A fully compressible four-equation model for multicomponent two-phase flow coupled with a real-fluid phase equilibrium-solver is suggested. It is composed of two mass, one momentum, and one energy balance equations under the mechanical and thermal equilibrium assumptions. The multicomponent characteristics in both liquid and gas phases are considered. The thermodynamic properties are computed using a composite equation of state (EoS), in which each phase follows its own Peng-Robinson (PR) EoS in its range of convexity, and the two-phase mixtures are connected with a set of algebraic equilibrium constraints. The drawback of complex speed of the sound region for the two-phase mixture is avoided using this composite EoS. The phase change is computed using a phase equilibrium-solver, in which the phase stability is examined by the Tangent Plane Distance approach; an isoenergetic-isochoric flash including an isothermal-isobaric flash is applied to determine the phase change. This four-equation model has been implemented into an in-house IFP-C3D software. Extensive comparisons between the four-equation model predictions, experimental measurements in flash boiling cases, and available numerical results were carried out, and good agreements have been obtained. The results demonstrated that this four-equation model can simulate the phase change and capture most real-fluid behaviors for multicomponent two-phase flows. Finally, this validated model was applied to investigate the behaviors of n-dodecane/nitrogen mixtures in one-dimensional shock and double-expansion tubes. The complex wave patterns were unraveled, and the effects of dissolved nitrogen and the volume translation in PR EoS on the wave evolutions were revealed. A three-dimensional transcritical fuel injection is finally simulated to highlight the performance of the proposed four-equation model for multidimensional flows.

Computation of high pressure Diesel injection requires improvement of present spray atomization and droplet breakup models. The surface wave instability atomization (Wave) model of Reitz [2] has been coupled to a new breakup model (FIPA) which is based on the experimental correlations of Pilch et al.[3]. It has been integrated in the 3D KMB code [1] derived from the Kiva 2 code [4] of Los Alamos already including a stochastic Lagrangian description of sprays. The droplet breakup FIPA model was first fitted and validated using the monodisperse drop breakup experiments of Liu and Reitz [5]. The response of the modified spray model including the global Wave-FIPA breakup model is compared to well characterized data obtained in a high pressure and temperature vessel. This vessel is fitted with a common-rail injection system with a single hole injector tip. Conditions simulating a direct injection diesel engine are obtained (ρg = 25kg/m3, Pg = 3 MPa and 6.1 MPa, Tg = 400K and 800K, Pinj from 40 to 150 MPa). Liquid and vapor penetrations in the vessel are well reproduced, even for high injection pressure cases and with or without evaporation.

The Lagrangian-Eulerian approach is commonly used to simulate engine sprays. However typical spray computations are strongly mesh dependent. This is explained by an inadequate space resolution of the strong velocity and vapor concentration gradients. In Diesel sprays for instance, the Eulerian field is not properly computed close to the nozzle exit in the vicinity of the liquid phase. This causes an overestimated diffusion that leads to inaccuracies in the modeling of fuel-air mixing. By now it is not possible to enhance grid resolution since it would violate requested assumptions for the Lagrangian liquid phase description. Besides, a full Eulerian approach with an adapted mesh is not practical at the moment mainly because of prohibitive computer requirements. Keeping the Lagrangian-Eulerian approach, a new methodology is introduced: the full Lagrangian-Eulerian Coupling (CLE). It consists in retaining vapor and momentum along parcel trajectories as long as the mesh is unsufficient to resolve the steep gradients. Vapor and momentum are gradually released on the mesh following specified diffusion laws. This model is briefly described. CFD simulations are performed using the KMB code, a modified version of KIVA-II. Comparisons are presented of computed and measured penetrations of liquid and vapor in a high pressure, high temperature Diesel simulation cell. The new CLE model is shown to reproduce properly the evaporating spray structure and penetration while having a very limited mesh sensitivity. DI Diesel engine calculations using a rather crude mesh show a very good agreement of liquid and vapor penetrations. This insures an improved predictivity of the combustion in full load cases.

Because of intense flow recirculations and strong local depression, cavitation occurs in high-pressure Diesel injectors. Because experiments are very difficult to perform for injection conditions (small length and time scales, high-speed flow, etc.), multidimensional modeling seems to be an appropriate tool in order to better understand the flow features inside and at the exit of the injector nozzle. The purpose of this paper is to present the application of the homogeneous equilibrium modeling (HEM) approach for the simulation of cavitating flows inside a Diesel multihole injector. The validation of the model for typical cavitating flow configurations is presented. The HEM approach allows one to reproduce different cavitation regimes observed experimentally. Indeed, numerical results obtained on a simplified injector [7] agree well with experimental visualizations of cavitation and multiple flow fields. Also, the computed steady-state discharge coefficients of a single hole injector are close to the measured values. Furthermore, numerical results reproduce qualitatively the experimental images of cavitation. Finally, computations of cavitating flows in a six-hole narrow-angle Diesel injector, taking into account the needle displacement, are discussed. It is shown that transient injector exit conditions (i.e., fluid velocity at the injector exit, void fraction, cone angle, etc.) are mainly due to the cavitation collapse especially, during the opening and closing of the injector needle. Therefore, transient computational fluid dynamics code boundary conditions have to be taken into account to improve spray atomization and combustion modeling.