Derivation and analysis of two-dimensional composition space equations for multi-regime combustion using orthogonal coordinates

Abstract

Interactions between premixed and non-premixed reaction zones can lead to complex mixed combustion regimes, here denoted as multi-regime combustion, which pose challenges to many conventional combustion modeling approaches. Such conditions occur in most practical combustors and can originate from partial premixing, mixture inhomogeneities/stratification, hot product recirculation, or local flame extinction and re-ignition. Therefore, novel equations are derived for modeling multi-regime combustion which are formulated with respect to a two-dimensional composition space spanned by mixture fraction and reaction progress variable. Contrary to previous works, the dependency of the progress variable on the mixture fraction is considered in the new model. This is achieved by splitting the progress variable gradient into an aligned and an orthogonal component with respect to the mixture fraction gradient and the latter is used to define the second coordinate. In the theory that follows, a balance equation for the progress variable on mixture fraction iso-surfaces is formulated. Using this balance equation together with the orthogonal coordinate system, the transformation of species and temperature equations to the 2D composition space yields a novel set of equation without so-called cross-terms. This is advantageous since cross-terms obtained with previous approaches lack a general closure and it is uncertain if it exists at all. Furthermore, the approach allows to naturally distinguish between non-premixed and premixed combustion regimes, auto ignition, and it covers multi-regime combustion characteristics. The theory is validated and discussed by means of a fully resolved solution of a laminar triple flame using detailed chemistry. At first, regions which exhibit premixed, non-premixed or multi-regime combustion characteristics are identified. The triple flame solution then serves as a database from which all relevant theoretical relations are post-processed and validated. In comparison to budgets of conventional 1D flamelet equations for premixed and non-premixed combustion it is shown that only the full set of transport terms considered in the 2D equations accurately balances chemical source terms everywhere in the triple flame, especially in regions where multi-regime combustion prevails.