Simulation of a small loss of coolant accident by using RETINA V1.0D code

RETINA has been developed for modeling of two-phase flow situations in full-scope simulators of nuclear power plants. A special feature of RETINA is that both RETINA V1.0D (drift-flux — 5 equations) and RETINA V1.0-2V (two-fluid — 6 equations) approach are available in the code and the same constitutive relations are used in both cases. The governing equations are discretized implicitly, and an automatic derivation algorithm determines the Jacobian matrix, which is partitioned taking into account the special structure of nuclear power plants. Partitioned inverse formula is used to solve the global equation system providing the possibility of multi-level parallelization. Heat structures are modeled in two dimensions and are coupled to the flow equations explicitly. Since the code will be used in real-time simulators, we paid special attention to time-effective solution. In this paper, we demonstrate the ability of our code by simulating a small loss of coolant accident Paks Model Circuit (PMK). The simulation results are compared to real measurements obtained by Paks Model Circuit.     

Measurement of Leakage Flow Induced Vibrations of Cylinder

For development of a two-phase flow analysis code by use of two-velocity two-temperature (2V2T) model, six basic equations completely independent and consistent with one another are derived for several possible types of thermodynamical unequilibrium conditions. Characteristic of the basic equations is that evaporation and condensation take place in the saturated water and saturated vapor separately. These phase change equations in the saturated state are rigorously derived using the thermodynamical law.

The energy conservation equation of each phase is derived from the well known total two-phase flow energy equation, using the first law of thermodynamics and conservation equations of mass and momentum of each phase. This derivation method will give assurance that all conservation equations are consistent with one another.

To form simplest 2V2T model, the terms of wall and interphase friction, and heat transfer to the two-phase flow and between phases are considered in this paper.     

Modeling and validation of a mechanistic tool (MEFISTO) for the prediction of critical power in BWR fuel assemblies

Westinghouse is currently developing the MEFISTO code with the main goal to achieve fast, robust, practical and reliable prediction of steady-state dryout Critical Power in Boiling Water Reactor (BWR) fuel bundle based on a mechanistic approach. A computationally efficient simulation scheme was used to achieve this goal, where the code resolves all relevant field (drop, steam and multi-film) mass balance equations, within the annular flow region, at the sub-channel level while relying on a fast and robust two-phase (liquid/steam) sub-channel solution to provide the cross-flow information. The MEFISTO code can hence provide highly detailed solution of the multi-film flow in BWR fuel bundle while enhancing flexibility and reducing the computer time by an order of magnitude as compared to a standard three-field sub-channel analysis approach.Models for the numerical computation of the one-dimensional field flowrate distributions in an open channel (e.g. a sub-channel), including the numerical treatment of field cross-flows, part-length rods, spacers grids and post-dryout conditions are presented in this paper. The MEFISTO code is then applied to dryout prediction in BWR fuel bundle using VIPRE-W as a fast and robust two-phase sub-channel driver code. The dryout power is numerically predicted by iterating on the bundle power so that the minimum film flowrate in the bundle reaches the dryout criteria. Predicted dryout powers (including trends with flow, pressure, inlet subcooling and power distribution) and predicted dryout locations (both axial and radial) are compared to experimental results, using the entire Westinghouse SVEA-96 Optima3 dryout database, and are shown to yield excellent results.     

A numerical technique for analysis of transient two-phase flow in a vertical tube using the Drift Flux Model

This paper presents a numerical solution of one-dimensional transient two-phase flow in a vertical channel using the Drift Flux Model (DFM). The DFM treats the two phases as a mixture, but allows slippage between the gas and the liquid phase. The DFM was used for the calculation of velocity and fraction of each phase, combined with the most relevant closure relationships models for condensation, wall evaporation, and phasic velocities. The solution of the three conservation equations for the mixture and a continuity equation for the gas phases is obtained by a semi-implicit numerical method. A finite volume method is used to discretize the governing equations on a staggered grid in the computational domain. Satisfactory agreement is shown between predicted void fraction, RELAP5 code and available experimental data under both transient and steady state conditions. Numerical solution was also obtained for a wide two-phase flow conditions: system pressure, surface heat flux, mass flow rate and inlet sub-cooling to check the model ability to predict void fraction accurately. It is concluded, therefore, that the DFM is able to predict void fraction in subcooled flow boiling with sufficient accuracy. For pressures lower than 30 bars, the DFM overestimated the void fraction in comparison with the experimental data by about 15%. The model requires less computational power to simulate than other approaches and has no limitations on the nodalization process for numerical stability. It is therefore expected that development of presented model will be useful for the assessment of experimental data, as well as performing pre-test numerical experimentation.     

BACCHUS; A numerical approach to two-phase flow in a rod bundle

We present in this paper the computer code BACCHUS, to analyze the thermal-hydraulics in a rod bundle in single or two-phase flow regime. The model is 2-D and uses the porous body approach. The two-phase model is an extension of the classical homogeneous model, and includes a differential non-equilibrium equation. Results are shown for the extension of the boiling region in a 19-pin bundle.     

Stability analysis of inclined stratified two-phase gas-liquid flow

The present investigation involves the modeling of gas-liquid interface in a two-phase stratified flow through a horizontal or nearly-horizontal circular duct. The most complete and fundamental model used for these calculations is known as the one-dimensional two-fluid model. It is the most accurate of the two-phase models since it considers each phase independently and links both phases with six conservation equations. The mass and momentum balance equations are written in dimensionless form. The dimensionless mass and momentum balance equations are combined with the method of characteristics and an explicit method to simulate the flow. At first, the linear stability of the flow is investigated by disturbing the liquid flow with a small perturbation. An improved version of the one-dimensional two-fluid model for horizontal flows is developed as a set of non-linear hyperbolic governing equations. The importance of this research lies in obtaining a model that accounts for the effects of flow and geometrical conditions (such as liquid viscosity, surface tension). It is shown that, for positive values of the slope angle (upward inclination), the slug flow becomes more probable, whereas negative values of the slope angle (downward inclination) induce a more stable stratified flow.     

Experimental and numerical simulation of air-water two-phase flow in the rod bundle with grid spacer

1 Introduction Grid spacer is the key part of reactor fuel assem-bly. The presence of spacers in fuel assemblies affectsvarious thermal-hydraulic characteristics of the reactorcore. The grid spacer with fine performance can im-prove thermal-hydraulic performance of the core fuelassembly and enhance the critical heat flux withouttoo much augment of the pressure loss. As a result,the implementation of grid spacer with high thermalperformance provides more thermal margin, then in-creases s…     

转盘柱中存留分数的CFD模拟研究

转盘柱中分散相存留分数是影响其设计放大的重要因素。本工作通过计算流体力学(CFD)软件对转盘柱中水-煤油两相流水力学性能进行模拟计算。两相逆流操作,水是连续相,煤油为分散相。求得了流场分布和分散相存留分数分布,并研究了两相表观流速以及转盘转速对存留分数的影响,模拟结果与已发表的文献实验数据吻合较好。CFD模拟为减少水力学实验和进一步研究转盘柱水力学性能和传质打下了基础。     

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.     

Computational analysis of two-phase flow in horizontal bundles

Phase distribution during boiling flow in horizontal channels and fuel bundles tends to be asymmetric, particularly at low flows, due to gravity induced separation of the phases. Standard models and computational techniques developed for flow on vertical rod bundles cannot adequately simulate this tendency in horizontal flows, so more advanced techniques involving thermal and mechanical disequilibrium between phases are required.The paper describes the development and application of a drift flux code ASSERT (Advanced Solution of Subchannel Equations in Reactor Thermalhydraulics) which models departure from mechanical and thermal equilibrium between phases. Details of the model and computational technique are given, and parametric studies are shown to illustrate the capability of the code to simulate two-phase flow in horizontal bundles.Fundamental to the successful application of such a code are phenomenological studies aimed at the quantification of the empirical relationships selected for use. The paper concludes with a detailed study of mechanisms governing two-phase flow between neighbouring horizontal channels, isolating the driving effects of pressure gradient, gravity head and turbulent interchange by means of comparison with available experimental data.     

相界面浓度输运方程在一维两流体模型中的应用研究

为解决一维两流体模型核电厂系统分析程序中使用流型图所带来的缺陷,提高系统分析程序计算的准确性,探索在一维两流体模型中应用相界面浓度输运方程（IATE）对两相流动进行预测。采用FORTRAN语言开发耦合了IATE的一维两流体模型求解器（Solver-IATE）,并对其进行验证。基于SolverIATE对小直径绝热圆管内向上泡状流进行了数值模拟,并与采用流型图的计算结果进行了对比。研究结果表明：采用IATE计算的相界面浓度结果比采用流型图的计算结果更接近实验值。因此,在一维两流体模型中使用IATE可以提高其计算相界面浓度的准确性,进而提高一维两流体模型核电厂系统分析程序计算两相间相互作用项的准确性,能更准确预测反应堆的瞬态响应特性。     

Development of one-dimensional two-fluid model with consideration of void fraction covariance effect

Accurate evaluation of gas-liquid two-phase flow behavior within rod bundle geometry is crucial for the safety assessment of the nuclear power plants. In safety assessment codes, two-phase flow in rod bundle geometry has been treated as a one-dimensional flow. In order to obtain the reliable one-dimensional two-fluid model, it is essential to utilize proper area-averaged models for governing equations and constitutive relations. The area-averaged interfacial drag term utilized to evaluate two-phase interfacial drag force is typically given by the drift-flux parameters which consider the velocity profile in two-phase flow fields. However, in a rigorous sense, the covariance due to void fraction profile is ignored in traditional formulations. In this paper, the rigorous formulation of one-dimensional momentum equation was derived by taking consideration of void fraction covariance, and a new set of one-dimensional momentum equation and constitutive relations for interfacial drag was proposed. The newly obtained set of formulations was embedded into TRAC-BF1 code and numerical simulation was performed to compare against the traditional model without covariance. It was found that effect of covariance was almost negligible for steady-state adiabatic conditions, but for high void fraction condition with added perturbation, the traditional model underpredicted the damping ratio at around 8%.     

Verification of the two-phase stratified-flow model in by separate effect tests

The code which is being developed by the Gesellschaft für Anlagen- und Rcaktorsicherheit (GRS) mbH is intended to cover, by means of a single code, the entire spectrum of loss-of-coolant and transient accidents in pressurized and boiling water reactors. The actual version Mod 1.1-Cycle A has a five-equation two-phase model based on the conservation laws for liquid mass, liquid energy, vapor energy and overall momentum. The relative velocity between liquid and vapor is determined by a full-range drift-flux model for two-phase flow in horizontal and vertical pipes. The verification of this drift-flux model is carried out by both large-scale experiments and single-effect tests. The single-effect test ECTHOR investigates stratified flow during the clearance of a water-filled loop seal by a forced air flow through the loop. ECTHOR is a French test for the consideration of two-phase flow regimes in pipes for the development of the codes. The experiments are dedicated to investigating typical two-phase flow during small break loss of coolant accidents (LOCA) in pressurized water reactors (PWR).As a measure, the remaining water level in the loop is determined as a function of the air flow rate. For the verification, a comparison between and computations, on the one hand, and experiments on the other hand is carried out. The results compare very well to each other. Test runs on different numerical grids show convergence to an asymptotic limit with increasing grid refinement.     

TRACE simulation of sodium boiling in pin bundle experiments under loss-of-flow conditions

In the framework of PSI's FAST code system, the thermal–hydraulic code TRACE is being extended for representation of sodium two-phase flow. As the currently available version (v.5) is limited to the simulation of only single-phase sodium flow, its applicability range is not enough to study the behavior of a Generation IV sodium-cooled fast reactor (SFR) during transients in which boiling is anticipated. The work reported here concerns the extension of the non-homogeneous, non-equilibrium two-fluid models, which are available in TRACE for steam-water, to sodium two-phase flow simulation. The conventional correlations for ordinary gas–liquid flows are used as basis, with optional correlations specific to liquid metal where necessary. A number of new models for representation of the constitutive equations specific to sodium, with a particular emphasis on the interfacial transfer mechanisms, have been implemented and compared with the original closure models.A first assessment of the extended TRACE version has been carried out, by using the code to model experiments that simulate a loss-of-flow (LOF) accident in a SFR. One- and two-dimensional representations of the test section have been considered. Comparison of the 1D model predictions, with both experiment and SIMMER-III code predictions, confirm the ability of the extended TRACE code to predict the principal sodium boiling phenomena. Two-dimensional representation of the test section, however, has been found necessary for providing more detailed comparisons with the experimental data and thereby studying, in greater detail, the influence of the physical models on the calculated results.The paper thus presents a first-of-its-kind application of TRACE to two-phase sodium flow. It shows the capability of the extended code to predict sodium boiling onset, flow regimes, pressure evolution, dryout, etc. Although the numerical results are in good agreement with the experimental data, the physical models should be further improved. Other integral experiments are planned to be simulated, in order to further develop and validate the two-phase sodium flow modeling.     

Implementation and assessment of improved models and options in TRAC-BF1

A summary of modifications and options introduced in TRAC-BF1 is presented and is shown that the predicting capabilities of the modified version of the code are greatly improved. These changes include the introduction of a different heat transfer package during reflooding, the implementation of a simple single-phase limit procedure for forcing the two phases to acquire the same velocity if one phase disappears, a close assessment of the annular flow interfacial shear correlation, implementation of a simple radiation model which seems to alleviate some numerical-oscillation problems induced by the existing highly complex model. Furthermore, different options were introduced and tested like upwinding some terms of the momentum equations (which seems to solve a number of problems reported in the past), the second upwind scheme for the convective terms of the phasic momentum equations and the implementation and assessment of a completely different annular flow interfacial shear correlation. The modified TRAC-BF1 is assessed against some bottom-flooding separate-effect experiments, a ‘benchmark' top flooding simulation as well as against the TLTA test No. 6423. In the process of this task, the different options are assessed and discussed and is shown that the predictions of the modified code are physically sound and close to the measurements, while almost all the predicted variables are free of unphysical spurious oscillations. The modifications introduced solve a number of problems associated with the frozen version of the code and result in a version which can be confidently used for LB-LOCA analyses.     

Numerical simulation of multi-dimensional two-phase flow based on flux vector splitting

This paper describes a new approach to the numerical simulation of transient, multidimensional two-phase flow. The development is based on a fully hyperbolic two fluid model of two-phase flow using separated conservation equations for the two phases. Features of the new model include the existence of real eigenvalues, and a complete set of independent eigenvectors which can be expressed algebraically in terms of the major dependent flow parameters. This facilitates the application of numerical techniques specifically developed for high speed single-phase gas flows which combine signal propagation along characteristic lines with the conservation property with respect to mass, momentum and energy. Advantages of the new model for the numerical simulation of 1- and 2-dimensional two-phase flow are discussed.     

棒束定位格架空气-水两相分布数值模拟

用计算流体动力学程序CFX4．2对棒束定位格架通道内空气．水两相流体三维流动进行了数值模拟。在计算中，采用了考虑界面横向效应的两流体模型，用该模型计算模拟了通道的l/4区域和定位格架交混叶片．获得了流体区域的两相流速和相分布；并分析了定位格架交混叶片对流动和相分布的影响。结果表明．带定位格架棒束流道内空气-水两相流动数值模拟基本合理．该方法可用来初步分析复杂通道内的两相流动。     

Derivation of new mass,momentum, and energy conservation equations for two-phase flows

System codes are used to analyze nuclear reactor systems during steady state and transient operations. These codes are able to predict pressure drop, void fraction distributions and temperature distributions for various coolants, heated flow geometries, and heat configurations. They also include models for various two-phase flow regimes, but extreme flow conditions that involve significant phase change can tax the current code capabilities. Current system codes have mass, momentum, and energy conservation equations for two fields (liquid and vapor), resulting in a model with six conservation equations. Recent developments in limited applications of a few of these codes have added a separate droplet field from the continuous liquid. This is part of a trend toward the inclusion of more fields (and requisite conservation equations) in system codes. The representation of two phase flow phenomena is improved by increasing the number of fields. Conservation equations based on six fields (liquid, vapor, small bubble, large bubble, small droplet and large droplet) are derived in this work.     

基于ECC安注热混合试验的LOCUST 1.2分析与验证

在失水事故（LOCA）工况下安注系统投入使用时,蒸汽与安注冷却剂会发生流体热力学混合,热混合过程中冷腿段的冷却是直接影响堆芯再淹没与否的重要因素。中国广核集团有限公司自主研发了一款两相流热工水力系统分析软件LOCUST,可用于压水堆核电厂事故工况的分析计算。基于西安交通大学堆芯应急冷却系统（ECCS-XJTU）试验台架进行的堆芯应急冷却（ECC）安注热混合试验,本文使用LOCUST软件对ECC热混合试验进行了几何建模及计算分析。ECC热混合试验工况主要为不同流量下主管纯蒸汽与安注管过冷水的混合,蒸汽流量为25~125 kg/h,过冷水流量为100~500 kg/h。模拟计算结果和试验结果的对比分析表明：试验段出口质量流量计算值的最大相对误差在13.8%以内,混合后温度计算值的最大相对误差在8%以内,LOCUST在计算高温蒸汽和过冷水混合时的计算结果相对保守,总体上验证了LOCUST在LOCA下两相热混合安注计算的可靠性和准确性。     

Conservative conservation equations: Numerical approach and code-to-code benchmarks

One of the principle features of RELAP5-based system thermal hydraulic codes is the use of a two-fluid, non-equilibrium, non-homogeneous, hydrodynamic model for the transient simulation of the two-phase system behavior. This model includes six governing equations to describe the mass, energy, and momentum of the two fluids. The current version of RELAP-5 is not a fully conservative code because it uses both non-conservative and conservative numerical approximation forms of conservation equations. The current version of RELAP5 versions have mass and energy errors during time advancements, either resulting in (a) automatic reduction of time steps used in the advancement of the equations and increased run times or (b) the growth of unacceptably large errors in the transient results. Therefore, fully conservative conservation equations and closure equations have recently been developed to address this problem. This article demonstrates the numerical approach to implement the developed fully conservative conservation equations into RELAP5 and the results of RELAP5 including developed conservative form of conservation equations. RELAP5 versions including conservative and non-conservative conservation equations are compared for various tests from a single pipe to a whole Pressurized Water Reactor (PWR) model.