COLLAPSE OF CYLINDRICAL CAVITATING REGION AND CONDITIONS FOR EXISTENCE OF ELLIPTICAL FORM OF CAVITATING VORTEX ROPE

ABSTRACT Conditions for existence of cavitating vortex rope with elliptical cross-section are derived using Lagran-gian coordinates. Solution is valid for incompressible inviscid fluid and is based on continuity equation, Euler equation, Laplace equation for stress in shell and polytropic law of ideal gas. Further, collapse of cavitating cylindrical vortex rope under the impact of unsteady outside pressure field has been theoretically investigated. The solution is carried out in Lagrangian coordi-nates. It is assumed that the particle path is coincident with helix lying on cylindrical surface, which changes its radius according to the volumetric change. Mathematical model is formulated very generally, which enables to input different circumferential veloc-ity profiles. KEYWORDS Cavitating, Rayleigh-Plesset, elliptical, vortex rope, collapse NOMENCLATURE a j [m] curvilinear coordinate system c 0 [m.s -1 ] axial velocity component c r [m.s -1 ] radial velocity component c ϕ [m.s -1