Advanced three-dimensional two-phase flow simulation tools for application to reactor safety (ASTAR)

This paper summarizes the cumulative work undertaken in the frame of the EU shared-cost action “ASTAR Project”—the current status and future perspectives in the field of advanced numerical simulation of three-dimensional two-phase flow processes. This 3-year running project, which started in September 2000, involves seven partner institutes from around Europe. Specific emphasis is given to the further development of characteristic-based upwind differencing (also called “hyperbolic”) numerical methods and their application to transient two-phase flow. The paper summarizes the common basis adopted for the physical and mathematical modelling of two-phase flow in the form of a single-pressure “two-fluid” model and the various numerical solution techniques developed by the partners. Several benchmark exercises are presented which have been used as verification and assessment procedures for comparing the different modelling and numerical approaches. Comments on the suitability, accuracy, numerical stability, algorithmic robustness and computational efficiency serve as indicators for the possible extension of these methods to future code development activities. Two further tasks of the ASTAR project dealt with the production of high quality experimental field data in the LINX facility of PSI, for the validation of CFD models for two-phase bubbly flow, and the coupling of a two-phase CFD module with a system code. Details of these tasks have been published separately, and will not be recalled in this paper.     

Fluid mixing and flow distribution in a primary circuit of a nuclear pressurized water reactor—Validation of CFD codes

The EU project FLOMIX-R was aimed at describing the mixing phenomena relevant for both safety analysis, particularly in steam line break and boron dilution scenarios, and mixing phenomena of interest for economical operation and the structural integrity.This report will focus on the computational fluid dynamics (CFD) code validation. Best practice guidelines (BPG) were applied in all CFD work when choosing computational grid, time step, turbulence models, modelling of internal geometry, boundary conditions, numerical schemes and convergence criteria. The strategy of code validation based on the BPG and a matrix of CFD code validation calculations have been elaborated. CFD calculations have been accomplished for selected experiments with two different CFD codes (CFX, FLUENT). The matrix of benchmark cases contains slug mixing tests simulating the start-up of the first main circulation pump which have been performed with three 1:5 scaled facilities: the Rossendorf coolant mixing model ROCOM, the Vattenfall test facility and a metal mock-up of a VVER-1000 type reactor. Before studying mixing in transients, ROCOM test cases with steady-state flow conditions were considered. Considering buoyancy driven mixing, experimental results on mixing of fluids with density differences obtained at ROCOM and the FORTUM PTS test facility were compared with calculations. Methods for a quantitative comparison between the calculated and measured mixing scalar distributions have been elaborated and applied. Based on the “best practice CFD solutions”, conclusions on the applicability of CFD for turbulent mixing problems in PWR were drawn and recommendations on CFD modelling were given. The results of the CFD calculations are mostly in-between the uncertainty bands of the experiments. Although no fully grid-independent numerical solutions could be obtained, it can be concluded about the suitability of applying CFD methods in engineering applications for turbulent mixing in nuclear reactors.     

Investigations on mixing phenomena in single-phase flow in a T-junction geometry

The paper deals with T-junction mixing experiments carried out with wire-mesh sensors. The mixing of coolant streams of different temperature in pipe junctions leads to temperature fluctuations that may cause thermal fatigue in the pipe wall. This is practical background for an increased interest in measuring and predicting the transient flow field and the turbulent mixing pattern downstream of a T-junction. Experiments were carried out at a perpendicular connection of two pipes of 51 mm inner diameter. The straight and the side branches were supplied by water of different electrical conductivity, which replaced the temperature in the thermal mixing process. A set of three wire-mesh sensors with a grid of 16 × 16 measuring points each was used to record conductivity distributions downstream of the T-junction. Besides the measurement of profiles of the time averaged mixing scalar over extended measuring domains, the high resolution in time and space of the mesh sensors allow a statistic characterization of the stochastic fluctuations of the mixing scalar in a wide range of frequencies. Information on the scale of turbulent mixing patterns is obtained by cross-correlating the signal fluctuations recorded at different locations within the measuring plane of a sensor.     

On the relevance of low side flows for thermal loads in T-junctions

The mixing of coolant streams of different temperatures in pipe junctions leads to temperature fluctuations that may cause thermal fatigue in the pipe wall. Numerous T-junction experiments are known from literature, which were performed to study the nature of thermal loads in the pipe walls occurring during the mixing of hot and cold liquid. It is common to all known experiments that the experimental boundary conditions are set to reflect cases, in which the flow velocities in both main and side branches of the T-junctions are of the same order of magnitude. In the present experiments, carried out using wire-mesh sensors, it was observed that very low flow velocities in the side branch compared to the main pipe may lead to conditions potentially severe for thermal fatigue due to the low frequency of the temperature fluctuations occurring. The T-junction presented here consists of a perpendicular connection of two pipes of 50 mm inner diameter. The straight and the side branches are supplied with water of different electrical conductivities, to enable performing generic, isothermal tests on turbulent mixing with the idea to model the temperature fluctuations in thermal mixing processes. A pair of wire-mesh sensors, each with a grid of 16 × 16 measuring points, are used to record conductivity distributions in the downstream of the T-junction as well as directly at the junction in both branches. At very low flow rates in the side branch, a characteristic entrainment of liquid from the main branch into the side branch was found. Typically the entrainment flow in the side branch results in relatively high fluctuations at the low-frequency range. While the sensor in the main flow shows fluctuations with a power spectrum similar in character to mixing experiments with comparable flow velocities in both branches of the T-junction. The phenomenon of entrainment of water from the main branch into the side branch against the main flow direction vanishes at a certain critical velocity in the side branch.     

热管式辐射器热工水力优化分析

热管式辐射器广泛应用于空间系统废热排放,其管道复杂,包含热管、翅片和包壳等复杂结构。针对热管式辐射器的流动与换热问题,本文采用CFD软件与自主研发程序RATHAL相结合的方法。先用CFD软件计算流动管道及集流环上的流量分配,再将该结果代入RATHAL程序中计算得到辐射器的温度分布。根据计算结果,以均匀温度分布为目的,对现有结构提出了合理的优化意见。结果表明,采用CFD软件与自主研发程序RATHAL相结合的方法能尽量真实并高效地模拟辐射器的流量分配与温度分布情况,且经过优化后辐射器集流环间的温差大幅缩小、设计更加合理。     

Extension of the inhomogeneous MUSIG model for bubble condensation

Bubble condensation plays an important role, e.g. in sub-cooled boiling or steam injection into pools. Since the condensation rate is proportional to the interfacial area density, bubble size distributions have to be considered in an adequate modeling of the condensation process. The effect of bubble sizes was clearly shown in experimental investigations done previously at the TOPFLOW facility of FZD. Steam bubbles were injected into a sub-cooled upward pipe flow via orifices in the pipe wall located at different distances from measuring plane. 1 mm and 4 mm injection orifices were used to vary the initial bubble size distribution. Measurements were done using a wire-mesh sensor. Condensation is clearly faster in case of the injection via the smaller orifices, i.e. in case of smaller bubble sizes. Recently the Inhomogeneous MUSIG model was implemented into the CFD code CFX from ANSYS enabling the simulation of poly-dispersed flows including the effects of separation of small and large bubbles due to bubble size dependent lift force inversion. It allows to divide the dispersed phase into size classes regarding the mass as well as regarding the momentum balance. Up to now transfers between the classes in the mass balance can be considered only by bubble coalescence and breakup (population balance). Here an extension of the model is proposed to include the effects due to phase transfer. The paper focuses on the derivation of equations for the extension of the Inhomogeneous MUSIG model and presents some first results for verification and validation.     

核电厂管线中的热分层现象

由于阀门渗漏使核电厂安注系统冷水注入到充满热水的连接安注系统与主管道的支管中，而发生的热分层和温度振荡现象的研究对于确保核电厂的安全和可靠运行具有重要意义。运用计算流体力学软件CFX，采用k－ε湍流模型，以研究某核电厂安注系统支管中热分层现象的实验为对象，模拟了阀门渗漏冷水进入含有高温水的支管以后所发生的热分层现象，数值模拟的结果与实验测量结果吻合。在此基础上，通过改变阀门渗漏冷水的流量、支管的结构等参数，进一步研究支管中热分层现象与这些参数的内在关系，从而得出了影响热分层现象的主要原因及热分层现象发生的一些规律。     

Unsteady Elbow Pipe Flow to Develop a Flow-Induced Vibration Evaluation Methodology for Japan Sodium-Cooled Fast Reactor

This paper describes the current status of flow-induced vibration evaluation methodology development for primary cooling pipes in the Japan sodium-cooled fast reactor (JSFR), with particular emphasis on recent research and development activities that investigate unsteady elbow pipe flow. Experimental efforts have been made using 1/3-scale and 1/10-scale single-elbow test sections for the hot-leg pipe. The 1/10- scale experiment simulating the hot-leg pipe indicated no effect of pipe scale in comparison with the 1/3- scale experiment under inlet-rectified-flow conditions. The next experiment using the 1/3-scale test section was performed to investigate the effect of swirl flow at the inlet. Although the flow separation region was deflected at the downstream from the elbow, the experiment clarified a less significant effect of swirl flow on pressure fluctuation onto the pipe wall. An additional experiment was intended to study the effect of elbow curvature. The experiments with water revealed no clear flow separation in a larger curvature elbow case than that of the JSFR. Since the interference of multiple elbows should be investigated to understand turbulent flow in the cold-leg pipe geometry, 1/15-scale experiments with double elbows were carried out to clarify that flow in the first elbow influenced a flow separation behavior in the second elbow. Simulation activities include Unsteady Reynolds Averaged Navier Stokes equation (URANS) approach with a Reynolds stress model using a commercial computational fluid dynamics (CFD) code and Large Eddy Simulation (LES) approach using an in-house code. A hybrid approach that combined with RANS and LES was also applied using a CFD code. Several numerical results appear in this paper, focusing on its applicability to the hot-leg pipe experiments. These simulations reasonably agreed with the experimental data using the 1/3-scale test section.     

A population balance approach considering heat and mass transfer—Experiments and CFD simulations

Bubble condensation in sub-cooled water is a complex process, to which various phenomena contribute. Since the condensation rate depends on the interfacial area density, bubble size distribution changes caused by breakup and coalescence play a crucial role.Experiments on steam bubble condensation in vertical co-current steam/water flows have been carried out in an 8 m long vertical DN200 pipe. Steam is injected into the pipe and the development of the bubbly flow is measured at different distances to the injection using a pair of wire mesh sensors. By varying the steam nozzle diameter the initial bubble size can be influenced. Larger bubbles come along with a lower interfacial area density and therefore condensate slower. Steam pressures between 1 and 6.5 MPa and sub-cooling temperatures from 2 to 12 K were applied. Due to the pressure drop along the pipe, the saturation temperature falls towards the upper pipe end. This affects the sub-cooling temperature and can even cause re-evaporation in the upper part of the test section. The experimental configurations are simulated with the CFD code CFX using an extended MUSIG approach, which includes the bubble shrinking or growth due to condensation or re-evaporation. The development of the vapour phase along the pipe with respect to vapour void fractions and bubble sizes is qualitatively well reproduced in the simulations. For a better quantitative reproduction, reliable models for the heat transfer at high Reynolds number as well as for bubble breakup and coalescence are needed.     

Gas–liquid flow around an obstacle in a vertical pipe

This paper presents a novel technique to study the two-phase flow field around an asymmetric obstruction in a vertical pipe with a nominal diameter of DN200. Main feature of the experiments is the shifting of a half-moon shaped diaphragm causing the obstruction along the axis of the pipe. In this way, the 3D void field is scanned with a stationary wire-mesh sensor that supplies data with a spatial resolution of 3 mm over the cross-section and a measuring frequency of 2.5 kHz. Besides the measurement of time-averaged void fraction fields and bubble-size distributions, novel data evaluation methods were developed to extract estimated liquid velocity profiles as well as lateral components of bubble velocities from the wire-mesh sensor data. The combination of void fraction fields and velocity profiles offer the opportunity to analyse a two-phase flow in a geometry that owns a series of features characteristic for complex components of power and chemical plant equipment. Such characteristics are sharp edges with flow separation, recirculation areas, jet formation, stagnation points and curved stream-lines.

The tests were performed with an air–water flow at nearly ambient conditions and with a saturated steam–water mixture at 6.5 MPa. The superficial velocities of liquid and gas or, respectively, vapour were varied in a wide range.

The flow structure upstream and downstream of the obstacle is characterized in detail. Bubble size dependent effects of bubble accumulation and migration are discussed on basis of void-fraction profiles decomposed into bubble-size classes. A pronounced influence of the fluid parameters was found in the behaviour of bubbles at the boundary of the jet coming from the non-obstructed part of the cross-section. In case of an air–water flow, bubbles are restrained from entering the jet, a phenomenon which was not observed in high-pressure steam–water flow. A detailed uncertainty analyse of the velocity assessments finishes the presented paper. A blind pre-test calculation with CFX-10 based on the assumption of a mono-disperse bubbly flow has reproduced the overall void and velocity profiles. The results are used for the assessment of the influence of local accelerations on the liquid velocity measurement.     

A two-dimensional model for fluid-structure interaction in curved pipes

A “channel” model was developed for the purpose of simulating the interactive fluid-structural response of curved pipes to pressure pulses. Simulation is shown to have been achieved analytically in both the axisymmetric (“breathing”) and transverse (“bending”) modes of interactive behavior.An experimental program which was aimed at the validation of the model is also described. Tests were run in both straight and curved pipe configurations. Comparisons between measurements and model calculations demonstrate the validity of the model within the range of parameters under consideration.The model was implemented into the DISCO code for nonlinear fluid-shell interaction.     

Benchmark database on the evolution of two-phase flows in a vertical pipe

Based on many years of experience, a new extensive and high-quality database was obtained for steady-state upward air-water flows in a vertical pipe with an inner diameter of 195.3 mm using the wire-mesh sensor technology. During the experiments, the sensor was always mounted on the top of the test section while the distance between gas injection and measuring plane was varied up to 18 different L/D by using gas injection chambers at different vertical positions. The gas was injected via holes in the pipe wall. In this new test series the pressure was kept at 0.25 MPa (absolute) at the location of the active gas injection while the temperature was constant at 30 °C ± 1 K. The experiments were done for 48 combinations of air and water superficial velocities varying from 0.04 m/s to 1.6 m/s for water and 0.0025 m/s to 3.2 m/s for air. From the raw data time-averaged data as: radial gas volume fraction profiles, bubble size distributions, radial volume fraction profiles decomposed according to the bubble size and the radial profiles of the gas velocity were calculated. The consistency of this data was thoroughly checked. They are characterized by a high resolution in space, which makes them suitable for the development and validation of CFD-grade closure models, e.g. for bubble forces and coalescence and break-up. It is also an ideal base to validate CFD approaches for poly-dispersed flow. For this reason it is proposed to use the database as a benchmark for modelling poly-dispersed flows.     

Verification of the thermohydraulic models used in improved-assessment codes for the RELAP5 and KORSAR two-phase flow models

A methodology for finding the confidence intervals for the optimal values of the coefficients in the closure relations used in improved-estimate thermohydraulic codes is developed. When a coefficient used in a code falls within the confidence interval constructed using the proposed technique, the code model is considered to be statistically verified on the experimental data based used. The methodology is used to verify the two-phase flow model used in the American RELAP5 thermohydraulic code and the domestic KORSAR thermodydraulic code based on the experimental data on the volume steam content in vertical tubes.Translated from Atomnaya Énergiya, Vol. 97, No. 6, pp. 446–450, December, 2004.This revised version was published online in April 2005 with a corrected cover date.     

ITER中国氦冷固体实验包层模块温度场和氦气流场三维数值分析

采用通用计算流体力学软件Fluent对应用于国际热核实验堆(ITER)的实验包层模块(TBM)的第一壁Be、Be球床中子增殖区、Li4SiO4陶瓷球床氚增殖区、以及结构材料的温度场和氦气流道内流场进行了三维数值模拟,研究了TBM的温度场及冷却管道内的氦气流场的分布.结果表明,除极小区域外,材料的温度在该材料所允许的工作范围之内;氦气表现出很好的流动和换热特性.     

The inhomogeneous MUSIG model for the simulation of polydispersed flows

A generalized inhomogeneous multiple size group (MUSIG) model based on the Eulerian modeling framework was developed in close cooperation of ANSYS-CFX and Forschungszentrum Dresden-Rossendorf and implemented into the CFD code CFX. The model enables the subdivision of the dispersed phase into a number of size groups regarding the mass balance as well as regarding the momentum balance.

In this work, the special case of polydispersed bubbly flow is considered. By simulating such flows, the mass exchanged between bubble size classes by bubble coalescence and bubble fragmentation, as well as the momentum transfer between the bubbles and the surrounding liquid due to bubble size dependent interfacial forces have to be considered. Particularly the lift force has been proven to play an important role in establishing a certain bubble size distribution dependent flow regime.

In a previous study [Krepper, E., Lucas, D., Prasser, H.-M., 2005. On the modeling of bubbly flow in vertical pipes. Nucl. Eng. Des. 235, 597–611] the application of such effects were considered and justified and a general outline of such a model concept was given. In this paper the model and its validation for several vertical pipe flow situations is presented. The experimental data were obtained from the TOPFLOW test facility at the Forschungszentrum Dresden-Rossendorf (FZD). The wire-mesh technology measuring local gas volume fractions, bubble size distributions and velocities of gas and liquid phases were employed.

The inhomogeneous MUSIG model approach was shown as capable of describing bubbly flows with higher gas content. Particularly the separation phenomenon of small and large bubbles is well described. This separation has been proven as a key phenomenon in the establishment of the corresponding flow regime. Weaknesses in this approach can be attributed to the characterization of bubble coalescence and bubble fragmentation, which must be further investigated.     

Analysis of the capability of system codes to model cavitation water hammers: Simulation of UMSICHT water hammer experiments with TRACE and RELAP5

The capabilities of the nuclear system transient codes TRACE and RELAP5 to model coupled two-phase flow and pressure wave propagations in a pipe are assessed by analyzing the UMSICHT PPP cavitation water hammer experiments 329 and 135 after valve closure. Time-dependent pressure, flow behaviour, and the generation and collapse of vapor bubbles at the valve and the first bridge are discussed. We show that both codes are able to model the flow behaviour of the water hammer for the high pressure and high temperature case 329 (initially 10–13 bar and 420 K), however condensation heat transfer for the base case needed to be increased in order to accurately model the magnitude of the first pressure excursion. The experimental broadening and damping of the subsequent pressure peaks by Fluid-Structure Interaction (FSI) phenomena arising from the interaction of the flow with the vibrations of the piping structure are not considered in the modeling results. For the lower pressure and temperature case 135 (initially 1–4 bar and 294 K), the TRACE code provides a good approximation of the propagation of the pressure wave and the void fraction behaviour, already with base case conditions, while RELAP5 overpredicts the vapor generation along the pipe and, as a result, considerably underpredicts the pressure amplitudes and overpredicts the water hammer frequency.     

A numerical study on turbulence attenuation model for liquid droplet impingement erosion

The bent pipe wall thinning has been often found at the elbow of the drain line and the high-pressure secondary feed-water bent pipe in the nuclear reactors. The liquid droplet impingement (LDI) erosion could be regarded to be one of the major causes and is a significant issue of the thermal hydraulics and structural integrity in aging and life extension for nuclear power plants safety. In this paper two-phase numerical simulations are conducted for standard elbow geometry, typically the pipe diameter is 170 mm. The turbulence attenuation in vapor-droplets flow is analysed by a damping function on the energy spectrum basis of single phase flow. Considering the vapor turbulent kinetic energy attenuation due to the involved droplets, a computational fluid dynamic (CFD) tool has been adopted by using two-way vapor-droplet coupled system. This computational fluid model is built up by incompressible Reynolds Averaged Navier–Stoke equations using standard k–ε model and the SIMPLE algorithm, and the numerical droplet model adopts the Lagrangian approach, a general LDI erosion prediction procedure for bent pipe geometry has been performed to supplement the CFD code. The liquid droplets diameter, velocity, volume concentration are evaluated for the effects of carrier turbulence attenuation. The result shows that carrier turbulence kinetic energy attenuation is proved to be an important effect for LDI erosion rate when investigating the bent pipe wall thinning phenomena.     

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.     

Single-phase cross-mixing measurements in a 4 × 4 rod bundle

The wire-mesh sensor technique has been successfully introduced into a fuel rod bundle geometry for the first time. In this context, a dedicated test facility (SUBFLOW) has been designed and constructed at Paul Scherrer Institut (PSI) in a co-operation with the Swiss Federal Institute of Technology (ETH Zürich). Two wire-mesh sensors designed and built in-house were installed in the upper part of the vertical test section of SUBFLOW, and single-phase experiments on the turbulent mass exchange between neighboring sub-channels were performed. For this purpose, salt tracer was injected locally in one of the sub-channels and conductivity distributions in the bundle measured by the wire-mesh sensor. Both flow rate and distance from the injection point were varied. The latter was achieved by using injection nozzles at different heights. In this way, the sensor located in the upper part of the channel could be used to characterize the progress of the mixing along the flow direction, and the degree of cross-mixing assessed using the quantity of tracer arriving in the neighboring sub-channels. Fluctuations of the tracer concentration in time were used for statistical evaluations, such as the calculation of standard deviations and two-point correlations.