UNDERWATER EXPLOSION BUBBLES. 2. THE EFFECT OF GRAVITY AND THE CHANGE OF SHAPE
Abstract
A systematic method is presented for determining the shape and rise of an underwater explosion bubble. The water is assumed to be incompressible and unbounded, and the pressure is assumed to be uniform throughout the bubble at all times. The bubble is assumed to be initially spherical. The velocity of the fluid is assumed to be derivable from a potential function satisfying Laplace's equation so that the pressure in the water is given by a Bernoulli equation. Suitable boundary conditions are imposed; a moving coordinate system is introduced so that the origin remains at the center of gravity of the bubble; and convenient dimensionless parameters are chosen. A solution of Laplace's equation is assumed in the form of a power series of the dimensionless parameter sigma, the ratio of the equilibrium bubble radius to the hydrostatic head above the initial bubble center. The terms of zero order in sigma correspond to the classical theory of a spherical bubble. Including first-order terms results in the bubble center rising according to the Herring rise formula (NDRC Division 6, Report C4-SR20, 1941). Second-order terms indicate a change in bubble shape without changing the rise formula. Third-order terms further change the shape of the bubble and also modify the rise formula. These effects are in agreement with observation. For the equilibrium bubble, failure of the equations is expected to occur when sigma t squared=0.8, and the real breakdown for any bubble is expected when sigma t squared=1.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1953
- Accession Number
- AD0015682
Entities
People
- Ignace I. Kolodner
- Joseph B. Keller
Organizations
- Kansas State University