THE PERFORMANCE OF TRANSIT TIME FLOWMETERS IN HEATED GAS MIXTURES

Transcription

1 Proeedings of FEDSM ASME Fluids Engineering Division Summer Meeting June 2-25, 998 Washington DC FEDSM THE PERFORMANCE OF TRANSIT TIME FLOWMETERS IN HEATED GAS MIXTURES John D. Wright Proess Measurement Division Chemial Siene and Tehnology Laboratory National Institute of Standards and Tehnology Gaithersburg, Maryland USA ABSTRACT An ultrasoni transit time flowmeter was tested over Reynolds numbers from to in a alibration faility that generates gas flows with ontrolled temperature and omposition. The gas mixtures were omposed of air, nitrogen, arbon dioxide, water vapor, and argon, and the mixture temperature ranged from 29 K to 45 K. The test program was onduted to determine the sensitivity of the flowmeter output to gas omposition and temperature and to find the appropriate dimensionless quantities for the presentation of alibration results. Plots of disharge oeffiient versus Reynolds number ollapse the data well for all of the onditions tested. Comparisons between the experimentally measured disharge oeffiients and those predited by omputer models using postulated veloity profiles are presented, and they show good qualitative agreement. The effets of thermal expansion on sound path length and pipe diameter were signifiant over the tested temperature range. NOMENCLATURE A Cross setional area of pipe Sound speed Disharge oeffiient C d k T Path length thermal orretion m Referene mass flow t up, t dn Transit times up and downstream V Path mean veloity (of the fluid) V B Bulk mean veloity (of the fluid) Length of the sound path Angle of sound path Gas density Thermal expansion oeffiient subsripts and supersripts H Handbook value m Meter value Referene temperature ondition T Atual temperature ondition INTRODUCTION In reent years, ultrasoni transit time flowmeters designed for use in gas flows have beome ommerially available. These meters have good auray, do not obstrut the flow (or lead to any signifiant pressure losses), and have a wide flow rangeability ( to or more). Transit time flowmeters are good andidates for the measurement of gas mixtures that vary in temperature and omposition, suh as vehile exhaust, the exhaust from furnaes, or humid air. PRINCIPLE OF OPERATION An ultrasoni transit time flowmeter uses two ultrasoni transduers to transmit sound pulses alternately upstream and downstream through the flow (Lynnworth, 989, Brown, 99). The times required for the sound to travel in the opposite diretions an be used to alulate both the sound speed and the mean fluid veloity along the path followed by the sound ( path mean veloity ). The aousti transduers are generally positioned flush with the inner surfae of the pipe wall and at an angle to the pipe axis (). The refletive Copyright 998 by ASME

2 5 Figure. The arrangement of ultrasoni, pressure, and temperature sensors in the tested transit time flowmeter. arrangement used in the present test is shown in Fig.. For the transit time flowmeter, assuming only axial veloity omponents, the governing equations are: V, () 2 os( ) tdn tup. (2) 2 tdn tup The path mean veloity (V ) may be multiplied by a disharge oeffiient (C d ) to obtain a value for the bulk mean veloity (V B ), V C V. (3) B d The value of the disharge oeffiient varies with flow due to hanges in the veloity profile shape, but often, meter manufaturers hoose a range of flows over whih the meter is designed to operate and assume that the disharge oeffiient is a onstant over this range. The hanges in veloity profile shape whih ause variation in the disharge oeffiient and also the transition from laminar to turbulent flow are funtions of the Reynolds number. Based on the understanding of the influene quantities for a transit time flowmeter and dimensional analysis, a plot of disharge oeffiient versus Reynolds number is an appropriate way to present alibration data. This method of presentation should ollapse the 5 Bogue-Metzner Log Power law Gilmont Laminar Figure 2. Transit time flowmeter disharge oeffiients versus Reynolds number for various analytial veloity profile funtions. alibration data from various operating onditions to a single alibration urve, and is the most robust and onvenient approah for prediting the neessary disharge oeffiient for some new, untested operating ondition. Yeh and Mattingly (997), Lynnworth (989), and Brown (99) have postulated ertain analytial veloity profile funtions available in the literature and omputed preditions of the effets of Reynolds number on the disharge oeffiient of a single path transit time flowmeter. A version of suh a predition is presented in Fig. 2. Disharge urves for the Bogue and Metzner (963) profile, log funtion profile, power law, and Gilmont (996) profile are shown. The paraboli veloity profile from Poiseuille flow gives a onstant disharge oeffiient of for laminar flow (Re < 2). For 2 < Re < 3 (the transition region) the flow is intermittently laminar and turbulent and the available analytial veloity profile funtions are not deemed reliable for disharge oeffiient preditions. One motivation for the experimental study of the transit time flowmeter in heated gas mixtures was to validate, over a wide range of onditions, that Re and C d are appropriate quantities for the presentation and extrapolation of meter alibration data. Further goals were to shed light on the behavior of the disharge oeffiient in the transition region and to asertain whih analytial profile funtions are best suited for disharge oeffiient preditions, partiularly at Reynolds numbers below 3 where the differenes between the analytial funtions are most pronouned. 2 Copyright 998 by ASME

3 EXPERIMENT DESCRIPTION A transit time flowmeter with high temperature ultrasoni transduers operating at 5 MHz was installed in a horizontal flow tube. The sound was refleted off the far wall of the pipe between the transduers with a 45 path. The inside diameter of the 36 stainless steel flow tube was 7.74 m, and the flow tube was 49 m long. For most of the tests, the meter was oriented so that the sound path fell in a vertial plane (transduers on top of the flow tube). A pressure tap was loated on the side wall at the flowmeter enterline (i.e., half way between the two transduers, see Fig. ). A temperature tap was loated 2 m downstream from the flowmeter enterline, and a resistane temperature devie (RTD) was inserted into the flow tube. The outlet of the flow tube disharged to the room whih was maintained at 292 K 2 K. Two more RTD s were inserted into the flow tube exit so that they were 4.7 m downstream from the flowmeter enterline (see Fig. ). One of these RTD s was.4 m from the rown of the flow tube while the other was.4 m from the bottom. These two RTD s permitted the measurement of temperature differenes between the top and bottom of the flow. The flow tube was wrapped with 2.5 m thik fiberglass insulation. Upstream from the flow tube was an approah pipe of the same inside diameter, 6 pipe diameters long, and the joint onneting the flow tube and approah pipe was smooth. The approah pipe was heated and insulated. A proportional-integral-derivative ontroller with the set point equal to the temperature of the flowing gas set point was used to ontrol the approah pipe heaters. The known flows were generated with the NIST Heated Gas Mixture Flow Faility (HGMFF). The details of the faility design and an unertainty analysis of the mass flow measurement have been desribed in an earlier publiation (Wright and Espina, 997). The faility meters pure air, nitrogen, arbon dioxide, and argon with ritial flow nozzles that have been alibrated using established NIST gas flow standards (piston and bell provers). Water vapor is added in a saturator vessel and the mass flow of water is alulated from a dew point temperature measurement. The metered gas mixture an be heated by an eletri irulation heater to temperatures between 292 K and 7 K. The flow range of the faility is nominally (6 to 6) standard L / min (slm) for air and (6 to 2) slm for simulated exhaust mixtures. The set point onditions established for the flowmeter test were designed to over a wide range of flows and gas properties (i.e., density, visosity, and omposition). The flow set points were: (8, 4, 28, 43, 56,, 7, 23, 28, 35, 42, and 5) slm. The temperature and omposition onditions were: () humid air (2 % 2 H 2 O and 88 % air) at 394 K, (2) simulated exhaust (3.5 % CO 2, 2 % H 2 O, % Ar, and 73.6 % N 2 ) at 394 K, (3) dry air at 444 K, (4) dry air at 394 K, (5) dry air at 344 K, and (6) dry air at 292 K. After eah set point hange, onditions were allowed to stabilize for 5 minutes or more before data olletion ommened. For eah test, two sets of five, thirty seond averages were olleted at eah flow set point, yling through the flows in dereasing, then inreasing order. UNCERTAINTY OF THE BULK MEAN VELOCITY For the transit time flowmeter evaluation, it was neessary to alulate the bulk mean veloity of the flow at the meter test setion, via the following equation, V B m. (4) A The HGMFF measures mass flow with a relative expanded unertainty of % of reading or less (Wright and Espina, 997). 3 Unertainty in the pipe ross setional area was less than. % with the thermal expansion orretions desribed in the following setion. The unertainty of the density an be traed to the equation of state, as well as the pressure and temperature measurements made at the test setion. The pressure measurements have an expanded unertainty of.2 % and the expanded unertainty in the alibration of the RTD s is.3 %. The average temperature of the flow was alulated by an area weighted quadrature formula using the three RTD s installed at the top, middle, and bottom of the pipe. Temperature stratifiation leads to greater unertainty in the average temperature measurement for lower flows and higher temperature set points. A plot of the unertainty of the volumetri flows used as the standard, refleting the greater average temperature unertainties for the high temperature tests is given in Fig. 3. The relative expanded unertainties are nominally % exept at the lowest three flows, where temperature stratifiation leads to V B relative expanded unertainty as high as 3.4 % for the 444 K test. The unertainties at room temperature are smallest and remain about.7 % even at the lowest flows (no stratifiation). THERMAL EXPANSION Changes in the pipe area due to thermal expansion were taken into aount using 5 6 m / (m K) and 2 2 A 2 T T. Over the 5 K temperature hange of the tests, thermal expansion results in ross setional area (and mean veloity) hanges of.45 %. Standard onditions are K and 325 Pa. 2 Volume or mole fration. 3 All unertainties are 95 % onfidene level values, overage fator k = 2, Taylor and Kuyatt (994). 3 Copyright 998 by ASME

4 3.5 Unertainty (%) Flow (standard L / min) Humid Air 394 K Exhaust 394 K Air 444 K Air 394 K Air 344 K Air 292 K Figure 3. Unertainty of the bulk mean veloity values used as the referene values of the tests. 5 5 Bogue-Metzner Log Power law Gilmont Dry Air 292 K Laminar Figure 4. Disharge oeffiient for analytial profile funtions along with the 292 K experimental results. Unfortunately, preditions of the effets of thermal expansion on the aousti path length,, are not as straightforward as the flow tube area orretions. A thermal orretion would involve at least three different thermal expansion oeffiients (the flow tube material, the sensor support materials, and the transduer materials) as well as temperature measurements at different loations in the assembly. A different design ould alleviate the diffiulties, but it is also possible to alibrate out the effets of temperature hanges on the path length. Meter measurements of sound speed were gathered at eah set point temperature (after the entire system had reahed thermal equilibrium). The test was arried out at the highest flow set point where good measurements of the gas temperature an be made (stratifiation is negligible). The sound speed values alulated by the meter using a onstant path length were ompared to handbook values for the sound speed at the measured temperature (Hilsenrath et al., 955). The handbook and meter sound speeds an be used to form a fator, k T, whih orrets for the effets of thermal expansion on the path length as a funtion of temperature. k T T H T m Suh a orretion was applied to all of the flowmeter data olleted and it was as large as % for the 5 K temperature hange. H m (5) RESULTS AND DISCUSSION Figure 4 presents the 292 K experimental data along with the C d preditions from analytial profile funtions. The Gilmont profile mathes the experimental data best, partiularly for the low Reynolds number onditions. The worst disagreement between the Gilmont preditions and the experimental values is 6 % at Re = 4. Figures 5 and 6 show semi-log plots for all of the test onditions in dimensional and non-dimensional forms. (Points at flows < liters / min have been removed from Fig. 5 for saling onveniene). From these figures it is lear that the disharge oeffiient and Reynolds number effetively ollapse the alibration data for a wide range of flow onditions. The plots show the individual 3 seond averages, so there are points at eah test ondition. For Re > 4, Reynolds number saling redues the data satter by a fator of two. In Fig. 6, one an see that for Re between 5 and, the 292 K data has muh less satter than the heated data points ( % vs. 3 %). However, the two 292 K data sets at Re of 5 and 25 show satter of over 5 %, due to transition or the laminar profile shape hanging over time. The heated tests show greater satter than the room temperature data due to unsteady temperature and veloity profiles aused by temperature stratifiation in the flow. As the Reynolds number falls below,, mixing within the flow drops, and buoyany leads to higher temperatures at the top of the pipe than at the bottom. Temperature stratifiation ours one the Reynolds number is low enough that buoyany fores are signifiant when ompared to the axial inertial fores of the flow. Buoyany fores lead to distortion of the veloity profile as well. 4 Copyright 998 by ASME

5 5 5 Humid Air 394 K Exhaust 394 K Dry Air 444 K Dry Air 394 K Dry Air 344 K Dry Air 292 K Volumetri Flow (atual liters / min) Figure 5. Semi-log plot of dimensional results: disharge oeffiient versus flow for all test onditions. 5 5 Humid Air 394 K Exhaust 394 K Dry Air 444 K Dry Air 394 K Dry Air 344 K Dry Air 292 K Figure 6. Semi-log plot of non-dimensional results: disharge oeffiient versus Reynolds number for all test onditions. 5 Copyright 998 by ASME

6 6 5 5 Dry Air 394 K (Horizontal) Dry Air 394 K (Vertial) Dry Air 292 K (Horizontal) Dry Air 292 K (Vertial) Figure K and 394 K results for horizontal and vertial sound path orientations. One the Reynolds number passes through transition to the laminar flow regime, the mixing drops further and temperature stratifiation beomes even more extreme. For the heated tests, at these lowest Reynolds numbers, the veloity profile is asymmetrial and C d departs dramatially from the preditions omputed for the ideal analytial profiles as well as the 292 K results. To prove that profile distortion was the ause of the C d departure for Re < 4, the meter was rotated 9 so that the sound path fell in the horizontal plane (instead of the vertial plane). While the 292 K behavior was nominally the same for both meter orientations, data at 394 K data showed muh higher disharge oeffiients for Re < (Fig. 7), demonstrating that the 292 K profile is essentially axisymmetri, while the 394 K profile is not. Figure 8 presents the temperature stratifiation measured by the three RTD s positioned at the top, middle, and bottom of the pipe for various Reynolds numbers at the three heated temperature set points. The stratifiation data is given as the differene between the top and bottom RTD s as a perent of the average temperature at the test setion. As expeted, stratifiation inreases with the temperature set point. The stratifiation was partiularly great for the two lowest Reynolds numbers tested ( and 9) sine the mixing within the laminar flow is low. The figure shows that for the 444 K test at Re =, the temperature stratifiation was 6 %. Time traes of the temperature data have been examined for the heated tests, and it an be seen that in some ases the temperature profile did not reah equilibrium after more than 3 minutes. Clearly the temperature stratifiation and the orresponding veloity profile distortions reah steady state very slowly. Temp. Stratifiation (%) T = 344 K T = 394 K T = 444 K Figure 8. Temperature stratifiation (as a perent of the average temperature at the test setion) versus Reynolds number for the three heated test onditions. CONCLUSIONS A transit time flowmeter has been tested over a wide range of gas property onditions. Transit time flowmeters are suitable for appliation in hot gas mixtures. However, the effets of profile shape and thermal expansion must be onsidered. In these experiments, it has been shown that the disharge oeffiient and Reynolds number effetively ollapse transit time flowmeter alibration data. Therefore, the disharge oeffiient and Reynolds number an be used to orret for the effets of profile shape on meter output for a partiular meter piping arrangement. Using the dimensionless quantities improves the satter in the alibration data sets by a fator of two. Applying a disharge oeffiient that is a funtion of Reynolds number would improve transit time flowmeter auray, partiularly at Reynolds numbers below 3, where the hange in C d with respet to Re is relatively large. If the gas omposition is known, the flowmeter measurements of sound speed an be used to alulate the gas temperature. The gas omposition, temperature, path mean veloity, and a pressure measurement are the inputs neessary to alulate a Reynolds number. Therefore, it is pratial to implement the desribed alibration improvements within ommerial flowmeter eletronis. In this study, it has been found that the effets of thermal expansion on the pipe ross setional area and on the sound path length are signifiant. For the 5 K temperature range in these tests the effets were.45 % and % respetively. A simple method for measuring the path length hanges as a 6 Copyright 998 by ASME

7 funtion of temperature using the meter sound speed determinations has been desribed. The designers of flow tubes and transduer holders should be ognizant of the thermal expansion issues so that the expansion an be predited analytially or aurately extrapolated to more extreme temperatures. Also, the designs should be as repeatable as possible through many temperature yles so that the path length does not reep and lead to alibration drift. The disharge oeffiient preditions based on the Gilmont profile best math the experimental results. The Gilmont preditions show the sharpest deline in disharge oeffiient with dereasing Re. Taylor, B. N. and Kuyatt, C. E, Guidelines for Evaluating and Expressing the Unertainty of NIST Measurement Results, NIST Tehnial Note 297, 994. Wright, J. D. and Espina, P. I., 997, Flowmeter Calibration Faility for Heated Gas Mixtures, National Conferene of Standards Laboratories Proeedings, Atlanta, Ga., July, 997, pp Yeh, T. T. and Mattingly, G. E., 997, Computer Simulations of Ultrasoni Flowmeter Performane in Ideal and Non-Ideal Pipeflows, 997 ASME Fluids Engineering Division Summer Meeting, June At Re <, the heated tests showed signifiantly more data satter than the room temperature tests, due primarily to signifiant temperature stratifiation between the top and the bottom of the flow tube beomes signifiant. For laminar flows, the temperature stratifiation and veloity profile distortion beome so severe that large departures from the room temperature behavior are observed ( %). For the heated test onditions and the lowest flows, the temperature and veloity profiles did not reah steady state even after more than 3 minutes. The use of flow onditioners and orienting the meter so that the gas flows vertially instead of horizontally should redue the effets of heat transfer and stratifiation on the flowmeter performane. ACKNOWLEDGMENTS The author would like to aknowledge the thoughtful assistane of Dr. T. T. Yeh. REFERENCES Bogue, D. C. and Metzner, A. B., 963, Veloity Profiles in Turbulent Pipe Flow, I&EC Fundamentals, Vol. 2, No. 2. Brown, A. E., 99, Ultrasoni Flowmeters in Flow Measurement: Pratial Guides for Measurement and Control, D. W. Spitzer, ed., Instrument Soiety of Ameria, Researh Triangle Park, NC, pp. 45. Gilmont, R., 996, Veloity Profile of Turbulent Flow in Smooth Cirular Pipes, Measurements and Control, pp Hilsenrath, J. et. al., 955, Tables of Thermal Properties of Gases, NBS Cirular 564. Lynnworth, L. C., 989, Ultrasoni Measurements for Proess Control: Theory, Tehnique, Appliations, Aademi Press, San Diego, CA. 7 Copyright 998 by ASME