On the temporal stability of steady-state quasi-1D bubbly cavitating nozzle flow solutions

Quasi-1D unsteady bubbly cavitating nozzle flows are considered by employing a homogeneous bubbly liquid flow model, where the non-linear dynamics of cavitating bubbles is described by a modified Rayleigh–Plesset equation. The various damping mechanisms are considered by a single damping coefficient lumping them together in the form of viscous dissipation and by assuming a polytropic law for the expansion and compression of the gas. The complete system of equations, by appropriate uncoupling, are then reduced to two evolution equations, one for the flow speed and the other for the bubble radius when all damping mechanisms are considered by a single damping coefficient. The evolution equations for the bubble radius and flow speed are then perturbed with respect to flow unsteadiness resulting in a coupled system of linear partial differential equations (PDEs) for the radius and flow speed perturbations. This system of coupled linear PDEs is then cast into an eigenvalue problem and the exact solution of the eigenvalue problem is found by normal mode analysis in the inlet region of the nozzle. Results show that the steady-state cavitating nozzle flow solutions are stable only for perturbations with very small wave numbers. The stable regions of the stability diagram for the inlet region of the nozzle are seen to be broadened by the effect of turbulent wall shear stress

Homogene Kondensation in stationären transsonischen strömungen durch Lavaldüsen und um profile

U ovom diplomskom radu proučavaju se lančasti kontinuumi. Rad je podijeljen na četiri poglavlja. U prvom poglavlju upoznajemo se s metričkim i topološkim prostorima te njihovim svojstvima, sličnostima i razlikama. U drugom poglavlju proučavamo pojam otvorenog pokrivača te svojstva kompaktnosti, posebno u metričkim prostorima, a zatim u euklidskom prostoru. U trećem poglavlju definiramo pojam povezanog topološkog prostora, a u četvrtom definiramo lančaste kontinuume te proučavamo njihova svojstva.In this thesis we examine chainable continua. This thesis is divided four chapters. In the first chapter we introduce metric and topological spaces and we study their properties, their similarities and differences. In the second chapter we examine the notion of an open cover and properties of compactness, in particular in metric spaces and in Euclidean space. In the third chapter we define the notion of a connected topological space and in fourth chapter we define chainable continua and we study their properties