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

Computing Shock Waves in Cloud Cavitation

This paper presents a numerical investigation of some of the phenomena involved in the nonlinear dynamics of a homogeneous bubbly mixture bounded by an oscillatory wall. This problem represents an idealization of the flow in a typical vibratory cavitation damage device. Results are presented showing that wave steepening and ultimately shock wave formation occur as the magnitude of the excitation increases. The propagation characteristics of the waves through the bubbly medium have also been studied. Strong pressure peaks of short duration, corresponding to the coherent collapse of the bubble clusters, are computed and accurately resolved, both in space and time. As the amplitude of the excitation is increased a series of period doubling bifurcations occurs. The nonlinear dynamics of the oscillating bubble cluster are observed to follow a subharmonic route to chaos

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

The linear spectrum of OSp(32|1) Chern-Simons supergravity in eleven dimensions

We study linearized perturbations of eleven-dimensional $OSp(32|1)$ Chern-Simons supergravity. The action contains a term that changes the value of the cosmological constant, as considered by Horava. It is shown that the spectrum contains a 3-form and a 6-form whose field strengths are dual to each other, thus providing a link with the eleven-dimensional supergravity of Cremmer, Julia and Scherk. The linearized equations for the graviton and Rarita-Schwinger field are shown to be the standard ones as well.Comment: Minor additions. To appear in PRL. 4 pages, twocolumn, Revtex

Sensitivity Studies for the Exercise I-1 of the OECD/UAM Benchmark

OECD/NEA has initiated an international Uncertainty Analysis in Modeling (UAM) benchmark focused on uncertainties in modeling of Light Water Reactor (LWR). The first step of uncertainty propagation is to perform sensitivity to the input data affected by the numerical errors and physical models. The objective of the present paper is to study the effect of the numerical discretization error and the manufacturing tolerances on fuel pin lattice integral parameters (multiplication factor and macroscopic cross-sections) through sensitivity calculations. The two-dimensional deterministic codes NEWT and HELIOS were selected for this work. The NEWT code was used for analysis of the TMI-1, PB-2, and Kozloduy-6 test cases; the TMI-1 test case was investigated using the HELIOS code. The work has been performed within the framework of UAM Exercise I-1 "Cell Physics.

First Order Description of D=4 static Black Holes and the Hamilton-Jacobi equation

In this note we discuss the application of the Hamilton-Jacobi formalism to the first order description of four dimensional spherically symmetric and static black holes. In particular we show that the prepotential characterizing the flow coincides with the Hamilton principal function associated with the one-dimensional effective Lagrangian. This implies that the prepotential can always be defined, at least locally in the radial variable and in the moduli space, both in the extremal and non-extremal case and allows us to conclude that it is duality invariant. We also give, in this framework, a general definition of the ``Weinhold metric'' in terms of which a necessary condition for the existence of multiple attractors is given. The Hamilton-Jacobi formalism can be applied both to the restricted phase space where the electromagnetic potentials have been integrated out as well as in the case where the electromagnetic potentials are dualized to scalar fields using the so-called three-dimensional Euclidean approach. We give some examples of application of the formalism, both for the BPS and the non-BPS black holes.Comment: A clarifying discussion on the existence of the prepotential and a comment on multiple attractors are added; typos corrected, references adde

The minimal N=4 no-scale model from generalized dimensional reduction

We consider the generalized dimensional reduction of pure ungauged N=4, D=5 supergravity, where supersymmetry is spontaneously broken to N=2 or N=0 with identically vanishing scalar potential. We explicitly construct the resulting gauged D=4 theory coupled to a single vector multiplet, which provides the minimal N=4 realization of a no-scale model. We discuss its relation with the standard classification of N=4 gaugings, extensions to non-compact twists and to higher dimensions, the N=2 theories obtained via consistent Z_2 orbifold projections and prospects for further generalizations.Comment: 1+28 pages, no figures, JHEP3 LaTeX, published versio