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Bubble Diameter Evaluation in Pool Scrubbing Geometries
Abstract
Calculating the bubble diameter accurately is crucial for predicting the De-contamination Factor (DF) in pool scrubbing codes. Currently, empirical correlations that depend on flow regimes and conditions are used to estimate bubble diameters in pool scrubbing codes, leading to a discrepancy between predicted and experimental DFs. The Interfacial Area Transport Equation (IATE) has the potential to improve the DF estimations in pool scrubbing codes as it can dynamically calculate the bubble diameter by estimating Interfacial Area Concentration (IAC) through mechanistically modeled bubble breakup and coalescence mechanisms. However, most of these models were developed for fully developed pipe flow conditions, which are not suitable for pool scrubbing gas-liquid flow conditions. To evaluate the IATE's applicability in pool scrubbing geometries, the OpenFOAM Computational Fluid Dynamics (CFD) code was used to investigate the hydrodynamics of a high inlet velocity pool scrubbing experiment on a large scale. The investigated bubble interaction mechanisms showed that the models heavily rely on the effects of Shear Induced Turbulent (SIT) through turbulent velocity fluctuations, although Bubble Induced Turbulent (BIT) is more dominant in pool scrubbing conditions. It was found that a relatively lower critical Weber number is required for bubble breakup mechanisms to take effect in pool scrubbing geometries, and only area averaging leads to missing information in pool scrubbing geometries due to its scale, therefore, void weighted area averaging must be used. The SMD calculated using IATE and experimental results showed relatively good agreement near the exit, but IATE overestimated the SMD in the transition and downstream region.
... The drag, lift, turbulent dispersion, and virtual mass forces are used for interphase modeling. The details can be found in our previous work [5]. ...
... In this study, is set to 2 based on the literature review [5], considering the nature of gas flow in a pool. Eq. (1), coupled with the field equations of the twofluid model, will be used to solve for Interfacial Area Concentration ( ) in pool scrubbing experiments. ...
The objective of this study is to propose a novel correlation that promises a more accurate representation of bubble size variations in the swarm region at pool scrubbing conditions, requiring only information on the inlet conditions and eliminating the need for complex flow parameter assessments. The recently published experiment studies by Abe et al. (2018), Fujiwara et al. (2024) and Behzadipour et al. (2022) have utilized large experimental facilities with advanced techniques such as Wire Mesh Sensors (WMS) and Refractive Bubble Instrument (RBI) optical probes to measure crucial flow and geometrical variables. Leveraging the data from these experiments and employing three-dimensional Computational Fluid Dynamics (CFD) with well-established turbulence, interphase, and diameter models, this study successfully implements a framework for proposing a novel bubble size correlation.
This study investigates Equivalent Spherical Diameter (ESD) estimation at high inlet velocity pool scrubbing conditions using the Interfacial Area Transport Equation (IATE) diameter model including bubble-induced turbulence and interphase modeling. The compatibility of area-averaged Sauter Mean Diameter (SMD), area-averaged Local Equivalent Diameter (LED), and void-weighted area-averaged LED approaches to estimate the ESD are explored and the proposed model is validated against available experimental data. The study reveals that the prevalent constant ESD assumption in pool scrubbing codes is not universal by showcasing a decreasing trend along the column due to intensive bubble breakup. The area-averaged LED approach fails to capture this trend, while the area-averaged SMD and void-weighted area-averaged LED approaches provide accurate estimations aligned with experimental data. Turbulence parameters, interfacial forces, and diameter modeling are identified as crucial for accurate predictions of flow and geometrical variables by setting up the OpenFOAM framework. A sensitivity analysis indicates that the inlet velocity has an acceptable effect on the ESD along the column. The ESD increases near the exit and decreases in the swarm region by increasing the inlet velocities. Turbulent in-tensity reduces ESD across all column sections while changes in aspect ratio minimally impact ESD. The study shows promise in developing correlations that take into account the spatial variation of ESD in pool scrubbing conditions.
The fundamental information of bubble plume such as interfacial area, three-dimensional velocity, and bubble diameter are necessary to develop a kinematic pool scrubbing model for uncertainty reduction of severe accident analysis. In this study, an algorithm was introduced to polygonize the cross-sectional void fraction of the wire-mesh sensor and reconstruct it in 3D to track the individual bubbles detected. Based on the result, the interfacial area and three-dimensional velocity of individual bubbles in a bubble plume were obtained. The results show that the interfacial area from MELCOR model tends to overestimate the analyzed results due to remaining of large bubbles in the downstream. In addition, the effect of subcooling temperature and steam fraction on bubble formation was evaluated by applying the developed method into condensable gas experiments. The interfacial area increased significantly under high subcooling temperature and steam fraction due to atomization of bubbles caused by steam condensation.
In this paper the principles of the FOAM C++ class library for continuum mechanics are outlined. The intention is to make it as easy as possible to develop reliable and efficient computational continuum mechanics (CCM) codes: this is achieved by making the top level syntax of the code as close as possible to conventional mathematical notation for tensors and partial differential equations. Object orientation techniques enable the creation of data types which closely mimic those of continuum mechanics, and the operator overloading possible in C++ allows normal mathematical symbols to be used for the basic operations. As an example, the implementation of various types of turbulence modelling in a FOAM computational uid-dynamics (CFD) code is discussed, and calculations performed on a standard test case, that of flow around an square prism, are presented. To demonstrate the exibility of the FOAM library, codes for solving structures and magneto-hydrodynamics are also presented w...
Compared to conventional gas–liquid bubble columns, gas–liquid columns including both gas and liquid flows have been investigated less due to their complex hydrodynamics and operational difficulties. In this study, simultaneous non-intrusive methods of column shell vibration and pressure fluctuation measurements were coupled with direct photography and image analysis for bubble characterization. Various statistical and frequency analyses were conducted on the acceleration and pressure fluctuations signals to determine their capability of interpreting bubble behavior inside the column. The standard deviation of vibration signals showed less sensitivity to bubble behavior compared to that of pressure fluctuations. The skewness of vibration and pressure fluctuations could detect bubble regime transition points at all studied gas and liquid velocities while vibration and pressure fluctuations kurtosis could only detect the main transition point of the column at a moderate liquid velocity. It was found that besides regular statistical methods, the energy of pressure signals could predict bubble regime transition points successfully. While vibration-based inspection showed more sensitivity to bubble size distribution (similar to the standard deviation of pressure signals), frequency analysis on pressure signals proved to be a strong representative of bubble Sauter mean diameter alteration by liquid flow variation at constant gas velocities. Moreover, by means of energy-based discrete wavelet transformation, we defined the exact pathway of various sub-signal gradual evolutions throughout a wide range of operating conditions of gas and liquid velocities and captured regime transition points accordingly. The proposed methods in this work can be used for non-intrusive hydrodynamic characterization in industrial bubble columns.
This report describes the technical bases and use of two updated versions of a computer code initially developed to serve as a tool for calculating aerosol particle retention in boiling water reactor (BWR) pressure suppression pools during severe accidents, SPARC-87 and SPARC-90. The most recent version is SPARC-90. The initial or prototype version (Owczarski, Postma, and Schreck 1985) was improved to include the following: rigorous treatment of local particle deposition velocities on the surface of oblate spherical bubbles, new correlations for hydrodynamic behavior of bubble swarms, models for aerosol particle growth, both mechanistic and empirical models for vent exit region scrubbing, specific models for hydrodynamics of bubble breakup at various vent types, and models for capture of vapor iodine species. A complete user's guide is provided for SPARC-90 (along with SPARC-87). A code description, code operating instructions, partial code listing, examples of the use of SPARC-90, and summaries of experimental data comparison studies also support the use of SPARC-90. 29 refs., 4 figs., 11 tabs.
The interfacial area transport equation is derived from the statistical model of fluid particle number transport equation. The resulting equation includes the source and sink terms due to the particle interactions and interfacial phase change. The consistency of this new approach is demonstrated in terms of the macroscopic continuity equation of a bubbly flow field. The basic mechanisms affecting these source and sink terms are discussed. The general framework to develop the closure relations for the fluid particle interaction and phase change terms is presented. Finally, the one-dimensional interfacial area transport equation is used to identify possible methods to relate the source and sink terms to experimentally measurable interfacial parameters, such that experiments can be used to establish models for these terms.
An analysis is presented of the removal of aerosol particles and gaseous fission products from steam-noncondensable gas mixtures rising through water pools. The pool is divided into a gas injection zone, a bubble rise zone and a pool surface zone. The formulation of the governing conservation equations is relatively general with a quasi-steady one-dimensional formulation for the gas phase, and an unsteady, well stirred, formulation for the liquid phase. An associated computer code for performing the calculations, SUPRA, is described. Results of parametric calculations are given for conditions expected in a BWR severely degraded core accident sequence. Parameters studied include aerosol particle size and distribution, mass fraction of noncondensable gas, gas mass flow rate, quencher submergence depth, and pool water temperature.
This paper presents an assessment of various models which can be used for the multidimensional simulation of multiphase flows, such as may occur in nuclear reactors. In particular, a model appropriate for the direct numerical simulation (DNS) of multiphase flows and a mechanistically based, three-dimensional, four-field, turbulent, two-fluid computational multiphase fluid dynamics (CMFD) model are discussed. A two-fluid bubbly flow model, which was derived using potential flow theory, can be extended to other flow regimes, but this will normally involve ensemble-averaging the results from direct numerical simulations (DNS) of various flow regimes to provide the detailed numerical data necessary for the development of flow-regime-specific interfacial and wall closure laws.
One of the phenomena involved in the assessment of the radioactive source termto the environment during a severe nuclear reactor accident is the retention of aerosols and fission product vapours in water pools during their passage from the core to the containment.The development of the BUSCA (Bubble Scrubbing Algorithm) code, which models these phenomena, was initiated by the SRD and is undergoing further development within the European Pool Scrubbing Group. Up to date, it has been validated against the ACE (Advanced Containment Experiments) Phase A experiments.
In the two-fluid model, interfacial concentration is one of the important parameters. The objective of this study is to develop an interfacial area equation with the source and sink terms being properly modeled. For bubble coalescence, the random collisions between bubbles due to turbulence, and the wake entrainment process due to the relative motions of the bubbles, were included. For bubble breakup, the impact of turbulent eddies is considered. Compared with measured axial distributions of the interfacial area concentration under various flow conditions, the adjustable parameters in the source/sink terms were obtained for the simplified one-dimensional transport equation.
The present paper describes an Eulerian two-fluid model for the prediction of dispersed two-phase (gas/liquid and liquid/liquid) flow at high volume fractions of the dispersed phase. The model is based on the standard Eulerian approaches for modelling two-phase flow that have hitherto been limited in validity to dilute systems. An extension to high phase fractions is made here and this involves two aspects. First, the closure models for inter-phase forces (namely drag and lift) are modified to account for the high concentration of the dispersed phase. Second, a turbulence model based on the k–ε equations for the mixture of the two phases is formulated. This turbulence model is suitable for computations at all phase fraction values and reduces to the equivalent single phase model in the extremes when only one or other of the phases is present. The model uses a response function to link the turbulent fluctuations of the continuous and dispersed phases. The variation of this response function with phase fraction is determined from experimental evidence made available recently. The overall model is applied to the prediction of air/water bubble flow in a pipe with a sudden enlargement where phase fractions can reach 25% and for which experimental data exist. The calculations show that marked improvement in the quality of the predictions, as compared to measurements, is obtained over the available model for dilute systems.
The motivation of the present study originated from the necessity of the closure relation for the interfacial area concentration in the application of the two-fluid model. Considering that the two-fluid model describes a two-phase flow most accurately, the constitutive relation for the interfacial area concentration is indispensable in the accurate safety assessment of the nuclear reactor system. In the present study, the interfacial area transport equation applicable to a wide range in bubbly flow conditions was developed in view of establishing the constitutive relation for the interfacial area concentration. In the transport equation, the source and sink terms were established through mechanistic modeling of the major fluid particle interactions. In the course of modeling efforts, the large bubble interactions were also studied. Noting furthermore that the available data basis for the local two-phase parameters was quite limited, the state-of-the-art local measurement technique was developed based on the previous conductivity probe technique. Significant improvements were made in both the probe design and the signal processing, which enabled the newly developed probe to be applicable to a wide range of two-phase flow regimes. In the present experiment, detailed local two-phase flow parameters were acquired at three axial locations in the adiabatic rectangular vertical air-water loop under atmospheric pressure for 9 different flow conditions in bubbly, dispersed-bubbly, and distorted-bubbly flow conditions. With the acquired data, the theoretical model was evaluated. In view of this, the one-dimensional steady-state one-group interfacial area transport equation was formulated by applying the Eulerian area-average to the local formulation. The overall agreement between the data and the model prediction was good within ±10% difference. In the sensitivity analysis of the individual contributions from different interaction mechanisms, active fluid particle interactions were clearly demonstrated and the dominant mechanism varied depending on the flow conditions. In general, the turbulent impact break-up and the random collision coalescence mechanisms were dominant in the highly turbulent flow conditions, whereas the bubble expansion and the wake induced coalescence mechanisms were dominant in the bubbly or bubbly to cap-bubbly flow transition conditions.
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