Initial Void Fraction Research Articles

Ductile fracture prediction of additively manufactured Ti-6Al-4 V alloy based on void growth and coalescence of a unit-cell model

In this work, we have studied the fracture mechanism and proposed a micromechanical method with a unit cell model to predict the ductile fracture of additively manufactured (AMed) Ti-6Al-4 V alloy. The tensile experiments with smooth round bars and notched round bars were conducted to investigate the mechanical properties and ductile fracture behavior of materials. The proposed unit-cell model was validated by quasi-static tensile fracture tests to predict the ductile failure of titanium alloy manufactured by laser power bed fusion (L-PBF) under different stress states, which include a wide range of stress triaxialities. An equivalent initial void fraction was introduced to evaluate the ductile behavior of the titanium alloy. Our investigation shows that the stress states significantly influence the void coalescence behavior of AMed Ti-6Al-4 V alloy, and the fracture locus of L-PBF fabricated Ti-6Al-4 V alloy under different stress states was successfully predicted by the proposed unit-cell model under proportional loading. Our study provides useful guidance for the future design and application of metal materials for additive manufacturing.

Numerical simulation of gas-liquid two-phase flow in a disc pump under different inlet bubble diameters

Visual investigation and numerical simulation were utilized to analyze the internal flow pattern transformation and bubble diameter variation of a gas-liquid two-phase flow disc pump. The results reveal that increasing the intake volume fraction (IGVF) from 1.12% to 27.67% changes the flow pattern in the suction chamber from bubbly to agglomerate bubbly, slug flow, and separated flow. Due to the particularity of the impeller structure of the disc pump, the blades in the leaf area of the front and rear cover plates play a barrier role. The gas phase gathers most violently at the edge of the blade in the leaf area, while the flow channel in the middle leafless area is wider and has higher permeability. At 1500r/min and 7.11% inlet volume void fraction, the local void fraction extreme value of the front edge of the blade in the blade area of the front cover plate increases to three times the initial void fraction, while the void fraction extreme value of the middle section of the bladeless area decreases to two-thirds of the initial void fraction. This research can be used to analyze the gas phase distribution and migration law in the disc pump impeller.

Weakly nonlinear propagation of pressure waves in bubbly liquids with a polydispersity based on two-fluid model equations

Herein, the weak, nonlinear propagation of pressure waves in an initially quiescent liquid containing many small spherical gas bubbles is theoretically studied. We focus on the initial, polydispersity features of the bubble radius and bubble number density. Our analysis was not based on any assumptions about explicit polydispersity forms. Using equations based on a two-fluid model and the method of multiple scales with perturbation expansions, the Korteweg–de Vries–Burgers equation for a low-frequency long wave and nonlinear Schrödinger equation for a high-frequency short wave were derived. In both cases, the polydispersity contributes to the advection and dissipation effects of waves, and every coefficient in both equations includes the initial void fraction as one of the most important parameters, owing to the use of the two-fluid model.

Assessment of Irregular Biomass Particles Fluidization in Bubbling Fluidized Beds

Biomass as a clean and renewable source of energy has immense potential to aid in solving the energy crisis in the world. In order to accurately predict the fluidization behavior of biomass particles using the Eulerian–Eulerian approach and the kinetic theory for granular flows (KTGF), employing appropriate models that adapt to irregularly shaped particles and can precisely predict the interaction between particles is crucial. In this study, the effects of varying radial distribution functions (RDF), frictional viscosity models (FVM), angles of internal friction (ϕ), and stress blending functions (SBF) on the performance of two-fluid models (TFM) were investigated. Simulation predictions were compared and validated with the previous experiments in the literature on Geldart B biomass particles of walnut shells. When applying sphericity to account for size irregularities of biomass particles, the results of this study demonstrated that predictions of both the Ma–Ahmadi and the Carnahan–Starling RDFs along with the Schaeffer FVM agree with experimental data. More specifically, the bubbling behavior prediction slightly favored the use of the Ma–Ahmadi RDF for biomass particles. The results also revealed the importance of using FVM regardless of the initial void fraction. The use of the Schaeffer FVM became more important as time proceeded and particle bulk density decreased. With the change of ϕ and the application of SBF, no significant differences in the time-averaged results were observed. However, when ϕ ranges were between 30 and 40, the predictions of bubbling behavior became more greatly aligned with experimental results.

Investigation on multi-physical field simulations of blade ECM using vertical flow

Electrochemical machining (ECM), an advanced manufacturing technology, is widely used in aero-engine blades machining. In traditional ECM, the electrolyte flows through the inter-electrode gap (IEG), generating hydrogen bubbles and heat, which affect the conductance and thus influence the machining quality. This paper focuses on the effect of bubble movement on the flow field and the machining quality of ECM. A novel vertical flow mode of electrolyte is proposed according to the bubbles dynamics analysis. Multi-physical fields simulations of blade ECM using vertical and horizontal flows were carried out. With an initial gas void fraction, flow rate, and temperature at the inlet of 0, 19.7 m/s, and 302.65 K, respectively, in both flow modes, the vertical flow reduces the gas void fraction, flow rate, and temperature at the outlet by 2.4%, 0.4 m/s, and 0.6 K, and increases the conductance by 0.47 S/m. Thus, the vertical flow of the electrolyte is beneficial in reducing the gas void fraction and controlling the temperature rise, while enhancing the conductance. Then, the corresponding experiments using a vertical flow were carried out. The maximum machining deviation ranges from 3.4 to 75.6 μm and surface roughness Ra < 0.35 μm. The machining quality is high and the variation observed in the experiments is consistent with the simulation results, the validity and correctness of the simulations are verified. Thus, the vertical flow mode proposed in this paper is appropriate, can be used for other complex structures in ECM.

Contribution of initial bubble radius distribution to weakly nonlinear waves with a long wavelength in bubbly liquids

In this study, the weakly nonlinear propagation of plane progressive pressure waves in an initially quiescent liquid was theoretically investigated. This liquid contains several small uniformly distributed spherical polydisperse gas bubbles. The polydispersity considered here represents various types of initial bubble radii, and the liquid contains multiple bubbles, each with an initial radius. Using the method of multiple scales, we first derived the Korteweg–de Vries–Burgers (KdVB) equation with a correction term as a nonlinear wave equation. This equation describes the long-range wave propagation with weak nonlinearity, low frequency, and long wavelength in the polydisperse bubbly liquid using the basic equations in a two-fluid model. The utilization of the two-fluid model incorporates the dependence of an initial void fraction on each coefficient in the nonlinear, dissipation, and dispersion terms in the KdVB equation. Furthermore, unlike previous studies on waves in polydisperse bubbly liquids, we achieved the formulation without assuming an explicit form of the polydispersity function. Consequently, we discovered the contribution of polydispersity to the various effects of wave propagation, that is, the nonlinear, dissipation, and dispersion effects. In particular, the dispersion effect of the waves was found to be strongly influenced by polydispersity.

Effect of suction process on the growth of a convective gas bubble in diver’s tissues

The motivation of this research is to study the effect of suction process on a growing gas bubble and concentration distribution around this bubble in tissues of divers who surface too quickly. The effect of bubble motion is also considered. The method of combined variables is used to solve the problem by combining the radial and time variables into one variable by using a suitable similarity transformation that enables to divide the diffusion equation into two ODEs, the first concerns to concentration distribution and the other concerns to the bubble radius evolution. The resultant formulae are valid for both growth stages whenever the ambient pressure is variable at ascending of the diver, or constant as the diving stops or at sea-level. The effects of physical parameters are discussed when applying suction process and show that the dominant parameter is the initial void fraction. The research findings reveal the role of suction process to activate the systemic blood circulation and delay the growth of gas bubbles in the tissues and reduce the incidence of decompression illness (DCI). This research also provides evidence and agrees with the previous experimental studies to support the use of suction therapy to reduce the DCI harmful effects.

Modeling acoustic cavitation with inhomogeneous polydisperse bubble population on a large scale

A model for acoustic cavitation flows able to depict large geometries and time scales is proposed. It is based on the Euler–Lagrange approach incorporating a novel Helmholtz solver with a non-linear acoustic attenuation model. The method is able to depict a polydisperse bubble population, which may vary locally. The model is verified and analyzed in a setup with a large sonotrode. Influences of the initial void fraction and the population type are studied. The results show that the velocity is strongly influenced by these parameters. Furthermore, the largest bubbles determine the highest pressure amplitude reached in the domain, which corresponds to the Blake threshold of these bubbles. Additionally, a validation is performed with a small sonotrode. The model reproduces most of the experimentally observed phenomena. In the experiments, neighboring bubbles are found which move in different directions depending on their size. The numerical results show that the responsible mechanism here is the reversal of the primary Bjerknes force at a certain pressure amplitude.

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.

GTN Damage Modelling of the AA6063 Using Image Processing

In this paper, an innovative way of calculating the Gurson–Tvergaard–Needleman parameter has been developed for AA 6063. AA 6063 is an aluminum alloy comprising the alloying ingredients magnesium and silicon. The Aluminum Association maintains the standard that governs its composition. It has strong mechanical properties and may be heat treated and welded. Image processing technique has been used to calculate the damage constant for the AA 6063. The image of the sample has been taken under a microscope of undeformed and fractured material. Then the images are analyzed using the Open CV tool in a python open-source environment. The initial and final void fraction of the sheet has been calculated. Damage models, particularly the Gurson–Tvergaard–Needleman (GTN) model, are widely used in numerical simulation of material deformations. Each damage model has some constants which must be identified for each material. The direct identification methods are costly and time-consuming. A combination of experimental, numerical simulation and optimization have been used to determine the constants in the current work. Numerical simulation of the dynamic test was performed utilizing the constants obtained from quasi-static experiments. The results showed a high precision in predicting the specimen's profile in the dynamic testing.

Thermophysical bubble dynamics in N-dimensional Al2O3/H2O nanofluid between two-phase turbulent flow

The purpose of this work is to apply a new method for the growth behavior of bubble dynamics in N-dimensional turbulent Al2O3/H2O-nanofluid for bubble dynamics applications in polymers and climate change models under the influence of surface tension and viscosity. This paper also investigates the factors affecting the dynamics of vapor bubble growth in N-dimensions for turbulent nanofluid. The turbulent flow of the nanofluid in N-dimensions in this study is examined at Re ranging from 3000 to 5000, and concentration from 4 to 6%. The theoretical analysis is conducted using the MPZ technique considering the initial time of bubble growth. The obtained results reveals that the radius of the bubble is proportional to the thermal diffusivity and inversely proportional to the surface tension, viscosity, critical bubble radius, concentration rate of Al2O3-nanoparticles, and initial void fraction. We also found that the growth of the vapor bubble in a nanofluid turbulent flow is less than that of the Newtonian fluid. To the best of our knowledge, the efficient utilization of N-dimensional turbulent Al2O3 nanoparticles in bubble dynamics leads to more reduction for bubble growth process than other previous models. Additionally, the stability analysis is examined via phase plane algorithm with nonlinear ODEs.

Numerical Study on Weakly Nonlinear Evolution of Pressure Waves in Water Flows Containing Many Translational Bubbles Acting a Drag Force

Weakly nonlinear (i.e., finite but small amplitude) propagation of plane progressive pressure waves in compressible water flow uniformly containing many spherical gas bubbles is numerically investigated with a special attention to a drag force acting bubbles and translation of bubbles. The gas and liquid phases are flowing with initially independent velocities. Drag force and virtual mass force are introduced as interfacial momentum transports. Translation and spherically symmetric oscillations are considered as bubble dynamics. In this paper, under these assumptions, we numerically solve the KdVB (Korteweg-de Vries-Burgers) equation previously derived by ourselves (Yatabe et al., Phys. Fluids, 33 (2021), 033315) from basic equations based on a two-fluid model. The main results are summarized as follows: (i) The drag force acting on bubbles increases a dissipation effect of waves and drastically changes the phase and amplitude of waves. (ii) Although the translation of bubbles increases the nonlinear effect of waves, its contribution to waveform is quantitatively small. (iii) The effect of the drag force decreases with decreasing the initial void fraction and with increasing the initial bubble radius. That of the translation decreases with decreasing the initial void fraction, and is almost independent of the initial bubble radius. (iv) The spatiotemporal evolution of two type of dissipation effects (i.e., dissipation terms) due to the acoustic radiation and to the drag force is different tendency.

An exhaustive theoretical analysis of thermal effect inside bubbles for weakly nonlinear pressure waves in bubbly liquids

Weakly nonlinear propagation of pressure waves in initially quiescent compressible liquids uniformly containing many spherical microbubbles is theoretically studied based on the derivation of the Korteweg–de Vries–Burgers (KdVB) equation. In particular, the energy equation at the bubble–liquid interface [Prosperetti, J. Fluid Mech. 222, 587 (1991)] and the effective polytropic exponent are introduced into our model [Kanagawa et al., J. Fluid Sci. Technol. 6, 838 (2011)] to clarify the influence of thermal effect inside the bubbles on wave dissipation. Thermal conduction is investigated in detail using some temperature-gradient models. The main results are summarized as follows: (i) Two types of dissipation terms appeared; one was a well-known second-order derivative comprising the effect of viscosity and liquid compressibility (acoustic radiation) and the other was a newly discovered term without differentiation comprising the effect of thermal conduction. (ii) The coefficients of the KdVB equation depended more on the initial bubble radius rather than on the initial void fraction. (iii) The thermal effect contributed to not only the dissipation effect but also to the nonlinear effect, and nonlinearity increased compared with that observed by Kanagawa et al. (2011). (iv) There were no significant differences among the four temperature-gradient models for milliscale bubbles. However, thermal dissipation increased in the four models for microscale bubbles. (v) The thermal dissipation effect observed in this study was comparable with that in a KdVB equation derived by Prosperetti (1991), although the forms of dissipation terms describing the effect of thermal conduction differed. (vi) The thermal dissipation effect was significantly larger than the dissipation effect due to viscosity and compressibility.

Vapour bubble growth within a viscous mixture non-Newtonian fluid between two-phase turbulent flow

ABSTRACT We present the theoretical study and mathematical modelling of vapour bubble growth in a non-Newtonian fluid, viscous, superheated liquid for the turbulent flow. The mathematical model is formulated and solved analytically by using the continuity equation, momentum equation and heat equation. The initial time of bubble growth is taken into account. The radius of bubble is proportional to some physical parameters, such as the thermal diffusivity, superheating liquid, Peclet number and initial void fraction, while it is inversely proportional to the surface tension and the dynamic of viscosity. Results indicated that the growth of bubble in the case of constant viscosity is greater than in the case of variable viscosity, and also the growth of bubble in a non-Newtonian fluid for turbulent flow is lower than in the Newtonian fluid for turbulent flow.

Comparing the formation and propagation features of subcritical and supercritical thermal detonation waves

During a severe accident in a nuclear reactor, an ex-vessel steam explosion may occur when the molten core come into contact with the liquid coolant, the crucial factor in the fuel-coolant interaction is the fragmentation of melt into small droplets, which rapidly increase the heat transfer to the coolant, and could lead to a steam explosion and formation of a pressure wave with a disastrous consequence for the surrounding components. In this research a numerical simulation of a steam explosion was performed using the VAPEX-D code which is being developed at the Department of NPP in “Moscow Power Engineering Institute” for the simulation of fuel-coolant interactions. Using the microinteractions concept, the propagation of thermal detonation waves was studied, and the characteristics of subcritical and supercritical waves were compared. A sharp increase in pressure is noted during the transition from subcritical mode to supercritical mode of propagation. A parametric study was performed where the volume fraction of corium was varied to determine the critical value at which the thermal detonation wave decayed. The study shows that increasing the melt volume fraction, will increase the maximum pressure and the velocity of the thermal detonation wave. While varying the initial void fraction showed that the thermal detonation wave can propagate in a very low melt volume fraction.

Numerical study on evolution of weakly nonlinear waves into an acoustic soliton in bubbly water

Finite but small amplitude (i.e., weakly nonlinear) propagation of pressure (or acoustic) waves in an initially quiescent water uniformly containing many spherical microbubbles is numerically studied. Especially, an effective equation for the case of low frequency long wave is the Korteweg–de Vries–Burgers (KdVB) equation, which consists of the nonlinear, dissipation, and dispersion terms. Two major solutions of KdVB equation are a shock wave (i.e., dissipative case) and a soliton (i.e., dispersive case). The purpose of this study is the elucidation of spatio-temporal evolution of these three terms (not coefficients) and that of resultant waveforms. The results are summarized as follows: (a) a solitary pulse waves were formed by the nonlinear and dispersion terms and well-known nonlinear interaction was observed; (b) the number of formed solitons was dependent on the initial waveform such as Gaussian, shock, and rectangular waveforms; (c) the number of formed solitons was strongly dependent on the initial void fraction.

Weakly nonlinear theory and numerics on pressure wave propagation in a flowing water containing many translational bubbles acting a drag force

Focusing on the effect of translational motion of bubbles and drag force acting bubbles, we theotetically and numerically tackle weakly nonlinear propagation of plane progressive pressure waves in a compressible water flow uniformly containing a number of spherical gas bubbles. At an initial state, gas and liquid phases are flowing with each velocity. Drag force and virtual mass force are introduced in an interfacial transport across the bubble–liquid interface. As bubble dynamics, translation and spherically symmetric oscillation are considered. The bubbles do not coalesce, break up, disappear, and appear. The gas viscosity, the thermal conductivities of the gas and liquid are discarded. From the singular perturbation analysis up to the second order of approximation, we have two types of Korteweg–de Vries–Burgers (KdVB) equation with a newly introduced term without a differentiation due to the drag force from the basic equations for bubbly flows in a two-fluid model; the drag term is classified into the linear and nonlinear terms. The translation affects the nonlinear effect of waves and the drag force affects the dissipation effect of waves. We finally numerically solve the KdVB equation to compare three dissipation factors, i.e., acoustic radiation damping due to the liquid compressibility, liquid viscosity, and drag force for various initial void fraction and bubble radius.

Numerical analysis of the effect of bubble distribution on multiple-bubble behavior.

Understanding multiple-bubble behavior in a megasonic field is essential for efficient megasonic nanodevice cleaning without pattern damage. In this study, we numerically studied the effects of equilibrium radius and initial void fraction on multiple-bubble behavior and induced pressure. We analyzed the nonspherical collapse, coalescence, and breakup of bubbles in a megasonic field using a compressible, locally homogeneous model of a gas-liquid two-phase medium. Bubbles were simulated with a uniform equilibrium radius or with a bubble size distribution. Our results indicate that the bubble behavior and induced pressure depended mainly on the initial void fraction. For the case of bubbles with uniform equilibrium radius, small bubbles generated high wall pressure at large initial void fractions. When there was a size distribution, bubbles with small equilibrium radii contributed little to the wall pressure because of the damping effect of the oscillation of larger bubbles. Furthermore, the addition of a large bubble suppressed the resonant behavior of the bubbles that induced high wall pressure.

Numerical study on formation of an acoustic soliton in bubbly liquids based on weakly nonlinear wave equation

Oscillation of microbubbles in bubbly liquids induces a dispersion effect of waves into weakly nonlinear pressure waves, and its propagation process is described by a KdV-Burgers (KdVB) equation for a long wave case. We numerically predict an evolution of waveform by solving the KdVB equation derived by Kanagawa et al. (2010, 2011) via a finite difference method. As a result, (i) an initial Gaussian waveform is distorted due to a nonlinear effect, and a steepening of waveform is observed on about 20 000 period; (ii) the dispersion effect is observed at a steep part of waveform, and its part becomes sharp as the initial void fraction increases; (iii) the initial waveform change into an attenuated soliton on about 100 000 period due to a dissipation effect, and the attenuation of soliton is noteworthy as the initial void fraction decreases; (iv) balance of the nonlinear, dispersion, and dissipation effects thereby forms an attenuated soliton, and its amplitude strongly depends on the value of the initial void fraction. Furthermore, the period of soliton formation depends on the type of initial waveform. Although the nonlinear, dissipation, and dispersion effects were qualitatively balanced in the KdVB equation, we conclude that these effects independently appear in the sound field.

Research on dynamical overflow characteristics of a vertical H2S‐containing natural gas well

AbstractThis work aims to explore the overflow characteristics of a vertical H2S‐containing natural gas well. A two‐phase flow model for H2S‐containing natural gas well combining with a transient temperature prediction model was established to simulate the overflow process of a vertical H2S‐containing natural gas well. The model was validated by reproducing the field data of Well Longhui #2. The effects of H2S content, mud displacement, drilling fluid density, geothermal gradient, and reservoir permeability on the overflow characteristics of a vertical H2S‐containing natural gas well were studied and analyzed in this work. Results indicate that bubble, slug, and churn flows constitute the main flow patterns in the whole overflow process. The higher the H2S content is, the more obviously the gas void fraction increases. The phase change position of H2S is closer to the wellhead at lower H2S content. An increase in mud displacement indicates the decreases in overflow time. As drilling fluid density increases, the release position of H2S moves up, and the overflow time and shut‐in casing pressure increase. The initial gas void fraction is higher and the gas invasion volume will be larger in gas reservoirs with higher permeability. As the reservoir permeability increases, the shut‐in casing pressure rises while the overflow time declines. With higher geothermal gradient, the wellbore temperature tends to be higher at the same depth, leading to an increase in the H2S solubility. The gasification starting position is further away from the wellhead at higher geothermal gradient. The results of this work could provide important theoretical basis and technical guidance for drilling engineers to reduce a blowout risk during drilling of H2S‐containing natural gas well.