Acoustic field distribution in the measuring space of ultrasonic volumetric flowmeter is mainly determined by the performance of the transducer and the flow field under actual conditions. A hybrid approach combining measured boundary conditions and numerical method was used to predict the acoustic field, in order to solve the problem that only using numerical method has the difficulty in accurately modeling important calculation parameters of actual transducer. The vibration boundary condition of calculation model is accurately obtained by using a laser scanning vibrometer to measure vibration velocity of discrete points on transducer surface and following a data fitting computation, which means that the transducer with the most modelling uncertainty is replaced by the experimental data. The flow fields inside the ultrasonic volumetric flowmeter under different volume flowrates were calculated by computational fluid dynamics, and then the simulation results were inserted into the numerical calculation model as the background field. The acoustic field can be predicted by solving the governing equation derived from linear wave acoustic equations in non-uniform flow with the help of the finite element software COMSOL. The proposed hybrid approach is validated by comparing the predicted and experimental data.
Nan-nan ZHAO,Liang HU,Kai MAO,Wen-yu CHEN,Xin FU. Hybrid determination method for acoustic field of ultrasonic volumetric flowmeter. Journal of ZheJiang University (Engineering Science), 2020, 54(8): 1466-1473.
Tab.2Effective amplitude of output voltage signal at different flowrates
Fig.10Comparison between predicted pressure and measured voltage
[1]
O'SULLIVANI J, WRIGHT W M Ultrasonic measurement of flow using electrostatic transducers[J]. Ultrasonics, 2002, 40 (1–8): 407- 411
[2]
LYNNWORTH L C, LIU Y Ultrasonic flowmeters: half-century progress report, 1955–2005[J]. Ultrasonics, 2006, 44 (Suppl ement): 1371- 1378
[3]
RAJITA G, MANDAL N. Review on transit time ultrasonic flowmeter [C]// 2nd International Conference on Control, Instru-mentation, Energy and Communication (CIEC). Kolkata: IEEE, 2016: 88-92.
[4]
LYGRE A, VESTRHEIM M, LUNDE P, et al Numerical simulation of ultrasonic flowmeters[J]. Ultrasonics International, 1987, 25 (6): 196- 201
[5]
BOONE M, VERMAAS E A A new ray-tracing algorithm for arbitrary inhomogeneous and moving media, including caustics[J]. Journal of the Acoustical Society of America, 1991, 90 (4): 2109- 2117
doi: 10.1121/1.401638
[6]
IOOSS B, LHUILLIER C, JEANNEAU H Numerical simulation of transit-time ultrasonic flowmeters: uncertainties due to flow profile and fluid turbulence[J]. Ultrasonics, 2002, 40 (9): 1009- 1015
doi: 10.1016/S0041-624X(02)00387-6
[7]
KUPNIK M, O'LEARY P, SCHRODER A, et al. Numerical simulation of ultrasonic transit-time flowmeter performance in high temperature gas flows [C] // IEEE Symposium on Ultrasonics. Honolulu: IEEE, 2004: 1354-1359.
[8]
ZHENG D, MEI J, WANG M Improvement of gas ultrasonic flowmeter measurement nonlinearity based on ray tracing method[J]. Iet Science Measurement and Technology, 2016, 10 (6): 602- 606
doi: 10.1049/iet-smt.2015.0310
[9]
郑丹丹, 王蜜, 孙彦招 速度分布对气体超声体积流量计声传播规律的影响[J]. 天津大学学报: 自然科学与工程技术版, 2017, 50 (11): 1169- 1175 ZHENG Dan-dan, WANG Mi, SUN Yan-zhao Effect of velocity distribution on acoustic propagation of gas ultrasonic flowmeter[J]. Journal of Tianjin University: Science and Technology, 2017, 50 (11): 1169- 1175
[10]
HUGHES T J R The finite element method: linear static and dynamic finite element analysis[J]. Religion, 2003, 6 (2): 222
[11]
LERCH R Simulation of piezoelectric devices by two- and three-dimensional finite elements[J]. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 1990, 37 (3): 233- 247
doi: 10.1109/58.55314
[12]
WOJCIK G L, VAUGHAN D K, ABBOUD N, et al. Electrome-chanical modeling using explicit time-domain finite elements [C] // Proceedings of the IEEE Ultrasonics Symposium. Baltimore: IEEE, 1993: 1107-1112.
[13]
ECCARDT P C, LANDES H, LERCH R Applications of finite element simulations to acoustic wave propagation within flowing media[J]. International Journal of Computer Applications in Technology, 1998, 11 (3): 163- 169
[14]
PIERCE, ALLAN D Wave equation for sound in fluids with unsteady inhomogeneous flow[J]. The Journal of the Acoustical Society of America, 1990, 87 (6): 2292
doi: 10.1121/1.399073
[15]
LUCA A, MARCHIANO R, CHASSAING J C Numerical simulation of transit-time ultrasonic flowmeters by a direct approach[J]. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 2016, 63 (6): 886- 897
[16]
孙伟, 胡文祥. 热黏滞效应对振膜-微声腔耦合系统的影响[C]// 上海-西安声学学会第四届声学学术交流会. 常州: 《声学技术》编辑部, 2015: 22-26. SUN Wei, HU Wen-xiang. Influence of viscothermal effects on coupling system of membrane-micro acoustic cavity [C]// 4th Symposium on Acoustics of Shanghai-Xi'an Acoustic Society. Changzhou: Editorial Department of Acoustic Technology, 2015: 22-26.
[17]
张海澜. 理论声学[M]. 北京: 高等教育出版社, 2012.
[18]
ASTLEY R J, EVERSMAN W Wave envelope and infinite element schemes for fan noise radiation from turbofan inlets[J]. AIAA Journal, 1984, 22 (12): 1719- 1726
doi: 10.2514/3.8843
[19]
MYERS M K On the acoustic boundary condition in the presence of flow[J]. Journal of Sound and Vibration, 1980, 71 (3): 429- 434
doi: 10.1016/0022-460X(80)90424-1
[20]
何祚镛, 赵玉芳. 声学理论基础[M]. 北京: 国防工业出版社, 1981.
[21]
QIN L H, TANG Z Y, HU L, et al Numerical Analysis of transducer installation effect on ultrasonic gas flow meter[J]. Applied Mechanics and Materials, 2014, 687?691: 1019- 1025
doi: 10.4028/www.scientific.net/AMM.687-691.1019
[22]
International Organization of Legal Metrology. Gas meters: Part 1: metrological and technical requirements document rec: OIML R 137-1 I [S]. Paris: International Organization of Legal Metrology, 2006.