SPEED OF SOUND MEASUREMENTS IN GAS-MIXTURES AT VARYING COMPOSITION USING AN ULTRASONIC GAS FLOW METER WITH SILICON BASED TRANSDUCERS Torbjör Löfqvist, Kęstutis Sokas, Jerker Delsig EISLAB, Departmet of Computer Sciece ad Electrical Egieerig Luleå Uiversity of Techology, Luleå, Swede This paper cocers speed of soud measuremets performed i three differet gas mixtures at costat temperature ad pressure while the cocetratio of the gases was varied. The performed experimets used a ultrasoic, sig-aroud, gas flow meter equipped with silico based trasducers. The ceter frequecy of the trasducers was 800 khz. Speed of soud was measured i moo-, di- ad triatomic gases: argo (Ar), oxyge (O ) ad carbo dioxide (CO ), i either air or itroge (N ) as a backgroud gas. The gas uder ivestigatio was mixed with the backgroud gas i a test chamber ad the cocetratio of the gas uder examiatio was varied betwee 0% ad 100%. A gas chromatograph was used i order to accurately determie the compositio of the gas mixture. The experimets show that measured speed of soud, as a fuctio of gas compositio, agrees with the speed of soud obtaied from theory. The achieved data also show that the speed of soud measuremets was performed with low stadard deviatio. Thus, oe ca coclude that this type of ultrasoic gas flow meter is well suited i determiig gas cocetratio i a biary gas mixture as well as flow velocity. The techique could be of value i both idustrial ad medical applicatios. Itroductio A regular ultrasoic trasit-time flow meter has the iheret capability of performig simultaeous measuremets of both flow velocity ad speed of soud i the medium flowig through the meter. The speed of soud i a gas depeds o the compositio of the gas as well as o its temperature ad pressure. By usig the speed of soud iformatio from the flow meter, it is potetially possible to determie the compositio of the gas flowig through the meter. The problem of determiig the gas compositio i a gas mixture by acoustic methods has bee a field of research for decades. Various techiques has bee iveted ad ivestigated, like e.g. phase shift methods, acoustic iterferometry methods ad pulse techiques. I the pulse techique, the propagatio time is measured for a pulse set by oe trasducer to a secod trasducer at a fixed distace. From that, the speed of soud i ca be determied. This techique has successfully bee used i biary gas compositio measuremets by Hallewell et.al. [1], Joos [] ad others. The problem of determiig gas compositio by acoustic methods has recetly bee addressed by Dai & Lueptow [3], [4] who used ultrasoic spectroscopy i determiig the compositio of three-gas mixtures. The method used, utilizes the spectral cotet of the ultrasoic pulse paired with molecular vibratio relaxatio time modelig of the gas mixture, a rewardig but quite complex techique. I this paper, we explore the possibilities of usig a regular, trasit-time, ultrasoic flow meter uder atmospheric pressure ad room temperature i determiig the compositio of a biary gas mixture. Theory Classically, the speed of soud i a ideal gas could writte as c 0 = (γr 0 T/M) 1/. Now, if we cosider a mixture of ideal gases, the expressio above could be rewritte. By assumig that the specific heat ratio γ is writte as the mole weighted specific heat ratio for the mixture ad that the molecular weight of the mix M is the mole fractio weighted sum of the mole weights of the costituets as
ad = i i xicpi γ (1) xicvi M = x i M i () i I (1) above, C vi is the specific heat at costat volume ad C vi = C pi - R 0. Usig (1) ad () i the equatio for the speed of soud we arrive at xicpi c 1 0 = R0T i= (3) ximi xi ( Cpi R0 ) i= 1 i= 1 where R 0 is the uiversal gas costat, T the absolute temperature, x i the mole fractio of the i:th compoet, M i the molecular weight ad C pi the heat capacity at costat pressure. I the experimetal setup used i this study, temperature ad gas cocetratio, i.e. mole fractio, is simultaeously measured. The speed of soud i the gas mixture is the determied by equatio (3). Experimetal method ad materials The meter used i the experimets preseted i this study is a ultrasoic gas flow meter equipped with silico-based ultrasoud trasducers, which have a ceter frequecy of 800 khz. The flow meter uses the well-kow sig-aroud techique ad detailed descriptios of the techique could be foud i e.g. Lyworth [5]. For the meter, oe ca derive a equatio for the speed of soud i the air flowig through the meter based o the up- ad dow-stream propagatio times for the ultrasoic pulses, i.e. L 1 1 c = +, (4) t1 t where c is the speed of soud, L is the distace betwee the trasducers ad t 1 ad t are the up ad dow-stream propagatio times. A geeral error propagatio aalysis, Colema ad Steele [6], is performed o (4). We the obtai the ucertaity limits o c from the followig expressio. 1 / 3, 1 c δ c = δξ i (5) i = ξ i where δ c is the ucertaity limit o speed of soud. ξ i represets the i:th variable ad δξ i is its ucertaity limit. The same type of ucertaity aalysis is also performed for the speed of soud, equatio (3). The ucertaities for the differet parameters are show i table. The ucertaity limit rage for the speed of soud obtaied from the flow meter is foud to be δ c = 0.54 0.57 m/s, or ~ 0.16 %, at 95% cofidece level. The most sigificat source of error for δ c is foud to be the ucertaity i the distace betwee the trasducers. The stadard deviatio o speed of
soud values obtaied from the flow meter is foud to be of at least oe order of magitude smaller tha the ucertaity stemmig from the distace betwee the trasducers. Variable Value Ucertaity δψ i L 61,4 mm ± 0,1mm t 1, t ~ 0,178 10-3 ms ± 3,3 10-8 sec T ~ 0 ºC ± 0.5 ºC TABLE 1. Ucertaity values for the ultrasoic gas flow meter ad equatio (3). From the ucertaity aalysis of equatio (3) we fid that the ucertaity limit δ c0 = 0.59 0.14 m/s or ~ 0.16 0.04 %. The sources of ucertaity for the ucertaity limit δ c0 are temperature ad mole fractio values but the oly source of ucertaity cosidered i this study is temperature. The ucertaity limit δ c0 could be reduced cosiderably by usig a temperature sesor with better precisio tha the thermometer used i this study. Three gases were ivestigated at room temperature ad atmospheric pressure. Argo (Ar) ad oxyge (O ) were mixed with itroge (N ) as a backgroud gas ad their mole fractios raged from 0% to 100%. Carbo dioxide (CO ) was mixed with air as a backgroud gas ad the carbo dioxide mole fractio raged from 0.07% to 3.148%. All the experimets were performed i the temperature rage betwee 19 C to 0 C. Values o the specific heat for each gas at costat pressure was calculated for differet temperatures usig empirical relatios from Mora & Shapiro [7]. Backgroud gas Gas mixed with backgroud gas Rage of mixig. Mole fractio [%] Air CO 0.07 3.148 N O 0 100 N Ar 0 100 TABLE. Backgroud gases ad the gases they are mixed with. The backgroud gas is mixed with a icreasig amout of the mixig gas durig the course of the experimet. All gases used i the experimets were of laboratory grade. For the measuremets of speed of soud i the gases metioed above, a custom made chamber of Plexiglas was used. The chamber was equipped with a ilet for the gas uder ivestigatio, a outlet where samples of the gas mixture were draw ad two water locked outlets. This eables the pressure i the chamber to be kept costat ad very close to the ambiet atmospheric pressure. The sample outlet was coected to a gas chromatograph that aalysed the compositio of the gas mixture i the chamber. The flow meter was mouted o the iside of the chamber lid, which sealed hermetically to the chamber body. A small fa was placed i the chamber i order to create flow through the flow meter as well as mix the gas uder ivestigatio with the backgroud gas. The temperature of the gas mixture was moitored usig a thermometer that was placed iside the chamber. The chamber was iitially filled with the backgroud gas. The gas uder ivestigatio was durig the experimet allowed to eter the chamber at a very low flow rate ad to be mixed with the backgroud gas. A gas chromatograph, a Varia Chrompack Micro GC CP-003P, was used i performig the aalysis of gas samples that were take from the gas chamber. Before each experimet, the gas chromatograph was calibrated usig calibratio gases. Durig the experimets, the gas chromatograph ad the gas flow meter recorded cocurret measuremets every third miute o gas compositio, flow velocity ad speed of soud.
Discussio of results The figures 1 to 3 show the speed of soud as a fuctio of gas cocetratio, or mole fractio. Both experimetal ad theoretical values o the speed of soud i the gas mixtures are plotted. It is see that the experimetally obtaied values agree well with the values obtaied from calculatios usig equatio (3). Oe ca also observe that the experimetally obtaied speed of soud for the ivestigated gases argo, oxyge ad carbo dioxide at 100% cocetratio correspods well to literature data o speed of soud at room temperature ad atmospheric pressure, see Kaye & Laby [8], Lide [9]. 350 Experimetal 345 335 330 35 30 315 0 10 0 30 40 50 60 70 80 90 100 Ar i N mole fractio [%] FIGURE 1. Speed of soud i itroge (N ) - argo (Ar) mix as a fuctio of argo cocetratio. The lie represets speed of soud calculated from equatio (3) ad the circles represet experimetal data. The temperature is 19.5 ± 0.5 ºC. 350 Experimetal 345 335 330 35 30 0 10 0 30 40 50 60 70 80 90 100 O i N mole fractio [%] FIGURE. Speed of soud i itroge (N ) oxyge (O ) mix as a fuctio of oxyge cocetratio. The lie represets speed of soud calculated from equatio (3) ad the circles represet experimetal data. The temperature is 19.3 ± 0.5 C.
343 Experimetal 34.5 34 341.5 341.5 339.5 0 0.5 1 1.5.5 3 3.5 CO i air, mole fractio [%] FIGURE 3. Speed of soud i air carbo dioxide (CO ) mix as a fuctio of carbo dioxide cocetratio. The lie represets speed of soud calculated from equatio (3) ad the circles represet experimetal data. The temperature is 19. ± 0.5 C. Coclusio Speed of soud was measured i moo-, di- ad triatomic gases; argo (Ar), oxyge (O ) ad carbo dioxide (CO ) mixed with i either air or itroge. It was foud that the measured speed of soud show good agreemet with data obtaied from theory. It is cocluded that by simultaeous measuremets of temperature ad speed of soud, the ultrasoic flow meter could be applied i determiig the mole fractio of the costituets i flowig biary gas mixtures. The largest sources of ucertaity are foud to be the temperature measuremet of the gas ad the measuremet of the distace betwee the two trasducers i the flow meter. Employig a more precise temperature measuremet ad a better calibratio procedure for the meter are essetial to reduce these ucertaities. The ivestigated measuremet techique could be of value i applicatios where flow ad mixig ratio of gases are importat, for istace, i moitorig of gas combustio processes or breathig-air moitorig for aaesthetics or other medical purposes. Refereces [1] Hallewell G., Crawford G., McShurly D., Oxoby G., Reif R., A Soar Based Techique for the Ratiometric Determiatio of Biary Gas Mixtures, Nuclear Istrumets ad Methods i Physics Research, A64:19-34, 1988. [] Joos R.N., Muller H., Lider G., A Ultrasoic Sesor for the Aalysis of Biary Gas Mixtures, Sesors ad Actuators B, 15-16:413-419, 1993. [3] Dai Y., Lueptow R.M., Acoustic Atteuatio i a Three-Gas Mixture: Theory, J. Acoust. Soc. Am., 109 (5), 001. [4] Dai Y., Lueptow R.M., Acoustic Atteuatio i a Three-Gas Mixture: Results, J. Acoust. Soc. Am., 110 (6), 001. [5] Lyworth L.C., Ultrasoic measuremets for process cotrol theory, techiques, applicatios, Academic Press, 1989. [6] Colema H.W., Steele W.G., Experimetatio ad ucertaity aalysis for egieers. d ed., Joh Wiley & Sos, 1999. [7] Mora J.M., Shapiro H.N., Fudametals of egieerig thermodyamics, d ed., J. Wiley & Sos, New York, USA, 1993. [8] Kaye G.W.C., Laby T.H., Tables of physical ad chemical costats (16 th editio), Essex, Great Britai, 1995. [9] Lide D.R., CRC Hadbook of chemistry ad physics (81 st editio), Boca Rato, Florida, USA: CRC Press, Ic., 001.