A comprehensive model for the quantification of linear and nonlinear regime laser-induced fluorescence of OH under A2Σ+←X2Π(1,0) excitation

An analytic model termed the ‘integrated quasi-steady-state’ (IQSS) model for the comprehensive quantification of both linear and nonlinear regime laser-induced fluorescence (LIF) is presented. The IQSS model is optimized for the hydroxyl radical (OH), subject to nanosecond A2Σ+←X2Π(1,0) excitation at pressures close to atmospheric. The IQSS model is particularly relevant to experimental conditions where the LIF signal is both spectrally and temporally integrated, such as in planar laser-induced fluorescence experiments. The IQSS model is based around a quasi-steady-state solution to a four-level rate-equation approximation of the OH molecule; this quasi-steady-state solution is then integrated with a triangular functional form for both the spatial and temporal variations to produce an analytic solution. In order to accurately predict LIF in the nonlinear regime, it is shown that both the temporal and the spatial variations of the laser pulse—or ‘wings’ of the laser pulse—must be adequately accounted for in the LIF model formulation. The IQSS model is successfully verified against detailed numerical simulations for variations in the laser irradiance, quenching environment and temperature. Experimentally, the IQSS model is successfully validated by comparing the predicted and measured OH LIF vs. irradiance dependence in the product gases of a methane–air laminar flame.