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.     

Simulation of two-phase flows in vertical tubes with the CTFD code FLUBOX

The computational two-fluid dynamics (CTFD) code FLUBOX is developed at GRS for the multidimensional simulation of two-phase flows. The single-pressure two-fluid model is used as basis of the simulation. A basic mathematical property of the two-fluid model of FLUBOX is the hyperbolic character of the advection. The numerical solution methods of FLUBOX make explicit use of the hyperbolic structure of the coefficient matrices. The simulation of two-phase flow phenomena needs, apart from the conservation equations for each phase, an additional transport equation for the interfacial area concentration. The concentration of the interfacial area is one of the key parameters for the modeling of interfacial friction forces and interfacial transfer terms. A new transport equation for the interfacial area concentration is in development. It describes the dynamic change of the interfacial area concentration due to mass exchange and a force balance at the phase boundary. Results from FLUBOX calculations for different experiments of two-phase flows in vertical tubes are presented as part of the validation.     

流道方位及运动对沸腾两相流动传热行为的影响

基于两流体模型与固壁非稳态导热模型,结合有关关联式组合与参数综合比选下的模型验证,建立分析流道内沸腾流动传热的瞬态数值模拟程序。通过引入运动下附加加速度模型,研究流道形位与运动等因素对流道内沸腾流动与传热的影响。诸因素对沸腾传热系数、流动压降、固壁温度以及传热流动的瞬态行为影响的计算分析结果对相关堆芯流道的试验设计与应用具有指导意义。     

两流体模型在环形窄缝内的应用研究

采用EPRI最新开发的Chexal-Harrison相壁相间摩擦模型和简化的相壁相间传热模型,构造了适用于环形窄缝内沸腾传热和流动的两流体模型,并编制了热工水力计算程序——THYME程序.与实验数据比较,分析了环形窄缝套管在不同负荷下Relap5/Mod3.2程序和本文程序的计算结果.计算结果表明,Relap5/Mod3.2低估了环形蒸发管的蒸汽温度,本文计算结果与实验数据较为一致.     

Sabena: Subassembly boiling evolution numerical analysis

This paper describes the computer code SABENA that has been used in subassembly sodium boiling evolution numerical analysis as a contribution to fast breeder reactor safety analysis. SABENA is a two-fluid model subchannel code system to calculate coolant boiling and two-phase flow in a rod bundle together with external loop characteristics which affects the overall boiling behavior in the bundle section. With the use of relatively simple but reasonable constitutive models, the SABENA code has been applied to and validated against many multi-pin sodium boiling problems. The results have shown excellent agreement with the experiments. The numerical methods and models employed in the code have proven to be robust and efficient in light of the extreme severity of the conditions characterizing low-pressure sodium boiling.     

蒸汽发生器二次侧汽液两相流数值模拟

以大亚湾核电站蒸汽发生器为原型,在相似原理的指导下,建立了蒸汽发生器“单元管”三维物理模型,采用Particle模型和热力学相变模型,并基于CFX软件实现了蒸汽发生器二回路侧两相流流动与沸腾换热特性数值模拟。计算结果表明：满负荷运行时,沿传热管高度升高,蒸汽发生器的传热系数及截面含汽率均呈上升趋势,其平均传热系数的数值模拟结果与Rohsenow经验关联式计算结果间的误差为8.4%,出口质量含汽率与大亚湾核电站实际运行参数相符。热相变模型在蒸汽发生器两相流数值模拟中的成功应用,可为蒸汽发生器热工水力的准确分析提供参考。     

流动欠热沸腾空泡份额的研究

影响欠热沸腾传热的主要因素是含汽率和系统压力。系统压力直接影响加热面上汽泡的大小,从而影响壁面向液体的传热量。欠热沸腾区任一点的热平衡含汽率可由通道内的热工参数和流动参数求出,然后据此求出通道中某点的空泡份额。文中给出了计算加热通道内流动欠热沸腾区空泡份额的计算关系式,该关系式在给定的参数范围内与实验结果符合较好。     

A numerical assessment of copper oxide and alumina nanoparticles during CHF occurrence

Subcooled nucleate boiling in forced convection has been drawing significant attention in many fields due to its good heat transfer efficiency and high heat removal capacity. Such advancement in sub-cooled nucleate boiling is the result of continuing efforts from experimental, theoretical and numerical researchers, particularly focusing on critical heat flux (CHF). CHF heat transfer regimes are inefficient and the occurrence of CHF can cause a large temperature gradient in the heated wall leading to physical burnout. One way to increase the level of the CHF is to add certain nanoparticles to the base fluid. The present paper compares the effects of the addition of copper oxide and alumina nanoparticles on CHF phenomenon within the general-purpose computational fluid dynamics (CFD). The governing equations solved are generalized phase continuity, momentum and energy equations. Wall boiling phenomena are modeled using the baseline mechanistic nucleate boiling model developed in Rensselaer Polytechnic Institute (RPI). To simulate the critical heat flux phenomenon, the RPI model is extended to the dry-out phenomenon by partitioning wall heat flux to both liquid and vapor phases considering the existence of thin liquid wall film. It was shown that the presence of copper oxide in comparison with alumina nanoparticles in the base fluid, delays the dryout phenomenon more dramatically and in specific concentration, CHF threshold would be enhanced and consequently the safety margins of the operation would be improved.     

蒸汽发生器二次侧两相流传热特性数值研究

以AP1000核电站蒸汽发生器为原型,建立蒸汽发生器二次侧"平均通道"模型,利用计算流体动力学软件ANSYS CFX,基于相界面模型对蒸汽发生器二次侧两相流流动和沸腾换热过程进行研究。结果表明:数值模拟计算方法能准确模拟蒸汽发生器二次侧汽液两相流沸腾和传热过程;满负荷运行时,流体由预热区经过泡核沸腾区过渡到稳定沸腾区,含汽率和传热系数沿流动方向逐渐增大,出口含汽率与该型号蒸汽发生器设计值符合较好,平均传热系数的模拟结果和JensLottes经验关联式的预测值基本一致。     

Improvement of the subcooled boiling model for low-pressure conditions in thermal-hydraulic codes

The functioning of the subcooled boiling model adopted in a thermal-hydraulic computer program has been investigated in detail, for low-pressure conditions, and necessary refinements have been incorporated into the code. The investigation has been carried out in two stages; in the first stage, the performance of the interfacial heat transfer/condensation is studied. Necessary refinements to the vertical flow map for the transition from bubbly to slug flow regimes and the interpolation with the ‘umbrella’ limitation that bounded the interfacial heat transfer values are carried out. Simulations of low-pressure subcooled boiling experiments were performed with the refined code version and a reasonable agreement with the experimental void fraction data was obtained. In addition, a high-pressure experiment was also simulated with the refined code version to check if these revisions do not affect the code performance at high pressures. No significant adverse effects were observed. In the second stage of the study, the performance of the wall heat flux partitioning model adapted in the code was investigated. In particular, the effectiveness of the ‘pumping factor’ formulation in the above model and its functioning at low-pressure conditions was investigated. Different ‘pumping factor’ formulations available in the literature were implemented into the code. Simulations of low-pressure subcooled boiling experiments were performed with the refined code version and the appropriate ‘pumping factors’ to be used for low-pressure conditions were determined.     

矩形窄通道内汽泡滑移与冷凝前期生长模型研究

矩形窄流道内汽泡生长会直接改变相界面浓度,从而影响流道的传热传质性能。为获得适用于窄流道内不同类型的汽泡生长模型,基于通体可视的实验本体,开展壁面沸腾流动换热实验。基于传热能量方程,研究过冷沸腾中汽泡滑移与冷凝前期两种情况下汽泡生长模型。实验结果表明汽泡呈现两种形式的生长,即汽泡滑移生长以及冷凝前期生长。建立了两种情况下的汽泡生长模型,实验数据验证模型误差在20%以内。因此,本研究能为沸腾两相数值模拟提供更加精细化的汽泡生长模型,从而提高汽泡行为的预测精度。     

A semi-implicit numerical scheme for transient two-phase flows on unstructured grids

A component-scale two-phase analysis code, CUPID, has been developed for a realistic simulation of transient two-phase flows in light water nuclear reactor components. In the CUPID code, a two-fluid three-field model is adopted and the governing equations are solved on an unstructured grid to make CUPID very useful for flow analysis in complicated geometries. For the numerical solution scheme, the semi-implicit method of the RELAP5 code, which has been proved to be very stable and accurate for most practical applications, was used with some modifications for an application to an unstructured non-staggered grid. This paper presents the modified semi-implicit numerical method for an unstructured grid and the preliminary results of the calculations.     

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.     

Study on Pb-Bi-water direct contact boiling two-phase flow and heat transfer

For the development of 45w%Pb-55w%Bi cooled direct contact boiling water small fast reactor (PBWFR), Pb-Bi-water direct contact boiling two-phase flow loop has been fabricated and operated. The loop consists of a Pb-Bi flow loop (four heater pin bundle, a chimney, an upper plenum, a level meter tank, an air-water cooler, and an electromagnetic flow meter) and a water-steam flow loop (a pump, a preheated, an injection nozzle, the chimney, the upper plenum with mist separators and dryers, a condenser, a buffer tank, and an air-water cooler). At the rated operating condition system pressure is 7 MPa. The sub-cooled water was injected into a Pb-Bi flow in the chimney. A power of the heater pin bundle was controlled to obtain the inlet and outlet temperatures of the heater bundle. The Pb-Bi and steam flows were simulated analytically using one-dimensional models of frictional and form losses and a drag force. The Pb-Bi-steam two-phase frictional pressure loss was calculated by means of the two-phase flow multiplication factor of Lockhart-Martinelli model. It was found that Pb-Bi temperature decreased quickly in the chimney due to high heat transfer rate of Pb-Bi-water direct contact boiling. The volumetric overall heat transfer coefficient was 60–310 kW/m³K, and decreased with the superheat.     

Wall function approach for boiling two-phase flows

One of the important goals of the NURESIM project is to assess and improve the simulation capability of the three-dimensional two-fluid codes for prediction of local boiling flow processes. The boiling flow is strongly affected by local mechanisms in the turbulent boundary layer near the heated wall. Wall-to-fluid transfer models for boiling flow with the emphasis on near-wall treatment are being addressed in the paper. Since the computational grid of the 3D two-fluid models is too coarse to resolve the variable gradients in the near-wall region, the use of wall functions is a common approach to model the liquid velocity and temperature profile adjacent to the heated wall.The wall function model for momentum, based on the surface roughness analogy has been discussed and implemented in the NEPTUNE_CFD code. The model has been validated on several upward boiling flow experiments, differing in the geometry, working fluid and operating conditions. The simulations with the new wall function model show an improved prediction of flow parameters over the boiling boundary layer. Furthermore, a wall function model for the energy equation, based on enhanced two-phase wall friction has been derived and validated.     

Numerical simulations of basic interfacial instabilities with incompressible two-fluid model

The incompressible two-fluid model for stratified flow was improved. The interface of the stratified two-phase flow was successfully recognized and sharpened within the two-fluid model. After the advection step of volume fraction the numerical diffusion of the interface was reduced in such a way that the thickness of the interface is kept constant during the simulation. The surface tension force was implemented in the system of the two-fluid model equations. The two basic instabilities of stratified flows: Rayleigh-Taylor and Kelvin-Helmholtz instability were used to validate the proposed two-fluid model. The proposed two-fluid model with interface sharpening presents a step towards the simulations of mixed flows, where locally dispersed flow or stratified flow will be simulated with appropriated submodels within the two-fluid model.     

Analytical modeling of flashing-induced instabilities in a natural circulation cooled boiling water reactor

A dynamic model for natural circulation boiling water reactors (BWRs) under low-pressure conditions is developed. The motivation for this theoretical research is the concern about the stability of natural circulation BWRs during the low-pressure reactor start-up phase. There is experimental and theoretical evidence for the occurrence of void flashing in the unheated riser under these conditions. This flashing effect is included in the differential (homogeneous equilibrium) equations for two-phase flow. The differential equations were integrated over axial two-phase nodes, to derive a nodal time-domain model. The dynamic behavior of the interface between the one and two-phase regions is approximated with a linearized model. All model equations are presented in a dimensionless form. As an example the stability characteristics of the Dutch Dodewaard reactor at low pressure are determined.     

Implementation of a second-order upwind method in a semi-implicit two-phase flow code on unstructured meshes

A two-phase flow analysis code, CUPID, has been developed for a realistic simulation of thermal–hydraulic phenomena in nuclear reactor components. In the CUPID code, a two-fluid three-field model is adopted and the governing equations are solved on unstructured meshes. To obtain the numerical solution, the semi-implicit method of the RELAP5 code was used with some modifications for a cell-centered finite volume method. In this work, a second-order upwind method was implemented for the convective terms of the CUPID code. To get the slopes of the convective quantities, we adopted the Frink’s reconstruction method (1994, AIAA Paper 94-0061) and modified it for an application to arbitrary polyhedral cells. To stabilize the numerical solutions, the Barth and Jesperson’s slope limiter was used. In order to evaluate the enhanced accuracy and ensure the robustness of the implemented scheme, numerical tests were performed using conceptual single- and two-phase flow problems, which include a strong phase change and very heterogeneous phase distributions.     

CFD analysis on subcooled boiling phenomena in PWR coolant channel

Eulerian two-fluid model coupled with wall boiling model was employed to calculate the three dimensional flow field and heat transfer characteristics in a hot channel with vaned spacer grid in PWR. The heat transfer from pellet-gap-cladding to coolant was also taken into account by a system coupled code MpCCI. The wall boiling model utilized in this study was validated by Bartolomei experiment data, and a good agreement can be observed. By solving the governing equation in a two-way coupled method, the distribution of temperature in the pellet-gap-cladding region and the distribution of temperature, void fraction and velocity of two-phase flow in coolant channel can be obtained. The influences of spacer grid and mixing vane on the thermal-hydraulic characteristics were analyzed. The heat transfer capacity was strongly improved by the spacer grid and mixing vane, while the flow resistance was also enlarged. Localized volume fraction of vapor phase decreased due to mixing vane, which will decrease the possibility of the departure from nucleate boiling (DNB) and increase the critical heat flux (CHF). By analyzing the temperature and void fraction at cladding outer surface, the critical regions where hot spot may occur were determined.     

Wave propagation in two-phase flow of magnetic fluid under a nonuniform magnetic field

The effect of nonuniform magnetic field on the linear and nonlinear wave propagation phenomena in two-phase pipe flow of magnetic fluid is investigated theoretically to realize the effective energy conversion system using boiling two-phase flow of magnetic fluid. Firstly, the governing equations of two-phase flow based on the unsteady thermal nonequilibrium two-fluid model are presented and the linear void wave propagation phenomena in boiling two-phase flow are numerically analyzed by using the finite volume method. Next, the nonlinear pressure wave propagation in gas-liquid two-phase flow is numerically analyzed by using the finite different method. According to these theoretical studies on the wave propagation phenomena in two-phase flow of magnetic fluid, it seems to be a reasonable proposal that the precise control of the wave propagation in two-phase flow is possible by effective use of the magnetic force.