On the Acoustical Dynamics of Bubble Clouds

Recently, Morch [1,2,3,4] Chahine [5,6] and others have focused attention on the dynamics of a cloud or cluster of cavitating bubbles and have expanded on the work of van Wijngaarden [7,8] and others. Unfortunately, there appear to be a number of inconsistencies in this recent work which will require further study before a coherent body of knowledge on the dynamics of clouds of bubbles is established. For example, Morch and his co-workers [1,2,3] have visualized the collapse of a cloud of cavitating bubbles as involving the inward propagation of a shock wave; it is assumed that the bubbles collapse virtually completely when they encounter the shock. This implies the virtual absense of non-condensable gas in the bubbles and the predominance of vapor. Yet in these circumstances the mixture in the the cloud will not have any real sonic speed. As implied by a negative L.H.S. of equation (9), the fluid motion equations for the mixture would be elliptic not hyperbolic and hence shock wave solutions are inappropriate

Acoustical Absorption and Scattering Cross-Sections of Spherical Bubble Clouds

The present work investigates the acoustical absorption and scattering cross-sections of spherical bubble clouds subject to harmonic far field pressure excitation. Bubble dynamics effects and energy dissipation due to viscosity, heat transfer, liquid compressibility and relative motion of the two phases are included. The equations of motion for the average flow and for the bubble radius are linearized and a closed form solution is obtained. Due to the presence of natural oscillatory modes and frequencies, the acoustical cross-sections of the cloud are very different from those of each individual bubble in the cloud, as well as from the acoustical cross-sections of a single large bubble with the same volume of vapor and gas. In general the acoustical properties of any given volume of the dispersed phase depend strongly on the degree of dispersion because of the complex interactions of the dynamics of the bubbles with the whole flow

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

Modeling Activities on Cavitating Flows at Centrospazio

The present paper illustrates recent theoretical and numerical activities on cavitating flows carried out at CENTROSPAZIO in the last few years. Specifically, it deals with the development and application of a modified isenthalpic cavitation model that accounts in an approximate but physical way for the occurrence of thermal cavitation effects and the concentration of active cavitation nuclei in the liquid. Expanding on the work of Brennen (1994), the model leads to a quasi-homogeneous barotropic description of cavitating flows, whose sound speed smoothly reduces to that of the liquid in the limit for low void fractions, thus eliminating the inconsistencies of previous formulations. Thermal effects are accounted for by assigning a single parameter expressing the nondimensional thickness of the thermal boundary layer in the liquid surrounding the growing cavities. The value of this parameter is related to the concentration of active cavitation nuclei, whose value can therefore be alternatively used to specify the impact of thermal cavitation effects. Applications to cavitating journal bearings, hydrofoils and helical inducers relevant to space engineering are presented

Cavitation and Rotordynamic Activities at Centrospazio

Centrospazio has long been carrying out an articulated program of experimental, theoretical and numerical research on cavitation and two-phase flow dynamics in connection with liquid propellant rocket fuel feed systems. The areas of involvement dealt with in recent years range from the modeling and simulation of cavitation to the study of rotordynamic fluid forces in whirling and cavitating axial inducers and journal bearings. Specifically, this paper illustrates the development of a new cavitation model accounting in an approximate but physical way for the occurrence of thermal cavitation and liquid quality effects, and the realization of the CPRTF (Cavitating Pump Rotordynamic Test Facility), a water loop for the measurement of rotordynamic fluid forces on whirling and cavitating turbopump impellers, and the TCT (Thermal Cavitation Tunnel), a modified version of the CPRTF for cavitation experiments in fluid dynamic and thermal cavitation similarity. Representative results of the application of cavitation model to journal bearings, hydrofoils and helical inducers and the typical performance of the CPRTF and TCT are presented

Developing an observational rubric of writing: Preliminary reliability and validity evidence

The purpose of this paper is (1) to report on the design of the early writing observational writing rubric designed to observe and describe change over time in the writing of children emerging into conventional literacy (ages 6–7) within an instructional setting and (2) to investigate the initial reliability and validity of the rubric. We used an extant data set that included 52 videos of writing instruction in Reading Recovery lessons (approximately 520 minutes) and pre- and post-intervention test data, for 24 students, taken at multiple time points across a 20-week period. Dependent sample t-tests and HLM were used to ascertain if the rubric was sensitive to change over occasions. We also considered if the scores correlated with external literacy measures. The findings suggest that the rubric has good initial reliability and validity and is a useful tool for researchers to observe and measure change over time as young children write in an instructional setting; further validation work is required for use in other settings

A New Cavitating Pump Rotordynamic Test Facility

The present paper illustrates the operational characteristics of the CPRTF (Cavitating Pump Rotordynamic Test Facility), an experimental apparatus specifically designed for the measurement of rotordynamic fluid forces acting on turbopump impellers in fluid dynamic and inertial/thermal cavitation similarity conditions. The realization of the CPRTF is currently in progress under ASI (Agenzia Spaziale Italiana) funding and consists in the upgrade of the CPTF (Cavitating Pump Test Facility), already available at Centrospazio, Consorzio Pisa Ricerche, Pisa, Italy. The experimental apparatus, operating in water, will be capable of carrying out the measurement of the steady and unsteady forces exerted by the flow on the impellers of cavitating/noncavitating turbopumps. More generally, the facility is designed as a flexible, versatile and inexpensive apparatus that can be readily be adapted to carry out detailed experimental investigations on practically any kind of fluid dynamic phenomena relevant to high performance turbopumps. The main operational requirements, development choices and design trade-offs that led to the final configuration of the facility are illustrated and its performance in testing of cavitating/noncavitating turbopumps under fluid dynamic and thermal cavitation similarity are discussed. Experimental results from a number of turbopump configurations and operational conditions are presented to illustrate the present capabilities of the facility

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