Herman-Wallis corrections in dual-pump CARS intensities for combustion temperature and species

Interaction between vibration and rotation in light molecules is responsible for many spectroscopic corrections to the fundamental rigid-rotor model. In this context, we discuss the interpretation of the coherent anti-Stokes Raman scattering (CARS) intensity that is recurrently considered in combustion science to measure high temperatures. Intensity changes are quantified by the Herman-Wallis (HW) factor and, unlike other recent works appearing on the subject where the focus is on thermometry, the present work examines the consequences for the quantitative detection of chemical species. Indeed, the diagnostic potential of CARS spectra is not limited to gas-phase thermometry in that multiple species detection is also possible. To this end, we describe an experiment based on a conventional set-up designed according to the principles of dual-pump CARS that, in our case, allows for the simultaneous measurements of temperatures and mole fractions of nitrogen and oxygen observed in a reference flame operated at equivalence ratios below or near stoichiometry. Two HW factors are compared with common reference to the experimental spectra and the results show that, beyond the confirmation of thermometric corrections of about 0.5% for nitrogen CARS, the choice between different vibrational HW models significantly affects the measurement of mole fractions. The effect reaches 1% for nitrogen at stoichiometric conditions, whereas the sensitivity of oxygen to HW models reaches 2.5%.