Hierarchical structure of slow manifolds of reacting flows

Nowadays the mathematical description of chemically reacting flows uses very often reaction mechanisms with far above hundred or even thousand chemical species (and, therefore, a large number of partial differential equations must be solved), which possibly react within more than a thousand of elementary reactions. These chemical kinetic processes cover time scales from nanoseconds to seconds. An analogous scaling problem arises for the length scales. Due to these scaling problems the detailed simulation of three-dimensional turbulent flows in practical systems is beyond the capacity of even today's super-computers. Using simplified sub-models is a way out of this problem. The question arising in mathematical modeling of reacting flows is then: How detailed, or down to which scale has each process to be resolved (chemical reaction, chemistry-turbulence-interaction, molecular transport processes) in order to allow a reliable description of the entire process. Both the chemical source term and the transport term have one important property, namely, they cause the existence of low-dimensional attractors in composition space. When these manifolds can be constructed (described) and parametrized by a small number of variables, it can be used to reformulate and reduce the mathematical description for modeling reacting flows. In this work the hierarchical nature of these low-dimensional manifolds of slow motions is discussed. It is demonstrated how this important feature of reacting flows is accounted for by the standard model reduction methods (like e.g. PEA and QSSA methods) as well as by recently developed concepts of model reduction. The use of the hierarchical nature for identification of the low-dimensional manifolds to devise hierarchical modeling concepts (e.g. for turbulent reacting flows) is additionally discussed

Automatic Construction of REDIM Reduced Chemistry with a Detailed Transport and Its Application to CH4 Counterflow Flames

Extinction limits are important quantities of counterflow diffusion flames. An accurate prediction of extinction limits is necessary for the design of engineering combustion devices involving flame quenching. In this work, the reaction-diffusion manifold (REDIM) reduced chemistry with a detailed transport model is applied for the numerical investigation of extinction limits of counterflow diffusion flames. Unlike other tabulated flamelet models where very detailed information about a particular combustion system is required, the REDIM reduced chemistry can be generated based on the detailed reaction mechanisms, requiring only a minimal additional knowledge of the considered combustion system. Recently, an automatic generation of the REDIM has been introduced and tested for premixed flames. This newly developed algorithm starts with a 1D reduced model, and any higher dimension of the REDIM reduced model can be constructed automatically without any additional information. Such an algorithm largely simplifies the generation of the REDIM reduced chemistry. The focus of this work is to apply this newly developed algorithm for the construction of two-dimensional (2D) and three-dimensional (3D) REDIMs for counterflow diffusion flames. It is shown how 2D and 3D REDIM reduced chemistry can be generated automatically in a generic way according to a hierarchical concept. An oxygen-enriched MILD combustion system CH4/CO2 versus the O-2/CO2 counterflow diffusion flame, whose extinction strain rates had been measured experimentally, is selected as an illustrative example for discussion and validation. The relative errors of predicted extinction strain rates using a 3D REDIM are much less than the experimental uncertainty and the differences using different detailed chemical mechanisms