Asymptotic behavior of the flow near the center of a collapsing spherical cavity
Abstract
In his analysis of the spherically symmetric collapse of an empty cavity in water, Hunter (1960) has obtained a similarity solution of the exact flow equations to describe the flow in the neighborhood of the collapse point. A caloric equation of state of the modified Tait form (Cole, 1948) was used to describe the thermodynamic properties of water. In the present paper, the second term is formulated for the expression describing the asymptotic behavior of the gas flow in the neighborhood of the collapse point. Hunter's similar solution in combination with this second term yields the speed of sound at the free boundary, in correspondence with the equation of state employed.
 Publication:

PMTF Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki
 Pub Date:
 April 1980
 Bibcode:
 1980PMTF.......116K
 Keywords:

 Asymptotic Methods;
 Cavitation Flow;
 Gas Dynamics;
 Gas Flow;
 Collapse;
 Equations Of State;
 Flow Equations;
 Flow Geometry;
 Free Boundaries;
 Shock Waves;
 Thermodynamic Properties;
 Astrophysics