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For the modelling of surrounding air in the numerical part of this study, the ideal gas equation of state was used. e. with the fit parameter P ∞ = 0 . e. γ = c p ⁄ c v = Γ + 1 . The quantities c p and c v represent the specific heats at constant pressure and volume, respectively. For some materials, P ∞ can be quite large; examples are water and metals, for which P ∞ is of the order of megabars. 4) Here, we substituted the specific internal energy e from Eq. 2) into Eq. 3). 13 ⋅ 10 Pa . Principal Hugoniot for the Stiffened Gas EOS The locus of possible final states due to the shock compression for a fluid initially at normal density, pressure and zero mass velocity will be referred to as principal Hugoniot.

A water droplet of radius of 100µm collides with an impact velocity of 500 m/s with a flat substrate. Due to the very small time scales ( 10 – 14 – 10 – 11 s , obtained according to CFL condition) and high velocities at which the emerging waves propagate, the first issue that should be addressed is weather the present resolution (up to 4 million grid points) can realistically capture the phenomena. Thus, as a first step, we investigate the grid independence and convergence of the solution. 1 Solution Convergence & Grid Independence The grid independence of the results has been established by both one- and two-dimensional capturing of the accurate shock position and shape.

Mathematical Model & Computational Methodology Fig. 2. Droplet and air density distribution prior to the impact: Emergence and reflection of the bow shock in the air and weak perturbations in the liquid bulk (due to the liquid-air interactions on a droplet surface). Parameters: Impact velocity 500 m/s, motionless air. [numerical result with non-linear colour map (HDF)]. 3 Numerical Modelling The code FronTier, used for the current simulations was developed by a group of researchers at the New York University and the University of Stony Brook [37]-[41].

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