Development of a turbulent liquid flux model for Eulerian–Eulerian multiphase flow simulations

•Development of a Quasi-Multiphase Eulerian (QME) approach for liquid atomization.•Assessment of first order closure unreliability for turbulent liquid flux modeling.•Proposition of a new second order closure for turbulent liquid flux modeling.•Assessment of QME solver capabilities on a jet in crossflow test case. The present work introduces a multiphase Eulerian solver, developed in the framework of the CFD suite OpenFOAM, aimed at including all the major physical phenomena that characterize liquid fuel atomization. The study begins with the Eulerian solver derived from the Eulerian Lagrangian Spray Atomization (ELSA) model [Borghi, R., Vallet, A., Sep. 1999. Modelisation eulerienne de l'atomisation d'un jet liquide. Comptes Rendus de l'Academie des Sciences - Series IIB - Mechanics-Physics-Astronomy 327 (10), 1015–1020, Vallet, A., Burluka, A. A., Borghi, R., 2001. Development of a eulerian model for the atomization of a liquid jet. Atomization and Sprays 11 (6), 619–642.]. This approach is suitable to describe the liquid-gas flow for all liquid volume fraction from bubbly, dense to spray flows without any assumption on the topology of the phase (droplets, bubbles, ligaments or any continuous structures). However, due to its single phase flow formalism, the slip velocity between phases is hidden in the turbulent liquid flux term inside the liquid volume fraction equation. An innovative second order closure for this variable is here proposed and implemented. A detailed analysis of the resulting Quasi-Multiphase Eulerian (QME) solver capabilities is performed in RANS context exploiting a jet in crossflow test case with available experimental and computational data. The test is extremely challenging as it involves a high density ratio (R) (i.e. two cases at R = 10 and R = 1000 were simulated) and it explores the entire range of liquid phase concentration from purely liquid to dispersed phase. The comparison with the experimental results shows that the proposed approach leads to a comprehensive and physically consistent description of the phenomena related to liquid injection.