Knowledge of the atmosphere-ocean fluxes of greenhouse gases is important to improving our understanding of global warming. The most accurate estimate of flux is via the direct eddy correlation (EC) method, which requires measurements of the vertical wind velocity and gas concentration fluctuations at rates of several Hz.
A collaborative team from Queens University Belfast, working under Dr. S.J.N. Mitchell, the National University of Ireland, Galway, led by Professor B. Ward and the Woods Hole Oceanographic Institution, has been funded under the U.S.-Ireland R&D Partnership Program to develop an EC flux package suitable for use on ships and buoys. To meet the sensitivity requirement for the gas concentration sensor, the team is exploring the use of Photoacoustic Spectroscopy (PAS).
PAS excites molecular vibrations using infrared light. The intensity of the light typically is modulated at acoustic frequencies, and the subsequent collisional de-excitation of the gas produces a sound wave. It has been common to sense this using miniature microphones, but their wide bandwidth limits the detection sensitivity and, to meet our measurement requirements, new detectors are needed.
Several approaches have been proposed. One, pioneered by Gasera Ltd. (Finland), makes use of a silicon cantilever whose motion is sensed using optical interferometry. A second approach, developed by the Laser Science Group at Rice University, is called quartz-enhanced PAS (QEPAS), and uses a resonant quartz tuning fork, which, because of its high Q factor, results in an extremely sensitive detector.
Developing a robust modeling capability for these kinds of detectors facilitates prototyping by enabling us to estimate the expected performance of various approaches before committing to building them. These systems present a true multiphysics problem in that they combine acoustics, fluid dynamics and structural mechanics, and the COMSOL Multiphysics software is proving to be a very useful tool for modeling them.
As an example, presented here are some initial results using COMSOL Multiphysics to model the response of a QEPAS detector. The response of a tuning fork is characterized by its resonant frequency and Q. The latter describes the system damping, which is due to the viscosity of the surrounding gas, the re-radiation of sound and structural damping in the fork material. Additionally, the structure of the acoustic field was modeled within the sample cell and the piezoelectric transduction of the mechanical signal. The Pressure Acoustics and Piezo Solid components were used within the Acoustics Module, and material properties were taken from the Materials Library.
The 3-D model takes advantage of the symmetry plane along the center axis of the tuning fork, and we represented the initial laser power absorption as a line source through the fork's center. This line source forces an acoustic pressure wave that couples mechanically to the tuning fork through a fluid load boundary condition.
The quadrupole nature of the on-resonance re-radiation pattern of the tuning fork structure is visible by comparing it to the off-resonance solution. Damping reduced the resonance frequency from 32.547 to 32.539 kHz, and the Q from 95,726 to 23,242. By contrast, in published experiments a tuning fork excited in vacuum had a Q of 93,4576 and a resonance frequency of 32.764 kHz. At one atmosphere, the Q was reduced to 13,271 and the resonance frequency shifted down by 7.5 Hz.
We have also used our numerical model to investigate related designs, such as the addition of acoustic resonator tubes surrounding the fork. Future work will apply COMSOL Multiphysics modeling to other detector approaches.