Numerical Approach to the Safety Evaluation of Sodium—Water Reaction

A numerical simulation method of multi-dimensional and multi-phase reacting flow (SERAPHIM code) has been developed to evaluate the sodium-water reaction (SWR) phenomena in a steam generator of liquid metal fast reactor (LMFR). A compressible multi-fluid and one-pressure model is adopted and pressure and velocity fields are updated simultaneously by the HSMAC method. Two types of reaction models are considered; one is a surface reaction and the other is a gas-phase reaction. The surface reaction model assumes that water vapor reacts with the liquid sodium at the gas-liquid interface. If chemical reaction heating is large enough, liquid sodium is vaporized resulting in a gas-phase reaction. In the surface reaction, the reaction rate is assumed to be infinitely large. Several overall reaction equations are taken into account in the gas-phase reaction and the reaction rates are described in the form of the Arrhenius law. In the present study, adequacy of the analytical procedures for compressible multi-phase flow is validated by a benchmark calculation of the Edwards pipe blowdown problem. As a numerical example, two- and three-dimension analyses of the single-tube geometry and the two-dimension analyses of the 43-tubes geometry are carried out. It is concluded that the numerical quantification of the SWR accident by the SERAPHIM code is practicable and further use of the SERAPHIM code is useful to resolve safety issues immanent in the SWR.     

一种稳定性增强及高精度数值方法在RELAP5中的实现与评价

在计算稳定性的改进方面,修正RELAP5程序中的虚拟质量力(Virtual mass force)形式,同时添加了新的界面压力项(Interface pressure);在计算精度的改进方面,采用具有总变差减小(Total variation diminish,TVD)特点的高精度通量限制器(Flux limiter)方法取代RELAP5程序原本的一阶迎风方法来离散质量和能量守恒方程中的对流项。在模拟水平管道内空泡份额微扰随时间发展的数值实验中,相比改进前的RELAP5,改进后的RELAP5计算得到的微扰幅度并未增长;在模拟液相沉降的数值实验中,改进前的RELAP5程序计算得到了不真实的空泡份额分布,而改进后的RELAP5在不同的网格数量下能够得到收敛的稳定解。对Ransom水龙头数值实验和Marviken CFT 15大破口喷放实验的计算表明,改进后的具有二阶TVD格式的RELAP5程序能够得到更接近实验数据的计算结果。     

Calculation method for diffusional gas release with grain boundary resolution

The problem of diffusional release of stable fission gas atoms in nuclear fuel including grain boundary resolution is described. A numerical method for solving the set of resulting non-linear differential equations in time varying conditions is presented. The method is an extension to the locally accurate method (LOAM) published earlier. The extended LOAM accounts for the kinetic evolution of the gas content in the grain boundary. The fission gas release and the time to reach the saturation concentration at the grain boundaries by the extended method are compared to analytical solutions under steady state conditions. The results of this comparison show the excellent capability of the extended LOAM. The performance of the extended method in time varying conditions is tested by calculating the fission gas release for hundreds of complicated temperature–power histories. The extended LOAM is found to be able to calculate the fission gas release with ±1% accuracy in time varying conditions by using only three equal volume nodes. The computing time of the extended LOAM is less than twice the time needed by the LOAM without grain boundary resolution.     

基于MOOSE平台的高阶全隐式核反应堆一回路系统分析

基于多物理场耦合平台MOOSE开发了模块化系统安全分析程序ZEBRA,并采用高阶全隐式离散格式建立了核反应堆一回路系统模型,对核反应堆系统中子扩散、二维固体导热和一维流体进行耦合计算。针对单管流动传热问题,对ZEBRA程序进行了耦合验证,对比了稳态工况下一阶、二阶空间离散格式和瞬态工况下Implicit-Euler、Crank-Nicolson、BDF2 这3种时间离散格式的求解精度,并对压水堆回路系统稳态和降功率瞬态工况进行了模拟分析。结果表明,高阶空间离散格式具有较高的求解精度,BDF2时间离散格式与理论解符合最好;压水堆回路系统温度、速度、压力分布合理,稳态、瞬态计算结果与RELAP5程序计算结果符合良好。      

Fluid-structure interaction analysis of a hypothetical core disruptive accident in LMFBRs

To ensure safety, it is necessary to assess the integrity of a reactor vessel of liquid-metal fast breeder reactor (LMFBR) under HCDA. Several important problems for a fluid-structural interaction analysis of HCDA are discussed in the present paper. Various loading models of hypothetical core disruptive accident (HCDA) are compared and the polytropic processes of idea gas (PPIG) law is recommended. In order to define a limited total energy release, a “5% truncation criterion” is suggested. The relationship of initial pressure of gas bubble and the total energy release is given. To track the moving interfaces and to avoid the severe mesh distortion an arbitrary Lagrangrian–Eulerian (ALE) approach is adopted in the finite element modeling (FEM) analysis. Liquid separation and splash from a free surface are discussed. By using an elasticity solution under locally uniform pressure, two simplified analytical solutions for 3D and axi-symmetric case of the liquid impact pressure on roof slab are derived. An axi-symmetric finite elements code FRHCDA for fluid-structure interaction analysis of hypothetical core disruptive accident in LMFBR is developed. The CONT benchmark problem is calculated. The numerical results agree well with those from published papers.     

INFORMATION FOR OVERSEAS CONTRIBUTORS

A new computational methodology of sodium-water reaction (SWR), which occurs in a steam generator of a liquid-sodium-cooled fast reactor when a heat transfer tube in the steam generator fails, has been developed considering multidimensional and multiphysics thermal hydraulics. Two kinds of reaction models are proposed in accordance with a phase of sodium as a reactant. One is the surface reaction model in which water vapor reacts directly with liquid sodium at the interface between the liquid sodium and the water vapor. The reaction heat will lead to a vigorous evaporation of liquid sodium, resulting in a reaction of gas-phase sodium. This is designated as the gas-phase reaction model. These two models are coupled with a multidimensional, multicomponent gas, and multiphase thermal hydraulics simulation method with compressibility (named the ‘SERAPHIM’ code). Using the present methodology, a numerical investigation of the SWR under a pin-bundle configuration (a benchmark analysis of the SWAT-1R experiment) has been carried out. As a result, the maximum gas temperature of approximately 1,300_C is predicted stably, which lies within the range of previous experimental observations. It is also demonstrated that the maximum temperature of the mass weighted average in the analysis agrees reasonably well with the experimental result measured by thermocouples. The present methodology will be promising to establish a theoretical and mechanical modeling of secondary failure propagation of heat transfer tubes due to such as an overheating rupture and a wastage.     

A simple approach to the prediction of waterhammer transients in a pipe line with entrapped air

The pressure histories within entrapped air bubbles in a pipe line during a waterhammer transient are treated theoretically. A convenient integral method is introduced, which takes full account of air/water interface movement and liquid compressibility. The significance of the method is that it provides a simple equation set for approximating, with good accuracy and with a small degree of conservatism, the solution to a problem that otherwise involves coupled partial differential equations on time dependent domains with non-linear boundary conditions. The accuracy of the method is defined by its comparison with available numerical-solution-predictions and measurements of the pressure within an entrapped-air-bubble at a dead end in a pipe. The method is shown to be a computationally simple and efficient way of assessing the impact of liquid compressibility on pressure rise when multiple water columns and air pockets are present in a pipe line.     

Simplified two and three dimensional HTTR benchmark problems

To assess the accuracy of diffusion or transport methods for reactor calculations, it is desirable to create heterogeneous benchmark problems that are typical of whole core configurations. In this paper we have created two and three dimensional numerical benchmark problems typical of high temperature gas cooled prismatic cores. Additionally, a single cell and single block benchmark problems are also included. These problems were derived from the HTTR start-up experiment. Since the primary utility of the benchmark problems is in code-to-code verification, minor details regarding geometry and material specification of the original experiment have been simplified while retaining the heterogeneity and the major physics properties of the core from a neutronics viewpoint. A six-group material (macroscopic) cross section library has been generated for the benchmark problems using the lattice depletion code HELIOS. Using this library, Monte Carlo solutions are presented for three configurations (all-rods-in, partially-controlled and all-rods-out) for both the 2D and 3D problems. These solutions include the core eigenvalues, the block (assembly) averaged fission densities, local peaking factors, the absorption densities in the burnable poison and control rods, and pin fission density distribution for selected blocks. Also included are the solutions for the single cell and single block problems.     

动态棒价值测量软件包LIGHT的开发与数值验证

动态棒价值测量是一种快速测量控制棒组价值的方法。基于测量过程和相关的反应堆物理数值计算方法，开发了动态棒价值测量软件包LIGHT。LIGHT可产生进行动态棒价值测量所需的参数，包括静态空间因子、动态空间因子和缓发中子参数。针对基准问题和AP1000核电厂进行了数值计算并进行了比较。分析表明，计算结果具有较高的精度，说明建立的计算模型及开发的程序是正确的。     

液态铅铋合金回路氧输运特性的数值研究

为研究液态铅铋合金（LBE）冷却剂系统气态氧控装置——膨胀箱中覆盖气体的氧输运特性,利用计算流体动力学（CFD）软件ANSYS Fluent对氧输运进行了数值计算。根据覆盖气体流动特性和混合气体中低氧分压特点,对膨胀箱气相空间进行简化,将气-液交界面视为氧浓度恒定的自由表面边界,采用组分输运模型计算气体和液态LBE之间传质后的液态LBE氧浓度。结果表明,传质系数随液态LBE入口流速增大而增大,液态LBE入口流速增大则膨胀箱内气-液对流强度增加,有利于增强膨胀箱的氧输运;膨胀箱中液态LBE温度越高,则氧输运的平均传质系数越大;在液态LBE入口流速一定时,平均传质系数可表示为温度的递增函数。在饱和氧浓度阈值内,入口氧浓度和气-液交界面氧浓度不影响膨胀箱的传质系数,对液态LBE回路的氧浓度控制有利。本研究定量获得了使液态LBE回路处于合理氧浓度范围内的操作条件,为实验及系统设计提供数据参考。      

Monte Carlo simulation of nonlinear reactive contaminant transport in unsaturated porous media

In the current proposed solutions of radioactive waste repositories, the protective function against the radionuclide water-driven transport back to the biosphere is to be provided by an integrated system of engineered and natural geologic barriers. The occurrence of several nonlinear interactions during the radionuclide migration process may render burdensome the classical analytical–numerical approaches. Moreover, the heterogeneity of the barriers’ media forces approximations to the classical analytical–numerical models, thus reducing their fidelity to reality. In an attempt to overcome these difficulties, in the present paper we adopt a Monte Carlo simulation approach, previously developed on the basis of the Kolmogorov–Dmitriev theory of branching stochastic processes. The approach is here extended for describing transport through unsaturated porous media under transient flow conditions and in presence of nonlinear interchange phenomena between the liquid and solid phases. This generalization entails the determination of the functional dependence of the parameters of the proposed transport model from the water content and from the contaminant concentration, which change in space and time during the water infiltration process. The corresponding Monte Carlo simulation approach is verified with respect to a case of nonreactive transport under transient unsaturated flow and to a case of nonlinear reactive transport under stationary saturated flow. Numerical applications regarding linear and nonlinear reactive transport under transient unsaturated flow are reported.     

热工水力系统程序中数值水锤问题研究

基于两流体六方程的热工水力系统程序在计算蒸汽即将从控制体中消失或水即将充满控制体工况时,由于空泡份额较小的两相混合物和纯液相之间可压缩性的不连续变化以及离散动量方程的离散方法,可能会出现虚拟的压力峰值,即数值水锤现象。本文以热工水力系统分析程序RELAP5为参考对数值水锤问题的缓解方案进行了分析研究,给出了详细的检测逻辑以及修正方案,并应用于普赖尔管问题和冷凝实验工况的计算分析。结果显示,数值水锤缓解方案的启用能够缓解两流体程序中针对该类问题由于数值方法带来的压力瞬态效应,从而能够明显地降低压力峰值,避免了严重扭曲瞬态解的出现。数值水锤缓解方案减缓这一虚拟压力峰值,有利于提高程序计算的稳定性;针对该问题此方法可为同类型系统程序的开发及模型优化提供参考。      

The dependence of wall lubrication force on liquid velocity in turbulent bubbly two-phase flows

Based on the significance of a computational fluid dynamics (CFD) simulation of dispersed two-phase flow systems in many engineering fields, especially in nuclear energy systems, extensive analytical and numerical studies of wall lubrication force for vertical upward turbulent bubbly two-phase flow are presented. An analytical expression of the wall lubrication force considering the effect of liquid velocity is developed and analyzed. A numerical methodology for evaluating the wall lubrication force coefficients is proposed, which is based on the assumption that the balance of the forces acting on a bubble perpendicularly to the flow direction determines the establishment of radial void fraction profiles. Wall lubrication force coefficients are determined based on a reasonable agreement in radial void fraction profiles between numerical results predicted by the CFD EAGLE (elaborated analysis of gas–liquid flows evolution) code and extensive experimental database in the open literature as well as experiments performed at the Korea Atomic Energy Research Institute-vertical air–water loop test facility. Liquid velocity dependence of wall lubrication force is clearly shown in both analytical and numerical ways in the present study, and new correlations are then proposed for the wall lubrication force coefficients.     

Computation accuracy and efficiency of a power series analytic method for two- and three- space-dependent transient problems

The establishment of solutions to large-scale three-dimensional (3-D) reactor benchmark problems is needed to serve as standards for the verification of design codes and for the detailed error analysis of calculational methods. A number of partially and fully inserted control rods, represented by absorber added to certain subassemblies, cause a strong nonseparable power distribution. In addition, the existence of a very large thermal flux peak in the reflector makes this a very difficult and challenging problem to solve.PWS code has been developed to include a numerical solution for the time-dependent neutron diffusion equations for the nuclear reactor analysis. The new technique employs a new parameter (α) which can reduce the rapid increase in magnitude of the power series coefficients. These coefficients, in turn, are determined by back substitutions in the non-linear canonical diffusion equations and treating terms of the same degree to obtain a modified recurrence relation which is valid for any type of the stiff non-linear kinetic diffusion equations.The validity of the algorithm was tested with three kinds of well-known two-group benchmark problems. The first one is the two-dimensional TWIGL seed-blanket reactor kinetics problem. The second is the two- and three-dimensional LAR BWR benchmark problem simulating a rod drop accident of a BWR core. The third is the three-dimensional LMW LRA transient problem which simulates an operational transient involving rod movements. The obtained results with the proposed PWS code are compared with those provided by other reference codes, indicating an overall agreement and excellent performance.     

One- and two-dimensional standing pressure waves and one-dimensional travelling pulses using the US-NRC nuclear systems analysis code TRACE

A variety of nuclear system transients can lead to rapid and large local pressure changes that propagate along the hydraulic system at the speed of sound, both in single phase and in two-phase fluids. Because of the relevance for safety issues, nuclear system codes like TRACE need to be assessed with respect to their capabilities to predict pressure wave behaviour. Therefore, we have analyzed the propagation of pressure waves in one-dimensional and two-dimensional configurations, i.e. a pipe and a slab, filled with liquid water. The pressure waves are driven by one-sided pressure boundary conditions, in the one-dimensional case of harmonic or Gaussian shape and in the two-dimensional case also of harmonic shape. The selected harmonic pressure boundary conditions lead to standing pressure waves, while using the Gaussian shape boundary conditions one-dimensional pressure pulses are injected and propagate through the pipe. The agreement of the TRACE results with the analytical solutions are, in general very good to good for the one-dimensional cases with respect to the pressure maxima and a small difference is only obtained in the wave speed.At the resonance frequencies of the one-dimensional standing waves, the code is tested to the extreme and shows that enforcing small time step sizes is crucial for the performance of the code. Non-linear effects are observed in the code results for the large amplitudes encountered at the closest neighborhood of the resonances, where the analytical linear standing wave solution diverges and the linear approximation is outside of its validity range. Also for these non-linear standing waves TRACE yields qualitatively physically correct behaviour as the pressure amplitudes are limited and a plateau is reached.For the one-dimensional pressure pulse of Gaussian shape the change of pulse amplitude and shape was analyzed in a longer system. The maximum amplitude of the pulse is slightly reduced as the pulse travels along the pipe. The effect of numerical diffusion on leading and trailing fronts is slightly asymmetric due to the donor-cell approach used in the numerical integration scheme of TRACE. The accuracy of the code is not negatively influenced by the reflections of the pulse at the boundaries of the pipe. As for the standing waves, the accuracy of the travelling pulse solution calculated by TRACE is negatively affected when the time steps are too large, while the effects of the spatial discretization are rather minor.For the case of two-dimensional standing waves in a slab, a lowest spatial harmonic generated with one wave node in the direction parallel to the pressure driving boundary is considered. TRACE results show an overall good agreement with the linear analytical solution. This good agreement includes for low to medium excitation frequencies the damping properties of the skin effect perpendicular to the pressure boundary, which does not exist in one-dimensional pressure wave propagation, the transition to a harmonic shape of the wave also perpendicular to the pressure boundary and the frequency dependence of the resonance spectrum for further increased frequencies with the rapid changes of the wavelengths encountered. Effects of the model set-up and code limitations with respect to the two-dimensional TRACE model set-up using a TRACE VESSEL component in connection with pressure boundary conditions are discussed, in particular with respect to the underestimation of the damping in the skin effect frequency range and the numerical damping for higher frequencies. All in all, the TRACE code is able to calculate one- and two-dimensional pressure wave propagation in liquid water, when an appropriate spatio-temporal numerical discretization is chosen.     

离心式上充泵小流量工况转换瞬态流动特性

为研究核电站离心式上充泵由上充工况向小流量工况转换运行过程中的瞬态流动特性,基于RANS方程和RNG k-ε湍流模型,采用商业软件CFX对其进行定常数值模拟,并通过试验验证了数值计算方法的正确性。在此基础上,继续对该瞬态过程进行数值计算,得到上充泵内部流动瞬态压力及速度的变化规律。结果表明：在由上充工况向小流量工况转变过渡过程中,叶轮、导叶、出口涡壳的流道内压力有不同程度的上升趋势;在瞬态转变过程中,随着流量的减小,上充泵内部漩涡范围增大,流动形式也愈来愈差,导致压力和速度波动幅值增大;由于动静干涉影响,叶轮与导叶交界面附近监测点的压力和速度波动程度高于其他监测点的波动程度,双蜗壳流道内圈的波动高于外圈的波动。     

Application of “Hydration Model” to Evaluate Gas Phase Transfer of Ruthenium and Technetium from Reprocessing Solutions

In order to evaluate the amounts of gas phase transferred ruthenium (Ru), and technetium (Tc), simulations were made for the continuous evaporator used in a reprocessing plant to concentrate high level liquid waste. The concentrations and activities of nitric acid and water, which controlled the reaction rate and gas-liquid equilibrium in the evaporator solution, were evaluated using the previously developed “Hydration Model”. When the feed solution contained 2.7 M (=mol/dm³) of nitric acid, the nitric acid concentration in the evaporator solution reached its maximum at the concentration factor (CF) of 6 (CF: concentration ratio of FPs in evaporator and feed solutions). The activities of nitric acid and water were saturated at values of 0.01 and 0.43, respectively, after the CF reached 6. The simulation predicted decontamination factors DFs of 2×10⁵ and 8×10³ for Ru and Tc, respectively, for a typical evaporation conditions with an operational pressure of 6,700 Pa, and FPs of 0.02 to 1.4 M. The simulation results agreed with the verification experiment, which will be described in next paper, within a factor of 2 for the amount of gas-phase transferred Ru during evaporation. The factor for the amount of gas-phase transferred Tc was estimated as 5 from the measurement error in the gas-liquid equilibrium constant.     

断电停机过渡过程中核主泵气液两相流动特性研究

为研究断电停机过渡过程中核主泵气液两相瞬态流动特性,借助CFD技术对不同含气量下核主泵内的气液两相流动变化规律及径向力进行了研究,并对计算结果进行试验验证。结果显示,数值模拟数据与试验数据变化趋势吻合,断电停机过渡过程中,在叶轮背面附近产生旋涡,旋涡的存在使气相区域变大且相应的气体体积分数增加。随着流量的减少和转速的降低,叶轮和导叶内存在大量的气相,导致叶轮转换能量的能力减弱。含气量较小时,叶轮内气体体积分数先达到最大值后开始呈离散状回旋下降。而含气量较大时,叶轮内的气体体积分数随流量的减少而增加。含气量对流道内流体的速度影响较大,尤其是对靠近叶片进口方向的流体。随着含气量的增加,叶轮的径向力不平衡程度开始减弱,其最大不平衡径向力由正负值不等转变为以负值为主。     

Analysis of one-dimensional pressure pulse propagation in a closed fluid system

This paper describes a unique numerical method for linear inviscid fluid hammer analysis based on the method of characteristics. The uniqueness lies in that it uses the analytical solutions of the wave equation in place of the compatibility relatins of the more conventional method of characteristics. The numerical solution is obtained by a simple superposition technique for tracing the waves traveling along each characteristic and extending the solution from one constant time line to the next. Using a predetermined finite difference net of grids with equal spacings, an elimination is made of the spatial interpolation, thereby maintaining the wave amplitudes in their full strength in the numerical procedure. This is in contrast to the case of a nonlinear problem in which the pressure peaks are always flattened to some degree in the interpolation procedure.The computer program NAHAMMER is a system analysis code adequate for short-term pressure transients of most engineering problems of significance involving a moderate pressure source. It considers the simplified one-dimensional, linear, inviscid set of governing equations with an isentropic flow assumption. A closed fluid-network system is considered to be composed of a multiple of one-dimensional pipe sections and components that are connected by various joints. An analytical solution is obtained under an acoustic approximation for a simple system and the result shows good agreement with the numerical solution. As examples of the application of the method, complex problems of engineering importance are calculated and the results are presented.     

通用型中子输运程序VITAS应用研究

为提高确定论全堆芯中子输运程序的适用性,开发了通用型中子输运程序 VITAS。针对TAKEDA3 基准题(矩形组件)、TAKEDA4 基准题(六角形组件)、Dodds 基准题(R-Z 几何)和 C5G7-TD5 基准题(压水堆高保真计算)的验证结果表明,高阶的空间和角度基函数能够使结果稳定地向参考解渐进收敛,达到与多群蒙卡相当的计算精度水平。与参考解相比,TAKEDA3 基准题有效增殖系数(k_eff)偏差低于 60pcm(1pcm=10^-5),控制棒价值偏差为-3pcm,中子通量密度分布均方根(RMS)偏差为 1.03%;TAKEDA4 基准题 k_eff偏差低于 20pcm,控制棒价值偏差为 32pcm,中子通量密度分布 RMS 偏差为 0.70%;Dodds 基准题的功率最大偏差低于 1%;C5G7-TD5 基准题的功率偏差低于 0.9%。本文研究表明 VITAS 有望成为一套精确求解中子输运问题的通用型计算工具。