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

Soot emissions from internal combustion engines and aviation gas turbine engines face increasingly stringent regulation, but available experimental datasets for sooting turbulent combustion model development and validation are largely lacking, in part due to the difficulty of making quantitative spaceand time-resolved measurements in this type of flame. To address this deficiency, we have performed a number of different laser and optical diagnostic measurements in sooting, nonpremixed jet flames fueled by ethylene or a prevaporized JP-8 surrogate. Most laser diagnostic techniques inherently lose their quantitative rigor when significant laser beam and signal attenuation occur in sooting flames. However, the ‘3-line’ approach to simultaneous measurement of soot concentration (on the basis of laser extinction) and soot temperature (on the basis of 2-color pyrometry) actually relies on the presence of significant laser attenuation to yield accurate measurements. In addition, the 3-line approach yields complete time-resolved information. In the work reported here, we have implemented the 3-line diagnostic in well-controlled non-premixed ethylene and JP-8 jet flames with a fuel exit Reynolds number of 20,000 using tapered, uncooled alumina refractory probes with a 10 mm probe end separation. Bandpass filters with center wavelengths of 850 nm and 1000 nm were used for the pyrometry measurement, with calibration provided by a hightemperature blackbody source. Extinction of a 635 nm red diode laser beam was used to determine soot volume fraction. Data were collected along the flame centerline at many different heights and radial traverses were performed at selected heights. A data sampling rate of 5 kHz was used to resolve the turbulent motion of the soot. The results for the ethylene flame show a mean soot volume fraction of 0.4 ppm at mid-height of the flame, with a mean temperature of 1450 K. At any given instant, the soot volume fraction typically falls between 0.2 and 0.6 ppm with a temperature between 1300 and 1650 K. At greater heights in the flame, the soot intermittency increases and its mean concentration decreases while its mean temperature increases. In the JP-8 surrogate flame, the soot concentration reaches a mean value of 1.3 ppm at mid-height of the flame, but the mean soot temperature is only 1270 K. Elevated soot concentrations persist for a range of heights in the JP-8 flame, with a rise in mean temperature to 1360 K, before both soot volume fraction and temperature tail off at the top of this smoking flame.

Joint Temperature-Volume Fraction Statistics of Soot in Turbulent Non-Premixed Jet Flames of Ethylene and a JP-8 Surrogate.

Synchrotron x-ray fluorescence has been used to measure temperatures in optically dense gases where traditional methods would fail. These data provide a benchmark for stringent tests of computational fluid dynamics models for complex systems where physical and chemical processes are intimately linked. The experiments measured krypton number densities in a sooting, atmospheric pressure, nonpremixed coflow flame that is widely used in combustion research. The experiments not only form targets for the models, but the simulations also identify potential sources of uncertainties in the measurements, allowing for future improvements.

In situ temperature measurements in sooting methane/air flames using synchrotron x-ray fluorescence of seeded krypton atoms

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.

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

A computational study has been carried out to assess the effectiveness of a porous medium as a passive control device suitable for reducing the drag in a normal-shock-wave/boundary-layer interaction at transonic speeds with a view toward application in aircraft wings. Reduction in overall drag is achieved via recirculation inside the porous medium, which primarily weakens the shock structure and hence reduces the wave drag. The study has been carried out for a Mach 1.3 normal-shock-wave/boundary-layer interaction on a flat plate in the presence of a porous medium beneath the region of interaction. The computations are performed as steady-state RANS calculations using Menter’s SST $$k-\omega /k-\epsilon $$
 model for turbulence closure. A parametric study that investigates the dependency of the effectiveness of control on dimensions of the cavity (length and depth), relative position of the cavity, and porosity of the medium has been carried out. It is observed that the change in overall drag is pronounced for parameters which result in significant changes to the size of the lambda-shock structure, such as the length of the cavity upstream of the inviscid shock location. Among the parameters investigated, porosity is seen to strongly affect the boundary-layer properties, with increase in porosity resulting in higher viscous drag.

Drag reduction in transonic shock-wave/boundary-layer interaction using porous medium: a computational study

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

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

Pressure scaling of collisional broadening parameters of krypton
(absorber) 4p6S01→→5p[3/2]2
transition centered at 107.3 nm in the presence of nitrogen
N2 (perturber) is investigated. The absorption spectrum
in the vicinity of the transition is obtained from the two-photon
excitation scan of krypton in the presence of the perturber at different
prescribed pressures varying from a few torrs to 10 atm. The absorption
spectra reveal noticeable asymmetry at atmospheric pressure, and the
asymmetry becomes increasingly pronounced with pressure; however, the
absorption spectra at sub-atmospheric pressures tested are symmetric. The
absorption spectra are fitted with synthetic asymmetric Voigt profiles
across all pressures, wherein the asymmetry parameter is varied to capture
the asymmetry at different pressures. The collisional shift
(δC), the symmetric equivalent collisional full width at
half maximum (wC,0), and the asymmetry parameter
(a) are determined from the synthetic fits at various pressures.
All the parameters are observed to vary linearly with pressure over the
entire range of the pressure values tested. The mechanisms that cause the
asymmetry in the absorption spectra are also discussed.

Abinash Sahoo

Papers

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

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

Pressure scaling of the collisional broadening parameters of Kr 4p6S01→→5p[3/2]2 transition.

Numerical Investigation of Transonic Flow over Porous Medium Using Immersed Boundary Method