Impact of a long thin body on a cylindrical cavity in liquid: A plane problem

An approach is developed to the investigation of the shock interaction between a long thin cylindrical body and a cylindrical cavity in an infinite compressible perfect liquid. This process accompanies the supercavitation of the body. Three typical cases of cross-sectional dimensions of the body and the cavity are examined. For each case, a mixed nonstationary boundary-value problem with an unknown moving boundary is formulated. The unknown quantities are expanded into Fourier series. An auxiliary problem is solved using the Laplace transform to establish the relationship between the pressure and the velocity on the cavity surface. As a result, the problem is reduced to an infinite system of Volterra equations of the second kind solved simultaneously with the equation of transverse motion and the equation of the contact boundary. An asymptotic solution valid at the initial stage of interaction is obtained for all the three cases, and a numerical solution is found for the most typical case __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 6, pp. 32–53, June 2006.