Quantifying flare combustion efficiency using an imaging Fourier transform spectrometer.

Mid-wavelength infrared (MWIR) imaging Fourier transform spectrometers (IFTSs) are a promising technology for measuring flare combustion efficiency (CE) and destruction removal efficiency (DRE). These devices generate spectrally resolved intensity images of the flare plume, which may then be used to infer column densities of relevant species along each pixel line-of-sight. In parallel, a 2D projected velocity field may be inferred from the apparent motion of flow features between successive images. Finally, the column densities and velocity field are combined to estimate the mass flow rates for the species needed to calculate the CE or DRE. Since the MWIR IFTS can measure key carbon-containing species in the flare plume, it is possible to measure CE without knowing the fuel flow rate, which is important for fenceline measurements. This work demonstrates this approach on a laboratory heated vent, and then deploys the technique on two working flares: a combustor burning natural gas at a known rate, and a steam-assisted flare at a petrochemical refinery. Analysis of the IFTS data highlights the potential of this approach, but also areas for future development to transform this approach into a reliable technique for quantifying flare emissions.Implications: Our research is motivated by the need to assess hydrocarbon emissions from flaring, which is a critical problem of global significance. For example, recent studies have shown that methane destruction efficiency of flaring from upstream oil may be significantly lower than the commonly assumed figure of 98%; work by Plant et al. , in particular, suggest that this discrepancy amounts to CO2 emissions from 2 to 8 million automobiles annually, considering the US alone. Similarly, the international energy agency (IEA) estimates a global flare efficiency of 92%, which translates in 8 million tons of CH4 emitted by flares in 2020. Highlighted by these studies and supported by the World Bank initiatives toward zero routine flaring emissions, there is an urgent need for oil and gas industry to assess their flare methane emission, and overall hydrocarbon emissions. At the very least, it is critical to identify problematic flare operating conditions and means to mitigate flare emissions. Focusing on remote quantification of plume species, the measurement technique and quantification method presented in this paper is a considerable step forward in that direction by computing combustion efficiency and key components for destruction efficiency.

Raman Spectroscopic Analysis of the Reaction between Al-Si Coatings and Steel.

Hot-stamped ultrahigh strength steel components are pivotal to automotive light-weighting. Steel blanks, often coated with an aluminum-silicon (Al-Si) layer to protect them from oxidation and decarburization, are austenitized within a furnace and then simultaneously quenched and formed into shape. The Al-Si coating melts within the furnace and reacts with iron from the steel to yield an intermetallic phase that provides some long-term corrosion protection. During the intermediate liquid phase, some of the coating may transfer to the furnace components, leading to maintenance costs and operational downtime. A detailed understanding of the coating transformation mechanism is needed to avoid such production issues while ensuring that final intermetallic coatings conform to specifications. We introduce cross-sectional Raman microscopic mapping as a method to rapidly elucidate the coating transformation mechanism. Raman spectroscopic fingerprints for relevant intermetallic compounds were determined using synthesized Al-Fe-Si ternary and Al-Fe binary compounds. These fingerprints were used to map the spatial distribution of intermetallic compounds through cross sections of Al-Si-coated 22MnB5 specimens that were heated at temperatures between 570 and 900 °C. These chemical maps show that the intermetallic fraction of the coating does not grow significantly until formation of η (Al5Fe2) at the steel interface, suggesting that η facilitates extraction of iron from the steel and subsequent diffusion through the coating. Under the heating conditions used here, a series of reactions ultimately lead to a silicon-rich τ2 (Al3FeSi) phase on top of the binary η phase. The technique presented here simplifies structural analysis of intermetallic compounds, which will facilitate prototyping of strategies to optimize hot stamping.

Spatially resolved measurement of the distribution of solid and liquid Si nanoparticles in plasma synthesis through line-of-sight extinction spectroscopy.

In many high-temperature gas-phase nanoparticle synthesis processes, freshly nucleated particles are liquid and solidify during growth and cooling. This study presents an approach to determine the location of the liquid-to-solid phase transition and the volume fraction and number density of particles of both phases within a gas phase reactor. Spectrally-resolved line-of-sight attenuation (LOSA) measurements are applied to a silicon nanoparticle aerosol generated from monosilane in a microwave plasma reactor. A phantom-based analysis using particle number density, particle size, and temperature distribution from direct numerical simulation (DNS) of the reacting flow indicates that the contributions from the two particle phases can be decoupled under practical conditions, even with noisy data. The approach was applied to analyze spatially and spectrally resolved LOSA measurements from the hot gas flow downstream of the plasma zone where both solid and liquid silicon particles coexist. Extinction spectra were recorded along a line perpendicular to the flow direction by a spectrometer with an electron-multiplying charge-coupled device (EMCCD) camera, and two-dimensional projections were deconvolved to obtain radial extinction coefficient distributions of solid and liquid particles across the cross-section of the flow. Particle number densities of both particle phases were retrieved simultaneously based on the size-dependent extinction cross-sections of the nanoparticles. The particle-size distribution was determined via thermophoretic sampling at the same location with subsequent transmission electron microscopy (TEM) analysis. The particle temperature distribution was determined from the particle's thermal radiation based on line-of-sight emission (LOSE) measurements. The approach for phase-selective data analysis can be transferred to other materials aerosol systems as long as significant differences exist in extinction spectra for the related different particle classes.

Laser-induced incandescence for non-soot nanoparticles: recent trends and current challenges.

Laser-induced incandescence (LII) is a widely used combustion diagnostic for in situ measurements of soot primary particle sizes and volume fractions in flames, exhaust gases, and the atmosphere. Increasingly, however, it is applied to characterize engineered nanomaterials, driven by the increasing industrial relevance of these materials and the fundamental scientific insights that may be obtained from these measurements. This review describes the state of the art as well as open research challenges and new opportunities that arise from LII measurements on non-soot nanoparticles. An overview of the basic LII model, along with statistical techniques for inferring quantities-of-interest and associated uncertainties is provided, with a review of the application of LII to various classes of materials, including elemental particles, oxide and nitride materials, and non-soot carbonaceous materials, and core-shell particles. The paper concludes with a discussion of combined and complementary diagnostics, and an outlook of future research.

Efficient Bayesian inference of absorbance spectra from transmitted intensity spectra.

High-resolution absorption spectroscopy is a promising method for non-invasive process monitoring, but the computational effort required to evaluate the data can be prohibitive in high-speed, real-time applications. This study presents a fast method to estimate absorbance spectra from transmitted intensity signals. We employ Bayesian statistics to combine a measurement model with prior information about the shape of the baseline intensity and absorbance spectrum. The resulting linear least-squares problem shifts most of the computational effort to a preparation step, thereby facilitating quick processing and low latency for any number of measurements. The method is demonstrated on simulated tunable diode laser absorption spectroscopy data with additive noise and a fluctuating fringe. Results were highly accurate and the method was computationally efficient, having a processing time of only 2 ms per spectrum.

Kalman filter approach for uncertainty quantification in time-resolved laser-induced incandescence.

Time-resolved laser-induced incandescence (TiRe-LII) data can be used to infer spatially and temporally resolved volume fractions and primary particle size distributions of soot-laden aerosols, but these estimates are corrupted by measurement noise as well as uncertainties in the spectroscopic and heat transfer submodels used to interpret the data. Estimates of the temperature, concentration, and size distribution of soot primary particles within a sample aerosol are typically made by nonlinear regression of modeled spectral incandescence decay, or effective temperature decay, to experimental data. In this work, we employ nonstationary Bayesian estimation techniques to infer aerosol properties from simulated and experimental LII signals, specifically the extended Kalman filter and Schmidt-Kalman filter. These techniques exploit the time-varying nature of both the measurements and the models, and they reveal how uncertainty in the estimates computed from TiRe-LII data evolves over time. Both techniques perform better when compared with standard deterministic estimates; however, we demonstrate that the Schmidt-Kalman filter produces more realistic uncertainty estimates.

General error model for analysis of laser-induced incandescence signals.

This paper presents a novel error model for TiRe-LII signals and illustrates how the model can be used to diagnose a detection system, quantify uncertainties in TiRe-LII, and characterize fluctuations in the measured process. Noise in a single TiRe-LII measurement shot obeys a Poisson-Gaussian noise model. Variation in the aerosol results in shot-to-shot fluctuations in the measured signals. These fluctuations induce a quadratic relationship between the mean and variance of a set of signals. We show how this model can elucidate aspects of the measurement system and fundamental properties of the aerosol, by comparing the noise model to four sets of experimental data.

Measurement-based meshing, basis selection, and prior assignment in chemical species tomography.

Gas distributions imaged by chemical species tomography (CST) vary in quality due to the discretization scheme, arrangement of optical paths, errors in the measurement model, and prior information included in reconstruction. There is currently no mathematically-rigorous framework for comparing the finite bases available to discretize a CST domain. Following from the Bayesian formulation of tomographic inversion, we show that Bayesian model selection can identify the mesh density, mode of interpolation, and prior information best-suited to reconstruct a set of measurement data. We validate this procedure with a simulated CST experiment, and generate accurate reconstructions despite limited measurement information. The flow field is represented using the finite element method, and Bayesian model selection is used to choose between three forms of polynomial support for a range of mesh resolutions, as well as four priors. We show that the model likelihood of Bayesian model selection is a good predictor of reconstruction accuracy.

Improving chemical species tomography of turbulent flows using covariance estimation.

Chemical species tomography (CST) experiments can be divided into limited-data and full-rank cases. Both require solving ill-posed inverse problems, and thus the measurement data must be supplemented with prior information to carry out reconstructions. The Bayesian framework formalizes the role of additive information, expressed as the mean and covariance of a joint-normal prior probability density function. We present techniques for estimating the spatial covariance of a flow under limited-data and full-rank conditions. Our results show that incorporating a covariance estimate into CST reconstruction via a Bayesian prior increases the accuracy of instantaneous estimates. Improvements are especially dramatic in real-time limited-data CST, which is directly applicable to many industrially relevant experiments.

Bayesian approach to the design of chemical species tomography experiments.

Reconstruction accuracy in chemical species tomography depends strongly on the arrangement of optical paths transecting the imaging domain. Optimizing the path arrangement requires a scheme that can predict the quality of a proposed arrangement prior to measurement. This paper presents a new Bayesian method for scoring path arrangements based on the estimated a posteriori covariance matrix. This technique focuses on defining an objective function that incorporates the same a priori information about the flow needed to carry out limited data tomography. Constrained and unconstrained path optimization studies verify the predictive capabilities of the objective function, and that superior reconstruction quality is obtained with optimized path arrangements.

Non-stationary Bayesian estimation of parameters from a body cover model of the vocal folds.

The evolution of reduced-order vocal fold models into clinically useful tools for subject-specific diagnosis and treatment hinges upon successfully and accurately representing an individual patient in the modeling framework. This, in turn, requires inference of model parameters from clinical measurements in order to tune a model to the given individual. Bayesian analysis is a powerful tool for estimating model parameter probabilities based upon a set of observed data. In this work, a Bayesian particle filter sampling technique capable of estimating time-varying model parameters, as occur in complex vocal gestures, is introduced. The technique is compared with time-invariant Bayesian estimation and least squares methods for determining both stationary and non-stationary parameters. The current technique accurately estimates the time-varying unknown model parameter and maintains tight credibility bounds. The credibility bounds are particularly relevant from a clinical perspective, as they provide insight into the confidence a clinician should have in the model predictions.

Laser-absorption tomography beam arrangement optimization using resolution matrices.

Laser-absorption tomography experiments infer the concentration distribution of a gas species from the attenuation of lasers transecting the flow field. Although reconstruction accuracy strongly depends on the layout of optical components, to date experimentalists have had no way to predict the performance of a given beam arrangement. This paper shows how the mathematical properties of the coefficient matrix are related to the information content of the attenuation data, which, in turn, forms a basis for a beam-arrangement design algorithm that minimizes the reliance on additional assumed information about the concentration distribution. When applied to a simulated laser-absorption tomography experiment, optimized beam arrangements are shown to produce more accurate reconstructions compared to other beam arrangements presented in the literature.

Infrared species tomography of a transient flow field using Kalman filtering.

In infrared species tomography, the unknown concentration distribution of a species is inferred from the attenuation of multiple collimated light beams shone through the measurement field. The resulting set of linear equations is rank-deficient, so prior assumptions about the smoothness and nonnegativity of the distribution must be imposed to recover a solution. This paper describes how the Kalman filter can be used to incorporate additional information about the time evolution of the distribution into the reconstruction. Results show that, although performing a series of static reconstructions is more accurate at low levels of measurement noise, the Kalman filter becomes advantageous when the measurements are corrupted with high levels of noise. The Kalman filter also enables signal multiplexing, which can help achieve the high sampling rates needed to resolve turbulent flow phenomena.

Parameter selection methods for axisymmetric flame tomography through Tikhonov regularization.

Deconvolution of optically collected axisymmetric flame data is equivalent to solving an ill-posed problem subject to severe error amplification. Tikhonov regularization has recently been shown to be well suited for stabilizing this deconvolution, although the success of this method hinges on choosing a suitable regularization parameter. Incorporating a parameter selection scheme transforms this technique into a reliable automatic algorithm that outperforms unregularized deconvolution of a smoothed data set, which is currently the most popular way to analyze axisymmetric data. We review the discrepancy principle, L-curve curvature, and generalized cross-validation parameter selection schemes and conclude that the L-curve curvature algorithm is best suited to this problem.

Deconvolution of axisymmetric flame properties using Tikhonov regularization.

We present a method based on Tikhonov regularization for solving one-dimensional inverse tomography problems that arise in combustion applications. In this technique, Tikhonov regularization transforms the ill-conditioned set of equations generated by onion-peeling deconvolution into a well-conditioned set that is less susceptible to measurement errors that arise in experimental settings. The performance of this method is compared to that of onion-peeling and Abel three-point deconvolution by solving for a known field variable distribution from projected data contaminated with an artificially generated error. The results show that Tikhonov deconvolution provides a more accurate field distribution than onion-peeling and Abel three-point deconvolution and is more stable than the other two methods as the distance between projected data points decreases.