In Situ Estimation of the Coefficient of Stress Source in the Eulerian–Lagrangian Spray Atomization Model

Liquid jet atomization is one of the key processes in many engineering applications, such as IC engines, gas turbines, and the like, to name a few. Simulating this process using a pure Eulerian or a pure Lagrangian framework has its own drawbacks. The Eulerian–Lagrangian spray atomization (ELSA) modeling seems like a viable alternative in such scenarios. ELSA simulations consist of solving an additional transport equation for the surface area density (Σ) of the issuing jet. In this study we have proposed a dynamic approach to compute the turbulent timescale constant (α₁), which appears in the source of Σ-transport equation and is responsible for restoring the surface area back to its equilibrium. The dynamic approach involves an analytical computation of the turbulent timescale constant (α₁), thereby eliminating the need for ad hoc adjustments to surface area values during computational fluid dynamics (CFD) simulations. Unlike previous research which suggests using constant values in the range (0, 1] for the α₁-constant, we found that these values can be as high as 60,000 for the engine combustion network (ECN) spray-A nozzle conditions. The analytical closure procedure dampens the spurious overshoots seen in the sigma-Y field and maintains values close to the equilibrium conditions. The proposed approach is implemented in CONVERGE, a commercially available CFD code and validated by comparing against available experimental data.