ADAPTIVE ASYMMETRIC DOUBLE-PATH

ULTRASONIC TRANSIT-TIME GAS FLOWMETER

Mario Kupnik∗, Andreas Schroder†, and Martin Groschl†∗Edward L. Ginzton Laboratory, Stanford University, Stanford, CA-94305-4088†Institute of General Physics, Vienna University of Technology, A-1040, Austria

Abstract – In this study we demonstrate that adouble-path ultrasonic transit-time gas flowmeter canbe extended significantly in its rangeability by shiftingthe two receiving transducers by the same amount inflow direction, such that the length of one sound pathis increased, the other decreased. Such an asymmetricconfiguration is optimized in terms of signal-to-noiseratio (SNR) for the range of higher flow velocities,because it compensates for the parasitic carry-along(sound drift) effect. Further, this approach enables therealization of an adaptive asymmetric UFM, wherethe two receiving transducers can be shifted duringoperation for optimum SNR depending on the gas flowvelocity. Our results show that the asymmetric configu-ration increases UFM rangeability without drawbacks.

I. INTRODUCTION

Ultrasonic gas flowmeters (UFMs) utilizing thetransit-time method, which is the most widely usednon-intrusive ultrasonic method for flow metering, areadvantageous for many applications because of theirhigh accuracy; almost zero pressure drop; and thenonexistence of moving parts. At least one pair ofultrasonic transducers is required to measure the up-stream and downstream ultrasonic transit times for thecalculation of the gas flow velocity without knowledgeof the speed of sound [1].

In many applications, constraints associated withthe possible pipe diameter are a limiting factor interms of the rangeability of the UFM. On the otherside, shorter sound path lengths in such smaller UFMsattenuate the ultrasonic waves less, and, therefore,ultrasonic transducers utilizing higher frequencies canbe used [2]. The advantage is a better time resolutionand the capability to operate outside noise-dominatedfrequency ranges [3]. Because of their better acousticimpedance match to gases, compared to piezoelectrictransducers, capacitive ultrasonic transducers (CUTs)or capacitive micromachined ultrasonic transducers(CMUTs) are excellent candidates. The main draw-back of using higher frequencies (300-800 kHz) are

T T

R RR R

x∆

gas flow

Fig. 1. A double-path UFM extended in its rangeability byshifting both receiving transducers (R) by the same shift distance(∆x) in flow direction to compensate for the carry-along effect(sound drift).

narrower ultrasound beams (main lobe), which causeproblems in terms of low SNRs at higher gas flowvelocities due to the parasitic carry-along (sound drift)effect [4]. In [5] a solution is presented, where thetransducers are inclined at an angle to the inter-transducer centerline in order to overcome the carry-along effect. This solution is applicable for bothsingle-path and multi-path measurement cell config-urations.

If at least two independent sound paths, i.e. oneupstream and one downstream oriented path, are avail-able, another solution to compensate for the carry-along effect can be realized. Usually, a double-pathUFM has equal distances between receiver and trans-mitter in both of its sound paths, i.e. it is a symmetricconfiguration in terms of its ideal sound path lengths,which is also the case in the solution described in [5].

In our solution the two receiving transducers areshifted by the same shift distance (∆x) in flow di-rection, such that one path is increased, the otherdecreased. The result of this idea is an asymmet-ric UFM (Fig. 1), with a significant improvementin terms of rangeability. Compared to the solutionreported in [5], our solution enables a simple UFM

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Movable insert forreceiving transducers

Curved sealing plate(inside the pipe)

Mounting holes forreceiving transducers

Mounting holes fortransmitting transducers

Adjustment unit

Pressure monitoring

Holes for heating elements

Temperaturemonitoring

Mounting holes for sealing plate

Fig. 2. Design drawings (different views) to illustrate the realization of an adaptive asymmetric UFM. The movable insert enablesshifting both receiving transducers with and against the flow direction during UFM operation. The curved sealing plate is mountedinside the pipe. (Drawing by courtesy of AVL List GmbH, Graz, Austria.)

realization where the two receiving transducers canalso be shifted during UFM operation. Consequently,this paper introduces an adaptive asymmetric UFMthat can adjust itself to the optimum conditions tomaximize SNR over a wide measurement range.

II. REALIZATION OF AN ADAPTIVE ASYMMETRIC

UFM

By using a movable insert for the two receivingtransducers, an adjustment unit, and a curved seal-ing plate inside the pipe, the idea of an adaptiveasymmetric UFM can be implemented (Fig. 2). Theprototype has a pipe diameter of 50 mm and utilizesfour identical CUTs, operated at a center frequencyof 350 kHz in a wetted configuration, i.e. in directcontact to the gas. The four wetted transducers arepositioned such that no protrusion into the pipe occurs,achieved with four transducer port cavities (Fig. 3).

III. DERIVATION OF UFM EQUATIONS

It is essential to consider the transducer port cavitiesfor the derivation of the UFM equations for the gasflow velocity v and the speed of sound c. Both arethe mean values along the sound paths. Details of thisderivation are described in [6].

In the case of the asymmetric UFM the derivationneeds to be extended such that the shift distance (∆x)is considered. By using the measured temperature

T T

gas flow

R RR R

x∆

Position of transducer membrane

0L L−

02

L

0T c⇒ α

Transducer portcavitiy

x∆

α

β1

2portL

1pipeL

Fig. 3. Schematic of how the shift distance (∆x) and trans-ducer port cavities are considered for the derivation of the UFMequations (v, c) for the asymmetric configuration.

information (T ) from inside the transducer port cavity,the speed of sound c0 can be calculated and theequations for the downstream transit time as a functionof (∆x), i.e.

tdown (∆x) =L1pipe (∆x)

c+ v sin(β(∆x))+

L1port (∆x)c0 (T )

(1)

and for the upstream transit time

tup (∆x) =L2pipe (∆x)

c− v sin(γ(∆x))+

L2port (∆x)c0 (T )

(2)

can be written (Fig. 3), where L1pipe (∆x) andL2pipe (∆x) are the ideal sound path lengths inside the

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(a) (c)(b)

(e)(d) (f)

(h)(g) (i)

x = 0 mm x = 6.5 mm x = 10 mm

x x x

Fig. 4. Best-case-normalized receiving amplitudes depending on the maximum gas flow velocity vmax (a, b, c); measured gas massflow values compared to reference values obtained from a certified hot wire anemometer (d, e, f); relative differences with respect toreference mass flow (g, h, i); all for a symmetric (∆x = 0 mm) and two asymmetric (∆x = 6.5 mm, ∆x = 10 mm) UFM configurations.

pipe, L1port (∆x) and L2port (∆x) are the ideal soundpath lengths inside the transducer port cavities, andβ(∆x) and γ(∆x) are the resulting inclination anglesof the ideal sound path lengths, all in downstream andupstream direction, respectively. These two equationscan be easily solved for v and c to get the UFMequations for the asymmetric UFM.

IV. PROOF OF PRINCIPLE AND RESULTS

For the experiments, we installed the UFM in a gasflow loop with a maximum gas flow velocity of 38 m/s(Mach number 0.11). A flow conditioner consistingof a bundle of small pipes (∅5 mm) inside thestarting length before the UFM was used to minimize

parasitic effects of vortexes. In all experiments weused three different values for the shift distance ∆x(0, 6.5 and 10 mm). A determination of transit-timesin both channels at 350 kHz and zero gas flow, whileincreasing the shift distance ∆x, revealed that ourdetection algorithm started to fail when the value of∆x = 14 mm was reached. Including a safe margin,a shift distance of 10 mm gives an optimum non-adaptive configuration of an asymmetric UFM withthe specifications (dimensions, frequency) describedabove.

In a first experiment we increased the gas flowvelocity from 0 m/s to the maximum value of 38 m/s

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in steps of 2 m/s and measured the amplitudes of thereceived signals (stationary over 30 s) in both channels(Fig. 4(a), (b) and (c)). The receiving amplitudesare best-case-normalized by dividing all values bythe measured amplitudes of the received signals atzero gas flow and zero shift distance. As expected,in the case of the symmetric UFM (∆x = 0) thenormalized amplitudes of the received signals droppedfrom 0 dB at 0 m/s to -11 dB at 38 m/s (Mach number0.11). When the receivers were shifted by +10 mm inflow direction, the amplitudes rose from ∼-12 dB inaverage at 0 m/s to -1.5 dB at 38 m/s, implying asignificant extension of the rangeability.

In a second experiment, which had the main goalto verify that equations (1) and (2) are suitable forthe derivation of the UFM equations, we used theasymmetric UFM in the air flow loop to measurethe gas flow velocity v and the speed of sound cand calculated the mass flow rate by using the mea-sured pressure [6]. As reference we used a hot wireanemometer (Sensyflow P DN 80, ABB AutomationProducts GmbH, Alzenau, Germany), which was cer-tified to have an expanded measurement uncertaintyof −0.44% (coverage factor 2) in average over themass flow range from 30 to 360 kg/h. The mass flowvalue was increased in steps of ∼20 kg/h from 0 kg/hto 260 kg/h and the hot wire anemometer was used tomeasure the mass flow rate over an integration time of30 s. The result of the direct comparison to the massflow rate obtained with the asymmetric UFM, againfor the three different shift distances 0, 6.5 and 10 mm,is depicted in Figs. 4(d)-(i). The averaged relativedifference to the reference value for the symmetricUFM was 0.32% with a standard deviation of 1.8%.

Only mass flow values larger than 30 kg/h wereconsidered for this calculation, due to the specifiedlower limit of measurement range of 30 kg/h of thehot wire anemometer used as reference. Further, itshould be mentioned that a fully developed turbulentflow profile was assumed for the calculation of themeter factor (0.933).

In the case of 6.5 mm and 10 mm shift distance, theaveraged relative difference increases to 1.92% with astandard deviation of 0.9% and 3.18% with a standarddeviation of 1.4%, respectively. The reduction of thestandard deviation for the cases 6.5 mm and 10 mmshift distance, can be explained by the larger averagereceived amplitudes over the whole gas flow velocityrange. Furthermore, this indicates that shifting thetwo receiving transducers causes only a systematic

additional error contribution, which can be reducedby calibration. In this context it should be mentionedthat the asymmetric UFM was not calibrated beforethese measurements.

V. CONCLUSION

A double-path UFM can be extended in its range-ability by shifting both receiving transducers by thesame amount in the flow direction. The extensionof the rangeability of such an asymmetric double-path UFM is due to the compensation for the carry-along (sound drift) effect. An analytical solution forthe UFM equations (v, c) exists. Because of thesimplicity of the approach to shift the two receivingtransducers by the same amount in the direction offlow, an adaptive asymmetric double-path UFM can berealized. Such a configuration can adjust itself (controlloop), depending on the flow condition, for optimumsignal-to-noise ratio over a wide measurement range.The asymmetric configuration increases the UFMrangeability without significant drawbacks.

ACKNOWLEDGMENT

This work was supported in part by AVL ListGmbH, Graz, Austria. The work of Mario Kupnik wassupported by the FWF Austrian Science Fund. Theauthors would like to thank L. Lynnworth, LynnworthTechnical Services, Waltham, MA, for many fruitfuldiscussions and his support. Further, the authors thankF. Purkathofer for generating the 3D drawings shownin Fig. 2.

REFERENCES

[1] L. C. Lynnworth, Ultrasonic Measurements for Process Con-trol; Theory, Techniques, Applications. San Diego: Acad-emic Press, Inc., 1989.

[2] I. J. O’Sullivan and W. M. D. Wright, “Ultrasonic measure-ment of gas flow using electrostatic transducers,” Ultrasonics,vol. 40, pp. 407–411, 2002.

[3] P. Brassier, B. Hosten, and F. Vulovic, “High-frequencytransducers and correlation method to enhance ultrasonic gasflow metering,” Flow Meas. Instr., vol. 12, pp. 201–211, 2001.

[4] M. Kupnik, P. O’Leary, A. Schroder, and I. Rungger, “Nu-merical simulation of ultrasonic transit-time flowmeter per-formance in high temperature gas flows,” in Proc. IEEEUltrason. Symp., 2003, pp. 1354–1359.

[5] K. S. Mylvaganam, “High-Rangeability Ultrasonic GasFlowmeter for Monitoring Flare Gas,” IEEE Trans. Ultrason.,Ferroelect., Freq. Contr., vol. 36, pp. 144–149, 1989.

[6] M. Kupnik, A. Schroder, P. O’Leary, E. Benes, andM. Groschl, “Adaptive pulse repetition frequency techniquefor an ultrasonic transit-time gas flowmeter for hot pulsatinggases,” IEEE Sensors Journal, vol. 6, no. 4, pp. 906–915,2006.

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