Chemical species tomography of turbulent flows: Discrete ill-posed and rank deficient problems and the use of prior information

• Published in: Journal of quantitative spectroscopy & radiative transfer 2016-03, Vol.172, p.58-74
• Main Authors: Daun, Kyle J., Grauer, Samuel J., Hadwin, Paul J.
• Format: Article
• Language: English
• Subjects: Chemical species tomography; Fluid dynamics; Ill posed problems; Inverse analysis; Radiative transfer; Reconstruction; Small scale; Spectroscopy; Tomography; Turbulence; Turbulent
• ISSN: 0022-4073; 1879-1352
• DOI: 10.1016/j.jqsrt.2015.09.011

Due to the inherent ill-posed nature of chemical species tomography (CST) problems, additional information based on the presumed species distribution must be introduced into the reconstruction procedure. The role that this prior information plays in tomographic reconstruction differs depending on whether the CST problem is discrete ill-posed or rank-deficient. The former case arises mainly in laboratory studies involving small scale problems with high degrees of optical access and often a stationary flow field, while the later occurs when the number and arrangement of measurements are limited by the size and/or the optical access afforded by the containing geometry. This paper elucidates the difference between these two types of CST problems, and reviews various ways that prior information can be used to enhance reconstruction accuracy of CST experiments on turbulent flows. •Chemical species tomography problems are either discrete ill-posed or rank deficient.•Discrete ill-posed problems must be regularized, which limits spatial resolution.•Rank deficient problems need prior information to recover the nullspace component.•The role of prior information can be explicated through Bayesian analysis.