Numerical investigation of the interactions between a low-hypersonic shock wave and a water droplet: VOF and DI methods comparison

Abstract

In this paper, we present the hydrodynamic mechanisms which occur between a low-hypersonic shock wave and a millimetric water droplet. To do so, two numerical models, based respectively on the Volume of Fluid (VOF) and Diffuse Interfaces (DI) approaches, are developed. The goal is to compare the results obtained with the models in order to evaluate which is the most accurate to describe the evolution of the physical phenomena. The studied Mach number and initial droplet diameter are 4.25 and 1.135 mm, respectively. Each model allows the compressible Euler equations to be solved in a 2D-axisymmetric configuration. The evolution of both air and liquid phases is modelled by a stiffened gas equation of state. For qualitative validation, the numerical results are compared to experimental data recently presented in the literature. In this work, the authors used a shock tube test facility and a shadowgraph visualization technique to observe the phenomenology over a long time. Their investigation shows that the droplet deformation, detached bow shock and recompression waves are well captured by the two models until a Rayleigh dimensionless time of 1.5. Beyond this critical time, and up to 3, some differences appear between the two numerical approaches, especially on the droplet deformation. Globally, the droplet deformation is better described with the VOF model, while the DI model appears to be more accurate when it comes to the evaluation of the position of the bow shock. In the discussion section, some ideas are proposed to improve the models.