Velocity-space analysis method for hazardous fragments in debris clouds

A Whipple shield is a double-plate structure commonly used to protect space fragments from impacting spacecraft. The space fragment impacts the outer plate and is broken into a debris cloud with dispersed energy and momentum, which reduces the risk of penetrating the bulkhead. Hazardous fragments with greater mass and energy in the debris cloud are the main threats to the bulkhead. Based on the finite element and smoothed-particle hydrodynamics (FE-SPH) adaptive method, this study aims to establish a generic analysis method for hazardous fragments in the debris clouds, which includes identifying stable debris clouds, quantifying the lethality of hazardous fragments to the rear plate, determining the critical spacing of the double plate in the Whipple shield, describing the hazardous fragment distribution, and characterizing the energy angular distribution of hazardous fragments. The FE-SPH adaptive method enables the extraction of individual characteristics and distribution information of the hazardous fragments. The criteria of hazardous fragments are given based on the lethality of fragments on the rear plate. A quantitative criterion for a stable debris cloud (whose fragments are no longer breaking) was established, which provides a minimal double-plate spacing L_min to ensure an effective Whipple structure. We introduce the velocity distribution of the fragments for analyzing the stable debris cloud. The maximum velocity angle θ₉₉ of hazardous fragments is proposed to quantitatively analyze their distribution range. An orthogonal test shows that θ₉₉ is related to the ratio of the plate thickness to the sphere diameter (H/D) and the projectile velocity V. Intensive test results indicate that θ₉₉ is a function of V and H/D. By evaluating the applicable scope, the fitted function works well when the projectile is disintegrated. Finally, this study investigates the energy angular distribution of the hazardous fragments. The debris clouds are qualitatively divided into intact, ruptured, and disintegrated regions.