A one-way coupled model for the vibration of tuning fork-based trace gas sensors driven by a thermoacoustic wave

摘要

We present a single computational model for both quartz-enhanced photoacoustic spectroscopy and resonant optothermoacoustic detection trace gas sensors. These sensors employ a quartz tuning fork to detect the acoustic pressure and thermal waves generated when a laser excites a trace gas. The model is based on a coupled system of equations developed by Morse and Ingard for pressure and temperature in a fluid. The pressure and temperature solutions drive the resonant vibration of the tuning fork, which is modeled using the equations of linear elasticity. At high ambient pressure, excellent agreement is obtained with laboratory experiments. This result provides the first quantitative match between a fully computational simulation and experiments for a QEPAS sensor. Such a model could ultimately facilitate sensor design optimization. At low ambient pressure (less than 60 Torr), quantitative agreement is obtained after reweighting the contributions from the pressure and thermal components of the signal. While this result is a substantial improvement over previous results in which a scaling factor was required to obtain agreement at any ambient pressure, at low pressures, it appears that a more accurate physical model may be required to match experimental data.