Accurate prediction of the dynamics of a deformable and freely-moving drop in a uniform gas stream is essential for numerous applications involving droplets, such as spray cooling and liquid fuel injection. When the droplet Weber number is finite but moderate, the drop deviates from its spherical shape and deforms as it is accelerated by the gas stream. Since the drag depends on the drop shape, rigorously resolving the drop shape evolution is necessary for accurate predictions of the drop’s velocity and position. In this study, 2D axisymmetric interface-resolved simulations were performed using the Basilisk solver. The sharp gas-liquid interface is resolved using a geometric Volume-of-Fluid (VOF) method. The quadtree mesh is used to discretize the 2D domain, providing flexibility to dynamically refine the mesh in user-defined regions. The adaptation criterion is based on the wavelet estimate of the discretization errors of the color function and all velocity components. Parametric simulations are conducted by systematically varying the Weber and Reynolds numbers. The instantaneous drop shapes are characterized using spherical harmonic modes. The temporal evolution of the drag and the spherical harmonic mode coefficients are investigated to identify correlations between the drag and the spherical harmonic mode coefficients. The simulation data are also utilized to develop point-particle models for Euler-Lagrange simulations of sprays consisting of a large number of drops. Due to the complex interplay between droplet drag and deformation, accurate models cannot be developed through conventional physics-based approaches. Therefore, a data-driven approach will be adopted. The spherical harmonic mode coefficients up to the sixth mode are used to characterize the drop shape. The evolutions of the spherical harmonic mode coefficients from the simulation results for cases in the test set are used to train the Non-linear Auto-Regressive with Exogenous input Neural Network (NARXNN) model. The predicted mode coefficients are then used as input to train an additional NARXNN model for the drop acceleration.

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