2420 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 56, NO. 6, DECEMBER 2007

Self-Monitoring Ultrasonic Gas Flow MeterBased on Vortex and Correlation Method

Yaoying Lin and Volker Hans

Abstract—Ultrasound is advantageous for gas flow velocity mea-surements, owing to its high sensitivity to all kinds of turbulencesin the streaming fluid. The cross-correlation method and vortexmeasurement behind a bluff body have been proven to be good.The most important and difficult problem is ultrasound signalprocessing. A complex modulated signal has be demodulated byundersampling. The real and imaginary parts of the complexsignal can be determined by Hilbert transformation. The demodu-lated phase or amplitude signal can be applied to cross-correlationfunctions for the detection of flow velocity. The vortex frequencycan be detected by a simple analog signal processing device. Thecombination of vortex and cross-correlation measurements resultsin a self-monitoring system. The pattern of a group of vorticesis used to determine the transition time of the fluid between twosensor pairs. Measurement results show that the relative error ofgas flow velocity with the bluff body is evidently smaller than thatwithout the bluff body.

Index Terms—Correlation, self-monitoring system, signalprocessing, ultrasound, vortex.

I. INTRODUCTION

AN increased market of flow-measuring instruments us-ing ultrasound has been observed in recent years. This

technique has such evident advantages as noncontact mea-surements, lack of mechanical parts in motion, low pressurelosses, and low maintenance. Generally, the principle of time-of-flight measurements based on the Doppler effect is used[1]–[4]. The cross-correlation methods to determine the flowvelocity are well known but not widely spread due to difficultsignal processing [5]–[8]. Furthermore, this procedure does notmeasure the average flow velocity but does measure the mostfrequent value (modal value) of the skewed velocity componentdistribution [7]–[9].

For vortex measurements based on the effect of Karmanvortex street, pressure sensors are conventionally used.Considering the low sensitivity of the sensors to pressure, bigbluff bodies are often utilized, because big bluff bodies causebig pressure drops [3], [4]. An initial investigation of the detec-tion of the vortex frequency by ultrasound is described in [10]and [11]. Comprehensive research is presented in [12]. Thephysical connections between vortices and ultrasonic waves

Manuscript received June 12, 2006; revised August 27, 2007. This work wassupported by a grant from Deutsche Forschungsgemeinschaft.

Y. Lin is with Honeywell International, Inc., Morristown, NJ 07960 USA(e-mail: yaoyinglin@yahoo.com).

V. Hans is with the Chinese–German College (CDHK), Tongji University,Shanghai, China.

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TIM.2007.908137

Fig. 1. Sketch of the experimental setup (upper figure) and measurementchamber (lower figure).

have been interpreted, and different kinds of bluff body shapesand various kinds of streaming have been examined.

The most important problem of the application of ultra-sound in gas flow measurement is ultrasound signal processing.Vortices or turbulences in the fluid modulate the carrier fre-quency of 100 kHz in amplitude as well as in phase. Themodulating frequency is low, and its sidebands in the spectrumare very narrow to the carrier frequency.

The combination of the principle of vortex and cross-correlation measurements results in a self-monitoring mul-tisensor system. This combined system leads to a smallermeasured relative error than the separate systems, as shownin the following. In addition, it simplifies both the digital andthe analog signal processing. The self-monitoring ability ofthis combination enables the reliability of the measurementsystem.

II. SIGNAL PROCESSING

A. Digital Signal Processing

The complex modulated signal can be demodulated by un-dersampling. As well known, sampling leads to the repetitionof the original spectrum in the frequency domain. However,this also means that the original spectrum can be shifted to anyeligible frequency range. In particular, the carrier frequency canbe shifted to zero by undersampling the carrier frequency withinteger submultiples, while the modulation frequency remainsat its real value. The theorem of Shannon must be consideredfor the modulating frequency. In the case in question, the carrier

0018-9456/$25.00 © 2007 IEEE

LIN AND HANS: SELF-MONITORING ULTRASONIC GAS FLOW METER BASED ON VORTEX AND CORRELATION METHOD 2421

Fig. 2. Undersampled Hilbert transform.

frequency was 220 kHz, the modulation frequency was in therange of up to 4 kHz, and the undersampling frequency waschosen as 20 kHz.

Experiments have been done in a pipe with a diameter of100 mm and an inflow length of 5 m to get a fully developedflow profile. A calibrated turbine meter was used as a reference.The sketch of the experimental setup and the measurementchamber is shown in Fig. 1.

Three pairs of ultrasonic sensors were installed in the mea-surement chamber to investigate the influence of differentdistances between sensors. For each measurement and for thecorrespondent analysis, only two channels were used.

Assuming that the influences causing amplitude modulation(AM) and phase modulation (PM) are independent of eachother, such signals are called quadrature-amplitude-modulatedsignals. To determine the time-dependent amplitude and phase,the real and imaginary parts of the signal must be measured.

The real part can be directly measured. To determine theimaginary part of the signal, the Hilbert transform proves tobe the best tool. It can be realized by sampling with a 90◦ shiftrelative to the first sample for the real part. It is self-evident thatthe same effect is obtained if the 90◦-shifted sampling point isshifted by n × 360◦, as illustrated by Fig. 2. Then, the anglebetween the two sampling points is 90◦ + n × 360◦, whichshall be called the undersampled Hilbert frequency [13]. Forthis undersampled Hilbert frequency, the theorem of Shannonmust be considered. This means that the Hilbert frequency mustbe bigger than twice the sampling frequency (i.e., the frequencyto sample the real parts). For the example with a samplingfrequency of 20 kHz, as mentioned, the Hilbert frequency mustbe bigger than 40 kHz. Considering the 90◦ shift, the Hilbertfrequency is, at least, 41.9 kHz, corresponding to 23.86 µsin the time domain. This very short time corresponds to adisplacement of 596 µm of the fluid at a velocity of 25 m/s.It can be taken for granted that the fluid does not changeits properties within this time, considering that the fluid is aNewtonian fluid.

In many cases, particularly, at high flow velocities, phaseangle ϕ(t) exceeds 180◦, which is mostly caused by an offsetof noise. Then, the arctan function for the determination of thephase angle cannot be calculated. A stochastical evaluation ofthe density distribution of the phase angle has been proven to begood in [14] and [15]. Another new application is an extendedKalman filter (EKF) [13].

A disturbed flow has been generated by a 90◦ bend.Comparisons with quadrature amplitude demodulation (QAD)

Fig. 3. Phase demodulation through QAD (upper plot) and EKF (lower plot)in a disturbed flow at 2 m/s.

show no difference at low modulation degrees, confirming thetheory of EKF (Fig. 3). However, at high flow velocities andhigh modulation degrees combined with a high noise level,the superiority of EKF becomes evident. The phase angle canbe clearly detected and is free of noise, as shown in Fig. 4.

This advantage becomes particularly apparent in further sig-nal processing, as in cross-correlation functions. Correspondingexamples are shown in Fig. 5.

The point of maximum similarity between two signals fromeach of the two channels is computed by using the mathematicalcross-correlation function Φs1s2, which is given by

Φs1s2 = limT→∞

12T

T∫

−T

s1(t)s2(t − τ)dt. (1)

The cross-correlation function shows a higher peak valuethan that obtained through QAD, which leads to a more accuratecalculation of the flow velocity.

2422 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 56, NO. 6, DECEMBER 2007

Fig. 4. Phase demodulation through QAD (upper plot) and EKF (lower plot)in a disturbed flow at 25 m/s.

Fig. 5. Cross-correlation function of the phase signal demodulated by QAD(upper plot) and EKF (lower plot) in a disturbed flow at 25 m/s.

B. Analog Signal Processing

As is well known, the product of two sinusoidal functionsresults in an amplitude-modulated signal with two sidebands inthe spectrum. In the case of vortex measurement, the modulatedreceiver signal will be multiplied by the carrier frequency. Thespectrum contains the low modulation frequency caused by thevortices and the high carrier frequency, which can be eliminated

Fig. 6. Analog signal processing in the vortex measurement.

Fig. 7. Ultrasonic receiver signal in the vortex measurement at a flow velocityof 20 m/s. Upper signal: Filtered multiplied signal. Lower signal: Amplitude-modulated ultrasonic signal through vortices.

Fig. 8. Self-monitoring system resulting from the combination of the vortexand cross-correlation measurements.

by low-pass filtering, as shown in Fig. 6. A practical measure-ment example is shown in Fig. 7 for the vortex measurement ata flow velocity of 20 m/s.

In the case of vortex measurement, the AM is dominant,and the frequency can be clearly detected. In the correlationmeasurement, however, particularly at low flow velocities, theAM is not as strong as the PM. Therefore, this method is notsuitable for the pure cross-correlation method [13].

C. Self-Monitoring Flow Measurement System

The combination of the vortex and cross-correlation methodsresults in a self-monitoring system. The principal setup isshown in Fig. 8.

Vortices are generated behind a bluff body. The frequency ofthe vortices can be measured with the first ultrasonic receiverbehind the bluff body. Additionally, the pattern of a group ofvortices is used to determine the transition time of the fluidflowing from the first receiver to the second receiver by crosscorrelation. The signals received by the sensors in the conven-tional correlation measurements are generated by natural turbu-lences in the fluid. These natural turbulences are random withstatistical distribution. The signals turn into periodic sinusoidalsignals when we put the bluff body in the fluid, which generatesthe Karman vortex street behind the bluff body. The turbulencesare now not natural but are artificial vortices generated by thebluff body. Therefore, in contrast to conventional correlation

LIN AND HANS: SELF-MONITORING ULTRASONIC GAS FLOW METER BASED ON VORTEX AND CORRELATION METHOD 2423

Fig. 9. Cross-correlation function with a vortex at 2 m/s (upper plot) and25 m/s (lower plot). Dashed line: Without bluff body. Solid line: Withbluff body.

measurements, the signals received by the ultrasonic sensorsare not random but are periodic. The velocity component distri-bution is symmetric, and the average flow velocity correspondsto the mean value of the distribution function.

The systematic error, as mentioned in the case of pure cross-correlation measurement, is eliminated; the measured relativeerror, therefore, decreases.

The experimental results of cross-correlation functions with(solid line) and without the bluff body (dash line) are shownin Fig. 9. For a better illustration, examples are shown for adistance of 90 mm between the sensor pairs. The upper figureshows the cross-correlation function at a low flow velocityof 2 m/s; the lower figure shows that for a high velocity of25 m/s. The cross-correlation coefficient with the bluff bodyis a little smaller at low velocity but apparently bigger at highflow velocity. Additionally, the deviation of the transit time atthe two peaks is distinguishable, as a result of the periodicand random signal measurement. For bigger coefficients, thedistance between the sensor pairs should be shortened. The bestresults have been obtained with a distance of 30 mm.

To compare the measurement results, the concept of relativeerror is applied. The relative error is defined by the followingequation:

Relative error = (measured value − set value)/set value.

Fig. 10 shows the measured relative error of flow velocity fordistances between sensor pairs of 30 mm (upper) and 90 mm(lower). It is obvious that the measured relative error with thebluff body is obviously smaller than that without the bluff body.The different measurement principles show the advantage of thecombination of vortex and cross-correlation measurements.

Fig. 10. Measured relative error of flow velocity for distances between sensorpairs of 30 mm (upper plot) and 90 mm (lower plot).

III. SUMMARY

The self-monitoring ultrasonic gas flow meter proposed inthis paper is based on the combination of the vortex andcorrelation methods. This flow meter yields a smaller measuredrelative error than the separate correlation method by eliminat-ing the systematic error that exists in the principle of correlationmeasurement. What is more, the flow meter therefore possessesself-monitoring ability when the two separate methods workat the same time. This improves the reliability of the gasflow meter.

REFERENCES

[1] F. S. Tse, Measurement and Instrumentation. New York: Marcel Dekker,1989.

[2] E. Schrüfer, Elektrische Messtechnik. Munchen, Germany: Hanser-Verlag. 2004-11-30 3.

[3] J. Bentley, Principles of Measurement Systems. White Plains, NY:Longman, 1983.

[4] R. C. Baker, Flow Measurement Handbook. Cambridge, U.K.:Cambridge Univ. Press, 2000.

[5] M. S. Beck, Cross Correlation Flow Meters: Their Design andApplication. Bristol, U.K.: IOP, 1987.

[6] W. Shu, “Durchflussmessung in Rohren mit Hilfe von künstlichen undnatürlichen Markierungen,” Ph.D. dissertation, Universität Karlsruhe,Karlsruhe, Germany, 1987.

[7] F. Schneider, “Eine Analyse der Entstehung der Messsignale bei derkorrelativen Ultraschalldurchflussmessung in turbulenter Strömung,”Ph.D. dissertation, Universität Essen, Essen, Germany, 2001.

[8] V. Skwarek, “Verarbeitung modulierter Ultraschallsignale in Ein- undMehrpfadanordnungen bei der korrelativen Durchflussmessung,” Ph.D.dissertation, Universität Essen, Essen, Germany, 2000.

[9] Fluid Mechanics of Flow Metering, W. Merzkirch, Ed. New York:Springer-Verlag, 2005.

[10] V. Hans, G. Poppen, E. V. Lavante, and S. Perpeet, “Interaction betweenvortices and ultrasonic waves in vortex shedding flow meters,” in Proc.FLUCOME, 1997, vol. 1, pp. 43–46.

[11] H. Windorfer and V. Hans, “Experimental optimization of bluff bodies inultrasound vortex shedding flow meters,” in Proc. FLOMEKO, 2000.

2424 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 56, NO. 6, DECEMBER 2007

[12] H. Windorfer, “Optimierung von Wirbelfrequenzmessgeräten mit demod-ulierten Ultraschallsignalen,” Ph.D. dissertation, Universität Essen, Essen,Germany, 2001.

[13] Y. Lin, “Signal Processing and Experimental Technology in UltrasonicFlow measurement,” Ph.D. dissertation, Universität Duisburg-Essen,Essen, Germany, 2004.

[14] M. Niemann, “Signalverarbeitung in der Ultraschall-Durchflussmessung,” Ph.D. dissertation, Universität Essen, Essen,Germany, 2002.

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Yaoying Lin was born in China in 1977. She re-ceived the Bachelor’s and Master’s degrees in sci-ence in China in 1999 and 2002, respectively, and theDoctor’s degree in engineering from the Universityof Duisburg-Essen, Essen, Germany, in 2004.

From 2003 to 2005, she was a Scientific Coworkerwith the Institute of Measurement and Control, Uni-versity of Duisburg-Essen. From 2005 to 2006, shewas a Scientific Assistant with the University of Na-tional Defence, Hamburg, Germany. Since January2007, she has been an Application Engineer with

Honeywell International, Inc., Morristown, NJ. Her research interests includemeasurement and control.

Volker Hans born in Germany in 1938. He re-ceived the degree from the Technical Universityof Braunschweig, Braunschweig, Germany, and theDoctor’s degree from the Technical University ofKaiserslautern, Kaiserslautern, Germany, in 1974.

He was offered a chair at the University ofHamburg, Hamburg, Germany, in 1979 and at theUniversity of Kassel, Kassel, Germany, in 1980.In 1987, he took over a chair and the Institute ofMeasurement and Control, University of Duisburg-Essen, Essen, Germany, where he was the Dean of

the faculty and the Vice President. In 1992, he was appointed ConsultantProfessor with the Northwestern Polytechnical University of Xi’an, Xi’an,China. In 2005, he was appointed Professor with the Chinese–German College(CDHK), Tongji University, Shanghai, China.