Finite element modeling of ultrasound measurement systems for gas. Comparison with experiments in air

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.