Cavern Boundary Research Articles

Axisymmetric cavitation flow around a body in a tube

The problem of the axisymmetric flow around a body in a circular tube with arbitrary shape of the meridian section is reduced to the numerical solution of a system of two integral equations to determine the shape of the cavern and the intensity of the vortex rings arranged on the solid boundaries and the cavern boundary. Results of computations of the cavitation flow around a sphere, ellipsoid of revolution, and cone in a cylindrical tube, and also for a cone in converging and expanding tubes and in a hydrodynamic tunnel with the actual shape of the converging and working sections, are presented.

Axisymmetric flow around bodies in the developed cavitation mode

As a rule, axisymmetric cavitation flows are investigated by means of numerical computations in the absence of analytic solutions. However, substantial difficulties are still encountered here which are discussed in detail in the survey report of Birkhoff [1]. One of the integral equation methods used earlier for numerical computations of a plane cavitation flow [2] is considered below. General considerations about its application for the computations of axisymmetric flows are presented in [3]. This method turns out to be effective for the numerical computations of axisymmetric flows, as well as for an analytical investigation of the curvature of the meridian section of the cavern boundary near the point of its separation from the body. This latter question has been examined earlier in [4], where it has been shown for the case of a circular cone with a rectilinear generator that the curvature becomes infinite. The order of the infinity has not been established.

Selfmodelled GAS flow from the surface of a circular cone or wedge with an associated shock wave

Gas flow in modern energy transport systems, wind tunnels etc., is in general described by a system of non-stationary equations. Because of the geometrical symmetry of the system, it is usually possible to discard one of the space coordinates in the equations. For selfmodelled flows the number of independent variables is reduced to two. The approach to problems of this latter type is therefore considerably simplified, in spite of the fact that the equations may be of a mixed type. We shall consider the seifmodelled magnetic flow of a gas from the walls of a circular cone or two-dimensional sector as applied to the theory of a pulse discharge in a conical chamber (see [l] - [2]). In the case of an ideally conducting medium (strong skin effect) a cavern, increasing with time and filled by magnetic field, is formed between the chamber walls and the gas. The influence of the magnetic field is similar to the action of a rotationally symmetric piston, compressing the gas towards the axis of symmetry and forcing it from the conical chamber. To determine the shape of the cavern we have to use the condition for the equality of the magnetic pressure and the gas pressure at the cavern boundary. We consider in this paper the gas-dynamical problem of conical compression. The pressure on the piston and other required functions have been found for a given law of expansion of the cavern. For selfmodelled motion this law may be written in the following genral form: r 1 = [ tf( θ 1)] 6, where t is time, and r 1 and θ 1 are the polar coordinates of the piston. Conical compression is obtained in the limit as δ → ∞. in this compression a shock wave is associated with the vertex of the conical chamber. A numerical solution of the problem is obtained by the characteristics method. In this case it is a matter of indifference in principle whether the pressure distribution over the piston, or the piston motion, is given.