Kolaps válcové kavitujíc oblasti a podmínky pro existenci eliptického tvaru kavitujícího vírového copu

Collapse of cylindrical region and conditions for existence of elliptical vortex form of cavitating vortex rope

journal article - other

en

Conditions for existence of cavitating vortex rope with elliptical cross-section are derived using Lagrangian 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 coordinates. 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 velocity profiles.

Jsou odvozeny podmínky pro existenci eliptického tvaru kavitujícícho vírového copu s využitím Lagrangeových souřadnic. Řešení , platné pro nestlačitelnou neviskózní kapalinu, je založeno na rovnici kontinuity, Eulerově rovnici a Laplaceově rovnici pro napětí ve válcové skořepině. Dále byl vyšetřován kolaps válcové oblasti vystavené nestacionárnímu tlakovému poli. Řešení je opět provedeno Lagrangeovými souřadnicemi. Výsledek je formulován obecně pro libovolný předpis rychlostního pole. Conditions for existence of cavitating vortex rope with elliptical cross-section are derived using Lagrangian 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 coordinates. 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 velocity profiles.

Conditions for existence of cavitating vortex rope with elliptical cross-section are derived using Lagrangian 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 coordinates. 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 velocity profiles.

kavitující, Rayleigh-Plesset, eliptický, kolaps

cavitating, Rayleigh-Plesset, elliptical, vortex rope, collapse

2007

24.10.2007

Politehnica University of Timisoara

Timisoara

1224-6077

Scientific Bulletin of the "Politehnica" University of Timisoara

52

6

109–118

9