The measurement of void waves in bubbly two-phase flows

The propagation of void fraction disturbances (i.e. void waves) in bubbly two-phase air-oil flow was investigated experimentally.The void wave data often showed two simultaneous void wave propagations; in particular, the classical kinematic void wave and a faster void wave propagation associated with bubble clusters. Significantly, the bubbly-to-slug flow regime transition was found to be associated with amplification of the void waves associated with the propagating bubble clusters.These data should be valuable for the assessment of the closure laws used in two-fluid models and for the development of mechanistic models for the bubbly-slug flow regime transition.     

Interaction forces model on a bubble growing for nuclear best estimate computer codes

This paper presents a mathematical model that takes into account the bubble radius variation that take place in a boiling water nuclear reactor during transients with changes in the pressure vessel, changes in the inlet core mass flow rate, density-wave phenomena or flow regime instability. The model with expansion effects was developed considering the interaction force between a dilute dispersion of gas bubbles and a continuous liquid phase. The closure relationships were formulated as an associated problem with the spatial deviation around averaging variables as a function of known variables. In order to solve the closure problem, a geometric model given by an eccentric unit cell was applied as an approach of heterogeneous structure of the two-phase flow. The closure relationship includes additional terms that represent combined effects between translation and pulsation due to displacement and size variation of the bubbles, respectively. This result can be implanted straightforward in best estimate thermo-hydraulics models. An example, the implementation of the closure relationships into TRAC best estimate computer code is presented.     

Experimental and numerical studies of void fraction distribution in rectangular bubble columns

Bubbly flow is encountered in a wide variety of industrial applications ranging from flows in nuclear reactors to process flows in chemical reactors. The presence of a second phase, recirculating flow, instabilities of the gas plume and turbulence, complicate the hydrodynamics of bubble column reactors.This paper describes experimental and numerical results obtained in a rectangular bubble column 0.1 m wide and 0.02 m in depth. The bubble column was operated in the dispersed bubbly flow regime with gas superficial velocities up to 0.02 m/s. Images obtained from a high speed camera were used to observe the general flow pattern and have been processed to calculate bubble velocities, bubble turbulence parameters and bubble size distributions. Gas disengagement technique was used to obtain the volume averaged gas fraction over a range of superficial gas velocities. A wire mesh sensor was applied, to measure the local volume fraction at two different height positions. Numerical calculations were performed with an Eulerian–Eulerian two-fluid model approach using the commercial code CFX.The paper details the effect of various two-fluid model interfacial momentum transfer terms on the numerical results. The inclusion of a lift force was found to be necessary to obtain a global circulation pattern and local void distribution that was consistent with the experimental measurements. The nature of the drag force formulation was found to have significant effect on the quantitative volume averaged void fraction predictions.     

The inhomogeneous MUSIG model for the simulation of polydispersed flows

A generalized inhomogeneous multiple size group (MUSIG) model based on the Eulerian modeling framework was developed in close cooperation of ANSYS-CFX and Forschungszentrum Dresden-Rossendorf and implemented into the CFD code CFX. The model enables the subdivision of the dispersed phase into a number of size groups regarding the mass balance as well as regarding the momentum balance.

In this work, the special case of polydispersed bubbly flow is considered. By simulating such flows, the mass exchanged between bubble size classes by bubble coalescence and bubble fragmentation, as well as the momentum transfer between the bubbles and the surrounding liquid due to bubble size dependent interfacial forces have to be considered. Particularly the lift force has been proven to play an important role in establishing a certain bubble size distribution dependent flow regime.

In a previous study [Krepper, E., Lucas, D., Prasser, H.-M., 2005. On the modeling of bubbly flow in vertical pipes. Nucl. Eng. Des. 235, 597–611] the application of such effects were considered and justified and a general outline of such a model concept was given. In this paper the model and its validation for several vertical pipe flow situations is presented. The experimental data were obtained from the TOPFLOW test facility at the Forschungszentrum Dresden-Rossendorf (FZD). The wire-mesh technology measuring local gas volume fractions, bubble size distributions and velocities of gas and liquid phases were employed.

The inhomogeneous MUSIG model approach was shown as capable of describing bubbly flows with higher gas content. Particularly the separation phenomenon of small and large bubbles is well described. This separation has been proven as a key phenomenon in the establishment of the corresponding flow regime. Weaknesses in this approach can be attributed to the characterization of bubble coalescence and bubble fragmentation, which must be further investigated.     

外加扰动下垂直管内气-液两相流空隙波特性

采用双环电导探针技术实验研究了外加扰动对垂直上升管内气-液两相流空隙波特征的影响。研究结果表明,气-液两相流空隙波对外加周期性扰动具有频率选择性。在泡状流区,低频扰动能诱发与扰动等频的空隙波;在泡状流／弹状流转变区,低频扰动能加速气泡合并,促进泡状流向弹状流转变;而在弹状流区空隙波特征对外界扰动并不敏感。空隙波的传播速度受外界扰动频率的影响,随着扰动频率的增大,空隙波波速先减少又增大。本文的实验研究发现,存在对气-液两相流空隙波特征影响最为显著的临界扰动频率,在本实验条件和参数范围内,该临界扰动频率为20Hz。     

Propagation of Pressure Wave in Air-Water Two-Phase System, (I)

In an attempt to gain information on the propagation characteristics of pressure waves in a two-phase system consisting of gas and liquid, experiments were performed on a nonflowing air-water mixture in a range of pressures from 1.0 to 7.5 bar and void fractions from 0 to 60%. Stepwise pressure disturbancies were applied to a water column dispersed with rising air bubbles by bursting diaphragm. The pressure transients at several points down the fluid column were measured with strain gage type pressure transducers and recorded on magnetic tapes.

The nonlinearity of the pressure wave records was scarcely marked. The propagation velocity of pressure wave front down the fluid column was found almost independent of the magnitude of the pressure change applied, nor whether it was depressive or compressive. At higher void fractions where the flow regime became sluggy, the measured propagation velocities showed increasing deviation from the calculated values based on the nonslip homogeneous adiabatic model, though good agreements were obtained at lower void fractions of bubbly regime. Evidence was offered in disproof of the effect of heterogeneity due to slug regime as the preliminary step to attribute this discrepancy to the effect of slip in Part (II).     

Numerical simulation of cloud rise phenomena associated with nuclear bursts

We present numerical simulations of cloud evolution from nuclear explosions using high-resolution numerical methods. Our numerical approach includes a fluid mechanical model that is a combination of a compressible code (GEODYN) and a low Mach code (LMC). Early stages of nuclear explosions that are characterized by the blust wave propagation are simulated with an explicit code (GEODYN) that solves the compressible Navier–Stokes equations via a high-order Godunov scheme. As soon as the blust wave weakens (≈10 s) the subsequent cloud rise due to buoyancy forces can be effectively simulated by the LMC code. LMC is an implicit code based on a pressure projection technique, and derived from the compressible Navier–Stokes equations using an asymptotic analysis in Mach number. It analytically eliminates time step restrictions based on sound wave propagation and it is computationally efficient and accurate for simulations of cloud rise dynamics at later stages. We perform a series of cloud rise scenarios ranging from an idealized bubble rise problem to realistic air bursts. We analyze effects of compressible dynamics on cloud evolution at different stages. It is found that in a realistic configuration, interaction of the reflected shock wave from the ground with the fireball significantly affects cloud evolution, in contrast to the equivalent idealized bubble rise simulations. We validate the code predictions against available experimental data. It is demonstrated that, by providing the initial source from the compressible GEODYN code, late time flow evolution can be successfully simulated with the fast, efficient and accurate LMC code.     

Impact of gas in sodium flow on the temperature variation in an LMFBR rod bundle

The impact of gas in sodium flow on the temperature variation in an LMFBR rod bundle was studied in two types of experiments: (1) The gas fraction of the subchannels as well as the gas bubble spectra across the outlet of an unheated 61-rod bundle with wire spacers were measured in water/air flow. The distributions of the gas fractions at the inlet of the bundle were performed under uniform and non-uniform conditions. The results show that the distribution of the averaged gas fractions between the individual subchannels at the outlet of the bundle was almost the same as the distribution at the inlet. The measured bubble spectra show a dependency existing between the bubble frequencies, the bubble lengths, and the gas fraction in a subchannel. (2) A model for computing the transient temperature distributions within a heated rod was supported by experiments performed in a sodium/argon flow. For slug flow conditions a comparison indicates that the measured variations of wall temperatures can be well interpreted as being functions of the bubble contact time, rod power, and gas fraction in the flow.     

Modeling of bubble shape in horizontal and inclined tubes

An experimental and theoretical study on the bubble shape of intermittent flow in the horizontal and inclined pipes has been carried out. The experiment results show that the bubble shape depends on the Froude number, bubble length and pipe inclination. The bubble with staircase pattern tail is observed at low Froude numbers, which is corresponding to plug flow. A model for the prediction of the bubble shape in horizontal and inclined pipes is proposed. The model is able to predict the bubble shape, flow pattern transition between plug and slug flow regimes as well as nose-tail inversion phenomenon observed in the downwardly inclined pipe. Validation shows the model can well predict the bubble shapes in horizontal and inclined pipes. The model discloses that the transition between plug and slug flow regimes occurs within a region. The Froude number range for plug flow regime in the downwardly inclined pipe is much wider than that in the horizontal or upwardly inclined pipe. The assumption of fully developed liquid film under the long bubbles tends to under-estimate the liquid fraction in this part of the slug structure, especially, for the intermittent flow in the upwardly inclined pipe with high Froude numbers.     

矩形小尺度加热通道流型构成及过渡准则研究

基于可视化实验系统研究了矩形小尺度加热通道内主要流型构成,从微观角度深入研究气-液两相在流型过渡临界状态下的受力情况,构建了基于力学模型假定的流型过渡准则,并采用可视化实验数据对该模型进行了验证。结果表明,泡沫流-受限气泡流过渡准则预测准确度为93.94%,受限气泡流-环状流过渡准则预测准确度为94.07%,模型预测结果与实验数据基本吻合。      

垂直上升管内泡状流压力波传播

研究了垂直上升管内气液两相泡状流压力波的传播速度和衰减规律,为了提高压力波测量精度．实验中设计了不影响两相流动结构的调频式压力扰动装置．实验结果表明,随着含气率的增加,泡状流中压力波波速开始陡降,当含气率大于0．05以后波速缓慢下降;衰减系数随含气率的增加连续增加：工质的流速对压力波的传播没有影响;压力波的传播速度及其衰减与扰动频率有关．随着扰动频率的增加,波速及其衰减都增加本文实验验证了泡状流压力波色散特性的临界频率现象．即高于临界频率．压力波的色散特性消失．在本试验条件和参数范围内．临界扰动角频率为300Hz．     

Mitigation Technologies for Damage Induced by Pressure Waves in High-Power Mercury Spallation Neutron Sources (III)—Consideration of the Effect of Microbubbles on Pressure Wave Propagation through a Water Test—

The effects of microbubbles dispersed in a liquid on a high-rising-rate pressure wave were experimentally investigated with water. Intense, high-rising-rate pressure waves with a rise time of about 1.5 ms were produced by a spark discharge in water, and gas microbubbles were produced by two different bubble generators. Particular attention was focused on the attenuation effect of microbubbles on propagating pressure waves. The dependence of the attenuation effect on the radius and void fraction of the microbubbles was carefully examined. It was found that when the microbubbles are sufficiently small (e.g., about 50 μm in peak radius), the amplitude of wall vibration induced by the spark-induced pressure wave is dramatically decreased with an increase in void fraction. The present study provides strong experimental evidence that microbubbles can act as a strong absorber for high-rising-rate pressure waves as recently predicted numerically.     

A mechanistic model of critical heat flux under subcooled flow boiling conditions for application to one- and three-dimensional computer codes

Based on a review of visual observations at or near critical heat flux (CHF) under subcooled flow boiling conditions and consideration of CHF triggering mechanisms, presented in a companion paper [Le Corre, J.M., Yao, S.C., Amon, C.H., 2010. Two-phase flow regimes and mechanisms of critical heat flux under subcooled flow boiling conditions. Nucl. Eng. Des.], a model using a two-dimensional transient thermal analysis of the heater undergoing nucleation was developed to mechanistically predict CHF in the case of a bubbly flow regime. The model simulates the spatial and temporal heater temperature variations during nucleation at the wall, accounting for the stochastic nature of the boiling phenomena. It is postulated that a high local wall superheat occurring underneath a nucleating bubble at the time of bubble departure can prevent wall rewetting at CHF (Leidenfrost effect). The model has also the potential to evaluate the post-DNB heater temperature up to the point of heater melting.Validation of the proposed model was performed using detailed measured wall boiling parameters near CHF, thereby bypassing most needed constitutive relations. It was found that under limiting nucleation conditions; a peak wall temperature at the time of bubble departure can be reached at CHF preventing wall cooling by quenching. The simulations show that the resulting dry patch can survive the surrounding quenching events, preventing further nucleation and leading to a fast heater temperature increase. The model was applied at CHF conditions in simple geometry coupled with one-dimensional and three-dimensional (CFD) codes. It was found that, within the range where CHF occurs under bubbly flow conditions (as defined in Le Corre et al., 2010), the local wall superheat underneath nucleating bubbles is predicted to reach the Leidenfrost temperature. However, a better knowledge of statistical variations in wall boiling parameters would be necessary to correctly capture the CHF trends with mass flux (or Weber number).     

基于竖直圆管空气-水两相流实验的相间曳力模型研究

研究两相流相间阻力特性对系统程序关键本构模型封闭具有重要意义。本文基于竖直圆管开展了空气-水两相流实验,采用四探头电导探针对空泡份额、气泡弦长和界面面积浓度等气泡参数的径向分布进行了测量。结果表明空泡份额和气泡弦长呈现“核峰型”分布,而界面面积浓度并没有表现出随流速的单调关系。进一步开发了泡状流和弹状流的相间曳力模型,考虑了液相表观流速与管径对气泡尺寸分布的影响,建立了临界韦伯数与不同液相流速的关系。计算得到的空泡份额和界面面积浓度与实验数据整体符合较好,验证了模型的可靠性,为两相流相间阻力特性研究提供参考意义。     

Effects of interfacial shear condition and trailing-corner radius on the wake vortex of a bubble

Comparative effects between the interfacial shear condition and the trailing-corner radius () on the wake vortex of a bubble are studied. In the investigation, the standard k– model is employed, and the two types of bubble: solid and gaseous, have different interfacial boundary condition. Namely, for solid bubbles the no-slip condition is imposed, resulting in a non-zero interfacial shear condition, while for gaseous bubbles the free-slip condition is imposed, yielding a zero interfacial shear condition. The flow condition is set for a slug flow with the bubble drifting at a terminal velocity corresponding to the Reynolds number of 35,000. The results show that, the flow can be roughly divided into two flow regimes: the small- and large- regimes. In the small- regime, the trailing-corner radius plays a dominant role and the difference in the interfacial shear condition has little effects on the wake vortex, causing the wake vortices of the two bubble types to be similar in shape, size, and circulation. In contrast, in the large- regime, the interfacial shear condition can manifest and affect flow separation and the wake vortex, causing significant differences between the wake vortices from the two bubble types. Namely, as is increased towards the large- regime, the wake vortex of the solid bubble changes relatively little while that of the gaseous bubble significantly decreases in size. At small- the circulations around the wake vortex of both types of bubble are almost identical initially. However, as is increased towards the large- regime, the circulation of the gaseous bubble decreases with increasing at a more pronounced rate than that of the solid bubble. These results show that it is the absence of interfacial shear in the large- regime that causes the wake vortex to be more sensitive to the trailing-corner radius.     

A dynamic intragranular fission gas behavior model

A model for the non-equilibrium behavior of intragranular fission gas in uranium oxide fuel is developed to study the fundamental phenomena that determine fission gas effects. The dynamic behavior of point defects and the variations in stoichiometry are explicitly represented in the model. The principle of distribution moment invariance is used to allow approximations that significantly reduce computational expense without sacrificing accuracy. A dynamic intragranular gas release and swelling (DIGRAS) computer code, that is based on the non-equilibrium model, was developed for both steady-state and transient applications. The code utilizes implicit multistep numerical integration methods, and is designed to give detailed information on all the physical processes that contribute to fission gas behavior.Simulations of steady-state irradiations indicate that the gas bubble re-solution process is very significant and results in very few large bubbles. The assumptions of equilibrium bubble sizes for normal steady-state irradiations in fast reactors appears to be adequate. On the contrary, a fully dynamic fission gas and point defect treatment was found necessary for transient simulations. The fuel stoichiometry was found to play an important role in determining bubble kinetics. This is mainly due to the strong dependence of point defect populations on stoichiometry. In fast transients, bubbles were found to be highly overpressurized, which suggests that a mechanistic plastic growth model is also needed.     

Upward vertical two-phase flow local flow regime identification using neural network techniques

Traditionally, the flow regimes in two-phase flow are considered in a global sense. However, a local flow regime is required to understand and model the interfacial structures present in the flow. In this work, a new approach has been used to identify both global and local flow regimes in a two-phase upward flow in a 50.8 mm internal diameter pipe under adiabatic conditions. In the present method, the bubble chord length distributions, which are measured simultaneously with three double-sensor conductivity probes, have been used to feed a self-organized neural network. The global flow regime identification results show a reasonable agreement with the visual observation for all the flow conditions. Nonetheless, only the local flow regimes measured at the center of the pipe agree with the global ones. The local flow regime combinations found are analyzed using the flow map information, cross-correlations between the probe signals, and previous correlations. In this way, it is possible to identify eight different global flow regime configurations.     

Flow structure and bubble characteristics of steam–water two-phase flow in a large-diameter pipe

The flow structure and bubble characteristics of steam–water two-phase upward flow were observed in a vertical pipe 155 mm in inner diameter. Experiments were conducted under volumetric flux conditions of J_G<0.25 m s⁻¹ and J_L<0.6 m s⁻¹, and three different inlet boundary conditions to investigate the developing state of the flow. The radial distributions of flow structure, such as void fraction, bubble chord length and gas velocity, were obtained by horizontally traversing optical dual void probes through the pipe. The spectra of bubble chord length and gas velocity were also obtained to study the characteristics of bubbles in detail. Overall, an empirical database of the multi-dimensional flow structure of two-phase flow in a large-diameter pipe was obtained. The void profiles converged to a so-called core-shaped distribution and the flow reached a quasi-developed state within a relatively short height-to-diameter aspect ratio of about H/D=4 compared to a small-diameter pipe flow. The PDF histogram profiles of bubble chord length and gas velocity could be approximated fairly well by a model function using a gamma distribution and log–normal distribution, respectively. Finally, the correlation of Sauter mean bubble diameter was derived as a function of local void fraction, pressure, surface tension and density. With this correlation, cross sectional averaged bubble diameter was predicted with high accuracy compared to the existing constitutive equation mainly being used in best-estimate codes.