The Spike Dynamics Source Model for Ejecta in the FLAG Code

Abstract

The Lagrangian hydrocode FLAG employs a subgrid model to represent the ejection of particulate mass (“ejecta”) from a shocked metal surface. With a conforming mesh used in typical simulations, the calculations of ejecta production, properties and launch are carried out independently on each mesh face lying on the surface of the metal. Based on experimental evidence [1] that ejecta production is greatest when the shock releases to the liquid state, the ejection process is modeled as a Richtmyer-Meshkov instability (RMI) of the liquid metal surface, in which the metal spikes that form break up to become ejecta. The model applies to the case in which surface perturbations such as machining grooves can be well approximated as a single-mode sinusoidal perturbation; in this case the RMI spikes are actually sheets. The FLAG model includes (1) a description of RMI spike and bubble growth rates [2] and (2) the Self-Similar Velocity Distribution (SSVD) model of the velocity field within a spike as varying linearly from zero (in the fluid frame) at the base to a maximum value at the tip [3]. We report here on the improvement of this model by incorporating (3) a spike breakup treatment based on the Taylor Analogy Breakup (TAB) model [5], as extended to apply to sheet breakup [6,7], and (4) a new model for the inflow of metal into the base of the spikes. Combining all these elements allows us to self-consistently reconcile the evolving shape of the spikes (elongation and thinning) with the inflow, and with the corresponding properties of the bubbles, under the assumption of incompressibility. Since the model describes the motion of each fluid element into and along the spike, and subsequent fragmentation of the spike into ejecta, it predicts not only mass ejection rate but also the sizes and velocities of the particles launched in this process. We describe the new self-consistent model and its implementation in FLAG.