A quantitative technique for species concentration determination for lifetimes exceeding the laser free temporal range
Picosecond time-resolved laser-induced fluorescence (PTILIF) was designed to gain a better understanding of laminar and turbulent flame environments by measuring spatially and temporally varying concentrations of minor species in such flames. PITLIF’s ability to simultaneously determine the electronic quenching rate coefficient and species concentration allows the measurements to be quantitative. However, PITLIF has suffered in the past from two, independent upper fluorescence lifetime limits of approximately 3 ns, which has restricted the types of flame chemistries and target molecules that could be investigated. The present work details a new program, Stacker, written to overcome these two lifetime constraints.^ Stacker was created to account for the overlapping of successive fluorescence decay signals that result when the measured signal extends beyond the free temporal range of the laser (12.5 ns). This overlap, defined as pulse stacking, is a function of the fluorescence lifetime, but is considered negligible below approximately 3 ns in PITLIF. Beyond this lifetime an inflation of the measured decay amplitude ensues, which if left uncorrected distorts the calculation of the total number density of the target molecule within the probe volume. ^ To account for this inflation, a relationship between the desired, un-stacked amplitude and the measured, stacked amplitude was developed, namely A = Astacked 1-e-T/t , where T is the free temporal range of the laser (12.5 ns), τ is the fluorescence lifetime, and 1-e(− T/τ) is referred to as the Amplitude Correction Coefficient (ACC). This relation circumvents the first ∼3 ns lifetime limitation.^ The second lifetime limitation is a consequence of the breakdown of a decoupling approximation inherent to the linear iteration scheme utilized in Saturate and Compare. To overcome this limitation the Levenberg-Marquardt Algorithm (LMA) was employed and serves as the kernel for Stacker.^ The efficacy of Stacker was verified by analyzing NO fluorescence data from three different non-premixed CH4/N2 - air counterflow flames. The data contain a spread in fluorescence lifetimes from 1.18 to 7.51 ns. Stacker and Saturate and Compare lifetimes were compared against predicted values using quenching cross-sections from the literature. In each flame tested, Stacker lifetimes exhibited excellent agreement with predictions based on cross-sections from Settersten et al. (2006) for lifetimes up to 7.51 ns.^
Galen B. King, Purdue University, Normand M. Laurendeau, Purdue University.