Transient behaviour of a gaseous cavity attached to a projectile in a two phase flow

Abstract

The cavities we consider can be created by the entry of a body into water or during the vertical launch of a projectile by means of an expanding gas.

When the characteristic Fronde Dumber F₀ is large, the resulting two phase flow exhibits an elongated cavity. Within the framework of the slender bodies theory, it can be shown that the ratio of the cavity length to a transverse dimension of the body is of order F₀ ² /3.

The significant parameter concerning the gas motion is σ_a F ₀ ^4/3 /3, σ_a being the order of magnitude of the gas density. When this parameter is small, the gas inside the cavity may be considered as homogeneous. This event generally occurs when a projectile is driven out of an underwater silo by an expanding gas. A bubble then forms between its base and the launching tube. Two new parameters appear :one is related to the expansion of the gas and the other to the difference between the surrounding hydrostatic pressure and the gas pressure at the exit of the projectile base.

The interest of our asymptotic appraoch is obvious. At first, it yields a substantial economy in testing, because the parameters brought to light are less numerous than those resulting from a classical dimensional analysis. Secondly, the asymptotic equations can be solved by simple calculations in order to obtain usefull results, able to appraise the evolution of the phenomena versus the detected dominant parameters.

Experimental results obtained up to cavity sealing are in good agreement with our theoretical predictions.