# Large-Eddy Simulation of Droplet Deformation and Fragmentation Under Shock Wave Impact
## 5 Conclusions  
This study investigated the aerodynamic breakup of water droplets induced by air shock waves traveling at different Mach numbers. The numerical simulations were carried out using the LES approach combined with a hybrid VOF-DPM technique. The obtained results confirm previous theoretical and experimental findings regarding the physical mechanisms driving droplet fragmentation.  
In fact, the LES method, balancing computational efficiency with solution accuracy, effectively captures flow instabilities and the main turbulent flow structures during the shock-droplet interaction, offering key insights into water body deformation and breakup under high-speed airflow. At lower Weber numbers, the breakup transitioned between RTI and stripping regimes, indicating a multimodal regime. The flow around the droplet was similar to that of a sphere at comparable Reynolds number, with vortex shedding near the midsection. A toroidal vortex and reverse flow initially developed, generating annular waves that influenced the subsequent fragmentation. The sheet stripping mechanism was consistently observed across simulations, with KH waves becoming particularly pronounced at higher Mach number. In fact, two distinct stripping mechanisms affect the droplet surface evolution: the primary mechanism generates a main stream of fragments from the droplet's equator to the flattened rear, while the secondary mechanism operates at the front. Also, larger fragments form in regions of intense stripping, then evolving into a fine mist. The droplet undergoes continuous stretching and compression, with more pronounced deformation at higher Mach numbers. The sub-droplet size distribution shifts toward smaller values with increasing Weber number, confirming the model's accuracy compared to experimental observations.  
Overall, the present hybrid Eulerian-Lagrangian approach proved effective in capturing the complexities of droplet aerobreakup, as demonstrated by both qualitative and quantitative analyses. Compared to previous RANS-based studies, the present LES method offers a more robust and detailed understanding of the complex dynamics involved in droplet breakup under post-shock conditions. However, future research employing different SGS models could provide further assessments of the proposed formulation, where the combination of LES with DPM and VOF techniques appears very promising. Potentially, the method may lead to more accurate predictive models for advanced engineering applications such as fuel atomization and spray dynamics.  
Conceptualization, G.D.S.; methodology, V.R. and G.D.S.; validation, V.R. and G.D.S.; investigation, V.R.; resources, G.D.S.; data curation, V.R.; writing--original draft preparation, V.R.; writing--review and editing, G.D.S.; visualization, V.R.; supervision, G.D.S. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
The authors thank [PERSON], University of California at Santa Barbara, for kindly providing the experimental images reported in Figure 3. The authors acknowledge the CINECA award under the ISCRA initiative (Project HP10 BB0905) for the availability of high-performance computing resources.  
The authors declare no conflicts of interest.