The Steam injection through multi-hole spargers into the pressure suppression pool (PSP) is used in light water reactors to prevent containment over-pressure. The development of thermal stratification in the PSP can reduce its cooling capacity and results in higher containment pressures compared to completely mixed pool conditions. Explicit modelling of direct contact condensation (DCC) of steam at the steam-water interface is a challenge for contemporary codes. Effective Heat Source (EHS) and Effective Momentum Source (EMS) models have been proposed to enable the prediction of thermal stratification and mixing transients induced by steam condensation in a large pool. The general idea of the EHS/EMS is to resolve the effect of the DCC phenomena on a large pool, instead of explicit modelling of the small-scale phenomena at steam-water interface. The EHS/EMS models can be implemented using (i) respective boundary conditions at the boundary of the Steam Condensation Region (SCR) or (ii) using source terms in the heat and momentum transport equations. In previous work, EHS/EMS models were implemented using the second approach and validated against data from PPOOLEX and PANDA tests. It was found that results are sensitive to the spatial distribution of the source terms. Since the current data are not sufficient to provide a reasonable distribution, a preliminary study of the first method was done in this paper. The goal of this work is to develop a ‘Unit Cell’ model by using respective boundary conditions for steam injection through multi-hole sparger. The condensed turbulent jet is resolved by introducing the liquid jet with the same effective momentum and heat as the injected steam. A uniform velocity profile solved by EMS model and the temperature boundary solved by EHS model is provided on each injection hole of the sparger wall. Validation is conducted against sparger test in PANDA facilities.

NuScale is a small nuclear reactor that relies on natural circulation. Its modular production and inherent safety can not only be used to generate electricity in some remote areas, but also provide energy for water desalination and regional heating. However, the dynamic characteristics of the NuScale are different from those of the traditional PWRs because of its passive characteristic. Therefore, it is necessary to study and analyze the system dynamic characteristics of NuScale. The NuScale PWR model is established based on MATLAB&Simulink. It includes point-reactor kinetics model with six groups delayed neutrons, coolant system and steam generator system. The model is established based on the conservation equations of mass, energy and momentum. And the correctness of the model is verified by the comparison between the steady-state calculation results and the design parameters. Transient calculation results are verified by mechanism analysis. To evaluate the dynamic characteristics of NuScale, the sine function changes with different frequencies in reactor reactivity and feedwater mass flow rate are introduced. The amplitude and phase responses of reactor power, secondary loop steam pressure, secondary loop mass flow rate, secondary loop steam temperature, and coolant average temperature are recorded. Then the Bode plot can be drawn with amplitude and phase responses in different frequencies. To evaluate the NuScale dynamic characteristics, frequency domain analysis is performed.

The Pressure Suppression Pool (PSP) in a Boiling Water Reactor (BWR) is served as a heat sink to prevent containment over-pressure. The steam can be injected through the multi-hole spargers. The development of thermal stratification where a thermocline with a large temperature gradient appears in the pool can lead to the higher pressure in the dry well compared with completely mixing pool conditions. Prediction of the thermal phenomenon in the pool is necessary for the support of system design and operation. Thus, the Effective Heat Source (EHS) and Effective Momentum Source (EMS) models have been proposed. The models can be applied to CFD code by using (i) source terms in the transport equations or (ii) using respective boundary conditions at the Steam Condensation Region (SCR). Previous validation against PPOOLEX and PANDA tests using the source terms approach faced challenges in momentum distribution. Therefore, a preliminary investigation of using the second method was performed. The encouraging results implied that it is possible to further develop this approach. The goal of this work is to further develop the EHS/EMS models for the steam injection through a multi-hole sparger through the SCR model (i.e approach (ii)) and to validate it against the experimental data obtained from PANDA HP5 tests. Modeling guidelines are proposed. The temperature evolutions and vertical velocity profiles of these tests are compared to the simulation results. The agreement suggests that this model can provide an adequate estimation of the pool behavior.

An experiment performed in SPARC experimental facility, was simulated with the computational fluid dynamics code OpenFOAM. The experiment took place in two phases. In the first phase, a helium-air layer was generated, which was then eroded with a vertical air jet injected in the vessel axis during the second experimental phase. A three-dimensional and a quasi-two-dimensional numerical models of a cylindrical vessel were developed and mesh convergence studies were performed. The mixing process was simulated as a single-phase flow with common momentum equation. Included gas species mass fractions are considered as passive scalars and are calculated using the transport equation. However, term describing the molecular diffusion cannot be neglected in our case and had to be added to diffusion equation implemented in default OpenFOAM solver. The k-ε turbulence model with additional buoyancy term implemented in OpenFOAM was used for turbulence modelling. Despite improvement of the physical model and following the Best Practice Guidelines, the results obtained with OpenFOAM CFD code still, at some locations, differ substantially from the experimental results. A modified definition of low Reynolds number eddy viscosity correction function is proposed, which significantly improves the agreement between measurements and calculation results.

High fidelity velocity field experimental data in a liquid metal plenum is presented and compared with numerical simulations. While work has already been established for fluids like air and water, research on low Pr fluids (Pr ≪ 1) (e.g. liquid metals) has fewer experimental data sets with validation-quality data. Work in advanced reactors using liquid metal coolant requires validated numerical simulations for safety analyses. The Gallium Thermal-hydraulic Experiment (GaTE) facility is outfitted with acoustic backscattering measurement techniques to generate the high fidelity distributed flow field data in a liquid metal plenum (a 1/20th scale of the Department of Energy’s sodium cooled Advanced Burner Test Reactor design). The high spatial and temporal resolution of the sensors are required to capture the fluctuations of velocity to allow a more direct comparison to the numerical simulations. For these simulations the coupled mass and momentum equations under the large eddy simulation (LES) framework were solved with the wall-adapting local eddy-viscosity (WALE) model for sub-grid scale formulations. Since the temperature transients of interest for reactor safety have a period of about a minute in the GaTE system, there may not be enough time to allow statistical tools to check one-to-one correspondence. So the data collection period for both data sets was extended to allow convergence of the mean and a larger sample size for other statistics during system steady-state, isothermal tests. Two characteristic velocities of the plenum inlet barrel were investigated (U = 40, 60 mm/s; Re = 7,000, 11,000). Probability distributions show good agreement between experiment and simulation with the difference only in the low-probability tails that LES is not expected to simulate. The time averaged mean axial distribution of the vertical velocity also shows good agreement between the two setups.

The containment spray system is of great importance for the nuclear power plant to reduce the pressure and temperature, as well as concentration of radioactive aerosols released from reactor core under the severe accident. The main aim of present study is to develop a simplified model for aerosol removal by spray system, the model is employed to predict the variation of aerosol concentration in containment and reveal the key mechanism influencing aerosol removal. In the present model, the air flow entrained by spraying droplet is considered which is computed by solving simplified one-dimension momentum equations rather than the standard N-S equation. For the validation of the model, a small size sprinkle experiment facility is built. The facility is equipped with non-intrusive instruments such as particle size spectrometer for aerosol spectrum measurement, HELOS/R for measuring the droplet spectrum. The result of aerosol removal of the present model is compared with the result of the full coverage model and the experimental result. In the experiment, polydisperse aerosol is used and the removal rate of aerosols with different sizes is compared against the result of the present model and the full coverage model. The velocity of entrained gas flow and the distribution of droplets are displayed. The computational result reveals the aerosol removal constant distribution along the height.

A theoretical model for Density Wave Oscillations (DWOs) flow instability in parallel rectangular channels under periodic heaving motion is established with a lumped mathematical model based on homogenous hypothesis. The parallel rectangular channels comprise of the entrance section, the heating section, the riser section and the upper- and lower plenums, which guarantee the isobaric pressure drop condition between channels and the model consists of boiling channel model, pressure drop model, parallel channel model, additional pressure drop model generated by heaving motions, the constitutive and numerical models. The effect of periodic perturbation is introduced through additional pressure drop in the momentum equation. The model is validated with experimental data of a twin-rectangular-channel flow instability experiment under static condition. Then the flow instability in parallel-rectangular-channel system is studied under periodic perturbation and the margin of flow instability and the threshold power of the system under static condition is calculated as basis condition for comparison. The effect of the amplitude and period of perturbation is analyzed analytically and the results show that the amplitude and period of perturbation shows little effect on flow instability. While when the additional pressure difference introduced by heaving motion is comparable with that under static condition, the effect of amplitude becomes stronger. And the period of perturbation strongly effects the threshold power when it is identical to that of natural period of the system, which can be explained by resonance between the perturbation and the system. And this effect is even stronger when the asymmetric heating condition is introduced.

Interfacial drag force, which indicates the momentum transfer between liquid phase and vapor phase, is a key constitutive equation in the two-fluid model. Based on the “drift-velocity approach” (utilized in RELAP5/MOD3) and the “drag coefficient approach” (utilized in RELAP5/MOD2 and CTF), three improvements are proposed, which are: 1) improved drag coefficient closure, 2) improved drag coefficient formulation approach, 3) improved bubble radius closure approach. The comparison among the two original approaches and the three improved approaches has been made with the ORNL experiment data in high pressure-low flow condition and the results have been discussed. Results indicates: 1) the EPRI correlation predicts the void fraction worse than the drag coefficient approaches; 2) the drag coefficient correlations in CTF predicts the void fraction better than improved drag coefficient formulation approach, which are the original equations in Ishii’s model; 3) the improved drag coefficient formulation approach predicts similarly with the original RELAP5/MOD2 correlations, though it gets rid of the dependence on interfacial area concentration; 4) improved bubble radius closure approach over-predicts the void fraction, however more experiment tests should be calculated before a conclusion is drawn.

This study recaps the experimental effort to characterize a transverse plane flow field in a tightly-packed, 61-pin, wire-wrapped, hexagonal fuel bundle prototypical for a sodium fast reactor. The motive was to produce high spatiotemporal experimental data for computational fluid dynamics turbulence model validation. The matched-index-of-refraction and laser-based optical measurement techniques were utilized on an isothermal experimental flow facility. Measurements were performed on a transverse plane perpendicular to the axial flow. Fluid flow in the three types of subchannels (corner, exterior, and interior) were quantified. All measurements have been performed at a bundle-averaged Reynolds number of approximately 10,400. Results include flow statistics such as ensemble-averaged velocity, root-mean-square fluctuating velocity, and Reynolds stress. Of interest was the flow behavior around the restriction caused by the wire spacer and hexagonal duct wall, where recirculation regions formed. Regions of maximum and minimum momentum transfer coincided with regions of maximum and minimum fluctuations. These regions highlight locations of maximum and minimum cooling of the fuel pins. The experimental data will be used to benchmark computational fluid dynamics simulations of the sodium fast reactor fuel bundle using Reynolds-averaged Navier Stokes and large-eddy simulation turbulence modeling methods.

An ongoing Sandia National Laboratories’ (SNL) research study is evaluating a potential design of an injectable sacrificial material (SM) system that could contain and cool corium ejected from a reactor vessel lower head failure during a potential severe accident involving melting fuel at a commercial light water nuclear reactor (LWR). An injectable system could be installed at any existing LWR, without significant modification to the cavity or to the drywell pedestal region of the plant. The conceptual design under consideration is a passive system. The SM is being optimized to quickly cool the corium mixture while creating gas to form porosity in the solid, such that subsequent water flooding can penetrate the structure and provide additional cooling. The SM would form a barrier and limit corium-concrete interactions. This three-year project takes a joint experimental and computational approach. In this paper, we will first discuss the success of our small-scale experiments conducted on the interactions between the surrogate corium material (SCM) and SM, used to evaluate the injectable concept. A larger experimental study, currently underway, will further validate the injectable concept, with a focus on accurately measuring interactions. This paper details the modeling study and its progress, including modeling the experiments on a surrogate system and extending the model to bench-scale corium flow from validation experiments. The project’s modeling studies will use the SNL engineering code suite SIERRA Mechanics to understand the interaction of injectable SM and molten corium and predict corium spreading. Spreading is modeled using a level set method to track the front in conjunction with a pressure-stabilized finite element method on the fully three-dimensional mass, momentum, and energy conservation equations. Using this diffuse-interface method, the corium spreading front can be tracked and an appropriate pseudo-solidification viscosity models can be implemented to accurately model the corium spreading physics. Finally, an injectable SM delivery system is discussed along with its deployment to the six-common commercial LWR designs currently operating in the United States. At the end of this project, a simplified model based on SIERRA simulations will be developed for implementation into MELCOR, a severe reactor analysis code, developed at SNL for the U.S. Nuclear Regulatory Commission. This will allow us to demonstrate the ability of the injectable SM system to mitigate the ex-vessel corium spreading, provide containment and negate the release of radionuclides.

Mechanical non-homogeneous and thermal non-equilibrium phenomenon exists in two-phase critical flow compared with single phase flow. A one-dimensional two-fluid critical flow model is developed for initially subcooled water flowing in pipe or orifices. The model accounts for thermal nonequilibrium between the liquid and vapor bubbles and for interphase relative motion. In this model, an improved correlation to calculate flashing inception location and surperheat is proposed. The model consists of six conservation equations as well as a seventh equation representing bubble growth in bubbly flow. Closure of the set of governing equations is performed with constitutive relationships which determine the interfacial momentum terms due to mass exchange, wall to liquid and wall to vapour frictional forces, liquid to gas interfacial force and interfacial heat transfer rate. The model considers the development of three flow regimes, namely, bubbly, churn and annular flow regimes. Model predictions compare favorably with experimental data over a wide range of pressures and pipe diameters and lengths.

In order to simulate the transfer of mass, momentum and energy in the gas-liquid two-phase flow system, tremendous work focused on the phenomenon, mechanisms and models for two-phase flow in different channels, such as circular pipe, rectangular channel, rod bundle and annulus. Drift-flux model is one of the widely used models for its simplicity and good accuracy, especially for the reactor safety analysis codes (RELAP5 and TRAC et al.) and sub-channel analysis code (COBRA, SILFEED and NASCA et al.). Most of the adopted drift-flux models in these codes were developed based on the void fraction measured in pipe and annulus, which were different with the actual nuclear reactor. Although some drift-flux models were developed for rod bundles, they were based on the void fraction on the whole cross-section not in subchannel in rod bundles due to the lack of effective measuring methods. A novel sub-channel impedance void meter (SCIVM) has been developed to measure the void fraction in sub-channel of 5 × 5 rod bundles, which is adopted to evaluate these existing drift-flux models for rod bundles. By comparison, the values of drift-flux parameters have large differences among different correlations, which are suggested to be reconsidered. Based on the experimental data and physical laws, Lellouche-Zolotar and Chexal-Lellouche correlations show a better performance for drift velocity. If the predicting error of void fraction is the only concerned parameter, Chen-Liu, Ishizuka-Inoue and Chexal-Lellouche correlations are recommended for averaged relative error less than 30%. More experiments are suggested to focus on the distribution parameter and drift velocity through their definition.

Steam generator is a key component for realizing the heat exchange between the secondary sodium circuit and the tertiary circuit water in the sodium-cooled fast reactor. Any tiny crack of the heat-transfer tube in the steam generator may lead to the contact of water and sodium, resulting in the sodium-water reaction and the generation of hydrogen, reaction heat and other corrosive products, which further corrode the break and the adjacent tubes. In order to effectively curb the further development of small leak, timely detection of the occurrence of sodium-water reactions is particularly important. With the background of the small leak sodium water reaction caused by the crack of the steam generator heat transfer tube, in this paper the migration behavior of hydrogen in the secondary sodium circuit is analyzed, based on the mass, momentum and energy conservation equations, and the concentration of hydrogen in the secondary sodium circuit is numerically calculated one-dimensionally. The results show that the hydrogen concentration at a certain point in the circuit increases with the increase of water leaking time as a whole, when the water injection is intermittent, the hydrogen concentration at a certain point in the circuit fluctuates periodically and the basal concentration becomes higher and higher, which provides a reference for the arrangement of the secondary loop small leak detection system.

Hydrogen explosion is one of the severe threats to the integrity of containment for nuclear power plant which has drawn many experts attention to make great efforts on hydrogen related issues, espeically after the Fukushima Dai-ichi nuclear power station accident took place. However, the issue of hydrogen distribution hasn’t been closed as a result of related complex process of hydrogen transport and the particular design of each kind of facility. In the present study, CFD method has been applied to the pre-analysis on the characteristic of hydrogen mixing and stratification in a computational containment model for the sake of probable phenomena identification and instrumentaion design of experimental study in the next phase. Firstly, physical models have been verified by the experimental data from THAI HM2. Based on the determined numerical models, five typical groups of cases have been simulated, considering the effect of initial momentum, injection location, and injection direction. During the cases, only helium has been released in the vessel isothermally, on behalf of hydrogen. The results show that the backflow from the wall to the main stream in the dome and the buoyancy force may strongly dominate the helium flow, thus affacting the mixing and stratification. The eccentric injection and horizontal injection may also influence the helium distribution, in which the wall effects and rapid shifting may play important roles. However, the inference will be examined in the experiments later. All the work will be helpful for safety design and analysis of newly-built containment in China.

Thermal stratification phenomena occurring in the upper plenum during a scram transient have an important influence on the structural integrity and the passive safety of sodium-cooled fast breeder reactor (SFR). A two-dimensional thermal-hydraulic analysis code was developed under cylindrical coordinate based on conservation laws of mass, momentum and energy. Block-structured grids were generated to resolve the problems with complicated geometric properties. A second-order scheme based on midpoint rule was applied for the discretization of convection and diffusion terms. Two RANS-type turbulent models, i.e. the standard k–ε model (SKE) and the realizable k–ε model (RKE), are available in this code. A sodium test with scaled model, characterized by large aspect ratio, of a Japanese prototype SFR was used for the validation, mainly from the viewpoints of vertical temperature profiles and rising characteristics of the stratification interface. Results showed that this code could reproduce overall basic behaviors of thermal stratification. The sodium with higher temperature stayed largely stagnant in the upper region under buoyancy effect. Due to the high heat conductivity of sodium, momentum transportation made its leading function. Thus, the RKE model which accounts for the mean deformation rate gave better outcomes than the SKE model.

Passive cooling systems driven by natural circulation are common design features of proposals for advanced reactors. The natural circulation systems are inherently more unstable than forced circulation ones due to its nonlinear nature and low driving force. Any disturbance, e.g. flashing or boiling inception, in the driving force will affect the flow which in turn will influence the driving force leading to an oscillatory behavior. Owing to safety concerns, flashing instability particularly for advanced boiling water reactors has been broadly investigated, and many test facilities have been constructed in the past. A number of numerical analyses of experimental test cases are available. Nevertheless, there exists a need to update the method from one-dimensional system codes to high-resolution computational fluid dynamics (CFD). In the present work flashing-induced instability behavior and flow pattern in the riser of the GENEVA facility, which is a downscale of a reactor containment passive cooling system, is investigated using the commercial CFD code ANSYS CFX. A two-fluid model is adopted for the unstable turbulent gas-liquid flow, and the HZDR baseline closure is used to model interphase mass, momentum, heat transfer as well as bubble-induced turbulence. The simulated fluid temperature, pressure and local void fraction at different heights of the riser are compared with the measured ones. The limitation and possibility of the CFD technique for such complex two-phase scenarios are discussed, and suggestions for improving the predictability of simulations are made.

In this study, computational fluid dynamics simulation of gas-droplet flow in a spray injection in a THAI vessel is performed and the heat and mass transfer between the gas and the droplets are investigated. The purpose of the numerical simulation was validation of a CFD model to use in a hydrogen risk assessment in a containment building under severe accident conditions. The numerical simulation has to cover the physical phenomena that occur when spray water is injected downward into stationary gas in a large closed vessel. In order to model the two phase flow of the gas and droplets, two different modelling approaches are applied, one based on the Lagrangian approach and the other based on the Eulerian approach. In both approaches, the gas-droplet interactions are modelled using the two-way Lagrangian particle model and dispersed multiphase model to simulate gas-droplet interaction, two way coupling of momentum, and the heat and mass transfer between gas phase and droplet phase. For droplet heat and mass transfer, convective heat transfer and diffusion limited mass transfer are assumed. The calculated change in the temperature of the gas shows qualitative agreement with the experimental results but the gas temperature decrease was over predicted with both approaches. The calculated pressure shows good agreement with experimental results in both approaches. Both approaches also show similar prediction of temperature and pressure; therefore, they can both be applied to the containment analysis. The heat transfer coefficient in the gas-droplet heat transfer should be modified to be suitable for the spray flow. When considering that the spray system in the containment building is to be operated de-pressurized, the CFD model for the spray flow should be suitable for the thermal hydraulic analysis of the containment building.

In order to study the dynamic characteristics and fluid structure interactions of tubular structures under the action of fluid in reactor, such as fuel rod bundles and heat transfer tube bundle of steam generator, the dynamic equations and the acoustic wave equations of structures are discretized by finite element method. The acoustic wave equations are simplified from continuity equation and momentum equation of fluid field. Based on the fluid structure coupling method, the dynamic characteristics of the tube under the internal flow, external flow and combined action of internal and external flow are calculated respectively. The influence of flow field domain, element type and grid number on the dynamic characteristics of the tube is also analyzed. Secondly, based on the computational fluid dynamics and computational structural dynamics, the interaction between the two physical fields of fluid and structure is considered simultaneously. The finite volume method is used to discretize the fluid control equations and the turbulent flow is investigated using the large eddy simulation method (LES). The Newmark algorithm is used to solve the structural dynamic equations. Combined with the dynamic mesh control technique, a numerical model for flow induced vibration of three-dimensional flexible tube is established. Finally, the flow induced vibration of a three dimensional flexible single tube and a square arrangement tube bundle is calculated using the numerical model. By comparing with the existing research results, it is found that the numerical simulation results are in good agreement with the experimental results. Thus, the correctness of the model is verified. It is also shown that the numerical model established in this paper can be used to simulate the dynamic characteristics and flow induced vibration of tubular structures.

Prediction of Critical Heat Flux and dryout is crucial for BWRs. Today 1-D models based on empirical correlations are used in order to model these phenomena. However, in order to get a better physical understanding and be able to model more complex geometries CFD modeling of annular flow is developed. The complexity of annular flows makes modeling of the different interactions involved challenging. In the present study a three-field approach is used in order to model annular flow; steam, liquid droplets and liquid film represent the different fields which are coupled to each other, i.e. both mass and momentum are exchanged between the modeled fields. The steam and droplets are modeled using Euler-Lagrangian multiphase CFD model and the liquid film is modeled through empirical models implemented at the wall boundary. The implemented model is validated against experimental data with good agreement. In order to enlarge the model validity range further improvements are needed especially concerning the entrainment modeling.

The 200 MW th nuclear heat reactor II (NHR200-II) is a typical integral pressurized water reactor (iPWR) being developed by the institute of nuclear and new energy technology (INET) in Tsinghua university. The NHR200-II, which has inherent safety features such as full-range natural circulation, passive residual heat removal, self-pressurization and control rod hydraulically driving, can be adopted as a clean base-load energy source for a sea-water desalination plant having the process of multi-effect desalination with thermal vapor compression (MED-TVC). Dynamic modelling of the sea-water desalination plant coupled by the NHR200-II and MED-TVC is necessary for the design of its plant control strategy, which is important for the stable and efficient operation. In this paper, a lumped parameter dynamic model of NHR200II-based sea-water desalination plant with the process of MED-TVC is proposed based upon the conservation laws of mass, momentum and energy. The modeling verification in both the steady-state and open-loop dynamic-state are given, which show the suitability of applying this model for control system design. Finally, the closed-loop responses in the case of power-level maneuver from 100% to 50% full power is given.