Bubble Number Density Research Articles

Weakly nonlinear evolution of pressure waves in a polydisperse bubbly liquid

Weakly nonlinear propagation of plane pressure waves in initially quiescent liquids containing spherical bubbles with a small initial polydispersity of the bubble radius and bubble number density is theoretically studied to clarify the effect of the polydispersity on wave propagation. The wavelength is comparable with the bubble radius and the incident frequency of waves is with an eigenfrequency of the bubble. We consider two different cases of the size of the polydispersity (i.e., small and large polydispersities) and assume that the polydispersity appears at a field far from a sound source. The polydispersity is formulated into a set of perturbation expansions. Bubble oscillations are spherically symmetric, and bubbles do not coalesce, break up, appear, and disappear. The basic set is composed of the conservation laws of mass and momentum for gas and liquid phases based on a two-fluid model, equation of motion for bubble wall, and so on. From the perturbation analysis up to the third order of approximation, two cases of nonlinear wave equation for a long-range propagation of waves were derived. We concluded that the polydispersity affects the advection of waves and is expressed as a variable coefficient.

Number density of bubbles under ultrasonic horn measured from stroboscopic images

Although image measurement is essential in the analysis of acoustic cavitation bubbles, it is impossible to determine the position of the bubble along the optical axis of the imaging system from the images. Thus, the number density of the bubbles cannot be measured from the image. This paper proposed a method to determine bubbles’ positions along the optical axis using the bubble image brightness. The relationship among the bubble position along the optical axis, the bubble diameter, and the bubble image brightness is clarified using the bubble in the single bubble system. A measurement method of the bubble number density based on this relationship is established. Using this method, the time-averaged spatial distribution of bubble number density under ultrasonic horn is revealed.

The effects of post-irradiation isochronous annealing on defects evolution and hardening in Hastelloy N alloy

The nickel-based Hastelloy N alloy samples were implanted with helium ions at room temperature and then annealed at 600°C (sample S2), 800°C (sample S3) and 900°C (sample S4) for 1 hour, respectively. The effects of post-irradiation isochronous annealing on defects evolution and hardening in the alloy were investigated by transmission electron microscopy (TEM) and nanoindenter. TEM characterization shows that the mean diameter and number density of helium bubbles in sample S2 keep unchanged. It is found that the increments of helium bubbles size in samples S3 and S4 are mainly caused by migration and coalescence (MC) and Ostwald ripening (OR) mechanisms, respectively. Additionally, the MC mechanism can promote the formation of dislocation loops due to matrix atoms diffusion. In sample S4, the recovery effects of defects are striking, resulting in a significant reduction in the number density of dislocation loops. The values of Vac. / He. at different regions have been calculated to explain the size variation of helium bubbles in all the samples. Moreover, nanohardness increments calculated by dispersed barrier hardening (DBH) model agree with those measured by nanoindentation.

Numerical study on the cumulative effect of supersaturated TDG through the spillway

The cascade development of water resource will lead to cumulative effect of supersaturated total dissolved gas (TDG) on the ecological environment, which will cause lethal disease to fish. The TDG dissipates slowly in deep reservoir areas and if supersaturated TDG can't recover through the spillway then it will lead to continuous accumulation in the stilling basin. In order to investigate the cumulative effect of supersaturated TDG of hydropower cascades, a validated TDG numerical model with the VOF method and DES model was used to simulate a spillway discharge of Tongjiezi dam with supersaturated TDG and 100% TDG inflow. In this model, bubble size change is calculated by bubble number density equation and TDG is simulated by transport equation considering the gas-liquid mass transfer. Comparing with the TDG 100% inflow case, it indicated forebay TDG level caused by the upstream dams should be considered and involved in the downstream TDG evaluation. This paper also proposed an engineering measure with baffle blocks in the spillway which can reduce entrained bubble mass and TDG saturation level at the entry point than the case without blocks. It shows baffle blocks in the spillway can effectively reduce the cumulative effect of supersaturated TDG. It is a critical step for the mitigation of accumulation of supersaturated TDG through the spillway and the results provide reference about mitigation measure of supersaturated TDG for hydropower cascades.

Reconciling bubble nucleation in explosive eruptions with geospeedometers

Magma from Plinian volcanic eruptions contains an extraordinarily large numbers of bubbles. Nucleation of those bubbles occurs because pressure decreases as magma rises to the surface. As a consequence, dissolved magmatic volatiles, such as water, become supersaturated and cause bubbles to nucleate. At the same time, diffusion of volatiles into existing bubbles reduces supersaturation, resulting in a dynamical feedback between rates of nucleation due to magma decompression and volatile diffusion. Because nucleation rate increases with supersaturation, bubble number density (BND) provides a proxy record of decompression rate, and hence the intensity of eruption dynamics. Using numerical modeling of bubble nucleation, we reconcile a long-standing discrepancy in decompression rate estimated from BND and independent geospeedometers. We demonstrate that BND provides a record of the time-averaged decompression rate that is consistent with independent geospeedometers, if bubble nucleation is heterogeneous and facilitated by magnetite crystals.

Modelling fission gas behaviour in fast reactor (U,Pu)O[formula omitted] fuel with BISON

The physics-based fission gas behaviour model available in the BISON fuel performance code provides satisfactory predictive capabilities for application to light-water reactor conditions. In this work, we present a model extension for application to fast reactor (U,Pu)O2 fuel. In particular, we detail the introduction of a lower bound to the number density of grain-face bubbles, representing a limit to the coalescence process once extensive bubble interconnection is achieved. This new feature is tested first against an experimental database for UO2-LWR, and secondly is validated against integral irradiation experiments for fast reactor (U,Pu)O2 fuel rods irradiated in the FFTF (Fast Flux Test Facility) and in the JOYO reactors. The comparisons of BISON results with the experimental data are satisfactory and demonstrate an improvement compared to the standard version of the code.

Improvement of helium swelling resistance of nickel-based alloy via proper SiCNP dispersion

Ni-Mo-SiCNP alloy is a promising candidate as a structural material for building high-temperature molten salt reactors in the future. The irradiation damage resistance of this alloy is a key factor in determining its application prospects. In this study, Ni-Mo-SiCNP alloy samples containing different dispersion amounts (0.5, 1.5, and 2.5 wt.%) of SiCNP were irradiated with 1 MeV He+ ions at a dose of 3 × 1016 ion/cm2 at 750 °C. The evolution of helium bubbles was observed using transmission electron microscopy. The results show that with an increase in the dispersion amount of SiCNP, the number density of helium bubbles increases whereas the mean size decreases gradually. It is shown that a proper dispersion amount of SiCNP can effectively improve the helium swelling resistance of nickel-based alloys. Moreover, the related mechanism of the suppressed swelling was revealed.

Phase transitions in an expanding universe: stochastic gravitational waves in standard and non-standard histories

We undertake a careful analysis of stochastic gravitational wave production from cosmological phase transitions in an expanding universe, studying both a standard radiation as well as a matter dominated history. We analyze in detail the dynamics of the phase transition, including the false vacuum fraction, bubble lifetime distribution, bubble number density, mean bubble separation, etc., for an expanding universe. We also study the full set of differential equations governing the evolution of plasma and the scalar field during the phase transition and generalize results obtained in Minkowski spacetime. In particular, we generalize the sound shell model to the expanding universe and determine the velocity field power spectrum. This ultimately provides an accurate calculation of the gravitational wave spectrum seen today for the dominant source of sound waves. For the amplitude of the gravitational wave spectrum visible today, we find a suppression factor arising from the finite lifetime of the sound waves and compare with the commonly used result in the literature, which corresponds to the asymptotic value of our suppression factor. We point out that the asymptotic value is only applicable for a very long lifetime of the sound waves, which is highly unlikely due to the onset of shocks, turbulence and other damping processes. We also point out that features of the gravitational wave spectral form may hold the tantalizing possibility of distinguishing between different expansion histories using phase transitions.

Does Salting-Out Effect Nucleate Nanobubbles in Water: Spontaneous Nucleation?

Nanobubble technology has a wide range of applications in wastewater treatment, medical sectors, food processing, and agriculture sectors. However, the fundamental understanding of the mechanism of nanobubble nucleation and a reliable method for differentiating nanobubbles and nanoparticles are still under infancy. In this work, we have answered this question by investigating the nano-entities nucleation during the salting-out effect. The solubility of gases in aqueous salt solution decreases with the salt concentration, and it is often termed as thesalting-out effects. The dissolution of salt in water undergoes dissociation of salt and further solvation of ions with water molecules. The solvation weakens the affinity of gaseous molecules, and thus it releases the excess dissolved gas. Now it is interesting to know that what happens to the excess gas released during salting-out? While it is also imperative to note that the gas transfer in the bulk liquid often occurs in the form of bubbles. With this hypothesis, we have experimentally investigated that whether the salting-out effect nucleates nanobubble or not. What is the strong scientific evidence to prove that they are nanobubbles? Does the salting-out parameter affect the number density? The answers to such questions are essential for the fundamental understanding of the origin and driving force for nanobubble generation. We have provided three distinct proofs for the nano-entities to be the nanobubbles, namely, (1) by freezing and thawing experiments, (2) by destroying the nanobubbles under ultrasound field, and (3) we also proposed a novel method for refractive index estimation of nanobubbles to differentiate them from nano drops and nanoparticles. The refractive index (RI) of nanobubbles was estimated to be 1.012 for mono- and di-valent salts and 1.305 for trivalent salt. The value of RI closer to 1 provides strong evidence of gas-filled nanobubbles. The bubble number density and mean diameter have been measured by nanoparticle tracking analysis (NTA) and corroborated with Cryo-TEM. Both positive and negative charged nanobubbles nucleate during the salting-out effect depending upon the valency of salt. The nanobubbles during the salting-out effect are stable only for up to three days. This shorter stability could plausibly be due to reduced colloidal stability at a low surface charge.

Predicting the Sonochemical Efficiency for Water Decontamination: An Upscaled Numerical Approach

AbstractA numerical modeling approach is presented, predicting the sonochemical efficiency for water decontamination integrally based on microscale activity of a single bubble, coupled to macroscale energetic balance on a batch sonochemical reactor volume. The sonochemical efficiency is axed on the powerful oxidative effect of HO• radicals on organic substrates. Spatial average values of bubble number densities were estimated at each instant of the acoustic period along a reactor of a hypothetical length λ. As a direct result, the kinetics of the sonochemical emergence of HO• led to spatial average production rates of 0.251 and 0.299 µmol dm−3min−1 under respective frequencies of 20 and 443 kHz, for a defined irradiation time of 50 µs.

A new bubbly flow detection and quantification procedure based on optical laser-beam scattering behavior

In this paper a new bubbly flow measurement procedure is proposed which can be used to both detect and quantify some main features of such flows. The proposed procedure is based on the optical scattering behavior of a laser-beam passing through a bubbly flow. A series of experiments are conducted to evaluate the procedure and important parameters involved such as length of bubbly flow, bubble number density and size distribution. Experimental results confirm the capabilities of the procedure for the detection and quantification of bubbly flows. Also, an optical model of the laser beam behavior in bubbly flow is derived to reevaluate the problem and its results are compared with the obtained experimental results. Outcomes of the optical model, which is in good agreement with the experimental results, emphasizes and describes the strong correlation between the injection strength parameter and forward scattered light intensity. Also, bubble size distribution is found to be in close connection with the amplitude of scattered light fluctuations. Therefore, upon the measurement of optical laser-beam scattering behavior passing through a bubbly flow, various properties of such flows could be determined.

On the irradiation tolerance of nano-grained Ni–Mo–Cr alloy: 1 MeV He+ irradiation experiment

The irradiation damage behavior was studied in the nano-grained Ni–Mo–Cr alloy (nano-grained GH3535), which was irradiated by He ion to various dose. The evolution of defects and hardness changes are characterized by transmission electron microscopy and nanoindentation to explore the irradiation tolerance of the nano-grained GH3535 and the coarse-grained GH3535 (annealed GH3535), where the later was chosen as reference material to make comparison with nano-grained GH3535. The results show that though both the average size and number density of He bubbles increase with an increase in the irradiation dose, the smaller volume fraction is found in the nano-grained GH3535 compared with the coarse-grained GH3535 under the same irradiation condition. This indicates that the nano-grained GH3535 possess better irradiation swelling resistance than the coarse-grained GH3535. However, the increase in the hardness of the nano-grained GH3535 is more significant than in the coarse-grained GH3535 under the same irradiation dose. This suggests stronger irradiation-induced hardening of the nano-grained alloy comparing to coarse-grained alloy, due to the impeding effect caused by grain boundaries decorated with He bubbles. This study provides insight into the design of irradiation-tolerant nickel-based alloys for nuclear industry applications.

Effects of temperature on nucleation and collapse of volatile bubbles in the high density polyethylene melt

High density polyethylene/n-Hexane system was adopted to investigate the bubbles nucleation and collapse in polymer melt with a visualization apparatus at different temperatures. The results showed that the initial bubble number, initial total bubble volume and the mean bubble diameter all increased with the temperature increasing, and the bubble diameter distribution changed from single peak distribution to bimodal distribution. Moreover, the effect of temperature on the maximum bubble diameter was mainly reflected in the change of the pressure in bubbles due to the change of the volatile content in the polyethylene melt. For bubble collapse, the collapse time became longer but the bubble collapse rate became faster with the temperature increasing, and a fitting model was established in which the collapse coefficient n was used to describe the collapse rate. Through dimension analysis, the correlation between the collapse coefficient n and the melt surface tension σ, zero-shear melt viscosity η0, diffusion coefficient D, maximum bubble diameter dmax, melt density ρ, initial bubble number density Nini were established and the variation of D with temperature could be predicted as an exponential correlation.

Experimental investigations on the bubbly wake of a transom stern model using optical laser beam scattering characteristics

In this paper a new procedure for detection and quantification of the main features of ship models bubbly wake is presented. The method is based on light scattering characteristics of laser beams passing through the wake of ship models. An optical light scattering model is developed and validated in a series of steady bubbly flow tests in a water tank, with time-invariant mean multiphase flow properties. Then a series of unsteady tests are conducted in a towing tank so as to study bubbly wake properties of a transom stern model. Temporal wake strength and its final detection time and length are measured using light scattering measurements. Light scattering analysis provides longitudinal, lateral, and vertical distributions of the wake without any flow intrusion. Also by combining the experimental and analytical results, a complementary assay for determination of average bubble size and bubble number density distribution is presented. Effects of model velocity on the bubbly wake features of the transom stern are also investigated using the suggested procedures. Results indicate that increasing the model velocity increases the total bubbly wake length and lifetime. Details of the wake lateral distribution reveal the prominent contribution of transom stern diverging waves on the bubbly wake air entrainment.

Validation of interfacial area concentration model for simulating bubbly and cap/slug flow behaviors in large diameter pipes using LSTF, ATLAS, and horizontal pipe experiment data

This study discusses Interfacial Area Concentration (IAC) models developed for bubbly and cap/slug flow regimes in a large diameter pipe incorporating recently developed small bubble fraction correlations in various flow conditions. The main focus of this study was the robust simulation of the behaviors of bubbly and cap/slug flows in large diameter pipes observed in Large Scale Test Facility (LSTF), Advanced Thermal-hydraulic test Loop for Accident Simulation (ATLAS), and horizontal flow test facility. Since the IAC was one of the key parameters to achieve this, an IAC model for large diameter pipes was first derived based on the existing Hibiki-Ishii IAC model for bubbly flow, and the Shen-Hibiki IAC model for cap bubbly-to-churn flow. The volume fraction of group-1 bubbles, i.e., small spherical bubbles, in the IAC model, which have been developed based on the assumption that the group-1 bubbles exponentially decay in the slug flow regime, was refined. As a result, a more physical model of the group-1 bubble number density that remains constant in the cap/slug flow regime was imposed for large diameter pipes. The validity of the IAC model for large diameter pipes in predicting the interfacial drag force between gas and liquid phases in large pipes of multiple test facilities was then examined. The validation of the proposed IAC model was conducted through simulations of 1) the loss of Residual Heat Removal (RHR) during the mid-loop operation of the LSTF, 2) the 6-inch Small Break Loss of Coolant Accident (SBLOCA) of the ATLAS, and 3) the two-phase flow behaviors under a wide range of fluid conditions in the horizontal pipe test facility. Improved results were obtained with the proposed model as it indicated that there was good agreement between the calculated results and the experimental data throughout the whole transient.

Evolution of bubble size distribution, number density, and shape in semi‐batch vertical gas–liquid Taylor vortex flow

AbstractBubble size distribution and bubble ellipticity were measured as a function of axial position in a vertically oriented semi‐batch gas–liquid Taylor vortex reactor with varying gas flow rate and inner cylinder rotation speed producing axial Reynolds numbers in the range 23.8–119 and azimuthal Reynolds numbers up to 4.2 × 104. The mean bubble size increases monotonically with axial distance from the bottom of the reactor at the location of gas injection. The functional form of the growth of the mean bubble size with axial position depends upon the azimuthal Reynolds number. Specifically, when the azimuthal Reynolds number is less than 1.3 × 104, the mean bubble size increases linearly with axial distance from the bubble injection point. In contrast, for azimuthal Reynolds numbers greater than this critical value, the mean bubble size increases with axial distance in a sigmoidal manner.

Numerical Analysis of Effect of Initial Bubble Size on Captured Bubble Distribution in Steel Continuous Casting Using Euler-Lagrange Approach Considering Bubble Coalescence and Breakup

A mathematic model considering the bubble coalescence and breakup using the Euler-Lagrange approach has been developed to study the effect of the initial bubble size on the distribution of bubbles captured by the solidification shell. A hard sphere model was applied for dealing with the bubble collision. Advanced bubble coalescence and breakup models suitable for the continuous casting system and an advanced bubble captured criteria have been identified established with the help of user-defined functions of FLUENT. The predictions of bubble behavior and captured bubble distribution agree with the water model and plant measurements well respectively. The results show that the number of small bubbles captured by solidification shell is much higher than that of large bubbles. What is more, the number of captured bubbles at the sidewalls decreases with the distance from the meniscus. For the case of large gas flow rate (gas flow fraction of 8.2%), the initial size of bubbles has little effect on bubble captured distribution under various casting speeds. When the gas flow rate is small (gas flow fraction of 4.1%), the number density of captured bubbles increases as the initial bubble size increases, and the effect of initial bubbles size on captured bubble number density is amplified when the casting speed decreases. The average captured bubble diameter is about 0.12–0.14 mm. Additionally, for all cases, the initial bubble size hardly affects the average size of captured bubbles.

Development of Bubble Size Correlation for Adiabatic Forced Convective Bubbly Flow in Low Pressure Condition Using CFD Code

In a multidimensional two-phase flow analysis, bubble size significantly affects interfacial transfer terms such as mass, momentum, and energy. With regard to bubbly flow, the application of a simple correlation-type bubble size model presents certain advantages, including short calculation times and ease of usage. In this study, we propose a semi-theoretical correlation developed from a steady state bubble number density transport equation for predicting the distribution of local bubble size using a computational fluid dynamics (CFD) code. The coefficients of the new correlation were determined using the local bubble parameters obtained on the basis of three existing vertical air-water experiments. Finally, these were implemented in commercial CFD code and evaluated against experimental data, which showed that the proposed correlation exhibits good prediction capability for forced convective air-water bubbly flows under low pressure conditions.

Helium implantation effects on the tensile response of nano-twinned copper

Metallic materials used in fission and fusion reactors will internally accumulate numerous lattice defects and bubbles because of high radiation. An in-depth understanding on the influence of bubbles is significant to the safety and life assessment of relevant engineering equipment. Here, molecular dynamics simulations are performed to investigate the effects of twin boundary (TB) spacing, inner-bubble pressure, temperature and bubble number density on uniaxial tensile deformation behaviors of helium bubbles implanted nano-twinned copper (nt-Cu). Simulation results reveal that the TB can significantly enhance the strength of nt-Cu because of the Hall–Petch effect. The increase of inner-bubble pressure reduces the critical stress of dislocation emission, which in turn reduces the yield stress. High temperature softens the models and increases the inner-bubble pressure. The weaken effect of pressure component is remarkable in the yield strength, while that has little impact on the elastic modulus and the average flow stress. In addition, the larger bubble number density is accompanied by the lower elastic modulus, yield stress and average flow stress. The present findings provide valuable suggestions for upgrading the design and fabrication of high radiation-resistant metallic materials.

A thermally-limited bubble growth model for the relaxation time of superheated fuels

We propose a novel approach to evaluate the relaxation time of vapor bubble growth in the context of the flash boiling of a superheated liquid. In alternative to the empirical correlation derived from superheated water experiments almost fifty years ago, the new model describes the thermally-dominated growth of vapor bubbles in terms that are dependent on the local Jakob number (the ratio of sensible heat to latent heat during phase change) and the number density of vapor bubbles. The model is tested by plugging the resulting relaxation time into the Homogenous Relaxation Model (HRM). Flash-boiling simulations carried out with HRM are compared with n-pentane (C5H12) injection and boil-off experiments conducted with a real-size, axial-hole, transparent gasoline injector discharging into a constant-pressure vessel. The long-distance microscopy images from the experiments, processed to derive the projected liquid volume (PLV) of the spray, provide a unique set of time-resolved validation data for direct fuel injection simulations. At conditions ranging from flaring to mild and minimal flash boiling, we show that switching to the new relaxation time improves the agreement with the measured PLV profiles with respect to the standard empirical model. Particularly at flaring conditions, the predicted increase in gas cooling caused by rapid vapor production is shown to be more consistent with the observed boil-off.