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A novel flowrate measurement method for small-diameter pipeline based on bidirectional acoustic resonance
Flow Measurement and Instrumentation 70 (2019) 101656
Contents lists available at ScienceDirect
Flow Measurement and Instrumentation journal homepage: http://www.elsevier.com/locate/flowmeasinst
A novel flowrate measurement method for small-diameter pipeline based on bidirectional acoustic resonance Tiantian Huang a, *, Lingyun Ye a, Yayue Hu a, Kaichen Song b a b
College of Biomedical Engineering & Instrument Science, Zhejiang University, Zheda Road 38#, 310027 Hangzhou, China School of Aeronautics and Astronautics, Zhejiang University, Zheda Road 38#, 310027 Hangzhou, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Flowrate Acoustic-resonance Standing-wave tube Electro-acoustic hybrid
Traditional acoustic flowmeters are difficult to use in small-caliber, low-velocity piping systems. In this study, a novel method for fluid velocity measurement in small-diameter pipelines is developed based on the characteristic of acoustic resonance and standing wave tube. This method solves the problem of mutual interference between bidirectional acoustic loops, and realizes the simultaneous measurement of bidirectional resonant frequency. The tiny variation of flow velocity in a small-diameter pipeline can be sensitive by measuring the difference in bidirectional high-order resonance frequency. Experimental results show that the measurement system with a 15 mm diameter pipe has good linearity and high sensitivity to low velocity. Hence, this new method widens the application scope of acoustic flowmeters, especially in small-diameter, low-velocity piping systems.
1. Introduction Acoustic flow measurement technology based on ultrasonic wave has many advantages, such as high response and absence of pressure loss [1]. Ultrasonic flowmeters are widely used in pipelines with large di ameters (more than DN50), which are common in the gas industry [2–5]. However, the traditional ultrasonic flowmeter exhibits limited precision when used for small-diameter, low-velocity measurements due to the following reasons [6]. First, the acoustic path in small-diameter pipes is too short [7], and the difference in transit time required for accurate flow measurement is extremely small [8]. Second, flow velocity is extremely lower than acoustic velocity, and this difference causes high uncertainty in transit time measurement. The diameter of a practical ultrasonic flowmeter is usually more than 20 mm, and the minimum flow velocity required to maintain accuracy is more than 0.2 m/s. For the flowrate measurement of small-diameter pipes, the main approach utilized at present is to increase the propagation distance of the acoustic wave in various ways. The most common practice is to design a zigzag-type acoustic transmission path [9,10]. Changes in the shape of the pipeline, such as “π” style, can also produce an increased acoustic transmission path [8]. In addition, multipath configuration essentially increases the total propagation path in a multi-channel par allel manner [11–14]. These methods improve the performance of flowrate measurement but also cause problems. Specifically, zigzag
transmission results in increased energy loss, and the signal-to-noise ratio is limited by the attenuation of the waves in the fluid. The accu racy of π style is dependent on a uniform velocity distribution over the measuring section. The multipath acoustic transducer’s configuration is limited by the diameter of small pipes. Moreover, the accumulation of time can also play the effect of prolonging the sonic propagation dis tance. The “sing-around type” method based on frequency difference measurement has a good application value in thin pipe flowmeters. However, the accuracy of this method is limited when a rapid response is required [15,16]. The method of measuring fluid velocity by using long-wavelength acoustic waves has gradually developed in recent years [17,18]. When the acoustic frequency satisfies f < 1:84 2πR c0 (R is the pipe radius and c0 is the acoustic velocity), the acoustic waves in a circular pipe only prop agate along the axis in the fundamental or plane wave mode to maximize the distance of acoustic propagation for fluid velocity measurement [19]. When the diameter of the pipeline is less than 20 mm, the acoustic frequency must be below 10 kHz. Early flow measurement systems using long acoustic waves have been verified as suitable for small-diameter pipes [20]. A difference in forward and backward resonant fre quencies is observed when the fluid velocity is steady. Flowrate mea surement is realized by calculating the resonant frequency difference. However, the resonance is not continuous when the two directions work alternately. When the flow is unsteady, the measurement will be
* Corresponding author. E-mail address: [email protected] (T. Huang). https://doi.org/10.1016/j.flowmeasinst.2019.101656 Received 10 December 2018; Received in revised form 11 October 2019; Accepted 31 October 2019 Available online 6 November 2019 0955-5986/© 2019 Elsevier Ltd. All rights reserved.
T. Huang et al.
Flow Measurement and Instrumentation 70 (2019) 101656
Fig. 1. Schematic of the bidirectional resonance method.
uncertain. The same problem occurs with “sing-around type” flowme ters. The configuration with two sets of transducers is the best option to improve the precision and rapidity of systems. However, the problem of mutual interference becomes prominent when bidirectional acoustic loops are operated synchronously [21]. A new method that uses the principle of a bidirectional synchronous resonator is proposed in this study. This method is suitable for flow measurement in small-diameter, low-velocity pipelines. An approach of solving mutual interference by using a standing wave tube is applied to address the problem of asynchronous measurement of bidirectional loops in traditional acoustic flowmeters. Synchronous measurement of the bidirectional loop is realized. An experimental platform is built to verify the validity of the measurement method. Related experiment re sults indicate that the measurement of small-diameter, low-flowrate pipelines with standing wave tube has good sensitivity and linearity, even a small lower flow limit. In the following section, the principle description and experimentation of the measurement system will be introduced and analyzed.
gain of the entire system is greater than 1 and the acoustic phase satisfies the condition, the resonant loop realizes self-oscillation. For the forward resonant loop, the equivalent resonant cavity length becomes shorter and the resonant frequency becomes larger when the flow velocity in the pipeline is not zero. For the backward resonant loop, the equivalent resonant cavity length becomes longer and the resonant frequency becomes smaller. Resonance frequency offset is caused by the fluid flowrate, which can be obtained by measuring the difference be tween forward and backward resonant frequencies. In consideration of low flowrate measurement, fluid velocity is much lower than the speed of sound. Thus, the resonance frequency shift caused by fluid flow is also small. The self-excited oscillation of the resonant system contains not only fundamental frequency resonance but also many high-order harmonics, which can be expressed as f ¼N
ðN ¼ 1; 2; 3…Þ
(2)
The resonant frequency of the forward (f1 ) and backward (f2 ) reso nant loops can be expressed as
2. Bidirectional acoustic resonance fluid velocity measurement method
f1 ¼ N1
The proposed method of flowrate measurement is shown in Fig. 1, where u is the velocity of the fluid in the pipe and L is the distance from the acoustic transmitter to the receiver. Transmitter 1 and Receiver 1 are the emission transducer and receiver along the direction of fluid flow, respectively, and P1 represents the sound waves in this direction. Transmitter 2 and Receiver 2 represent the transmit transducer and receiver against the flow direction of the fluid, respectively, and P2 represents the sound waves in this direction. It is assumed that the pipe system meets the conditions of sound wave transmission in plane wave form. When the fluid is stationary, sinusoidal sound waves whose wavelengths are exactly the 1 n ðn ¼ 1; 2; 3…Þ length of the resonator are emitted from the transmitter and reach the receiver after a certain time. Then, the transmitter is excited again after processing with an external circuit. The entire loop can be regarded as a ring resonator because the propagation time of the electrical signal is much smaller than the propagation time of the acoustic signal. The sinusoidal wave whose wavelength is equal to the cavity length is the fundamental wave of the resonant loop, and the corresponding frequency is base frequency, which can be calculated as c f ¼ þ δ; L
c þ δ; L
f2 ¼ N2
cþu þ δ; L c
u L
þ δ;
ðN1 ¼ 1; 2; 3…Þ;
(3)
ðN2 ¼ 1; 2; 3…Þ;
(4)
The resonant frequency difference can be calculated as Δf ¼
f1 N1
f2 u ¼2 ; L N2
ðN1 ¼ 1; 2; 3…; N2 ¼ 1; 2; 3…Þ:
(5)
The expression of fluid velocity can be obtained using the formula above. L u ¼ Δf : 2
(6)
Here, the high-order harmonic frequency amplifies the resonance frequency shift caused by fluid flow. The influence of fluid flow can be enlarged by selecting a large N value to improve the measurement sensitivity, which increases the frequency difference between forward and backward resonant loops. 3. Realization of bidirectional loop synchronous measurement by using a standing wave tube A forward and backward process is necessary to measure the flow accurately and effectively eliminate system errors, such as those in temperature. However, adopting two loops in alternating working mode inevitably introduces errors into the measurement because the instan taneous change in velocity causes inconsistency between two
(1)
where δ is a systematic error, c is the speed of sound, and L is the length of the resonator. The external circuit provides additional gain to supply the attenuation of acoustic wave produced by propagation. When the 2
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Flow Measurement and Instrumentation 70 (2019) 101656
Fig. 2. Application of the standing wave tube for the separation of forward and backward acoustic waves.
measurements. Bidirectional synchronous measurement is the ideal mode, but sound waves are easily superimposed, and mutual interfer ence is generated during the simultaneous operation. To solve this conflict, we utilized standing wave tube in the resonant loops, thereby eliminating the acoustic disturbances of the forward and backward loops theoretically. Standing wave is a sound field superposed by two planes with same frequency but travel in opposite directions. In the standing wave tube, the equation of the incident sound wave is assumed to be � � 2π p1 ¼ sin ϖt x ; (7) λ
has a simple harmonic vibration at the same frequency, but the ampli tude varies with position. The maximum amplitude of sound pressure is equal to the amplitude of incident wave, and the corresponding position is called antinode. The minimum amplitude of sound pressure is close to zero and the corresponding position is called node [20]. According to Eq. (9), the location of the antinode and node can be obtained. The lo cations of nodes are:
where λ and ϖ are wavelength and angular frequency of acoustic wave. The incident acoustic wave is reflected at the end of the standing wave tube and can be expressed as � � 4π 0 2π p2 ¼ sin ϖt L þ x ; (8) λ λ
xantinodes ¼ L
xnodes ¼ L
λ ð2k1 þ 1Þ; 4
0
k1 ¼ 0; 1; 2; 3…
(10)
And the locations of the antinodes can be expressed as: 0
λ k2 ; 2
k2 ¼ 0; 1; 2; 3…
(11)
The acoustic energy is approximately zero at the node, and becomes the largest at the antinode. For the standing wave tube with a certain length, sound waves with different frequencies generate different posi tions of the node and antinode. Given this characteristic of the standing wave tube, nodes and antinodes could be used to separate the different frequency acoustic waves of the two loops. So it is an effective way to combine standing wave tubes into flow measurement pipeline. Fig. 2 shows a schematic of the principle for achieving the separation of forward and backward frequencies. To overcome the interference of nearby strong local acoustic waves, the acoustic receiver of the back ward loop can be set in the forward standing wave tube, where the backward node and the forward antinode are coincident. Then, the
where L is the length of the standing wave tube. The sound pressure in the standing wave tube obtained by superimposing the incident wave and reflected wave can be expressed as � � � � 2π 0 2π 2π 0 p ¼ p1 þ p2 ¼ 2 sin ϖt (9) L cos x L λ λ λ 0
Thus, when a standing wave is formed, each fluid particle in the tube
Fig. 3. Experimental platform. 3
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Flow Measurement and Instrumentation 70 (2019) 101656
Fig. 4. Schematic of the electroacoustic mixed resonant circuit.
velocity measurement system consists of two standing wave tubes, a copper pipe, two circuit boards, and two through-hole mufflers. The standing wave tubes and copper pipe are designed in accordance with the results obtained in Section 3. The test pipe and the standing wave tubes are closely connected with very narrow slit. The slit is at least less than 0.01 mm, and sealed with PTFE tape. The through-hole mufflers are installed at both ends of the measurement system. They can eliminate the acoustic reflection caused by acoustic impedance mutation on both sides of the system and reduce the external noise in the resonant system. The through-hole mufflers can also prevent the reflection of sound waves and external noise from influencing the original internal pressure distribution. The air compressor blows air into one muffler; the air en ters the flow measurement system and arrives at the reference flowmeter from another muffler. Although the propagation time of the electrical signal is disregarded in the calculation and analysis of the resonant loop, the processing of the electrical signal is crucial in the actual system. The two circuit boards in Fig. 3 are designed for different resonant frequencies. To shield the circuit from electromagnetic interference, the circuit boards are installed in the shielding box in the actual experiment. Fig. 4 shows a schematic of the electroacoustic mixed resonant circuit, which mainly includes an electroacoustic conversion module and an acoustic-electro conversion module. After the acoustic–electro conversion module converts the acoustic signal into an electrical signal, the preamplifier circuit replenishes the signal gain, the filter circuit selects the desired high-order harmonic frequencies, and the automatic gain control (AGC) circuit ensures that the signal has a uniform amplitude. Electroacoustic drive signals are provided directly by the received sinusoidal acoustic signals. The transducer is driven by the power amplifier circuit to re-emit the acoustic wave. Combined with the standing wave characteristics of sound waves in the pipeline, the circuit system forms two sets of auto matic frequency selectors. Velocity information can be obtained when the two groups of real-time resonance frequencies are collected.
backward acoustic receiver can completely avoid the influence of nearby forward acoustic wave on the basis of guaranteeing the strength of the backward acoustic wave. A forward receiver should also be set at the coincidence point of the backward node and forward antinode in the backward standing wave tube to ensure that the forward sound waves are received without being subjected to the backward acoustic wave. In this system, another objective is to emit sound waves generated by the transducer in the standing wave tube into the pipeline as strong as possible. Thus, the pipe should pass through the standing wave tube at the position of the corresponding frequency’s antinode. It means that the pipeline passes from the forward standing wave tube at the position of the forward antinode, and the backward standing wave tube at the po sition of the backward antinode. Meanwhile, to facilitate the sound wave that passes in and out of the pipe, several long slots must be set on the side wall of the pipe at the intersection of the pipe and the standing wave tubes. Combined with the attenuation and plane wave cut-off conditions, parameter selection of the standing wave tube must be performed ac cording to the actual situation. Here, a set of parameters are obtained according to the results of the calculation. The length of the resonator is 2287 mm, and the diameter is 15 mm. The fundamental frequency of the resonator is 150 Hz at the speed of 343 m/s. If the high-order frequency in the forward loop uses N ¼ 64, then f ¼ 9.6 kHz; if the high-order fre quency in the backward loop uses N ¼ 60, then, f ¼ 9 kHz. The radius of the standing wave tube is 10 mm, the length of the standing wave tube is set to seven times the wavelength of 9.3 kHz, and the length L’ ¼ 258.3 mm. The backward acoustic receiver is placed at the position of x ¼ 107:5mm in the forward standing wave tube, and the forward acoustic receiver is placed at the position of x ¼ 115:5mm in the back ward standing wave tube. The location of the intersection of the forward standing wave tube and the pipe is at the position of x ¼ 79:8mm; the position where the backward standing wave tube intersects with the pipe is at x ¼ 86:85mm. 4. Experimental results and analysis
4.2. Experimental results and discussion
4.1. Experiment platform
Eq. (6) shows that the fluid flow velocity is proportional to the fre quency difference. The measured resonant frequency difference was compared with the fluid flow measured by the reference flowmeter to verify the bidirectional high-order acoustic resonance velocity method. When the room temperature is controlled at 20 � C and the gas is stationary in the pipeline, the forward and backward loops can achieve synchronous and stable resonance. The actual forward resonance fre quency is 9543.6 Hz, and the backward resonance frequency is 8926.9 Hz. The experimental value differs from the theoretical value because the propagation time of the electrical signal is disregarded, and the length of the entire resonant loop is slightly different during the installation process. Therefore, the difference between the experimental and calculated values is reasonable.
As shown in Fig. 3, the experimental platform is mainly composed of a gas source, reference flowmeter, and bidirectional high-order acoustic resonance velocity measurement system. A thermal mass flowmeter (MF5700 gas flowmeter) is used as the reference due to its advantage in low flowrate measurement. Generally, the lower limit of velocity mea surement accuracy of an ordinary ultrasonic flowmeter can only reach 0.2 m/s, whereas that of the thermal mass flowmeter can reach at least 0.01 m/s and guarantee 2% measurement accuracy [22]. The focus of this experiment is the low velocity section, which is a suitable option at the present principle verification stage. The host computer collects the resonant frequency of the resonance loops through the frequency acquisition circuit board. The bidirectional high-order acoustic resonant 4
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Flow Measurement and Instrumentation 70 (2019) 101656
Fig. 5. Relation between forward flowrate and frequency difference within error bars.
Fig. 6. Relation between the backward flowrate and the frequency difference within error bars.
Both resonance frequencies are normalized to visualize the rela tionship between the frequency difference and flowrate. The relation ship between the frequency difference and the instantaneous flow of the reference flowmeter is shown in Fig. 5, where the abscissa is the instantaneous flowrate measured by the reference flowmeter (the co ordinate unit is converted to m/s from L/min according to the conven tion of ultrasonic flowmeter) and the ordinate is the resonant frequency difference of the forward and backward loops. Fig. 5 shows the result of repeated measurements of some flowrate points, the scatter is the data point of average, and the error bars represent the variance of multiple measurements. In the figure, the frequency difference and the flowrate maintain a good linearity, and the maximum repeatability error is 0.0148 m/s. This measurement method does not limit the direction of gas flow. For verification, we measured the backward flow using the same approach as that for the forward flow measurement by adjusting the position of the reference flowmeter and gas source. The relationship between the frequency difference and the flow is shown in Fig. 6. The frequency difference and the flowrate in the backward measurement are indicated by a negative value to show the difference from the forward
measurement result. The coordinates have the same definition as those in Fig. 5. The measurement results show that the system can ensure good linearity even when the fluid flows backward. The system does not need to limit the flow direction during flow measurement and has strong measurement flexibility. Fig. 7 shows a set of experimental data points for flow measurement. It suggests that, the resonant frequency difference is sensitive to the change in the flow, even in the domain of low flowrate. The maximum linearity error is 5.09%, which is superior to the initial linearity error in other studies [6]. Furthermore, especially in the low flow area, there is no obvious decline trend in accuracy. The lower limit of measurement is less than 0.03 m/s, and is same or superior than traditional ultrasonic flowmeters such as AquaTrans serial of GE. At present, the experimental system is vulnerable to the influence of temperature. Hence, the mea surement error in the calibration process is difficult to reduce. However, the system still maintains good sensitivity and linearity in low flow velocity range. Evidently, the performance of the principle verification system demonstrated that this flowrate measurement method has a very large improvement space. Actually, this method can be applied to air, natural gas and various 5
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Flow Measurement and Instrumentation 70 (2019) 101656
Fig. 7. A set of experimental data points for flow measurement and their linear fitting curve.
gases. And the approach of bidirectional synchronous measurement will ensure that the flowrate measurement is not influenced by the sonic velocity in theory. Hence, the measurement would almost not be affected by temperature. But in the actual experiment, it was found that the frequency difference varies with temperature and presents a certain linear relationship. The greatest possibility comes from the asymmetry of the bidirectional resonant circuit, which makes the current system sensitive to temperature.
[4] H. Nishiguchi, T. Sawayama, K. Nagamune, Evaluation of the propagation time difference in low-pressure city gas flow using a clamp-on ultrasonic flowmeter, Jpn. J. Appl. Phys. (07JC017) (2017) 561. [5] W. Kang, et al., Effect of ultrasonic noise generated by pressure control valves on ultrasonic gas flowmeters, Flow Meas. Instrum. 60 (2018) 95–104. [6] Y. Yu, G. Zong, Note: ultrasonic liquid flow meter for small pipes, Rev. Sci. Instrum. 83 (02610721) (2012). [7] H. Ishikawa, et al., Development of a new ultrasonic liquid flowmeter for very low flow rate applicable to a thin pipe, in: 9th International Symposium on Semiconductor Manufacturing (ISSM2000), IEEE, TOKYO, JAPAN, 2000, pp. 383–386. [8] A.R. Guilbert, M. Law, M.L. Sanderson, A novel ultrasonic/thermal clamp-on flowmeter for low liquid flowrates in small diameter pipes, Ultrasonics 34 (2–5) (1996) 435–439. [9] M.L. Sanderson, H. Yeung, Guidelines for the use of ultrasonic non-invasive metering techniques, Flow Meas. Instrum. 13 (2002) 125–142. PII S0955-5986(02) 00043-24. [10] Y. Jiang, et al., A model-based hybrid ultrasonic gas flowmeter, IEEE Sens. J. 18 (11) (2018) 4443–4452. [11] L. Qin, et al., Application of extreme learning machine to gas flow measurement with multipath acoustic transducers, Flow Meas. Instrum. 49 (2016) 31–39. [12] H. Zhou, et al., Multipath ultrasonic gas flow-meter based on multiple reference waves, Ultrasonics 82 (2018) 145–152. [13] L. Qin, et al., Flowrate determination for arbitrary multipath arrangement based on generalized inverse of matrix, IEEE Sens. J. 17; 17 (12; 12) (2017) 3625–3634. [14] Q. Chen, W. Li, J. Wu, Realization of a multipath ultrasonic gas flowmeter based on transit-time technique, Ultrasonics 54 (1) (2014) 285–290. [15] J.R. Gatabi, et al., An improved measurement algorithm for increasing the accuracy of sing-around type ultrasonic flow meters, Mechanika (2) (2012) 209–213. [16] J. Delsing, A new velocity algorithm for sing-around-type flow meters, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 34 (4) (1987) 431–436. [17] J.P.R. Abbott, et al., Feasibility of a long-wavelength acoustic flowmeter for measuring smokestack emissions, J. Acoust. Soc. Am. 139 (4) (2016), 2120-2120. [18] J.P.R. Abbott, et al., Determining average flow speed in a scale model smokestack by measuring correlated noise through a long-wavelength acoustic flow meter, J. Acoust. Soc. Am. 140 (4) (2016), 3259-3259. [19] L.E. Kinsler, et al., Fundamentals of Acoustics, fourth ed., John Wiley & Sons, Inc, 1999. [20] E.S. IKPE, et al., A standing-wave flow measurement system for small-diameter pipes using long acoustic-waves, Rev. Sci. Instrum. 64 (9) (1993) 2666–2672. [21] K. Amri, et al., Fluid flow velocity measurement using dual-ultrasonic transducer by means of simultaneously transit time method, in: 2015 4th International Conference on Instrumentation, Communications, Information Technology, and Biomedical Engineering (ICICI-BME), IEEE, NEW YORK, 2015, pp. 113–116. [22] M. Farzaneh-Gord, et al., Potential use of capillary tube thermal mass flow meters to measure residential natural gas consumption, J. Nat. Gas Sci. Eng. 22 (2015) 540–550.
5. Conclusion A bidirectional high-order acoustic resonance flowrate measurement method is proposed to address the difficulty in improving flowrate measurement sensitivity and accuracy in small-diameter, low-velocity pipelines. The method realizes the synchronous work of forward and backward measurement units. This method is described in detail, and the measurement system is verified through an experiment. The results show that the high-order resonant frequency amplifies the frequency offset caused by the fluid flow. The resonant frequency is sensitive to a tiny change in flowrate, and the measurement system has good linearity and small lower flow limit, indicating that this method is particularly suitable for the measurement of small-diameter, low-flowrate pipelines. An in-depth investigation of this new method would open up new application possibilities for acoustic flowmeters. Declaration of competing interest The authors declared that they have no conflicts of interest to this work. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted. References [1] L.C. Lynnworth, Y. Liu, Ultrasonic flowmeters: half-century progress report, 19552005, Ultrasonics 441 (2006) E1371–E1378. [2] D. Zheng, et al., A method based on a novel flow pattern model for the flow adaptability study of ultrasonic flowmeter, Flow Meas. Instrum. 29 (2013) 25–31. [3] D. Zheng, D. Zhao, J. Mei, Improved numerical integration method for flowrate of ultrasonic flowmeter based on Gauss quadrature for non-ideal flow fields, Flow Meas. Instrum. 41 (2015) 28–35.
6
Contents lists available at ScienceDirect
Flow Measurement and Instrumentation journal homepage: http://www.elsevier.com/locate/flowmeasinst
A novel flowrate measurement method for small-diameter pipeline based on bidirectional acoustic resonance Tiantian Huang a, *, Lingyun Ye a, Yayue Hu a, Kaichen Song b a b
College of Biomedical Engineering & Instrument Science, Zhejiang University, Zheda Road 38#, 310027 Hangzhou, China School of Aeronautics and Astronautics, Zhejiang University, Zheda Road 38#, 310027 Hangzhou, China
A R T I C L E I N F O
A B S T R A C T
Keywords: Flowrate Acoustic-resonance Standing-wave tube Electro-acoustic hybrid
Traditional acoustic flowmeters are difficult to use in small-caliber, low-velocity piping systems. In this study, a novel method for fluid velocity measurement in small-diameter pipelines is developed based on the characteristic of acoustic resonance and standing wave tube. This method solves the problem of mutual interference between bidirectional acoustic loops, and realizes the simultaneous measurement of bidirectional resonant frequency. The tiny variation of flow velocity in a small-diameter pipeline can be sensitive by measuring the difference in bidirectional high-order resonance frequency. Experimental results show that the measurement system with a 15 mm diameter pipe has good linearity and high sensitivity to low velocity. Hence, this new method widens the application scope of acoustic flowmeters, especially in small-diameter, low-velocity piping systems.
1. Introduction Acoustic flow measurement technology based on ultrasonic wave has many advantages, such as high response and absence of pressure loss [1]. Ultrasonic flowmeters are widely used in pipelines with large di ameters (more than DN50), which are common in the gas industry [2–5]. However, the traditional ultrasonic flowmeter exhibits limited precision when used for small-diameter, low-velocity measurements due to the following reasons [6]. First, the acoustic path in small-diameter pipes is too short [7], and the difference in transit time required for accurate flow measurement is extremely small [8]. Second, flow velocity is extremely lower than acoustic velocity, and this difference causes high uncertainty in transit time measurement. The diameter of a practical ultrasonic flowmeter is usually more than 20 mm, and the minimum flow velocity required to maintain accuracy is more than 0.2 m/s. For the flowrate measurement of small-diameter pipes, the main approach utilized at present is to increase the propagation distance of the acoustic wave in various ways. The most common practice is to design a zigzag-type acoustic transmission path [9,10]. Changes in the shape of the pipeline, such as “π” style, can also produce an increased acoustic transmission path [8]. In addition, multipath configuration essentially increases the total propagation path in a multi-channel par allel manner [11–14]. These methods improve the performance of flowrate measurement but also cause problems. Specifically, zigzag
transmission results in increased energy loss, and the signal-to-noise ratio is limited by the attenuation of the waves in the fluid. The accu racy of π style is dependent on a uniform velocity distribution over the measuring section. The multipath acoustic transducer’s configuration is limited by the diameter of small pipes. Moreover, the accumulation of time can also play the effect of prolonging the sonic propagation dis tance. The “sing-around type” method based on frequency difference measurement has a good application value in thin pipe flowmeters. However, the accuracy of this method is limited when a rapid response is required [15,16]. The method of measuring fluid velocity by using long-wavelength acoustic waves has gradually developed in recent years [17,18]. When the acoustic frequency satisfies f < 1:84 2πR c0 (R is the pipe radius and c0 is the acoustic velocity), the acoustic waves in a circular pipe only prop agate along the axis in the fundamental or plane wave mode to maximize the distance of acoustic propagation for fluid velocity measurement [19]. When the diameter of the pipeline is less than 20 mm, the acoustic frequency must be below 10 kHz. Early flow measurement systems using long acoustic waves have been verified as suitable for small-diameter pipes [20]. A difference in forward and backward resonant fre quencies is observed when the fluid velocity is steady. Flowrate mea surement is realized by calculating the resonant frequency difference. However, the resonance is not continuous when the two directions work alternately. When the flow is unsteady, the measurement will be
* Corresponding author. E-mail address: [email protected] (T. Huang). https://doi.org/10.1016/j.flowmeasinst.2019.101656 Received 10 December 2018; Received in revised form 11 October 2019; Accepted 31 October 2019 Available online 6 November 2019 0955-5986/© 2019 Elsevier Ltd. All rights reserved.
T. Huang et al.
Flow Measurement and Instrumentation 70 (2019) 101656
Fig. 1. Schematic of the bidirectional resonance method.
uncertain. The same problem occurs with “sing-around type” flowme ters. The configuration with two sets of transducers is the best option to improve the precision and rapidity of systems. However, the problem of mutual interference becomes prominent when bidirectional acoustic loops are operated synchronously [21]. A new method that uses the principle of a bidirectional synchronous resonator is proposed in this study. This method is suitable for flow measurement in small-diameter, low-velocity pipelines. An approach of solving mutual interference by using a standing wave tube is applied to address the problem of asynchronous measurement of bidirectional loops in traditional acoustic flowmeters. Synchronous measurement of the bidirectional loop is realized. An experimental platform is built to verify the validity of the measurement method. Related experiment re sults indicate that the measurement of small-diameter, low-flowrate pipelines with standing wave tube has good sensitivity and linearity, even a small lower flow limit. In the following section, the principle description and experimentation of the measurement system will be introduced and analyzed.
gain of the entire system is greater than 1 and the acoustic phase satisfies the condition, the resonant loop realizes self-oscillation. For the forward resonant loop, the equivalent resonant cavity length becomes shorter and the resonant frequency becomes larger when the flow velocity in the pipeline is not zero. For the backward resonant loop, the equivalent resonant cavity length becomes longer and the resonant frequency becomes smaller. Resonance frequency offset is caused by the fluid flowrate, which can be obtained by measuring the difference be tween forward and backward resonant frequencies. In consideration of low flowrate measurement, fluid velocity is much lower than the speed of sound. Thus, the resonance frequency shift caused by fluid flow is also small. The self-excited oscillation of the resonant system contains not only fundamental frequency resonance but also many high-order harmonics, which can be expressed as f ¼N
ðN ¼ 1; 2; 3…Þ
(2)
The resonant frequency of the forward (f1 ) and backward (f2 ) reso nant loops can be expressed as
2. Bidirectional acoustic resonance fluid velocity measurement method
f1 ¼ N1
The proposed method of flowrate measurement is shown in Fig. 1, where u is the velocity of the fluid in the pipe and L is the distance from the acoustic transmitter to the receiver. Transmitter 1 and Receiver 1 are the emission transducer and receiver along the direction of fluid flow, respectively, and P1 represents the sound waves in this direction. Transmitter 2 and Receiver 2 represent the transmit transducer and receiver against the flow direction of the fluid, respectively, and P2 represents the sound waves in this direction. It is assumed that the pipe system meets the conditions of sound wave transmission in plane wave form. When the fluid is stationary, sinusoidal sound waves whose wavelengths are exactly the 1 n ðn ¼ 1; 2; 3…Þ length of the resonator are emitted from the transmitter and reach the receiver after a certain time. Then, the transmitter is excited again after processing with an external circuit. The entire loop can be regarded as a ring resonator because the propagation time of the electrical signal is much smaller than the propagation time of the acoustic signal. The sinusoidal wave whose wavelength is equal to the cavity length is the fundamental wave of the resonant loop, and the corresponding frequency is base frequency, which can be calculated as c f ¼ þ δ; L
c þ δ; L
f2 ¼ N2
cþu þ δ; L c
u L
þ δ;
ðN1 ¼ 1; 2; 3…Þ;
(3)
ðN2 ¼ 1; 2; 3…Þ;
(4)
The resonant frequency difference can be calculated as Δf ¼
f1 N1
f2 u ¼2 ; L N2
ðN1 ¼ 1; 2; 3…; N2 ¼ 1; 2; 3…Þ:
(5)
The expression of fluid velocity can be obtained using the formula above. L u ¼ Δf : 2
(6)
Here, the high-order harmonic frequency amplifies the resonance frequency shift caused by fluid flow. The influence of fluid flow can be enlarged by selecting a large N value to improve the measurement sensitivity, which increases the frequency difference between forward and backward resonant loops. 3. Realization of bidirectional loop synchronous measurement by using a standing wave tube A forward and backward process is necessary to measure the flow accurately and effectively eliminate system errors, such as those in temperature. However, adopting two loops in alternating working mode inevitably introduces errors into the measurement because the instan taneous change in velocity causes inconsistency between two
(1)
where δ is a systematic error, c is the speed of sound, and L is the length of the resonator. The external circuit provides additional gain to supply the attenuation of acoustic wave produced by propagation. When the 2
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Fig. 2. Application of the standing wave tube for the separation of forward and backward acoustic waves.
measurements. Bidirectional synchronous measurement is the ideal mode, but sound waves are easily superimposed, and mutual interfer ence is generated during the simultaneous operation. To solve this conflict, we utilized standing wave tube in the resonant loops, thereby eliminating the acoustic disturbances of the forward and backward loops theoretically. Standing wave is a sound field superposed by two planes with same frequency but travel in opposite directions. In the standing wave tube, the equation of the incident sound wave is assumed to be � � 2π p1 ¼ sin ϖt x ; (7) λ
has a simple harmonic vibration at the same frequency, but the ampli tude varies with position. The maximum amplitude of sound pressure is equal to the amplitude of incident wave, and the corresponding position is called antinode. The minimum amplitude of sound pressure is close to zero and the corresponding position is called node [20]. According to Eq. (9), the location of the antinode and node can be obtained. The lo cations of nodes are:
where λ and ϖ are wavelength and angular frequency of acoustic wave. The incident acoustic wave is reflected at the end of the standing wave tube and can be expressed as � � 4π 0 2π p2 ¼ sin ϖt L þ x ; (8) λ λ
xantinodes ¼ L
xnodes ¼ L
λ ð2k1 þ 1Þ; 4
0
k1 ¼ 0; 1; 2; 3…
(10)
And the locations of the antinodes can be expressed as: 0
λ k2 ; 2
k2 ¼ 0; 1; 2; 3…
(11)
The acoustic energy is approximately zero at the node, and becomes the largest at the antinode. For the standing wave tube with a certain length, sound waves with different frequencies generate different posi tions of the node and antinode. Given this characteristic of the standing wave tube, nodes and antinodes could be used to separate the different frequency acoustic waves of the two loops. So it is an effective way to combine standing wave tubes into flow measurement pipeline. Fig. 2 shows a schematic of the principle for achieving the separation of forward and backward frequencies. To overcome the interference of nearby strong local acoustic waves, the acoustic receiver of the back ward loop can be set in the forward standing wave tube, where the backward node and the forward antinode are coincident. Then, the
where L is the length of the standing wave tube. The sound pressure in the standing wave tube obtained by superimposing the incident wave and reflected wave can be expressed as � � � � 2π 0 2π 2π 0 p ¼ p1 þ p2 ¼ 2 sin ϖt (9) L cos x L λ λ λ 0
Thus, when a standing wave is formed, each fluid particle in the tube
Fig. 3. Experimental platform. 3
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Fig. 4. Schematic of the electroacoustic mixed resonant circuit.
velocity measurement system consists of two standing wave tubes, a copper pipe, two circuit boards, and two through-hole mufflers. The standing wave tubes and copper pipe are designed in accordance with the results obtained in Section 3. The test pipe and the standing wave tubes are closely connected with very narrow slit. The slit is at least less than 0.01 mm, and sealed with PTFE tape. The through-hole mufflers are installed at both ends of the measurement system. They can eliminate the acoustic reflection caused by acoustic impedance mutation on both sides of the system and reduce the external noise in the resonant system. The through-hole mufflers can also prevent the reflection of sound waves and external noise from influencing the original internal pressure distribution. The air compressor blows air into one muffler; the air en ters the flow measurement system and arrives at the reference flowmeter from another muffler. Although the propagation time of the electrical signal is disregarded in the calculation and analysis of the resonant loop, the processing of the electrical signal is crucial in the actual system. The two circuit boards in Fig. 3 are designed for different resonant frequencies. To shield the circuit from electromagnetic interference, the circuit boards are installed in the shielding box in the actual experiment. Fig. 4 shows a schematic of the electroacoustic mixed resonant circuit, which mainly includes an electroacoustic conversion module and an acoustic-electro conversion module. After the acoustic–electro conversion module converts the acoustic signal into an electrical signal, the preamplifier circuit replenishes the signal gain, the filter circuit selects the desired high-order harmonic frequencies, and the automatic gain control (AGC) circuit ensures that the signal has a uniform amplitude. Electroacoustic drive signals are provided directly by the received sinusoidal acoustic signals. The transducer is driven by the power amplifier circuit to re-emit the acoustic wave. Combined with the standing wave characteristics of sound waves in the pipeline, the circuit system forms two sets of auto matic frequency selectors. Velocity information can be obtained when the two groups of real-time resonance frequencies are collected.
backward acoustic receiver can completely avoid the influence of nearby forward acoustic wave on the basis of guaranteeing the strength of the backward acoustic wave. A forward receiver should also be set at the coincidence point of the backward node and forward antinode in the backward standing wave tube to ensure that the forward sound waves are received without being subjected to the backward acoustic wave. In this system, another objective is to emit sound waves generated by the transducer in the standing wave tube into the pipeline as strong as possible. Thus, the pipe should pass through the standing wave tube at the position of the corresponding frequency’s antinode. It means that the pipeline passes from the forward standing wave tube at the position of the forward antinode, and the backward standing wave tube at the po sition of the backward antinode. Meanwhile, to facilitate the sound wave that passes in and out of the pipe, several long slots must be set on the side wall of the pipe at the intersection of the pipe and the standing wave tubes. Combined with the attenuation and plane wave cut-off conditions, parameter selection of the standing wave tube must be performed ac cording to the actual situation. Here, a set of parameters are obtained according to the results of the calculation. The length of the resonator is 2287 mm, and the diameter is 15 mm. The fundamental frequency of the resonator is 150 Hz at the speed of 343 m/s. If the high-order frequency in the forward loop uses N ¼ 64, then f ¼ 9.6 kHz; if the high-order fre quency in the backward loop uses N ¼ 60, then, f ¼ 9 kHz. The radius of the standing wave tube is 10 mm, the length of the standing wave tube is set to seven times the wavelength of 9.3 kHz, and the length L’ ¼ 258.3 mm. The backward acoustic receiver is placed at the position of x ¼ 107:5mm in the forward standing wave tube, and the forward acoustic receiver is placed at the position of x ¼ 115:5mm in the back ward standing wave tube. The location of the intersection of the forward standing wave tube and the pipe is at the position of x ¼ 79:8mm; the position where the backward standing wave tube intersects with the pipe is at x ¼ 86:85mm. 4. Experimental results and analysis
4.2. Experimental results and discussion
4.1. Experiment platform
Eq. (6) shows that the fluid flow velocity is proportional to the fre quency difference. The measured resonant frequency difference was compared with the fluid flow measured by the reference flowmeter to verify the bidirectional high-order acoustic resonance velocity method. When the room temperature is controlled at 20 � C and the gas is stationary in the pipeline, the forward and backward loops can achieve synchronous and stable resonance. The actual forward resonance fre quency is 9543.6 Hz, and the backward resonance frequency is 8926.9 Hz. The experimental value differs from the theoretical value because the propagation time of the electrical signal is disregarded, and the length of the entire resonant loop is slightly different during the installation process. Therefore, the difference between the experimental and calculated values is reasonable.
As shown in Fig. 3, the experimental platform is mainly composed of a gas source, reference flowmeter, and bidirectional high-order acoustic resonance velocity measurement system. A thermal mass flowmeter (MF5700 gas flowmeter) is used as the reference due to its advantage in low flowrate measurement. Generally, the lower limit of velocity mea surement accuracy of an ordinary ultrasonic flowmeter can only reach 0.2 m/s, whereas that of the thermal mass flowmeter can reach at least 0.01 m/s and guarantee 2% measurement accuracy [22]. The focus of this experiment is the low velocity section, which is a suitable option at the present principle verification stage. The host computer collects the resonant frequency of the resonance loops through the frequency acquisition circuit board. The bidirectional high-order acoustic resonant 4
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Fig. 5. Relation between forward flowrate and frequency difference within error bars.
Fig. 6. Relation between the backward flowrate and the frequency difference within error bars.
Both resonance frequencies are normalized to visualize the rela tionship between the frequency difference and flowrate. The relation ship between the frequency difference and the instantaneous flow of the reference flowmeter is shown in Fig. 5, where the abscissa is the instantaneous flowrate measured by the reference flowmeter (the co ordinate unit is converted to m/s from L/min according to the conven tion of ultrasonic flowmeter) and the ordinate is the resonant frequency difference of the forward and backward loops. Fig. 5 shows the result of repeated measurements of some flowrate points, the scatter is the data point of average, and the error bars represent the variance of multiple measurements. In the figure, the frequency difference and the flowrate maintain a good linearity, and the maximum repeatability error is 0.0148 m/s. This measurement method does not limit the direction of gas flow. For verification, we measured the backward flow using the same approach as that for the forward flow measurement by adjusting the position of the reference flowmeter and gas source. The relationship between the frequency difference and the flow is shown in Fig. 6. The frequency difference and the flowrate in the backward measurement are indicated by a negative value to show the difference from the forward
measurement result. The coordinates have the same definition as those in Fig. 5. The measurement results show that the system can ensure good linearity even when the fluid flows backward. The system does not need to limit the flow direction during flow measurement and has strong measurement flexibility. Fig. 7 shows a set of experimental data points for flow measurement. It suggests that, the resonant frequency difference is sensitive to the change in the flow, even in the domain of low flowrate. The maximum linearity error is 5.09%, which is superior to the initial linearity error in other studies [6]. Furthermore, especially in the low flow area, there is no obvious decline trend in accuracy. The lower limit of measurement is less than 0.03 m/s, and is same or superior than traditional ultrasonic flowmeters such as AquaTrans serial of GE. At present, the experimental system is vulnerable to the influence of temperature. Hence, the mea surement error in the calibration process is difficult to reduce. However, the system still maintains good sensitivity and linearity in low flow velocity range. Evidently, the performance of the principle verification system demonstrated that this flowrate measurement method has a very large improvement space. Actually, this method can be applied to air, natural gas and various 5
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Fig. 7. A set of experimental data points for flow measurement and their linear fitting curve.
gases. And the approach of bidirectional synchronous measurement will ensure that the flowrate measurement is not influenced by the sonic velocity in theory. Hence, the measurement would almost not be affected by temperature. But in the actual experiment, it was found that the frequency difference varies with temperature and presents a certain linear relationship. The greatest possibility comes from the asymmetry of the bidirectional resonant circuit, which makes the current system sensitive to temperature.
[4] H. Nishiguchi, T. Sawayama, K. Nagamune, Evaluation of the propagation time difference in low-pressure city gas flow using a clamp-on ultrasonic flowmeter, Jpn. J. Appl. Phys. (07JC017) (2017) 561. [5] W. Kang, et al., Effect of ultrasonic noise generated by pressure control valves on ultrasonic gas flowmeters, Flow Meas. Instrum. 60 (2018) 95–104. [6] Y. Yu, G. Zong, Note: ultrasonic liquid flow meter for small pipes, Rev. Sci. Instrum. 83 (02610721) (2012). [7] H. Ishikawa, et al., Development of a new ultrasonic liquid flowmeter for very low flow rate applicable to a thin pipe, in: 9th International Symposium on Semiconductor Manufacturing (ISSM2000), IEEE, TOKYO, JAPAN, 2000, pp. 383–386. [8] A.R. Guilbert, M. Law, M.L. Sanderson, A novel ultrasonic/thermal clamp-on flowmeter for low liquid flowrates in small diameter pipes, Ultrasonics 34 (2–5) (1996) 435–439. [9] M.L. Sanderson, H. Yeung, Guidelines for the use of ultrasonic non-invasive metering techniques, Flow Meas. Instrum. 13 (2002) 125–142. PII S0955-5986(02) 00043-24. [10] Y. Jiang, et al., A model-based hybrid ultrasonic gas flowmeter, IEEE Sens. J. 18 (11) (2018) 4443–4452. [11] L. Qin, et al., Application of extreme learning machine to gas flow measurement with multipath acoustic transducers, Flow Meas. Instrum. 49 (2016) 31–39. [12] H. Zhou, et al., Multipath ultrasonic gas flow-meter based on multiple reference waves, Ultrasonics 82 (2018) 145–152. [13] L. Qin, et al., Flowrate determination for arbitrary multipath arrangement based on generalized inverse of matrix, IEEE Sens. J. 17; 17 (12; 12) (2017) 3625–3634. [14] Q. Chen, W. Li, J. Wu, Realization of a multipath ultrasonic gas flowmeter based on transit-time technique, Ultrasonics 54 (1) (2014) 285–290. [15] J.R. Gatabi, et al., An improved measurement algorithm for increasing the accuracy of sing-around type ultrasonic flow meters, Mechanika (2) (2012) 209–213. [16] J. Delsing, A new velocity algorithm for sing-around-type flow meters, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 34 (4) (1987) 431–436. [17] J.P.R. Abbott, et al., Feasibility of a long-wavelength acoustic flowmeter for measuring smokestack emissions, J. Acoust. Soc. Am. 139 (4) (2016), 2120-2120. [18] J.P.R. Abbott, et al., Determining average flow speed in a scale model smokestack by measuring correlated noise through a long-wavelength acoustic flow meter, J. Acoust. Soc. Am. 140 (4) (2016), 3259-3259. [19] L.E. Kinsler, et al., Fundamentals of Acoustics, fourth ed., John Wiley & Sons, Inc, 1999. [20] E.S. IKPE, et al., A standing-wave flow measurement system for small-diameter pipes using long acoustic-waves, Rev. Sci. Instrum. 64 (9) (1993) 2666–2672. [21] K. Amri, et al., Fluid flow velocity measurement using dual-ultrasonic transducer by means of simultaneously transit time method, in: 2015 4th International Conference on Instrumentation, Communications, Information Technology, and Biomedical Engineering (ICICI-BME), IEEE, NEW YORK, 2015, pp. 113–116. [22] M. Farzaneh-Gord, et al., Potential use of capillary tube thermal mass flow meters to measure residential natural gas consumption, J. Nat. Gas Sci. Eng. 22 (2015) 540–550.
5. Conclusion A bidirectional high-order acoustic resonance flowrate measurement method is proposed to address the difficulty in improving flowrate measurement sensitivity and accuracy in small-diameter, low-velocity pipelines. The method realizes the synchronous work of forward and backward measurement units. This method is described in detail, and the measurement system is verified through an experiment. The results show that the high-order resonant frequency amplifies the frequency offset caused by the fluid flow. The resonant frequency is sensitive to a tiny change in flowrate, and the measurement system has good linearity and small lower flow limit, indicating that this method is particularly suitable for the measurement of small-diameter, low-flowrate pipelines. An in-depth investigation of this new method would open up new application possibilities for acoustic flowmeters. Declaration of competing interest The authors declared that they have no conflicts of interest to this work. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted. References [1] L.C. Lynnworth, Y. Liu, Ultrasonic flowmeters: half-century progress report, 19552005, Ultrasonics 441 (2006) E1371–E1378. [2] D. Zheng, et al., A method based on a novel flow pattern model for the flow adaptability study of ultrasonic flowmeter, Flow Meas. Instrum. 29 (2013) 25–31. [3] D. Zheng, D. Zhao, J. Mei, Improved numerical integration method for flowrate of ultrasonic flowmeter based on Gauss quadrature for non-ideal flow fields, Flow Meas. Instrum. 41 (2015) 28–35.
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