Response Surface Modeling of Aerosol Release Fraction in Sodium Pool Combustion

A response surface model has been proposed to evaluate an aerosol release fraction during sodium pool fire in a liquid metal fast reactor (LMFR). Air containing aerosols are radiative and they influence the allocation of combustion heat from the flame to atmospheric gas or sodium pool. Hence, the aerosol release fraction needs to be quantified based on the behavior of the aerosols and physics of mass and heat transfer. However, the aerosol release fraction is one of user-specified parameters of computer codes for the sodium fire safety analysis of the LMFR. In the present study, a response surface model of the aerosol release fraction has been developed based on numerical experiments of aerosol dynamics. For developing the model, aerosol dynamic equation has been solved coupled with thermal-hydraulics and chemical reaction. The authors obtained good agreement of the aerosol release fraction between the numerical experiments and the past experiments. Therefore, the aerosol behavior model has been validated with regard to the pool combustion phenomena and is reasonably applicable to the numerical experiment. Three influential variables on the release fraction are identified as pool temperature, gas temperature and oxygen molar fraction in the air. The proposed response surface model is a quadratic expression of the influential variables and can be easily employed in the sodium fire analysis code.     

Dynamics of liquid sodium pool spreading under sodium fire conditions

The spreading of burning liquid sodium has been investigated using a depth-averaged shallow water equation for isothermal and non-isothermal (burning) conditions. In the latter case, the spreading is one-way coupled with the flame through a separate energy equation for the pool, with appropriate source terms for radiative and conductive heat transfer from the flame, and a sink term (for the continuity equation) to account for loss due to burning. Pool fires on soil and concrete surface have been considered with appropriate friction and heat transfer terms in the momentum and energy equations, respectively. Using this model, numerical simulations have been carried out for a wide range of leak rates, and for a range of burning rates of liquid sodium. Results obtained from the non-isothermal model show that the non-isothermal effects of liquid sodium spreading can safely be neglected for the case or spreading of burning liquid sodium on a typical ground surface such as concrete or soil. Based on these conclusions, dimensionless correlations are proposed for the prediction of spreading parameters such as, equilibrium pool radius, pool formation time, and for mass inventory under pool fire conditions for liquid sodium. These parameters which are obtained from the spreading code can be specified, as input parameters for the existing sodium fire safety codes.     

Validation study of computer code sphincs for sodium fire safety evaluation of fast reactor

A computer code sphincs solves coupled phenomena of thermal hydraulics and sodium fire based on a multi-zone model. It deals with an arbitrary number of rooms, each of which is connected mutually by doorways and penetrations. With regard to the combustion phenomena, a flame sheet model and a liquid droplet combustion model are used for pool and spray fires, respectively, with the chemical equilibrium model based on the Gibbs free energy minimization method. The chemical reaction and mass and heat transfer are solved interactively. A specific feature of sphincs is detailed representation of thermalhydraulics of a sodium pool and a steel liner, which is placed on the floor to prevent sodium-concrete contact. The authors analyzed a series of pool combustion experiments, in which gas and liner temperatures are measured in detail. It has been found that good agreement is obtained and the sphincs code has been validated with regard to pool combustion phenomena. Further research needs are identified for pool spreading modeling considering thermal deformation of steel liner and measurement of pool fluidity property as a mixture of liquid sodium and reaction products. The sphincs code is to be used mainly in the safety evaluation of the consequence of a sodium fire accident in a liquid metal cooled fast reactor as well as fire safety analysis in general.     

钠冷快堆中池式钠火的计算分析

文章论述了根据池式钠火的特点建立了理论模型 ,编制了SPOOL程序。该程序模拟钠燃烧过程中钠和氧气的化学反应 ,钠燃烧热在各种介质中不同方式的传递 ,钠气溶胶的产生、沉积 ,以及在各种通风条件下多种介质的质量和能量交换等瞬态过程 ,描述了钠燃烧过程中各种特征参数随时间的变化。其主要的计算参数包括房间内气体的压力和温度、房间建筑结构的温度、钠气溶胶质量浓度等等。用俄罗斯别洛雅尔斯克核电站实验和法国卡桑德拉 3号实验的数据 ,对SPOOL程序进行验证的结果表明 ,该程序的计算结果可信。该程序为国内钠冷快堆中池式钠火事故的安全分析提供了分析方法     

雾状钠火钠滴燃烧比率的模拟及应用

将雾状钠火中钠滴的燃烧分成预燃阶段和燃烧阶段，利用雾状钠火程序计算得到钠滴燃烧比率和时间的关系曲线，分别用幂函数、指数函数和线性函数对曲线进行拟合，拟合效果较好。拟合函数中包含钠滴下落时间和钠滴最大燃烧比率等参数，这些参数可通过钠滴下落燃烧试验或雾状钠火程序计算得到。通过推导得到了雾状钠火燃烧和单个钠滴燃烧的关系，钠滴燃烧比率的拟合函数被用来模拟雾状钠火燃烧的过程，包括用于计算已燃烧的钠质量、空气中未燃烧的钠质量、进入钠池的钠质量和雾状钠火的燃烧速率。当雾状钠火燃烧过程中钠泄漏流量恒定不变时，空气中未燃烧的钠质量和钠泄漏流量呈正比，雾状钠火的燃烧速率和钠泄漏流量呈正比。雾状钠火的燃烧速率和钠火造成的事故工艺间内的温度与压力变化直接相关。雾状钠火的燃烧速率被用来求解钠气溶胶的生成速率、钠燃烧火焰层和空气之间的传热、钠燃烧火焰层和墙壁之间的传热。总之，使用简单的函数模拟钠滴的燃烧比率曲线，将雾状钠火燃烧当成事故工艺间的热源和钠气溶胶源作为输入，便可模拟雾状钠火的整个燃烧过程，计算得到工艺间温度、压力和钠气溶胶浓度的变化。钠滴的燃烧比率曲线、雾状钠火的燃烧速率曲线还可与试验数据进行对比验证后作为雾状钠火模拟的输入，这种模拟方法可用于钠火事故安全分析中雾状钠火的模拟。     

池式钠火事故下燃烧产物气溶胶行为研究

在钠冷快堆的安全评估中,分析钠泄露导致的池式钠火事故下燃烧产物的气溶胶行为尤为重要。本文采用将池式钠火燃烧模型与气溶胶动力学模型耦合的方式,开发了池式钠火事故下燃烧产物气溶胶行为分析程序REBAC-SFR,基于该程序模拟了SAPFIRE-D1和ABCOVE池式钠火实验,并与实验数据进行了对比。结果表明,本文开发的程序具有良好的可靠性和正确性,可为钠工艺间内池式钠火事故下燃烧产物气溶胶行为分析研究提供理论工具。      

钠冷快堆钠池火事故数值模拟

为了估计和预测钠火事故的后果，构建了以“有火焰薄层”为理论基础的燃烧模型和热传输模型，给出了程序计算结果与试验值的比较。比较结果证实，该计算结果可信、模型合理。程序可用来分析和预测钠池火事故。     

同位素热源火灾事故环境模拟试验及仿真分析

为考核空间同位素热源火灾事故安全性,开展了同位素热源火灾模拟试验及数值仿真研究。提出了同位素热源火灾模拟试验及试验系统设计的相关方法;对热源火烧环境热响应特性进行了数值仿真,探讨了预热阶段产品表面辐射率、对流换热系数等的影响,以及运输及发射剖面火灾事故热源热响应特征;基于仿真结果开展了某空间同位素热源火灾模拟试验。结果表明,预热阶段,产品温度主要受目标预热温度、表面辐射率等因素影响;火烧阶段,产品烧蚀层温度上升较快,发射场事故下热源各层温升速率较运输事故下的大,但放射性同位素芯块仍处于安全温度;试验中火焰呈火羽流形态,具有大尺度 低频率扰动特征,火焰熄灭30 min后,热源表面温度降至约180 ℃,整体结构良好。     

Equilibrium considerations in aerosol formation during sodium combustion

Combustion of liquid sodium is of interest in the safety assessment of liquid metal cooled fast breeder reactor systems. In the present study, a detailed thermodynamic analysis of sodium-air system has been carried out for equivalence ratios in the range of 0.1–1.9 and for flame temperatures ranging from 1100 to 1950 K. In addition to this, decomposition calculations presented for product aerosols such as sodium oxide (Na₂O), sodium dioxide (Na₂O₂) and sodium hydroxide (NaOH) in normal oxygen and oxygen-deficient conditions (which are some form of phase diagrams of these aerosols) are used rigorously to find out the predominant aerosol that should be present in and outside the burn pan for a pool fire of liquid sodium. The conditions of occurrence of various sodium oxides under two different fire conditions namely pool and jet fires have been worked out. It is established that heterogeneous reactions involving sodium oxide are responsible for the formation of sodium dioxide and sodium hydroxide. It is necessary to take account of the rates of these heterogeneous reactions as well as the equivalence ratio-dependent decomposition calculations to correctly estimate the aerosol product mix in practical situations.     

Experiments on sodium fires and their aerosols

A number of new sodium fire and aerosol experiments were undertaken to provide data for LMFBR safety analyses: (1) Experiments on the burning of single drops of liquid sodium falling in air have been performed to aid in model development for sodium spray fire codes. (2) The leakage of sodium oxide aerosols through a straight smooth capillary tube, representative of the maximum size of a hypothetical gas leak in the wall of the secondary containment of an LMFBR, has been studied. Even in those cases in which the capillary did not plug, <11% of the entering mass was of a respirable size as it emerged from the capillary. In addition, there were a number of conditions under which the capillary plugged. (3) Experiments on the behavior of high temperature, high concentration aerosols have shown a rapid depletion of the aerosol concentration in the first 6 sec following injection of 800 g/m³ aerosols at 1000°C into a closed vessel. This depletion has been correlated with the early formation of 100 to 200 μm agglomerates which fall out promptly.     

Validation study of computer code for sodium fire safety evaluation of fast reactor

A computer code solves coupled phenomena of thermal hydraulics and sodium fire based on a multi-zone model. It deals with an arbitrary number of rooms, each of which is connected mutually by doorways and penetrations. With regard to the combustion phenomena, a flame sheet model and a liquid droplet combustion model are used for pool and spray fires, respectively, with the chemical equilibrium model based on the Gibbs free energy minimization method. The chemical reaction and mass and heat transfer are solved interactively. A specific feature of is detailed representation of thermalhydraulics of a sodium pool and a steel liner, which is placed on the floor to prevent sodium–concrete contact. The authors analyzed a series of pool combustion experiments, in which gas and liner temperatures are measured in detail. It has been found that good agreement is obtained and the code has been validated with regard to pool combustion phenomena. Further research needs are identified for pool spreading modeling considering thermal deformation of steel liner and measurement of pool fluidity property as a mixture of liquid sodium and reaction products. The code is to be used mainly in the safety evaluation of the consequence of a sodium fire accident in a liquid metal cooled fast reactor as well as fire safety analysis in general.     

Numerical investigation of multi-dimensional characteristics in sodium combustion

Multi-dimensional sodium combustion behavior has been numerically investigated in the present paper. A new computer code AQUA-SF has been developed for this purpose. The code includes two sodium combustion models (so called ‘spray combustion’ and ‘pool combustion’), a mass and heat transfer model considering a six-flux gas radiation and a coagulation and sedimentation model of sodium oxide and hydroxide aerosols. The sodium spray combustion rate is evaluated by a summation of the combustion rate of each sodium droplet with an individual diameter. A flame sheet model is applied to situations where sodium spreads out on the floor and a pool combustion takes place. The model assumes an infinitely thin flame above the pool surface and is based on a mass and energy balance in the flame. As the results of numerical analyses of a sodium spray combustion test, a location of high-temperature core region and a maximum temperature agrees with the experiment. Good agreements of an overall transient behavior are obtained in a large-scale sodium combustion test analysis. The numerical analyses also demonstrate that the distributions of temperature and chemical species concentration vary with sodium combustion modes. If sodium scatters and the spray combustion is dominant, the distributions vary in space. When a large amount of sodium exists on a floor and the pool area is enlarged, the distributions are more uniform in space.     

Experimental and analytical investigation of intermittent flame effect on radiant emission for pool fires

The radiation plays an important role in the fire protection safety of equipments, especially for cable trays in switchgear rooms of a nuclear power plant. Therefore, many research works had been focused on the radiant heat emitted from a fire over the last decades. The radiant heat is essentially emitted from both the persistent and intermittent flames. However, no previous studies had investigated this heat contributed from the intermittent flame. Therefore, experimental and analytical works are proposed in this paper to investigate the effect of intermittent flame on the radiant heat. Based on the experimental measurements for a 30 cm pool fire, at least 36% of total radiant heat is emitted from the intermittent flame, demonstrating the significance of its contribution of the radiant heat. In addition, a new analytical radiant model is also proposed herein, which considers the intermittent flame effect, the flame oscillation characteristics and the smoke contribution. Compared with the experimental data for the pool fires with the diameters of 14–38 cm, the distributions of radiant heat fluxes predicted by the present analytical model show good agreement qualitatively and quantitatively. The relative errors between experiments and predictions are less than about 10%.     

Sodium pool combustion phenomena under natural convection airflow

Sodium pool fire is a design basis accident of sodium-cooled fast reactor. In this study, a numerical method for multi-dimensional modeling of sodium pool fire has been developed. It considers coupling of thermal-hydraulics, chemical reaction and aerosol dynamics equations. From the present multi-dimensional computation, phenomena of sodium pool fire are understood such as flow and temperature fields and aerosol mass distribution of various sizes. It has been found that the burning rate varies along the radial direction and the mass and heat transfer around the pool peripheral is maximum and most influential. The thermal-hydraulic phenomena in the near-surface region are very important to determine the sodium pool fire consequence such as the burning rate and aerosol emission. The area-averaged burning rate and aerosol release fraction calculated by the present numerical method are in agreement with experimental data.     

Sodium Fire Code SFIRE1C for Pool Fire Characteristics

Sodium pool fire code, SOFIRE II, written for the constant value of stoichiometric combustion ratio and heat of reaction is used to compute the buildup of pressure and temperature in a containment. In the SOFIRE II model, for the formation of a mixture of Na₂O and Na₂O₂ in the sodium pool, the input stoichiometric combustion ratio and heat of formation values need to be varied to corresponding values admissible for the mixture. In the present work, the SOFIRE II one-cell model is revised and the present version SFIRE1C (Sodium FIRE 1 Cell model) accounts for the formation of Na₂O in an early stage of the fire and shifts to the formation of Na₂O₂ at a later stage. Thus SFIRE1C computes in a more realistic manner the reaction products which are formed in the pool. The model for sodium oxide aerosol release is also modified in this version, by incorporating a more appropriate aerosol release rate equation. The calculated values using the SFIRE1C one-cell model are compared with sodium pool fire experimental results.     

Analysis of radionuclide retention in water pools

An analysis is presented of the removal of aerosol particles and gaseous fission products from steam-noncondensable gas mixtures rising through water pools. The pool is divided into a gas injection zone, a bubble rise zone and a pool surface zone. The formulation of the governing conservation equations is relatively general with a quasi-steady one-dimensional formulation for the gas phase, and an unsteady, well stirred, formulation for the liquid phase. An associated computer code for performing the calculations, SUPRA, is described. Results of parametric calculations are given for conditions expected in a BWR severely degraded core accident sequence. Parameters studied include aerosol particle size and distribution, mass fraction of noncondensable gas, gas mass flow rate, quencher submergence depth, and pool water temperature.     

CFD modeling and thermal-hydraulic analysis for the passive decay heat removal of a sodium-cooled fast reactor

In this study, a pool-typed design similar to sodium-cooled fast reactor (SFR) of the fourth generation reactors has been modeled using CFD simulations to investigate the characteristics of a passive mechanism of Shutdown Heat Removal System (SHRS). The main aim is to refine the reactor pool design in terms of temperature safety margin of the sodium pool. Thus, an appropriate protection mechanism is maintained in order to ensure the safety and integrity of the reactor system during a shutdown mode without using any active heat removal system. The impacts on the pool temperature are evaluated based on the following considerations: (1) the aspect ratio of pool diameter to depth, (2) the values of thermal emissivity of the surface materials of reactor and guard vessels, and (3) innerpool liner and core periphery structures. The computational results show that an optimal pool design in geometry can reduce the maximum pool temperature down to ∼551 °C which is substantially lower than ∼627 °C as calculated for the reference case. It is also concluded that the passive Reactor Air Cooling System (RACS) is effective in removing decay heat after shutdown. Furthermore, thermal radiation from the surface of the reactor vessel is found to be important; and thus, the selection of the vessel surface materials with a high emissivity would be a crucial factor for consideration in safety design. This study provides future researchers with a guideline on designing safety measures for the fourth generation of the fast reactors with no particular reference to any specific manufacturer.     

CONTAIN-LMR程序中池式钠火事故分析计算模型的验证

CONTAIN-LMR是针对以液态钠为冷却剂的反应堆而开发的安全壳事故一体化分析程序。我国目前的CONTAIN-LMR程序版本为2000年左右从法国引进,还未进行过面向工程设计的系统性地程序开发和验证。本文主要针对CONTAIN-LMR程序中模拟池式钠火事故的分析模型进行详细分析,并采用国际上的池式钠火实验进行验证,实验验证结果表明CONTAIN-LMR程序可以较准确地模拟池式钠火事故造成的钠工艺间内的温度、压力升高及放射性钠气溶胶行为。本文的研究结果初步表明CONTAIN-LMR程序可用于钠冷快堆的钠火事故分析。     

Fires in large scale ventilation systems

This paper summarizes the experience gained simulating fires in large scale ventilation systems patterned after ventilation systems found in nuclear fuel cycle facilities. The series of experiements discussed includes: (1) combustion aerosol loading of 0.61×0.61m HEPA filters with the combustion products of two organic fuels, polysterene and polymethylemethacrylate; (2) gas dynamic and heat transport through a large scale ventilation system consisting of a 0.61 m duct 90 m in length, with dampers, HEPA filters, blowers, etc.; (3) gas dynamic and simultaneous transport of heat and solid particulate (consisting of glass beads with a mean aerodynamic diameter of 10μ) through the large scale ventilation system; and (4) the transport of heat and soot, generated by kerosene pool fires, through the large scale ventilation system.The FIRAC computer code, designed to predict fire-induced transients in nuclear fuel cycle facility ventilation systems, was used to predict the results of experiments (2) through (4). In general, the results of the predictions were satisfactory. The code predictions for the gas dynamics, heat transport, and particulate transport and deposition were within 10% of the experimentally measured values. However, the code was less successful in predicting the amount of soot generation from kerosene pool fires, probably due to the fire module of the code being a one-dimensional zone model. The experiments revealed a complicated three-dimensional combustion pattern within the fire room of the ventilation system. Further refinement of the fire module within FIRAC is needed.     

液池内气溶胶对孔板鼓泡体积影响的实验研究

液池内的孔板鼓泡是安全壳内气体过滤排放过程中的重要现象。过滤过程中,孔板鼓泡体积直接影响气泡的上升速度与气液接触面积,因此是影响过滤器过滤效率的重要参数之一。随着过滤的进行,液池内滞留的气溶胶可能成为孔板鼓泡体积的影响因素之一。本文采用可视化实验,对含BaSO₄和TiO₂气溶胶液池内的孔板鼓泡过程进行研究,观察和分析孔板鼓泡体积的变化规律,进而获取气溶胶对孔板鼓泡体积的影响机制。研究表明,高温液池和TiO₂会使得生成气泡体积增加,添加BaSO₄的影响并不明显,实验还发现了生成气泡顶部含“小气腔”的情况,表面张力及“小气腔”的变化是气泡体积改变的主要机制。