Conditional source-term estimation evaluations for partially-premixed flames
Keywords: conditional source-term estimation
combustion
mechanical engineering
numerical modelling
computational fluid dynamics

Partially-premixed flames, characterised by both premixed and non-premixed flame structures, have been identified to be of particular importance within most practical combustion-powered devices. However, as most existing combustion models assume a single flame structure, the present understanding of partially-premixed flames under lean mixture conditions and high turbulence intensity is still limited, and further research is needed to better represent these processes numerically. A detailed overview of different approaches used in combustion modelling for simultaneously capturing premixed and non-premixed flames, classified as either geometrical models (relying on the laminar burning velocity) or statistical models (relying on the probability density function), is presented. A new study validating for the first time a previously developed empirical laminar burning velocity correlation from Oxford for iso-octane/ethanol fuel blends is carried out. A complementary analysis involving simplified three-dimensional spark-ignition engine simulations is also performed using the new Oxford correlation coupled with ECFM-3Z within a Reynolds-Averaged Navier-Stokes (RANS) turbulence framework. Here, the importance attributed to the laminar burning velocity in the closure of the mean chemical source-term is found to decrease the range of applicability of geometrical models significantly, motivating the use of statistical modelling. Conditional source-term estimation (CSE) is a statistical combustion model that invokes the conditional moment closure (CMC) hypothesis to approximate the mean chemical source-term in an averaged transport equation. An inversion process estimates the conditional scalar field. Previous CSE studies have shown that this model could successfully predict the characteristics of both premixed and non-premixed flames, regardless of the combustion regime. However, limited work has been undertaken to assess the modelling capabilities of CSE to account for partially-premixed structures. To investigate further, a previously developed CSE model coupled with the flamelet generated manifold (FGM) is applied to study the Engine Combustion Network (ECN) diesel \textquotedblleft Spray A\textquotedblright\hspace{1mm}case within a RANS framework. The proposed combustion model accounts for detailed chemistry and turbulence-chemistry interaction effects, essential for capturing the strong coupling between fluid dynamics and chemical kinetics. It is found that the CSE-FGM approach successfully demonstrates the capability of realistically predicting diesel-fueled transient spray combustion. However, there are slight discrepancies with experimental ignition delay times and flame lift-off lengths under low-temperature conditions within this approach due to the inclusion of a single control scalar based on mixture fraction. Adopting doubly CSE (DCSE) and, as such, two conditioning variables relying on mixture fraction and progress variable provides far greater modelling capabilities compared to the conventional CSE. However, while a generalised mixture fraction definition has been provided and well accepted by the community, various progress variable definitions have been adopted over the years for different applications. This study focuses on the effect of progress variable selection on the conditional fluctuations obtained with one-condition conditional averages and doubly conditional averages from two of the most well-known burners. Among the four progress variables tested, it is found that the definition attributed to the progress variable within a doubly conditional moment closure approach has no particular importance in the closure of the chemical source-term. The results obtained with principal component analysis promote the use of a progress variable definition based on temperature for chemistry tabulation techniques, considering that species diffusivity is often simplified by assuming unity Lewis numbers. Lastly, this work also suggests that DCSE will likely be needed for capturing partially-premixed flames, combustion under high levels of turbulence intensity (where the inclusion of turbulence-chemistry interaction is compulsory), and reactive flows encountered in practical combustion systems.