**1. Introduction**

The fuel flow through injector nozzles affects the spray formation, the atomization phenomenon of the liquid fuel and, therefore, the efficiency of the combustion process and pollutant emission. Modern passenger cars and trucks use higher injection pressures than early models to improve the atomization of fuel in order to reduce soot emission of internal combustion engines. Diesel engine injectors often operate at injection pressures about 2000 bar. The high injection pressure and the abrupt change of the orifice section of the injector allows to have a pressure drop below the saturated vapor pressure and consequently the development of cavitation. Cavitation has a great effect on both the fuel injection process and the performance of an engine. Cavitation generated at the entrance of the orifice affects the fluid flow and the atomization of the injected liquid jet [1–3]. Cavitation is often observed in pumps, inducers, hydraulic turbines, propellers, fuel injectors, and other fluid devices [4, 5]. However, cavitation has positive effects in some

biomedical and industrial applications such as shock wave lithotripsy, water disinfection and organic compounds decomposition, etc. [6, 7].

The study investigation of cavitation phenomenon in the injection orifice is useful even important to control and optimize the atomization process.

The high injection pressure (> 2000 bar), the high speed flow [8] and the small dimensions of the injection nozzle make the studies experimental. In addition, experiments were performed on large-scale and transparent injector configurations to visualize the phenomenon of cavitation [3, 9–15].

Confronted with experimental difficulties, several theoretical and numerical studies have been developed to study this cavitation problem in a real diesel injector [16–22]. In a previous study [17], we studied numerically, using the mixing model, the effect of the wall roughness of the orifice injection on the cavitation phenomenon. In another work [23], we studied the effect of inlet corner radius of orifice injection on the flow characteristic and the development of cavitation. We noticed a reduction in the intensity of cavitation when corner radius increases.

The relative risk of erosion of the inner wall of the diesel injector orifice due to cavitation has been studied by [16, 22]. Xue et al. studied the effect of cavitation in a multi-hole injector on the transient flow characteristic in a 3D asymmetric configuration using a two-phase (liquid–vapor) model [21]. The effect of the needle lift was analyzed by these authors. They showed a difference in velocity profile and cavitation within the holes.

Torelli et al. [24] performed a 3D simulation in a five-hole diesel mini-injector to model the internal flow of the nozzle using three types of fuel (full-range naphtha, light naphtha and n-Dodecane). They have show that the cavitation is strongly related to the saturating vapor pressure of different fuel.

In this chapter, we aim to investigate the cavitating flow inside a Diesel injector using the mixture model and taking into account the turbulence. A parametric analysis of the size and the shape of the injector is carried out. The entropy production inside the diesel injector in several cases: -single phase and laminar flow,- single phase and turbulent flow and –tubulent cavitating flow is analyzed. Furthermore, the flow is simulated in the steady state as well as in the unsteady state.

### **2. Theoretical model**

In this mixture model, the fluid (fuel) is composed of three phases: liquid, vapor and non-condensable gases (CO) which the mixture density is given by [25].

$$
\rho\_m \rho\_m = a\_v \rho\_v + a\_\mathbf{g} \rho\_\mathbf{g} + \left(\mathbf{1} - a\_v - a\_\mathbf{g}\right) \rho\_l \tag{1}
$$

where *ρ* is the density and α is the volume fraction. The indices *l*, *v* and *g* denote the liquid, vapor and gas phases, respectively.

The mass fraction *f*<sup>i</sup> can be calculated from this equation

$$f\_i = \frac{a\_i \times \rho\_i}{\rho\_m} \tag{2}$$

The transport equations describing the cavitating flow inside the diesel injector are:


*Analysis of Geometric Parameters of the Nozzle Orifice on Cavitating Flow and Entropy… DOI: http://dx.doi.org/10.5772/intechopen.99404*
