Search

A spectral cascade-transport model has been developed and applied to turbulent channel flows ( Re τ = 550, 950, and 2000 based on friction velocity, u τ ; or Re δ = 8500; 14,800 and 31,000, based on the mean velocity and channel half-width). This model is an extension of a spectral model previously developed for homogeneous single and two-phase decay of isotropic turbulence and uniform shear flows; and a spectral turbulence model for wall-bounded flows without resolving the boundary layer. Data from direct numerical simulation (DNS) of turbulent channel flow was used to help develop this model and to assess its performance in the 1D direction across the channel width. The resultant spectral model is capable of predicting the mean velocity, turbulent kinetic energy and energy spectrum distributions for single-phase wall-bounded flows all the way to the wall, where the model source terms have been developed to account for the wall influence. The model has been implemented into the 3D multiphase CFD code NPHASE-CMFD and the latest results are within reasonable error of the 1D predictions.

This paper is primarily concerned with the development of three dimensional (3-D) multiphase computational fluid dynamics models for use in Pressurized Water Nuclear Reactor (PWR) design and analysis. These models were developed during the last 40 years, that is, during the time since the first NURETH meeting in 1980. The major topics in this paper include: the development of a 3-D two-fluid model for the MCFD prediction of phase distribution in turbulent adiabatic and diabatic bubbly flows. The mechanistic prediction of departure from nucleate boiling (DNB), and the direct numerical simulation (DNS) of bubbly flows. While significant progress has been made in the modeling and prediction of bubbly flows, specific recommendations are made in this paper for further improvements and for the extension of this type of MCFD model to other flow regimes.

The theoretical and experimental foundations of so-called bubble nuclear fusion are reviewed. In the nuclear fusion process, a spherical cavitation cluster m in diameter is produced of spherical bubbles at the center of a cylindrical chamber filled with deuterated acetone using a focused acoustic field having a resonant frequency of about 20 kHz. The acoustically-forced bubbles effectuate volume oscillations with sharp collapses during the compression stage. At the final stages of collapse, the bubble cluster emits 2.5 MeV D-D fusion neutron pulses at a rate of per second. The neutron yield is s. In parallel, tritium nuclei are produced at the same yield. It is shown numerically that, for bubbles having sufficient molecular mass, spherical shock waves develop in the center of the cluster and that these spherical shock waves (microshocks) produce converging shocks within the interior bubbles, which focus energy on the centers of the bubbles. When these shock waves reflect from the centers of the bubbles, extreme conditions of temperature ( K) and density ( kg m) arise in a (nano)spherical region ( m in size) that last for s, during which time about ten D-D fusion neutrons and tritium nuclei are produced in the region. A paradoxical result in our experiments is that it is bubble cluster (not streamer) cavitation and the sufficiently high molecular mass of (and hence the low sound speed in) D-acetone () vapor (as compared, for example, to deuterated water ) which are necessary conditions for the formation of convergent spherical microshock waves in central cluster bubbles. It is these waves that allow the energy to be sufficiently focused in the nanospherical regions near the bubble centers for fusion events to occur. The criticism to which the concept of 'bubble fusion' has been subjected in the literature, in particular, most recently in Uspekhi Fizicheskikh Nauk (Physics – Uspekhi) journal, is discussed.

Methodology for performing large scale parallel numerical simulations of two-phase flow is presented that uses a three-dimensional (3-D) finite element method (FEM) solver, PHASTA, to perform the simulation and a parallel mesh adaptation code, phParAdapt, to iteratively refine and coarsen regions of the solution domain. This version of PHASTA uses a stabilized FEM to discretize the 3-D Incompressible Navier–Stokes (INS) equations plus a level set method to capture the two-phase interface. The phParAdapt code takes the current parallel mesh along with the PHASTA flow solution and, using various user-specified correction indicators as input, performs a parallel mesh refinement/coarsening procedure. Utilizing local mesh modification operators, element sizes are adjusted to equally distribute the errors across the distributed mesh during the mesh refinement/coarsening procedure. Numerical simulations ranging from simple canonical test problems up to an experimental annular steam/water flow condition were performed to illustrate this methodology. The annular flow simulation captured the instabilities that generate both the ripple and roll wave like structures on the steam/water interface and the droplet entrainment mechanisms expected in annular two-phase flows.

The quantitative prediction of bubbly flow around a maneuvering surface ship is critical in determining its hydrodynamic performance and its acoustic and optical signatures. It is a challenging multiscale problem that relies heavily on subgrid models of turbulence and air entrainment. In this manuscript we analyze this problem using a phenomenological air entrainment model that predicts the location and rate of air entrainment around a surface ship. This subgrid model was coupled with a two-fluid Reynolds averaged Navier Stokes (RaNS) bubbly flow model and used to evaluate the flow field around a naval surface ship in straight ahead and turning motions. For straight ahead motion the predicted void fraction distributions aft of the stern were compared with experiments at three different ship speeds and good agreement was found. The qualitative differences in the location of the air entrainment and the resulting bubbly flow between straight ahead and steady turning motions were discussed and compared with experimental observations at sea. To our knowledge this study presents the first quantitative numerical prediction of void fraction distributions around a full-scale surface ship, well matching the experimental measurements.

Both RaNS (Reynolds-averaged Navier–Stokes) and DES (Detached Eddy Simulation) type turbulence models were used in conjunction with a two-fluid model of bubbly flow and a new subgrid air entrainment model to predict air entrainment and transport in a hydraulic jump. It was found that the void fraction profiles predicted by both methods are in agreement with the experimental data in the lower shear layer region, which contains the air bubbles entrained at the so-called toe of the hydraulic jump. In contrast, in the upper roller region behind the toe, the averaged results of the DES turbulence model gives accurate predictions while a RaNS turbulence model does not. This is because the DES turbulence model successfully captures the strong fluctuations on the free surface which allows it to entrain air near the top of the roller region. In contrast, RaNS type turbulence model results in a steady, smooth interface which fails to capture the wave-induced bubble sources in that region. To our knowledge, this study is the first successful quantitative numerical simulation of the overall void fraction profiles in a hydraulic jump.

DNS simulations of two-phase turbulent bubbly channel flow at Re τ = 180 (Reynolds number based on friction velocity and channel half-width) were performed using a stabilized finite element method (FEM) and a level set approach to track the air/water interfaces. Fully developed turbulent single-phase solutions obtained previously using the same stabilized FEM code were used as the initial flow field, and an appropriate level-set distance field was introduced to represent the air bubbles. Surface tension and gravity forces were used in the simulations to physically represent the behavior of a bubbly air/water two-phase flow having a liquid/gas density ratio of 858.3. The simulation results were averaged to obtain the liquid and gas mean velocity distributions, the local void fractions as well as the local turbulent kinetic energy and dissipation rate of the liquid phase. The liquid phase parameters were compared with the corresponding single-phase turbulent channel flow to determine the bubbles’ influence on the turbulence field.

The simulation of free surface bubbly flows using a two-fluid model remains a challenging problem in part due to the lack of a comprehensive air entrainment model that can predict the rate and location of air entrainment for a wide range of flows. In this study we derive a sub-grid model and implement it in a computational multiphase fluid dynamics (CMFD) framework to solve the Reynolds-averaged two-fluid equations. We assess the performance of our model in simulating bubbly flows underneath a plunging liquid jet and a hydraulic jump while varying the characteristic velocity. We compare the void fraction predictions with their experimental counterparts and conclude that the air entrainment model and the two-fluid modeling approach yield accurate results everywhere for the plunging jet and in the turbulent shear layer for the hydraulic jump. The inability of the proposed approach to recover the high void fraction in the roller region of the hydraulic jump is attributed to the failure of RaNS model to resolve the large coherent vortices observed in this region.

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.

This paper presents an analysis of the interaction of pressure-drop oscillations (PDO) and density-wave oscillations (DWO) for a typical NASA type phase change system. A transient lumped parameter model is developed for use in the analysis of the dynamics of this type of system. A compressible volume (e.g., an accumulator vessel) dynamics model was also developed and PDO/DWO interactions are investigated.

The development and assessment of spectral turbulence models requires knowledge of the spectral turbulent kinetic energy distribution as well as an understanding of the terms which determine the energy distribution in physical and wave number space. Direct numerical simulation (DNS) of turbulent channel flow yields numerical “data” that can be, and was, analyzed using a spatial Fast Fourier Transform (FFT) to obtain the various spectral turbulent kinetic energy balance terms, including the production, dissipation, diffusion, and the non-linear convective transfer terms.

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, capturing 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 pool's surface, forming an annular air cavity which surrounds the liquid jet. A toroidal liquid eddy which is subsequently 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.

The accurate prediction of air entrainment is critical in simulating various important multiphase (air/water) flows. In this paper, we present a sub-grid air entrainment model that quantitatively predicts the rate of air entrainment and subsequent disperse bubbly flow for a plunging jet. The derivation of this model is based on the two-stage (i.e., low and high liquid jet velocity) air entrainment mechanisms suggested by Sene [Sene KJ. Air entrainment by plunging jets. Chem Eng Sci 1988;43(10):2615–23]. This model was validated against extensive experimental data for water jets in air over a wide range of liquid velocities (from around 1 to 10 m/s) for the total rate of air entrainment. It was then implemented into an Eulerian/Eulerian two-fluid computational multiphase fluid dynamics (CMFD) model, wherein the liquid and the bubbles are modeled as two distinct continua. This multiphase model, supplemented by the new sub-grid air entrainment model, was used to predict the void fraction distribution underneath plunging water jets at different depths and water jet velocities. It was found that this approach yields results that match the experimental observations very well.

This paper presents an assessment of various models that can be used for the multidimensional analysis of single and multiphase flows in nuclear reactor systems. In particular, a model appropriate ...

This paper presents the direct numerical simulation (DNS) of various incompressible and compressible single and two-phase flows. It is shown that very detailed information on the flow structure can be obtained using a suitable adaptive grid 3D solver. In addition, it is demonstrated how to use these detailed numerical “data” to obtain interfacial closure models for use in two-fluid, computational multiphase fluid dynamic (CMFD) formulations. These advanced generation 3D CMFD models can, in-turn, be used for nuclear reactor design and analysis.

Direct numerical simulations (DNS) of incompressible turbulent channel flows at Re τ = 180 and 395 (i.e., Reynolds number, based on the friction velocity and channel half-width) were performed using a stabilized finite element method (FEM). These simulations have been motivated by the fact that the use of stabilized finite element methods for DNS and LES is fairly recent and thus the question of how accurately these methods capture the wide range of scales in a turbulent flow remains open. To help address this question, we present converged results of turbulent channel flows under statistical equilibrium in terms of mean velocity, mean shear stresses, root mean square velocity fluctuations, autocorrelation coefficients, one-dimensional energy spectra and balances of the transport equation for turbulent kinetic energy. These results are consistent with previously published DNS results based on a pseudo-spectral method, thereby demonstrating the accuracy of the stabilized FEM for turbulence simulations.

The analysis of turbulent two-phase flows requires closure models in order to perform reliable computational multiphase fluid dynamics (CMFD) analyses. A spectral turbulence cascade-transport model, which tracks the evolution of the turbulent kinetic energy from large to small liquid eddies, has been developed for the analysis of the homogeneous decay of isotropic single and bubbly two-phase turbulence. This model has been validated for the decay of homogeneous, isotropic single and two-phase bubbly flow turbulence for data having a 5 mm mean bubble diameter. The Reynolds number of the data based on bubble diameter and relative velocity is approximately 1400.

Self-nucleated and external neutron nucleated acoustic (bubble fusion) cavitation experiments have been modeled and analyzed for neutron spectral characteristics at the detector locations for all separate successful published bubble fusion studies. Our predictive approach was first calibrated and validated against the measured neutron spectrum emitted from a spontaneous fission source ( 252 Cf), from a Pu–Be source and from an accelerator-based monoenergetic 14.1 MeV neutrons, respectively. Three-dimensional Monte-Carlo neutron transport calculations of 2.45 MeV neutrons from imploding bubbles were conducted, using the well-known MCNP5 transport code, for the published original experimental studies of Taleyarkhan et al. [Taleyarkhan, et al., 2002. Science 295, 1868; Taleyarkhan, et al., 2004. Phys. Rev. E 69, 036109; Taleyarkhan, et al., 2006a. PRL 96, 034301; Taleyarkhan, et al., 2006b. PRL 97, 149404] as also the successful confirmation studies of Xu et al. [Xu, Y., et al., 2005. Nuclear Eng. Des. 235, 1317–1324], Forringer et al. [Forringer, E., et al., 2006a. Transaction on American Nuclear Society Conference, vol. 95, Albuquerque, NM, USA, November 15, 2006, p. 736; Forringer, E., et al., 2006b. Proceedings of the International Conference on Fusion Energy, Albuquerque, NM, USA, November 14, 2006] and Bugg [Bugg, W., 2006. Report on Activities on June 2006 Visit, Report to Purdue University, June 9, 2006]. NE-213 liquid scintillation (LS) detector response was calculated using the SCINFUL code. These were cross-checked using a separate independent approach involving weighting and convoluting MCNP5 predictions with published experimentally measured NE-213 detector neutron response curves for monoenergetic neutrons at various energies. The impact of neutron pulse-pileup during bubble fusion was verified and estimated with pulsed neutron generator based experiments and first-principle calculations. Results of modeling-cum-experimentation were found to be consistent with published experimentally observed neutron spectra for 2.45 MeV neutron emissions during acoustic cavitation (bubble) fusion experimental conditions with and without ice-pack (thermal) shielding. Calculated neutron spectra with the inclusion of ice-pack shielding are consistent with the published spectra from experiments of Taleyarkhan et al. [Taleyarkhan, et al., 2006a. PRL 96, 034301] and Xu et al. [Xu, Y., et al., 2005. Nuclear Eng. Des. 235, 1317–1324] where ice-pack shielding was present, whereas without ice-pack shielding the calculated neutron spectrum is consistent with the experimentally observed neutron spectra of Taleyarkhan et al. [Taleyarkhan, et al., 2002. Science 295, 1868; Taleyarkhan, et al., 2004. Phys. Rev. E 69, 036109] and Forringer et al. [Forringer, E., et al., 2006a. Transaction on American Nuclear Society Conference, vol. 95, Albuquerque, NM, USA, November 15, 2006, p. 736; Forringer, E., et al., 2006b. Proceedings of the International Conference on Fusion Energy, Albuquerque, NM, USA, November 14, 2006] and also that from GEANT computer code [Agostinelli, S., et al., 2003. Nuclear Instrum. Methods Phys. Res. A 506, 250–303] predictions [Naranjo, B., 2006. PRL 97 (October), 149403] in which ice shielding was also absent. The results of this archive confirm for the record that the confusion and controversies caused from past reports [Reich, E., 2006. Nature (March) 060306. news@nature.com ; Naranjo, B., 2006. PRL, 97 (October) 149403] have resulted from their neglect of important details of bubble fusion experiments. Results from this paper demonstrate that ice-pack shielding between the detector and the fusion neutron source, gamma photon leakage and neutron pulse-pileup due to picosecond duration neutron pulse emission effects play important roles in affecting the spectra of neutrons from acoustic inertial confinement thermonuclear fusion experiments.

Direct numerical simulations (DNS) of air entrainment by the breaking bow waves of naval surface ships are outside of the computational reach of the most powerful computers in the foreseeable future. This creates a need for physically-based models of air entrainment for applications in numerical simulations for ship design. Due to the non-linear dependence of the terminal bubble velocity with diameter most air entrainment flows have a high void fraction region immediately below the free surface. We present a model that locates this region employing the local liquid velocity and the distance to the interface. Using this model and the bubble size distributions measured by Deane and Stokes [Deane BD, Stokes MD. Scale dependence of bubble creation mechanisms in breaking waves. Nature 2002;418:839–44] we have simulated the air entrainment in the breaking wave experiments of Wanieski et al. [Waniewski TA, Brennen CE, Raichlen F. Measurement of air entrainment by bow waves. J Fluids Eng 2001;123:57–63]. Comparison against these experimental data is good. We then apply this model to simulate the flow around naval combatant DTMB 5415 and the research vessel Athena. The model predicts air entrainment in regions where it was actually observed at sea, namely the breaking bow wave, along the water/air/hull contact line and in the near-wake. To the best of our knowledge this is the first model of air entrainment that compares favorably with data at laboratory scale and also presents the right trends at full-scale.

Sonoluminescence and sonofusion phenomena may occur when vapor bubbles implode. This paper reviews the status of our understanding of the bubble dynamics involved in these interesting phenomena. In particular, the experimental and analytical evidence supporting the observed production of neutrons and tritium due to thermonuclear fusion within imploding bubble clusters is reviewed and discussed from the perspective of nuclear engineers. Moreover, prospects for scaling-up the neutron yield and some possible applications of this exciting new technology are discussed.

Advanced generation three-dimensional (3-D) two-fluid models and computational multiphase fluid dynamic (CMFD) solvers give good predictions of dispersed flows on earth (i.e., at 1 g), where the lift, wall, and turbulent dispersion forces determine the lateral void fraction distribution. However, for microgravity (μ-g) conditions these buoyancy-related forces become quite small and two-fluid model predictions are generally inadequate. This implies that some of the physics lost during ensemble averaging was not included back into the two-fluid model with the closure laws that were used. Recent modeling advances that include the effect of the phasic velocity fluctuations on the phase distribution are presented. The resultant two-fluid model was evaluated and compared with various data sets for steady, fully developed turbulent conditions using a novel one-dimensional (1-D) CMFD solver that is numerically very efficient. It was found that with the addition of these new physical mechanisms to the closure laws...

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.

In a bubbly flow, the presence or absence of the dispersed phase (gas) at a given instant and a given point in space depends on two factors, namely: (a) the forces acting on the bubble (or, more generally the dispersed particle) as a whole and responsible for its movement, and (b) the shape (geometry) of the bubble, which contributes to define if the spatial point in question lays inside or outside the bubble at that instant. Based on that point of view, we propose herein a two-fluid model that involves a particle-center-averaging procedure for the disperse phase, and a re-interpretation and post-processing of the results obtained. This center-averaged approach averages the disperse phase (bubbles) based on a particle center indicator function, while retaining standard phase indicator averaging for the continuous phase (liquid). The solution fields obtained are then post-processed to introduce the geometry of the bubbles in order to recover the values that are representative of the measured fields. The key idea here is to separate the geometric aspect from the dynamic aspect of the problem into two independent, successive steps. Tracking the bubble centers makes it possible to model the wall-induced forces more accurately. We take advantage of this fact to propose models for the wall normal force for very small Weber numbers and for Weber numbers of order unity. The additional tangential drag induced by the wall is also examined in light of recent experimental evidence. The resultant two-fluid model may be easily incorporated into existing two-fluid model codes. Results obtained with the new model showing agreement with experimental data are also presented.

A model for the wallinduced forces on bubbles for application in two-fluid model simulations of bubbly flows has been derived. The wall-induced force is obtained as the integral of an excess pressure calculated from the solution of the lubrication equation. Our numerical results are compared with experiments and it is shown that the wall-induced force is a function of the buoyancy and added mass forces, modulated by a smoothed Heaviside function that accounts for the proximity to the wall. This model explicitly accounts for the Reynolds, Eotvos and Weber numbers of the bubble and is valid in a larger range of these numbers than previous models.

This paper presents an assessment of various models which can be used for the multidimensional simulation of multiphase flows, such as may occur in nuclear reactors. In particular, a model appropriate for the direct numerical simulation (DNS) of multiphase flows and a mechanistically based, three-dimensional, four-field, turbulent, two-fluid computational multiphase fluid dynamics (CMFD) model are discussed. A two-fluid bubbly flow model, which was derived using potential flow theory, can be extended to other flow regimes, but this will normally involve ensemble-averaging the results from direct numerical simulations (DNS) of various flow regimes to provide the detailed numerical data necessary for the development of flow-regime-specific interfacial and wall closure laws.

Research teams from various organizations have joined forces to create the Acoustic Fusion Technology Energy Consortium (AFTEC) to promote the development of sonofusion and its related science and technology. Technically known as acoustic inertial confinement fusion, sonofusion was derived from a related phenomenon, sonoluminescence. Sonofusion involves the application of sound waves to a deuterium-rich liquid to create pressure oscillations that implode tiny bubbles filled with deuterium vapor. The bubbles' violent collapse can cause some of the deuterium nuclei to undergo fusion. Fusion produced no greenhouse gases and, unlike conventional nuclear fission reactors, it produces no noxious radioactive wastes that last for thousands of years. Much more extensive research, however, is required before it is clear whether sonofusion can become a new energy source.

We present analytical results for stable stratified wavy two-phase flow and functional forms for the various interfacial force densities in a two-fluid model. In particular, we have derived analytically the components of the non-drag interfacial force density [Drew, D.A., Passman, S.L., 1998. Theory of Multicomponent Fluids. Springer-Verlag, New York; Nigmatulin, T.R., Drew, D.A., Lahey, R.T., Jr., 2000. An analysis of wavy annular flow. In: International Conference on Multiphase Systems, ICMS’2000, Ufa, Russia, June 15–17], Reynolds stress tensor, and the term, (p˜cli−p¯cl)∇αcl, where p˜cli is interfacial average pressure, p¯cl the average pressure, and αcl is the volume fraction of the continuous liquid phase. These functional forms should be useful for assessing two-fluid closure relations and Computational Multiphase Fluid Dynamics (CMFD) numerical models for stratified wavy flows. Moreover, it appears that this approach can be generalized to other flow regimes (e.g., annular flows).

This paper extends the experimental and numerical results presented previously and addresses the major criticisms raised. In addition, the most recent results are discussed. In acoustic cavitation experiments with chilled (ɛ0 °C) deuterated acetone (C3D6O), the production of tritium and 2.45 MeV neutrons [which are characteristic of deuterium-deuterium (D-D) fusion] was observed during vapour bubble implosions in an acoustic pressure field. Similar experiments with deuterated acetone at room temperature (ɛ20 °C) and control experiments with normal acetone (C3H6O), at both 0 and 20 °C, showed no statistically significant increases in either tritium level or neutron emissions. Numerical simulations of the processes that account for the shock waves generated in the liquid and within the collapsing bubbles supported these experimental observations and showed that high densities and temperatures (° 108 K) may be achieved during bubble cloud implosions, yielding the conditions required for D-D nuclear fusion reactions. The present paper treats the bubble fusion experiments and theoretical results in greater detail than was possible in the previous publications, contains some refinements, addresses some important questions raised by reviewers and critics and discusses possible applications of this interesting phenomenon.

Two-fluid turbulent dispersion models have been compared with direct numerical simulations (DNS) of a decaying turbulence bubbly flow in the low Stokes number limit, St≈10−3. Because of the absence of empiricism, DNS results represent an excellent means of assessing turbulent dispersion models. Sufficiently far away from the inlet of the channel, where the turbulence was fully developed, these turbulent dispersion models were able to predict the DNS results when a Schmidt number, Scb=0.83, was used. This result highlights the fact that even bubbles of diameter, Db=42 μm, considerably smaller than the Kolmogorov length scale, η=75 μm, do not behave as passive scalars for which Scb=1. In addition, these models were also assessed against a bubbly mixing layer flow having a low Stokes number, St

When a gas bubble is properly excited it will oscillate and may undergo implosions during which the gas in the bubble can become so compressed that a plasma is formed, resulting in the emission of photons. That is, light pulses may occur during implosions. This phenomenon has been known of for more than 60 years and is called sonoluminescence. It is of great interest to scientists and engineers for high temperature chemical reactions, remediation of contaminated liquids and, more recently, the possibility of thermonuclear fusion. Measurements using mixed frequency ultrasonic bubble excitation were performed for different dissolved noble gases at various temperatures. The transient radius of the bubble was measured using Mie scattering and sonoluminescence (i.e., photon) emission was detected using two photomultipliers, which were also band pass filtered to be sensitive to different parts of the emission spectrum. The reduction in the ambient radius was identified as being directly related to bubble stabil...

This paper reviews the state-of-the-art in the prediction of multidimensional multiphase flow and heat transfer phenomena using a four field, two-fluid model. It is shown that accurate mechanistic computational fluid dynamic (CFD) predictions are possible for a wide variety of adiabatic and diabatic flows using this computational model. In particular, the model is able to predict the bubbly air/water upflow data of Serizawa (Serizawa, A., 1974. Fluid dynamic characteristics of two-phase flow. Ph.D. thesis, (Nuclear Engineering), Kyoto University, Japan), the downflow data of Wang et al. (Wang, S.K., Lee, S.J., Lahey Jr., R.T., Jones, O.C., 1987. 3-D turbulence structure and phase distribution measurements in bubbly two-phase flows. Int. J. Multiphase Flow 13 (3), 327–343), the isosceles triangle upflow data of Lopez de Bertodano et al. (Lopez de Bertodano, M., Lahey Jr., R.T., Jones, O.C., 1994b. Phase distribution in bubbly two-phase flow in vertical ducts. Int. J. Multiphase Flow 20 (5), 805–818), the heated annular R-113 subcooled boiling data of Velidandala, et al. (Velidandla, V., Pulta, S., Roy, P., Kaira, S.P., 1995. Velocity field in turbulent subcooled boiling flow. ASME Preprint HTD-314, 107–123) and the R-113 CHF data of Hino and Ueda (Hino, R., Ueda, T., 1985. Studies on heat transfer and flow characteristics in subcooled boiling-part 2, flow characteristics. Int. J. Multiphase Flow 11, 283–297). It can also predict external two-phase flows, such as those for spreading two-phase jets (Bonetto, F., Lahey Jr., R.T., 1993. An experimental study on air carryunder due to a plunging liquid jet. Int. J. Multiphase Flow 19 (2), 281–294) and multiphase flows around the hull of naval surface ships (Carrica, P.M., Bonetto, F., Drew, D.A., Lahey, R.T., 1999. A polydispersed model for bubbly two-phase flow around a surface ship. Int. J. Multiphase Flow 25 (2), 257–305).

This paper presents experimental data for dispersed liquid/liquid upflows. Water was the continuous phase and mineral oil was the dispersed droplet phase. For this flow regime reduced gravity bubbly flow phenomena was simulated because the mineral oil and water had almost the same density. The mean velocity and turbulence fields, the size distributions of the oil droplets, the volume fraction, and interfacial area density distribution were measured using fiber optic Laser Doppler Anemometer (LDA) and phase Doppler Anemometer (PDA) systems. Significantly, the results presented in this paper are similar to those for bubbly air/water flows in microgravity conditions (Kamp el at., 1995).

A spherically-symmetric problem is considered in which a small gas bubble at the centre of a spherical flask filled with a compressible liquid is excited by small radial displacements of the flask wall. The bubble may be compressed, expanded and made to undergo periodic radial oscillations. Two asymptotic solutions have been found for the low-Mach-number stage. The first one is an asymptotic solution for the field far from the bubble, and it corresponds to the linear wave equation. The second one is an asymptotic solution for the field near the bubble, which corresponds to the Rayleigh–Plesset equation for an incompressible fluid. For the analytical solution of the low-Mach-number regime, matching of these asymptotic solutions is done, yielding a generalization of the Rayleigh–Plesset equation. This generalization takes into account liquid compressibility and includes ordinary differential equations (one of which is similar to the well-known Herring equation) and a difference equation with both lagging and leading time. These asymptotic solutions are used as boundary conditions for bubble implosion using numerical codes which are based on partial differential conservation equations. Both inverse and direct problems are considered in this study. The inverse problem is when the bubble radial motion is given and the evolution of the flask wall pressure and velocity is to be calculated. The inverse solution is important if one is to achieve superhigh gas temperatures using non-periodic forcing (Nigmatulin et al. 1996). In contrast, the direct problem is when the evolution of the flask wall pressure or velocity is given, and one wants to calculate the evolution of the bubble radius. Linear and nonlinear periodic bubble oscillations are analysed analytically. Nonlinear resonant and near-resonant periodic solutions for the bubble non-harmonic oscillations, which are excited by harmonic pressure oscillations on the flask wall, are obtained. The applicability of this approach bubble oscillations in experiments on single-bubble sonoluminescence is discussed.

Local measurements of the velocity and phase distribution were made for solid/liquid two-phase flows in a horizontal pipe using a multidimensional laser Doppler anemometer (LDA) system. The pipe used had a 30.6 mm inner diameter and was made of a special optically clear material, Fluorinated Ethylene Propylene (FEP), which has the same index of refraction as water. The test section and laser probes were submerged in water so that no optical corrections were necessary. Simultaneous measurements of the liquid and particle phases were obtained and discriminated based on differences in the residence time that each particle had when crossing the LDA's measurement volume. Positive buoyant and negative buoyant solid spherical particles, about 2 mm in diameter, were used in this study. A complete data set of the phasic mean velocities, turbulence and volume fractions were taken for each particle type. The results presented herein are complete and self-consistent, and can be used to assess the predictive ...

A three-dimensional two-fluid model has been developed using ensemble-averaging techniques. The two-fluid model was closed for adiabatic two-phase bubbly flows using cell averaging which accounted for the dispersed phase distribution in the region of the averaging volume. The phasic interfacial momentum exchange includes the surface stress developed on the interface which is induced by the relative motion of the phases. The surface stress has been obtained by treating the interface as an elastic spherical shell. A characteristic analysis revealed that the one-dimensional system of two-fluid conservation equations which were derived is well-posed over a range of void fractions with increased value of the interfacial pressure. The propagation of void fraction disturbances (i.e. the void wave) has also been analyzed by performing a dispersion analysis. The speed, stability and damping of the linear void waves have been obtained. To study finite amplitude void waves, the system of equations has been transformed into a moving coordinate system, and asymptotic solutions of the transformed nonlinear void wave equation have been obtained. The speed and the stability of different types of nonlinear void waves have been found to be sensitive to the closure relations of the two-fluid model. Among the different constitutive parameters, the interfacial pressure difference in the continuous phase and the void fraction gradient in the non-drag force are found to be the most significant in determining behavior of void waves in bubbly flows. The derived void wave speed agrees well with the void wave data of bubbly air–water flow.

A moving-boundary nodal model has been derived for the linear and non-linear stability analysis of boiling channels. This model is based on the integration of the conservation (partial differential) equations in space and an approximation of the integral with a weighted average of the integrated variable evaluated at the boundaries of the nodes. The resulting system of ODEs has been used to evaluate the linear stability of a boiling vertical channel. The results obtained with this model, using a relatively small number of nodes, compare favorably with experimental results and calculations obtained with distributed parameter and fixed node models, which require the use of many axial nodes. Supercritical and subcritical Hopf bifurcations have been identified, and the frequency response of the model has been evaluated. These results have been used as the criteria for the determination of the number of single-phase nodes needed for a given frequency range.

The lateral force on a tethered rigid sphere submerged in a turbulent, uniform shear flow of water was measured. Periodic and non-periodic motions of the sphere were observed depending on flowrate, shear and sphere density. The direction of the observed lateral force was opposite to that predicted by inviscid theory and increased in magnitude as the sphere’s Reynolds numbers based on relative velocity, Re ,a nd average shear, Rer, increased. The lateral force was found to correlate with the product Re Rer. The data suggests that a sign reversal occurs at relatively small values of the product Re Rer, where the lateral force is dominated by inviscid eAects. The results are explained assuming that the lateral forces on rigid spheres are a consequence of two competing factors: namely, inviscid lift forces and the vortex shedding-induced lateral forces which are dominant for higher Reynolds numbers. An estimate of the kinetic energy in the wake was used to show that the vortex shedding-induced lateral forces correlate with the product Re Rer and are in a direction opposite to the inviscid lift force. Combining the experimental data of this study with similar data a correlation for the lift coeAcient of spheres in turbulent shear flows was developed. This correlation is applicable to turbulent multiphase flows having a spherical dispersed phase. # 1999 Elsevier Science Ltd. All rights reserved.

A new artificial viscosity (Q) model, based on physical conservation corrections for momentum, and a new artificial heat transfer (H) formulation are developed for the analysis of one-dimensional compressible fluid transients in plane, cylindrical, and spherical geometries. The accuracy of these formulations is verified against various benchmark shock tube problems. A Q-induced geometric error for cylindrical and spherical geometry is defined and the benefits of the Q formulation presented are demonstrated. It is also shown that these formulations can control the total variation of the solution and have superior shock-capturing capabilities. Comparisons are made with the original Q formulations of J. von Neumann and R. D. Richtmyer (1950, J. Appl. Phys.21, 232), W. F. Noh's Q&H shock-following method (1987, J. Comput. Phys.72, 78), and the piecewise-parabolic method of P. Colella and P. R. Woodward (1984, J. Comput. Phys.54, 174). The comparisons demonstrate the advantages of the new method. Numerical examples for more realistic equations of state which show the robustness of the method are also presented.

An analysis of dilute, turbulent particle/liquid two-phase flow is presented. The three-dimensional conservation equations that govern turbulent motion in solid/fluid flows are derived using ensemble averaging, and the unknown terms in these equations are constituted to achieve closure. These closure terms include the shear stress due to interparticle collisions, the corresponding terms in the Reynolds stress equation, the force and dissipation due to particle-wall collisions, and the interfacial work due to particle/turbulent eddy interaction. The resultant two-fluid model was then evaluated using a computational fluid dynamic (CFD) solver and the predictions were compared with experimental data. Good agreement was observed for a variety of flow conditions.

A three dimensional polydisperse model for bubbly two-phase flow around a surface ship is presented. The Boltzmann equation for the bubble mass probability density function is evaluated using a multigroup approach with groups of constant bubble mass. The intergroup transfer mechanisms are bubble breakup, coalescence and the dissolution of air into the ocean, and their effects on the two-phase flow field are analyzed. A three dimensional two-fluid model is used for each bubble mass group to calculate the group’s average gas velocity, resulting in four scalar equations per group. The air entrainment process is modeled using simulated breaking bow waves and the steady-state evolution of the gas bubbles for zero Froude number is obtained. It was found that intergroup transfer is very important in these flows. Some of the research areas that need further improvement for the numerical prediction of polydisperse two-phase flow around a ship have been identified and are discussed.

A two-fluid model suitable for the calculation of the two-phase flow field around a naval surface ship is presented. This model couples the Reynolds-averaged Navier–Stokes (RANS) equations with equations for the evolution of the gas-phase momentum, volume fraction and bubble number density, thereby allowing the multidimensional calculation of the two-phase flow for monodisperse variable size bubbles. The bubble field modifies the liquid solution through changes in the liquid mass and momentum conservation equations. The model is applied to the case of the scavenging of wind-induced sea-background bubbles by an unpropelled US Navy frigate under non-zero Froude number boundary conditions at the free surface. This is an important test case, because it can be simulated experimentally with a model-scale ship in a towing tank. A significant modification of the background bubble field is predicted in the wake of the ship, where bubble depletion occurs along with a reduction in the bubble size due to dissolution. This effect is due to lateral phase distribution phenomena and the generation of an upwelling plume in the near wake that brings smaller bubbles up to the surface. © 1998 John Wiley & Sons, Ltd.

The spherically-symmetric problem of the oscillations of a small gas bubble in the center of a spherical flask filled with a compressible liquid that is excited by small radial displacement of the flask's wall is considered. Two asymptotic solutions have been found for the low Mach number stage. The first one is an asymptotic solution for the field far from the bubble, and it corresponds to linear wave theory. The second one is an asymptotic solution for the boundary layer near the bubble and it corresponds to an incompressible fluid. In the analytical solution of the low Mach number step matching of these asymptotic solutions is done. A generalization of the Rayleigh = Plesset equation for a compressible liquid is given in the form of two ordinary difference-differential equations that take into account the pressure waves which are reflecting from the bubble and those that are incident on the bubble from the flask wall. The initial value problem for the initiation of the bubble oscillations due ...

This paper is concerned with the modeling of severe accident phenomena in boiling water reactors (BWR). New models of core melting and in-vessel corium debris relocation are presented, developed for implementation in the APRIL computer code. The results of model testing and validation are given, including comparisons against available experimental data and parametric/sensitivity studies. Also, the application of these models, as parts of the APRIL code, is presented to simulate accident progression in a typical BWR reactor.