Large eddy simulation of the Delft Adelaide Flame III using a quadrature-based method of moments

In this work, the recently developed split-based Extended Quadrate Method of Moments (S-EQMOM) is combined with a LES/presumed PDF-based flamelet/progress variable approach to achieve the predictions of soot particle size distributions in a turbulent non-premixed jet flame. The advantage of the S-EQMOM is that a continuous soot particle number density function (NDF) is able to be reconstructed by superimposing kernel density functions (KDFs) of presumed shape (gamma or log-normal distribution) that interact through the particle coagulation. Moreover, the S-EQMOM primary nodes are determined individually for each KDF yielding improvement in the numerical robustness compared to classical EQMOM. The above numerical framework is employed to predict soot particle formation in the Delft Adelaide flame III, which is a benchmark flame of the International Sooting Flame (ISF) workshop. The target flame is featured by low/high sooting propensity/intermittency and by relatively comprehensive flow/scalar/soot data available for validating the model framework. Simulation results are compared with the experimental results and discussed for both the gas phase and the particulate phase. A satisfactory quantitative agreement has been obtained especially in terms of soot volume fraction. The ability of the S-EQMOM to provide information on particle size distribution indicates a dominant unimodal distribution along the flame centerline

A 3D computational study of the formation, growth and oxidation of soot particles in an optically accessible direct-injection spark-ignition engine using quadrature-based methods of moments

The accurate prediction and assessment of soot emissions in internal combustion engines play a central role in the development of modern, sustainable powertrains. The modeling of soot requires high-fidelity models capturing both the gaseous soot precursors with suitable mechanisms and an accurate description of all physico-chemical processes related to the solid particulate. Semi-empirical models based on acetylene are frequently used but are limited in covering complex fuel compositions. For this reason, we present the coupling of a detailed quadrature-based method of moments (QMOM) soot model to a state-of-the-art flow solver for the simulation of gasoline engines. A close coupling with the underlying gas phase and the additional consideration of polycyclic aromatic hydrocarbons (PAHs) as precursors allow an accurate description of the entire cause-and-effect chain. The fully coupled model is then applied in a 3D-CFD simulation of an optically accessible research engine to investigate the formation, growth and oxidation of soot particles. Experimental high-speed measurements of soot- luminescence and extinction were used for validation purposes. Together with all preceding models along the engine cycle, the newly implemented model is used to identify the root cause of the observed soot formation hotspots. Particular emphasis is placed on the effects of soot oxidation

A numerically robust method of moments with number density function reconstruction and its application to soot formation, growth and oxidation

Several method of moments (MOM) models were developed recently to describe the evolution of soot particle populations. However, especially soot oxidation is still very challenging in MOM, as pointwise information of the underlying soot particle number density function (NDF) is usually unknown and thus, the prediction of smallest particles that oxidize completely is not easy. The recently proposed Extended Quadrature Method of Moments (EQMOM) (Yuan, Laurent, & Fox, 2012) has the potential to resolve this issue providing a continuous NDF reconstruction based on the set of transported moments. While its general suitability for soot was already demonstrated in the literature, the EQMOM moment inversion procedure reveals several numerical difficulties. In this work, we propose an EQMOM modification called split-based EQMOM that builds upon the general idea of EQMOM to represent the NDF by a weighted sum of superimposed, non-negative, continuous kernel density functions (KDFs), avoiding, however, the numerical problems of its original version. The model is based on a split of the entire NDF into a sum of overlaying density functions, whose evolution is governed by individual population balance equations (PBFs). These PBFs are derived and implemented in a novel Monte Carlo (MC) framework which is applied to simulate two fuel-rich burner-stabilized laminar premixed flames with different sooting behaviours. Results are compared to a classical MC model to demonstrate the suitability. Next, the MC data is used to assess the suitability of lognormal, gamma and inverse Gaussian distributions to approximate the NDF shape by employing the Wasserstein metric as criterion. This information is finally used to formulate an improved EQMOM soot model, which is then evaluated for both fuel-rich and oxidizing conditions. For the latter, the two-stage burner experiments of Echavarria, Jaramillo, Sarofim, & Lighty (2011) is considered, where particle oxidation is the dominant process. It is demonstrated that the proposed MOM model allows an accurate and numerically robust description of soot formation, growth and also oxidation

Detailed particle nucleation modeling in a sooting ethylene flame using a Conditional Quadrature Method of Moments (CQMOM)

A detailed kinetic mechanism for soot formation and evolution was applied in a method of moments framework using the concept of 'Conditional Quadrature Method of Moments' (CQMOM). Particle nucleation and growth pathways are described in detail tracking moments of the number density function for large PAH soot clusters and agglomerates in both stable and radical forms. Individual entities of these groups were examined in terms of their size and H/C ratio wherein the latter provides information on the chemical structure and the reactivity of the particles. Next the CQMOM implementation of the soot model is employed to predict particle formation in a lightly sooting burner-stabilized premixed ethylene flame with φ = 2.1 equivalence ratio. The suitability of the soot model to predict particle matter captured the onset of soot formation by nucleation and the subsequent growth

Modeling soot formation in premixed flames using an Extended Conditional Quadrature Method of Moments

The scope of this study is the application of the recently developed univariate moment method Extended Quadrature Method of Moments (EQMOM) (Yuan et al., 2012) to model soot formation in flames. Furthermore, it is combined with another advanced moment approach, called the Conditional Quadrature Method of Moments (CQMOM) (Yuan and Fox, 2011), and this extension leads to a bivariate model. Retaining the efficiency of a moment method, EQMOM enables the reconstruction of the number density function. CQMOM is a numerically robust multivariate moment method which allows a bivariate soot particle description in terms of particle volume and surface to take into account aggregation. The joint Extended Conditional Quadrature Method of Moments (ECQMOM) model combines the advantages of the two methods to arrive at a numerically efficient bivariate moment method which captures both the particle size distribution and the formation of aggregates. Both the EQMOM and the ECQMOM model are validated against experimental results for premixed burner-stabilized ethylene flames. Thereby, the gas phase is modeled using a modified version of a very detailed, well-established kinetic scheme, which is adapted to be consistent with the moment methods introduced. The results demonstrate the suitability of the applied models to describe both soot precursors and soot evolution in flames. Furthermore, the ability of the moment approaches to represent the statistical soot model accurately is evaluated comparing EQMOM and ECQMOM to other numerical approaches, which are based on the Monte Carlo method, the standard Gaussian Quadrature Method of Moments and the Gaussian-Radau Quadrature Method of Moments, respectively