The background and results for two simplified read schemes for krypton tagging velocimetry (KTV) are presented. The first scheme utilizes the excitation/re-excitation approach found in the literature but replaces the pulsed dye laser used for the re-excitation step with a continuous wave, narrowband laser diode. The second scheme is a single-laser setup with no read laser where the fluorescence of the tagged Kr is imaged at successive times. Results are presented and compared to historical data for experiments performed in 99%N2/1% Kr and 95% air/5% Kr underexpanded jets. The approach with the laser diode has a higher signal, while the single-laser approach yields more consistent results. Both schemes maintain an SNR comparable to that in the literature, but with a simpler setup that enables future high-repetition rate KTV experiments.

Simplified read schemes for krypton tagging velocimetry in N 2 and air

Experiments were performed to demonstrate a dual-wavelength excitation krypton planar laser-induced fluorescence (Kr PLIF)-based 2D temperature imaging technique in a laminar non-sooting CH4/N2 diffusion flame. The technique exploits the thermochemical dependence of the overlap integral arising from Kr absorption and excitation laser spectra to yield the temperature without the need to know the local mixture composition. The choice of the two excitation wavelengths is made using the knowledge of the fuel mixture and pressure. The two excitation wavelengths lie within the same 4p6S01→→5p[32]2 transition, and their selection is informed such that the resulting Kr PLIF signal ratio depends primarily on the temperature and negligibly on local composition. Mean temperature fields show excellent agreement when compared to Fluent simulations across different regions of the combustion domain, while the single-shot temperature field exhibits slightly degraded accuracy. Overall, the technique provides very similar figures of merit compared to conventional composition-dependent thermometry approaches and showcases a promising scope for application in complex reacting flows.

Demonstration of a two-line Kr PLIF thermometry technique for gaseous combustion applications.

This paper presents multi-path, two-photon excitation cross-section calculations for krypton, using first-order perturbation theory. For evaluation of the two-photon-transition matrix element, this paper formulates the two-photon cross-section calculation as a matrix mechanics problem. From a finite basis of states, consisting of 4p, 5s, 6s, 7s, 5p, 6p, 4d, 5d, and 6d orbitals, electric dipole matrix elements are constructed, and a Green’s function is expressed as a truncated, spectral expansion of solutions, satisfying the Schrodinger equation. Electric dipole matrix elements are evaluated via tabulated oscillator strengths, and where those are unavailable, quantum-defect theory is used. The relative magnitudes of two-photon cross-sections for eight krypton lines in the 190–220 nm range are compared to experimental excitation spectra with good agreement. This work provides fundamental physical understanding of the Kr atom, which adds to experimental observations of relative fluorescence intensity. This is valuable when comparing excitation schemes in different environments for krypton fluorescence experiments. We conclude that two-photon excitation at 212.556 nm is optimal for single-laser, krypton tagging velocimetry or krypton planar laser-induced fluorescence.

Two-photon cross-section calculations for krypton in the 190–220 nm range

A two-line Kr PLIF approach is presented for thermometry in moderately sooting flames. This technique leverages the spectral line-broadening phenomenon to choose the two excitation wavelengths whose Kr PLIF signal ratio effectively cancels out the composition dependence while retaining the temperature dependence. Furthermore, the Kr PLIF ratio for the chosen wavelengths also exhibits a monotonic trend with temperature, and span a wide range of values to ensure adequate dynamic range on the measurements. The technique is evaluated in the near field of an ethylene laminar jet flame where the peak soot loading was about $$0.15~\mathrm{ppm}$$
 . Krypton gas was added in small amounts to both fuel mixture and air co-flow. Comparing the Kr PLIF fields with the LII fields showed that the main source of interference to Kr PLIF signal is from the soot interference, which contributed to a maximum of $$20-50\%$$
 of the total signal at different axial locations. Interestingly, the interference from PAH molecules was observed to be less than $$1\%$$
 of the total signal. The soot interference was retained during data processing to obtain an evaluation of the measurement uncertainty caused by the soot interference and the maximum soot loading that could be tolerated. The temperature in the regions away from soot layers exhibit very consistent values with literature, where the value extended from close to $$300~\mathrm{K}$$
 in the fuel core and air co-flow through about $$2200~\mathrm{K}$$
 in the reaction zone. The presence of soot, however, caused a noticeable depreciation in the measured temperature by about $$200~\mathrm{K}$$
 at the peak sooting location. It is further noted that the mean systematic error of $$50~\mathrm{K}$$
 is expected at $$f_v = 60~\mathrm{ppb}$$
 . This limit is observed to be a strong function of the fractional contribution of the soot interference to the overall signal and can be substantially extended by subtracting the soot interference and using higher excitation energies.

Two-dimensional temperature field imaging in laminar sooting flames using a two-line Kr PLIF approach

Temperature is an important thermochemical property in combusting flows that holds the key to uncovering pollutant formation, flame extinction, and heat release In a practical combustion environment, the local composition is typically unknown, which hinders the effectiveness of many traditional non-intrusive thermometry techniques This study aims to offset this limitation by developing a laser-based thermometry technique that does not require prior knowledge of the local composition Two methods for obtaining temperature are demonstrated in this work, both of which make use of the spectral line broadening of an absorbing species (krypton) seeded into the flow In the first method, the local Doppler broadening is extracted from an excitation scan to yield the corresponding temperature, while the second method utilizes compositional scaling information of the collisional broadening and collisional shift to determine the temperature Both methods are demonstrated by measuring the radial temperature profile of a steady laminar CH4/N2 diffusion flame with an air co-flow The accuracy of the temperature measurements obtained using both methods are evaluated using corresponding temperature profiles determined from computational simulations

Composition-independent mean temperature measurements in laminar diffusion flames using spectral lineshape information

Collisional broadening of krypton 4 p 6 S 0 1 → → 5 p [ 3 2 ] 2 transition centered at 107.3 nm caused by common combustion species is investigated in this work. The present work investigates the compositional and thermodynamic dependencies of the collisional parameters between collision partners with similar electronic energy level gaps. In this situation, the classical expression of dispersive energy during collisions cannot be simplified to obtain closed form equations for the collisional parameters. The broadening parameters, namely collisional full width at half maximum (wc) and collisional shift (δc) are obtained through a two-photon excitation scan of krypton (Kr) present in a mixture containing krypton and the collision partner at 295 K and 101 kPa. The compositional scaling of wc and δc are compared with scaling at situations corresponding to both large and small perturber electronic energy level gaps as compared to the absorber’s electronic energy level gap. In the Kr PLIF system, wc scaling corresponds to a situation where the perturber electronic energy level gap is significantly larger than absorber energy level gap, whereas δc scaling corresponds to when the absorber electronic energy level gap is significantly larger than the perturber electronic energy level gap. Further, contributions from non-dispersive forces are computed to be significantly smaller than dispersive forces, which results to the observed tight scaling. The observed compositional scaling is shown to be consistent with a different collisional partner system (NO as the absorber and combustion species as perturbers), indicating that the scaling obtained with the krypton system is general to situations with perturbers and absorbers having similar electronic energy level spacing.

Collisional broadening of Kr (4p6S01→→5p[32]2) transition with combustion species as collision partners

2D Temperature Field Measurement in a Sooting Flame using the 2-line Kr PLIF Thermometry Technique

Temperature scaling of collisional broadening parameters for krypton (absorber) 4p6S01→5p[3/2]2 electronic transition centered at 107.3 nm in the presence of major combustion species (perturber) is investigated. The absorption spectrum in the vicinity of the transition is obtained from the fluorescence due to the two-photon excitation scan of krypton. Krypton was added in small amounts to major combustion species such as CH4, CO2, N2, and air, which then heated to elevated temperatures when flowed through a set of heated coils. In a separate experimental campaign, laminar premixed flat flame product mixtures of methane combustion were employed to extend the investigations to higher temperature ranges relevant to combustion. Collisional full width half maximum (FWHM) (wC) and shift (δC) were computed from the absorption spectrum by synthetically fitting Voigt profiles to the excitation scans, and their corresponding temperature scaling was determined by fitting power-law temperature dependencies to the wC and δC data for each perturber species. The temperature exponents of wC and δC for all considered combustion species (perturbers) were −0.73 and −0.6, respectively. Whereas the temperature exponents of wC are closer to the value (−0.7) predicted by the dispersive interaction collision theory, the corresponding exponents of δC are in between the dispersive interaction theory and the kinetic theory of hard-sphere collisions. Comparison with existing literature on broadening parameters of NO, OH, and CO laser-induced fluorescence spectra reveal interesting contributions from non-dispersive interactions on the temperature exponent.

Dominic Zelenak

Papers

Demonstration of a two-line Kr PLIF thermometry technique for gaseous combustion applications.

Composition-independent mean temperature measurements in laminar diffusion flames using spectral lineshape information

Collisional broadening of Kr (4p6S01→→5p[32]2) transition with combustion species as collision partners

2D Temperature Field Measurement in a Sooting Flame using the 2-line Kr PLIF Thermometry Technique

Temperature dependence of collisional broadening and shift for the Kr 4 p 6 S 01→5 p [3/2] 2 electronic transition