Eulerian–Lagrangian spray atomization model coupled with interface capturing method for diesel injectors

Abstract

Traditional Discrete Particle Methods (DPM) such as the Euler–Lagrange approaches for modeling atomization, even if widely used in technical literature, are not suitable in the near injector region. Indeed, the first step of atomization process is to separate the continuous liquid phase in a set of individual liquid parcels, the so-called primary break-up. Describing two-phase flow by DPM is to define a carrier phase and a discrete phase, hence they cannot be used for primary breakup. On the other hand, full scale simulations (direct simulation of the dynamic DNS, and interface capturing method ICM) are powerful numerical tools to study atomization, however, computational costs limit their application to academic cases for understanding and complementing partial experimental data. In an industrial environment, models that are computationally less demanding and still accurate enough are required to meet new challenges of fuel consumption and pollutant reduction. Application of DNS-ICM methods without fairly enough resolution to solve all length scales are currently used for industrial purposes. Nevertheless, effects of unresolved scales are generally cast aside. The Euler-Lagrange Spray Atomization model family (namely, ELSA, also called, Σ−Y or Ω−Y) developed by Vallet and Borghi pioneering work (Vallet and Borghi, 1999a), and (Vallet et al., 2001), at the contrary aims to model those unresolved scales. This approach is actually complementary to DNS-ICM method since the importance of the unresolved term depends directly on mesh resolution. For full interface resolution, the unclosed terms are negligible, except in the far-field spray when the unresolved terms become dominant. Depending on the complexity of the flow and the available computational resources, a Large Eddy Simulation (LES) formalism could be employed as modeling approach. This work focus on the two main terms that drive these different modeling approaches namely the sub-grid turbulent liquid flux and the unresolved interface. Thanks to the open source library OpenFoam® (Weller et al., 1998) this work is an attempt to review and to release an adapted modeling strategy depending on the available mesh resolution. For validation, these solvers are tested against realistic experimental data to see the overall effect of each model proposal. It was found that both showed good agreement with experiments, and particularly under Diesel Spray injection conditions, the sub-grid scales represent the major driving force, thus diffusing the interface rapidly at the exit of the injector.