Effects of the LES-Mode SGS Viscosity Formulation on the Hybrid URANS/LES Modeling of Turbulent Fuel Sprays

The LES hybridization of standard two-equation turbulence closures is often achieved leaving formally unchanged the turbulent viscosity expression in the URANS and LES modes of operation. Although generally convenient in terms of ease of implementation, this choice leaves some theoretical consistency questions unanswered, the most obvious being the actual meaning of the two transported turbulent scalars and their exact role in the modeled viscosity build-up. A possible remedy to this is represented by the simultaneous modification of one or both the turbulent transport equations and of the turbulent viscosity formula, for which a standard LES behavior is enforced whenever needed. The present work compares a conventional DES-based hybrid model with a consistency-enforcing modified variant for turbulent fuel spray simulation. In our case, LES-mode consistency is accomplished by excluding the second turbulent scalar quantity from the viscosity calculation. In this way, the turbulent kinetic energy acts as SGS kinetic energy and the SGS viscosity is evaluated according to the well known one-equation LES implementation. The conventional and modified hybrid models are applied to the simulation of the ECN non-reacting spray-A case, which is representative of a typical high-speed turbulent fuel spray injection. Moreover, the analysis is extended to study the effect of different fuel injection pressures and ambient conditions. The spray is modeled using Eulerian-Lagrangian approach, with primary and secondary breakup taken into account by means of the Kelvin-Helmholtz-Rayleigh-Taylor model. Simulations are carried out using the open source code OpenFOAM. As a result, the modified hybrid model is found to be suitable to properly capture the relevant physics of the spray. In addition, different behaviors are observed for the two hybridization strategies: while the conventional model operates basically as a pure-LES, the consistency-enforcing modified variant applies a more intense switching between URANS and LES modes of operation. This leads to some benefit, in terms of accuracy, with respect to the pure-LES approach when a possibly not optimized mesh is used.