Berechnung der Profilkavitation mit der Theorie für Kavitationsblasen in asymmetrischen Druckfeldern und in Vielblasensystemen

Abstract

The topic of the present paper are cavitation phaenomaens on hydrofoils. In the first part there is discussed, with regard to the growing of a single bubble in incompressible liquid, the validity of the classical assumption of a homogenious pressure field surrounding a bubble, in view of the high pressure gradient near the nose of the foil. Even if the assumption of spherical symmetrical shape of the bubble is kept on, the flow around the bubble leads to a modification of the pressure field, causing the motion of the bubble wall. The main result is, that this modification is principal due to the relative motion between the bubble and the fluid, caused by the press ure gradient. In a fluid with normal particle concentration this pressure gradients will be much smaller than in pure liquid because of the reduction of tensile stresses; so the relative motion between water and bubble and therefore the modification of the pressure field also will be much smaller. Cavitation processes with respect to the particel concentration are the subject of the second part. Till now there are two methods of describing the cavitation process on foils. In the singularity methods the region, in which the incompressible calculated pressure is lower than the equilibrium vapor pressure, is assumed to be the cavitation region. The flow around this region is described by additional sources and vortices; the cavitation region is calculated stepwise in this way. This Method makes possible also the computation of the thickness of the sheet by using the Nishiyama-Condition /1/, but does not take into account the real physikal process of the growing of the sheet, especially the role of the particle distribution. This is done by Chao /8/ by computing the cavitation region using the theory of bubble dynamics with respect to the reduction of tensile stresses. The present paper presents the attempt to extend the in /8/ developed method. Instead ofsingle bubbles there are researched whole clusters ofbubbles, whose initial shape, however, must be defined in an arbitrary way. In this way the growing-together of the bubbles will be taken into account, and the computation of the vertikal extention of the sheet will be possible. The results are compared with those maintained by the method of Chao, and, with regard to the thickness of the sheet, by the Nishiyama-condition. It has turned out that the results for the cavity thickness are considerable lower than the empirical results according to the Nishiyamacondition. So the result of this attempt is, that the presented Method means no improvement related to earlier attempts. The theory of clusters was shown to be useful, however, for the description of the collapse of the sheet. The cavitation region along the extent ofits collapse is treated as a plane cluster. The advantage ofthis model is that its validity does not depend on the length of the foil; especially it makes possible the consideration ofscale effects (see also /16/, Chap. IV,5 and /1/, Chap. 28).