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Diffraction correction for precision measurements of sound velocity in gas. Is full receiver modelling needed?

  • April 2021
  • Conference: 44th Scandinavian Symposium on Physical Acoustics
  • At: Online
Authors:
Eivind Nag Mosland at University of Bergen
Eivind Nag Mosland
Espen Storheim at Nansen Environmental and Remote Sensing Center
Espen Storheim
Per Lunde at University of Bergen
Per Lunde
Magne Vestrheim at University of Bergen
Magne Vestrheim
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Proceedings of the 44th Scandinavian Symposium on Physical Acoustics, Online, Feb. 1–2, 2021
ISBN 978-82-8123-021-7 1
Diffraction correction for precision measurements of
sound velocity in gas. Is full receiver modelling
needed?
Eivind Nag Mosland1, Espen Storheim2, Per Lunde1,
Magne Vestrheim1, Jan Kocbach3
1 Department of Physics and Technology, University of Bergen, Bergen, Norway
2 Nansen Environmental and Remote Sensing Center, Bergen, Norway
3 NORCE, Bergen, Norway
Contact email: eivind.mosland@uib.no
Extended abstract
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
Proceedings of the 44th Scandinavian Symposium on Physical Acoustics, Online, Feb. 1–2, 2021
ISBN 978-82-8123-021-7 2
  
 
 
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 
 𝑧         


et al.
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
 
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 
 
 
  𝑎        𝑘    
      
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  
   


 

 
         

Proceedings of the 44th Scandinavian Symposium on Physical Acoustics, Online, Feb. 1–2, 2021
ISBN 978-82-8123-021-7 3



𝑓𝑇𝑉𝑅𝑓
𝑅𝑉𝑅
         

 
 
      

          


𝜌𝑐

        


 

 
 

 



 
 
  
Proceedings of the 44th Scandinavian Symposium on Physical Acoustics, Online, Feb. 1–2, 2021
ISBN 978-82-8123-021-7 4



         


  


       

  


References
[1] 

[2] 
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[3]  Physical Acoustics

[4] 
 Proc. 26th Scand. Symp. on Phys. Acoust.

[5]   

Proc.21st Int. North Sea Flow Meas. Workshop, 

[6]             
     Proc. 37th Int. North Sea Flow Meas.
Workshop
[7] 

Proc. 34th Scand. Symp. on Phys. Acoust., 
[8]             

 
[9] 

[10] 

    

[11] 

... 2,3 For real transducers, simpler one-dimensional models and more advanced finite amplitude models of the transducer have been used to study the generated acoustic beam and the diffraction correction. [4][5][6][7] Diffraction correction models have proven useful, for example, in measuring sound speed and absorption in fluid and solid media. [2][3][4] An error in the phase angle of the diffraction correction of a few degrees or less may be significant in high-precision applications like custody transfer flow metering. ...
Parabolic equation simulation of diffraction effects in a sound beam propagating through a flowing fluid
Conference Paper
Full-text available
  • May 2023
Ultrasonic transit time difference flow meters are today industrially accepted for custody transfer measurements of oil and for natural gas. Such meters are currently planned to be used also subsea and in remote operations, where the calibration possibilities are few. In such applications the speed of sound measured by these meters will be a powerful input for estimation of density and calorific value of the flowing oil or gas. The ultrasonic transit time measurements in such meters are carried out in a flowing oil or gas, over a range typically between 4 and 40 in. For precise transit time measurements over such ranges, diffraction corrections may be of high importance. Diffraction effects for an acoustic beam generated by a uniform piston source and propagating through a flowing fluid are therefore studied numerically. The flow direction will be perpendicular to the propagation direction of the acoustic beam. The investigation is based on a narrow-angle three-dimensional parabolic equation. Effects both on amplitude and on phase will be presented.
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... For uniform piston transducers in a non-flowing fluid, this effect is well understood and can be studied by use of the Rayleigh integral [5,6]. For more real transducers radiating into a non-flowing fluid, models of the transducer have been implemented in order to study the generated acoustic beam and the diffraction correction [7,8,9,10]. This includes both 1D models and finite element calculations of the transducer. ...
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Finite element modeling of ultrasound measurement systems for gas. Comparison with experiments in air
Article
  • Oct 2018
Quantitative modeling of ultrasound measurement systems is of considerable value for design, analysis, and interpretation of measurements, methods, and systems. In this work, a model is developed for description of transmit-receive measurement systems based on radial-mode transducer operation in a homogeneous fluid medium. Axisymmetric finite element (FE) modeling is used for the transmitting and receiving piezoelectric transducers and sound propagation in the medium. Transmission-line modeling is used for transmitting and receiving cabling and electronics. The model potentially accounts for the full frequency response of the transducers, including radial and thickness modes, mode coupling, and interaction with the medium. Reciprocal transducers are assumed in the model, and linearity in all parts of the system. Near field effects are accounted for using diffraction correction. Simulations are compared with measurements for the transmit-receive voltage-to-voltage transfer function of two piezoelectric ceramic disk transducers vibrating in air at 1 atm, over the frequency range of the first two radial modes of the disks, and the time domain voltage waveforms at the electric terminals of the transmitting and receiving transducers. The results demonstrate that quantitative simulations of the measurement system can be done with reasonable accuracy. Potentials of improvement are identified and discussed.
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3. The Measurement of Ultrasonic Attenuation
Article
This chapter has recapitulated the methods for making and correcting ultrasonic attenuation measurements such that the results will be accurate absolute quantitative numbers. In many scientific applications of ultrasonic attenuation, the absolute numbers are necessary to provide verification of theories. At least, the scientist must be cognizant of the variances he may introduce by making measurements that he cannot correct back to absolute numbers. Refer, for instance, to Fig. 16 in which it is clear that the diffraction loss correction may be larger than the intrinsic attenuation. Relative measurements on specimens of different thicknesses and/or velocities become meaningless unless they can be corrected for beam spreading. One might hope that relative measurements on a single specimen versus temperature or magnetic field might suffice, but the possible changes in velocity modifying the Seki parameter S = 2lv/a²f should be accounted for and reported, at least. Most important are careful experimentation, cognizance of the errors, and systematic recording of all of the parameters.
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Numerical Calculation of the Diffraction Corrections for the Precise Measurement of Ultrasound Phase Velocity
Article
Calculations and tables are given for the exact diffraction corrections to the results of ultrasound phase velocity measurement for circular transducers of equal radius. Simple formulae have been obtained for the diffraction corrections within the approximations of plane and spherical waves.
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The Piston Source at High Frequencies
Article
  • Jan 1951
For a circular plane piston of radius a, producing an ultrasonic beam with propagation constant k (or 2π/λ), an expression is derived for the velocity potential or the acoustic pressure, averaged with respect to magnitude and phase over a “measurement circle” equal in area to the piston and centered in the beam. The expression should be highly accurate for ka ⩾ 100, at distances z from the source governed by (z/a) 3 ⩾ ka . It agrees well with results computed, in another way, by Huntington, Emslie, and Hughes. The assumption that relatively near the source there is a collimated beam of plane waves is shown to be not very accurate; the averaged pressure falls off monotonically over all distances considered. The velocity potential at the rim of the “measurement circle” is also computed, and compared with the plane wave assumption.
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Transient diffraction effects on ultrasonic flow meters for gas and liquid
  • Jan 2003
  • P Lunde
  • K.-E Frøysa
  • M Vestrheim
P. Lunde, K.-E. Frøysa and M. Vestrheim, "Transient diffraction effects on ultrasonic flow meters for gas and liquid," Proc. 26 th Scand. Symp. on Phys. Acoust., Ustaoset, Norway, Jan. 26-29, 2003.
Gas quality parameters where gas composition cannot be measured online
  • Jan 2019
  • E N Mosland
  • C Saetre
  • K.-E Frøysa
E. N. Mosland, C. Saetre and K.-E. Frøysa, "Gas quality parameters where gas composition cannot be measured online," Proc. 37 th Int. North Sea Flow Meas. Workshop, Tønsberg, Norway, Oct. 22-25, 2019.
Diffraction correction in ultrasonic fields for measurements of sound velocity in gas. Conventional and alternative methods
  • Feb 2011
  • E Storheim
  • P Lunde
  • M Vestrheim
E. Storheim, P. Lunde and M. Vestrheim, "Diffraction correction in ultrasonic fields for measurements of sound velocity in gas. Conventional and alternative methods," Proc. 34 th Scand. Symp. on Phys. Acoust., Geilo, Norway, Jan. 30 to Feb. 2, 2011.
Diffraction effects in the ultrasonic field of transmitting and receiving circular piezoceramic disks in radial mode vibration. FE modelling and comparison with measurements in air
  • Jan 2015
  • E Storheim
E. Storheim, "Diffraction effects in the ultrasonic field of transmitting and receiving circular piezoceramic disks in radial mode vibration. FE modelling and comparison with measurements in air", PhD thesis, Dept. of Physics and Tech., University of Bergen, Bergen, Norway, 2015.
Finite Element Modeling of Ultrasonic Piezoelectric Transducers
  • Jan 2000
  • J Kocbach
J. Kocbach, "Finite Element Modeling of Ultrasonic Piezoelectric Transducers", PhD thesis, Dept. of Physics, University of Bergen, Bergen, Norway, 2000.