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Projectile penetration into an immersed granular bed is a common phenomenon in both geophysics and engineering, encompassing various scenarios such as immersed crater formation and offshore soil-structure interaction. It involves the complex physical interaction between the fluid and granular materials. In this study, we investigate the dynamics of projectile penetration into a granular bed immersed in a fluid using a coupled computational fluid dynamics and discrete element method (CFD-DEM). The granular bed is composed of polydisperse particles, and the projectile is modeled as a rigid sphere. The morphology of crater formation, the dynamics of the projectile, and the drag force characteristics in immersed cases were studied in detail and compared to the dry scenario. The numerical results show that the final penetration depth of the projectile follows an empirical relation derived from experimental observations, where the falling height and the drag force during penetration obey a power-law function and a modified generalized Poncelet law, respectively. The interstitial fluid not only provides direct drag force, but also enhances the effective drag force of the granular bed by improving its generalized friction and effective viscosity in different configurations. Micro-analyses of the velocity evolution and contact force network in different stages of the fluid–solid interaction were performed to clarify the penetration dynamics. This research provides insights into the mechanisms of projectile penetration and the effects of interstitial fluid on granular media, which are crucial in engineering applications such as offshore anchoring, ball penetration tests in soft sediments, and soil-structure interactions. Graphical Abstract
Projectile penetration into an immersed granular bed is a common phenomenon in both geophysics and engineering, encompassing various scenarios such as immersed crater formation and offshore soil-structure interaction. It involves the complex physical interaction between the fluid and granular materials. In this study, we investigate the dynamics of projectile penetration into a granular bed immersed in a fluid using a coupled computational fluid dynamics and discrete element method (CFD-DEM). The granular bed is composed of polydisperse particles, and the projectile is modeled as a rigid sphere. The morphology of crater formation, the dynamics of the projectile, and the drag force characteristics in immersed cases were studied in detail and compared to the dry scenario. The numerical results show that the final penetration depth of the projectile follows an empirical relation derived from experimental observations, where the falling height and the drag force during penetration obey a power-law function and a modified generalized Poncelet law, respectively. The interstitial fluid not only provides direct drag force, but also enhances the effective drag force of the granular bed by improving its generalized friction and effective viscosity in different configurations. Micro-analyses of the velocity evolution and contact force network in different stages of the fluid–solid interaction were performed to clarify the penetration dynamics. This research provides insights into the mechanisms of projectile penetration and the effects of interstitial fluid on granular media, which are crucial in engineering applications such as offshore anchoring, ball penetration tests in soft sediments, and soil-structure interactions. Graphical Abstract
Ejecta splashing is accompanied by the formation of impact craters in oblique impact of a sphere onto a granular target. We investigated the morphology and scaling of the ejection, together with the evolution and final size of crater by performing a series of experiments, varying the impact angle θ and impact speed V0. The experiment categorized the crater shapes in the space parameters Fr and θ and revealed that the maximum ejecta height exhibits two regimes related to Froude number, while the crater length, width, and depth are all collapsed to a master line. Then, the evolution characteristics of the corolla dimensions (top diameter, neck size, bottom diameter, and height) are determined. Moreover, a simple ballistic model taking into account the air drag force acting on the ejecta has been proposed to predict the dynamic processes of the corolla in oblique impacts. Furthermore, the opening of the crater formation deduced by the dynamics of the corolla formed and the collapsing process (i.e., the splashed sand avalanching down along the wall of the crater) have been investigated in detail using a simplified Bouchaud–Cates–Ravi–Edwards model. Our theoretical model demonstrated high accuracy in reproducing the evolution of a crater during impacting and in predicting the final crater scaling after avalanching.
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