Direct Numerical Simulations of Oscillating Liquid Droplets: a Method to Extract Shape Characteristics
Jonathan Reutzsch  1@  , Gautham Varma Raja Kochanattu  2@  , Matthias Ibach  1@  , Corine Kieffer-Roth  1@  , Simona Tonini  2@  , Gianpietro Elvio Cossali  2@  , Bernhard Weigand  1@  
1 : Institut für Thermodynamik der Luft- und Raumfahrt, Universität Stuttgart (ITLR)
Pfaffenwaldring 31, 70569 Stuttgart -  Germany
2 : University of Bergamo
Viale Marconi 5 24044 Dalmine -  Italy

Oscillating droplets have been an object of various theoretical studies for more than a century and is one of the classic problems in fluid dynamics - from the first mathematical model of an inviscid liquid drop in vacuum formulated by Rayleigh, to Lamb, who considered viscous forces, through to more complicated subsequent approaches (e. g. Prosperetti). Furthermore, many numerical simulations have been conducted to investigate oscillating drops. However, the interplay between analytics and numerics is still not considered sufficiently and is capable of improvement. Thus, the main idea of this work is to extract data from numerical simulations to obtain an extensive comparison between numerics and the available analytical solutions. Furthermore, the numerical results should serve as a basis to improve existing analytical models and to motivate developing further models, for example for droplet oscillations with higher deviations or considering evaporation.
We present a method to extract the drop surface coordinates from the numerical simulations of oscillating droplets and perform a spectral decomposition into Legendre polynomials, hence, extracting the different oscillation modes. The simulations are conducted with the multiphase DNS-code FS3D. Furthermore, the implementation of the method into the code is part of this work in order to achieve an efficient workflow, which is desirable due to the high computational load of DNS. Several simulations of oscillating water droplets at standard conditions are performed, comprising 3D setups as well as deviation of the droplet shape from spherical case and variation of physical properties, for instance viscosity. The different oscillation modes are extracted with the mentioned method. Subsequently, they are compared and investigated with regard to their occurrence, characteristics, frequencies, damping behavior etc. For small deviations the dominant modes are analyzed among others by using FFT and compared to the frequency values extracted from analytical equations of Lamb and Prosperetti. We show that the technique is versatile to all different initializations of the droplets, hence, a powerful tool to capture physical changes and suitable for a detailed comparison and interplay between numerics and analytics. Nevertheless, it is a first step in investigating droplet oscillations in such a manner and the work will be extended for various conditions and setups, like droplets with evaporation, higher deviations or Newtonian properties.

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