Development of the Vortex Mass Flowmeter with Wall Pressure Measurement

Transcription

1 10.478/msr MEASUREMENT SCIENCE REVIEW, Volume 1, No. 1, 01 Development of the Vortex Mass Flowmeter with Wall Pressure Measurement Zhiyong Li 1,, Zhiqiang Sun 1, 1 School of Energy Science an Engineering, Central South University, Changsha 41008, China Hunan Key Laboratory of Energy Conservation in Process Inustry, Central South University, Changsha 41008, China zqsun@csu.eu.cn Mass flow measurement is essential to the unerstaning an control of processes concerning flui flow. The availability of reliable mass flowmeters, however, is far inaequate to meet the eman. In this paper we evelope a practical vortex mass flowmeter with wall pressure measurement. The meter coefficient of mass flow rate was acquire through experiments with air at Reynols numbers from to Here we show that the meter coefficient of mass flow rate is nearly constant at Reynols numbers greater than To further exten the lower limit, a correction factor relate to the Reynols number was introuce into the vortex mass flowmeter. The results show that the relative errors of the vortex mass flowmeter evelope are basically within ±5%. This evice can satisfy a iversity of requirements of mass flow measurement in engineering fiels. Keywors: Mass flow measurement, vortex mass flowmeter, vortex sheing, wall pressure, meter coefficient of mass flow rate, correction factor T 1. INTRODUCTION HE MEASUREMENT of mass flow rate has become a basic requirement in many commercial transactions involving conveyance of fluis over the last two ecaes [1]. This is partly ue to the increasing value of proucts [], but it is also ue to an increasing realization that volumetric flow measurement is often inappropriate [], [4]. However, so far the availability of mass flowmeters is much too inaequate to meet the eman. Mass flow measurement is generally categorize as irect or inirect. Direct mass flow measurement with a single instrument is rare. Heretofore the approaches to irect mass flow rate are achieve by measuring Coriolis acceleration, or angular momentum, or temperature rise resulting from heat aition [5], [6]. In engineering applications, inirect mass flow measurement is wiely accepte because of its simple installation an low maintenance. It is apparent that mass flow rate can be obtaine by multiplying volumetric flow rate by flui ensity. Moreover, inirect mass flow rate can also be accomplishe by properly manipulating output signals from multiple sensors [7]. The major isavantage of inirect mass flow measurement is the nee for a suitable compensating algorithm. Thereby eveloping reliable mass flowmeters is of essential interest to the flow measurement community. Since its introuction in the late 1960s, vortex flowmeter has been recognize as a promising flowmetering evice an is wiely accepte to measure the flow rate of gas, liqui, or even some multiphase flows [8]. The measurement principle of vortex flowmeter is base on the phenomenon of Kármán vortex street, in which the frequency of vortex sheing is proportional to the average flui flow velocity [9], [10]. Due to its insensitiveness to most parameters of the flui incluing ensity, temperature, an pressure, the vortex flowmeter is consiere as a potential solution to mass flow measurement. The first attempt of using a vortex flowmeter to obtain mass flow rate was mae by Itoh an Ohki [11]. They ivie the lift force acting on the vortex sheer by the vortex sheing frequency, an yiele a signal that was proportional to the mass flow rate. Zhang et al. extracte the vortex sheing frequency an the pressure rop across a bluff boy from the wall pressure ifference by a single sensor, an relate the mass flow rate irectly to the quotient of pressure rop ivie by vortex sheing frequency [1]. Sun achieve the measurement of mass flow rate of homogeneous gas-liqui bubble flow with combine use of a Venturi tube an a vortex flowmeter [1]. These investigations establish, in principle, the basis of mass flow measurement using a vortex flowmeter. Accoring to the authors knowlege, however, stuies concerning the esign of vortex mass flowmeter evices have not been reporte in the literature. This paper is aime at eveloping a prototype vortex mass flowmeter of use value. Measurement performance of the vortex mass flowmeter is teste in a bell prover calibration system at Reynols numbers from to Meter coefficients of mass flow rate are acquire by experiments. A correlation for etermining appropriate correction factor at low Reynols numbers is establishe. Finally, the measurement errors of the evelope vortex mass flowmeter are analyze an iscusse.. PRINCIPLES & METHODOLOGY A. Mass flow measurement base on vortex sheing If two tappings are place upstream an ownstream of a bluff boy, as shown in Fig.1, the etecte wall pressure ifference contains both flui oscillation an pressure rop cause by the vortex sheing. From the fluctuation of the wall pressure ifference, we can extract the vortex sheing frequency: U f = St (1) m 0

2 MEASUREMENT SCIENCE REVIEW, Volume 1, No. 1, 01 m = 1 π D 1 D + arcsin where St represents the imensionless Strouhal number, U is the average flui flow velocity, m is the area ratio, is the with of the bluff boy, an D is the inner iameter of the flow passage. Fig.1. Schematic iagram of vortex mass flowmeter: (a) Overall structure; (b) Dimensions of bluff boy (unit: mm). Meanwhile, the average pressure ifference represents the pressure rop an can be written as D () 1 Δ p = CpρU () where C p is the pressure coefficient, an ρ is the ensity of the flui. Diviing () by (1), we obtain Cpm = ( ρu) f St (4) For a specific vortex flowmeter, its geometric parameters are fixe, so the meter coefficient of mass flow rate is only a function of the Strouhal number an the pressure coefficient. Previous stuy alreay inicates that the Strouhal number an the pressure coefficient are constant within a wie range of Reynols numbers [1]. Within that range of Reynols numbers, the meter coefficient of mass flow rate also keeps constant, which means that the mass flow rate is in irect proportion to the ratio of average pressure rop to vortex sheing frequency. If the vortex sheing frequency an the pressure rop are extracte out of the ifferential wall pressure, irect mass flow measurement is achieve by a single sensor. Specific values of the meter coefficient of mass flow rate an its applie range of Reynols numbers nee to be etermine by experiments. B. Design of measuring evice The key component of the measuring evice of the vortex mass flowmeter is the bluff boy. We use a triangular prism as the bluff boy. The cross section of the triangular prism is actually a truncate isosceles triangle with its base facing the oncoming flui, as alreay shown in Fig.1. The with of the front face of the bluff boy is 7 mm, an the inner iameter D of the measuring conuit is 5 mm. Thereby the blockage ratio b, efine as /D, is 0.8 for the vortex mass flowmeter evelope. The reason for choosing the triangular bluff boy is that the two slope sies of the triangular prism ensure the flui just behin the front face to ecelerate graually an uniformly, which will inuce less oscillation in the course of vortex sheing. The two pressure tappings are locate 1.0D upstream an 0.D ownstream of the bluff boy, respectively. They are connecte to a ifferential pressure sensor with sampling tubes of mm iameter. The effect of the configuration of sampling tubes on the wall pressure measurement was iscusse in [14], [15]. Accoring to the estimation of the magnitue an frequency of the output vortex signals, we use a ynamic ifferential pressure sensor with 0.9 kpa measurement range, 1.0 ms response time, an 1.5% accuracy. The sensor an sampling tubes are encapsulate in a protection box on the sie of the measuring evice. The vortex mass flowmeter evelope is given in Fig.. Accoring to its efinition, the mass flow rate in a conuit with cross-sectional area A is Substituting ρu in (5) with (4), it yiels qm = ρua (5) q m = K m (6) f K m A St = (7) m C p where K m is the meter coefficient of mass flow rate. Fig.. The vortex mass flowmeter evelope. 1

3 MEASUREMENT SCIENCE REVIEW, Volume 1, No. 1, 01 C. Design of signal processing an inication We process the signal output from the pressure sensor with a -bit microcontroller STM. The STM series are esigne base on the Cortex-M CPU, which is of high performance-price ratio an low power consumption. The STM use has 7 MHz clock spee, 56 Kbytes of flash memory, an 48 Kbytes of RAM memory. We employ the raix fast Fourier transform (FFT) algorithm to extract the vortex sheing frequency in view of the scarcity of the RAM memory size in the microcontroller. A trigonometric table is prestore in the RAM to reuce the complexity of the calculation further. At the beginning of signal sampling, we use a large sampling frequency to acquire the ynamic feature of the entire signal. When a sampling is complete, the raix FFT algorithm is use to calculate the power spectral ensity of the signal to obtain the vortex sheing frequency. Accoring to the result, the sampling frequency is altere aaptively to achieve integer-multiple sampling, which can iminish markely or even eliminate the leakage of power spectrum. The time-average value of the signal from the pressure sensor is calculate to represent the pressure rop. A thin film transistor liqui crystal isplay (TFT-LCD) is use as the inicator of the vortex mass flowmeter. The TFT-LCD employs another STM as its microcontroller. The controller of the TFT-LCD is ILI90, which receives ata from the STM via 18-bit ata bus an isplays them on the screen in the form of signs as well as pictures. An analog resistive film input panel is embee on the top of the TFT-LCD with the 1-bit ADC controller ADS784 in charge of human-machine interaction. The communication between the microcontroller an the inicator is Mobus protocol base on RS485 interface. We use ASCII format to transmit ata in terms of the requirement for point-to-point communication.. EXPERIMENTS Experiments are performe with air as working flui at normal ambient temperature an atmospheric pressure. The experimental system primarily consists of a gas pump, a bell prover, the vortex mass flowmeter, an some connecting pipes an control valves, as shown in Fig.. The bell prover is use as the stanar flowmetering evice, an it has a volume of 00 L uner the working pressure of kpa. The uncertainty of the bell prover is calibrate to be 0.5% with pressure fluctuation less than 50 Pa. The reference mass flow rate provie by the bell prover is Fig.. Experimental set-ups. 4. RESULTS & DISCUSSION To make subsequent analyses more comparable, we efine the Reynols number using the with of the bluff boy as the characteristic length: ρu Re = (9) μ Figs.4 6 show variations of Strouhal number, pressure coefficient, an meter coefficient of mass flow rate, with the Reynols numbers. Strouhal number, pressure coefficient, an meter coefficient of mass flow rate are calculate by (1), (), an (7). The variations in Figs.4 6 are characterize by two pronounce phases accoring to the Reynols numbers. When Reynols number is less than , the Strouhal number, pressure coefficient, an meter coefficient of mass flow rate possess consierable ispersity an nonlinearity. This irregular behavior is mainly ue to the flui viscosity. It has been foun that performance of a vortex flowmeter eteriorates notably at low flow velocity when the influence of flui viscosity increases [16]. Beyon the critical Reynols number , the Strouhal number, pressure coefficient, an meter coefficient of mass flow rate are nearly constant at an average value of 0.178,.177 an m q mref = ρ q (8) a v St where ρ a is the ensity of air euce from the temperature an pressure in the bell prover, an q v is the volumetric flow rate calculate by the bell prover s volume change. The upstream an ownstream pipes connecting the vortex mass flowmeter were long enough to ensure vortex sheing fully evelope in the flow passage. The flow rate of air was altere by ajusting the control valves Fig.4. Strouhal numbers versus Reynols numbers.

4 MEASUREMENT SCIENCE REVIEW, Volume 1, No. 1, 01 C p Fig.5. Pressure coefficients versus Reynols numbers ) Choose proper correction factor accoring to Reynols number: if Reynols number is less than , then compute correction factor using (11); if Reynols number is greater than , then correction factor is set to 1. e.) Compute mass flow rate using (10). On the basis of the measurement results, we calculate the relative errors of the mass flow rates at Reynols numbers aopting the above steps, as shown in Fig.8. These errors are basically within ±5%, which satisfies most emans of mass flow measurement in engineering. Although compensate by the correction factors, however, the errors at low Reynols numbers are still fairly large an some even approach 10%. Thereby we shoul pay special attention to the lower limit of the vortex mass flowmeter. K c K m /m Fig.6. Meter coefficients of mass flow rate with Reynols numbers Fig.7. Correction factors at low Reynols numbers. 10 To exten the measurement range of vortex mass flowmeter at low Reynols numbers, we introuce a correction factor K c into (6): qm = KcKm (10) f With this efinition, the correction factors are compute at Reynols numbers ranging from to , as shown in Fig.7. A correlation between the correction factor an the Reynols number is establishe through polynomial fitting: Re Re K c = (11) whose square -norm R of the resiual is After figuring out an prestoring the meter coefficient of mass flow rate an the correction factors in the EEPROM of the signal processing unit, we take the following feasible steps to obtain the mass flow rate: a.) Acquire raw sensor signal of vortex mass flowmeter. b.) Extract vortex sheing frequency an pressure rop from sensor signal. c.) Compute flow velocity an Reynols number using (1) an (9). Error/% Fig.8. Measurement errors of vortex mass flowmeter. 5. CONCLUSIONS In this paper we escribe the evelopment of a prototype vortex mass flowmeter with wall pressure measurement. Performance of the vortex mass flowmeter is teste in a bell prover calibration system at Reynols numbers On the basis of the measurement results, the meter coefficient of mass flow rate is obtaine. It is foun that the meter coefficient of mass flow rate is nearly constant at m when Reynols numbers are greater than Correction factor relate to Reynols numbers is introuce to exten the measurement range of vortex mass flowmeter

5 MEASUREMENT SCIENCE REVIEW, Volume 1, No. 1, 01 at low Reynols numbers. The relative errors of the vortex mass flowmeter evelope are basically within ±5%, which can satisfy most requirements of mass flow measurement in engineering applications. However, it is also worth noting that the performance of the vortex mass flowmeter may eteriorate notably at low Reynols numbers ue to the flui viscosity. ACKNOWLEDGMENT We are grateful for the financial support from the National Natural Science Founation of China (Grant No ). REFERENCES [1] Deng, X., Yang, W.Q. (01). Fusion research of electrical tomography with other sensors for two-phase flow measurement. Measurement Science Review, 1 (), [] Hall, R. (1990) Measuring mass flow an ensity with Coriolis meters. InTech, 7 (4), [] Baker, R.C. (000). Flow Measurement Hanbook. New York: Cambrige University Press. [4] Kim, S.D., Lee, H.J., Oh, B.D. (010). Investigation on application of Parshal flume for flow measurement of low-flow season in Korea. Measurement Science Review, 10 (4), [5] Sharma, S.C., Patil, P.P., Vasuev, M.A., Jain, S.C. (010). Performance evaluation of an inigenously esigne copper (U) tube Coriolis mass flow sensors. Measurement, 4 (9), [6] Pereira, M. (009). Flow meters: Part 1. IEEE Instrumentation an Measurement Magazine, 1 (1), [7] Prasanna, U.R., Umanan, L. (010). Non-isruptive an null-eflection mass flow measurement by a pressure compensation technique. Flow Measurement an Instrumentation, 1 (1), [8] Sun, Z.Q., Zhang, H.J. (010). Measurement of the flow rate an volume voi fraction of gas-liqui bubble flow using a vortex flow meter. Chemical Engineering Communications, 197 (), [9] Venugopal, A., Agrawal, A., Prabhu, S.V. (011). Review on vortex flowmeter Designer perspective. Sensors an Actuators A: Physical, 170 (1-), 8-. [10] Pankanin, G.L. (005). The vortex flowmeter: Various methos of investigating phenomena. Measurement Science an Technology, 16 (), R1-R16. [11] Itoh, I., Ohki, S. (199). Mass flowmeter etecting fluctuations in lift generate by vortex sheing. Flow Measurement an Instrumentation, 4 (4), 15-. [1] Zhang, H.J., Huang, Y.M., Sun, Z.Q. (006). A stuy of mass flow rate measurement base on the vortex sheing principle. Flow Measurement an Instrumentation, 17 (1), 9-8. [1] Sun, Z.Q. (010). Mass flow measurement of gasliqui bubble flow with the combine use of a Venturi tube an a vortex flowmeter. Measurement Science an Technology, 1 (5), [14] Sun, Z.Q., Zhang, H.J., Zhou, J.M. (007). Investigation of the pressure probe properties as the sensor in the vortex flowmeter. Sensors an Actuators A: Physical, 16 (), [15] Sun, Z.Q., Zhang, H.J., Zhou, J.M. (008). Evaluation of uncertainty in a vortex flowmeter measurement. Measurement, 41 (4), [16] Goujon-Duran, S. (1995). Linearity of the vortex meter as a function of flui viscosity. Flow Measurement an Instrumentation, 6 (), 5-8. Receive May 1, 01. Accepte January 8, 01. 4