The effect of a side wall on cavity dynamics during the water entry of a sphere at low Froude numbers

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Abstract
This paper comprehensively investigates the non-axisymmetric cavity dynamics of a vertically entering sphere under the influence of nearby side-walls through experimental, numerical, and theoretical analyses. Initially, we explore the characteristics of cavity evolutions with the sidewall effect. The emergence of a twin-vortex during cavity pinch-off is observed, and detailed numerical simulations provide insights into its underlying mechanisms. Both the dimensionless distance (λ) and the Froude number Fr significantly influence the pinch-off type. A phase diagram in the λ−Fr parameter space is presented, revealing the interplay between these variables. Moreover, we investigate the sidewall effect on the pinch-off time and location at low Froude numbers. The findings indicate that as λ decreases, both the pinch-off time and depth of the cavity increase. Generally, the wall effect is relatively weak when λ exceeds 4. Additionally, the pinch-off time can be described by τ=kr/g, with the constant k determined by λ. Utilizing 2D cavity theory, we estimate the pinch-off time of the water entry cavity with the sidewall effect, revealing a consistent collapse behavior with the mechanics of a two-dimensional cavity.
Funding Information
  • National Natural Science Foundation of China (52201358)
  • National Natural Science Foundation of China (12072087)
  • National National Science Foundation of China (12332014)
  • Heilongjiang Postdoctoral Fund (LBH-Z23117)

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