STAGE M2 FIRST – Offre du 02/11/2023 – Deformation and breakup of drops by turbulent eddies

  • Encadrants : Ignacio Roa Antúnez & Jorge César Brändle de Motta

Many industrial processes involve atomization. During this process, large droplets break up into smaller  ones. Understanding the phenomena that cause droplets to break up is necessary for mastering the applications concerned, such as liquid injection into combustion chambers or the use of agricultural jets.
Drop rupture models exist, but are not yet sufficiently predictive [1]. In particular, one effect that is still not fully understood is that of turbulence. The question is to know under what conditions turbulence is capable of breaking up a drop. Direct numerical simulation (DNS) is an interesting tool for answering this question. In recent years, three pioneering papers have explored the capabilities of DNS to study drops and their breakup in turbulent flow. The first studied the probability of rupture in a homogeneous turbulent field [2]. The second analyzed the evolution of an ensemble of drops in a turbulent field, focusing on the interaction between the interface and the surrounding fluid [3]. Finally, a recent paper from our laboratory explored the relationship between curvature and droplet breakup [4].
The aim of this internship is to focus on taking advantage of the capabilities of DNS to explore the fluid-fluid interaction at the interface. The Kolmogorov-Hinze framework states that in turbulence, drops are broken by drop-scale vortices. In turbulent flows, however, the drop is subjected to eddies of many length scales. A comprehensive analysis of the wide spectrum of eddie scales present in turbulence will be performed, focusing on their contributions to droplet breakup. Recent studies have shed light on this topic, investigating the contribution of sub-bubble scale vortices to bubble breakup [5], and the effects of the surrounding fluid by studying the stretching of the fluid-fluid interface by outter eddies [6, 7].
For this analysis, the student will work with a numerical database of droplets generated in the in-house code ARCHER as part of a previous study [8], which is currently under expansion. The student will develop a methodology to isolate the different eddy scales and calculate the interface quantities (vortices/stretching), expanding the post-processing tool PyArcher. Furthermore, an analysis of the effect of the different length scales on the surface of each droplet will be carried out, focusing in particular on the last moments of the droplet lifetime.

[1] Solsvik, J., Tangen, S., & Jakobsen, H. A. (2013). On the constitutive equations for fluid particle breakage. Reviews in Chemical Engineering, 29(5), 241-356

[2] Perlekar, P., Biferale, L., Sbragaglia, M., Srivastava, S., & Toschi, F. (2012). Droplet size distribution in homogeneous isotropic turbulence. Physics of Fluids, 24(6)

[3] Dodd, M. S., & Ferrante, A. (2016). On the interaction of Taylor length scale size droplets and isotropic turbulence. Journal of Fluid Mechanics, 806, 356-412

[5] Qi, Y. et al. Fragmentation in turbulence by small eddies, Nat. Commun. 13 (2022) 469

[6] Chen, T., Liu, T., Wang, L. P., & Chen, S. (2019). Relations between skin friction and other surface quantities in viscous flows. Physics of Fluids, 31(10)

[7] Vela-Martín, A., & Avila, M. (2021). Deformation of drops by outer eddies in turbulence. Journal of Fluid Mechanics, 929, A38