# Computational study of the separation of regular sphere clusters in high-Mach-number flow

## TL;DR

This paper studies how clusters of spheres separate in high-speed airflow, using simulations to explore how their initial arrangement affects their motion and breakup.

## Contribution

The study introduces a new computational method to analyze the aerodynamic separation of regular sphere clusters in high-Mach-number flows.

## Key findings

- Skewed sphere pairs form stable lifting configurations, influencing separation dynamics in larger clusters.
- Shock surfing of downstream bodies significantly affects tetrahedral cluster separation.
- Cluster bluntness and asymmetry indices correlate with collective dynamics, but not always predictably.

## Abstract

A coupled computational-fluid-dynamics/finite-element methodology is implemented to investigate the free aerodynamic separation of clusters of equally sized spheres arranged in regular configurations in Mach-20 flow, representing an idealized meteoroid-fragmentation scenario. The regular nature of the initial agglomeration geometries – touching sphere pairs, tetrahedral four-sphere arrangements and face-centred-cubic 13-sphere configurations – allows a systematic exploration of both individual sphere motions and bulk cluster dynamics as the initial orientation is varied. For sphere pairs, a stable lifting configuration arises when the spheres are in contact in a skewed configuration, a phenomenon that can also emerge in the more populous clusters. In the tetrahedral survey, comprising 38 initial orientations, shock surfing of downstream bodies is found to play a significant role in driving the separation dynamics. Despite substantial variations in detailed sphere motions with initial orientation, the trajectory type and final lateral velocity collapse reasonably well with the initial polar angle of the sphere within the cluster. Indices describing the bluntness and asymmetry of the initial configuration are introduced and correlate well with the collective cluster dynamics, though not always in an intuitive way. For the 13-sphere clusters, the dependency of individual sphere lateral velocities follows a similar trend with initial polar angle to the four-sphere case, suggesting that a simplified separation model may be possible for such configurations. The influence of the initial cluster bluntness on the bulk dynamics is somewhat reduced, however, indicating a tendency towards more homogeneous separation as the cluster population is increased.