Multiple mapping conditioning for turbulent premixed combustion

Abstract

The objective of the present study is to introduce a numerical model that accurately describes turbulent premixed combustion processes. Modern combustion devices are designed with focus on a reduction of pollutant emissions, and a promising way to minimize the production of pollutants, such as nitrogen oxides and soot, is energy conversion by lean premixed combustion. In this work, a novel multiple mapping conditioning (MMC) model for turbulent premixed flames is presented. In the MMC approach the evolution equations are solved for an ensemble of stochastic particles. These equations are equivalent to the probability density function transport equations where the chemistry is solved directly. Therefore, MMC coupled with LES (large eddy simulation) provides a closure for the filtered chemical source term and is applicable in any combustion regime as no specific flame structure needs to be assumed. However, in MMC a mixing term that represents the diffusive and turbulent mixing is unclosed and needs to be modelled. An accurate closure of the MMC mixing term includes multiple aspects. First, conditioning on a reference variable introduced in MMC implies that the particles for mixing are chosen to be close in composition space. The composition of the particles is represented by a reference variable that is provided by the Eulerian field. The selection of an appropriate reference variable for premixed flames is not a trivial task. Secondly, a mixing time scale model should ensure that the particles are mixed at the correct speed, as only then the flame represented by the particles provides accurate predictions of the flame propagation speed and the flame structure. In the first step of the model development, MMC for laminar premixed flames is presented. The laminar flame simulation poses a big challenge for approaches involving stochastic particles as the random movements of the particles produce spurious fluctuations in the laminar limit. The flame front should provide a distinct separation between reactants and combustion products, and excessive mixing may lead to uncontrolled flame acceleration. This issue is addressed by introducing a novel mixing time scale model for laminar premixed flames that ensures that mixing between the hot product particles and the cold reactant particles is accurately captured. Overall, the new model predicts the flame propagation speed correctly, however, individual hot particles can jump in front of the flame and mix with cold reactants which leads to a flame acceleration and a decorrelation between the flame on the Eulerian field and the flame represented by the particles. To ensure continued correlation between the Eulerian and particle solutions that is needed for sensible conditioning of mixing, a relaxation of the reference variable is introduced. Hence, each particle has a "memory" of its previous composition and this ensures that localness of mixing in composition space is preserved. The reaction progress variable accurately represents the flame composition of the Eulerian field, and the 'relaxed' progress variable provides an appropriate reference field for MMC. The described MMC model is validated against resolved laminar flame simulations. MMC demonstrates correct predictions of the laminar premixed flame propagation speed and the flame composition. The next step presents a mixing time scale model for turbulent premixed combustion. In a flamelet regime the structure of a turbulent flame can be considered locally laminar, thus, the mixing time scale for laminar premixed flames is also characteristic for mixing within the turbulent flame front. For cases with strong turbulence, an appropriate mixing time scale is provided by the "anisotropic" model that accurately represents the turbulent mixing. The two time scales are combined by means of a blending function that can distinguish between different premixed combustion regimes. The blending function ensures that outside the flame front the mixing time scale for turbulent flows is always used. Inside the flame front, the mixing time scale is based on the level of turbulence-flame interactions. The described mixing time scale model is validated with the aid of a series of freely propagating turbulent premixed flames. The MMC predictions of the flame propagation speed and the flame structure agree with exact solutions provided by direct numerical simulations (DNS). In the final step, the DNS-consistent MMC model is coupled with LES of the flow field. On a typical LES mesh, a thin premixed flame front is often unresolved and the LES cannot provide a reliable reference field for MMC. Artificial thickening of the flame is introduced to create a well-resolved reference field for pair selection of the stochastic particles. The flame represented by the particles keeps a physically accurate thin structure. Thus, the thickness of the flame on the reference field and the thickness of the flame represented by the particles are different. Therefore, modifications of the particle mixing model are introduced to ensure the localness of mixing in composition space. MMC-LES is again validated against a series of freely propagating turbulent premixed flames and compared to DNS that include detailed chemistry. The MMC-LES matches the turbulent premixed flame speed and provides correct predictions of the flame composition and the slow formation of a pollutant such as NO. The presented MMC-LES model for turbulent premixed combustion appears in a closed form and can be applied to more complex combustor configurations.