On the shape of a slender axisymmetric nonstationary cavity

Very few studies have been made of three-dimensional nonstationary cavitation flows. In 1, 2], differential equations were obtained for the shape of a nonstationary cavity by means of a method of sources and sinks distributed along the axis of thin axisymmetric body and the cavity. In the integro-differential equation obtained in the present paper, allowance is made for a number of additional terms, and this makes it possible to dispense with the requirement ¦ In ¦ 1 adopted in 1, 2]. The obtained equation is valid under the weaker restriction 1. In 3], the problem of determining the cavity shape is reduced to a system of integral equations. Examples of calculation of the cavity shape in accordance with the non-stationary equations of 1–3] are unknown. In 4], an equation is obtained for the shape of a thin axisymmetric nonstationary cavity on the basis of a semiempirical approach. In the present paper, an integro-differential equation for the shape of a thin axisymmetric nonstationary cavity is obtained to order ² ( is a small constant parameter which has the order of the transverse-to-longitudinal dimension ratio of the system consisting of the cavity-forming body, the cavity, and the closing body). A boundary-value problem is formulated and an analytic solution to the corresponding differential equation is obtained in the first approximation (to terms of order ² In ), A number of concrete examples is considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 38–47, July–August, 1980.I thank V. P. Karlikov and Yu. L. Yakimov for interesting discussions of the work.