Bayesian Methods for Gas-Phase Tomography

Gas-phase tomography refers to a set of techniques that determine the 2D or 3D distribution of a target species in a jet, plume, or flame using measurements of light, made around the boundary of a flow area. Reconstructed quantities may include the concentration of one or more species, temperature, pressure, and optical density, among others. Tomography is increasingly used to study fundamental aspects of turbulent combustion and monitor emissions for regulatory compliance. This thesis develops statistical methods to improve gas-phase tomography and reports two novel experimental applications. Tomography is an inverse problem, meaning that a forward model (calculating measurements of light for a known distribution of gas) is inverted to estimate the model parameters (transforming experimental data into a gas distribution). The measurement modality varies with the problem geometry and objective of the experiment. For instance, transmittance data from an array of laser beams that transect a jet may be inverted to recover 2D fields of concentration and temperature; and multiple high-resolution images of a flame, captured from different angles, are used to reconstruct wrinkling of the 3D reacting zone. Forward models for gas-phase tomography modalities share a common mathematical form, that of a Fredholm integral equation of the first-kind (IFK). The inversion of coupled IFKs is necessarily ill-posed, however, meaning that solutions are either unstable or non-unique. Measurements are thus insufficient in themselves to generate a realistic image of the gas and additional information must be incorporated into the reconstruction procedure. Statistical inversion is an approach to inverse problems in which the measurements, experimental parameters, and quantities of interest are treated as random variables, characterized by a probability distribution. These distributions reflect uncertainty about the target due to fluctuations in the flow field, noise in the data, errors in the forward model, and the ill-posed nature of reconstruction. The Bayesian framework for tomography features a likelihood probability density function (pdf), which describes the chance of observing a measurement for a given distribution of gas, and prior pdf, which assigns a relative plausibility to candidate distributions based on assumptions about the flow physics. Bayes’ equation updates information about the target in response to measurement data, combining the likelihood and prior functions to form a posterior pdf. The posterior is usually summarized by the maximum a posteriori (MAP) estimate, which is the most likely distribution of gas for a set of data, subject to the effects of noise, model errors, and prior information. The framework can be used to estimate credibility intervals for a reconstruction and the form of Bayes’ equation suggests procedures for improving gas tomography. The accuracy of reconstructions depends on the information content of the data, which is a function of the experimental design, as well as the specificity and validity of the prior. This thesis employs theoretical arguments and experimental measurements of scalar fluctuations to justify joint-normal likelihood and prior pdfs for gas-phase tomography. Three methods are introduced to improve each stage of the inverse problem: to develop priors, design optimal experiments, and select a discretization scheme. First, a self-similarity analysis of turbulent jets—common targets in gas tomography—is used to construct an advanced prior, informed by an estimate of the jet’s spatial covariance. Next, a Bayesian objective function is proposed to optimize beam positions in limited-data arrays, which are necessary in scenarios where optical access to the flow area is restricted. Finally, a Bayesian expression for model selection is derived from the joint-normal pdfs and employed to select a mathematical basis to reconstruct a flow. Extensive numerical evidence is presented to validate these methods. The dissertation continues with two novel experiments, conducted in a Bayesian way. Broadband absorption tomography is a new technique intended for quantitative emissions detection from spectrally-convolved absorption signals. Theoretical foundations for the diagnostic are developed and the results of a proof-of-concept emissions detection experiment are reported. Lastly, background-oriented schlieren (BOS) tomography is applied to combustion for the first time. BOS tomography employs measurements of beam steering to reconstruct a fluid’s optical density field, which can be used to infer temperature and density. The application of BOS tomography to flame imaging sets the stage for instantaneous 3D combustion thermometry. Numerical and experimental results reported in this thesis support a Bayesian approach to gas-phase tomography. Bayesian tomography makes the role of prior information explicit, which can be leveraged to optimize reconstructions and design better imaging systems in support of research on fluid flow and combustion dynamics

A study on the relationship between internal nozzle geometry and injected mass distribution of eight ECN Spray G nozzles

[EN] Gasoline direct injection (GDI) nozzles are manufactured to meet geometric specifications with length scales on the order of a few hundred microns. The machining tolerances of these nominal dimensions are not always known due to the difficulty in accurately measuring such small length scales in a nonintrusive fashion. To gain insight into the variability of the machined dimensions as well as any effects that this variability may have on the fuel spray behavior, a series of measurements of the internal geometry and fuel mass distribution were performed on a set of eight nominally duplicate GDI “Spray G” nozzles provided by the Engine Combustion Network. The key dimensions of each of the eight nozzle holes were measured with micron resolution using full spectrum x-ray tomographic imaging at the 7-BM beamline of the Advanced Photon Source at Argonne National Laboratory. Fuel density distributions at 2 mm downstream of the nozzle tips were obtained by performing x-ray radiography measurements for many lines of sight. The density measurements reveal nozzle-to-nozzle as well as hole-to-hole density variations. The combination of high-resolution geometry and fuel distribution datasets allows spray phenomena to be linked to specific geometric characteristics of the nozzle, such as variability in the hole lengths and counterbore diameters, and the hole inlet corner radii. This analysis provides important insight into which geometrical characteristics of the nozzles may have the greatest importance in the development of the injected sprays, and to what degree these geometric variations might account for the total spray variability. The goal of this work is then to further the understanding of the relationship between internal nozzle geometry and fuel injection, provide input to improve computational models, and ultimately aid in optimizing injector design for higher fuel efficiency and lower emissions engines.This research was performed at the 7-BM beamline of the APS at Argonne National Laboratory. Use of the APS is supported by the U.S. Department of Energy (DOE) under Contract No. DE-AC02-06CH11357. We gratefully acknowledge the computing resources provided on Blues, a high-performance computing cluster operated by the Laboratory Computing Resource Center at Argonne National Laboratory. We thank Dr. Doga Gürsoy for the use of TomoPy and corresponding user support, as well as Dr. Xianghui Xiao at the APS 2-BM beamline for technical guidance in performing x-ray tomography. Argonne’s x-ray fuel injection research is sponsored by the DOE Vehicle Technologies Program under the direction of Gurpreet Singh and Leo Breton.Matusik, K.; Duke, D.; Sovis, N.; Swantek, A.; Powell, C.; Payri, R.; Vaquerizo, D.... (2017). A study on the relationship between internal nozzle geometry and injected mass distribution of eight ECN Spray G nozzles. En Ilass Europe. 28th european conference on Liquid Atomization and Spray Systems. Editorial Universitat Politècnica de València. 313-320. https://doi.org/10.4995/ILASS2017.2017.4766OCS31332

An Investigation of Geochemical Evidence for Three Paleo-Environments

Three paleo-environments were studied. The first project concerned the Manson Impact and the effect of the Black Hills on the resulting fall-out from this asteroid strike. Samples of the Crow Creek Member were taken east of the Black Hills in Nebraska and South Dakota and samples from the Red Bird Member were taken from the west, in Wyoming. These samples were examined for chemical weathering, soot, shocked quartz, and fossils. The Crow Creek samples had shocked quartz (indicative of an impact), severe chemical weathering, soot, and evidence of tsunamis. There were few calcareous fossils. The Red Bird showed no signs of chemical weathering, a distinct absence of soot and shocked quartz and an abundance of fossils. These results indicate that the Black Hills were large enough to pose an atmospheric and oceanic barrier to the effects of the Manson Impact. The second project dealt with dinosaur eggs which were found in Montana. The eggs were examined and subjected to Computed Tomography Scans. The egg-shell, matrix, and volcanic ash were studied. The egg-shell was found to be from an undescribed oolithic species, and revealed that a transgressive event transpired after the eggs had fossilized. The matrix revealed that the eggs were laid in a flood-plain. The ash revealed a high amount of tungsten and yielded a high percentage of potassium for future dating. The eggs themselves revealed that intact embryos were within. This project has provided information on dinosaur nesting behavior. In the third project corals were examined to determine the usefulness of sampling different architectural structures for evaluating environmental proxies. Coral was collected at the Verde Reef. The different architectural structures were sampled using SIMS, and LA-ICP-MS to selectively sample the small architectural structures. Oxygen isotope ratios and elemental: calcium ratios were compared among the different structures. It was found that dissepiments intake isotopic oxygen and elements at different rates than other structures. This has an impact in sampling corals for environmental proxies, but, because of the very small amount of mass contained in the dissepiments that bulk analyses would not be significantly affected

Three-dimensional visualisation and quantitative characterisation of fossil fuel flames using tomography and digital imaging techniques

This thesis describes the design, implementation and experimental evaluation of a prototype instrumentation system for the three-dimensional (3-D) visualisation and quantitative characterisation of fossil fuel flames. A review of methodologies and technologies for the 3-D visualisation and characterisation of combustion flames is given, together with a discussion of main difficulties and technical requirements in their applications. A strategy incorporating optical sensing, digital image processing and tomographic reconstruction techniques is proposed. The strategy was directed towards the reconstruction of 3-D models of a flame and the subsequent quantification of its 3-D geometric, luminous and fluid dynamic parameters. Based on this strategy, a flame imaging system employing three identical synchronised RG B cameras has been developed. The three cameras, placed equidistantly and equiangular on a semicircle around the flame, captured six simultaneous images of the flame from six different directions. Dedicated computing algorithms, based on image processing and tomographic reconstruction techniques have been developed to reconstruct the 3-D models of a flame. A set of geometric, luminous and fluid dynamic parameters, including surface area, volume, length, circularity, luminosity and temperature are determined from the 3-D models generated. Systematic design and experimental evaluation of the system on a gas-fired combustion rig are reported. The accuracy, resolution and validation of the system were also evaluated using purpose-designed templates including a high precision laboratory ruler, a colour flat panel and a tungsten lamp. The results obtained from the experimental evaluation are presented and the relationship between the measured parameters and the corresponding operational conditions are quantified. Preliminary investigations were conducted on a coal-fired industry-scale combustion test facility. The multi-camera system was reconfigured to use only one camera due to the restrictions at the site facility. Therefore the property of rotational symmetry of the flame had to be assumed. Under such limited conditions, the imaging system proved to provide a good reconstruction of the internal structures and luminosity variations inside the This thesis describes the design, implementation and experimental evaluation of a prototype instrumentation system for the three-dimensional (3-D) visualisation and quantitative characterisation of fossil fuel flames. A review of methodologies and technologies for the 3-D visualisation and characterisation of combustion flames is given, together with a discussion of main difficulties and technical requirements in their applications. A strategy incorporating optical sensing, digital image processing and tomographic reconstruction techniques is proposed. The strategy was directed towards the reconstruction of 3-D models of a flame and the subsequent quantification of its 3-D geometric, luminous and fluid dynamic parameters. Based on this strategy, a flame imaging system employing three identical synchronised RG B cameras has been developed. The three cameras, placed equidistantly and equiangular on a semicircle around the flame, captured six simultaneous images of the flame from six different directions. Dedicated computing algorithms, based on image processing and tomographic reconstruction techniques have been developed to reconstruct the 3-D models of a flame. A set of geometric, luminous and fluid dynamic parameters, including surface area, volume, length, circularity, luminosity and temperature are determined from the 3-D models generated. Systematic design and experimental evaluation of the system on a gas-fired combustion rig are reported. The accuracy, resolution and validation of the system were also evaluated using purpose-designed templates including a high precision laboratory ruler, a colour flat panel and a tungsten lamp. The results obtained from the experimental evaluation are presented and the relationship between the measured parameters and the corresponding operational conditions are quantified. Preliminary investigations were conducted on a coal-fired industry-scale combustion test facility. The multi-camera system was reconfigured to use only one camera due to the restrictions at the site facility. Therefore the property of rotational symmetry of the flame had to be assumed. Under such limited conditions, the imaging system proved to provide a good reconstruction of the internal structures and luminosity variations inside the This thesis describes the design, implementation and experimental evaluation of a prototype instrumentation system for the three-dimensional (3-D) visualisation and quantitative characterisation of fossil fuel flames. A review of methodologies and technologies for the 3-D visualisation and characterisation of combustion flames is given, together with a discussion of main difficulties and technical requirements in their applications. A strategy incorporating optical sensing, digital image processing and tomographic reconstruction techniques is proposed. The strategy was directed towards the reconstruction of 3-D models of a flame and the subsequent quantification of its 3-D geometric, luminous and fluid dynamic parameters. Based on this strategy, a flame imaging system employing three identical synchronised RG B cameras has been developed. The three cameras, placed equidistantly and equiangular on a semicircle around the flame, captured six simultaneous images of the flame from six different directions. Dedicated computing algorithms, based on image processing and tomographic reconstruction techniques have been developed to reconstruct the 3-D models of a flame. A set of geometric, luminous and fluid dynamic parameters, including surface area, volume, length, circularity, luminosity and temperature are determined from the 3-D models generated. Systematic design and experimental evaluation of the system on a gas-fired combustion rig are reported. The accuracy, resolution and validation of the system were also evaluated using purpose-designed templates including a high precision laboratory ruler, a colour flat panel and a tungsten lamp. The results obtained from the experimental evaluation are presented and the relationship between the measured parameters and the corresponding operational conditions are quantified. Preliminary investigations were conducted on a coal-fired industry-scale combustion test facility. The multi-camera system was reconfigured to use only one camera due to the restrictions at the site facility. Therefore the property of rotational symmetry of the flame had to be assumed. Under such limited conditions, the imaging system proved to provide a good reconstruction of the internal structures and luminosity variations inside the flame. Suggestions for future development of the technology are also reported

Tomographic Laser Absorption Imaging of Combustion Gases in the Mid-wave Infrared

This dissertation describes advancements in mid-infrared laser absorption tomography for spatio-temporal measurements of thermochemistry in reacting flows relevant to combustion systems. Tunable laser absorption spectroscopy is combined with tomographic reconstruction techniques to resolve small diameter ( < 1 cm) non-uniform flow fields with steep spatial gradients, leveraging emerging mid-wave infrared photonics. Multiple novel measurement methods, hardware configurations, and image processing techniques were investigated. Initially, a mid-infrared laser absorption tomography sensing method was developed for quantitative measurement of CO and CO2 concentrations and temperature distributions in turbulent premixed jet flames using a translation-stage-mounted optical system. This sensing approach was used to examine effects of varying fuel structure on carbon oxidation over a range of Reynolds number regimes. It was found that spatial and temporal resolution is limited in this method due to the finite laser beam size (~ 1 mm) and the slow mechanical translation of the optical system. To address these limitations, a novel laser absorption imaging (LAI) technique, that expands a single laser beam and replaces the detector with a high-speed infrared camera, was introduced to achieve enhanced spatial and temporal resolution for thermo-chemical imaging. As a demonstration of this new technique, distributions of combustion species were imaged in both axisymmetric and non-axisymmetric flow fields using linear tomography algorithms. For non-axisymetric flows, the limited view tomography problem often results in a blurring effect and artifacts in the reconstructed flow-field. In an effort to address these issues, state-of-the-art deep learning neural networks were developed and applied to solve the limited angle inversion. Initial results suggest that deep neural networks have potential to more accurately predict flame structures with fewer projection angles than linear tomography. This work provides a foundation for a new approach to quantitative time-resolved 3D thermo-chemical imaging in high-temperature reacting flows

Development and Characterization of a Chromotomosynthetic Hyperspectral Imaging System

A chromotomosynthetic imaging (CTI) methodology based upon mathematical reconstruction of a set of 2-D spectral projections to collect high-speed (100 Hz) 3-D hyperspectral data cube has been proposed. The CTI system can simultaneously provide usable 3-D spatial and spectral information, provide high-frame rate slitless 1-D spectra, and generate 2-D imagery equivalent to that collected with no prism in the optical system. The wavelength region where prism dispersion is highest (500 nm) is most sensitive to loss of spectral resolution in the presence of systematic error, while wavelengths 600 nm suffer mostly from a shift of the spectral peaks. The quality of the spectral resolution in the reconstructed hyperspectral imagery was degraded by as much as a factor of two in the blue spectral region with less than 1° total angular error in mount alignment in the two axes of freedom. Even with no systematic error, spatial artifacts from the reconstruction limit the ability to provide adequate spectral imagery without specialized image reconstruction techniques as targets become more spatially and spectrally uniform