Studies on Sodium Boiling Accidents in a Large Fast Breeder Reactor, (II) Radial Propagation of Sodium Boiling by Reactivity Effect

A computer code BORE was developed, with which analyses were performed on channel plugging accidents that would occur on a 1,500 MWe LMFBR. The BORE code calculated the dynamic characteristics of coolant boiling and fuel failure propagation radially in the core, and the requirements of core instrumentation systems were also analyzed. The results show that coolant boiling and/or fuel failure in a channel plugging accident are propagated only to a limited number of adjacent channels when sensors are installed that detect anomalies in channel flow, channel outlet temperature, boiling or reactivity. It is also concluded that the coolant void effect is not serious from the standpoint of safety when the time required for boiling propagation to adjacent channels can be made longer than 0.15 sec.     

CALIPSO—A computer code for the calculation of the thermodynamics, fluiddynamics and geometry changes following pin failure

The computer code CALIPSO calculates the thermodynamics and fluid-dynamics of fuel, fission gas and coolant as well as changes in geometry subsequent to pin failure in an anticipated liquid-metal fast breeder reactor (LMFBR) accident. In the documented version, CALIPSO is well suited for the analysis of the out-of pile SIMBATH experiments carried out at Kernforschungszentrum Karlsruhe (KfK) which simulate the above-mentioned accident with thermite technology. In two-dimensional geometry the fuel pin and its associated coolant channel, initially separated by the fuel cladding are treated as a single fluid domain. The conservation equations of mass, momentum and energy are solved separately for each component. The transient evolution of the temperature profile in the cladding is modeled in detail, thus permitting the analysis of various phase transition processes (melting, freezing and clad failure propagation). The coolant channel has a variable cross section and it is surrounded by an outer channel wall for single pin experiment analysis. Axially the coolant channel is connected to a simplified model of the whole sodium loop.     

A theoretical model with variable masses for the molten fuel-sodium thermal interaction in a nuclear fast reactor

In the model proposed in this paper, the reaction has been asumed to occur in two successive phases, A and B.

1. Phase A. A given number (function of time) of fuel particles come into intimate contact with a given mass of liquid sodium (function of time). The heat transfer process is characterized by good direct thermal contact between the fuel and the liquid coolant, and by a large contact area due to the small size of the particles. The heat transfer coefficient decreases with time due to the formation of a temperature profile inside the fuel particles. The heated volume of sodium is constrained by the surrounding unheated coolant and by the other materials present in the core. The mechanical constraint is schematized by a sodium column of finite length which is contained in a channel located above the reaction volume. The sudden expansion of the heated volume first produces acoustic waves which travel along the sodium column. Later the sodium column behaves like a piston which is pushed inertially upwards. The pressure rises, reaches a maximum, and then falls as soon as the expansion of the liquid sodium becomes inportant. At the time at which the pressure reaches the saturation point, sodium boiling starts and phase B begins.

2. Phase B. The heat transfer process is now characterized by a very large contact area, and by thermal contact between the fuel and coolant which becomes increasingly worse with time, due to the formation of a sodium vapour layer at the external surface of the fuel fragments. The sodium will boil in a large quantity, and will therefore produce large volume changes. The sodium piston will be further accelerated and its movement will allow the pressure in the reaction volume to decrease.

The model accounts for the time history of the temperatures of each fuel particle by means of the use of specially averaged temperature values. The calculation of the heat transfer coefficient during phase B is based on experimental results. The presence of fission gases can also be taken into account. A size distribution of fuel particles has also been incorporated into the model as well as the effect of friction due to the channel walls and that of the pressure losses at the outlet of the channel. Numerical evaluations are also included and the results are discussed. It has been concluded that the total work produced decreases with the time scale of the vapour film layer around the particles and increases with the speed at which the fuel breaks down into fragments and mixes with the liquid sodium. The effect of sodium column length has also been investigated.     

Sodium boiling: one-dimensional two-liquid modeling using the SOKRAT-BN computer code

The results of testing the thermohydraulic module of the SOKRAT-BN computing code for analyzing accidents with boiling of sodium coolant in fast reactors are presented. The computational results are compared with experimental data. It is shown that the thermohydraulic module of the SOKRAT-BN code models stationary sodium boiling well. Using as a basis the results obtained by modeling sodium boiling in a vertical heated channel, a system of closure relations for calculating two-phase sodium flow regimes, including the interphase velocity, was modified and checked. Modeling sodium boiling in a vertical annular channel also showed that the closure relations incorporated in the thermohydraulic module of the SOKRAT-BN code are suitable for calculating heat-exchange with a wall.     

Analysis of low-heat-flux sodium boiling test in a 37-pin bundle by the two-fluid model computer code SABENA

This paper summarizes the development of a new detailed multi-dimensional multi-field computer code SABENA and its application to an out-of-pile low-heat-flux sodium boiling test in a 37-pin bundle. The semi-implicit numerical method employed in the two-fluid six-equation two-phase flow model has proved in solving a wide spectrum of sodium boiling transients in a rod bundle under low pressure conditions. The code is capable of predicting the spatial incoherency of the boiling, dryout on fuel cladding surfaces and fuel pin heat transfer. Essential to the successful application of such a mechanistic model computer code are validational efforts aimed at the LMFBR accident phenomenology analyses. Through the simulation of the natural circulation boiling conditions, this study provides a consistent analytical interpretation of the experimental data. The important influences of such parameters as the inlet flow restriction and bundle geometry have been examined through interpretations of two-phase flow analysis including considerations of the flow instability induced dryout mechanism.     

The SABRE code for fuel rod cluster thermohydraulics

This paper describes the capabilities of the SABRE code for the calculation of single phase and two phase fluid flow and temperature in fuel pin bundles, discusses the methods used in the modelling and solution of the problem, and presents some results including comparison with experiments.The SABRE code permits calculation of steady-state or transient, single or two phase, flows and the geometrical options include general representation of grids, wire wraps, multiple blockages, bowed pins, etc. Transient flows may be calculated using either semi-implicit or fully implicit time solution methods and the temperature distributions within the fuel pins are determined as well as the velocity and temperature of the coolant. Two phase flows are calculated using a homogeneous boiling model, with the possibility of a specified slip between the two phases. General inlet boundary conditions are available (including pressure, velocity, total mass flow) and these may vary linearly with time; the outlet boundary condition is taken as constant pressure. The treatment of grids allows for irreversible head losses at entry and exit. The wire wrap model introduces a grid resistance tensor with its principal axes along and perpendicular to the wire, resulting in a very satisfactory modelling of inducement of swirl.The derivation and solution of the difference equations is discussed. Emphasis is given to the derivation of the spatial differences in triangular subchannel geometry, and the use of central, upwind or vector upwind schemes. The method of solution of the difference equations is described for both steady state and transient problems. Together with these topics we consider the problems involved in turbulence modelling and how it is implemented in SABRE. This includes supporting work with a fine scale curvilinear coordinate programme to provide turbulence source data. The problem of modelling boiling flows is discussed, with particular reference to the numerical problems caused by the rapid density change on boiling.The final part of the paper presents applications of the code to the analysis of blockage situations, the study of flow and power transients and analysis of natural circulation within clusters to demonstrate the scope of the code and compare with available experimental results. The comparisons include the calculation of a flow pressure drop characteristic of a boiling channel showing the Ledinegg instability, examples of overpower and flow rundown transients which lead to coolant boiling, and calculation of natural circulation within a rod cluster.     

行波堆TP-1堆芯热工水力单通道与子通道分析方法研究

以泰拉能源公司提出的钠冷行波堆TP-1为研究对象,通过钠冷行波堆瞬态安全分析程序TAST得到堆芯各组件内冷却剂、包壳和燃料棒的平均温度分布。用子通道分析程序SACOS-Na对TAST计算得到的最热组件进行详细分析计算,得到该组件内冷却剂的温度、压力和流速分布,并得到燃料棒和包壳的温度场。结果表明：单通道与子通道的结合使用能有效提高计算效率,提高反应堆设计的安全性。     

Benchmark Calculations of a Radiation Heat Transfer for a CANDU Fuel Channel Analysis using the CFD Code

To justify the use of a commercial Computational Fluid Dynamics (CFD) code for a CANDU fuel channel analysis, especially for the radiation heat transfer dominant conditions, the CFX-10 code is tested against three benchmark problems which were used for the validation of a radiation heat transfer in the CANDU analysis code, a CATHENA. These three benchmark problems are representative of the CANDU fuel channel configurations from a simple geometry to a whole fuel channel geometry. For the solutions of the benchmark problems, the temperature or the net radiation heat flux boundary conditions are prescribed for each radiating surface to determine the radiation heat transfer rate or the surface temperature, respectively by using the network method.

The Discrete Transfer Model (DTM) is used for the CFX-10 radiation model and its calculation results are compared with the solutions of the benchmark problems. The CFX-10 results for the three benchmark problems are in close agreement with these solutions, so it is concluded that the CFX-10 with a DTM radiation model can be applied to the CANDU fuel channel analysis where a surface radiation heat transfer is a dominant mode of the heat transfer.     

Thermal-hydraulic modeling of flow inversion in a research reactor

The course of loss of flow accident and flow inversion in a pool type research reactor, with scram enabled under natural circulation condition is numerically investigated. The analyses were performed by a lumped parameters approach for the coupled kinetic–thermal-hydraulics, with continuous feedback due to coolant and fuel temperature effects. A modified Runge–Kutta method was adopted for a better solution to the set of stiff differential equations. Transient thermal-hydraulics during the process of flow inversion and establishment of natural circulation were considered for a 10-MW IAEA research reactor. Some important parameters such as the peak temperatures for the hot channel were obtained for both high-enriched and low enriched fuel. The model prediction is also verified through comparison with other computer code results reported in the literature for detailed simulations of loss of flow accidents (LOFA) and the agreement between the results for the peak clad temperatures and key parameters has been satisfactory. It was found that the flow inversion and subsequent establishment of natural circulation keep the peak cladding surface temperature below the saturation temperature to avoid the escalation of clad temperature to the level of onset of nucleate boiling and sub-cooled void formation to ensure the safe operation of the reactor.     

A second order turbulence model based on a Reynolds stress approach for two-phase boiling flow. Part 1: Application to the ASU-annular channel case

High-thermal performance PWR (pressurized water reactor) spacer grids require both low pressure loss and high critical heat flux (CHF) properties. Numerical investigations on the effect of angles and position of mixing vanes and to understand in more details the main physical phenomena (wall boiling, entrainment of bubbles in the wakes, recondensation) are required.In the field of fuel assembly analysis or design by means of CFD codes, the overwhelming majority of the studies are carried out using two-equation eddy viscosity models (EVM), especially the standard K-? model, while the use of Reynolds Stress Transport Models (RSTM) remains exceptional.But extensive testing and application over the past three decades have revealed a number of shortcomings and deficiencies in eddy viscosity models. In fact, the K-? model is totally blind to rotation effects and the swirling flows can be regarded as a special case of fluid rotation. This aspect is crucial for the simulation of a hot channel in a fuel assembly. In fact, the mixing vanes of the spacer grids generate a swirl in the coolant water, to enhance the heat transfer from the rods to the coolant in the hot channels and to limit boiling.First, we started to evaluate computational fluid dynamics results against the AGATE-mixing experiment: single-phase liquid water tests, with Laser-Doppler liquid velocity measurements upstream and downstream of mixing blades. The comparison of computed and experimental azimuthal (circular component in a horizontal plane) liquid velocity downstream of a mixing vane for the AGATE-mixing test shows that the rotating flow is qualitatively well reproduced by CFD calculations but azimuthal liquid velocity is underestimated with the K-? model.Before comparing performance of EVM and RSTM models on fuel assembly geometry, we performed calculations with a simpler geometry, the ASU-annular channel case. A wall function model dedicated to boiling flows is also proposed.     

Vibration Characteristic of Heated Rod Induced by Subcooled Flow Boiling

A subcooled boiling loop with annular flow channel on an electrically heated rod at the channel axial center was used to make an experimental approach to investigate the vibration characteristic induced by subcooled flow boiling. The experiments were carried out to measure vibration induced in the rod under different conditions of incoming coolant subcooling temperature of 10–80 K, coolant flow rates of 0.1–0.35 × 10^?3 m³/s and imposed linear power densities of 17–600 W/cm. Distilled water was used as coolant in the loop. The vibration behavior of the rod was measured by using an accelerometer. Also, a high-speed motion analyzer system was used to analyze the bubble behaviors in the different subcooled boiling conditions.

The results show the intensive SBIV (subcooled boiling-induced vibration) which highly depends on dynamic force generated by rapid growth and collapse of vapor bubbles under high heat flux loading whilst they still attach to the heating surface. These behaviors were influenced strongly by the conditions of subcooling temperature, linear power density and flow rate.     

Effects of Coolant Flow on Light Water Reactor Fuel Behaviors during Reactivity Initiated Accident

This paper describes the in-pile experimental results to study the influences of coolant flow on fuel behaviors under reactivity initiated accident (RIA) conditions performed in the Nuclear Safety Research Reactor (NSRR). A single PWR type test fuel rod was irradiated by a large neutron pulse in the NSRR to simulate a prompt power excursion of RIA's. The effects of coolant flow were studied at a coolant flow velocity of 0.3~1.8m/s and a coolant temperature of 20~90°C under the atmospheric pressure. It was found that the cooling conditions had considerable influences on fuel thermal behaviors under prompt heat-up. The increase of coolant flow velocity and subcooling enhanced heat transfer coefficient at cladding surface during film boiling, which resulted in large decrease of maximum cladding temperature and film boiling duration, and consequently in the increase of fuel failure threshold energy. The data tendencies are summarized and the influences of coolant flow are discussed with some computer analyses.     

Effect of Gas Entrainment on Thermal-Hydraulic Performance of Sodium Cooled Reactor Core

With the view to determining whether or not gas entrained in the sodium coolant could cause overheating of a fast reactor core, the following items were studied:

1. The effect of gas entrainment on the coolant flow rate and on coolant temperature rise.

2. The effect of gas entrainment on the coolant heat transfer coefficient and film temperature drop.

Equations were derived to serve in estimating the thermal-hydraulic effect of the gas entrainment, and calculations performed therewith to obtain information on conditions corresponding to the Core A under operation in the Fermi Reactor.

The results of the present examination reveal that in the Fermi Reactor an amount of gas almost inconceivable as a practical possibility must be entrained before the coolant or the fuel surface would be heated to the boiling point of sodium.     

Applications of the multidimensional equations to complex fuel assembly problems

For the analysis of reactors with complex fuel assemblies or fine mesh applications as pin by pin neutron flux reconstruction, the usual approximation of the neutron transport equation by the multigroup diffusion equation does not provide good results. A classical approach to solve the neutron transport equation is to apply the spherical harmonics method obtaining a finite approximation known as the P_L equations. In this line, a nodal collocation method for the discretization of these equations on a rectangular mesh is used in this paper to analyse reactors with MOX fuel assemblies. Although the 3D P_L nodal collocation method becomes feasible due to the improvements in computer hardware, a complete treatment of the detailed structure of the fuel assemblies in actual three-dimensional geometry is still prohibitive, thus, an assembly homogenization method is necessary. A homogenization method compatible with our multidimensional P_L code is proposed and tested performing heterogeneous and homogenized calculations. In this work, we apply the method to 2D complex fuel assembly configurations.     

Effect of coolant channel width on group constants and multiplication factor of research reactors using MTR type low enriched uranium fuel

One dimensional transport theory lattice code wims-d/4 and three dimensional diffusion theory code citation have been used to study the effect of fuel loading on critical cores of low enriched uranium (LEU) fuelled material testing reactors (MTRs). The fuel loading in a fuel element was varied by changing the fuel density in the fuel meat. In order to keep the reactor critically moderated, the optimal coolant channel width for a given fuel loading was calculated. For the purpose of optimization, the group constants D, Σ_a and νΣ_f, and infinite multiplication factor (k_∞) were calculated as a function of coolant channel width using wims-d/4. An increase in ²³⁵U loading per fuel plate results in an increase in the optimal coolant channel width and k_∞. The calculated values were found to be in good agreement with the typical design of MTR. citation was then used to determine the critical cores for different fuel loading with optimized fuel dimensions. Both critical mass and volume were found to decrease with an increase in the fuel loading. The criticality studies of Pakistan research reactor-1 (PARR-1) are in good agreement with the predictions.     

Thermal hydraulic analysis of supercritical water reactor cooled by TiO2 nanofluid

Heat transfer study of nanofluids as coolant in SCWRs core has been performed at Helwan University. A thermal hydraulic code has been produced to study the effect of TiO₂ nanofluid water based as a coolant with comparison with pure water as a coolant. Various volume fractions of nanoparticles TiO₂ (2, 6 and 10%) were used in order to investigate its effects on reactor thermalhydraulic characteristics. Based on Parameters of a SCW Canadian Deuterium Uranium nuclear reactor (CANDU), the fuel assembly was modeled to study the effect of nanoparticles volume fraction on thermos-physical properties of basic fluid and the temperature distribution of fuel, cladding surface and coolant in axial direction. The theoretical results showed that the density, viscosity and thermal conductivity of the coolant increases with the increase of nanoparticles volume fraction, contrasting to specific heat, which decreases with the increase in nanoparticles volume fraction.     

Multi-fluid multi-phase subchannel analysis of subassembly accidents of LMFRs

Analyses of experiments simulating hypothetical subassembly accidents such as a large-scale inlet blockage in a Liquid Metal Cooled Fast Reactor (LMFR) have been performed with computer program KAMUI. With the use of relatively simple but reasonable constitutive models, the code has been applied to the SCARABEE experiments BE+1 and APL1 to validate the analytical capability against the accident conditions under the multi-pin geometry. The results show that the key events such as sodium boiling, clad melting, molten clad relocation, molten clad freezing were adequately simulated taking into account the effect of heat loss to the coolant flow in the outside channel of the test section.