*3.1. Numerical Model Set-Up*

The numerical model of the engine was developed using the commercial CFD code CONVERGE [37]. The numerical domain, as shown in Figure 1, included the complete single cylinder geometry and the intake/exhaust ports, allowing to perform complete cycle simulations.

**Figure 1.** Numerical domain and mesh features of the engine.

The mesh discretization was done using the cut-cell Cartesian method available in the code. The base mesh size was 3 mm throughout the domain in the reference grid configuration. Three levels of fixed embedding (0.375 mm of cell size) were added to the walls of the combustion chamber, ports and region near the fuel injector, to improve boundary layer prediction and the accuracy of spray atomization, droplet breakup/coalescence, etc. Mesh size in the chamber was reduced by two levels of embedding (0.75 mm of cell size) after the start of combustion, for an improved recreation of the interaction and reflection of the pressure waves while avoiding undesired spatial aliasing effects. The code also employed adaptive mesh refinement (AMR) to increase grid resolution by three levels of additional refinement (up to 0.375 mm minimum cell size) based on the velocity and temperature sub-grid scales of 1 ms<sup>−</sup><sup>1</sup> and 2.5 K, respectively. As a result, the total number of cells varied between 1.5 million at BDC and 0.5 million at Top Dead Centre (TDC). This mesh configuration was achieved after a grid sensitivity analysis [27], offering a grid-independent solution when simulating combustion and its produced unsteady pressure field in internal combustion engines.

The Mach Courant-Friedrich-Lewy was set to 1.0 during the combustion in order to properly capture the local pressure oscillations caused by combustion. Thereby, the calculation time-step was gathered between 0.05 and 0.5 μs. This value was also obtained from the previously referred work performed by Torregrosa et al. [27], whose demonstrated that the energy of the unsteady pressure field is highly sensitive to CFL Mach number, but also that the energy does not change when this parameter is close to or below one.

The renormalization group (RNG) *k* − *ε* URANS model [18] coupled with the heat transfer approach proposed by Angelberger et al. [38] was chosen for simulating the turbulent properties of the flow.

For combustion modelling, the SAGE detailed chemistry solver [39] was employed along with a multi-zone (MZ) approach, with bins of 5 K in temperature and 0.05 in equivalence ratio [40]. This combustion model, despite not using an explicit turbulent combustion closure [17], has demonstrated to perform well for simulating spray combustion under URANS schemes in previous works [41]. A reduced chemical kinetic mechanism for primary reference fuels (PRF) based on Brakora et al. [42] was used in this work to account for fuel chemistry. A blend of 5% n-heptane and 95% iso-octane was utilized for predicting the physical properties of the gasoline fuel, being a suitable surrogate for predicting the ignition features of the RON95 gasoline used in experiments. Activating iso-octane reactions, the chemical mechanism resulted in a 45 species and 152 reactions.

Coupled with appropriate turbulence models, Kodavasal et al. [43] demonstrated that a similar combustion approach allows an accurate reproduction of gasoline autoignition, while other researchers [29,44] established realistic rates of heat release under gasoline compression-ignited conditions.

The fuel injection was described by the standard Discrete Droplet Model (DDM) [45] and Kelvin Helmholtz (KH)–Rayleigh Taylor (RT) breakup model was employed to model spray atomization [46]. The injection rate was determined from the experimental injector characterization. This process measures the mass flow rate and spray momentum flux in a specific test rig [47,48] for the injection configurations defined a priori in similar real test conditions, in order to provide the most realistic injection features.

Cylinder wall temperatures were assumed to be constant and estimated using a lumped heat transfer model [49]. The instantaneous pressure signals registered at intake/exhaust manifolds were used to fix the inflow/outflow boundaries located at the end of the intake/exhaust ports. The temperature at these boundaries was considered constant and equal to the time-averaged value registered at the same manifolds.

This configuration has proven to accurately reproduce the in-cylinder pressure field oscillations over a wide range of operation conditions and combustion regimes [26,50,51].
