Richard T. Lahey

Theory of supercompression of vapor bubbles and nanoscale thermonuclear fusion

HYDRO code model of the spherically symmetric motion for a vapor bubble in an acoustically forced liquid is presented. This model describes cavitation bubble cluster growth during the expansion period, followed by a violent implosion during the compression period of the acoustic cycle. There are two stages of the bubble dynamics process. The first, low Mach number stage, comprises almost all the time of the acoustic cycle. During this stage, the radial velocities are much less than the sound speeds in the vapor and liquid, the vapor pressure is very close to uniform, and the liquid is practically incompressible. This process is characterized by the inertia of the liquid, heat conduction, and the evaporation or condensation of the vapor. The second, very short, high Mach number stage is when the radial velocities are the same order, or higher, than the sound speeds in the vapor and liquid. In this stage high temperatures, pressures, and densities of the vapor and liquid take place. The model presented herein has realistic equations of state for the compressible liquid and vapor phases, and accounts for nonequilibrium evaporation/condensation kinetics at the liquid/ vapor interface. There are interacting shock waves in both phases, which converge toward and reflect from the center of the bubble, causing dissociation, ionization, and other related plasma physics phenomena during the final stage of bubble collapse. For a vapor bubble in a deuterated organic liquid e.g., acetone, during the final stage of collapse there is a nanoscale region diameter 100 nm near the center of the bubble in which, for a fraction of a picosecond, the temperatures and densities are extremely high 10 8 K and 10 g/cm 3 , respectively such that thermonuclear fusion may take place. To quantify this, the kinetics of the local deuterium/deuterium D/D nuclear fusion reactions was used in the HYDRO code to determine the intensity of the fusion reactions. Numerical HYDRO code simulations of the bubble implosion process have been carried out for the experimental conditions used by Taleyarkhan et al. Science 295, 1868 2002; Phys. Rev. E 69, 036109 2004 at Oak Ridge National Laboratory. The results show good agreement with the experimental data on bubble fusion that was measured in chilled deuterated acetone.

Hydrodynamic simulation of air bubble implosion using a level set approach

The hydrodynamics of the implosion and rebound of a small (10@mm diameter) air bubble in water was studied using a three-dimensional direct numerical simulation (DNS). To study this problem, we developed a novel stabilized finite element method (FEM) employing a combination of ghost fluid and level set approaches. This formulation treats both the air and water as compressible fluids. Using this method, a transient three-dimensional (3-D) solution was obtained for the implosion (i.e., collapse) and rebound of an air bubble. These simulation results obtained were qualitatively similar to those observed/predicted in previous experimental/numerical studies. The 3-D simulations show that the conditions within the bubble are nearly uniform until the converging pressure wave is strong enough to create very large temperatures and pressures near the center of the bubble. These dynamics occur on very small spatial (0.1-0.7@mm), and time (ns) scales. The motion of the air/water interface during the initial stages of the implosion was found to be consistent with predictions using a Rayleigh-Plesset model. However, the simulations showed that during the final stage of energetic implosions, the bubble can become asymmetric, which is contrary to the spherical symmetry assumed in many previous numerical studies of bubble dynamics. The direct numerical simulations predicted two different instabilities, namely Rayleigh-Taylor type interfacial/surface and shape instabilities. During the violent collapse stage, the bubble deviates from spherical symmetry and deforms into an ellipsoidal-shaped bubble. A linear stability analysis based on spherical harmonics also indicates that an ellipsoidal bubble shape could be expected. Moreover, interfacial instabilities also appear during the later stage of the implosion process. Distinguishing these phenomena with the help of numerical simulations opens new opportunities to understand many features of recent experiments on sonoluminescence and sonofusion.

Analysis of chaotic instabilities in boiling systems

An analytic model for the investigation of non-linear dynamics in boiling systems has been developed. This model is comprised of a nodal formulation that uses one-dimensional homogeneous equilibrium assumptions for diabatic two-phase flow, a lumped parameter approach for heated wall dynamics, and point neutron kinetics for the consideration of nuclear feedback in a boiling water reactor (BWR) loop. This model indicates that a boiling channel coupled with a riser may experience chaotic oscillations. In contrast, a boiling channel without a riser that is subjected to a constant pressure drop (i.e. a parallel channel) may undergo a supercritical bifurcation (i.e. may experience a limit cycle), but chaos was not found. Flow instabilities in a two-phase natural circulation loop have been verified using the model presented in this paper. The predictions of the effects of the channel inlet resistance, outlet resistance and liquid level in the downcomer agree with the data of Kyung and Lee. Finally, an analysis of nuclear-coupled density-wave instabilities in a simplified BWR (SBWR) was performed. Significantly, even for low pressure conditions, a simplified SBWR appears to be stable during start-up and normal operations; however, a limit cycle may occur for abnormal operating conditions.

The development of a closed-form analytical model for the stability analysis of nuclear-coupled density-wave oscillations in boiling water nuclear reactors

Abstract A state-of-the-art one-dimensional thermal-hydraulic model has been developed to be used for the linear analysis of nuclear-coupled density-wave oscillations in a boiling water nuclear reactor (BWR). This model accounts for phasic slip, distributed spacers, subcooled boiling, space/time-dependent power distributions and distributed heated wall dynamics. In addition to a parallel channel stability analysis, a detailed model was derived for the BWR loop analysis of both the natural and forced circulation modes of operation. The model for coolant thermal-hydraulics has been coupled with the point kinetics model of reactor neutronics. Kinetics parameters for use in the neutronics model have been obtained by utilizing self-consistent nodal data and power distributions. The computer implementation of this model, NUFREQ-N, was used for the parametric study of a typical BWR/4, as well as for comparisons with existing in-core and out-of-core data. Also, NUFREQ-N was applied to analyze the expected stability characteristics of a typical BWR/4.

A study on single- and two-phase pressure drop in branching conduits

Abstract Models for predicting single- and two-phase pressure drop in wyes and tees have been developed and compared to air/water and steam/water data. It is shown that the model previously proposed by Saba and Lahey [1] can be used to predict the observed pressure drops in tees; however, it is not always reliable for wyes.

Parallel adaptive simulation of a plunging liquid jet

This paper is concerned with three-dimensional numerical simulation of a plunging liquid jet. The transient processes of forming an air cavity around the jet, captur- ing an initially large air bubble, and the break-up of this large toroidal-shaped bubble into smaller bubbles were analyzed. A stabilized finite element method (FEM) was employed under parallel numerical simulations based on adaptive, unstructured grid and coupled with a level-set method to track the interface between air and liquid. These simulations show that the inertia of the liquid jet initially depresses the pools surface, forming an annular air cavity which surrounds the liquid jet. A toroidal liquid eddy which is subse- quently formed in the liquid pool results in air cavity collapse, and in turn entrains air into the liquid pool from the unstable annular air gap region around the liquid jet.

Measurement of phase distribution in a triangular conduit

Abstract Measurements of phase-distribution phenomena were made for fully developed. turbulent air/water two-phase flow in a vertical isosceles-triangular test section. These measurements included the local void-fraction and liquid-phase velocity using an RF-excited local impedance probe and Pitot tube. respectively. It was found that substantial lateral “void drift” occurred. with the vapor phase collecting in the more open. high-velocity. region of the test section.

A spectral turbulent cascade model for single- and two-phase uniform shear flows

A spectral turbulent cascade-transport model was developed and applied to single-and two-phase turbulent uniform shear flows. This model tracks the development of the turbulent kinetic energy spectrum by splitting the turbulent kinetic energy into wave number bins. A separate transport equation accounts for the spectral production, dissipation and transport terms and is solved for each wave number bin. The predicted evolution of the turbulence level, turbulent production and turbulent dissipation is shown to be consistent with experimental data for turbulent uniform shear flows. The shear rate in the various experiments ranges from 12.9 to 46.8 s− 1 for air flows, 0.96 to 1.23 s−1 for water flows and was 2.9 s− 1 for bubbly two-phase air/water flow.

A characteristic analysis of void waves using two-fluid models

Abstract This paper examines mathematical techniques for evaluating waves in systems of partial differential equations (PDEs), such as those found in the two-fluid modeling of two-phase flows. In particular, this paper is concerned with a characteristic analysis of void waves for two-fluid models of two-phase flow. Such models are comprised of the phasic conservation equations, the interfacial jump conditions and the associated closure laws. The well-posedness of such systems of PDEs is considered herein with respect to the morphology of the mathematical model. Closure involves balancing the number of equations and state variables, as well as specifying all the parameters, initial conditions, and boundary conditions needed in the two-fluid model. In order to avoid algebraic complexity, only fairly simple two-fluid models will be considered in this paper. Nevertheless, the conclusions reached herein are also valid for much more detailed two-fluid models.

The effect of acoustically-induced cavitation on the permeance of a bullfrog urinary bladder

It is well known that ultrasound enhances drug delivery to tissues, although there is not a general consensus about the responsible mechanisms. However, it is known that the most important factor associated with ultrasonically-enhanced drug permeance through tissues is cavitation. Here we report results from research conducted using a experimental approach adapted from single bubble sonoluminescence experiments which generates very well defined acoustic fields and allows controlled activation and location of cavitation. The experimental design requires that a biological tissue be immersed inside a highly degassed liquid media to avoid random bubble nucleation. Therefore, live frog bladders were used as the living tissue due to their high resistance to hypoxia. Tissue membrane permeance was measured using radiolabeled urea. The results show that an increase in tissue permeance only occurs when cavitation is present near the tissue membrane. Moreover, confocal microscopy shows a direct correlation between permeance increases and physical damage to the tissue.