Extension of the ILDM method to the domain of slow chemistry

Abstract

This work focuses on the construction of reduced kinetic models and the use of these models for the simulation of combustion processes governed by strongly coupled thermo-chemical and convection/diffusion sub-processes. The ILDM method is used to reduce the system dynamics in the composition space to lower dimensional manifolds. This manifold approximates an invariant system manifold of slow motions. A modification of the ILDM approach based on a special system representation is suggested, which allows to use an ILDM of low dimension even in cases where the standard formulation would require a high dimension. In this way difficulties of generating relatively high dimensional ILDMs are overcome. The approach allows a more accurate description of coupled thermo-chemical and transport sub-processes. When the processes are split a method of extension of the ILDM manifold to cover all the domain of interest in the full state space is suggested. It is based on the assumption of slow chemistry inside the low-temperature zone of the flame. To verify the approach 1D stationary free flat laminar flames are investigated. It is shown that the approximation allows a representation of the full system dynamics governed by detailed chemical kinetics and molecular transport.

Investigation of the Dynamical Response of Methane/Air Counterflow Flames to Inflow Mixture Composition and Flow Field Perturbations

“…The results show, that it is possible to find lowdimensional manifolds even in the regions of slow chemistry. In this work, we focus on the REDIM method [24] to identify low reaction-diffusion manifolds, a method which is currently being developed and improved [24,25,40]. Until now, this method has not yet been used for analysis purposes.…”

“…For higher-dimensional cases this question is subject of further research. The starting solution for the iteration procedure is for example given by an extended ILDM (extended ILDMs are discussed in [40]) and the obtained stationary solutions ψ(θ, ∞) of the equation system (13) yield the manifold M with any converged solution ψ being a state on the manifold. Let us now discuss, how a already existing flame result can be analysed in the context of REDIM.…”

On-demand generation of reduced mechanisms based on hierarchically extended intrinsic low-dimensional manifolds in generalized coordinates

“…Bykov and Maas [43] suggest a domain-splitting algorithm, in which the extension of the ILDM into the SCD is constructed such that the extended manifold is a locally linear hyperplane, with this hyperplane joining the ILDM boundary with the unburnt point. Tables calculated with this approach yield good results in flame calculations [43] in the SCD, because the processes in this domain are mostly governed by mixing and can therefore be well approximated by a locally linear construction of the extension. Nevertheless, more accurate results would be obtained by an approach that takes into account that there are still some fast chemical processes in the SCD.…”

“…The boundary, where x has to be increased can be found by a definition following [44,45]: a gap condition defines the boundary, respectively, the existence limit of an n c -dimensional ILDM as w boundary : Reðk nc =k ncþ1 ÞPe^ð1=s phys Þ=Reðk ncþ1 ÞPe with e as a small, user-defined value and s phys as a physical timescale. It should finally be noted, that using x¼n f corresponds to using the approach presented in [43]. Figure 2 illustrates the concept with different ILDMs of the stoichiometric syngas-air system, which have been projected into the CO 2 -H 2 O-H-space.…”

“…Both theoretical and numerical aspects of the method have been investigated thoroughly (see e.g. [34][35][36][37][38][39][40][41][42][43][44][45][46]51] and references therein) and the use of ILDMs as pre-calculated lookup-tables in flame calculations has proven to be an efficient tool (e.g. [47,48]), though there is a major drawback: typically, no a priori knowledge is used about the part of state space accessed by the flame calculation and the pre-calculated ILDM tables have to cover their whole domain of existence (bounded by the mathematical existence and by additional physical constraints like e.g.…”