Application of reduced state spaces to laser-based measurements in combustion

A systematic exploitation of state variable correlations for increasing the accuracy and significance of laser-based measurements in combustion is proposed, formally developed and applied to an example. Correlations between state variables (species concentrations and temperature) lead to the phenomenon that the realizable states in a combustion system are on or close to low-dimensional manifolds in state space, allowing an approximate description of the system state in terms of a few variables. This makes it feasible to approximately determine the full state of a combustion system by means of just a few simultaneous laser-based measurements. As an example application of the method, a simple system with a low-dimensional manifold is constructed by steady and unsteady flamelets. The fuel and oxidizer correspond to a series of well-documented, turbulent, non-premixed methane/air jet flames (Sandia Flames A-F). This low-dimensional manifold is then used to determine state variables via polarized/depolarized Rayleigh-signals. The results show that even in very complex, turbulent flames, many quantities can be determined by means of just two signals. Some quantities are more prone to errors than others. The errors originate in the sensitivities of species with respect to signal noise and with respect to deviations of the actual states from the assumed, steady/unsteady-flamelet-based low-dimensional manifold.