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 twodimensional 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 1 multi-regime combustion prevails.

Identification of Flame Regimes in Partially Premixed Combustion from a Quasi-DNS Dataset

“…Instead of using gradients of species mass fractions, Favier and Vervisch (2001), Domingo et al (2002), Nguyen et al (2010) and Lamouroux et al (2014), Pouransari et al (2016) and Scholtissek et al (2020) discussed the alignment of mixture fraction Z and reaction progress variable c gradients. Applying this to the angle Takeno definition results in:…”

“…The regime markers based on flamelet analysis have their limitations when used in direct numerical simulation of turbulent flames because instantaneous flame fronts are subjected to unsteady effects, curvature, flame stretch and the direct interaction of different combustion regimes. Different approaches are available to overcome this by incorporating two-dimensional composition space equations (Scholtissek et al 2020), accounting for curvature effects (Scholtissek et al 2017) and analyzing the effect of tangential and preferential diffusion (Dietzsch et al 2018;Han et al 2019). The drift term approach by Wu and Ihme is not necessarily a marker for premixed and non-premixed regions.…”

A self-consistent extension of flamelet theory for partially premixed combustion

“…Of particular interest are partially premixed flames (also called multi-regime flames), in which premixed and non-premixed combustion modes can co-exist and interact [15,16]. Therefore, several different sets of two-dimensional composition space equations have been proposed in recent years as extensions of the classical flamelet theory [17][18][19][20][21][22], all of which make use of the mixture fraction, Z, and a second conditioning variable, generalized here as φ, to define the composition space, (Z, φ, τ ), where τ is a time-like variable.…”

“…Typically, φ is defined as some sort of reaction progress variable [17][18][19][20][21][22][23], but approaches using a second mixture fraction [24] or enthalpy [25] also exist. For a comprehensive review of the associated literature on two-dimensional composition space equations, the reader is referred to the recent works of Mueller and coworkers [21,23] and Scholtissek et al [22].…”

“…While the use of non-orthogonal coordinates represents the most common choice for the formulation of two-dimensional composition space equations, Scholtissek et al [22] have recently shown how an orthogonal coordinate system can be defined based on the mixture fraction and a conventional reaction progress variable, Y c . In particular, they introduced the following transformation rule from physical into composition space…”