Dynamic behavior of a solid particle bed in a liquid pool: SIMMER-III code verification

Dynamic behavior of solid particle beds in a liquid pool against pressure transients was investigated to model the mobility of core materials in a postulated disrupted core of a liquid metal fast reactor. A series of experiments was performed with a particle bed of different bed heights, comprising different monotype solid particles, where variable initial pressures of the originally pressurized nitrogen gas were adopted as the pressure sources. Computational simulations of the experiments were performed using SIMMER-III, a fast reactor safety analysis code. Comparisons between simulated and experimental results show that the physical model for multiphase flows used in the SIMMER-III code can reasonably represent the transient behaviors of pool multiphase flows with rich solid phases, as observed in the current experiments. This demonstrates the basic validity of the SIMMER-III code on simulating the dynamic behaviors induced by pressure transients in a low-energy disrupted core of a liquid metal fast reactor with rich solid phases.     

Development of multicomponent vaporization/condensation model for a reactor safety analysis code SIMMER-III: Extended verification using multi-bubble condensation experiment

Complex phenomena such as phase transitions and heat transfers in multiphase, multicomponent flows were modeled in the fluid-dynamics portion of SIMMER-III, which was developed to appropriately assess core disruptive accidents (CDAs) in liquid–metal fast reactors (LMFRs). A new multicomponent vaporization/condensation (V/C) model was developed and introduced to SIMMER-III by the authors. In the present study, a new series of multi-bubble condensation experiments was performed to demonstrate that SIMMER-III with the present V/C model is practically applicable to multicomponent, multiphase flow systems with phase transition. In the experiments, bubble diameters and void fractions were quantified from visualization images using original image-processing techniques. Comparing SIMMER-III predictions with experimental data, it was confirmed that SIMMER-III with the proposed V/C model could suitably represent the effects of noncondensable components on the condensation process in multi-bubble systems. This work has improved the reliability of SIMMER-III with regard to multicomponent phase-transition phenomena.     

Evaporation and condensation heat transfer with a noncondensable gas present

To evaluate the system pressure of an external water wall type containment vessel, which is one of the passive systems for containment cooling, the evaporation and condensation behavior under a noncondensable gas presence has been experimentally examined. In the system, steam evaporated from the suppression pool surface into the wetwell, filled with noncondensable gas, and condensed on the containment vessel wall. The system pressure was the sum of the noncondensable gas pressure and saturated steam pressure in the wetwell. The wetwell temperature was, however, lower than the supression pool temperature and depended on the thermal resistance on the suppression pool surface. The evaporation and condensation heat transfer coefficients in the presence of air as noncondensable gas were measured and expressed by functions of steam/air mass ratio. The evaporation heat transfer coefficients were one order higher than the condensation heat transfer coefficients because the local noncondensable gas pressure was much lower on the evaporating pool surface than on the condensing liquid surface. Using logal properties of the heat transfer surfaces, there was a similar trend between evaporation and condensation even with a noncondensable gas present.     

Experimental and empirical study of steam condensation heat transfer with a noncondensable gas in a small-diameter vertical tube

An experimental study was performed to investigate local condensation heat transfer coefficients in the presence of a noncondensable gas inside a vertical tube. The data obtained from pure steam and steam/nitrogen mixture condensation experiments were compared to study the effects of noncondensable nitrogen gas on the annular film condensation phenomena. The condenser tube had a relatively small inner diameter of 13 mm (about 1/2-in.). The experimental results demonstrated that the local heat transfer coefficients increased as the inlet steam flow rate increased and the inlet nitrogen gas mass fraction decreased. The results obtained using pure steam and a steam/nitrogen mixture with a low inlet nitrogen gas mass fraction were similar. Therefore, the effects of noncondensable gas on steam condensation were weak in small-diameter condenser tubes.A new correlation was developed to evaluate the condensation heat transfer coefficient inside a vertical tube with noncondensable gas, irrespective of the condenser tube diameter. The new correlation proposed herein is capable of predicting heat transfer rates for tube diameters between 1/2- and 2-in. because of the unique approach of accounting for the heat transfer enhancement via an interfacial shear stress factor.     

Analysis of gas–liquid metal two-phase flows using a reactor safety analysis code SIMMER-III

SIMMER-III, a safety analysis code for liquid-metal fast reactors (LMFRs), includes a momentum exchange model based on conventional correlations for ordinary gas–liquid flows, such as an air–water system. From the viewpoint of safety evaluation of core disruptive accidents (CDAs) in LMFRs, we need to confirm that the code can predict the two-phase flow behaviors with high liquid-to-gas density ratios formed during a CDA. In the present study, the momentum exchange model of SIMMER-III was assessed and improved using experimental data of two-phase flows containing liquid metal, on which fundamental information, such as bubble shapes, void fractions and velocity fields, has been lacking.

It was found that the original SIMMER-III can suitably represent high liquid-to-gas density ratio flows including ellipsoidal bubbles as seen in lower gas fluxes. In addition, the employment of Kataoka–Ishii’s correlation has improved the accuracy of SIMMER-III for gas–liquid metal flows with cap-shape bubbles as identified in higher gas fluxes. Moreover, a new procedure, in which an appropriate drag coefficient can be automatically selected according to bubble shape, was developed.

Through this work, the reliability and the precision of SIMMER-III have been much raised with regard to bubbly flows for various liquid-to-gas density ratios.     

Effect of noncondensable gas in a vertical tube condenser

An experimental study is performed to investigate the effects of noncondensable (NC) gas in the steam condensing system. A vertical condenser tube is submerged in a water pool where the heat from the condenser tube is removed by boiling heat transfer. The design of the test section is based on the passive condenser system in an advanced boiling water nuclear power reactor. Data are obtained for various process parameters, such as inlet steam flow rate, noncondensable gas concentration, and system pressure. Degradation of the condensing performance with increasing noncondensable gas is investigated. The condensation heat transfer coefficient and heat transfer rate decrease with noncondensable gas. The condensation heat transfer rate is enhanced by increasing the inlet steam flow rate and the pressure. The condensation heat transfer coefficient increases with the inlet steam flow rate, however, decreases with the system pressure. For the condenser submerged in a water pool with saturated condition, the strong primary pressure dependency is observed.     

含不凝性气体的蒸汽气泡凝结过程研究

利用高速摄像仪对高过冷度下含不凝性气体的蒸汽气泡冷凝及破裂过程进行可视化研究,以分析不凝性气体对气泡微细化沸腾(MEB)过程的影响。实验结果表明:初始不凝性气体体积份额x0小于2.5%时,气泡突然破碎成大量微小气泡;x0在2.5%~7.5%之间时,较大气泡只会分裂成数个小气泡;x0大于7.5%时,气泡界面非常稳定,不会发生破碎和分裂现象。此外,当蒸汽气泡中含有较多不凝性气体时,气泡凝结过程减弱,液体对气泡的惯性冲击减小,气泡不易破裂。由此可表明,在气泡微细化沸腾发生时,不凝性气体的存在会阻碍加热面上气泡的破碎,从而降低传热能力。     

Research on the steam–gas pressurizer model with Relap5 code

Steam–gas pressurizers are self-pressurizing, and since steam and noncondensable gas are used to sustain their pressure, they experience very complicated thermal–hydraulic phenomena owing to the presence of the latter. A steam–gas pressurizer model was developed using Relap5 code to investigate such a pressurizer's thermal–hydraulic characteristics.The important thermal–hydraulic processes occurring in the pressurizer model include bulk flashing, rainout, wall condensation with noncondensable gas, and interfacial heat and mass transfer. The pressurizer model was verified using results from insurge experiments performed at the Massachusetts Institute of Technology. It was found that noncondensable gas was one of the important factors governing the pressure response, and the accuracy of the developed model would change with different mass fractions and types of noncondensable gas.     

Jet-plume condensation of steam-air mixtures in subcooled water. Part 2: Code model

The system-analysis thermal-hydraulics code, TRACE, was used to model jet-plume condensation of steam and steam-air mixtures in a subcooled pool. The code model was used to compare the pool temperature development in a scaled-down test facility suppression pool (SP) represented by an idealized trapezoidal cross-section and 1/10 sector of a with scaled height ratio of 1/4.5 and volume ratio of 1/400. Thermal stratification and pool mixing data obtained in the experimental test section at different pool initial subcooling and steam/air mixture flow rates were used a validation suite to benchmark against the performance of the code. Agreement of the code simulations to experiments were seen in cases of pool mixing, however, instances of pool thermal stratification and transitional regimes between stratification and mixing were not predicted correctly by the code. The experimental database described in part 1 to this paper provides the benchmark suite to be used for future developmental improvement in areas of the code which may have future application to analysis of thermal heat removal rates in large pools.     

Development of multicomponent vaporization/condensation model for a reactor safety analysis code SIMMER-III: Theoretical modeling and basic verification

It is believed that the numerical simulation of thermal-hydraulic phenomena of multiphase, multicomponent flows in a reactor core is essential to investigate core disruptive accidents (CDAs) of liquid-metal fast reactors. A new multicomponent vaporization/condensation (V/C) model was developed to provide a generalized model for a fast reactor safety analysis code SIMMER-III, which analyzes relatively short-time-scale phenomena relevant to accident sequences of CDAs. The model characterizes the V/C process associated with phase transition through heat-transfer and mass-diffusion limited models to follow the time evolution of the reactor core under CDA conditions. The heat-transfer limited model describes the nonequilibrium phase-transition processes occurring at interfaces, while the mass-diffusion limited model is employed to represent effects of noncondensable gases and multicomponent mixture on V/C processes. Verification of the model and method employed in the multicomponent V/C model of SIMMER-III was performed successfully by analyzing a series of multicomponent phase-transition experiments.     

Numerical Analysis of the PHEBUS Containment Thermal Hydraulics

This paper describes numerical analysis of the PHEBUS FP containment thermal-hydraulics. PHEBUS FP is an international project undertaken with the aim of evaluating the behavior of radioactive fission products released from a LWR pressure vessel into the containment vessel during a hypothetical severe accident. Six integral in-pile tests have been planned and are being carried out at Cadarache, France. The European Union, the United States, Canada, Korea and Japan are participating in this project. From Japan, the Nuclear Power Engineering Corporation and the Japan Atomic Energy Research Institute are collaborating the other parties involved in the project.

Since the behavior of fission products is strongly dependent on the surrounding environmental conditions, accurate prediction of the thermal-hydraulics in the containment vessel is essential to accurately evaluate the behavior. Characteristics of condensation heat transfer in the presence of noncondensable gases play a key role in the PHEBUS thermal-hydraulics, especially under the condition of high noncondensable gas mass fraction. Many models for condensation heat transfer in the presence of noncondensable gases have been proposed. However, these models were not found suitable for PHEBUS analysis, because they were focused on the low noncondensable gas mass fraction condition.

In this study, a single-phase multi-component code, TFLOW-FP has been newly developed to predict thermal-hydraulics in the PHEBUS FP containment. Moreover, a new degradation factor correlation for the condensation heat transfer coefficient due to the presence of noncondensable gases has also been developed and incorporated into the code. This code was applied for analysis of the thermal-hydraulic benchmark tests and the first in-pile test, FPTO. The results show that the code can predict the total pressure, gas temperature distributions, the relative humidity in the containment vessel and steam condensation rate on the surface of condenser rods very well.     

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.     

Experimental analysis of heat transfer within the AP600 containment under postulated accident conditions

The new AP600 reactor designed by Westinghouse uses a passive safety system relying on heat removal by condensation to keep the containment within the design limits of pressure and temperature. Even though some research has been done so far in this regard, there are some uncertainties concerning the behavior of the system under postulated accident conditions. In this paper, steam condensation onto the internal surfaces of the AP600 containment walls has been investigated in two scaled vessels with similar aspect ratios to the actual AP600. The heat transfer degradation in the presence of noncondensable gas has been analyzed for different noncondensable mixtures of air and helium (hydrogen simulant). Molar fractions of noncondensables/steam ranged from (0.4–4.0) and helium concentrations in the noncondensable mixture were 0–50% by volume. In addition, the effects of the bulk temperatures, the mass fraction of noncondensable/steam, the cold wall surface temperature, the pressure, noncondensable composition, and the inclination of the condensing surface were studied. It was found that the heat transfer coefficients ranged from 50 to 800 J s⁻¹ K⁻¹ m⁻² with the highest for high wall temperatures at high pressure and low noncondensable molar fractions. The effect of a light gas (helium) in the noncondensable mixture were found to be negligible for concentrations less than approximately 35 molar percent but could result in stratification at higher concentrations. The complete study gives a large and relatively complete data base on condensation within a scaled AP600 containment structure, providing an invaluable set of data against which to validate models. In addition, specific areas requiring further investigation are summarized.     

Reply to: “Comments on studies on diversion cross-Flow between two parallel communicating channels by a lateral slot — Part I” by J. Weisman

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.     

A model for the performance of a vertical tube condenser in the presence of noncondensable gases

Some proposed vertical tube condensers are designed to operate at high noncondensable fractions, which warrants a simple model to predict their performance. Models developed thus far are usually not self-contained as they require the specification of the wall temperature to predict the local condensation rate. The present model attempts to fill this gap by addressing the secondary side heat transfer as well. Starting with a momentum balance which includes the effect of interfacial shear stress, a Nusselt-type algebraic equation is derived for the film thickness as a function of flow and geometry parameters. The heat and mass transfer analogy relations are then invoked to deduce the condensation rate of steam onto the tube wall. Lastly, the heat transfer to the secondary side is modelled to include cooling by forced, free or mixed convection flows. The model is used for parametric simulations to determine the impact on the condenser performance of important factors such as the inlet gas fraction, the mixture inlet flowrate, the total pressure, and the molecular weight of the noncondensable gas. The model performed simulations of some experiments with pure steam and air-steam mixtures flowing down a vertical tube. The model predicts the data quite well. The model described also provides a basis under which the presence of aerosol particles in the gas stream could be analyzed.     

Summary of fusion sessions at the SMiRT-5 conference

We describe a computer code that combines an Eulerian incompressible-fluid algorithm (SOLA) with a Lagrangian finite-element shell algorithm. The former models the fluid and the latter models the containing structure in an analysis of pressure suppression in boiling-water reactors. The code (PELE-IC) calculates loads and structural response from air blowdown and from the oscillatory condensation of steam bubbles in a water pool. The fluid, structure, and coupling algorithms are tested by recalculating problems that have known analytical solutions, including tank drainage, spherical bubble growth, coupling for circular plates, and submerged cylinder vibration. Code calculations are also compared with the results of small-scale blowdown experiments.     

Modeling of condensation heat transfer for a PRHRS heat exchanger in a SMART-P plant

A theoretical model using a heat and mass transfer analogy and a simple model using Lee and Kim's [Lee, K.-Y., Kim, M.H., 2008a. Experimental and empirical study of steam condensation heat transfer with a noncondensable gas in a small-diameter vertical tube. Nucl. Eng. Des. 238, 207-216] correlation were developed to investigate steam condensation in the presence of a noncondensable gas inside a vertical tube submerged in pool water. Rohsenow's correlation was used to consider the secondary pool-boiling heat transfer. Both models were assessed with the experimental data of Oh and Revankar [Oh, S., Revankar, S.T., 2005a. Investigation of the noncondensable effect and the operational modes of the passive condenser system. Nucl. Technol. 152, 71-86; Oh, S., Revankar, S.T., 2005b. Effect of noncondensable gas in a vertical tube condenser. Nucl. Eng. Des. 235, 1699-1712; Oh, S., Revankar, S.T., 2005c. Complete condensation in a vertical tube passive condenser. Int. Commun. Heat Mass Trans. 32, 593-602; Oh, S., Revankar, S.T., 2005d. Analysis of the complete condensation in a vertical tube passive condenser. Int. Commun. Heat Mass Trans. 32, 716-727; Oh, S., Revankar, S.T., 2006. Experimental and theoretical investigation of film condensation with noncondensable gas. Int. J. Heat Mass Trans. 49, 2523-2534; Oh, S., Gao, H., Revankar, S.T., 2007. Investigation of a passive condenser system of an advanced boiling water reactor. Nucl. Technol. 158, 208-218] for low pressure and Kim [Kim, S.J., 2000. Turbulent film condensation of high pressure steam in a vertical tube of passive secondary condensation system. Ph.D. dissertation, Korea Advanced Institute of Science and Technology] for high pressure, which were obtained from in-tube steam condensation with air in the pool water. These models predicted the data of Oh and Revankar well, but they slightly underestimated the data of Kim. The design of the Passive Residual Heat Removal System (PRHRS) condensation heat exchanger was evaluated with the theoretical model at real operating conditions (e.g., secondary pool-boiling, high system pressure). The PRHRS condensation heat exchanger designed was estimated to remove sufficiently the remaining heat in a reactor during a major accident.     

Computer calculations of air and steam blowdown suppression

We describe a computer code that combines an Eulerian incompressible-fluid algorithm (SOLA) with a Lagrangian finite-element shell algorithm. The former models the fluid and the latter models the containing structure in an analysis of pressure suppression in boiling-water reactors. The code (PELE-IC) calculates loads and structural response from air blowdown and from the oscillatory condensation of steam bubbles in a water pool. The fluid, structure, and coupling algorithms are tested by recalculating problems that have known analytical solutions, including tank drainage, spherical bubble growth, coupling for circular plates, and submerged cylinder vibration. Code calculations are also compared with the results of small-scale blowdown experiments.     

Condensation heat transfer characteristic in the presence of noncondensable gas on natural convection at high pressure

The steam-gas pressurizer in integrated small reactors experiences very complicated thermal-hydraulic phenomena. Especially, the condensation heat transfer with noncondensable gas under natural convection is an important factor to evaluate the pressurizer behavior. However, few studies have investigated the condensation in the presence of noncondensable gas at high pressure. In this study, therefore, a theoretical model is proposed to estimate the condensation heat transfer at high pressure using the heat and mass transfer analogy. For the high pressure effect, the steam and nitrogen gas tables are used directly to determine the density of the gas mixture and the heat and mass transfer analogy based on mass approach is applied instead of that based on the ideal gas law. A comparison of the results from the proposed model with experimental data obtained from Seoul National University indicates that the condensation heat transfer coefficients increase with increasing system pressure and with decreasing mass fraction of the nitrogen gas. The proposed model is also compared with other conventional correlations proposed in the literature. The proposed model demonstrates the capability to predict the condensation heat transfer coefficients at high pressure better than any other correlation. Finally, the condensate rate is compared to verify the application of the heat and mass transfer analogy at high pressure. The comparison results confirm that the heat and mass transfer analogy can be applied to evaluate the condensation heat and mass transfer at high pressure.     

Simulation of basic gas mixing tests with condensation in the PANDA facility using the GOTHIC code

The paper reports the results of the assessment of the GOTHIC code using the data of four basic tests with condensation performed in the PANDA large-scale facility. Three of these experiments featured vertical injection, and in one the transient response due to a high-momentum horizontal injection (jet) was investigated. The injected fluid was either saturated steam or a superheated mixture of steam and helium, and the fluid initially present in the vessels was pure air. The simulations were carried out using a detailed three-dimensional representation of the vessels. In general, the results of the simulations, which used a relatively coarse mesh, were in good agreement with the data. Limitations in modelling local phenomena controlled by complex flow patterns (e.g. heat transfer in the region of an impinging jet) and the need for refined meshes to reproduce certain aspects of the transients (e.g. erosion of the interface between layers of different gas composition) were also identified. Finally, the analyses indicated that in two tests the role played by re-vaporisation of the condensate film was unexpectedly large, and this effect should be more carefully considered in the containment analyses and future model developments.