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Investigation of the flow velocity profile in a metering section of an invasive ultrasonic flowmeter
Flow Measurement and Instrumentation 17 (2006) 201–206 www.elsevier.com/locate/flowmeasinst
Investigation of the flow velocity profile in a metering section of an invasive ultrasonic flowmeter Renaldas Raiˇsutis ∗ Ultrasound Institute of Kaunas University of Technology, Studentu st. 50, Kaunas LT-51368, Lithuania Received 3 August 2005; received in revised form 9 November 2005; accepted 23 November 2005
Abstract This paper describes a methodology for measurement and experimentally obtained results of local flow velocity components using invasive flow sensors (thermoanemometers) in the transit time ultrasonic flowmeter recesses. The investigations of the turbulent air flow (4000 < Re < 19 000 and flow rate from 14 m3 /h up to 55 m3 /h) propagation through the metering section were performed. It was estimated that the flow profile in the pipe is asymmetric due to aerodynamic properties of the recesses. Therefore, due to air intake, the curve of the flow profile is inclined to the downstream recess. Bigger flow fluctuations were obtained close to the boundaries between walls of the pipe and cavities of the recesses. The flow velocity in the cavity of the recess has a complicated shape and depends on the flow velocity in the pipe. Near the surface of ultrasonic transducer the flow velocity is more than a few times bigger in the upstream recess. However, far away from the surface of the transducer, due to vortex motion in the cavity of the recess, the flow velocity is bigger in the downstream recess. The reduction in flow velocity in the metering section, due to recesses, was observed experimentally. c 2005 Elsevier Ltd. All rights reserved. Keywords: Ultrasonic flowmeter; Recess; Flow profile; Thermoanemometer; Air velocity meter; Metering section
1. Introduction Ultrasonic gas and flow rate measurements are widely used in industrial and domestic applications [1,2]. The performance of ultrasonic flowmeters was significantly improved by exploiting acoustical measurement channels of different modifications, such as with multiple reflections of ultrasonic signals in a pipe, optimisation of the orientation angle of transducers with respect to the flow direction or application of multi-channel measurement systems [3,4]. In all these cases high accuracy of measurements in a wide range of flow velocities is obtained when the peculiarities of interaction of ultrasound waves with a gas flow are taken into account. For that purpose it is necessary to know the flow velocity profiles in the region where the acoustical measurement channel is located, taking into account the influence of recesses in the pipe, which are used to mount ultrasonic transducers. These ∗ Corresponding address: Ultrasound Institute of Kaunas University of Technology, Studentu st. 50, Kaunas LT-51368, Lithuania. Tel.: +370 37 351162; fax: +370 37 451489. E-mail address: [email protected].
c 2005 Elsevier Ltd. All rights reserved. 0955-5986/$ - see front matter doi:10.1016/j.flowmeasinst.2005.11.004
recesses influence the symmetry of the flow profile along the ultrasonic path, but probably do not affect the profile of the flow outside this region. If the total flow rate is calculated from the ultrasonic measurement data not taking into account the local character of the profile distortions, then an additional measurement error may occur. Therefore, the knowledge of the flow velocity profiles in the metering section of ultrasonic flowmeters is essential when high accuracy of measurements must be achieved in a wide range of flow velocities. The gas flow profiles in the cross-sections of the pipes without recesses are presented in [1–4] Theoretical investigations of gas flow profiles in pipes are reported in [3,5–7]. These investigations usually were carried out in measuring pipes without recesses for mounting of ultrasonic transducers. Therefore, the measured flow velocity profile is limited by the internal walls of the pipes. Actually the gas flow is distributed in the entire space inside a pipe including the recesses of ultrasonic transducers [8,9]. That influences the flow velocity profile in an acoustical channel where the ultrasound beam propagates. The results of the flow distributions in the recesses, obtained using computational fluid dynamic software,
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are presented in [9,10]; however, the authors do not analyse the 3D case. Some experimental results obtained using a single recess and a transducer array are presented in [11]. The objective of this research was an experimental investigation of the gas flow velocity profiles in the acoustical cylindrical measurement channel and in the recesses of ultrasonic transducers of an invasive ultrasonic flowmeter. For this purpose miniature invasive flow sensors such as a thermoanemometer and an air velocity meter were used. Instead of the gas flow, for simplification, there was selected filtered (against the dust) room air (flow rate up to 55 m3 /h up to 208 m3 /h) with stabilized flow, stabilized temperature 21 ◦ C and humidity 52%; the atmospheric pressure was 752 mm Hg. 2. Investigation set-up Measurements of gas flow profiles are complicated, because intrusive sensors distort the flow velocity profile. Optical methods are non-invasive; however, the metering section must be optically transparent and the equipment is suitable only for laboratory investigation [8]. Therefore, it was decided to perform velocity profile measurements with a miniature invasive thermoanemometer. In this investigation the microprocessor measurement unit ALMEMO 2280-8 with two sensors was used. Those sensors were the thermoanemometer FV A645 TH2, version d2.60 (flow velocity measurement range 0–2 m/s, resolution 0.001 m/s) and the air velocity meter FV A915 S140 (rotating vane, flow velocity measurement range 0–40 m/s, resolution 0.01 m/s). The air velocity meter was used as the reference meter to measure an average flow velocity v p at the centre of the straight section of the pipe. Measurements of gas flow profiles along the acoustical channel were performed with the thermoanemometer. The thermoanemometer was used for local flow velocity measurements along the diameter of the pipe. The dimensions of the bar-like housing (length 300 mm and diameter 9 mm) allow performing measurements in pipes up to 100 mm diameter in different directions. The sensitive element of the thermoanemometer is placed inside a cylindrical hole with diameter 5 mm, the centre of which is located 5 mm from the tip of the housing. Close to the hole with a flow sensor there is a second 5 mm diameter hole with a thermometer. This hole may distort the flow profile; therefore, in the case when temperature measurements are not necessary, this hole may be covered. In order to get a complete velocity profile along the acoustic path, the real ultrasonic transducers (whose diameters were 24 mm) were replaced by mock-ups, in the centre of which the cylindrical holes were made. The thermoanemometer was pushed through the holes and in this way the velocity profile was measured. During the flow profile measurements the axis of the hole of the thermoanemometer, in which the sensor is placed, may not coincide with the direction of the flow velocity vector. Such a situation is met when flow profile measurements are carried out along the acoustic path, which usually is at 45◦ with respect to the pipe axis. In this case it is not obvious how the measurement results can be affected by such misalignment.
Performance of the thermoanemometer may be characterised by directivity patterns in two perpendicular planes. The directivity patterns describe the dependence of the signal at the output of the meter at different angles between the flow vector and the axis of the hole. One plane is perpendicular to the axis of the thermoanemometer housing and this directivity pattern is called axial. It was estimated that the axial directivity pattern is in the sector ±30◦. The second plane coincides with the axes of the housing and the flow measurement hole and the corresponding directivity pattern is called angular. It was estimated that the angular directivity pattern is in the sector ±50◦ ; therefore, the mentioned thermoanemometer is suitable to perform measurements of the flow velocity along the acoustic path (at 45◦ with respect to the pipe axis) with sufficient accuracy. Due to the specification provided by ALMEMO the random errors of the thermoanemometer are less than ±3% (of final value). For example at the expected maximal flow velocity 2 m/s (flow rate 28 m3 /h), the absolute random error should not exceed ±0.06 m/s. The random errors of the vane anemometer are ±0.5% of final value, ±1.5% of measured value. 3. Investigation of the flow velocity profiles in the acoustical channel Due to the 3D character of gas flow profiles in pipes with recesses for ultrasonic transducers, experimental methods are most efficient for their investigation. The measurements should be performed along the acoustic path of the metering section, which is inclined with respect to the pipe axis. The objective was to determine regularities and symmetry deviations of the flow profiles in the region of the acoustic path with recesses. Distribution of flow velocities in the acoustical channel, e.g. inside the pipe and recesses of the transducers, was measured using the experimental set-up which is presented in Fig. 1a. The transit time flow section of the ultrasonic flowmeter was replaced by a plastic mock-up Fig. 1a. The plastic (PVCpolyvinylchloride) DN70 pipe 1 (internal roughness close to 5 µm) possesses the mounts (PVC) 2, 3 which are filled with ultrasonic transducer mock-ups 4 and 5 (polished Plexiglas, diameter 24 mm). These mock-ups are movable in the acoustical channel direction. Inside the transducer mockups the housing of the thermoanemometer 6 (FV A645 TH2) with flow sensing (heating) element 7 and thermometer 8 is placed. The anemometer is inclined 45◦ to the flow and it can be moved along the acoustical axis 9. Pipe section 10 was used to cover the hole for the air velocity meter 11 (FV A915 S140). The length of the straight pipe before the blowing engine and the air velocity meter was equal to 30 diameters of the pipe. The distance between the thermoanemometer and the air velocity meter was equal to 20 diameters of the pipe. In order to perform measurements of a gas flow velocity along the acoustical channel, a hole was drilled through transducer mock-up and the thermoanemometer was scanned through it. The centre of the hole coincides with the acoustical axis of the ultrasonic transducer. To avoid leakage of gas the mockup of the transducer fills the recess completely. The front
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Fig. 1. Experimental set-up for the measurement of gas flow profiles in the acoustical channel (a) and recesses (b—case A, c—case B and case C): 1—plastic pipe, 2, 3 — mounts of the transducers, 4, 5—transducer mock-ups, 6—housing of the thermoanemometer, 7—flow sensing element, 8—thermometer, 9—acoustical axis, 10—segment of the pipe, 11—air velocity meter, U —denotes air flow direction, D—diameter of the pipe, l—scanning distance of the thermoanemometer along the acoustical axis, lr —scanning distance of the thermoanemometer along the recess.
surface of the mock-up coincides with the front surface of the transducer. To achieve uniformity of the incident flow, the length of the straight pipe before the metering section with recesses was equal to 40 diameters of the pipe. For the pipe with diameter D = 70 mm, which was used in the measurement stand, and for the velocities v p > 1 m/s flows are only turbulent (Re > 4000). Measurements of the flow velocity profiles in the acoustical channel may be performed in two directions: upstream and downstream. The initial position of the anemometer is such that the edge of the hole with the flow sensing element coincides with the surface of the transducer mock-up. Scanning was performed by 4 mm steps. Measurements by thermoanemometer were performed at two different flow velocities v p (v p = 1 m/s and v p = 2 m/s, 4000 < Re < 9000, v p was measured by air velocity meter FV A915 S140) and the results are presented in Fig. 2. It was estimated that only the upstream measurements performed along the acoustic path are correct (as the configuration presented in Fig. 1). In the case of the upstream measurements the thermoanemometer was scanned windward along the acoustical axis from the upstream recess (Recess 1) to the downstream recess (Recess 2). In the case of the downstream measurements the thermoanemometer was scanned in the opposite direction. The downstream
Fig. 2. Flow velocity profile in the acoustical channel: 1—air flow velocity 1 m/s, 2—air flow velocity 2 m/s, l—scanning distance of the thermoanemometer along the acoustical axis, v—flow velocity in the acoustical channel measured by thermoanemometer; the error bars denote the standard deviation. The positions of the pipe walls are shown by the dashed arrows.
measurements are correct only in a small area near the pipe wall, however, since the flow profile becomes distorted across the pipe. The surface of the housing of the thermoanemometer,
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Fig. 3. Air flow velocity in the upstream and downstream recesses near the surfaces (l = 0) of the transducers mock-ups (case A): 1—upstream recess (Recess 1), 2—downstream recess (Recess 2), vr —flow velocity in the recess, v p —flow velocity in the pipe; the error bars denote the standard deviation.
Fig. 4. Flow velocity in the upstream recess (Recess 1) along the acoustical axis of a transducer (case A): 1—v p = 1 m/s, 2—v p = 2 m/s, 3—v p = 3 m/s, 4—v p = 4 m/s, vr —flow velocity in the recess, lr —scanning distance of the thermoanemometer along the recess; the error bars denote the standard deviation.
directed windward, is causing gas stream formations, which are diverting the main flow from the hole of the flow sensing element. Therefore, the measured flow velocity values decrease when the anemometer is moving deeper. In the case of the upstream measurements the sensing element was placed in the front part of the housing, which does not disturb the flow profile. At the average flow velocity in the pipe v p = 1 m/s, Re = 4000, flow rate 14 m3 /h, the flow profile is asymmetrical, with the maximum shifted to the downstream recess due to air intake (Fig. 2). Similar results are presented in the work describing ultrasonic particle velocimetry in a liquid with a contrast agent. However, the authors do not comment the asymmetry of the obtained profiles [11]. In the upstream recess, far away from the surface of the transducer mock-up, the flow velocity is less than in the downstream recess. At the interfaces between recesses and the pipe the flow velocities (in this case the average flow velocity, measured by air velocity meter FV A915 S140 before the transit time section, was v p = 2 m/s, flow rate 28 m3 /h, Re > 9000) are 80% less than the maximum value in the middle of the pipe (measured by thermoanemometer v = 1.87 m/s) for the upstream recess and 34% for the downstream recess. In such a case a part of the gas (air) flow is diverted to the cavities of the recesses and, as a result, the average flow velocity value in the metering section becomes smaller. This corresponds to the computational results presented in [9]. The recesses of ultrasonic transducers are situated asymmetrically with respect to the flow velocity in a pipe. It is important to measure the flow velocity in the downstream and upstream recesses; therefore, the housing of the thermoanemometer was placed only in the recess cavity. Measurements were carried out using the same set-up which was presented in Fig. 1a and b. The hole of the flow sensing element was located over the surface of the transducer mock-up. The results obtained at a fixed position of the thermoanemometer’s housing are presented in Fig. 3, where vr is the flow velocity in the recesses near the surfaces of the ultrasonic transducers (which were replaced by plastic
mock-ups) and v p is the average flow velocity in the straight section of the pipe. From the results obtained it follows that the difference of the flow velocity vr in the upstream and downstream recesses depends on the flow velocity in the pipe v p . The flow velocity near the surface of the transducer mock-up in the upstream recess is two times bigger than the flow velocity in the downstream recess and is 90% less than the maximum flow velocity in the pipe (v p = 15 m/s, Re = 70 000, flow rate 208 m3 /h). More detailed investigation of the flow velocity in the recesses of transducers was performed using a few different mock-up configurations, as is shown in Fig. 1b and c. Three positions were chosen for scanning (by 2 mm steps). First of all there was performed a scanning along the acoustical axis of the transducer in the recess (Fig. 1b, case A). Then there was performed scanning in the deeper path of the recess (Fig. 1c, case B) and finally in the shallow part of the recess (Fig. 1c, case C). The measurement results in the upstream recess (case A) are shown in Fig. 4. The value of the flow velocity in various depth of the recess has complicated dependence, which characterises aerodynamic properties of the recess space and depends on the flow velocity in the pipe. If the flow velocity in the pipe is less 1 m/s, the velocity flow (curve 1 in Fig. 4) is monotonously increasing from lr = 4 mm. For fast flows in the pipe (2 < v p < 4 m/s, 9000 < Re < 19 000, flow rate 55 m3 /h), the values of the flow velocity above the surface of transducer essentially increase. However, at 4 mm from the surface of the transducer the flow velocity is minimal. Further, the flow velocity increases and achieves a maximum at 12 mm away from the surface of the transducer mock-up. At the boundary between the recess and the pipe the flow velocity starts increasing. The measurement results of the flow velocity in the downstream recess are shown in Fig. 5. In this case dependence at the low flow velocity (curve 1 in Fig. 5) is similar to the
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Fig. 5. Flow velocity in the downstream recess (Recess 2) along the acoustical axis of a transducer (case A): 1—v p = 1 m/s, 2—v p = 2 m/s, 3—v p = 3 m/s, 4—v p = 4 m/s, vr —flow velocity in the recess, lr —scanning distance of the thermoanemometer along the recess; the error bars denote the standard deviation.
dependence at the low flow velocity in the upstream recess (curve 1 in Fig. 4), only the values of the flow velocity in downstream recess are bigger. The beginning of the curves 2, 3, 4 (Fig. 5) is similar to the same curves in the upstream recess (Fig. 4). At the higher flow velocities in the pipe (v p = 3 m/s and v p = 4 m/s) there are maxima in the region lr = (14–17) mm away from the surface of the transducer mock-up (Fig. 5). The maximum value of the flow velocity in the downstream recess achieves 50% compared to the average flow velocity in the straight section of the pipe (measured by air velocity meter FV A915 S140). Measurements in the recess cavity according to Fig. 1c (case B and case C) were carried out only upstream. The dependence of the flow velocity more deeply in the recess path (case B) has flow values a few times less (Fig. 6) compared to such values in the centre of the recess (Fig. 4). The first minimum of the flow velocity in the recess at different flow velocities in the pipe is not at the same distance from the surface of the transducer. In the shorter recess path there are bigger flow velocities (Fig. 7) and there is no significant minimum in curves 1, 2, 3. Recesses covered with a metallic grid were also investigated. From the results obtained it follows that a flow velocity up to v p = 1 m/s in the pipe does not create the significant flow in the recess near the surface (lr = 0 mm) of the transducer mock-up. If a grid is used, such a condition holds up to 2 m/s. It was determined that the use of a metallic grid (thickness of wires 0.2 mm and distance between wires 1 mm) decreases the flow velocity in the recess of a transducer about 0.2 m/s in the range of the flow velocity in the pipe v p from 3 to 10 m/s (14 000 < Re < 50 000). 4. Conclusions The presented technique is suitable to perform investigations of the flow profile deformations in the measurement channel of various configurations of invasive ultrasonic flowmeters.
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Fig. 6. Flow velocity in the deeper recess path (case B, upstream recess): 1— v p = 1 m/s, 2—v p = 2 m/s, 3—v p = 3 m/s, 4—v p = 4 m/s, vr —flow velocity in the recess, lr —scanning distance of the thermoanemometer along the recess; the error bars denote the standard deviation.
Fig. 7. Flow velocity in the shorter recess path (case C, upstream recess): 1— v p = 1 m/s, 2—v p = 2 m/s, 3—v p = 3 m/s, 4—v p = 4 m/s, vr —flow velocity in the recess, lr —scanning distance of the thermoanemometer along the recess; the error bars denote the standard deviation.
It gives information about the deformations of the flow velocity profile in the metering section of the invasive flowmeter and the dependency on the flow velocity in the pipe. It was determined that in the metering channel the profile of a turbulent flow is asymmetric due to recesses in which ultrasonic transducers are mounted. The flow profile is inclined to the direction of the downstream recess. The asymmetrical profile of the multiphase liquid flow, obtained by a transducer array mounted in a single recess, was also presented in [11]; however, the authors do not provide additional comments about its asymmetry. Dependencies of the flow velocity in the recess upon flow velocity in the pipe are rather complicated. They depend not only on the flow velocity in a pipe, but also on the aerodynamic properties of the recess cavity. A bigger error bar indicates the presence of a flow vortex inside the cavity of the recess.
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The presented experimental results prove the influence of the flow vortex, the presence of which was estimated by laser anemometry [8] and computational technique [9], inside the cavity of the transducer recess. Near the surface of the transducer the flow velocity is higher in the upstream recess, so the first maximum of the flow velocity in the upstream recess is near the surface of the transducer mock-up as well. After that follows the flow minimum at approximately 4 mm away from the surface of the transducer. The values of the flow velocity in downstream recesses, due to air intake, are bigger and achieve 50% in comparison with the average flow velocity in the straight section of a pipe. The reduction in flow velocity in the metering section, similar to the results obtained by other authors [9] using computational fluid dynamics package, was observed experimentally. The presented results are important as additional information for correction of the profile factor, which is a function of the flow velocity in the pipe and depends on the arrangement of the metering section. The measured flow profiles of the invasive metering section should improve mathematical models, which are frequently used in flow acoustics and analysed by other authors in [12,13]. Acknowledgments The author would like to thank to Prof. R. Kaˇzys and Dr. A. Vladiˇsauskas for discussions during the preparation of this paper.
References [1] Lynnworth LC. Ultrasonic flow meters. Physical acoustic. New York: Academic Press; 1979. [2] Spitzer DW. Flow measurement: Practical guides for measurement and control. USA: Instrument society of Amer; 1993. [3] Rychagov M, Tereshchenko S, Dean B, Lynworth L. Multipath flowrate measurements of symmetric and asymmetric flows. In: 1st world congress on industrial process tomography. 1999, p. 438–43. [4] Lynnworth LC. Ultrasonic gas flow meters. Meas Control 1995;92–101. [5] Chen XQ, Pereira JCF. Computation modelling of dilute gas particle flow in an ultrasonic gas flow meter. Flow Meas Instrum 1997;3–4:167–82. [6] Froysa KE, Lunde P. A ray theory approach to investigate the influence of flow velocity profiles on transit times in ultrasonic flow meters for gas and liquid. In: North sea flow measurement workshop. 2001. [7] Yeh TT, Mattingly GE. Computer simulations of ultrasonic flowmeter performance in ideal and non-ideal pipeflows. In: Proceedings of the 1997 ASME fluids engineering division summer meeting. 1997, p. 1–6. [8] K¨ochner H, Melling A, Baumg¨artner M. Optical flow field investigations for design improvements of an ultrasonic gas meter. Flow Meas Instrum 1996;3–4:133–40. [9] O’Sullivan IJ, Wright WMD. Ultrasonic measurement of gas flow using electrostatic transducers. Ultrasonics 2002;40:407–11. [10] Sahan RA, Gunes H, Liakopoulos A. A modelling approach to transitional channel flow. Comput Fluids 1998;1:121–36. [11] Carlson J, Ing RK. Ultrasonic particle velocimetry in multiphase flows. In: Proceedings of the IEEE international ultrasonics symposium. 2002, p. 740–3. [12] Willatzen M. Sound propagation in a moving fluid confined by cylindrical walls—a comparison between an exact analysis and the local-plane-wave approximation. J Sound Vibration 2001;247:719–29. [13] Willatzen M. Flow acoustics modelling and implications for ultrasonic flow measurement based on the transit-time method. Ultrasonics 2004;41: 805–10.
Investigation of the flow velocity profile in a metering section of an invasive ultrasonic flowmeter Renaldas Raiˇsutis ∗ Ultrasound Institute of Kaunas University of Technology, Studentu st. 50, Kaunas LT-51368, Lithuania Received 3 August 2005; received in revised form 9 November 2005; accepted 23 November 2005
Abstract This paper describes a methodology for measurement and experimentally obtained results of local flow velocity components using invasive flow sensors (thermoanemometers) in the transit time ultrasonic flowmeter recesses. The investigations of the turbulent air flow (4000 < Re < 19 000 and flow rate from 14 m3 /h up to 55 m3 /h) propagation through the metering section were performed. It was estimated that the flow profile in the pipe is asymmetric due to aerodynamic properties of the recesses. Therefore, due to air intake, the curve of the flow profile is inclined to the downstream recess. Bigger flow fluctuations were obtained close to the boundaries between walls of the pipe and cavities of the recesses. The flow velocity in the cavity of the recess has a complicated shape and depends on the flow velocity in the pipe. Near the surface of ultrasonic transducer the flow velocity is more than a few times bigger in the upstream recess. However, far away from the surface of the transducer, due to vortex motion in the cavity of the recess, the flow velocity is bigger in the downstream recess. The reduction in flow velocity in the metering section, due to recesses, was observed experimentally. c 2005 Elsevier Ltd. All rights reserved. Keywords: Ultrasonic flowmeter; Recess; Flow profile; Thermoanemometer; Air velocity meter; Metering section
1. Introduction Ultrasonic gas and flow rate measurements are widely used in industrial and domestic applications [1,2]. The performance of ultrasonic flowmeters was significantly improved by exploiting acoustical measurement channels of different modifications, such as with multiple reflections of ultrasonic signals in a pipe, optimisation of the orientation angle of transducers with respect to the flow direction or application of multi-channel measurement systems [3,4]. In all these cases high accuracy of measurements in a wide range of flow velocities is obtained when the peculiarities of interaction of ultrasound waves with a gas flow are taken into account. For that purpose it is necessary to know the flow velocity profiles in the region where the acoustical measurement channel is located, taking into account the influence of recesses in the pipe, which are used to mount ultrasonic transducers. These ∗ Corresponding address: Ultrasound Institute of Kaunas University of Technology, Studentu st. 50, Kaunas LT-51368, Lithuania. Tel.: +370 37 351162; fax: +370 37 451489. E-mail address: [email protected].
c 2005 Elsevier Ltd. All rights reserved. 0955-5986/$ - see front matter doi:10.1016/j.flowmeasinst.2005.11.004
recesses influence the symmetry of the flow profile along the ultrasonic path, but probably do not affect the profile of the flow outside this region. If the total flow rate is calculated from the ultrasonic measurement data not taking into account the local character of the profile distortions, then an additional measurement error may occur. Therefore, the knowledge of the flow velocity profiles in the metering section of ultrasonic flowmeters is essential when high accuracy of measurements must be achieved in a wide range of flow velocities. The gas flow profiles in the cross-sections of the pipes without recesses are presented in [1–4] Theoretical investigations of gas flow profiles in pipes are reported in [3,5–7]. These investigations usually were carried out in measuring pipes without recesses for mounting of ultrasonic transducers. Therefore, the measured flow velocity profile is limited by the internal walls of the pipes. Actually the gas flow is distributed in the entire space inside a pipe including the recesses of ultrasonic transducers [8,9]. That influences the flow velocity profile in an acoustical channel where the ultrasound beam propagates. The results of the flow distributions in the recesses, obtained using computational fluid dynamic software,
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are presented in [9,10]; however, the authors do not analyse the 3D case. Some experimental results obtained using a single recess and a transducer array are presented in [11]. The objective of this research was an experimental investigation of the gas flow velocity profiles in the acoustical cylindrical measurement channel and in the recesses of ultrasonic transducers of an invasive ultrasonic flowmeter. For this purpose miniature invasive flow sensors such as a thermoanemometer and an air velocity meter were used. Instead of the gas flow, for simplification, there was selected filtered (against the dust) room air (flow rate up to 55 m3 /h up to 208 m3 /h) with stabilized flow, stabilized temperature 21 ◦ C and humidity 52%; the atmospheric pressure was 752 mm Hg. 2. Investigation set-up Measurements of gas flow profiles are complicated, because intrusive sensors distort the flow velocity profile. Optical methods are non-invasive; however, the metering section must be optically transparent and the equipment is suitable only for laboratory investigation [8]. Therefore, it was decided to perform velocity profile measurements with a miniature invasive thermoanemometer. In this investigation the microprocessor measurement unit ALMEMO 2280-8 with two sensors was used. Those sensors were the thermoanemometer FV A645 TH2, version d2.60 (flow velocity measurement range 0–2 m/s, resolution 0.001 m/s) and the air velocity meter FV A915 S140 (rotating vane, flow velocity measurement range 0–40 m/s, resolution 0.01 m/s). The air velocity meter was used as the reference meter to measure an average flow velocity v p at the centre of the straight section of the pipe. Measurements of gas flow profiles along the acoustical channel were performed with the thermoanemometer. The thermoanemometer was used for local flow velocity measurements along the diameter of the pipe. The dimensions of the bar-like housing (length 300 mm and diameter 9 mm) allow performing measurements in pipes up to 100 mm diameter in different directions. The sensitive element of the thermoanemometer is placed inside a cylindrical hole with diameter 5 mm, the centre of which is located 5 mm from the tip of the housing. Close to the hole with a flow sensor there is a second 5 mm diameter hole with a thermometer. This hole may distort the flow profile; therefore, in the case when temperature measurements are not necessary, this hole may be covered. In order to get a complete velocity profile along the acoustic path, the real ultrasonic transducers (whose diameters were 24 mm) were replaced by mock-ups, in the centre of which the cylindrical holes were made. The thermoanemometer was pushed through the holes and in this way the velocity profile was measured. During the flow profile measurements the axis of the hole of the thermoanemometer, in which the sensor is placed, may not coincide with the direction of the flow velocity vector. Such a situation is met when flow profile measurements are carried out along the acoustic path, which usually is at 45◦ with respect to the pipe axis. In this case it is not obvious how the measurement results can be affected by such misalignment.
Performance of the thermoanemometer may be characterised by directivity patterns in two perpendicular planes. The directivity patterns describe the dependence of the signal at the output of the meter at different angles between the flow vector and the axis of the hole. One plane is perpendicular to the axis of the thermoanemometer housing and this directivity pattern is called axial. It was estimated that the axial directivity pattern is in the sector ±30◦. The second plane coincides with the axes of the housing and the flow measurement hole and the corresponding directivity pattern is called angular. It was estimated that the angular directivity pattern is in the sector ±50◦ ; therefore, the mentioned thermoanemometer is suitable to perform measurements of the flow velocity along the acoustic path (at 45◦ with respect to the pipe axis) with sufficient accuracy. Due to the specification provided by ALMEMO the random errors of the thermoanemometer are less than ±3% (of final value). For example at the expected maximal flow velocity 2 m/s (flow rate 28 m3 /h), the absolute random error should not exceed ±0.06 m/s. The random errors of the vane anemometer are ±0.5% of final value, ±1.5% of measured value. 3. Investigation of the flow velocity profiles in the acoustical channel Due to the 3D character of gas flow profiles in pipes with recesses for ultrasonic transducers, experimental methods are most efficient for their investigation. The measurements should be performed along the acoustic path of the metering section, which is inclined with respect to the pipe axis. The objective was to determine regularities and symmetry deviations of the flow profiles in the region of the acoustic path with recesses. Distribution of flow velocities in the acoustical channel, e.g. inside the pipe and recesses of the transducers, was measured using the experimental set-up which is presented in Fig. 1a. The transit time flow section of the ultrasonic flowmeter was replaced by a plastic mock-up Fig. 1a. The plastic (PVCpolyvinylchloride) DN70 pipe 1 (internal roughness close to 5 µm) possesses the mounts (PVC) 2, 3 which are filled with ultrasonic transducer mock-ups 4 and 5 (polished Plexiglas, diameter 24 mm). These mock-ups are movable in the acoustical channel direction. Inside the transducer mockups the housing of the thermoanemometer 6 (FV A645 TH2) with flow sensing (heating) element 7 and thermometer 8 is placed. The anemometer is inclined 45◦ to the flow and it can be moved along the acoustical axis 9. Pipe section 10 was used to cover the hole for the air velocity meter 11 (FV A915 S140). The length of the straight pipe before the blowing engine and the air velocity meter was equal to 30 diameters of the pipe. The distance between the thermoanemometer and the air velocity meter was equal to 20 diameters of the pipe. In order to perform measurements of a gas flow velocity along the acoustical channel, a hole was drilled through transducer mock-up and the thermoanemometer was scanned through it. The centre of the hole coincides with the acoustical axis of the ultrasonic transducer. To avoid leakage of gas the mockup of the transducer fills the recess completely. The front
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Fig. 1. Experimental set-up for the measurement of gas flow profiles in the acoustical channel (a) and recesses (b—case A, c—case B and case C): 1—plastic pipe, 2, 3 — mounts of the transducers, 4, 5—transducer mock-ups, 6—housing of the thermoanemometer, 7—flow sensing element, 8—thermometer, 9—acoustical axis, 10—segment of the pipe, 11—air velocity meter, U —denotes air flow direction, D—diameter of the pipe, l—scanning distance of the thermoanemometer along the acoustical axis, lr —scanning distance of the thermoanemometer along the recess.
surface of the mock-up coincides with the front surface of the transducer. To achieve uniformity of the incident flow, the length of the straight pipe before the metering section with recesses was equal to 40 diameters of the pipe. For the pipe with diameter D = 70 mm, which was used in the measurement stand, and for the velocities v p > 1 m/s flows are only turbulent (Re > 4000). Measurements of the flow velocity profiles in the acoustical channel may be performed in two directions: upstream and downstream. The initial position of the anemometer is such that the edge of the hole with the flow sensing element coincides with the surface of the transducer mock-up. Scanning was performed by 4 mm steps. Measurements by thermoanemometer were performed at two different flow velocities v p (v p = 1 m/s and v p = 2 m/s, 4000 < Re < 9000, v p was measured by air velocity meter FV A915 S140) and the results are presented in Fig. 2. It was estimated that only the upstream measurements performed along the acoustic path are correct (as the configuration presented in Fig. 1). In the case of the upstream measurements the thermoanemometer was scanned windward along the acoustical axis from the upstream recess (Recess 1) to the downstream recess (Recess 2). In the case of the downstream measurements the thermoanemometer was scanned in the opposite direction. The downstream
Fig. 2. Flow velocity profile in the acoustical channel: 1—air flow velocity 1 m/s, 2—air flow velocity 2 m/s, l—scanning distance of the thermoanemometer along the acoustical axis, v—flow velocity in the acoustical channel measured by thermoanemometer; the error bars denote the standard deviation. The positions of the pipe walls are shown by the dashed arrows.
measurements are correct only in a small area near the pipe wall, however, since the flow profile becomes distorted across the pipe. The surface of the housing of the thermoanemometer,
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Fig. 3. Air flow velocity in the upstream and downstream recesses near the surfaces (l = 0) of the transducers mock-ups (case A): 1—upstream recess (Recess 1), 2—downstream recess (Recess 2), vr —flow velocity in the recess, v p —flow velocity in the pipe; the error bars denote the standard deviation.
Fig. 4. Flow velocity in the upstream recess (Recess 1) along the acoustical axis of a transducer (case A): 1—v p = 1 m/s, 2—v p = 2 m/s, 3—v p = 3 m/s, 4—v p = 4 m/s, vr —flow velocity in the recess, lr —scanning distance of the thermoanemometer along the recess; the error bars denote the standard deviation.
directed windward, is causing gas stream formations, which are diverting the main flow from the hole of the flow sensing element. Therefore, the measured flow velocity values decrease when the anemometer is moving deeper. In the case of the upstream measurements the sensing element was placed in the front part of the housing, which does not disturb the flow profile. At the average flow velocity in the pipe v p = 1 m/s, Re = 4000, flow rate 14 m3 /h, the flow profile is asymmetrical, with the maximum shifted to the downstream recess due to air intake (Fig. 2). Similar results are presented in the work describing ultrasonic particle velocimetry in a liquid with a contrast agent. However, the authors do not comment the asymmetry of the obtained profiles [11]. In the upstream recess, far away from the surface of the transducer mock-up, the flow velocity is less than in the downstream recess. At the interfaces between recesses and the pipe the flow velocities (in this case the average flow velocity, measured by air velocity meter FV A915 S140 before the transit time section, was v p = 2 m/s, flow rate 28 m3 /h, Re > 9000) are 80% less than the maximum value in the middle of the pipe (measured by thermoanemometer v = 1.87 m/s) for the upstream recess and 34% for the downstream recess. In such a case a part of the gas (air) flow is diverted to the cavities of the recesses and, as a result, the average flow velocity value in the metering section becomes smaller. This corresponds to the computational results presented in [9]. The recesses of ultrasonic transducers are situated asymmetrically with respect to the flow velocity in a pipe. It is important to measure the flow velocity in the downstream and upstream recesses; therefore, the housing of the thermoanemometer was placed only in the recess cavity. Measurements were carried out using the same set-up which was presented in Fig. 1a and b. The hole of the flow sensing element was located over the surface of the transducer mock-up. The results obtained at a fixed position of the thermoanemometer’s housing are presented in Fig. 3, where vr is the flow velocity in the recesses near the surfaces of the ultrasonic transducers (which were replaced by plastic
mock-ups) and v p is the average flow velocity in the straight section of the pipe. From the results obtained it follows that the difference of the flow velocity vr in the upstream and downstream recesses depends on the flow velocity in the pipe v p . The flow velocity near the surface of the transducer mock-up in the upstream recess is two times bigger than the flow velocity in the downstream recess and is 90% less than the maximum flow velocity in the pipe (v p = 15 m/s, Re = 70 000, flow rate 208 m3 /h). More detailed investigation of the flow velocity in the recesses of transducers was performed using a few different mock-up configurations, as is shown in Fig. 1b and c. Three positions were chosen for scanning (by 2 mm steps). First of all there was performed a scanning along the acoustical axis of the transducer in the recess (Fig. 1b, case A). Then there was performed scanning in the deeper path of the recess (Fig. 1c, case B) and finally in the shallow part of the recess (Fig. 1c, case C). The measurement results in the upstream recess (case A) are shown in Fig. 4. The value of the flow velocity in various depth of the recess has complicated dependence, which characterises aerodynamic properties of the recess space and depends on the flow velocity in the pipe. If the flow velocity in the pipe is less 1 m/s, the velocity flow (curve 1 in Fig. 4) is monotonously increasing from lr = 4 mm. For fast flows in the pipe (2 < v p < 4 m/s, 9000 < Re < 19 000, flow rate 55 m3 /h), the values of the flow velocity above the surface of transducer essentially increase. However, at 4 mm from the surface of the transducer the flow velocity is minimal. Further, the flow velocity increases and achieves a maximum at 12 mm away from the surface of the transducer mock-up. At the boundary between the recess and the pipe the flow velocity starts increasing. The measurement results of the flow velocity in the downstream recess are shown in Fig. 5. In this case dependence at the low flow velocity (curve 1 in Fig. 5) is similar to the
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Fig. 5. Flow velocity in the downstream recess (Recess 2) along the acoustical axis of a transducer (case A): 1—v p = 1 m/s, 2—v p = 2 m/s, 3—v p = 3 m/s, 4—v p = 4 m/s, vr —flow velocity in the recess, lr —scanning distance of the thermoanemometer along the recess; the error bars denote the standard deviation.
dependence at the low flow velocity in the upstream recess (curve 1 in Fig. 4), only the values of the flow velocity in downstream recess are bigger. The beginning of the curves 2, 3, 4 (Fig. 5) is similar to the same curves in the upstream recess (Fig. 4). At the higher flow velocities in the pipe (v p = 3 m/s and v p = 4 m/s) there are maxima in the region lr = (14–17) mm away from the surface of the transducer mock-up (Fig. 5). The maximum value of the flow velocity in the downstream recess achieves 50% compared to the average flow velocity in the straight section of the pipe (measured by air velocity meter FV A915 S140). Measurements in the recess cavity according to Fig. 1c (case B and case C) were carried out only upstream. The dependence of the flow velocity more deeply in the recess path (case B) has flow values a few times less (Fig. 6) compared to such values in the centre of the recess (Fig. 4). The first minimum of the flow velocity in the recess at different flow velocities in the pipe is not at the same distance from the surface of the transducer. In the shorter recess path there are bigger flow velocities (Fig. 7) and there is no significant minimum in curves 1, 2, 3. Recesses covered with a metallic grid were also investigated. From the results obtained it follows that a flow velocity up to v p = 1 m/s in the pipe does not create the significant flow in the recess near the surface (lr = 0 mm) of the transducer mock-up. If a grid is used, such a condition holds up to 2 m/s. It was determined that the use of a metallic grid (thickness of wires 0.2 mm and distance between wires 1 mm) decreases the flow velocity in the recess of a transducer about 0.2 m/s in the range of the flow velocity in the pipe v p from 3 to 10 m/s (14 000 < Re < 50 000). 4. Conclusions The presented technique is suitable to perform investigations of the flow profile deformations in the measurement channel of various configurations of invasive ultrasonic flowmeters.
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Fig. 6. Flow velocity in the deeper recess path (case B, upstream recess): 1— v p = 1 m/s, 2—v p = 2 m/s, 3—v p = 3 m/s, 4—v p = 4 m/s, vr —flow velocity in the recess, lr —scanning distance of the thermoanemometer along the recess; the error bars denote the standard deviation.
Fig. 7. Flow velocity in the shorter recess path (case C, upstream recess): 1— v p = 1 m/s, 2—v p = 2 m/s, 3—v p = 3 m/s, 4—v p = 4 m/s, vr —flow velocity in the recess, lr —scanning distance of the thermoanemometer along the recess; the error bars denote the standard deviation.
It gives information about the deformations of the flow velocity profile in the metering section of the invasive flowmeter and the dependency on the flow velocity in the pipe. It was determined that in the metering channel the profile of a turbulent flow is asymmetric due to recesses in which ultrasonic transducers are mounted. The flow profile is inclined to the direction of the downstream recess. The asymmetrical profile of the multiphase liquid flow, obtained by a transducer array mounted in a single recess, was also presented in [11]; however, the authors do not provide additional comments about its asymmetry. Dependencies of the flow velocity in the recess upon flow velocity in the pipe are rather complicated. They depend not only on the flow velocity in a pipe, but also on the aerodynamic properties of the recess cavity. A bigger error bar indicates the presence of a flow vortex inside the cavity of the recess.
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The presented experimental results prove the influence of the flow vortex, the presence of which was estimated by laser anemometry [8] and computational technique [9], inside the cavity of the transducer recess. Near the surface of the transducer the flow velocity is higher in the upstream recess, so the first maximum of the flow velocity in the upstream recess is near the surface of the transducer mock-up as well. After that follows the flow minimum at approximately 4 mm away from the surface of the transducer. The values of the flow velocity in downstream recesses, due to air intake, are bigger and achieve 50% in comparison with the average flow velocity in the straight section of a pipe. The reduction in flow velocity in the metering section, similar to the results obtained by other authors [9] using computational fluid dynamics package, was observed experimentally. The presented results are important as additional information for correction of the profile factor, which is a function of the flow velocity in the pipe and depends on the arrangement of the metering section. The measured flow profiles of the invasive metering section should improve mathematical models, which are frequently used in flow acoustics and analysed by other authors in [12,13]. Acknowledgments The author would like to thank to Prof. R. Kaˇzys and Dr. A. Vladiˇsauskas for discussions during the preparation of this paper.
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