Introducing pre-impact air-cushioning effects into the Wagner model of impact theory

Moore, Matthew R.

doi:10.1007/s10665-021-10137-z

Introducing pre-impact air-cushioning effects into the Wagner model of impact theory

Moore, Matthew R.

Authors

Matthew R. Moore

Abstract

In this analysis, we consider the effects of non-quiescent initial conditions driven by pre-impact air–water interactions on the classical Wagner model of impact theory. We consider the problem of a rigid, solid impactor moving vertically towards a liquid pool. Prior to impact, viscous forces in the air act to deform the liquid free surface, inducing a flow in the pool. These interactions are then incorporated as initial conditions in the post-impact analysis. We derive expressions for the size of the effective contact set, the leading-order pressure and force on the impactor, and the speed and thickness of the jet at its base. In all cases, we show that the effect of the pre-impact behaviour is to cushion the impactor, reducing the size of the effective contact set and, hence, the force on the impactor. Small- and large-time asymptotic solutions are derived for general power-law impactors, and we show that the effects of the air die away as the impact progresses, so that we approach the classical Wagner solution.

Citation

Moore, M. R. (2021). Introducing pre-impact air-cushioning effects into the Wagner model of impact theory. Journal of engineering mathematics, 129(1), Article 6. https://doi.org/10.1007/s10665-021-10137-z

Journal Article Type	Article
Acceptance Date	Apr 24, 2021
Online Publication Date	Jun 22, 2021
Publication Date	2021-08
Deposit Date	Nov 17, 2021
Publicly Available Date	Nov 22, 2021
Journal	Journal of Engineering Mathematics
Print ISSN	0022-0833
Electronic ISSN	1573-2703
Publisher	Springer Verlag
Peer Reviewed	Peer Reviewed
Volume	129
Issue	1
Article Number	6
DOI	https://doi.org/10.1007/s10665-021-10137-z
Keywords	Air cushioning; Ship slamming; Water entry
Public URL	https://hull-repository.worktribe.com/output/3883138

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