## 1 Introduction  
Water injection (WI) technology is seen as a promising solution to make turbocharged spark ignition (SI) engines operate with higher compression ratios, higher boost pressures and stoichiometric combustions at high loads. This allows a reduction in brake-specific fuel consumption (BSFC) and thus in CO\({}_{2}\) emission on the overall engine map [1, 2]. In downsized turbocharged SI engines, at stoichiometric conditions and full load, it is necessary to control knock tendency and to fulfill the maximum allowable temperature at the turbine intake. In commercial SI engines, this is commonly performed by introducing an excess fuel in the combustion chamber and retarding the ignition timing, leading to lower thermodynamic efficiency. Water injection can replace the cooling effect of the air/fuel mixture enrichment with benefits in the BSFC. The introduction of water in the combustion chamber of an SI engine reduces the gas temperature level before the combustion takes place due to the water's high latent heat of vaporization that cools down the air/fuel mixture. [PERSON] et al. [2] numerically investigated the relative weight of water vaporization and the sole dilution effect in the charge-cooling process. They compared the effect of liquid- and vapor-water injection on the air-fuel mixture temperature, at the spark timing. They found a reduction in air-fuel mixture temperature with liquid-water injection five times higher than in the case of vapor injection, indicating the evaporation as the main driver of charge cooling. Moreover, the evaporated water acts similar to an inert gas during the combustion process and it reduces the combustion temperature by increasing the global heat capacity [3]. Starting in the 1920s, research has been progressing on the use of water in internal combustion engines [4], and many researchers presented works on water injection in the intake manifold (port injection) or directly in the cylinder (direct injection) of spark-ignition engines [5]. In Reference [6], [PERSON] et al. experimentally analyzed the influence of port water injection on the consumption and the thermal efficiency of a turbocharged direct injection engine. The tests were conducted at low speed and medium-high load, at stoichiometric condition. A reduction of about 3.5% in specific fuel consumption and an increase in thermal efficiency of about 1.5% were obtained when the maximum water/gasoline percentage of 50% was injected, thanks to the knock mitigation. The influence of advanced spark timing was found to be dominant compared to the effect of charge dilution on the combustion duration. Therefore, the combustion center was advanced of about 5 CAD. Further advantages can be obtained at high engine speed and full load. As aforementioned, in these conditions turbocharged engines run overfueled to keep the turbine temperature below the mechanical failure threshold. Advancing the knock-limited spark advance allow us to reduce the exhaust temperature, avoiding charge enrichment. [PERSON] et al. investigated the influence of port water injection on the performance of turbocharged direct-injection spark-ignition engine at full-load (18 bar BMEP) conditions. The port fuel injection allowed us to reduce the fuel enrichment of about 13% with a thermal efficiency increase of about 4.5% [7]. Similar results were found by [PERSON] et al., who experimentally tested the behavior of a small displacement turbocharged spark-ignition engine equipped with a port-water-injection system. They observed a reduction in fuel consumption between 6 and 12% at full load conditions, at varying engine speeds [1]. In Reference [8], [PERSON] et al. investigated the influence of direct water injection on knock mitigation and thermal efficiency. They found a relationship between the injection timing and charge cooling effect. When water injection is too advanced, the spray impinges against the cylinder walls, generating a liquid film.