Effect of Lagrangian-phase Modelling on Charge Stratification and Spatial Distribution of Threshold Soot Index for Toluene Reference Fuel Surrogates

Nowadays, soot emissions are one of the major concerns in Direct Injection Spark Ignition engines. Soot prediction models can be computationally expensive, especially when particle mass, number, and size distribution are to be forecast. While soot formation heavily depends on the chemical and physical characteristics of the fuel, the simulation of the exact composition of a real gasoline is computationally unfeasible. Thus, it is essential to find simplified yet representative pathways to reduce the computational cost of the simulations. On the one hand, the a-priori investigation of the factors influencing particulate onset can be a simplified approach to compare different solutions and strategies with much cheaper costs than the modelling of soot formation and oxidation mechanisms. On the other hand, the use of surrogate fuels is a practical approach to cope with the fuel chemical nature. Although they poorly mimic the evaporation properties of a real gasoline, Toluene Reference Fuels are broadly adopted to match combustion relevant properties of the real fuels. In this study, the spatial distribution of the Threshold Soot Index in the fluid domain is investigated for three surrogates characterized by an increasing content of toluene (0 mol%, 30 mol%, 60 mol%). The correlation between the sooting tendency and the fuel distribution in the combustion chamber before spark ignition time can provide useful preliminary indications, without spending the computational effort of the whole soot model multicycle resolution. In particular, two approaches for the lagrangian description of the injected fuel are investigated: a multicomponent approach and a single component one, this last driven by a high-fidelity lumped modelling of the surrogate properties for both liquid and vapor phase.


Introduction
Alternative fuels, innovative combustion processes and aftertreatment systems are the predominant research fields to further develop Internal Combustion Engines (ICEs) amid the propulsion system innovation process. While waiting for mass-market penetration of alternative mobility solutions such as BEVs and FCEVs [1] [2], ICEs are still populating the formation of local soot-prone areas within the combustion chamber, which can be addressed without the high computational burden of multicycle soot simulations. The effectiveness of a lumped fuel-modelling approach is critically investigated by evaluating the predictions of fuel and TSI distributions at spark time, to spot to what extent the lumped-single component approach is reliable and able to predict charge stratification and TSI distribution compared to a more refined, yet more expensive, multicomponent fuel modelling approach.

Surrogate fuel formulation
Surrogate formulation is carried out by defining the reference fuel properties of interest, and then by selecting what types of hydrocarbons and compounds to be employed. In this study, the target properties are RON, MON, and αₛₜ, which describe the main flame propagation and ignition quality of the mixture, then the sooting tendency is also accounted for. In this study, TSI [23] is chosen as the representative index for the soot formation propensity quantification. The surrogate components are: 2,2,4 trimethyl-pentane (C₈H₁₈) as representative of the iso-paraffins, n-heptane (C₇H₁₆) for n-paraffins, and toluene (C₆H₅CH₃) for aromatics. Surrogate compositions are obtained by actively targeting RON, MON, and αₛₜ of a commercial gasoline [16], and by varying the toluene content to get stark differences in TSI between the three surrogates. Although the aromatic content of commercial gasoline is limited to below 30-35 vol% [16], it was increased up to 60% to explore the robustness of the lumped-single component approach in predicting TSI distribution. The surrogate composition is obtained by solving three equations representing the constraints of: total mole fraction equal to unity, RON and MON target modelled with a linear by mole mixing rule. The final composition of each surrogate is reported for toluene, n-heptane, iso-octane mol% content respectively: 0-5.00-95.00 for PRF, 30.30-11.06 -58.64 for TRF30 and 60.61-17.12-22.27 for TRF60. The other relevant properties of the surrogates, such as the carbon (C) or hydrogen (H) atoms, liquid density (ρₗ) at 298 K, Molecular Weight (MW), Lower Heating Value (LHV), and the Normal Boiling Temperature (Tb) are reported in Table 1.

3D-CFD simulation general setup
The surrogates are tested in a single-cylinder naturally aspirated engine [8], operated at 2000 rpm at Wide Open Throttle (WOT); the engine runs with a compression ratio of 10:1 and at average stoichiometric conditions with a nominal injected mass of 28 mg. The Start of Injection is labeled as SOI 300, since the fuel is injected 300 degrees before Top Dead Center firing (bTDC) directly in the combustion chamber with a 6-hole injector, positioned on the symmetry plane. Given the geometric symmetry and the adopted RANS modelling approach, which is here preferred to other more refined alternatives [28][29] [30] to reduce the computational cost of the analyses, it is possible to simulate half combustion chamber, thus reducing the computational cost. The mesh has a minimum number of cells of ~112`000 (at TDC) and a maximum number of cells of ~290`000 (at BDC). For turbulence modelling, a k-ε RNG is adopted given the successful application in similar studies [31] [32]. Droplets are initialized following the approach proposed in [33][34] [35] whereas the spray break-up is modelled with Reitz-Diwakar's [36] model and the droplet-wall interaction with Senda's model [37]. Heat transfer is modeled using a recently improved version of the GruMo-Unimore heat transfer model [38][39] [40], which has proven to be successful in a wide range of engine applications [41].

Multicomponent approach for lagrangian phase
The multicomponent approach allows a high-fidelity description of each component of the surrogate fuel. Of particular interest for charge stratification is fuel evaporation, which depends on the equilibrium at the liquid-vapor interface; this in turn can be described using a simple Raoult's law or a more sophisticated description, as the one provided by the UNIQUAC Functional-group Activity Coefficients approach (UNIFAC) [42]. The latter relies on the use of activity coefficients γᵢ to provide a description of the partial pressure of Since activity coefficients account for the type of molecules and their interactions during the evaporation, the UNIFAC model is more reliable than the Raoult's law for applications involving surrogates, especially when different molecular structures are involved (e.g., the oxygenated compounds like ethanol for e-fuel surrogates).

Single-component approach for lagrangian phase
An alternative strategy to the multicomponent description, is the lumping of the individual fuel components into a single representative liquid [43] [44]. In this case, the properties are calculated from those of each hydrocarbon using mixing rules. To establish how effective the lumped-single component strategy is in terms of evaporation, charge stratification, and TSI spatial distribution prediction, it is necessary to derive a high-fidelity single component for each blend. In this study, for each one of the three surrogates, a temperature-dependent description of both liquid and gas phase properties is provided. The general method that is applied is: the properties are calculated with mixing rules that weight each component property based on its specific proportion in the composition. The mixing rules to compute the mean properties of mixtures are retrieved from literature. For the majority of the properties, a linear mixing rule, historically developed by Kay et al. and widely adopted for hydrocarbon mixtures [45], is exploited: = ∑ where is the generic property, is the mole/mass/volume fraction of the component, subscript i and mix stand for ith component and mixture respectively. The types of mixing rule used to calculate the properties of each surrogate are summarized in Figure 1. As for the gaseous phase, the NASA polynomials of the lumped-single components are calculated using a mole-fraction linear mixing rule and the results ( Figure 2) provide a description of the thermal properties of the vapor phase.  , where are fitting coefficients. Then, all the properties are given as input to the CFD code via user coding. Each component property is retrieved from the NIST database [46] and then all the final surrogate properties are reckoned using a linear mixing rule (Figure 1), but the viscosity μₗ of the liquid phase. As reported by [45] [18], the computation of the viscosity of liquid hydrocarbon mixtures using a linear mixing rule may not be an effective approach: Kim et al. [18] successfully used the Grunberg-Nissan equation, whereas in [45] a nonlinear by mole mixing rule is suggested. This last is used in this study (Equation 3).

Evaporation and charge stratification
The simulation results are reported at spark time, which occurs 15 degrees bTDC, as a representative condition initially experienced by the flame propagation. The temporal evolution of the spray evaporation described as the percentage of evaporated fuel Evap.% (xaxis) and the corresponding crank angle degree (y-axis) is summarized in Figure 4. The evaporation delay exhibited by the lumped approach stems from the approximation on the Heat of Vaporization and the partial pressure obtained using Raoult's law. However, differences in the evaporation rate partially influence charge stratification at spark time as suggested by the equivalence ratio scalar field Figure 5 and by the cell-wise occurrence frequency of equivalence ratio in Figure 6. It is also interesting to point out that the three surrogate fuels exhibit similar evaporation patterns since their Tb values are very close, as well as those of each component.

Threshold Soot Index distribution
Cell-wise TSI values are calculated via user coding as the surrogate TSI (Table 1) times the fuel mole fraction in the cell for the lumped-single component, whereas for the multicomponent approach a linear-by-mole mixing rule ∑ i ⋅ TSI i i is applied using the cellwise mole fractions of each component i and the corresponding TSI value retrieved form [23].The cell-wise value occurrence frequency in the domain is show in Figure 7: the histograms obtained by the multicomponent and by the lumped approach are superimposed to better spot the differences, which expectedly are very limited for the PRF, while tend to increase for the TRF30 and TRF60 blends. To quantify the TSI spatial distribution, the fluid domain is split in coaxial cylindrical sectors by varying the radius from 0 mm to 40 mm with a 10 mm stepping. To each one of the four sectors ( Figure 8) a TSI average value is calculated as the algebraic average of all the TSI cell-wise values, belonging to a specific sector. A satisfying agreement between the two lagrangian phase modelling approaches is reached for the averaged TSI values, as shown in Figure 9.

M. PRF
The values reported in Figure 9 provide the initial sooting tendency of the mixture, which the flame front will potentially experience during its propagation in the combustion chamber. However, local maxima of TSI also impact soot formation; it is therefore useful to spot cellwise differences obtained with the two approaches. In Figure 10, the TSI cell-wise distributions of high-TSI thresholds are reported as a complementary information to their averaged counterparts. A satisfying agreement for PRF is reached, whereas increasing variations of the TSI pattern can be spotted for the two TRFs.

Conclusions
This study lays out a numerical comparison between a single-component approach and a multi-component approach to model mixture stratification in an DISI engine, with focus on the predicted sooting tendency. Firstly, a methodology to retrieve gas and liquid phase properties for the lumped approach is presented. Then the comparison is carried out focusing on equivalence ratio and TSI spatial distribution at spark time. The main aim is to investigate to what extent the results provided by the lumped approach differ from those obtainable using a more detailed multicomponent with UNIFAC modelling. Three surrogate fuels, characterized by an increasing toluene content, are investigated. The most relevant observations stemming from this study are:   • For each surrogate, the lumped approach results in a slight evaporation delay when compared to the multicomponent one. This has a limited, yet observable, impact on the charge stratification for TRF30 and TRF60. • For PRF, TRF30, and TRF60 a satisfying agreement of the radial TSI average value is observed between the two approaches. • Spatial distribution of TSI peaks is very similar for the PRF surrogate, while increasing deviations between the single-component and the multi-component fuel representations are observed for the toluene-doped blends. On a final remark, this approach is tested for hydrocarbon mixtures and TRF surrogates of alkanes and aromatics constituents. The mixing rule extension to other types of surrogates, in which compounds of a different chemical nature (e.g., alcohols) are blended with the PIONA (Paraffins, Iso-paraffins, Olefins, Naphthenes, Aromatics) constituents, must be evaluated, since non-linear blending effects can be observed (e.g., azeotropic behavior).