Despite that combustion diagnostics have reached high levels of refinement, it remains difficult to make quantitatively accurate nonintrusive measurements of temperature and species concentrations in realistic combustion environments. The goal of the present study is to develop nonintrusive spectral radiation tools to allow efficient high-fidelity determination of temperature and species concentrations in laminar and turbulent combustion systems. Temperature and concentrations are deduced from medium-to-coarse resolution measurements of spectral transmissivity and emitted intensity for homogeneous gas media, nonhomogeneous gas media and turbulent systems considering the turbulence radiation interaction (TRI).
For a homogeneous gas medium, by minimizing the differences between measured and predicted transmissivity spectra, an inverse radiation model is developed to retrieve temperature and species concentrations simultaneously using the the Levenberg-Marquardt optimization method. This model has been validated by experimental measurements. The developed inverse radiation model is used to determine the optimal wavenumber range and resolution by retrieving temperature and species concentrations from a homogeneous gas column for a wide range of temperatures and concentrations. Multiple factors, including spectral region, spectral resolution, temperature and concentration range, and susceptibility to systematic error and random error have been considered. Results are obtained for homogeneous mixtures containing CO2, H2O or CO with N2.
In nonhomogeneous gas media, transmissvities are not sensitive to temperature and concentration distributions, making it impossible to reconstruct temperature and species concentrations fields from transmissivity spectra. Another inverse calculation model is developed using measured line-of-sight emitted spectral intensity data to retrieve temperature profiles. Because intensity spectra are also not sensitive to concentration profiles, this model can only deduce the temperature profile together with an average concentration. Due to the ill-posedness of this inverse problem, additional conditions or criteria are needed to be imposed to determine the most realistic solution. Most regularization methods transform an ill-posed inverse problem into a well-behaved one by adding auxiliary information based on desired or assumed characteristics. Tikhonov regularization imposes smoothness to the solution by adding a regularization term. Tikhonov regularization has been shown to be suitable for solving these ill-posed problems, but it is difficult to select an appropriate regularization parameter, especially for nonlinear problems. A new regularization selection method based on the theory of the discrepancy principle and the L-curve criterion is proposed and shows good generality for different temperature profile inversions. Several types of temperature profiles are retrieved accurately using this method.
For a turbulent system, the nonlinear interaction between turbulence and radiation has profound effects and cannot be neglected when developing inverse radiation tools. In the presence of TRI, temperature and concentration can never be measured directly. An inverse radiation model considering how turbulence and radiation interact along the detector's line-of-sight has been developed to deduce time-averaged and root-mean-square (rms) values of temperature and concentrations as well as the turbulent length scale from the time-averaged transmissivity and its rms spectrum for a single turbulent gas as well as a turbulent gas mixture.