D=4, N=2 Supergravity in the Presence of Vector-Tensor Multiplets and the Role of higher p-forms in the Framework of Free Differential Algebras

We thoroughly analyze at the bosonic level, in the framework of Free Differential Algebras (FDA), the role of 2-form potentials setting in particular evidence the precise geometric formulation of the anti-Higgs mechanism giving mass to the tensors. We then construct the (super)-FDA encoding the coupling of vector-tensor multiplets in D=4, N=2 supergravity, by solving the Bianchi identities in superspace and thus retrieving the full theory up to 3-fermions terms in the supersymmetry transformation laws, leaving the explicit construction of the Lagrangian to future work. We further explore the extension of the bosonic FDA in the presence of higher p-form potentials, focussing our attention to the particular case p=3, which would occur in the construction of D=5, N=2 supergravity where some of the scalars are properly dualized.Comment: 39 pages, improved introduction, section 4 and Appendices modified, typos corrected, citations adde

Poincare' dual of D=4 N=2 Supergravity with Tensor Multiplets

We study, in an arbitrary even number D of dimensions, the duality between massive D/2 tensors coupled to vectors, with masses given by an arbitrary number of ``electric'' and ``magnetic'' charges, and (D/2-1) massive tensors. We develop a formalism to dualize the Lagrangian of D=4, N=2 supergravity coupled to tensor and vector multiplets, and show that, after the dualization, it is equivalent to a standard D=4, N=2 gauged supergravity in which the Special Geometry quantities have been acted on by a suitable symplectic rotation.Comment: 15 pages, JHEP3 class, v2 typos corrected, references adde

Stability of Parallel Bubbly and Cavitating Flows

This paper examines the bubble dynamic effects on the stability of parallel bubbly and cavitating flows of low void fraction. Inertial effects associated with the bubble response and energy dissipation due to the viscosity of the liquid, the heat transfer between the two phases, and the liquid compressibility are included. The equations of motion are linearized for small perturbations and a modified Rayleigh equation for the inviscid stability of the two-dimensional parallel flow is derived. Numerical solutions of the characteristic problem for the modified Rayleigh equation of a free shear layer are obtained by means of a multiple shooting method. Depending on the dispersion of the gaseous phase in the bubbly mixture, the ambient pressure and the free stream velocities, the pressure of air bubbles can induce significant departures from the classical solution for a single phase fluid. Results are presented to illustrate the influence of the relevant flow parameters

D=4, N=2 Gauged Supergravity coupled to Vector-Tensor Multiplets

We construct the general four-dimensional N=2 supergravity theory coupled to vector and vector-tensor multiplets only. Consistency of the construction requires the introduction of the vector fields dual to those sitting in the same supermultiplets as the antisymmetric tensors, as well as the scalar fields dual to the tensors themselves. Gauge symmetries also involving these additional fields guarantee the correct counting of the physical degrees of freedom.Comment: Typos corrected, references adde

The Effects of Vapor/Gas Bubbles on the Rotordynamic Forces in Bearings

This paper presents an anylytical investigation of the effects that vapor/gas bubbles can have on the fluid-induced rotordynamic forces in a liquid-filled annulus between a cylindrical rotor and a surrounding cylindrical stator. It is demonstrated that such cavitation (vaporous or gaseous) can have important consequences in altering the rotordynamic characteristics of devices such as long journal bearings or long squeeze-film dampers. A linearized analysis which includes bubble dynamic effects is used to evaluate the rotordynamic effects caused by a small amplitude whirl motion of the rotor in both the high and low Reynolds number regimes of fluid motion. In the former case the Euler equations for a bubbly mixture are employed while, in the latter, a modified Reynolds lubrication equation is used. These are combined with a Rayleigh-Plesset analysis of the bubble dynamics which includes various bubble damping effects. It is shown that, in certain parametric regimes, the normal and tangential fluid-induced rotordynamic forces acting on the rotor can deviate substantially from their classical forms in single-phase flow

A Three-Dimensional Analysis of Rotordynamic Forces on Whirling and Cavitating Helical Inducers

This paper investigates the linearized dynamics of three-dimensional bubbly cavitating flows in helical inducers. The purpose is to understand the impact of the bubble response on the radial and tangential rotordynamic forces exerted by the fluid on the rotor and stator stages of whirling turbomachines under cavitating conditions. The flow in the inducer annulus is modeled as a homogeneous inviscid mixture, containing vapor bubbles with a small amount of noncondensable gas. The effects of several contributions to the damping of the bubbly dynamics are included in the model. The governing equations of the inducer flow are written in "body-fitted" orthonormal helical Lagrangian coordinates, linearized for small-amplitude perturbations about the mean flow, and solved by modal decomposition. The whirl excitation generates finite-speed propagation and resonance phenomena in the two-phase flow within the inducer. These, in turn, lead to a complex dependence of the lateral rotordynamic fluid forces on the excitation frequency, the void fraction, the average size of the cavitation bubbles, and the turbopump operating conditions (including, rotational speed, geometry, flow coefficient and cavitation number). Under cavitating conditions the dynamic response of the bubbles induces major deviations from the noncavitating flow solutions, especially when the noncondensable gas content of the bubbles is small and thermal effects on the bubble dynamics are negligible. Then, the quadratic dependence of rotordynamic fluid forces on the whirl speed, typical of cavitation-free operation, is replaced by a more complex behavior characterized by the presence of different regimes where, depending on the whirl frequency, the fluid forces have either a stabilizing or a destabilizing effect on the inducer motion. Results are presented to illustrate the influence of the relevant flow parameters

On the Inviscid Stability of Parallel Bubbly Flows

This paper investigates the effects of bubbly dynamics on the stability of parallel bubbly flows of low void fraction. The equations of motion for the bubbly mixture are linearized for small perturbations and the parallel flow assumption is used to obtain a modified Rayleigh equation governing the inviscid stability problem. This is then used for the stability analysis of two-dimensional shear layers, jets and wakes. Inertial effects associated with the bubbly response and energy dissipation due to the viscosity of the liquid, the heat transfer between the two phases, and the liquid compressibility are included. Numerical solutions of the eigenvalue problems for the modified Rayleigh equation are obtained by means of a multiple shooting method. Depending on the characteristic velocities of the various flows, the void fractions, and the ambient pressure, the presence of air bubbles can induce significant departures from the classical stability results for a single-phase fluid