Numerical Simulation of Unsteady Nozzle Flow and Spray Formation under Diesel Engine Conditions

In this paper a numerical approach for the prediction of the unsteady atomization process of liquid fuel in Diesel engine is presented. The dependences between the transient nozzle flow and spray formation are analysed. For that purpose models to simulate unsteady nozzle flows including the transient behaviour of cavitation and two-phase atomization process are employed. Results of transient flow through various 3D nozzle shapes (oneand multi-hole nozzle) and the resulting spray development are discussed. The flow predictions agree well with quantitative characteristics of nozzle flows and spray structures and with experimental results obtained for the case of the flow in a high speed diesel injector. * Corresponding author: [email protected] Associated Web site: http://www.dlr.de Proceedings of the 21 ILASS Europe Meeting 2007 Introduction The quality of liquid atomization is probably the most essential factor for reducing emissions in Diesel engines. The atomization process depends among other things on the velocity of the fuel exiting the injection nozzle and on the extent of cavitation within the nozzle. Exit velocity modulations strongly influence the breakup processes, the spray penetration and also the interdroplet and wall-droplet interactions. The internal flow through diesel fuel injector nozzles is very important for the reduction of emissions. But the relation between the injector flow and spray formation appears to be quite complicated. A typical nozzle is roughly 0.2 mm in diameter and 1 mm long. The fluid is moving at several hundred meters per second, making measurements of the flow difficult. Furthermore, cavitation within the nozzle and the unsteady nature of the flow complicates both, experiments and computations. Despite the importance of injector nozzle flows, the difficulties associated with their direct observation are most likely the reason for the limited the number of the available experimental data. Chaves, Obermeier [2-4] and Kubitzek [11] studied the relation between unsteady nozzle flows and spray structures modulations. Considering a time-dependent flow they have shown that cavitation can decrease due to increasing the supply pressure which is in contrast to observations made for steady conditions. Schmidt, Rutland and Corradini [16] studied numerically the formation of cavitation in different 2D nozzles for stationary flows. They also studied the effect of the nozzles shape on the development of cavitation [17] and found that the results of the single bubble calculations in 2D nozzles were acceptable and similar to simulations considering an axisymmetric nozzle. However the calculated behaviour of flows through an asymmetric nozzle was considerably different from the flow through a plan orifice. The asymmetric flow field tended to exhibit strong transients which would have a dramatic influence on the spray breakup. The transient nature of cavitation under stationary flow conditions has been investigated numerically by Chen and Heister [5]. Their results indicate that partially cavitating flows are typically periodic, with a period of the order of the orifice transit time. Time-dependent cavitation phenomena induced by pressure variation are presented in [7, 10]. In these papers the disappearance and re-occurrence of cavitation have been reproduced in numerical simulations. Further, non-stationary effects in 2D nozzles generated injecting water have been computed in [19, 20]. In these studies cavitation in an injection nozzle under time-depended inlet pressure conditions were investigated. Among recent publications the paper of Marcer et al. [12] deserves attention. They applied a VOF method to simulate a stationary Diesel injector flow considering three-phase flow (liquid, vapour Diesel fuel and external gas). Further, Giannadakis et al. [8] compared and evaluated Eulerian and Lagrangian cavitation models for steady pressure conditions. They addressed different physical mechanisms associated with the formation and further development of cavitation as well as their numerical modelling. In the literature a variety of injection conditions are considered. The injection velocity is modulated due to the passage of cavitation zones or bubbles through the hole exits and due to the fluctuations of the Diesel fuel pressure upstream the needle seat. According to Chaves [2] this modulation may contribute significantly to spray breakup. For any of these mechanisms there exist a number of semi-empirical models [1, 2, 9, 13 and 18]. But in order to use these models one needs to compute the injector flow which serves as initial conditions for the spray simulation. Numerical Method The whole process of fuel injection is split in two problems. First the exit velocity and mass flow rate at the nozzle outlet are simulated solving the NavierStokes equations together with a cavitation model which assumes a barotropic flow. The resulting flow field is afterwards applied as boundary and initial conditions for the spray computations. The two-phase nozzle flow (liquid and cavitation bubbles) is replaced mathematically by a single-phase flow characterized by an artificial barotropic equation of state, where density varies sharply between the density of vapour, if the pressure value decreases to the vapour pressure, and the density of liquid, when the pressure is slightly above the vapour pressure. The model includes the compressibility of both the liquid and the vapour phase. The governing continuity and momentum equations are the same as those of a single-phase flow. In Cartesian coordinates they read