Tomographic analysis of unsteady, reacting flows: Numerical investigation

The implementation of a new tomographic inversion method as a combustion diagnostic tool fur the study of unsteady, reacting flows is evaluated using numerical experiments to reconstruct two dimensional fuel concentration distributions obtained from a numerical simulation of a turbulent reacting square jet, Reconstructions of nonaxisymmetric fuel concentration distributions are performed at various downstream locations from the jet exit using only a few line integrals made along multiple offsets and viewing angles. The new inversion method expresses the concentration distributions to be reconstructed as a weighted sum of Karhunen-Loeve eigenfunctions, produced by the Karhunen-Loeve procedure. These Karhunen-Loeve eigenfunctions and their associated time coefficients are mathematically constructed to form an optimal representation of the concentration distributions in the square jet and systematically quantify their spatial and temporal downstream evolution. Near the exit of the jet, only one eigenfunction is needed, and farther downstream more eigenfunctions (up to 24) are needed to capture the significant features in the concentration distributions. Ultimately, accurate reconstructions of the fuel concentration distributions at downstream locations away from the jet exit are obtained using only 28 fine integrals, The effect of the number of eigenfunctions used in the reconstruction and the measurement configuration on the reconstruction accuracy is examined.