Emphasis is made on the dimension of the Jacobian matrix, as it is not fully understood how the species for the time-scale calculation have to be chosen. In other words, one can refer to the full set of species (thus all species will have the same "weight"), but also to a sub-set of

Modelling the physics of combustion remains a challenge due to a large range of temporal and physical scales which are important in these systems. Detailed chemical kinetic mechanisms are used to describe the chemistry involved in the combustion process yielding highly coupled partial differential equations for each of the chemical species used in the mechanism. Recently, Principal Components Analysis (PCA) has shown promise in its ability to identify a low-dimensional manifold describing the reacting system. Several PCA-based models have been developed which may be well-suited for combustion problems; however, several challenging aspects of the model must be addressed. In this paper, the parameterization of state-space variables and PC-transport equation source terms are investigated. The ability to achieve highly accurate mapping through various nonlinear regression methods is shown. In addition, the effect of PCA-scaling on the ability to regress the surface is investigated. Finally, the present work demonstrates the capabilities of the model by solving a reduced system represented by several PC-transport equations for a perfectly stirred reactor (PSR) configuration.

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There is a large range of time and length scales of turbulent fluctuations in an entrained flow coal gasifier. To figure out the turbulent effects on coal gasification processes and the controlling mechanisms of different regions in an entrained flow coal gasifier, the characteristic time and length scales for all major processes are estimated. On the basis of the comparison between the length/time scales of turbulent mixing in all ranges and the characteristic time of homo-and heterogeneous reactions, turbulent effects on reactions and coal gasification processes in different regions in an entrained coal gasifier are studied. In the flame region, there is a strong coupling effect between macro-scale turbulent fluctuation and heterogeneous reactions. The combustion of the volatile is strongly affected by the fluctuation of micro-scale Kolmogorov scales because the diffusion boundary layer of the particles is destroyed by this kind of fluctuation. In the nonflame region, the heterogeneous char gasification reactions are not affected by turbulent fluctuations; however, the coupling effect between turbulent mixing and gas-phase reactions should not be omitted.

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