## 1 Introduction  
It is well known that diesel engines are efficient thermal machines but emit significant levels of harmful gases such as CO\({}_{2}\), Particulate Matter (PM), NO\({}_{\rm x}\), CO, HC and SO\({}_{\rm x}\)[1]. Between these, PM and NO\({}_{\rm x}\) are especially important in diesel engines. Smoke emissions, related to PM, mostly composed of soot, are related to several diseases but are not globally regulated [2]. On the other hand, ever increasing NO\({}_{\rm x}\) emission limits have been imposed by regional and international authorities [3]. According to this, several procedures have been developed in the recent years to reduce NO\({}_{\rm x}\) emissions in diesel engines such as EGR, water injection, modification of the injection parameters and after-treatments [4; 5; 6; 7]. Between these measurements, this paper focuses on multiple injection strategies using pilot injections. This strategy affects mixing and combustion [8]. Several works about the advantages and disadvantages of pilot injections can be found in literature. One of the main disadvantages is that soot can increase because pilot injections aggravate spray characteristics and particulates can be formed at the rich region [9; 10]. In order to avoid this problem, some authors recommend combining multiple injections with other systems such as EGR [11] or high injection pressures [12], while other researchers indicate that it is possible to obtain both NO\({}_{\rm x}\) and particulate reduction using only multiple injections. In this regard, [PERSON] et al. [13] analyzed the pilot injection timing and duration and found that NO\({}_{\rm x}\) emission levels are mainly influenced by the pilot duration, whereas smoke emission is influenced by both variables. [PERSON] et al. [14] analyzed the time and quantity of the pilot injection. [PERSON] et al. [15] analyzed the effect of the dwelling time, i.e., the time between two consecutive injections, obtaining reductionsin noise, \(\rm NO_{x}\) and particulates. [PERSON] et al. [16] varied the fuel distribution in each pulse and the dwelling time between pulses and obtained a reduction in \(\rm NO_{x}\) and particulates but also a 3%-4% increase in consumption. [PERSON] et al. [17] analyzed the number of pre-injections and obtained reductions in both \(\rm NO_{x}\) and HC. [PERSON] et al. [18] analyzed the effect of the injection angle when using multiple injections. Other works such as those of [PERSON] et al. [19] and [PERSON] et al. [20] obtained \(\rm NO_{x}\) and consumption reductions but recommended employing a small amount of pilot quantity in order to maintain soot emissions. In addition to these aforementioned works based on diesel engines, other similar studies were realized using biodiesel [21], gasoline [22; 23; 24], dual fuel [25; 26; 27; 28] and other fuels [29; 30; 31; 32; 33; 34]. Numerical simulations also provide interesting information to analyze multiple injections. Particularly, in the field of Computational Fluid Dynamics (CFD), one can refer to the work of [PERSON] et al. [35], who analyzed advanced injection strategies to achieve partially premixed combustion in a diesel engine; [PERSON] and [PERSON] [36], who analyzed injection strategies to optimize two-stage combustion; [PERSON] et al. [37], who analyzed the effect of injection timing; [PERSON] and [PERSON] [38], who analyzed the effect of split injection in a direct-injection diesel engine; [PERSON] et al. [39], who analyzed the effect of injection pressure; [PERSON] et al. [40], who analyzed second injection timings; [PERSON] et al. [41], who analyzed several fuel injection strategies on a gasoline engine; [PERSON] et al. [42], who analyzed two-stage fuel injection with EGR; [PERSON] et al. [43; 44], who analyzed several configurations of pilot injections; and [PERSON] [45], who analyzed alternative injection patterns. Despite this literature about multiple injections, it is important to develop a reliable tool to characterize the most appropriate injection pattern.