title: Spectrally Resolved Absorption Tomography for Reacting, Turbulent Gas Phase Systems: Theory and Application
Creators: name: Emmert, Johannes
Publisher: name: UNSPECIFIED
Year: 2022

description: This work proposes tomographic absorption spectroscopy as a complementary measurement method to other non-intrusive methods that are applied in the research of reactive gas-phase flows. A coherent methodological framework based on conventional Bayesian inference is presented, that contains new methods and improvements in several key procedures. The framework relies on linear hyperspectral absorption tomography, that is favored for its higher computational efficiency compared to nonlinear tomography, and separates tomographic reconstruction and spectroscopic regression. The methods target the analysis of direct absorption spectroscopic measurements like direct tunable diode laser absorption spectroscopy. The improved key procedures include a spatial resolution measure based on a modified Maximum-a-posteriori covariance matrix. This resolution measure is applicable to sparse and dense beam arrangements alike, without inconsistencies arising from unprobed mesh nodes. The compatibility with resolution measures based on point spread functions is demonstrated in simulations. Additionally, the design question of the spatial-temporal resolution trade-off is discussed on spatio-temporal correlation maps with a constraint imposed by the effective measurement data-rate. Typical data-rates of spectrally resolved tomographic absorption spectroscopy setups often do not allow for capturing turbulent structures. In consequence, the optimum trade-off for quasi-stationary systems often is the focus on spatial resolution, neglecting temporal resolution. A regularization parameter choice method, relying on residuals of the spectroscopic regressions, is introduced. The idea is to balance noise amplification through under-regularization, and incompatibility with the spectroscopic model through excessive spatial-averaging of temperature structures due to over-regularization. This method allows to partially reclaim the informative advantage of nonlinear tomography, by inferring information on temperature structures from the nonlinear temperature dependence of the spectroscopic model. The selected prior parameters are shown to result in spatial resolutions matching spatial structures in the application cases. The same model error used to judge the compatibility with the spectroscopic model for parameter selection, leads to a temperature bias if temporally averaged data of a turbulent system is fitted by a homogeneous spectroscopic model. Ideas from methods to prevent this bias in spatial averaging are transferred to temporal averaging. The resulting temperature fluctuation model reduces the bias and additionally gives a qualitative measure of temperature fluctuations. The often neglected problem of estimating absorbance spectra from intensity traces is treated with Bayesian inference. This new Bayesian absorbance estimation method is shown to be numerically efficient if large numbers of absorbance traces are to be inferred like in tomography. Unlike fitting methods it is compatible with inhomogeneous line-of-sights without modification or computational penalties. Further, the incident intensity shape is not restricted to arbitrary model functions, but modeled with all degrees of freedom. The framework of methods is applied to practically relevant scenarios in the industrial characterization of selective catalytic reduction systems, and in the research of oxy-fuel combustion. The application cases feature different levels of complexity, with turbulent and laminar flows, stationary and instationary processes, axisymmetric and two dimensional flows, as well as homogeneous and inhomogeneous temperature distributions. Also the scalability of the methods is demonstrated by experiments with beam counts from 8 to 10440, and (pseudo) temporal resolutions of up to 5 kHz. For all application cases a specific discussion of uncertainty and spatial resolution is provided.