- Email: [email protected]
Acoustic gas sensors using airborne sound properties
Sensors and Actuators B 68 Ž2000. 162–167 www.elsevier.nlrlocatersensorb
Acoustic gas sensors using airborne sound properties L. Zipser ) , F. Wachter, H. Franke ¨ HTW, UniÕersity of Applied Sciences, Friedrich-List-Platz 1, D-01069 Dresden, Germany
Abstract Known acoustic gas sensors use SAW-elements or mechanical resonators, covered with a sensitive layer, as primary transducers. Some of these indirect-working acoustic gas sensors are selective. But they show instabilities relating to contamination and high temperatures. These disadvantages can be eliminated by using as sensing effect the direct variability of properties of airborne sound in gas mixtures, e.g. the variable isentropic and anisentropic speed of sound and the resonance absorption. Potentialities in design of different types of electric-acoustic and fluidic-acoustic gas sensors are described. As an example, a fluidic-acoustic humidity sensor is presented. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Acoustic gas sensor; Speed of sound; Sound absorption; Acoustic humidity sensor
1. Introduction Fluidic-acoustic gas sensors using as primary sensing effect the variability of airborne sound properties Že.g. isentropic or anisentropic speed of sound or acoustic resonance absorption. are distinguished by high reliability, immunity to extreme temperatures, contamination or aggressive media and by short response time w1x. This opens a wide field of industrial application. However, these sensors are non-selective. Sensitivity, accuracy and dynamic behaviour of these sensors depend on the actually used sensing effect and on sensor design. In the following, the most important sensing effects as well as potentialities and problems in designing fluidicacoustic and electric-acoustic gas sensors are described and discussed.
2. Acoustic sensing effects
components K i , i s 1 . . . n, the speed c is is a function of mi the mass concentrations x i s n of the components Ý is1 m i K i w2x:
c is s c is Ž x i , Mi ,Cp i ,T . s
)
Ý x i Cp i
RT n
is1 n
Ý x i Mi Ý Ž x i Cp i y R . is1
is1
Ž 1. T absolute temperature, R gas constant, M molecular weight, and Cp heat capacity. With Eq. Ž1. and the sum of mass concentrations Ý nis1 x i s 1 it is possible to determine the concentrations x 1 and x 2 of binary gas mixtures from measured speeds c is . Fig. 1 shows the variation of the isentropic speed c is in selected binary gas mixtures. In some special cases the dependence of c is on the mass concentration x i is not unequivocal, e.g. in argon–oxygen mixtures w3x.
2.1. Isentropic speed of sound 2.2. Anisentropic speed of sound In a wide room or in a wide channel, sound propagates without essential loss of energy, i.e. its entropy is nearly constant Žisentropic.. Consequently, the speed of this sound propagation is called c is . For gas mixtures consisting of n
)
Corresponding author.
In a narrow channel at low frequencies an acoustic wave has sufficient time and contact area for frictional and thermal interactions with the channel walls. In this case the propagation of the acoustic wave is coupled with essential loss of energy and a rise of entropy. The propagation speed is reduced to the anisentropic speed cai - c is . The calculation of cai in narrow gas-filled channels is rather compli-
0925-4005r00r$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 5 - 4 0 0 5 Ž 0 0 . 0 0 4 7 8 - 0
L. Zipser et al.r Sensors and Actuators B 68 (2000) 162–167
163
cated w4–6x. The anisentropic speed cai can be defined as a quotient: sound frequency f divided by the imaginary part of the complex propagation factor of the acoustic wave. The difference between the frequency-independent isentropic speed c is in a wide channel and the anisentropic speed cai in a narrow channel rises with decreasing sound frequency f. The anisentropic speed cai in a gas mixture also depends on the mass concentrations x i of the i s 1 . . . n components: cai s cai Ž Cp i , Mi ,Õ, Pri , f , A,T , x i . .
Ž 2.
Fig. 2. Quotient cai r c is for different pure gases.
In detail is y1
cai s c is Ž x i . Re
ž(
1q Ž k Ž x i . y1 . 4 B f r f T Ž x i . 4 1y B f r f Õ Ž x i . 4
/
Ž 3.
with the B-function BŽ j . s
(
2 J1 Ž 8 j 3j .
(8 j j J Ž (8 j j. 3
3
Ž 4.
0
containing the parameters j s frf Õ or j s frf T , the Bessel functions J0 , J1 and the adiabatic exponent k Ž x i . of the gas. Further, the viscose frequency f Õ s 4ÕrA and the thermal frequency f T s f ÕrPr, with Prandtl’s number Pr Ž x i .. In Fig. 2 cai rcis-curves of pure gases are shown. The cai Ž x i .rcisŽ x i .-curves of binary gas mixtures are situated between the corresponding curves of the two pure gases.
air is about a s 0.03rm at 208C and 10 kHz. Along a reasonable measuring path of D s s 50 mm, a sound attenuation of only 0.15% is to be expected. Such negligible effects are of no use for sensors. Experiments show that if a standing acoustic wave is generated in a fluid medium, the sound absorption in it rises by about one or two orders of magnitude w7x. This significantly enhanced sound absorption in standing acoustic waves may be called resonance absorption. The distinct resonance absorption effect is usable as measuring effect for determining the concentration of components in gas mixtures. The absorption coefficient a depends on the properties of the gas. For a binary gas mixture with x 1 q x 2 s 1, the attenuation of the sound pressure amplitude along the distance D s can be approximated by p Ž x 1 . f p 0 e a 1 x 1qa 2 Ž1yx 1 .4a r D s
Ž 6.
2.3. Acoustic resonance absorption
where a r is a multiplication factor caused by the effect of resonance absorption.
In gases the absorption of planar sound waves causes a reduction of the pressure amplitude p corresponding to
3. Sensor design
p 2 s p 1eya D ;,
Ž 5.
with the sound absorption coefficient a and the running distance D s s s2 y s1. The sound absorption coefficient of
First of all, the configuration and characteristics of acoustic gas sensors using airborne sound effects depend on the kind of stimulating either standing acoustic waves in resonators or acoustic impulse sequences in transmission lines. 3.1. Electric-acoustic gas sensors
Fig. 1. Isentropic sound speed c is in binary gas mixtures at normal conditions.
In case of electric stimulation of an acoustic wave, electric-acoustic transducers provide the acoustic energy. For generating a standing acoustic wave, two electricacoustic transducers are arranged as reflectors at the ends of an n lr2-resonator ŽFig. 3a.. The resonator is filled with the binary gas mixture to be analysed. The transducers are connected via an electric amplifier to a feedback loop. If Barkhausen’s oscillation condition kÕ s 1 is fulfilled, transducers, amplifier and resonator form a harmonic oscillator. It generates, by interference, a standing wave in the n lr2-resonator. In the ideal case, if broadband transducers are used, the eigenfrequency fe of the
164
L. Zipser et al.r Sensors and Actuators B 68 (2000) 162–167
three sensing effects are available and the selectivity of the gas sensor increases. The temperature stability of electric-acoustic gas sensors is limited because the temperature-susceptible transducers must be directly coupled with the transmission line. While the temperature correction in fluidic-acoustic gas sensors can be properly solved by a reference oscillator, electric-acoustic gas sensors need an additional high-precision temperature sensor. Its output signal advantageously has to be transformed into a frequency signal. As an alternative the sensor temperature can be controlled w8x. A disadvantage of electric-acoustic gas sensors could be that, in the case of non-streaming measuring gases, the gas exchange in the transmission line occurs only by diffusion, resulting in long response times T90 sG 10 s. Fig. 3. Basic configuration of an electric-acoustic oscillator Ža. with n l r2-resonator and Žb. with acoustic transmission line L4 l.
oscillator is determined by the speed of sound c is . With Eq. Ž1. the eigenfrequency fe only depends on the concentrations x i of the gas mixture, i.e. feŽ x i . s G 1 cisŽ x i .. Gi is an oscillator constant. Commonly available transducers are narrow-band. Then the oscillator eigenfrequency fe is additionally determined by the frequency response function of the transducers. This can cause measurement errors and must be corrected electronically. For generating a sound impulse in an acoustic transmission line of length L 4 l ŽFig. 3b., a generator supplies an electric-acoustic transducer with a short electric wave packet. The transducer is connected with the line. The airborne acoustic impulse from the transducer passes a wide line during the transition time t s Lrcis or a narrow line in t s Lrcai . A second transducer at the other end of the line receives the acoustic impulse. Now, the incoming impulse is used either for triggering a new impulse at the sending transducer Žsing-around method. or for generating an acoustic response impulse from the transducer that was just the receiver Žping-pong method.. In both cases the impulse frequency f i depends on transition time t , i.e. f i Ž x i . s G 2 c isŽ x i .. Electric-acoustic gas sensors do not need a stabilised supply of pressure for generating sound. This is a general advantage. Moreover, in the wide pressure range where the measuring gas behaves like an ideal gas, the measuring result does not depend on the gas pressure w2x. The electrical stimulation of sound can be carried out with high amplitude accuracy. On condition that the influence of the transducers on the frequency response function of the transmission line is negligibly small, it is basically possible to determine not only the transition time t , but simultaneously the attenuation of sound corresponding to Eq. Ž6.. By implementing in the same sensor a wide and a narrow transmission line, two transition times t is and tai can be measured. So, for analysing a gas mixture, two or even
3.2. Fluidic-acoustic gas sensors In case of fluidic stimulation of an acoustic wave, a jet of the gas mixture to be analysed is the source of sound energy. For generating a standing acoustic wave in a lr2-resonator ŽFig. 4a., the jet is guided against a sharp edge where it produces edge tones of different frequencies. Subsequently, the gas mixture flows through the resonator, which is arranged adjacent to the edge. This resonator amplifies by interference only that frequency f, which corresponds to its eigenfrequency fe . Because the resonator length L s nŽ lr2 is constant, the eigenfrequency fe varies with the speed of sound c s l fe and according to Eqs. Ž1. or Ž2. with the mass concentrations x i , i.e. fe s feŽ x i .. For generating an acoustic impulse sequence in a transmission line ŽFig. 4b., the jet passes through a bistable
Fig. 4. Basic configuration of a fluidic-acoustic oscillator Ža. with l r2resonator and Žb. with acoustic transmission line L4 l.
L. Zipser et al.r Sensors and Actuators B 68 (2000) 162–167
fluidic amplifier with a feedback tube representing the transmission line. Basing on the Coanda effect, the jet produces a pressure impulse in one output channel. The feedback tube transmits this impulse to the amplifier input and switches the jet to the other output. This cycle is repeated continuously. At the amplifier outputs originates an impulse frequency f i . The acoustic impulse propagates the feedback tubes with the speed of sound c is . Due to Eqs. Ž1. or Ž2. for the impulse frequency follows f i s f i Ž x i .. For transducing the acoustic frequencies f into electric signals, piezo-electric transducers are commonly used. Fluidic-acoustic oscillators produce very strong signals. Therefore, the temperature-sensitive transducers can be placed in a wide distance apart from the oscillators, coupled by an acoustic transmission line. As a consequence, the oscillators can be made of a temperature-resistant material, which allows for high working temperatures. In experiments gas sensors made of aluminium were operated at up to 3508C. Temperature correction is also very simple by using a reference oscillator Žsee example.. Furthermore, the sensors can also be exposed to strong vibrations. The response time of fluidic-acoustic gas sensors is very short, because the measuring gas is sucked through the oscillator by an ejector. Response times T90 F 50 ms were measured. The vibration behaviour of fluidic oscillators is not influenced by vibrating mechanical parts. Hence, a wide uninfluenced frequency range D f can be used as a measuring range D f Ž x i max y x i min .. Disadvantageous is the need for a stabilised pressure difference between inlet and outlet of the oscillator. Pressure variations in the measuring gas can change the oscillator frequency. With fluidic-acoustic gas sensors it is not possible to measure reliably the sound attenuation corresponding to Eq. Ž6..
3.2.1. Example: fluidic-acoustic humidity sensor Fig. 5 shows the exploded view of a fluidic-acoustic humidity sensor for harsh applications. The sensor is mainly used for humidity control in the exhaust gas of industrial textile dryers. This exhaust gas has a temperature of 130–2508C and is loaded with dust, fibres and high-molecular vapours. The identical structures of the measuring oscillator Žindex m. and the reference oscillator Žindex r. are precisely milled in a thin plane plate. These oscillator plates are bounded on both sides with other plates, which contain the transit ducts for the gas mixture and the acoustic-electric transducers for transforming the pressure wave in the lr2-resonator into an electric signal. To be exact, the oscillator frequency f o depends not only on the length of the lr2-resonator and on the speed of sound c is , but also on the supply pressure D p s pout y p in of the oscillator: f o Ž Cis ,D p . s GB Ž D p . Ci .
Ž 7.
165
Fig. 5. Planar fluidic-acoustic humidity sensor.
The function B Ž D p . describes the influence of the supply pressure D p. G is the oscillator constant, summing up the geometry of the resonator and the jet-wedge configuration. For using a fluidic-acoustic oscillator as a gas sensor, the following problems have to be solved: Ø The function B Ž D p . should be approximately 1. Ø Disturbing fluctuations of the sound speed c is , caused by variations of the gas temperature T according to Eq. Ž1., must be corrected. Ø Supplying the oscillator with polluted gas mixtures for a long time can change the geometry of the oscillator and, in consequence, the constant G by sediments inside the resonator. These alterations must be eliminated or corrected to guarantee long-time stability of the gas sensor. We solved this problem with the aid of an automatic zero-point control. Ø Acoustic waves from the lr2-resonators must be transformed reliably into electric signals even under extreme process conditions. To realise the demand B Ž D p . f 1, special configurations of the oscillator geometry were developed w1x. For solving the problems of temperature correction and of stabilisation of the oscillator constant G, the reference principle can be used, i.e. the gas sensor is made of two identical fluidic-acoustic oscillators Žsee Figs. 5 and 6.. The first oscillator Žmeasuring oscillator. is supplied with the measuring gas. The second oscillator Žreference oscillator. is supplied with a reference gas, e.g. dry air. An ejector pump sucks a continuous gas flow through both oscillators. These are in close contact and hence thermally coupled. Consequently, the measuring gas and the refer-
L. Zipser et al.r Sensors and Actuators B 68 (2000) 162–167
166
ence gas have the same temperature T. In this case, with Eq. Ž1. and k s CprC v , the quotient Q of both frequencies does not depend on the temperature T : Qs
fm fr
s
Gm Gr
(
k m Ž x 1 . Mr Mm Ž x . k r
.
Ž 8.
In this way, fluidic-acoustic oscillators can be used for measuring the speed of sound c is at variable temperatures. Now it is assumed that the measuring gas consists of two qualitatively known components K 1 Žwater vapour. and K 2 Žair.. Dry air from the pressure supply is usually used as reference gas. Then the parameters M and k of both gases are well known. According to Eq. Ž8., the quotient Q depends on the concentrations x 1 and x 2 and on Gm and Gr . The instabilities of Gm and Gr can be eliminated in two steps by a zero-point control. The first step is the adjustment of the zero point. Both oscillators are supplied with the same gas, e.g. with dry air. Then according to Eq. Ž1. the speed of sound in both resonators is identically c isŽm. s c isŽr. . In this ideal case, i.e. for identical oscillators, follows Gm s Gr and fm Gm Qideal s s s 1. Ž 9. fr Gr In real cases the oscillator constants differ from each other, i.e. Gm / Gr and the quotient is fm DG Qreal s s 1 q s Q ideal q DQ Ž DG . . Ž 10 . fr Gr The small deviation < DQ Ž DG .< < 1 corresponds to the zero-point deviation of the static characteristic of the acoustic humidity sensor.
Fig. 7. Calibration characteristic of the humidity sensor at 1058C.
The second step is the correction of the zero point during measurements. The measuring oscillator is supplied with the measuring gas Žwet air.. The reference oscillator is supplied with dry air. Then, in the real case, the resulting quotient Q is a function of the concentration x 1 , i.e. of the humidity, and of the asymmetry of the oscillator constants DG: Q real s Ž x 1 ,DG . s Qideal Ž x 1 . q DQ Ž DG . .
Ž 11 .
The asymmetric term is known and can be corrected electronically. Now, with Eqs. Ž1. and Ž11. the concentration x 1 can be determined from the corrected value QidealŽ x 1 .. If the described reference conditions are strictly fulfilled, the influence of sensor properties is substantially eliminated. Consequently, the measuring results do not depend on individual sensor properties and we have an absolute method of humidity measurement. The calibration characteristic of the humidity sensor can therefore be calculated by using Eqs. Ž1., Ž7. and Ž10.. An experimental calibration is also possible, but requires a precisely working humidity generator for high temperature. Fig. 7 shows the calculated and the experimentally determined calibration characteristic. Both characteristics are in good agreement. The measuring accuracy under process conditions is about "3%. The detection limit for humidity measurements is 1g water vapour per kg wet air.
4. Conclusions
Fig. 6. Structure of the fluidic-acoustic humidity sensor.
The presented acoustic gas sensors can be used for the industrial online analysis of binary gas mixtures. In general, two types of acoustic gas sensors can be distinguished: fluidic-acoustic and electric-acoustic. The first type is usable even under extreme measuring conditions Žhigh temperature, contamination, aggressive media . . . ., but for operation as power supply it needs a stabilised pressure difference between sensor inlet and outlet. Electric-acoustic gas sensors are in a wide range insensitive to pressure variations in the measuring gas. They do not need
L. Zipser et al.r Sensors and Actuators B 68 (2000) 162–167
a supply pressure, but are more susceptible to high temperature, needs a precise temperature compensation and have a longer response time.
Acknowledgements
167
w6x L. Zipser, F. Wachter, Acoustic sensor for ternary gas analysis, ¨ Sensors and Actuators, B 26–27 Ž1995. 195–198. w7x L. Zipser, H. Franke, Acoustic sensor for aerosol measurements, Proc. IEEE Ultrasonics Symp. 1998 Oct.5–8, Sendai, Japan 1 Ž1998. 517–519. w8x B. Hok, J. Lofving, Acoustic Gas Sensor with ppm ¨ A. Bluckert, ¨ ¨ Resolution, EUROSENSORS XIII, Book of Abstracts, pp. 319–320.
The research on this topic was sponsored by the Deutsche Forschungsgemeinschaft DFG. Biographies References w1x L. Zipser, Fluidic-acoustic gas sensors, Sensors and Actuators, B 7 Ž1992. 592–595. w2x N. Elsner, Grundlagen der Technischen Thermodynamik, AkademieVerlag, Berlin, 1973. w3x F. Wachter, On ambiguous speed of sound in binary gas mixtures, ¨ Proc. World Conference Ultrasonic WCU97, Aug. 24–27 1997, Yokohama, Japan Ž1997. 28–229. w4x J.M. Kirshner, S. Katz, Design Theory of Fluidic Components, Academy Press, New York, 1975. w5x M.H. Schaedel, Fluidische Bauelemente und Netzwerke, Verlag Friedrich Vieweg & Sohn, Braunschweig, 1979.
Lothar Zipser studied electrotechnics at the Technical University, Dresden. He received his PhD degree in information theory in 1976 and his habilitation in fluid-acoustics in 1986. Since 1993 he has been working as a professor at the HTW, University of Applied Sciences, Dresden. Friedmar Wachter studied physics at the Technical University, Dresden. ¨ He received his PhD degree in mathematical cybernetics in 1986. Since 1996 he has been working as a professor at the HTW, University of Applied Sciences, Dresden. Heinz Franke studied physics at the Technical University, Dresden. He worked many years as a physicist in the computing industry. Since 1994 he has been involved in several projects concerning acoustic sensors and vibration analysis at the HTW, University of Applied Sciences, Dresden.
Acoustic gas sensors using airborne sound properties L. Zipser ) , F. Wachter, H. Franke ¨ HTW, UniÕersity of Applied Sciences, Friedrich-List-Platz 1, D-01069 Dresden, Germany
Abstract Known acoustic gas sensors use SAW-elements or mechanical resonators, covered with a sensitive layer, as primary transducers. Some of these indirect-working acoustic gas sensors are selective. But they show instabilities relating to contamination and high temperatures. These disadvantages can be eliminated by using as sensing effect the direct variability of properties of airborne sound in gas mixtures, e.g. the variable isentropic and anisentropic speed of sound and the resonance absorption. Potentialities in design of different types of electric-acoustic and fluidic-acoustic gas sensors are described. As an example, a fluidic-acoustic humidity sensor is presented. q 2000 Elsevier Science S.A. All rights reserved. Keywords: Acoustic gas sensor; Speed of sound; Sound absorption; Acoustic humidity sensor
1. Introduction Fluidic-acoustic gas sensors using as primary sensing effect the variability of airborne sound properties Že.g. isentropic or anisentropic speed of sound or acoustic resonance absorption. are distinguished by high reliability, immunity to extreme temperatures, contamination or aggressive media and by short response time w1x. This opens a wide field of industrial application. However, these sensors are non-selective. Sensitivity, accuracy and dynamic behaviour of these sensors depend on the actually used sensing effect and on sensor design. In the following, the most important sensing effects as well as potentialities and problems in designing fluidicacoustic and electric-acoustic gas sensors are described and discussed.
2. Acoustic sensing effects
components K i , i s 1 . . . n, the speed c is is a function of mi the mass concentrations x i s n of the components Ý is1 m i K i w2x:
c is s c is Ž x i , Mi ,Cp i ,T . s
)
Ý x i Cp i
RT n
is1 n
Ý x i Mi Ý Ž x i Cp i y R . is1
is1
Ž 1. T absolute temperature, R gas constant, M molecular weight, and Cp heat capacity. With Eq. Ž1. and the sum of mass concentrations Ý nis1 x i s 1 it is possible to determine the concentrations x 1 and x 2 of binary gas mixtures from measured speeds c is . Fig. 1 shows the variation of the isentropic speed c is in selected binary gas mixtures. In some special cases the dependence of c is on the mass concentration x i is not unequivocal, e.g. in argon–oxygen mixtures w3x.
2.1. Isentropic speed of sound 2.2. Anisentropic speed of sound In a wide room or in a wide channel, sound propagates without essential loss of energy, i.e. its entropy is nearly constant Žisentropic.. Consequently, the speed of this sound propagation is called c is . For gas mixtures consisting of n
)
Corresponding author.
In a narrow channel at low frequencies an acoustic wave has sufficient time and contact area for frictional and thermal interactions with the channel walls. In this case the propagation of the acoustic wave is coupled with essential loss of energy and a rise of entropy. The propagation speed is reduced to the anisentropic speed cai - c is . The calculation of cai in narrow gas-filled channels is rather compli-
0925-4005r00r$ - see front matter q 2000 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 5 - 4 0 0 5 Ž 0 0 . 0 0 4 7 8 - 0
L. Zipser et al.r Sensors and Actuators B 68 (2000) 162–167
163
cated w4–6x. The anisentropic speed cai can be defined as a quotient: sound frequency f divided by the imaginary part of the complex propagation factor of the acoustic wave. The difference between the frequency-independent isentropic speed c is in a wide channel and the anisentropic speed cai in a narrow channel rises with decreasing sound frequency f. The anisentropic speed cai in a gas mixture also depends on the mass concentrations x i of the i s 1 . . . n components: cai s cai Ž Cp i , Mi ,Õ, Pri , f , A,T , x i . .
Ž 2.
Fig. 2. Quotient cai r c is for different pure gases.
In detail is y1
cai s c is Ž x i . Re
ž(
1q Ž k Ž x i . y1 . 4 B f r f T Ž x i . 4 1y B f r f Õ Ž x i . 4
/
Ž 3.
with the B-function BŽ j . s
(
2 J1 Ž 8 j 3j .
(8 j j J Ž (8 j j. 3
3
Ž 4.
0
containing the parameters j s frf Õ or j s frf T , the Bessel functions J0 , J1 and the adiabatic exponent k Ž x i . of the gas. Further, the viscose frequency f Õ s 4ÕrA and the thermal frequency f T s f ÕrPr, with Prandtl’s number Pr Ž x i .. In Fig. 2 cai rcis-curves of pure gases are shown. The cai Ž x i .rcisŽ x i .-curves of binary gas mixtures are situated between the corresponding curves of the two pure gases.
air is about a s 0.03rm at 208C and 10 kHz. Along a reasonable measuring path of D s s 50 mm, a sound attenuation of only 0.15% is to be expected. Such negligible effects are of no use for sensors. Experiments show that if a standing acoustic wave is generated in a fluid medium, the sound absorption in it rises by about one or two orders of magnitude w7x. This significantly enhanced sound absorption in standing acoustic waves may be called resonance absorption. The distinct resonance absorption effect is usable as measuring effect for determining the concentration of components in gas mixtures. The absorption coefficient a depends on the properties of the gas. For a binary gas mixture with x 1 q x 2 s 1, the attenuation of the sound pressure amplitude along the distance D s can be approximated by p Ž x 1 . f p 0 e a 1 x 1qa 2 Ž1yx 1 .4a r D s
Ž 6.
2.3. Acoustic resonance absorption
where a r is a multiplication factor caused by the effect of resonance absorption.
In gases the absorption of planar sound waves causes a reduction of the pressure amplitude p corresponding to
3. Sensor design
p 2 s p 1eya D ;,
Ž 5.
with the sound absorption coefficient a and the running distance D s s s2 y s1. The sound absorption coefficient of
First of all, the configuration and characteristics of acoustic gas sensors using airborne sound effects depend on the kind of stimulating either standing acoustic waves in resonators or acoustic impulse sequences in transmission lines. 3.1. Electric-acoustic gas sensors
Fig. 1. Isentropic sound speed c is in binary gas mixtures at normal conditions.
In case of electric stimulation of an acoustic wave, electric-acoustic transducers provide the acoustic energy. For generating a standing acoustic wave, two electricacoustic transducers are arranged as reflectors at the ends of an n lr2-resonator ŽFig. 3a.. The resonator is filled with the binary gas mixture to be analysed. The transducers are connected via an electric amplifier to a feedback loop. If Barkhausen’s oscillation condition kÕ s 1 is fulfilled, transducers, amplifier and resonator form a harmonic oscillator. It generates, by interference, a standing wave in the n lr2-resonator. In the ideal case, if broadband transducers are used, the eigenfrequency fe of the
164
L. Zipser et al.r Sensors and Actuators B 68 (2000) 162–167
three sensing effects are available and the selectivity of the gas sensor increases. The temperature stability of electric-acoustic gas sensors is limited because the temperature-susceptible transducers must be directly coupled with the transmission line. While the temperature correction in fluidic-acoustic gas sensors can be properly solved by a reference oscillator, electric-acoustic gas sensors need an additional high-precision temperature sensor. Its output signal advantageously has to be transformed into a frequency signal. As an alternative the sensor temperature can be controlled w8x. A disadvantage of electric-acoustic gas sensors could be that, in the case of non-streaming measuring gases, the gas exchange in the transmission line occurs only by diffusion, resulting in long response times T90 sG 10 s. Fig. 3. Basic configuration of an electric-acoustic oscillator Ža. with n l r2-resonator and Žb. with acoustic transmission line L4 l.
oscillator is determined by the speed of sound c is . With Eq. Ž1. the eigenfrequency fe only depends on the concentrations x i of the gas mixture, i.e. feŽ x i . s G 1 cisŽ x i .. Gi is an oscillator constant. Commonly available transducers are narrow-band. Then the oscillator eigenfrequency fe is additionally determined by the frequency response function of the transducers. This can cause measurement errors and must be corrected electronically. For generating a sound impulse in an acoustic transmission line of length L 4 l ŽFig. 3b., a generator supplies an electric-acoustic transducer with a short electric wave packet. The transducer is connected with the line. The airborne acoustic impulse from the transducer passes a wide line during the transition time t s Lrcis or a narrow line in t s Lrcai . A second transducer at the other end of the line receives the acoustic impulse. Now, the incoming impulse is used either for triggering a new impulse at the sending transducer Žsing-around method. or for generating an acoustic response impulse from the transducer that was just the receiver Žping-pong method.. In both cases the impulse frequency f i depends on transition time t , i.e. f i Ž x i . s G 2 c isŽ x i .. Electric-acoustic gas sensors do not need a stabilised supply of pressure for generating sound. This is a general advantage. Moreover, in the wide pressure range where the measuring gas behaves like an ideal gas, the measuring result does not depend on the gas pressure w2x. The electrical stimulation of sound can be carried out with high amplitude accuracy. On condition that the influence of the transducers on the frequency response function of the transmission line is negligibly small, it is basically possible to determine not only the transition time t , but simultaneously the attenuation of sound corresponding to Eq. Ž6.. By implementing in the same sensor a wide and a narrow transmission line, two transition times t is and tai can be measured. So, for analysing a gas mixture, two or even
3.2. Fluidic-acoustic gas sensors In case of fluidic stimulation of an acoustic wave, a jet of the gas mixture to be analysed is the source of sound energy. For generating a standing acoustic wave in a lr2-resonator ŽFig. 4a., the jet is guided against a sharp edge where it produces edge tones of different frequencies. Subsequently, the gas mixture flows through the resonator, which is arranged adjacent to the edge. This resonator amplifies by interference only that frequency f, which corresponds to its eigenfrequency fe . Because the resonator length L s nŽ lr2 is constant, the eigenfrequency fe varies with the speed of sound c s l fe and according to Eqs. Ž1. or Ž2. with the mass concentrations x i , i.e. fe s feŽ x i .. For generating an acoustic impulse sequence in a transmission line ŽFig. 4b., the jet passes through a bistable
Fig. 4. Basic configuration of a fluidic-acoustic oscillator Ža. with l r2resonator and Žb. with acoustic transmission line L4 l.
L. Zipser et al.r Sensors and Actuators B 68 (2000) 162–167
fluidic amplifier with a feedback tube representing the transmission line. Basing on the Coanda effect, the jet produces a pressure impulse in one output channel. The feedback tube transmits this impulse to the amplifier input and switches the jet to the other output. This cycle is repeated continuously. At the amplifier outputs originates an impulse frequency f i . The acoustic impulse propagates the feedback tubes with the speed of sound c is . Due to Eqs. Ž1. or Ž2. for the impulse frequency follows f i s f i Ž x i .. For transducing the acoustic frequencies f into electric signals, piezo-electric transducers are commonly used. Fluidic-acoustic oscillators produce very strong signals. Therefore, the temperature-sensitive transducers can be placed in a wide distance apart from the oscillators, coupled by an acoustic transmission line. As a consequence, the oscillators can be made of a temperature-resistant material, which allows for high working temperatures. In experiments gas sensors made of aluminium were operated at up to 3508C. Temperature correction is also very simple by using a reference oscillator Žsee example.. Furthermore, the sensors can also be exposed to strong vibrations. The response time of fluidic-acoustic gas sensors is very short, because the measuring gas is sucked through the oscillator by an ejector. Response times T90 F 50 ms were measured. The vibration behaviour of fluidic oscillators is not influenced by vibrating mechanical parts. Hence, a wide uninfluenced frequency range D f can be used as a measuring range D f Ž x i max y x i min .. Disadvantageous is the need for a stabilised pressure difference between inlet and outlet of the oscillator. Pressure variations in the measuring gas can change the oscillator frequency. With fluidic-acoustic gas sensors it is not possible to measure reliably the sound attenuation corresponding to Eq. Ž6..
3.2.1. Example: fluidic-acoustic humidity sensor Fig. 5 shows the exploded view of a fluidic-acoustic humidity sensor for harsh applications. The sensor is mainly used for humidity control in the exhaust gas of industrial textile dryers. This exhaust gas has a temperature of 130–2508C and is loaded with dust, fibres and high-molecular vapours. The identical structures of the measuring oscillator Žindex m. and the reference oscillator Žindex r. are precisely milled in a thin plane plate. These oscillator plates are bounded on both sides with other plates, which contain the transit ducts for the gas mixture and the acoustic-electric transducers for transforming the pressure wave in the lr2-resonator into an electric signal. To be exact, the oscillator frequency f o depends not only on the length of the lr2-resonator and on the speed of sound c is , but also on the supply pressure D p s pout y p in of the oscillator: f o Ž Cis ,D p . s GB Ž D p . Ci .
Ž 7.
165
Fig. 5. Planar fluidic-acoustic humidity sensor.
The function B Ž D p . describes the influence of the supply pressure D p. G is the oscillator constant, summing up the geometry of the resonator and the jet-wedge configuration. For using a fluidic-acoustic oscillator as a gas sensor, the following problems have to be solved: Ø The function B Ž D p . should be approximately 1. Ø Disturbing fluctuations of the sound speed c is , caused by variations of the gas temperature T according to Eq. Ž1., must be corrected. Ø Supplying the oscillator with polluted gas mixtures for a long time can change the geometry of the oscillator and, in consequence, the constant G by sediments inside the resonator. These alterations must be eliminated or corrected to guarantee long-time stability of the gas sensor. We solved this problem with the aid of an automatic zero-point control. Ø Acoustic waves from the lr2-resonators must be transformed reliably into electric signals even under extreme process conditions. To realise the demand B Ž D p . f 1, special configurations of the oscillator geometry were developed w1x. For solving the problems of temperature correction and of stabilisation of the oscillator constant G, the reference principle can be used, i.e. the gas sensor is made of two identical fluidic-acoustic oscillators Žsee Figs. 5 and 6.. The first oscillator Žmeasuring oscillator. is supplied with the measuring gas. The second oscillator Žreference oscillator. is supplied with a reference gas, e.g. dry air. An ejector pump sucks a continuous gas flow through both oscillators. These are in close contact and hence thermally coupled. Consequently, the measuring gas and the refer-
L. Zipser et al.r Sensors and Actuators B 68 (2000) 162–167
166
ence gas have the same temperature T. In this case, with Eq. Ž1. and k s CprC v , the quotient Q of both frequencies does not depend on the temperature T : Qs
fm fr
s
Gm Gr
(
k m Ž x 1 . Mr Mm Ž x . k r
.
Ž 8.
In this way, fluidic-acoustic oscillators can be used for measuring the speed of sound c is at variable temperatures. Now it is assumed that the measuring gas consists of two qualitatively known components K 1 Žwater vapour. and K 2 Žair.. Dry air from the pressure supply is usually used as reference gas. Then the parameters M and k of both gases are well known. According to Eq. Ž8., the quotient Q depends on the concentrations x 1 and x 2 and on Gm and Gr . The instabilities of Gm and Gr can be eliminated in two steps by a zero-point control. The first step is the adjustment of the zero point. Both oscillators are supplied with the same gas, e.g. with dry air. Then according to Eq. Ž1. the speed of sound in both resonators is identically c isŽm. s c isŽr. . In this ideal case, i.e. for identical oscillators, follows Gm s Gr and fm Gm Qideal s s s 1. Ž 9. fr Gr In real cases the oscillator constants differ from each other, i.e. Gm / Gr and the quotient is fm DG Qreal s s 1 q s Q ideal q DQ Ž DG . . Ž 10 . fr Gr The small deviation < DQ Ž DG .< < 1 corresponds to the zero-point deviation of the static characteristic of the acoustic humidity sensor.
Fig. 7. Calibration characteristic of the humidity sensor at 1058C.
The second step is the correction of the zero point during measurements. The measuring oscillator is supplied with the measuring gas Žwet air.. The reference oscillator is supplied with dry air. Then, in the real case, the resulting quotient Q is a function of the concentration x 1 , i.e. of the humidity, and of the asymmetry of the oscillator constants DG: Q real s Ž x 1 ,DG . s Qideal Ž x 1 . q DQ Ž DG . .
Ž 11 .
The asymmetric term is known and can be corrected electronically. Now, with Eqs. Ž1. and Ž11. the concentration x 1 can be determined from the corrected value QidealŽ x 1 .. If the described reference conditions are strictly fulfilled, the influence of sensor properties is substantially eliminated. Consequently, the measuring results do not depend on individual sensor properties and we have an absolute method of humidity measurement. The calibration characteristic of the humidity sensor can therefore be calculated by using Eqs. Ž1., Ž7. and Ž10.. An experimental calibration is also possible, but requires a precisely working humidity generator for high temperature. Fig. 7 shows the calculated and the experimentally determined calibration characteristic. Both characteristics are in good agreement. The measuring accuracy under process conditions is about "3%. The detection limit for humidity measurements is 1g water vapour per kg wet air.
4. Conclusions
Fig. 6. Structure of the fluidic-acoustic humidity sensor.
The presented acoustic gas sensors can be used for the industrial online analysis of binary gas mixtures. In general, two types of acoustic gas sensors can be distinguished: fluidic-acoustic and electric-acoustic. The first type is usable even under extreme measuring conditions Žhigh temperature, contamination, aggressive media . . . ., but for operation as power supply it needs a stabilised pressure difference between sensor inlet and outlet. Electric-acoustic gas sensors are in a wide range insensitive to pressure variations in the measuring gas. They do not need
L. Zipser et al.r Sensors and Actuators B 68 (2000) 162–167
a supply pressure, but are more susceptible to high temperature, needs a precise temperature compensation and have a longer response time.
Acknowledgements
167
w6x L. Zipser, F. Wachter, Acoustic sensor for ternary gas analysis, ¨ Sensors and Actuators, B 26–27 Ž1995. 195–198. w7x L. Zipser, H. Franke, Acoustic sensor for aerosol measurements, Proc. IEEE Ultrasonics Symp. 1998 Oct.5–8, Sendai, Japan 1 Ž1998. 517–519. w8x B. Hok, J. Lofving, Acoustic Gas Sensor with ppm ¨ A. Bluckert, ¨ ¨ Resolution, EUROSENSORS XIII, Book of Abstracts, pp. 319–320.
The research on this topic was sponsored by the Deutsche Forschungsgemeinschaft DFG. Biographies References w1x L. Zipser, Fluidic-acoustic gas sensors, Sensors and Actuators, B 7 Ž1992. 592–595. w2x N. Elsner, Grundlagen der Technischen Thermodynamik, AkademieVerlag, Berlin, 1973. w3x F. Wachter, On ambiguous speed of sound in binary gas mixtures, ¨ Proc. World Conference Ultrasonic WCU97, Aug. 24–27 1997, Yokohama, Japan Ž1997. 28–229. w4x J.M. Kirshner, S. Katz, Design Theory of Fluidic Components, Academy Press, New York, 1975. w5x M.H. Schaedel, Fluidische Bauelemente und Netzwerke, Verlag Friedrich Vieweg & Sohn, Braunschweig, 1979.
Lothar Zipser studied electrotechnics at the Technical University, Dresden. He received his PhD degree in information theory in 1976 and his habilitation in fluid-acoustics in 1986. Since 1993 he has been working as a professor at the HTW, University of Applied Sciences, Dresden. Friedmar Wachter studied physics at the Technical University, Dresden. ¨ He received his PhD degree in mathematical cybernetics in 1986. Since 1996 he has been working as a professor at the HTW, University of Applied Sciences, Dresden. Heinz Franke studied physics at the Technical University, Dresden. He worked many years as a physicist in the computing industry. Since 1994 he has been involved in several projects concerning acoustic sensors and vibration analysis at the HTW, University of Applied Sciences, Dresden.