic features of a correlation flowmeter; flow disturbance sensors, sensor electronics and a cross-correlator. It measures flow velocity by measuring the time of flight of flow disturbances between the sensors. The wave form of the two signals fed to the correlator are similar, except that the wave form y(t) from the downstream transducer lags the wave form x(t) from the upstream transducer by the flow disturbance's transit time (d) between the two sensors. In an ideal system :

y(t) = k. ( t - df ).......................... 1

so that : ........................................................v = L / df...................................2

Because the wave forms x(t) and y(t) are similar, but effectively random, simple methods of time interval measurement cannot be used since neither wave form has a distinct event from which the start and finish of an interval can be identified. The delay is therefore determined by a method of pattern recognition in which the two patterns are records of the wave form x(t) and y(t), of duration (T) and (T+dm) respectively. The two records are compared at different time delays (d), from zero to the maximum (dm), and the delay at which they are most alike is the estimate of the flow's mean time delay (df). Similarity is assessed by the least squares criterion for which, with sufficiently long averaging time, maximum similarity corresponds to a maximum cross-correlation between signals x(t) and y(t). For sampled data, such as manipulated in a digital correlator, the cross-correlation estimate for a time delay (m.dt), obtained after taking N samples, is :

Cxy ( m , N ) = ( 1 / N ) i=1?N x . ( [ i - m ] . dt . y ( i . dt )................................... 3

When the signals are derived from turbulent flow by an arrangement as illustrated in Fig.1, the variation of Cxy (m, N) for different values of (d) typically vary as shown in Fig.2. Details of the correlation theory are discussed at length in Refs.5 and 6.


The bulk of the experimental results reported in this paper were obtained with the Hewlett-Packard (HP) correlator model 3721A, option 020. This laboratory instrument with absolute calibration of correlation estimates and time delays, produces auto-correlation and cross-correlation functions as traces on a crt, or plotted on a chart plotter, and could be used to determine a signals rms voltage. Used as part of the flowmeter the cross-correlation functions appeared on the crt as illustrated in Fig.2.

The self tracking two point difference correlator, specially designed for the flowmeter (5), was used to obtain Fig.13. It made correlation estimates at only the 18th and 22nd delay increments and adjusted the absolute delay time of these by altering the shift register's clocking rate. Automatic adjustment of this rate sought equality of the correlation estimates at the 18th and 22nd increments for which condition a virtual correlation peak lay at about the 20th. The correlator's only output, the frequency at which the shift register was clocked, was continuously variable and could be interpreted in terms of the correlation peak's absolute delay time. The inclusion of automatic gain control and peak search features gave the instrument a dynamic range of 30:1.

In the ultrasonic correlation flowmeter each sensor, Fig.1, is an electro-acoustic transducer, irradiated by ultrasonic energy transmitted as a constant amplitude, continuous sinusoid from a similar transducer placed diametrically across the flowmeter head. The signals from the sensors are high frequency waves with both amplitude and phase modulations, produced by interaction of the acoustic waves with the flow, and the 'sensor electronics' are basically demodulators. The prototype flowmeter used phase demodulators with separate oscillators driving each transmitting transducer arranged so that the phase shift through the combined electronic/acoustic system was controlled to almost eliminate electronic/acoustic produced correlogram distortions which previous work had found to be troublesome (4). It was achieved by severely clipping each demodulator's input and reference signals to produce a triangular phase shift to output voltage transfer characteristic, then forcing to work about the centre of a negative gradient, linear section of this by applying its integrated output voltage to a varicap diode within the tuning circuit of its associated oscillator.

Tests were done with 50, 100, 150 and 1050 mm nominal diameter flowmeter heads. Each had three pairs of diametrically opposed bosses spaced at D/2 and D so that transmitter/receiver transducer pairs could be installed with axial separations of D/2, D and 3D/2. By use of a sleeve arrangement bosses on the 50 mm head could accommodate 5 mm or 10 mm diameter transducers and bosses on the 100, 150 and 1050 mm heads could accommodate 10 or 20mm transducers. A set of four 5mm diameter transducers were made for use at approximately 5 MHz, and three sets of 10 mm and 20 mm transducers for use at approximately 2, 1 and 0.5 MHz. To help provide a more complete picture of the way sensor separation effected flow signal bandwidth and cross-correlation functions one pair of 3.5mm transducers were encapsulated 15.5mm apart in a housing which would fit into the standard 20mm bosses for use as two receiving transducers, transmitted to by a single transmitter. Flow measurement using the 50, 100 and 150mm flowmeter heads were made more than 30D downstream of a tube bundle straightner on a test rig with constant head tank, knif edge diverter and weigh tank. Because of space restrictions, measurements on the 1050mm head had to be made about 15D downstream of the reference 1050mm orifice plate which had been calibrated at Britain's National Engineering Laboratory.


In a number of 'setting-up' experiments useful calibration and visualization of phenomena was obtained. The phase shift to output voltage transfer characteristic of the sensor electronics' demodulators was measured as having a constant gradient of 1.375 volts/degree over a range of approximately +/- 10 degrees, by bench test using the sensor electrons with an oscillator. adjustable electronic phase shifter, oscillograph and digital volt meter. Using a ramp generator, with wide range, high frequency, voltage controlled oscillator and oscillograph with any transmitter/receiver pair of sensors installed within a water filled transducer head, and sweeping the frequency, demonstrated on a crt display a fine structure of narrow band resonances, caused by acoustic standing waves across the pipe, superimposed on the transducer's wide band thickness and radial resonance modes. Observing the variations of signal amplitude as a paddle wheel was moved across between the transducers confirmed the strong beam like nature of the acoustic field between the transducer pairs.

The flowmeter's system of finely adjusting transmitter frequency to control phase shift through each channel's acoustic/demodulator path enabled the identification of the method by which the acoustic carrier waves became modulated by flow. This was done by producing cross-correlation functions, using the HP correlator, with the transmitter/receiver transducer pair first connected so that both upstream and downstream beams propagated in the same direction, then repeating the measurements with the beams propagating in opposite directions. The outcome was that with the beams in the same direction correlation peaks were upright, with them in the reverse direction they were inverted, a result which could only occur, remembering the wide band, quasi-random nature of the signals and the maintenance of phase integrity within each channel's electro-acoustic system, if beams were modulated by the fluid's transverse velocity fluctuations. This modulation phenomena was confirmed by using the flowmeter on clean water flow with reversed beams then introducing progressively larger quantities of small air bubbles into the flow. With this arrangement peaks started off inverted, as before but as more air was introduced they diminished, disappeared, then reappeared as positive peaks which got more pronounced as more air was added. An indication of the strong signal producing capability of the minute air bubbles used in this test is revealed by the fact that about 0.2% air canceled an otherwise strong inverted correlation peak from a 100 mm flowmeter head used on 4 m/s water flow.


Fig.3 shows that the demodulator output signal increased linearly with both flow rate and transducer carrier frequency. Both results are consistent with the preliminary inverted correlation peak experiment showing the detection of velocity fluctuations, since the velocity of transverse velocity fluctuations, to modulate the acoustic beam, increases in proportion to mane flow rate (7), and the effect of those fluctuations on the wave pattern is proportional to the number of acoustic wavelengths across the pipe, hence to carrier frequency. Because signal strength was also proportional to the known 1.375 volts/degree gradient of the demodulator's phase/voltage transfer characteristic, the vertical axis of Fig3 is not plotted in the sensor electronics' dependent term, rms signal voltage, but in the more useful fundamental quantity phase shift/acoustic wavelength. The linearity of the carrier frequency, to signal strength relationship is shown by the fact that against phase shift/wavelength all measurement points, irrespective of the carrier frequency, fall on the same straight line, Fig.3. In Figs.4, 5 and 6 the vertical axes are also plotted in the fundamental quantity phase shift/wavelength although they might be more conveniently thought of as signal strength.

Figs. 4 and 5 show that signal strength scales in proportion to mean flow velocity, not Reynolds number, i.e. flowmeters of different size transporting fluid at the same velocity produce the same signal strength, provided the ratio of pipe diameter to sensor diameter is constant. If it is not, signal strength again scales with flow velocity but as would be expected decreases with decreasing pipe to sensor diameter ratio, Fig. 6.

Fig. 7 shows the results of some measurements of auto-spectrum half peak width used as the measure of the bandwidth of signals obtained from individual sensors. For a given pipe size it shows bandwidth to be linearly related to Reynolds number but uneffected by sensor diameter or pipe/sensor diameter ratio. It also shows that bandwidth measured from what could be typical industrial flow conditions are no higher than a few hundred hertz, so clearly the flow's highest frequency components, of the order (v/D).(ReD)0.5, go undetected (7). The linear dependence on flow rate is understandable on the basis that the transverse fluid velocity fluctuations which produce the signals increase in proportion to the transport velocity, (7). The dependence on flowmeter size, not sensor size or pipe/sensor diameter ratio, can be appreciated by considering the nature of turbulence and the approximately cylindrical volume of fluid that influences the beam. Visualizing turbulence as a range of different sized eddies rotating at rates in roughly inverse proportion to their diameter (7), it can be understood that the largest turbulent components must produce the largest signals since the contributions from small ones tend to cancel one another.

Detection is therefore dominated by the largest 'averaging' dimension of the detection volume which, for pipe/sensor diameters of five or less, is the pipe diameter. Accordingly bandwidth is dominated by the flowmeter's size and insufficiently influenced by sensor diameter or pipe/sensor diameter ratio. Since the tangential diameter of the largest eddies in fully developed turbulent flow is approximately the same as the transport velocity, and the form of averaging in any sized flowmeter should be the same, it follows that bandwidth per unit flow velocity should vary in inverse proportion to flowmeter size. Results show this to be approximately the case with the product B.D = 1500 (if D expressed in millimetres) for the 50, 100 and 150 mm flowmeters but equal to approximately 3400 for the 1.05 m flowmeter. The deviation of the latter may have been caused by non-fully developed flow conditions created by insufficient straight lengths following the orifice plate.

Having good signals from individual upstream and downstream transducers does not necessarily mean the signals will correlate well. Fig. 8 shows that high correlations can be achieved for sensor separation, of D/2, D and 3D/2, but that they decrease quite rapidly as the sensor separation increases. It also shows that below a certain 'threshold' flow velocity, cross-correlations fall with decreasing flow rate and Fig. 9 shows this 'threshold' increases as pipe/sensor diameter ration increases. The results of Fig. 9 agree with those of Fig. 5 in showing that the flowmeter scales in relation to flow velocity, rather than Reynolds number.

The correlation flowmeter works by determining the time delay of the correlation peak. How accurately this can be done depends on the peak's width, which depends on the correlatable bandwidth between signals from the upstream and downstream transducers. The results of Fig. 7 show the limit to this since the correlatable bandwidth between sensor signals cannot be greater than that from individuals. Fig. 10 shows how it degrades with increasing sensor separation, not in absolute terms but as the practically useful half peak width to peak delay ratio. Normalization of the width/delay ratio to a sensor separation of D, Fig. 11, highlights the trends in this information, namely that as regards bandwidth, decreasing the sensor separation below D/2, or increasing it beyond D, creates a diminishing return as regards peak width to peak delay ratio, i.e. a diminishing return on the basic information the correlator needs to achieve good resolution.

Fig. 13, the flowmeter's absolute calibration, shows the enormous range that can be obtained with the flowmeter, although it is hardly representative of its practical usefulness as an industrial instrument. It was obtained from measurements of the delay of the peak of graphical plots of cross-correlation functions produced by the HP correlator. To gather the data required the switching of many range settings on this 'manual' instrument, and integration times of up to 20 minutes at the lower flow rates. Flow readings were obtained right down to 5000 Reynolds number, the lower flow rate limit that might be expected of the instrument in view of its need for a time dependent flow tag. It seemed that the smooth plastic pipes, used for the tests to obtain this calibration and most of the other results, didn't allow the consistent maintenance of turbulence below this value since there was no difficulty detecting the strong turbulence present at slightly higher rates, see Figs. 3, 4 5 and 6. Of interest is that the flowmeter reads higher than true at all flow rates, progressively so as the flow rate reduces. This indicates the sensors to be selectively sensitive to flow components towards the pipe's centre line and suggests preferential sensitivity to disturbances within an approximately cylindrical volume of roughly transducer diameter lain lengthwise across the pipe's diameter, rather than an approximately cylindrical volume of pipe diameter coaxial-axial with the pipe (8, 9). A result which is in agreement with the previously identified beam like, rather than diffused, acoustic field between transducer pairs. Many factors contribute to the exact shape and position of the calibration curve; the flow's axial velocity profile, the sensor's preferential sensitivity to the restricted volume, preferential sensitivity to the larger and more vigorous turbulent components within that volume and the convection velocity distribution of those components, (9, 10). A change in any of these causes a calibration shift.

Fig. 13 is more representative of the flowmeter's performance in showing the absolute calibration of the industrial prototype flowmeter with the self-tracking, two-point-difference correlator. It was obtained by knowing that the correlator balanced at the 20th delay on its shift register and observing output frequency. As can be seen by comparing Fig.s 12 and 13, and later verified by measuring cross-correlation function plots, use of this correlator caused the flowmeter to calibrate slightly lower and more linearly than with the HP, from which peak readings were taken, because of the naturally slightly skew cross-correlation obtained from natural turbulence. By determining flow rate by points 'balanced' on the sides of the correlation peak the two-point-difference correlator measures delay from nearer the peak's centre of gravity which, as previously reported (11), appears to correspond more closely with the mean flow rate than does the delay of the peak's crest.


None of the components of the prototype flowmeter; transducers, signal handling electronics and two-point-difference correlator, caused any operational difficulties. For industrial packaging it is desirable to limit the transducer to sensor electronics distance to a few metres to reduce high frequency losses in transducer cables. It is also desirable, as with the prototype, to house the correlator in the same package as the sensor electronics to minimize the possibility of picking up periodic signals, e.g. 50/60 Hz, which greatly effect flow correlation functions and adversely effect the flowmeter's performance, and to make best use of the circa one kilohertz, flow proportional, output frequency of the two-point-difference correlator which is an excellent form of signal for long distance transmission. Power requirements are probably best served by mains directly into the sensor/correlator package which could be placed in an Ex(d) enclosure of use in Zone 1 or 2 hazardous areas. Sensors could also be packaged Ex(d), or perhaps certified Ex(e). Power requirements preclude the possibility of intrinsically safe (IS) certification for either sensors or sensor electronics.

In the transducer head design it is desirable to use a fairly small pipe diameter to sensor diameter to sensor diameter ratios to achieve good acoustic coupling, high cross-correlations, Fig. 9, and large flow signals, Fig. 6, although the latter can also be increased by increasing carrier frequency, Fig. 3. In fact the carrier frequency has to be chosen with some care to be sufficiently high to obtain good signal strength, and so maximize signal to noise ratio, yet not so high that phase excursions might exceed half a wave length and so drive the demodulators past the limits of their linear range. It can be shown (9), from the results reported in this paper, that the maximum frequency that can be used to detect fully developed clean flow with the ultrasonic correlation flowmeter is roughly :

f = S . C / [ 6 . D . G . Vm.(- 0.85 R2 + 5.8 ) ]..............................................4

If the flow is not fully developed, or contains a second phase, the carrier frequency needs to be lower. Since piezo-electric ceramics are expensive and not usually made larger than about 50 mm in diameter, flowmeters larger than 500 mm diameter begin to suffer badly from loss of correlatable signal caused by large pipe diameter to sensor diameter ratio, Fig. 9.

Large flowmeters also suffer from lack of correlatable bandwidth, Fig. 7, which, because of the third power relationship :

r = [ 100 / df ] . [ 0.23 / (B3 . T . sn) ] 0.5 ..................................................5

existing between bandwidth and response time (12, 5), greatly decreasing the attractiveness of flowmeters larger than 200 mm diameter. By using this equation, and introducing experimentally determined values for df, B, T and sn, it is possible to show that the variation of the flowmeter's repeatability with sensor separation varies approximately as shown in Fig. 14, a result which has been confirmed by direct measurements of the small changes of the output frequency of the two-point-difference correlator when metering steady flow rates.

In total it is desirable to use flowmeter heads with a sensor separation of about 0.5 D, head/transducer diameter ratios of about 5 and for most clean flow applications, carrier frequencies of between 0.5 and 2.0 MHz. Under these conditions equation 5 shows that roughly one percent repeatability can be obtained from a 25 mm flowmeter with 5 mm diameter transducers in 0.1 seconds when metering a 8 m/s flow, but it takes 9.4 seconds when metering a 0.5 m/s flow. By contrast a 200 mm flowmeter with 40 mm diameter transducers will only achieve the same repeatability after integrating an 8 m/s flow for 0.7 seconds or a 0.5 m/s flow for 170 seconds.


The work done between 1967 and 1977 showed that the correlation technique could be used in flow meters using a variety of different sensing techniques and turned a version using one of these, the modulation of ultrasound, into a proper industrial prototype. This instrument had many of the required characteristics in that it worked well on both clean and dirty flows and initial tests showed there were no fundamental problems in producing a clamp on version, although there were difficulties and metering performance was degraded. It suffered in that to achieve a good repeatability its response time in the larger sizes was unacceptably slow and it was very profile sensitive. With these handicaps it wasn't seen as offering a strong challenge to any sizable portion of the existing market and at the time was considered unlikely to easily recoup the outlay of completing the development, industrialization, certification and other manufacturing and marketing requirements for launching a new product. Some work has since continued by trying to use sophisticated data handling techniques to improve the instruments repeatability/response time.


1. Bently P.G. and Dawson D.G., "Fluid Flow Measurement by Transit Time Analysis of Temperature Fluctuations", Trans. Soc., Inst. Tech. vol. 18, pp 183-193, Sept. 1966.
2. Beck M.S., "Powder Flow Measurement Using Correlation Techniques", Ph.D. Thesis, Univ. Bradford, UK, 1969.
3. Lee K.T.,"Liquid and Slurry Flow Measurement Using Correlation Techniques", Ph.D.Thesis, Univ.Bradford, 1972
4. Couthard J., "Flow Measurement by Cross-Correlation of Ultrasonic Waves", Ph.D. Thesis, Univ. Bradford, 1973.
5. Hayes A.M., "Cross Correlator Design for Flow Measurement", Ph.D. Thesis, Univ. Bradford, UK, 1975.
6. Bendat J.S. and Piersol A.G., "Measurement and Analysis of Random Data", John Wiley & Son, 1966.
7. Tennekes H. and Lumley J.L., "" A First Course in Turbulence", MIT Press, Cambridge, Mass. USA, 1972.
8. Birger G.I., Izeritelnaya Technika, vol. 10, pp 53-55, 1962.
9. Battye J.S., "An Industrial Correlation Flowmeter", Ph.D. Thesis, Univ. Bradford, UK, 1977.
10. Heidrick T., Azad R.S. and Banerjee S., "Phase Velocities and Angle of Inclination for Frequency Components in Fully Developed Turbulent Flow Through Pipes", Proc. Symp. on Turbulence in Liquids, Missouri-Rolla Univ. pp. 149-157, 1971, USA.
11. Fisher M.J. and Davies P.O.A.L., "Correlation Measurement in a Non-Frozen Pattern of Turbulence", Jour. Fluid Mechanics, vol. 18, pp 97-116, 1964.
12. Burdic W.S., "Radar Signal Analysis", Prentice Hall Inc., 1968.