The ongoing tightening of emissions legislation is resulting in increasingly vigorous efforts to control the pollutants formed in hydrocarbon combustion systems in the transportation and power generation sectors. Synthetic fuels produced with renewable energy and, in particular, oxygenated fuels can improve both the overall carbon balance and local emissions, such as soot particles, without extensively modifying the present combustion devices. Oxymethylene ethers (OMEs), which are promising synthetic fuel candidates (Kohse-Höinghaus, 2021), deployable e.g. in self-ignition engines, have been proven in recent studies (Ferraro et al., 2021; Tan et al., 2021) to significantly reduce the sooting tendency of blended fuel flames. Compared to other alternative and oxygenated fuel candidates such as biodiesels and alcohols, oxymethylene ethers combine high oxygenation of around 50% by mass (Wang et al., 2016) with high propensity for self-ignition (Lumpp et al., 2011; Wang et al., 2016). While the combustion of pure OMEs exhibits almost the complete suppression of soot, an application as a blending fuel is a more realistically viable scenario in the short and medium term. The good miscibility of oxymethylene ethers in fossil diesel (Lin et al., 2019; Omari et al., 2019) supports this scenario. OME₃ to OME₅ in particular exhibit properties favourable to their use as fuel blends in compression ignition applications. For instance, the cetane number of OME₃ to OME₅ is in the range of 72–93 (Lautenschütz et al., 2016; 2017; Deutsch et al., 2017) and the flash, boiling and melting points are comparable to those of diesel fuel (Zheng et al., 2013; Omari et al., 2019). These suitable characteristics explain the recent research interest in this specific group of oxygenated fuels in the field of kinetic mechanism development (Sun et al., 2017; He et al., 2018; Cai et al., 2019; Li et al., 2020; Bai et al., 2021; Niu et al., 2021), their application in engine simulations (Lin et al., 2019; Lv et al., 2019; Ren et al., 2019) or for different synthesis methods (Gierlich et al., 2020; Klokic et al., 2020), and the assessment of the overall carbon impact (Mahbub et al., 2019; Bokinge et al., 2020). The application of oxymethylene ethers in engines in combination with their emission propensity has been investigated in several studies (Pellegrini et al., 2013; Barro et al., 2018; Huang et al., 2018; Liu et al., 2019; Ren et al., 2019; LeBlanc et al., 2020; Parravicini et al., 2020; Pélerin et al., 2020), while fewer investigations have been conducted, notably, into soot formation for pure or blended OMEs in canonical flames (Ferraro et al., 2021; Tan et al., 2021). Hence, this work addresses the potential of oxymethylene ether-3 (OME₃) and its effect on soot particle formation and growth to deeply understand the soot suppression phenomenon in a simple configuration and in blending with a well-known fuel such as ethylene. While studies containing small amounts of OME₃ blended into C₂H₄ have been performed for both premixed flames (Ferraro et al., 2021) and diffusion flames (Tan et al., 2021), the effects of blending increased amounts of OME₃ has not been investigated yet. Additionally, a systematic assessment between the blending ratio of OME_n fuels and their effects on the overall soot reduction and especially on the individual maturation steps in the soot evolution process is unknown to the authors. Detailed knowledge of the soot reduction potential including possible saturation effects for higher blending ratios is needed for an efficient application of synthetic fuels. Therefore, this study aims to analyze these aspects for OME₃ combustion. The correlation between the OME₃ blending ratio and the soot reduction will be numerically investigated. The analysis systematically evaluates the complete range of OME₃ blending ratios using detailed chemistry combined with a quadrivariate soot model enabling a deeper understanding of the effects of different amounts of OME₃ blending on the entire soot formation process.

Simulations are performed on a series of laminar burner-stabilized premixed flames burning ethylene blended with increasing amounts of OME₃ up to a pure OME₃/air flame at constant equivalence ratios. Detailed chemical kinetics in combination with the Conditional Quadrature Method of Moments (CQMOM) (Salenbauch et al., 2017, 2018), based on the physico-chemical soot model by D’Anna et al. (2010), are chosen to model soot formation, particle surface growth and other occurring particle processes. This approach enables a detailed investigation of the soot suppression behavior of OME₃ regarding the smaller carbon chemistry, and of different particle size classes, such as large polycyclic aromatic hydrocarbons, spherical clusters and larger aggregates including their chemical properties. The effect that increasing amounts of OME₃ exert on soot formation is evaluated in terms of both the total soot volume fraction and the particle size distribution. Additionally, the relationship between the OME₃ to ethylene blending ratio and the subsequent soot reduction is analyzed to verify whether OME₃ has only a dilution effect on the mixture or if it also has an active kinetic effect in the formation of soot gas-phase precursors, nano-organic carbon and soot particles. Finally, the range of OME₃ blending ratios yielding a soot suppression effect is identified to assess the overall potential of this oxygenated fuel. This study is performed for two different equivalence ratios covering lightly to highly sooting flame conditions.

The numerical modeling includes a description of the gas-phase chemistry and of the soot particle formation and evolution. The gas-phase chemistry is modeled by a detailed kinetic mechanism accounting for 141 species and 674 reactions in total. The decomposition and oxidation reactions of OME₃ (41 species and 213 reactions) are taken from Sun et al. (2017). The reactions of smaller and larger carbon species up to polycyclic aromatic hydrocarbons (PAHs) are described by the kinetic mechanism by D’Anna et al. (2010), Sirignano et al. (2010, 2013), and Conturso et al. (2017).

To describe the soot particle evolution, the physico-chemical soot formation model (D’Anna et al., 2010) is combined with the Conditional Quadrature Method of Moments. The numerical approach was developed in Salenbauch et al. (2017) and has been successfully applied in atmospheric premixed flames (Salenbauch et al., 2017, 2018; Ferraro et al., 2021). A short summary is described in the following. The gas-phase kinetics consider species up to pyrene, while larger PAHs are treated as lumped species. The soot model distinguishes between three different particle structures based on their state of aggregation (D’Anna et al., 2010). Soot precursors with a molecular mass larger than pyrene (molecules or large PAHs) are classified separately from the spherically shaped, solid soot particles which are formed through the inception step of several PAHs (clusters), and aggregates. These in turn are formed due to the agglomeration of several clusters with subsequent soot maturation steps leading to strongly bonded fractal-shaped particles. The physico-chemical nature of the soot model allows an assessment to be carried out based not only on the size and shape of the particles but also on their chemical properties such as the carbon to hydrogen ratio and their chemical reactivity. The soot processes are formulated based on Arrhenius-rate laws and include growth processes such as the H-Abstraction-C₂H₂-Addition (HACA) mechanism, the resonantly stabilized free radical mechanism or surface growth due to chemical processes. Surface growth and oxidation reactions are applied for all the three entities that describe the soot evolution such as large PAH, clusters and aggregates. Additionally, nucleation steps for different-sized large PAHs are accounted for, resulting in clusters with varying chemical properties as well as soot oxidation and oxidation-induced fragmentation, dehydrogenation and aggregation processes of several clusters, resulting in aggregates shaped like snowflakes, fractals or chains.

Due to the variety of the soot particles involved, classification and bundling similar to lumped species is necessary. The evolution of the chemical and physical properties of each particle class is described by the population balance equation (PBE) for the number density function (NDF) f ( ξ ̲ ; x ̲ , t ) , which depends on the spatial coordinates x ̲ , the time information t and the internal property vector ξ ̲ = [ ξ n c , ξ H / C , ξ s t a t , ξ t y p ] T . This vector contains two continuous properties ξ _nc , indicating the number of carbon atoms with ξ _nc ∈ [0, ∞), and ξ _H/C describing the carbon to hydrogen ratio with ξ _H/C ∈ [0, 1]. ξ _typ and ξ _stat are discrete dimensions representing the type of entities ξ _typ ∈ A, A = {large PAHs, clusters, aggregates}, and ξ _stat the chemical reactivity with ξ _stat ∈ B, B = {stable, radical}. Applying Bayes’s decomposition, the quadrivariate number density function f ( ξ ̲ ; x ̲ , t ) reads as follows f ( ξ ̲ ) = f H / C ξ H / C | ξ n c , ξ s t a t , ξ t y p ⋅ f n c ξ n c | ξ s t a t , ξ t y p ⋅ n ξ s t a t , ξ t y p , (1) where the time and spatial dependencies are omitted for brevity.

Here, the distributions f _H/C and f _nc are conditioned on the state ξ n c , ξ s t a t , ξ t y p and ξ s t a t , ξ t y p , respectively. The joint bivariate distribution n(ξ _stat , ξ _typ ) can have only six values for the different possible combinations (u, v) of the two discrete particle properties ξ _stat = ξ _stat,u and ξ _typ = ξ _typ,v . The reader may be referred to Salenbauch (2018) for further details. This simplification can be exploited in combination with the conditional density function definition to transform Eq. 1 into a system of six bivariate NDFs Π_(u,v) Π ( u , v ) ( ξ n c , ξ H / C ) = f H / C u , v ( ξ H / C | ξ n c ) ⋅ f n c u , v ( ξ n c ) ⋅ n u , v , (2) in which the conditional distribution f H / C u , v ( ξ H / C | ξ n c ) and the marginal distribution f n c u , v ( ξ n c ) are evaluated for each of the six combinations of (u, v).

The set of NDFs is not solved directly but only for a set of its statistical moments closed with the CQMOM approach. In this work, for all six combinations (u, v) two quadrature nodes are used for the internal coordinate ξ _nc and a single quadrature node for ξ _H/C conditioned on ξ _nc . The system of six bivariate NDFs is therefore represented by 36 additional moment transport equations. The numerical calculations have been performed with the in-house universal Laminar Flame (ULF) solver (Zschutschke et al., 2017), which includes the QMOM library (Salenbauch, 2018). The conservation equations for each individual species in the gas-phase and the equations of the moments representing the solid-phase are solved using a segregated approach. Small PAH species, from benzene to pyrene, and the species involved in the surface growth, oxidation and dehydrogenation reactions (H, OH, H₂, H₂O, C₂H₂, HCO, CO, O₂) are required for the calculation of the soot moments and their gas-phase chemistry is coupled with the soot chemistry. Herein, constant species and temperature fields are applied when evaluating the soot moments, while a constant set of moments and species consumption rate due to soot processes are employed when solving for the gas-phase. Coupling of the equations is ensured by iteratively solving and updating both sets of equations until convergence is reached. Due to the stiffness of the system of equations, a pseudo-time step procedure is applied to solve the one-dimensional stationary flame to ensure numerical stability. Additionally, the spatial coordinate of the one-dimensional flame can be transformed into a residence time (Blanquart, 2008; Salenbauch, 2018) allowing to solve the set of moment equations in terms of a homogeneous zero-dimensional reactor prescribing the species fields and thermophysical properties of the gas-phase in dependence of the residence time.

The CQMOM method does not provide access to the PSD information but it reconstructs the moments of the NDF using weighted Dirac-delta functions. Following Salenbauch et al. (2018), the entropy maximization (EM) concept is used here in post-processing to evaluate a continuous distribution of the particle sizes from a given number of moments, without prescribing the distribution shape. The idea from Mead and Papanicolaou (1984) is to find a univariate continuous distribution function f(ξ ₁) that maximizes the entropy (Shannon, 1948) H (f), being ξ ₁ the internal coordinate H ( f ) = − ∫ Ω ξ 1 f ( ξ 1 ) ln f ( ξ 1 ) d ξ 1 . (3)

Mead and Papanicolaou (1984) formulated the entropy for the unknown distribution function using Lagrangian multipliers and specified the moment set as constraints. This allows an explicit expression of the distribution function, which can be iteratively calculated by searching for its maximum. Further details on the numerical approach can be found in Salenbauch et al. (2017, 2018) and references therein.

In this section, the numerical setup and the investigated flames are described. A burner-stabilized flat flame is employed in this work. The flame configuration is adopted from previous experimental studies (Salamanca et al., 2012; Sirignano et al., 2014; Conturso et al., 2017; Russo et al., 2019; Ferraro et al., 2021) which used a capillary burner with an inner diameter of 5.8 cm including a stainless steel plate located 30 mm above the burner exit for flame stabilization. The combustion parameters are kept constant in both sets of flames investigated, varying only the blending ratio of OME₃ and ethylene. Laminar, premixed conditions at atmospheric pressure and a cold gas velocity of 0.1 m/s are considered, allowing a one-dimensional simulation approach. Two equivalence ratios, ϕ = 2.16 and ϕ = 2.46, are investigated based on neat ethylene flames investigated in a previous study (Ferraro et al., 2021), representing lightly and highly sooting conditions. More specifically, for neat ethylene fuel, the flame at ϕ = 2.16 presents minor formation of soot aggregates, while the flame at ϕ = 2.46 presents a significant amount of soot aggregate and a distinct bimodality of the PSD.

Temperature profiles experimentally measured in Russo et al. (2019) for the pure ethylene flames at corresponding equivalence ratios, are prescribed for all the simulations and are plotted in Figure 1. As with other alternative fuels (Conturso et al., 2017), the effect that adding smaller amounts of OME₃ up to 30% exerts on the flame temperature is assumed to be insignificant, while major effects are expected when higher percentages are used. Here, this procedure is adopted to separate the thermal effects of OME₃ blending from the chemical effects in the numerical simulations.

The mixture compositions at the inlet of the flames are stated in Table 1. Fuel compositions are investigated ranging from pure ethylene up to pure OME₃ with intermediate blending steps. The fuel is blended by keeping the overall carbon stream constant for all flames, while the relative amount of carbon atoms provided as OME₃ compared to the overall carbon fed to the flame is specified in the table. The oxygen (O₂) stream is adapted to match the equivalence ratios of ϕ = 2.16 and ϕ = 2.46. The fuel and oxygen streams are diluted with nitrogen (N₂) which is adapted to ensure there is an identical cold gas velocity in all the flames. Since the combustion parameters are kept constant for all flames in this study, all the changes regarding the soot formation can be associated with the difference in the fuel composition and fuel structure. While a previous study Ferraro et al. (2021) compared the numerical model against experimental data, this study extends the variation of the investigated parameters and sets its focus on the blending ratio between OME₃ and C₂H₄ using the same modeling approach. In Ferraro et al. (2021), the soot reduction trends of OME₃ observed in the experiments on flames with different equivalence ratios have been well captured by the numerical method. Additionally, this burner configuration has been employed to evaluate several oxygenated fuels and their sooting characteristics (Salamanca et al., 2012; Sirignano et al., 2014; Conturso et al., 2017; Russo et al., 2019), enabling cross-comparisons to be made.

A numerical study is performed simulating two series of laminar premixed burner-stabilized flames burning a mixture of C₂H₄ and OME₃ for two equivalence ratios, corresponding to highly and lightly sooting flame conditions. The sets cover flames with increasing blending ratios of OME₃ reaching from pure ethylene to pure OME₃ at a constant equivalence ratio and identical carbon streams. The soot precursors in the gas-phase, soot formation and PSD are analyzed using a detailed physico-chemical soot model.

The effects of OME₃ blending are found to be different for nanoparticles compared to larger aggregates. While the formation of larger aggregates is approximately linearly reduced for increasing amounts of OME₃ throughout the flame, the nanoparticle formation shows a non-monotonic correlation to the blending ratio and is mainly suppressed for higher amounts of OME₃, similarly to the combustion of pure OME₃.

The particle size distribution is reconstructed with the concept of entropy maximization at a fixed height above the burner of HAB = 20 mm. A substantially unchanged distribution of clusters for OME₃ blending ratios between approximately 0 and 60% and a decreasing number of particles for higher blending percentages can be identified for both equivalence ratios with a slight, intermediate increase in the particle number for the richer flame condition at around 70% OME₃ in the fuel, whereas the leaner configuration shows a monotonic reduction in the particle number. While the number of aggregates in the richer configuration is not significantly affected by smaller amounts of OME₃ blending, their particle size is mainly reduced, but a simultaneous reduction in the particle number and particle diameter is observed for the leaner configuration at this position in the flame.

These findings indicate that OME₃ blending mainly delays the soot formation processes and, as a consequence, suppresses the formation of larger aggregates at a specific position in the flame. This is due to the absence of direct carbon-to-carbon bonds in OME₃, which leads to a more complete oxidation process and therefore subtracts carbon from the soot growth pathways. The linear correlation for aggregate reduction suggests a predominant dilution effect rather than an active kinetic effect.