Bubble Model Research Articles

Numerical study on stress in a solid wall caused by the collapse of a cavitation bubble cloud in hydraulic fluid

The stress in a solid due to the collapse of a bubble cloud in hydraulic fluid is investigated by the numerical simulation, which considers the fluid-structure coupling and employs the bubbly flow model with Euler-Lagrange method. The dynamics of the bubble at the subgrid scale is described by the Keller-Miksis equation. Heat transfer at the bubble interface is considered to reproduce thermal damping effect. As the result of the fluid-structure coupling simulation, the high von Mises stress region is observed in the solid due to the collapse of the bubble cloud attached on the solid surface, and the propagation of longitudinal and transverse waves in the solid is reproduced. As the standoff distance YC from the solid surface to the center of the bubble cloud decreases, the peak von Mises stress in the solid increases, taking a maximum at YC=0.4RC, and then decreases. Thus, the peak von Mises stress is highest under the condition that the bottom quarter of the bubble cloud is on the wall. Due to the increase of the initial void fraction and the decrease of the initial bubble radius in the bubble cloud, the collapse pressure of the bubble cloud increases. Under certain conditions, the peak von Mises stress can be higher than the 0.2% yield stress value of 250MPa for a cast iron. This is expected to induce cavitation erosion of the solid surface.

The growth rate of nanotubes and the quantity of charge during anodization

Porous anodic oxides have attracted great attention because of their unique morphology and porous structure. At the same time, the study of the mechanism has become a hot topic. Here, in order to study the formation mechanism, the growth of porous oxides of Ti and Zr at different voltages has been studied. The results show that the growth rate of ZrO2 nanotube is much higher than that of TiO2 nanotube, and the length of ZrO2 nanotube is much longer than that of TiO2 nanotube. By comparing the current–time curves, it is found that the difference of growth rate of nanotube is related to the quantity of charge, that is, integral of current–time curve (Q=∫I dt). At the same time, it is also found that the growth rate of ZrO2 nanotubes is higher than that of TiO2 nanotubes. For example, the average growth rate of ZrO2 nanotubes is 0.422 μm/min, while the growth rate of TiO2 nanotubes is only 0.131 μm/min at 20 V. These interesting findings negate the idea of fluoride ion dissolution in the classical field-assisted dissolution theory. The oxygen bubble model and electronic current theory can well explain this conclusion.

An alternative technique for determining the number density of acoustic cavitation bubbles in sonochemical reactors

The present paper introduces a novel semi-empirical technique for the determination of active bubbles’ number in sonicated solutions. This method links the chemistry of a single bubble to that taking place over the whole sonochemical reactor (solution). The probe compound is CCl4, where its eliminated amount within a single bubble (though pyrolysis) is determined via a cavitation model which takes into account the non-equilibrium condensation/evaporation of water vapor and heat exchange across the bubble wall, reactions heats and liquid compressibility and viscosity, all along the bubble oscillation under the temporal perturbation of the ultrasonic wave. The CCl4 degradation data in aqueous solution (available in literature) are used to determine the number density through dividing the degradation yield of CCl4 to that predicted by a single bubble model (at the same experimental condition of the aqueous data). The impact of ultrasonic frequency on the number density of bubbles is shown and compared with data from the literature, where a high level of consistency is found.

The dynamics of cavitation bubbles in a sealed vessel

A model of cavitation bubbles is derived in liquid confined in an elastic sealed vessel driven by ultrasound. In this model, an assumption that the pressure acting on the sealed vessel due to bubble pulsations is proportional to total volume change of bubbles is made. Numerical simulations are carried out for a single bubble and for bubbles. The results show that the pulsation of a single bubble can be suppressed to a large extent in sealed vessel, and that of two matched bubbles with same ambient radius can be further suppressed. However, when two mismatched bubbles have the same ambient radii, an interesting breathing phenomenon takes place, where one bubble pulsates inversely with the other one. Due to this breathing phenomenon the suppression effect becomes weak, so the maximum radii of two mismatched bubbles can be larger than that of a single bubble or that of two matched bubbles in sealed vessel. Besides that, for two mismatched bubbles with different ambient radii, the small one in sealed vessel under some certain parameters can pulsate as strong as or even stronger than that of a single bubble in an open vessel.

Modeling DNA Opening in the Eukaryotic Transcription Initiation Complexes via Coarse-Grained Models.

Recently, the molecular mechanisms of transcription initiation have been intensively studied. Especially, the cryo-electron microscopy revealed atomic structure details in key states in the eukaryotic transcription initiation. Yet, the dynamic processes of the promoter DNA opening in the pre-initiation complex remain obscured. In this study, based on the three cryo-electron microscopic yeast structures for the closed, open, and initially transcribing complexes, we performed multiscale molecular dynamics (MD) simulations to model structures and dynamic processes of DNA opening. Combining coarse-grained and all-atom MD simulations, we first obtained the atomic model for the DNA bubble in the open complexes. Then, in the MD simulation from the open to the initially transcribing complexes, we found a previously unidentified intermediate state which is formed by the bottleneck in the fork loop 1 of Pol II: The loop opening triggered the escape from the intermediate, serving as a gatekeeper of the promoter DNA opening. In the initially transcribing complex, the non-template DNA strand passes a groove made of the protrusion, the lobe, and the fork of Rpb2 subunit of Pol II, in which several positively charged and highly conserved residues exhibit key interactions to the non-template DNA strand. The back-mapped all-atom models provided further insights on atomistic interactions such as hydrogen bonding and can be used for future simulations.

Formation and growth of R32/R1234yf nanobubble on smooth surface: Molecular dynamics simulations

The boiling process starts from the formation of bubbles on the heated surface and the bubble growth process determines the boiling heat transfer characteristics. It is of great significance to recognize the formation and growth mechanism of nanobubbles to improve the boiling heat transfer efficiency. R32/R1234yf has a great application potential in power system such as refrigeration and Organic Rankine Cycle. In this work, the bubble formation and growth process of pure and mixture working fluids on an ideal smooth heating surface were studied by MD. The influence of compositions on the bubble grow curve was analyzed with emphasis, the characteristics of local temperature and density distribution and bubble geometric parameters were also investigated. The results show that the addition of R1234yf in R32 can inhibit the nucleation and growth of bubbles. As the mole fraction of R1234yf increases, the inception time of bubble is delayed and the bubble grow rate decreases. In the inertia controlled stage, the bubble growth curves of R32/R1234yf mixtures are closer to those of R1234yf, the reason is that more R1234yf remains in the bubble during the rapid growth of bubble, resulting in the decrease of the mole fraction of R32 in the bubble near the interface. Based on the prediction model of bubble grow rate in liquid phase, a semi-theoretical model for predicting surface bubble grow rate is proposed by analogy, the average prediction deviation of the model is less than 10%.

How to Improve Accuracy of a Kick Tolerance Model by Considering the Effects of Kick Classification, Frictional Losses, Pore Pressure Profile, and Influx Temperature

Summary Kick tolerance (KT) calculation is essential for a cost-effective well design and safe drilling operations. While most exploration and production operators have a similar definition of KT, the calculation is not consistent because of different assumptions that are made and the computational power of KT calculators. Dynamic multiphase drilling simulators usually provide KT estimates with a minimum number of assumptions. They are much more accessible nowadays for use in predicting the behavior of multiphase flow in drilling and well control operations. However, as far as we observed, the simulation services are mainly used for complex and marginal wells in which low KT may impose additional casing strings, unconventional costly drilling practices, or a high risk of major well control events. Thus, companies often use simplified steady-state models for relatively uncomplicated wells through their own KT calculation worksheets. This practice is usually justified by the misconception that simplified models are always conservative and give less KT than actual conditions. In contrast, some simplifications may lead to higher operational risks due to an overestimated KT, depending on well conditions and parameters. The primary objective of this work was to perform a quality assurance/quality control on KT calculation practices in Company P. Later on, based on our findings, we determined some solutions to improve accuracy in the simplified KT worksheets commonly used by engineers across the company. This became a driver for generating a new KT worksheet (Company Model), in particular for situations in which engineers do not have access to a kick simulator. However, it should not mislead readers about the requirements of the simulator for complex and low-KT wells. Quality assurance/quality control and subsequent investigations found that there are some important criteria and parameters that affect KT calculations, but they are missing in many simplified models or ignored by engineers because they are unaware of or lack adequate references. After reviewing relevant academic literature, common practices and assessing several off-the-shelf software programs, we generated a computer program using Visual Basic for applications to address KT sensitivity to different parameters in steady-state conditions. The newly developed program is based on a single gas bubble model that applies the effect of annular frictional losses, influx temperature, gas compressibility factor, well trajectory, and bottomhole assembly (BHA). Moreover, the program differentiates between swabbing and underbalanced conditions. A logical test is applied to determine the type of kick before computing the relevant influx volume. This kick classification concept is ignored in many KT models; this is a common mistake that leads to misleading results. The annular pressure loss (APL) parameter is sometimes assumed to be zero in KT spreadsheets, while as an additional stress load on the wellbore, it affects the kick budget and must be considered.

A variable-gap model for helium bubbles in nickel

In nuclear fission reactors, the amount of helium produced in materials by transmutation reactions at the end of the lifetime may reach several thousands of atomic parts per million (appm). Such high levels of helium production can impact the evolution of microstructures, particularly by forming helium bubbles. To better understand the role of helium on the stability of bubbles, a “variable-gap model” was parametrized with molecular dynamics (MD) calculations performed in nickel. This model predicts binding energies in a good agreement with MD values, especially for large bubbles. For very small bubbles, the influence of magic number sizes and faceting is more complex than can be described with the model. For these cases, it is proposed to use MD values directly.

Multi-frequency sonoreactor characterisation in the frequency domain using a semi-empirical bubbly liquid model

Recently, multi-frequency systems were reported to improve performance in power ultrasound applications. In line with this, digital prototyping of multi-frequency sonoreactors also started gaining interest. However, the conventional method of simulating multi-frequency acoustic pressure fields in the time-domain led to many challenges and limitations. In this study, a multi-frequency sonoreactor was characterised using frequency domain simulations in 2-D. The studied system consists of a hexagonal sonoreactor capable of operating at 28, 40 and 70 kHz. Four frequency combinations were studied: 28–40, 28–70, 40–70 and 28–40–70 kHz. A semi-empirical, modified Commander and Prosperetti model was used to describe the bubbly-liquid effects in the sonoreactor. The root-mean-squared acoustic pressure was compared against experimental validation results using sonochemiluminescence (SCL) images and was noted to show good qualitative agreement with SCL results in terms of antinode predictions. The empirical phase speed calculated from SCL measurements was found to be important to circumvent uncertainties in bubble parameter specifications which reduces error in the simulations. Additionally, simulation results also highlighted the importance of geometry in the context of optimising the standing wave magnitudes for each working frequency due to the effects of constructive and destructive interference.

On the maximum cardinality cut problem in proper interval graphs and related graph classes

Although it has been claimed in two different papers that the maximum cardinality cut problem is polynomial-time solvable for proper interval graphs, both of them turned out to be erroneous. In this work we consider the parameterized complexity of this problem. We show that the maximum cardinality cut problem in proper/unit interval graphs is FPT when parameterized by the maximum number of non-empty bubbles in a column of its bubble model. We then generalize this result to a more general graph class by defining new parameters related to the well-known clique-width parameter.Specifically, we define an (α,β,δ)-clique-width decomposition of a graph as a clique-width decomposition in which at each step the following invariant is preserved: after discarding at most δ labels, a) every label consists of at most β sets of twin vertices, and b) all the labels together induce a graph with independence number at most α. We show that for every two constants α,δ>0 the problem is FPT when parameterized by β plus the smallest width of an (α,β,δ)-clique-width decomposition.

The effect of atmospheric pressure on the growth rate of TiO2 nanotubes: Evidence against the field-assisted dissolution theory

The growth mechanism of anodic TiO2 nanotubes has been a hot topic in recent years. The classical field-assisted dissolution (FAD) theory holds that the atmospheric pressure does not affect the growth of nanotubes, while the oxygen bubble model holds that the decrease of pressure is beneficial to the nanotube growth. In order to verify the oxygen bubble model, anodizing processes at three different pressures (0.1 MPa, 0.05 MPa and 0.005 MPa), three different currents and three different NH4F concentrations were studied. To the best our knowledge, some interesting results are obtained which cannot be obtained at standard atmospheric pressure (1 atm = 0.1 MPa). (1) In the same NH4F electrolyte, the same current density and the same temperature, the reduction of anodizing atmospheric pressure can improve the growth rate of TiO2 nanotubes. (2) Under the condition of the same temperature and current density, with the increase of NH4F concentration (0.3 wt%, 0.4 wt% and 0.5 wt%), the porosity of the nanotubes increases, and the growth rate of the nanotubes decreases obviously. These findings can serve as counterevidence to the FAD theory.

Modeling Coal Swelling during Pyrolysis at Elevated Pressure by Using a Single Bubble Model: Validation and Application

ABSTRACT Pressurized oxy-coal combustion technologies are attracting more attention of researchers because of their advantages of carbon capture. While the ambient pressure could significantly influence the coal pyrolysis behavior. In this study, Yulin coal was used for the pyrolysis experiment in a pressurized drop tube furnace. Pyrolysis temperature of 1273 K, and pressures of 1, 4, 7, 10 atm were considered. The swelling behavior of produced char was analyzed by the scanning electron microscope (SEM). The char evolution process during pyrolysis at elevated pressure was simulated by a revised single bubble model, in which the volatile releasing rate and yield by residence time can be obtained from the CPD (chemical percolation devolatilization) model. Results show that the revised single bubble model is suitable for predicting the char evolution over a wide range of pressure and heating rate. Optimum pressure is present in the range of 7–15 atm, where the swelling ratio and porosity reach the maximum value. This model can predict the two regimes of coal swelling in varied heating rates, which is more obvious at high pressure. The porosity development by time can also be output, and the variation trends are similar to the swelling ratio.

High heat transfer performance of foam freezing in phase change cold energy storage process

Phase change material (PCM) has high energy storage density, but the cold energy charging rate of PCM decreases seriously with the increase of frozen thickness. The foam freezing produced by cold air flow can sharply increase the freezing rate. This research attempts to establish a theoretical model to quantify the heat transfer performance of foam freezing. The internal structure of the foam was obtained by experiment. The heat transfer process of single bubble was simulated by FLUENT, and analytical models for single bubble and foam were established. It was found that the tangent bubble array had the same heat transfer effect as the actual foam in freezing, and the bubble temperature variation obeyed the exponential distribution. The radius of more than 50% bubbles was about 2.5 mm, and the convective heat transfer coefficient in the bubble was 65 W/(m2. K). The maximum completed heat transfer rate of foam freezing was 688 kW/m3, when the air temperature was -20 °C. Foam freezing was compared with common ice storage structures, and was found had an order of magnitude higher than those structures in the heat transfer coefficient of unit volume.

MULTIPHASE DRILLING KICK ANNULAR FLOW BEHAVIOUR IN VERTICAL AND INCLINED WELL PROFILES

One of the exponentially important drilling parameter has many misconceptions, and prompt confusion is the drilling kick. The current conventional approach assume a single-phase bubble model and neglect the multiphase flow in the drilling kick calculations, which lead to diversified solutions and misconceptions in well design. Hence, this study presents a mathematical model to analyse the behaviour of gas-liquid flow in different well profiles, which are vertical and deviated wells up to 60 degree inclination. The model analysed the annular pressure and temperature profiles as the influx rise to the surface. The methodology constructed to achieve the objective involve an iterative mathematical model to calculate pressure drop across the wellbore and temperature gradient for single-phase and multiphase flow models, indicating the type of flow regimes at each depth. The results show the impact of the selected parameters on the pressure and temperature generated, which eventually influence the drilling kick calculations. The annulus pressure increases 44.37% from multiphase vertical well annulus pressure to single-phase annulus pressure, and the pressureincrement is higher in highly deviated well profile. It is important to precisely and accurately estimate the gas void fraction since it influences all two-phase flow parameters such as pressure drop, mixture density, and gas velocity in the annulus. The pressure and temperature profile then developed into a model which incorporates the drilling kick concept. Apart from that, the Z deviation factor which indicates the gas solubility was also studied and included in the simulation.Keywords: Annular flow, flow regime, multiphase drilling kick, vertical well, inclined well

Comparison of Boundary Integral and Volume-of-Fluid methods for compressible bubble dynamics

The Boundary Integral Method (BIM) has been widely applied to simulate oscillating bubbles, for its high efficiency and accuracy. A conventional BIM assumes the fluid surrounding the bubble to be inviscid and incompressible. Wang & Blake (J. Fluid Mech., 659, 2010, 191–224) proposed an improved model for bubbles in a weakly compressible flow, which is referred to as CBIM. In this study, an all-Mach method (AMM) implemented in the free software program Basilisk for the simulation of compressible multiphase flows, and using a geometric Volume-of-Fluid (VoF), is employed to study and estimate the accuracy of BIM and CBIM at different Mach numbers. First, for a spherical bubble, an extended Rayleigh-Plesset equation, CBIM and AMM give very close results when Ma≲0.3. However, a deviation between these three schemes gradually becomes evident as Ma increases from 0.3 to 0.6. Second, for the nonspherical deformation of a bubble close to a wall, the results obtained from CBIM and AMM show many similarities, including the evolution of the nonspherical bubble morphology, jet impact velocity, and impact pressure on the wall. Apart from the liquid compressibility, the gas inertia/density is found to be another factor that may affect the applicability of CBIM. In addition, we compare the CBIM and BIM results against an experiment of a spark-generated cavitation bubble, in which the liquid compressibility is found to play a vital role. From the perspective of engineering applications, BIM can reproduce the main features of the bubble dynamics in the first cycle if the initial conditions are set properly. The new findings provide a reference for research of bubble dynamics in both fundamental and applied problems.

Evaluation of models for bubble-induced turbulence by DNS and utilization in two-fluid model computations of an industrial pilot-scale bubble column

This paper presents numerical studies on modeling of bubble induced turbulence at two significantly different scales. On the scale of a bubble swarm, direct numerical simulations are performed with a geometric volume-of-fluid method and the budget equation of liquid phase turbulence kinetic energy is analyzed. By a priori testing of models for the interfacial term in this equation, suitable closure relations are identified. On the scale of an industrial bubble column, simulations with a two-fluid model are performed with water and cumene as liquid phases under elevated pressures. Turbulence is taken into account by a mixture k–ε model, considering two closure relations for the interfacial term identified from the DNS. For both liquids, an influence of the model for the interfacial term on turbulence kinetic energy and gas holdup is found, which is, however, small at elevated pressures. Numerical results for local and overall gas holdup are in reasonable agreement with measurements reported for this industrial pilot-scale bubble column. For the overall gas holdup, an empirical correlation from literature is identified which predicts the present numerical results reasonably well.

Predictions of terminal rising velocity, shape and drag coefficient for particle-laden bubbles

The motion of particle-laden bubbles is common in the gas–liquid-solid three-phase process like flotation. In this study, the motion of particle-laden bubbles in the stagnant deionized water was obtained by high-speed dynamic imaging. The experimental ranges of the mean bubble diameter and particle diameter were 2.76–3.95 mm and 58.2–196.35 μm, respectively. Results show that the terminal rising velocity decreases with the increase in the diameter of covering particles and the decrease in bubble diameter. For the coverage below 50%, the terminal rising velocity decreases sharply as coverage increases; while for 50% to nearly 100%, decreases slowly. The sharp decrease is mainly because particles immobilize the bubble surface and increases the drag, which is similar to the effect of contaminants in liquid on bubble motion. When the coverage exceeding 50%, the interface mobility of particle-laden bubbles is completely retarded. The slow decrease is attributed to the decreasing net buoyancy caused by decreasing density difference between water and the particle-laden bubble. Based on the impact of particle coverage on bubble behavior, the measured data were compared with predictions by the available models of the terminal rising velocity and drag coefficient for the bare bubble in the contaminated liquid. Comparison results show that the terminal rising velocity model given by Zheng et al. (2020) and the drag coefficient model given by Wang et al. (2019) can be extended to particle-laden bubbles with a mean error of 4.8% and 0.6%, respectively. The aspect ratio of particle-laden bubbles is negatively correlated to the terminal rising velocity like that of bare bubbles. A new aspect ratio prediction model for particle-laden bubbles related to the ratio between coverage and the Eo number was introduced to facilitate direct prediction of the terminal rising velocity. The comprehensive prediction models of particle-laden bubbles behaviors given in this study are helpful for the design and optimization of equipment that contains bubble-particle aggregates.

Toward Mechanistic Wall Heat Flux Partitioning Model for Fully Developed Nucleate Boiling

Abstract Mechanistic models developed to predict partial nucleate boiling are not adequate for fully developed nucleate boiling due to differences in the prevailing heat transfer governing mechanisms. In place of the mechanistic model, several empirical correlations and semimechanistic models have been proposed over the years for the prediction of fully developed nucleate boiling as presented in this study but they are unsuitable for use in computational fluid dynamics (CFD) code. Recently, the simulation of fully developed nucleate boiling has become much more practical because of advancement in a computational method that involves the coupling of the interface capturing method (for slug bubbles) with the Eulerian multifluid model (for dispersed spherical bubbles). Nonetheless, there is a need for a mechanistic closure law for the fully developed nucleate boiling phenomenon that would complement this advancement in CFD. Toward this end, a mechanistic wall heat flux partitioning model for fully developed nucleate boiling is proposed in this study. This model is predicated on the hypothesis that a high heat flux nucleate boiling is distinguished by the existence of a liquid macrolayer between the heated wall and the slug or elongated bubbles, and that the macrolayer is interspersed with numerous high frequency nucleate small bubbles. With this hypothesis, the heat flux generated on the heated wall is partitioned into two parts: conduction heat transfer across the macrolayer liquid film thickness and evaporation heat flux of the microlayer of the nucleating small bubbles. The proposed model is validated against experimental data.

{mathcal {U}}-Bubble Model for Mixed Unit Interval Graphs and Its Applications: The MaxCut Problem Revisited

Interval graphs, intersection graphs of segments on a real line (intervals), play a key role in the study of algorithms and special structural properties. Unit interval graphs, their proper subclass, where each interval has a unit length, has also been extensively studied. We study mixed unit interval graphs—a generalization of unit interval graphs where each interval has still a unit length, but intervals of more than one type (open, closed, semi-closed) are allowed. This small modification captures a richer class of graphs. In particular, mixed unit interval graphs may contain a claw as an induced subgraph, as opposed to unit interval graphs. Heggernes, Meister, and Papadopoulos defined a representation of unit interval graphs called the bubble model which turned out to be useful in algorithm design. We extend this model to the class of mixed unit interval graphs and demonstrate the advantages of this generalized model by providing a subexponential-time algorithm for solving the MaxCut problem on mixed unit interval graphs. In addition, we derive a polynomial-time algorithm for certain subclasses of mixed unit interval graphs. We point out a substantial mistake in the proof of the polynomiality of the MaxCut problem on unit interval graphs by Boyacı et al. (Inf Process Lett 121:29–33, 2017. https://doi.org/10.1016/j.ipl.2017.01.007). Hence, the time complexity of this problem on unit interval graphs remains open. We further provide a better algorithmic upper-bound on the clique-width of mixed unit interval graphs.

Numerical investigation of non-condensable gas effect on vapor bubble collapse

We numerically investigate the effect of non-condensable gas inside a vapor bubble on bubble dynamics, collapse pressure, and pressure impact of spherical and aspherical bubble collapses. Free gas inside a vapor bubble has a damping effect that can weaken the pressure wave and enhance the bubble rebound. To estimate this effect numerically, we derive and validate a multi-component model for vapor bubbles containing gas. For the cavitating liquid and the non-condensable gas, we employ a homogeneous mixture model with a coupled equation of state for all components. The cavitation model for the cavitating liquid is a barotropic thermodynamic equilibrium model. Compressibility of all phases is considered in order to capture the shock wave of the bubble collapse. After validating the model with an analytical energy partitioning model, simulations of collapsing wall-attached bubbles with different stand-off distances are performed. The effect of the non-condensable gas on rebound and damping of the emitted shock wave is well captured.