RNN modeling for time-varying aerodynamic deformation and drag for a droplet at moderate Weber numbers

Aerodynamic deformation and breakup of droplets in gas flows are important in various natural and industrial applications. When an initially stationary droplet is subjected to a gas stream, the competition between destabilizing gas dynamic pressure and resisting surface tension is characterized by the Weber number (We). The present study is focused on the range of We lower than the critical threshold; as a result, the droplet does not break but rather undergoes deformation in an oscillatory manner. The droplet deformation influences the drag coefficient, which in turn plays a significant role in determining the trajectory of the droplet. In this study, 2D axisymmetric interface-resolved simulations were performed to resolve the droplet deformation and dynamics, using a mass-momentum consistent VOF method. The instantaneous drop shape is then decomposed into spherical harmonic modes. The time evolutions of the first ten spherical harmonic modes, the droplet centroid velocity, and the physical parameters are used to train the Non-linear Auto-Regressive with eXogenous input Neural Network (NARXNN) model. A NARXXNN model is first built to capture the time evolution of the drop deformation, and then the predicted mode coefficients and the drop velocity are used to train the second model for the drag. An excellent agreement between the model predictions and the simulation results is achieved.