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The EPRI (1991) and the Clark et al. (2014) drift-flux correlations implemented in RELAP5/MOD3 code were benchmarked against the low-pressure void fraction data collected by Clark et al. (2014) at ...

Accurate prediction of interfacial drag in the downcomer annulus is crucial for the assessment of downcomer void fraction for the loss of coolant accident analysis. The downcomer annulus is...

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.

We previously developed a one-dimensional (1-D) computation method with parameters adjusted from CCFL (countercurrent flow limitation) data in hot leg and pressurizer surge line models to generalize the prediction method for CCFL in nearly horizontal pipes. In the 1-D computation method, the constant value for the interfacial friction coefficient of fi = 0.03 was used. On the other hand, many correlations for the interfacial friction coefficient in horizontal and inclined pipes have been proposed. In this study, therefore, we carried out 1-D computations for CCFL in nearly horizontal pipes with the diameter of D = 0.03–0.75 m and the length to diameter ratio of L / D = 4.5–63 by using some selected correlations for the interfacial friction coefficient, which are a function of the gas or liquid Reynolds number. As a result, we confirmed that the correlation of the interfacial friction coefficient in terms of the Reynolds number cannot be used for large Reynolds numbers but fi = 0.03 can be used for the wide range of diameters. To improve the correlation with the gas or liquid Reynolds number, we proposed a modified correlation.

RELAP5/MOD3.2 is a thermal-hydraulic system analysis code used to predict the response of nuclear reactor coolant systems in the event of certain accident scenarios. It is important that RELAP and other system analysis codes are able to accurately predict various two-phase flow phenomena, particularly the interfacial transfers between the liquid and gas phases. It is also important to understand how much uncertainty exists in these predictions due to uncertainties in the constitutive relations used to close the two-fluid model. In this paper, the uncertainty in the interfacial drag calculated by RELAP5/MOD3.2 due to errors in the drift-flux models used to close the model is evaluated and compared to the correlation developed by Goda et al. (2003). The case of downward flow is considered due to the importance of co-current and counter-current downward flow for predicting behavior in the downcomer of reactor systems during small-break Loss of Coolant Accidents (LOCAs) in nuclear reactor systems. The overall uncertainty in the interfacial force calculations due to error in the distribution parameter models were found to have a bias of +8.1% and error of 20.1% for the models used in RELAP5, and a bias of −30.8% and error of 23.1% for the correlation of Goda et al. (2003). However this analysis neglects the effects of compensating errors in the drift-flux parameters, as the drift velocity is assumed to be perfectly accurate. More physically meaningful results could be obtained if the distribution parameter and drift velocity were calculated directly from local phase concentration and velocity measurements, however no studies were available which included all of this information.

A new drift-flux correlation has been developed to predict void fraction over a wide range of two-phase flow conditions in rod bundle geometries. An experimental database that represents low liquid flow and low pressure conditions in a scaled 8 × 8 rod bundle test facility is emphasized for this work. At these conditions, recirculating flow patterns may affect two-phase flow characteristics. Such effects may not be appropriately considered in earlier rod bundle correlations for drift velocity and distribution parameter. In the current approach, an existing drift-flux correlation that accounts for the effect of recirculating flow as two-phase flow regimes transition from bubbly to cap-bubbly flow is incorporated to determine distribution parameter. A performance analysis demonstrates that the proposed correlation improves upon existing correlations with an average relative error of ±4.5% when predicting the database utilized for in this work. The new correlation is also demonstrated to scale appropriately to prototypic plant conditions.

The prediction of the peak cladding temperature is key for the evaluation of the safety characteristics of nuclear reactor designs. One of the most important parameters in determining the peak cladding temperature is the two-phase mixture level in the core, which in turn depends on the void fraction in the core. In the two-fluid model, which is used in best-estimate thermal-hydraulic analysis codes such as RELAP and TRACE, the void fraction is largely determined by the interfacial drag. In the codes, the interfacial drag is determined based on drift-flux type correlations for the distribution parameter and void-weighted area-averaged drift velocity. It is essential that the model for the prediction of void fraction in the reactor core be accurate to ensure safe shutdown of the reactor. In light of this, a thorough review of the Chexal–Lellouche drift-flux type correlation currently used in RELAP5/MOD3.2.2 has been initiated to evaluate the scalability and uncertainty of the correlation. Analysis of the physical dependencies indicates some serious concerns regarding the presence of compensating errors in the models for the distribution parameter and void-weighted area-average drift velocity.

A numerical study is presented to examine the effects on countercurrent flow limitation (CCFL) of shape and size of hot leg models with a rectangular cross section. The CCFL was described in terms of Wallis parameters using the channel height H as the characteristic length. Numerical simulations, using the CFD software code FLUENT 6.3.26, were done for the air-water CCFL experiments carried out previously at Helmholtz-Zentrum Dresden-Rossendorf (HZDR) in the 1/3 scale hot leg model with a rectangular channel (HxW = 0.25x0.05 m2), and the results were compared with the air-water CCFL data obtained at Kobe University in the 1/5 scale hot leg model with rectangular cross section (HxW = 0.15x0.01 m2) and the results of simulations. It was found that both the height-to-width ratio and the size of the cross section affected the CCFL characteristics in the Wallis diagram. Comparison of CCFL characteristics in rectangular channels with those in circular channels showed that the hydraulic diameter, Dh, was a major cross section geometry term influencing the CCFL characteristics. CCFL constants of the Wallis correlation were about 0.61 on average for the range of 0.05 m < Dh < 0.75 m but became small for Dh < 0.0254 m, and these tendencies were well reproduced by the numerical simulations.

An experiment has been performed to measure void fraction at stagnant to low liquid flow conditions in a rod bundle. An 8 × 8 rod bundle test facility scaled from a boiling water reactor design was utilized at atmospheric pressure with air and water as working fluids. Superficial liquid velocity ranged from 0 to 1.0 m/s and superficial gas velocity ranged from 0.03 to 10.0 m/s. Area-averaged measurements of superficial liquid velocity, superficial gas velocity, and void fraction are used to calculate distribution parameter from a kinematic constitutive equation of the drift-flux model. Results indicate a significant increase in distribution parameter when mixture volumetric flux is relatively low. This observation may be attributed to recirculating flow patterns. An investigation is conducted for existing rod bundle drift-flux correlations because they may not appropriately consider these mechanisms at low liquid flow and low pressure conditions. Results suggest that improvements may be made if the effects of recirculating flow are taken into consideration.

The Best Estimate Plus Uncertainty (BEPU) method has been applied by the authors to analysis of the “intentional depressurization of steam generator secondary side” which is an accident management procedure in a small break loss-of-coolant accident with high pressure injection system failure. In the present study, experimental analyses using the RELAP5/MOD3.2 code were carried out for the ROSA/Large Scale Test Facility (LSTF) secondary-side depressurization tests. The two test cases were selected with different break sizes and different depressurization conditions to ensure the reliability for the accident scenario analyses. The uncertainty propagation analyses were performed through the random variations of input parameters whose uncertainty ranges and distributions were determined previously by the PIRT and the separate effects tests. One thousand random calculations were conducted to get the 95% upper limit values of the peak cladding temperature (PCT) by the Monte Carlo method. Furthermore, the 95%/95% tolerance limits for the PCT were obtained according to Wilks formula. It was confirmed that the code predicted well the major event progressions such as rod surface temperature and the 95% uncertainty bands included the measured values. Furthermore, the 95% upper limit values of the PCT are below the 95%/95% tolerance limit values. However, the statistical fluctuation of the tolerance limit values by Wilks first order formula is as large as the uncertainty value itself. The statistical fluctuation decreases with increasing order of Wilk formula. It is desirable to increase the order of Wilks formula to more than the second order to get the reliable safety margin.Copyright © 2016 by ASME

In order to evaluate flow patterns and CCFL (countercurrent flow limitation) characteristics in a PWR hot leg under reflux condensation, numerical simulations have been done using a two-fluid model and a VOF (volume of fluid) method implemented in the CFD software, FLUENT6.3.26. The two-fluid model gave good agreement with CCFL data under low pressure conditions but did not give good results under high pressure steam-water conditions. On the other hand, the VOF method gave good agreement with CCFL data for tests with a rectangular channel but did not give good results for calculations in a circular channel. Therefore, in this paper, the computational grid and schemes were improved in the VOF method, numerical simulations were done for steam-water flows at 1.5 MPa under PWR full-scale conditions with the diameter of 0.75 m, and the calculated results were compared with the UPTF data at 1.5 MPa. As a result, the calculated flow pattern was found to be similar to the flow pattern observed in small-scale air-water tests, and the calculated CCFL characteristics agreed well with the UPTF data at 1.5 MPa except in the region of a large steam volumetric flux.

In reflux condensation, steam generated in the reactor core and water condensed in a steam generator (SG) form countercurrent flow in a hot leg, which consists of a horizontal pipe, an elbow and an inclined pipe. Both countercurrent air–water and steam–water tests were previously carried out at Helmholtz-Zentrum Dresden-Rossendorf (HZDR) using the 1/3 scale rectangular channel simulating a PWR hot leg installed in the pressure chamber of the TOPFLOW facility. In this paper, in order to evaluate the effects of fluid properties, the steam–water CCFL (countercurrent flow limitation) tests at HZDR were simulated using the CFD software, FLUENT 6.3.26. The computational domain included the reactor vessel simulator, hot leg and SG inlet chamber in order to avoid uncertainties of boundary conditions at both ends of the hot leg. The VOF (volume of fluid) method and two-fluid (2F) model were used. In the 2F model, the combination of three correlations on the interfacial friction coefficients, which had been validated for the 1/15 and 1/5 scale tests at Kobe University, was used as a function of local void fractions. The CCFL characteristics predicted by the 2F and VOF agreed relatively well with the steam–water CCFL data at HZDR but overestimated the effects of fluid properties on CCFL. The VOF simulations were better able to reproduce the fluid properties than the 2F simulations.

Numerical simulations have been done to evaluate CCFL (countercurrent flow limitation) in a PWR hot leg under reflux condensation by using a VOF (volume of fluid) method implemented in the CFD software, FLUENT6.3.26. The calculated CCFL characteristics have been verified and agreed well with known values including the UPTF data at 1.5 MPa. Therefore, in this paper, parameter calculations using the VOF method were done for system pressures up to 8 MPa under PWR full-scale conditions with the diameter of 750 mm. As a result, calculated CCFL characteristics in the Wallis diagram were slightly mitigated from 0.1 MPa to 1.5 MPa with increasing system pressure, but they did not change from 1.5 MPa to 8 MPa. The CCFL database calculated in this study and values measured under air-water and steam-water conditions were used to derive a CCFL correlation and its uncertainty, where the CCFL constant was . Most of the CCFL data and the current correlation predictions were within the uncertainty of +-0.03.

A one-dimensional drift-flux model was developed and benchmarked with existing models in the present study. Different from existing empirical correlations, this newly developed 1-D drift-flux model started from the variations of two-phase flow distribution parameter C0 for non-dimensional superficial gas velocity 〈 j g + 〉 from low to high, which represents the variation of phase distribution patterns. Due to a combination of small-scale sub-channel effect and large-scale casing effect in a rod bundle, the Hibiki–Ishii’s drift velocity V gj + was introduced to describe the relative motion between two phases. A clear boundary of distribution parameter, C0, can be found when the non-dimensional superficial gas velocity 〈 j g + 〉 is closed to 0.5. A linearly increasing trend and an exponentially decreasing trend of C0 were found in the lower and higher gas sides divided by this boundary, respectively. Through the present model, one dimensional area-averaged gas velocity and void fraction can be determined for rod bundles in pool conditions. The prediction results were compared with several existing models and experimental data. The present model shows a good agreement with the existing experimental data and can be applied to both boiling and adiabatic air–water two-phase flows. In order to explain the peak values of C0 in low superficial gas velocity conditions, several possible superficial velocity and void fraction profiles were examined by considering the recirculation flow/void distributions.

In order to establish a reliable rod bundle database under pool conditions and to benchmark the existing models, a well-scaled 8 × 8 rod bundle test loop was designed based on the scaling criteria and a series of experiments was carried out with adiabatic air–water two-phase flow. Experiments for pool conditions covered the area-averaged void fraction 〈α〉 range of 0.12–0.93. Existing models and experimental data including boiling and air–water two-phase flow were compared and analyzed. Experimental results show that differences exist between large and small casing rod bundles as the flow structure changes with the casing scale. In addition, traditional drift-flux models for pipes may reflect the casing scale effect, but cannot be directly applied to the rod bundle geometry in pool conditions. Among the existing models for rod bundles, the Murase et al., 1986 , Kamei et al., 2008 , Ishizuka et al., 1995 give relatively better predictions in most regions. All benchmark results of existing models are tabulated in terms of void fraction prediction error for the present database.

In order to improve the countercurrent flow model of a transient analysis code, countercurrent air–water tests were previously conducted using a 1/15 scale model of the PWR hot leg and numerical simulations of the tests were carried out using the two-fluid model implemented in the CFD software FLUENT 6.3.26. The predicted flow patterns and CCFL characteristics agreed well with the experimental data. However, the validation of the interfacial drag correlation used in the two-fluid model was still insufficient, especially regarding the applicability to actual PWR conditions. In this study, we measured water levels and wave heights in the 1/15 scale setup to understand the characteristics of the interfacial drag, and we considered a relationship between the wave height and the interfacial drag coefficient. Numerical simulations to examine the effects of cell size and interfacial drag correlations on numerical predictions were conducted under PWR plant conditions. Wave heights strongly related with the water level and interfacial drag coefficient, which indicates that the interfacial drag force mainly consists of form drag. The cell size affected the gas velocity at the onset of flooding in the process of increasing gas flow rate. The gas volumetric fluxes at CCFL predicted using fine cells were higher than those using normal cells. On the other hand, the cell size did not have a significant influence on the process of decreasing gas flow rate. The predictions for the PWR condition using a reference set of interfacial drag correlations agreed well with the Upper Plenum Test Facility data of the PWR scale experiment in the region of medium gas volumetric fluxes. The reference interfacial drag correlations employed in this study can be applied to the PWR conditions.

In reflux cooling, the steam generated in the reactor core and the water condensed in a steam generator form a countercurrent flow in a hot leg. In order to investigate flow patterns in the hot leg under countercurrent flow conditions, countercurrent air-water tests were previously conducted using a 1/15th scale model of a PWR hot leg. Numerical simulation results for the tests using a three-dimensional twofluid model in FLUENT6.3.26, implemented with an appropriate set of correlations for the gas-liquid interfacial friction, were in good agreement with the measured data. In the present study, further numerical simulations were carried out for a full-scale hot leg under PWR plant conditions to investigate the effects of pipe diameter and fluid properties. The predicted countercurrent flow limitation characteristics were well correlated with the Wallis parameters and agreed well with the measured data from the 1/15th scale air-water tests as well as the full-scale steam-water UPTF tests. The results indica...

To examine the effects of fluid properties on countercurrent flow limitation (CCFL) in a hot leg of a pressurized water reactor (PWR), experiments are conducted using glycerol-water solutions and a 1/5 scale hot leg model with a rectangular channel. Numerical simulations are also carried out using a VOF (volume of fluid) method implemented in the CFD software, FLUENT 6.3.26. The increase in the liquid viscosity does not change the intercept coefficient C in the Wallis-type CCFL correlation but increases the proportional coefficient m, which indicates that the liquid viscosity does not affect the interfacial drag but influences the wall friction. CCFL predicted for steam-water flow at 5 MPa, corresponding to a high gas density and low liquid viscosity condition, is greatly mitigated, which indicates that the gas density has a significant effect on the interfacial drag.

One-dimensional (1D) sensitivity computations were carried out for air–water countercurrent flows in a 1/15-scale model of the hot leg and a 1/10-scale model of the pressurizer surge line in a pressurized water reactor (PWR) to generalize the prediction method for countercurrent flow limitation (CCFL) characteristics in slightly inclined pipes with elbows. In the 1D model, the wall friction coefficient fwG of single-phase gas flows was used. The interfacial drag coefficient of fi=0.03, an appropriate adjustment factor of NwL=6 for the wall friction coefficient fwL of single-phase liquid flows (NwG=1 for fwG of single-phase gas flows), and an appropriate adjustment factor of Nde=6 for the pressure loss coefficient ζe of elbows in single-phase flows were determined to give good agreement between the computed and measured CCFL characteristics. The adjusted factors were used to compute and then discuss effects of the inclination angle and diameter on CCFL characteristics.

We improved the computational grid and schemes in the VOF (volume of fluid) method with the standard 𝑘 − 𝜀 turbulent model in our previous study to evaluate CCFL (countercurrent flow limitation) characteristics in a full-scale PWR hot leg (750 mm diameter), and the calculated CCFL characteristics agreed well with the UPTF data at 1.5 MPa. In this paper, therefore, to evaluate applicability of the VOF method to different fluid properties and a different scale, we did numerical simulations for full-scale air-water conditions and the 1/15-scale air-water tests (50 mm diameter), respectively. The results calculated for full-scale conditions agreed well with CCFL data and showed that CCFL characteristics in the Wallis diagram were mitigated under 1.5 MPa steam-water conditions comparing with air-water flows. However, the results calculated for the 1/15-scale air-water tests greatly underestimated the falling water flow rates in calculations with the standard 𝑘 − 𝜀 turbulent model, but agreed well with the CCFL data in calculations with a laminar flow model. This indicated that suitable calculation models and conditions should be selected to get good agreement with data for each scale.

Air-water CCFL (countercurrent flow limitation) tests were previously carried out at Kobe University using the 1/5th scale rectangular channel and 1/15th scale circular tube simulating a PWR hot leg. Then numerical calculations for these tests and full-scale PWR conditions were made using the CFD code, FLUENT6.3.26. At Forschungszentrum Dresden-Rossendorf (FZD), similar tests were previously carried out for both air-water and steam-water flows using the 1/3rd scale rectangular channel simulating a PWR hot leg installed in the pressure chamber of the TOPFLOW facility. In this paper, numerical simulations for the air-water CCFL tests of FZD using FLUENT6.3.26 are presented and compared with the experimental data obtained at Kobe University and FZD. In the calculations, the VOF (volume of fluid) model or two-fluid (2F) model was used. In the 2F model, we used the combination of three correlations on the interfacial friction coefficients as a function of void fractions, which had been validated for the 1/15th and 1/5th scale tests at Kobe University. Calculation parameters were the air flow rates and air inlet locations, which were at the top of the reactor vessel simulator simulating the FZD test facility (inlet 1) and the opposite side of the hot leg junction simulating the test loops at Kobe University (inlet 2). Conclusions were as follows : (1) the calculated CCFL characteristics using the 2F model for the FZD tests agreed well with the 1/15th scale circular tube data obtained at Kobe University and the calculated results for full-scale PWR conditions, which supported the validity of the 1/3rd scale rectangular channel to simulate CCFL in circular tubes; (2) there were no significant differences between the calculated CCFL characteristics with the air inlet 1 and inlet 2, which indicated that the air inlet location did not influence CCFL behavior in a hot leg; and (3) comparison with the FZD data showed that the calculations using the 2F and VOF models overestimated the water flow rates for deflooding.

In the case of loss of the residual heat removal (RHR) systems under mid-loop operation during shutdown of a PWR plant, reflux cooling by a steam generator (SG) is expected, and the generated steam in a reactor core and the condensed water in the SG form a countercurrent flow in a hot leg, which consists of a horizontal pipe, an elbow and an inclined pipe. In order to improve a countercurrent flow model of a transient analysis code, countercurrent air-water tests were conducted using the 1/15th scale model of the PWR hot leg at Kobe University and the authors conducted numerical calculations of the 1/15th scale tests using the thermal-hydraulic analysis code FLUENT6.3.26 and an Euler-Euler model or a VOF model. In the tests and calculations, however, the expansion of the inclined pipe in the PWR hot leg was not simulated. In this study, using the VOF model, the authors conducted numerical calculations for a 1/15th scale model of the PWR hot leg with the expansion of the inclined pipe, which mitigates CCFL (countercurrent flow limitation) there. The calculated flow patterns in the hot leg using the VOF model were quite different with the data for the 1/15th tests without the expansion of the inclined pipe due to underestimation of CCFL characteristics at the upper end of the inclined pipe, but became similar with the observed results for the 1/15th scale model with the expansion of the inclined pipe due to the mitigation of CCFL at the inclined pipe. The results indicate that the VOF model could not correctly calculate air-water two-phase flows at the upper part of the inclined pipe but could calculate two-phase flows in the horizontal pipe.