•An issue of current 1D interfacial drag force formulation has been discussed.•A void fraction covariance correlation for a pipe has been developed.•A relative velocity covariance correlation for a ...pipe has been developed.•The covariance correlations can provide accurate 1D interfacial drag force. The covariance correlations have been validated by high-pressure pipe data.
Drift-flux parameters have been often used to formulate one-dimensional interfacial drag force in dispersed two-phase flow, which is one of key parameters to predict void fraction using one-dimensional thermal-hydraulic codes. This approach is called “Andersen approach”, which has been widely used in one-dimensional nuclear thermal-hydraulic system analysis codes such as TRACE, RELAP5 and TRAC-BF1. However, the current formulation of one-dimensional interfacial drag force ignores important void fraction covariance and relative velocity covariance when local interfacial drag force is converted to one-dimensional interfacial drag force. The impact of neglecting void fraction covariance and relative velocity covariance on one-dimensional interfacial drag force and relative velocity has been discussed in detail. In view of the importance of the drift-flux parameters, void fraction covariance and relative velocity covariance on one-dimensional formulation of the interfacial drag force, three constitutive equations have been developed for upward boiling two-phase flow in a vertical pipe. The validity of the modeled void fraction covariance and relative velocity covariance for subcooled and bulk boiling flow in a vertical pipe has been verified by boiling R12 data taken in a vertical pipe with the diameter of 19.2mm under the pressure simulating prototypic nuclear reactor thermal-hydraulic conditions. The correlation of void fraction covariance agrees with the boiling flow data in the vertical pipe with the mean absolute error, standard deviation, mean relative deviation and mean absolute relative deviation being 0.828, 3.43, 10.3% and 33.5%, respectively. The correlation of relative velocity covariance agrees with the boiling flow data in the vertical pipe with the mean absolute error, standard deviation, mean relative deviation and mean absolute relative deviation being −0.00394, 0.0663, −0.184% and 5.11%, respectively. Due to the great importance of the void fraction covariance and relative velocity covariance on one-dimensional interfacial drag force formulation, it is highly recommended to include the void fraction covariance and relative velocity covariance in the one-dimensional formulation of the interfacial drag force used in nuclear thermal-hydraulic system analysis codes.
In order to improve the prediction accuracy of one-dimensional interfacial force formulated by 'Andersen' approach, the distribution parameter in a drift-flux correlation, void fraction covariance, ...and relative velocity covariance has been modeled for dispersed boiling two-phase flow in a vertical rod bundle. The distribution parameter has been derived by a bubble-layer thickness model. The correlations of void fraction covariance and relative velocity covariance have been developed based on prototypic 8 × 8 rod bundle data. The correlation of void fraction covariance agrees with the bundle data with the mean absolute error, standard deviation, mean relative deviation, and mean absolute relative deviation being 0.00120, 0.0415, −0.173%, and 1.80%, respectively. The correlation of relative velocity covariance agrees with the bundle data with the mean absolute error, standard deviation, mean relative deviation, and mean absolute relative deviation being −0.00241, 0.0452, −0.0316%, and 2.52%, respectively. In view of the great importance of void fraction covariance and relative velocity covariance on the one-dimensional interfacial drag force formulation, it is highly recommended to include the void fraction covariance and relative velocity covariance in the one-dimensional formulation of interfacial drag force used in nuclear thermal-hydraulic system analysis codes.
•Constitutive equations for a vertical rod bundle are reviewed.•Dependence of distribution parameter on flow conditions is discussed.•1D momentum equation by considering void fraction distribution is ...discussed.•Effect of channel size on interfacial area concentration is discussed.
In view of the quality assurance of two-phase flow simulations, CSAU (Code Scalability, Applicability, and Uncertainty) methodology and code V & V (Verification and Validation) have been proposed. The estimation of simulation uncertainty is indispensable in using best-estimate computational codes. A key of successful two-phase flow simulations is to use the state-of-the-art constitutive equations to close the mathematical system used in two-phase flow analyses. The advanced constitutive equations should be developed based on “physics” behind phenomena and should consider scaling parameters which enable their application beyond test conditions used for a code validation. Two-phase flow simulations in a rod bundle is important in various industrial apparatuses such as heat exchangers and nuclear reactors. Constitutive equations for two-phase flows in a vertical rod bundles have been advanced in recent five years. In view of this, this paper provides a comprehensive review of most advanced constitutive equations for two-phase flow analyses in a vertical rod bundle. The constitutive equations of two-phase flow parameters reviewed in this paper are flow regime map, void fraction, void fraction covariance and relative velocity covariance, interfacial area concentration and wall friction. In addition, an exact formulation of one-dimensional momentum equation in two-fluid model considering void fraction distribution is discussed.
A steam generator thermal-hydraulic code based on homogeneous flow model has been useful based on its numerical stability and simpler formulation. One of key parameters for a steam generator ...thermal-hydraulic analysis is void fraction which determines two-phase mixture density and affects two-phase mixture velocity. These parameters are important for a heat transfer tube vibration analysis. A void fraction-quality correlation is very important to accurately convert the quality into the void fraction. The void fraction-quality correlation should preferably be applicable to parallel and cross flows in rod or tube bundles since two-phase flow in the steam generator encounters flow configuration change from the parallel flow along the tube bundle in the riser section of the steam generator to the cross flow in the U-bend section of the steam generator. A set of correlations depending on flow configuration such as parallel and cross flows, rod or tube array pattern and mass flux is developed based on legacy Smith correlation. The correlation agrees with the parallel and cross flow data with the mean absolute error (or bias) of 0.117% and the standard deviation (random error) of 2.26% and with the mean absolute error (or bias) of 0.760% and the standard deviation (random error) of 6.21%, respectively. The correlations are further simplified to a single correlation applicable for parallel and cross flow in rod or tube bundles. The Smith correlation with a modified constant entrainment parameter e being 0.5 is recommended for predicting void fraction in the steam generators. The Smith correlation with e = 0.5 is expected to be applicable for parallel and cross flows with various rod or tube array patterns including normal square, parallel triangular and normal triangular arrays.
•Performed literature review on basic two-phase flow porous media formulations.•Performed literature review on void fraction correlations and available database of two-phase flow in tube bundles.•Developed a new void fraction correlation for tube bundles based on legacy Smith correlation.•Compared the newly developed void fraction correlation with experimental data and performed the error analysis.•Simplified the newly developed void fraction correlation for parallel and cross flows in steam generators.
•Interfacial drag forces for interior, edge, and corner subchannels were formulated in a rod bundle.•Subchannel-average void fraction covariance was empirically modeled for saturated boiling ...flow.•Subchannel-average void fraction covariance was analytically modeled for subcooled boiling flow.•The covariance models were validated by steam-water data up to 8.6 MPa.•The relative velocity covariances were calculated from the void fraction covariances.
Accurate simulation of boiling two-phase flows in a rod bundle is indispensable for the robust, economical, and safe design of various heat transfer systems using the rod bundle configuration. Subchannel analysis codes are used for this purpose. Interfacial drag force modeling significantly affects the prediction accuracy of the void fraction. The void fraction and relative velocity covariances constitute the interfacial drag force. However, the covariances are currently not considered in existing subchannel codes due to a lack of reliable constitutive equations to calculate the void fraction and relative velocity covariances. This study aims to model the subchannel-average void fraction and relative velocity covariances for subcooled and saturated boiling flows in three types of subchannels in a rod bundle. The considered subchannels are interior, edge, and corner subchannels. The subchannel-average void fraction and relative velocity covariances for saturated boiling flow are modeled by the data obtained from local void fraction data collected for saturated boiling flow in an 8 × 8 rod bundle under pressures from 1.0 to 8.6 MPa. The subchannel-average void fraction and relative velocity covariances for subcooled boiling flow are modeled based on the bubble-layer thickness model. The modeled subchannel-average void fraction and relative velocity covariances are well validated with the experimental data. The modeled subchannel-average void fraction and relative velocity covariances are expected to be implemented in subchannel analysis codes to improve the void fraction prediction accuracy in each subchannel type.
Recent progress in nuclear thermal-hydraulics simulations has been largely focused on coupling with other computational packages, improved closure models for subcooled boiling and for bubbly flows, ...and the development of higher-fidelity simulation capabilities (Kulesza et al., 2016). While high-fidelity 3D simulation is important for model validation, scientific understanding, and some design calculations, it can be prohibitively expensive for system design applications or applications involving large geometries. Thus, there is also a need for practical, simplified approaches for those applications. The two-fluid model strikes a balance between detail and computational resources, but requires the accurate specification of several key constitutive models. These include (1) interfacial forces, (2) interfacial area concentration, (3) two-phase turbulence, and (4) wall and bulk boiling and condensation. In many modern CFD packages, uncertainties in the local interfacial area concentration can have strong effects on the ability to predict the other key parameters. This paper demonstrates that the drag force in 3D CFD can be formulated in much the same way as in 1D system analysis codes and that this approach can be used to formulate a model for interfacial area concentration. The method is also applied to two-group approaches to consider the difference in transport properties for different bubble size classes. This approach may open a method to calculate the interfacial forces without the need for interfacial area transport equations. This reduces the number of differential equations and avoids the modeling challenges associated with bubble breakup and coalescence kernels and the need to specify the inlet interfacial area concentration a priori. The new method is expected to decouple the effects of interfacial area uncertainty and calibrated coefficients, and should provide reasonable local bubble diameters for both group-1 and group-2 bubbles. The approaches proposed in this study are applicable to two-phase flow simulations in rather simple geometries such as upward two-phase flow in vertical channels. In view of many applications for upward two-phase flow in vertical channels, including nuclear reactor systems, the proposed methods are considered useful.
•Simplified two-group two-fluid model is proposed for CFD applications.•Drift velocity based drag force formulation is simpler and more robust for CFD calculations.•Local interfacial area concentration correlation is proposed based on new drag force formulation.•This approach is applicable to vertical upward two-phase flow.
In simulations of two-phase flow behavior in nuclear reactors, subchannel analysis codes are often used to evaluate the void fraction within a BWR fuel bundle in detail. When solving the momentum ...conservation equation averaged over a subchannel cross-section for upward two-phase flows, the distribution parameter is required to consider the void fraction and velocity distributions in the subchannel cross-section. In this paper, constitutive equations were developed for the distribution parameters for dispersed two-phase flows applicable to the inner, edge, and corner subchannels, which are typical subchannels in a fuel bundle. The distribution parameters could be calculated by giving the void fraction and the velocity distribution. Therefore, the distribution parameters were evaluated and modeled as a function of the geometrical parameters by assuming the void fraction and velocity distributions with bulk and subcooled boiling for each subchannel type. The developed constitutive equations were evaluated by comparing them with the distribution parameters estimated based on the NUPEC rod bundle void fraction test data. The developed distribution parameter model was implemented into the subchannel analysis code NASCA and compared with the measured cross-sectional average void fraction of the NUPEC rod bundle void fraction test data. In comparison with the original NASCA code, which assumed the distribution parameter to be unity, the improved NASCA with the distribution parameter model decreased the mean error of the measured cross-sectional average void fraction to less than half of the result of the original NASCA code, both in absolute and relative differences.
•Two-group interfacial area concentration models are implemented into TRAC-BF1 code.•Large and small interfacial area concentration models are developed for sensitivity analyses.•Sensitivity analyses ...of interfacial area effect on code predictions are conducted.•Sensitivity analyses include steady-state and transient flows and flow regime transition.•Interfacial area concentration has a minor effect on void fraction prediction in adiabatic flow.
In one-dimensional two-fluid model-based codes, an interfacial drag force appears in a momentum conservation equation. The interfacial drag force is an essential parameter in predicting a void fraction. The accurate modeling of the interfacial drag force is indispensable for evaluating thermal–hydraulic characteristics in a nuclear reactor core. The interfacial drag force is formulated as the product of an ‘overall’ drag coefficient and the square of the relative velocity between gas and liquid phases. The ‘overall’ drag coefficient is expressed by the product of a drag coefficient, interfacial area concentration, and density of continuous phase. The rigorous model of the drag coefficient depending on a bubble shape regime has been established. The modeling of the interfacial area concentration depending on a flow regime is one of the weakest links in thermal–hydraulic analysis. The interfacial area transport equation was proposed to predict the dynamic change of the interfacial area concentration but has not reached a level accurate enough to predict the interfacial area concentration. Due to its incomplete development situation, an alternative way to predict the interfacial area concentration through a semi-theoretical interfacial area correlation has been proposed. This study aims to elucidate the effect of the interfacial area concentration on void fraction prediction in a one-dimensional thermal–hydraulic analysis. A one-dimensional two-fluid model-based code, such as TRAC-BF1, has been modified by implementing two existing constitutive equations of the interfacial area concentration into the code. This study also introduces large and small interfacial area concentration models of the interfacial area concentrations. The large and small interfacial area concentration models are designed to intentionally provide hypothetical large and small interfacial area concentrations within physically possible ranges. A total of four interfacial area concentration models is tested under adiabatic two-phase flow conditions. Code calculations with the four different models under steady-state and transient-state conditions and flow regime transitions have identified that the effect of the interfacial area concentration on the void fraction is insignificant for the adiabatic two-phase flows. The findings obtained in this study suggest that a simple interfacial area correlation is sufficient in modeling the interfacial drag force for adiabatic two-phase flows. However, robust and accurate modeling of the interfacial area concentration is still indispensable for two-phase flows with phase change because the interfacial heat transfer term in an energy conservation equation includes the interfacial area concentration.
Drift-flux model for rod bundle geometry Ozaki, Tetsuhiro; Hibiki, Takashi
Progress in nuclear energy (New series),
August 2015, 2015-08-00, 20150801, Letnik:
83
Journal Article
Recenzirano
In view of an important role of a one-dimensional drift-flux correlation in nuclear thermal-hydraulic system analysis codes, several drift-flux correlations such as Lellouche–Zolotar, ...Chexal–Lellouche, TRAC-BF1 and Ozaki correlations have been reevaluated by rod bundle test data taken in FRIGG and NUPEC test facilities. The mean absolute error of void fraction representing a correlation bias of the Lellouche–Zolotar, Chexal–Lellouche, TRAC-BF1 and Ozaki correlations are, respectively, −1.0, 0.5, −6.3 and −3.3% for the FRIGG test data and 2.0, 2.3, −0.4 and −0.7% for the NUPEC test data. The effects of unheated rods, axial and radial power distributions, large unheated center rod and geometry of a shroud or casing on void fraction are identified. The presence of unheated rods with similar size of other heated rods tends to increase a distribution parameter in a drift-flux correlation, whereas the presence of a large unheated center rod tends to decrease the distribution parameter. The axial and radial power distributions do not have significant effect on void fraction within the tested axial and radial power distribution range. The Ozaki correlation is recommended for predicting void fraction in a BWR core but it is suggested to reduce the distribution parameter in the Ozaki correlation if a large unheated center rod exists in the core. It is indicated that drift-flux correlations developed based on bounded rod bundle test facility data may overestimate the distribution parameter for a PWR core.
•Drift-flux correlations for rod bundles were reevaluated by FRIGG and NUPEC data.•Inconsistency of void fraction data between FRIGG and NUPEC tests are identified.•Effects of unheated rods and power distribution on void fraction are identified.
