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.

To obtain a better subchannel analysis tool for PWR core, an investigation on the physical modelling was done via CFD analysis in this paper. A detailed discussion on the TH status was carried out to consider the suitability of the physical modelling in the subchannel analysis. The counteracted effect on the balance of the mass, momentum, and energy was found. Its influence on the physical mechanism was analyzed for the TH status in PWR core. Then it was found that the subchannel analysis based on each flow channel is very necessary for the accuracy of the 3D engineering TH analysis for the whole PWR core.

A detailed safety assessment of innovative Generation IV reactor designs with heavy-liquid metal coolants, such as lead and lead-bismuth eutectic (LBE), requires an evaluation of the maximum core temperature in several postulated scenarios. Considering the complex geometry of fuel assemblies (FAs), and the low Prandtl number of the coolants, this flow scenario is challenging for the models used in numerical simulations, e.g. for relating the turbulent transport of momentum and heat. Thus, reliable experimental data are needed for validation. In recent years, a series of comprehensive heat transfer tests in fuel pin bundle simulators was performed at ENEA (Italy) and KIT (Germany) in the framework of the European collaborative projects THINS and SEARCH. Both grid and wire spacer geometries are considered, in a wide range of operating conditions (temperature, flow velocity and power density) representative of the ALFRED and MYRRHA fuel assemblies, in natural and forced-convective flow regimes. Although different experimental approaches were followed by each group (e.g. thermocouple position and average data treatment), there is a relatively good agreement on results in the overlapping regions. These experimental studies indicate that the mean Nusselt number is in well agreement with the predictions of empirical correlations developed for sodium systems. In particular, for wire-spaced FA, heat transfer results show values close to the Kazimi-Carelli correlation both for low and high flow rates at ENEA and KIT respectively. For grid-spaced FA, results are more in agreement with Ushakov correlation. Furthermore, large temperature differences are measured by thermo-couples installed at selected rods and sub-channels. A discussion on the influences of the spacer design and bundle size is included. This wide comparison allows an overview of the research on the HLM cooled fuel assembly in Europe.

Eulerian steady one-dimensional two-fluid mass and momentum conservation equations for gas and water droplet coupled with the particle removal rate are formulated. The major flow variables are phasic velocities and pressure and they are obtained by integrating the four conservation equations and one particle removal rate along the horizontal throats of the venturi scrubbers by using the forth-order Runge-Kutta method. Popular correlations are used for the impaction parameter, the gas-to-water droplet drag coefficient and the droplet size. All the equations are integrated into one computer code named REMAERO based on the MATLAB. It is found that most particles are removed at the throat entrance as already known from the previous experiments and this is due to the particle removal rate proportional to the particle concentration. Particle removal efficiencies from the present method shows better agreement with existing experimental data than previous one-dimensional models.

The nuclear heating reactor (NHR) is a typical integral pressurized water reactor (iPWR) developed by the institute of nuclear and new energy technology (INET) of Tsinghua University, which has the safety advanced features such as the primary circuit integral arrangement, full-range natural circulation, self-pressurization. Power-level control is crucial for the operational stability and efficiency of the NHR, and the dynamic modeling is a basis for control system design and verification. From the conservation laws of mass, energy and momentum, a lumped-parameter dynamical model is proposed for the nuclear steam supply system (NSSS) based on the 200MW th nuclear heating reactor II (NHR200-II). The steady-state model validation is given by the comparing the parameter values of this model and that for plant design. Then, both the open-loop responses under the disturbances of reactivity and coolant flowrates as well as the closed-loop responses under the case of power ramp are given, where the rationality of the responses are analyzed from the viewpoint of plant physics and thermal-hydraulics. This model can be utilized for not only the control system design but also the development of a real-time simulator for the hardware-in-loop control system verification.

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.

The steam flow is simulated by FLUENT. The Lagrange-Euler method is used to simulate the droplet-laden flow in wave-type separators. Two-way coupling method is used to study the influence of the momentum transfer between droplets and carrier-phase in wave-type plate separators. A group of the trajectories of droplets with different diameters are performed in wave-type plate separator flow field. The result shows that the momentum transfer has tiny impact on the behaviors of droplets in a low velocity flow. However, the momentum transfer affects the behaviors of droplets more significantly with rising flow velocity. The one-way coupling method overestimates the diffusion of droplets. In addition, the momentum transfer affects the total pressure loss more significantly with rising volume fraction. The conclusion verifies the importance of the momentum transfer in droplet-laden flows, which could be used to simulate the behavior of droplets moving in a separator.

As one of the six selected optional innovative nuclear reactor in the generation IV International Forum (GIF), the Molten Salt Reactor (MSR) adopts liquid salt as nuclear fuel and coolant, which makes the characteristics of thermal hydraulics and neutronics strongly intertwined. Coupling analysis of neutronics and thermal hydraulics has received considerable attention in recent years. In this paper, a new coupling method is introduced based on the Finite Volume Method (FVM), which is widely used in the Computational Fluid Dynamics (CFD) methodology. Neutron diffusion equations and delayed neutron precursors balance equations are discretized and solved by the commercial CFD package FLUENT, along with continuity, momentum and energy equations simultaneously. A Temporal And Spatial Neutronics Analysis Model (TASNAM) is developed using the User Defined Functions (UDF) and User Defined Scalar (UDS) in FLUENT. A neutronics benchmark is adopted to demonstrate the solution capability for neutronics problems using the method above. Furthermore, a steady state coupled analysis of neutronics and thermal hydraulics for the Molten Salt Advanced Reactor Transmuter (MOSART) is performed. Two groups of neutrons and six groups of delayed neutron precursors are adopted. Distributions of the liquid salt velocity, temperature, neutron flux and delayed neutron precursors in the core are obtained and analyzed. This work can provide some valuable information for the design and research of MSRs.

The multi-inlet condenser has two steam inlets, the main steam inlet of main steam turbine and the steam inlet of auxiliary steam turbine. In this paper, it establishes a two-dimensional model for the multi-inlet condenser. The porous medium concept is used in the simulations. A porosity factor is incorporated into the governing equations to account for the flow volume reduction due to the tube bundles, baffles and other internal obstacles. The mathematical model is based on the fundamental governing conservation equations of mass and momentum, and the air mass fraction conservation equation. Then, the equations are solved by the SIMPLEC algorithm. Research results indicates that : 1) The physical fields, including pressure, velocity, thermal resistances and condensation rate, are obtained by numerical simulation of the multi-inlet condenser. 2) The performance of multi-inlet condenser is better than the performance of single-inlet condenser from the point of view of pressure drop. 3) There is an optimum angle of auxiliary steam inlet to make the minimum pressure drop. The optimum angle of the multi-inlet condenser used in this study is 50.65°.