Unsteady solutions of the spray flamelet equations - Huenchuguala, Felipe; Rivadeneira, Francisco; Scholtissek, Arne; Hasse, Christian; Gutheil, Eva; Olguin, Hernan (Combustion and flame, 2026)
Solutions of the spray flamelet equations reported in the literature during the last decade have been limited to very specific situations presenting steady evaporation profiles. Implicitly, this corresponds to the adoption of a continuous droplet injection strategy. In this work, it is shown how a relaxation of this restrictive assumption allows obtaining an entire spectrum of new solutions of the spray flamelet equations. For this, a Lagrangian description of the liquid phase in mixture fraction space is introduced, which is obtained by assuming that droplets travel along mixture fraction gradient trajectories. The resulting formulation is then employed to analyze ethanol/air non-premixed gas flamelets perturbed by mono-disperse sprays generated with continuous and discontinuous droplet injection strategies. It is observed that the latter leads to periodically oscillating solutions of the spray flamelet equations exhibiting time-averaged maximum temperatures up to 46 K higher than the ones obtained adopting the former. Additionally, a discontinuous injection strategy leads to an important extension of the ranges of initial droplet radii and velocities leading to burning flamelet structures (16% and 25%, respectively). Finally, it is illustrated how the developed approach also allows obtaining solutions of the spray flamelet equations for extinction/re-ignition phenomena, which have received no attention in the spray flamelet literature so far. The introduced formalism provides an appropriate basis for the future improvement of flamelet-based models for the simulation of turbulent spray flames. Novelty and significance This work presents the first unsteady solutions of the spray flamelet equations reported in the literature. These can be classified in two different groups: (i) Periodically oscillating unsteady flamelet structures and (ii) flamelets experiencing extinction/re-ignition phenomena. Until now, none of these had received any attention in the spray flamelet literature and, therefore, this study represents an important contribution towards the goal of bringing spray flamelet theory to the same level of development of its classical formulation for gas flames.