Numerical simulation of secondary flow in bubbly turbulent flow in sub-channel

Secondary flow in bubbly turbulent flow in sub-channel was simulated by using an algebraic turbulence stress model. The mass, momentum, turbulence energy and bubble diffusion equations were used as fundamental equation. The basis for these equations was the two-fluid model: the equation of liquid phase was picked up from the equation system theoretically derived for the gas-liquid two-fluid turbulent flow. The fundamental equation was transformed onto a generalized coordinate system fitted to the computational domain in sub-channel. It was discretized for the SIMPLE algorithm using the finite-volume method. The shape of sub-channel causes a distortion of the computational mesh, and orthogonal nature of the mesh is sometimes broken. An iterative method to satisfy a requirement for the contra-variant velocity was introduced to represent accurate symmetric boundary condition. Two-phase flow at a steady state was simulated for different magnitudes of secondary flow and void fraction. The secondary flow enhanced the momentum transport in sub-channel and accelerated the liquid phase in the rod gap. This effect was slightly mitigated when the void fraction increased. The acceleration can contribute to effective cooling in the rod gap. The numerical result implied a phenomenon of industrial interest. This suggested that experimental approach is necessary to validate the numerical model and to identify the phenomenon.     

液态铅铋合金湍流普朗特数及RANS模型优选

工程上常采用RANS湍流模型进行热工水力相关的数值模拟,然而液态铅铋合金（LBE）具有独特的热物性,常规湍流普朗特数模型和RANS湍流模型对其流动与传热模拟的适用性有待研究。为更准确地描述绕丝燃料组件内LBE的流动与换热过程,本文基于大涡模拟对湍流普朗特数模型和RANS湍流模型进行优选。首先,采用四种湍流普朗特数模型对绕丝燃料组件内LBE的流动与传热过程进行大涡模拟,对比分析实验数据和模拟结果并进行模型优选。基于优选的湍流普朗特数模型,评价RANS湍流模型对LBE数值模拟的适用性和准确性。结果表明,Cheng湍流普朗特数模型和SST k-ω模型对LBE流动与传热模拟的准确性和适用性最高。     

Thermal hydraulic behavior in the deteriorated turbulent heat transfer regime for a gas-cooled reactor

One of the key issues in a gas-cooled system with a passive heat removal measure is the correct prediction of thermal hydraulic behavior in the deteriorated turbulent heat transfer (DTHT) regime. Here, a simple one-dimensional analysis of a gas-cooled reactor system was performed to show its strong potential for operation in the DTHT regime. A numerical calculation using computational fluid dynamics (CFD) was done to verify the capability of the Launder-Sharma (LS) turbulence model to predict wall and bulk temperatures while a gas system is operating in the DTHT regime. The results by the LS model are compared to those by the high Reynolds turbulent model, a newly proposed correlation, and recently obtained experimental data. The comparison shows that the LS turbulence model can provide a reasonable prediction in the buoyancy-induced DTHT regime. Additionally, it was found that the LS model predicted strong laminarization near the entrance which deteriorated turbulent heat transfer further compared to the measurements, but re-turbulization took place much earlier than in the experiment which recovered the heat transfer to a normal turbulent heat transfer.     

液态金属钠在圆管中湍流传热特性研究

采用高Re k-ε模型与壁面函数法对液态金属钠在圆管中湍流传热特性进行数值计算,并与文献实验结果进行了比较,计算值与实验结果符合较好。同时应用该方法研究了湍流程度和加热条件对液态钠传热特性的影响。结果表明：湍流程度对传热的影响主要集中在流道前半段,后半段分子扩散对传热的影响逐渐凸现出来,使不同湍流程度流体传热特性的区别逐渐缩小。初始温度与热流密度对传热特性无明显影响。     

Two fluid model for two-phase turbulent jets

Eulerian two-fluid models are widely used in nuclear reactor safety and CFD. In these models turbulent diffusion of a dispersed phase must be formulated in terms of the fluctuating interfacial force and the Reynolds stresses. The interfacial force is obtained using the probability distribution function approach by Reeks (1992). This paper is the first application of this force to a case of engineering interest outside homogeneous turbulence. An Eulerian multidimensional two-fluid model for a cylindrical two-phase dispersed particle jet is proposed and compared with experimental data. The averaged conservation equations of mass and momentum are solved for each phase and the turbulent kinetic energy equation is solved for the continuous phase. The turbulent diffusion force and the Reynolds stresses are constituted within the context of the k- model of turbulence. A dissipation term has been added to the k- model for the turbulence modulation by the particles. Once the constitutive relations have been defined, the two-fluid model is implemented in a computational fluid dynamics code. It is shown that when the particles are very small the model is consistent with a convection-diffusion equation for particle transport where the diffusivity is defined according to Taylor's model (Taylor, G.I., 1921. Diffusion by continuous movements. Proc. London Math. Society, A20, pp. 196–211). The two-fluid model is also compared against two experimental data sets. Good agreement between the model and the data is obtained. The sensitivity of the results to various turbulent mechanisms is discussed.     

大空间内底部弧形加热段自然对流传热特性研究

为准确预测安全壳上封头的自然对流换热特性以保证堆芯余热安全排出，设计了采用底部弧形加热段的矩形封腔自然对流装置，研究导热率对底部弧形加热段和封腔内流体温度分布的影响，并基于开源软件OpenFOAM，采用数值模拟方法对比分析2种湍流模型和3种湍流热通量模型的适用性。结果表明，流体沿弧形面的流动受边界层和绕流脱体强化现象的影响，局部自然对流换热强度从顶部向两端先减小后增大；材料热导率对弧形面的温度分布影响比较大，但对于加热段外的流体温度分布影响极小；经过对AFM模型进行修正，得到了更适用于实验条件的模型参数值，修正后的模型对流体速度场的模拟更为准确且在更高功率工况下也得到验证。本研究可为后续方案设计的有效性评价提供参考。      

Numerical investigation on the heat transfer characteristics of a liquid-metal pool subjected to a partial solidification process

The main purpose of this paper is to investigate numerically the effects of solidification on the heat transfer characteristics of the liquid metal layer, for use in accident analyses. The situation is very similar to an overlying liquid melt pool that could be fooned in the reactor lower head during the late phase of a severe nuclear accident. Based on a computational model, MPCOOL, the numerical predictions were then assessed through a comparison with the experimental data that was obtained with various boundary temperature conditions and geometrical aspect ratios, especially for the Ra-Nu relationship. For the cases with solidification, the results of the comparison show that(a) the computational model does show a good agreement with heat transter rates inferred from the experimental data, with a few exceptions at the Ra numbers which suggest a turbulent transport; and also (b) the computational model underpredicts the heat transfer rates by about 6% than that inferred from the experimental data when it is integrally evaluated with the Ra-Nu correlation. The foregoing results are mainly due to the currently limited applicability of the computational model up to the laminar-to-turbulence transition flows and its application to the turbulence flows because it is always subjected to a model uncertainty between the laminar and turbulence. Next, an additional comparison for the cases with and without solidification was made to examine the effects of the solidification on the energy partition within the liquid metal layer and its effects on the directional heat transfer rates. The results of the comparison show that the computational model for the case without solidification predicts higher heat transfer rates by about 15% than when solidification is included, but there isn't any experimental data that directly supports this trend.     

CFX中湍流模型用于分析超临界水传热的适用性评价

通过两组典型实验数据,对商业软件CFX的12种湍流模型用于模拟超临界水竖直向上流动传热的性能进行评价。研究结果表明：强迫对流时,BSL代数应力模型与实验结果符合最好,但各模型间差异均不大;混合对流时,基于壁面函数的ε类型湍流模型不能模拟传热恶化趋势,自动壁面处理的ω类型湍流模型能模拟出传热恶化的趋势,但各模型预测结果和实验结果相差较大。评价结果表明近壁面的处理方式对模拟结果影响很大。此外,基于湍流普朗特数模拟湍流热流密度及未考虑密度脉动对传热的影响均是导致不能正确模拟超临界水传热行为的因素,建议对湍流模型进行改进。     

Machine learning of turbulent transport in fusion plasmas with neural network

Turbulent transport resulting from drift waves,typically,the ion temperature gradient(ITG)mode and trapped electron mode(TEM),is of great significance in magnetic confinement fusion.It is also well known that turbulence simulation is a challenging issue in both the complex physical model and huge CPU cost as well as long computation time.In this work,a credible turbulence transport prediction model,extended fluid code(ExFC-NN),based on a neural network(NN)approach is established using simulation data by performing an ExFC,in which multi-scale multi-mode fluctuations,such as ITG and TEM turbulence are involved.Results show that the characteristics of turbulent transport can be successfully predicted including the type of dominant turbulence and the radial averaged fluxes under any set of local gradient parameters.Furthermore,a global NN model can well reproduce the radial profiles of turbulence perturbation intensities and fluxes much faster than existing codes.A large number of comparative predictions show that the newly constructed NN model can realize rapid experimental analysis and provide reference data for experimental parameter design in the future.     

Indirect estimation method of the turbulence induced fluid force spectrum acting on a fuel rod

This paper proposes a methodology to identify a turbulent flow induced force acting on a nuclear fuel rod based on the indirect input force estimation theory in structural dynamics, which is useful to predict the forcing function when the input force cannot be measured directly. Since the nuclear fuel rod in a PWR (pressurized water reactor) is exposed to coolant flow, the turbulence induced force generates a fuel rod vibration which may cause a fretting wear on the surface of the rod. This study develops a method to estimate turbulence induced force spectrum indirectly for a real scale fuel rod loaded in a nuclear fuel test facility. The proposed method requires a reliable finite element (FE) model which simulates the fuel rod dynamics well; therefore, the FE model is discussed, especially regarding the procedure to determine the effective rod density. Since the pellets rattle inside the tube due to small gaps between the tube and pellets, especially at the beginning of the fuel's life, the contribution of the pellet mass to the density for the FE model cannot be determined clearly. It is shown that the appropriate density can be estimated by comparing the natural frequencies from the modal test results of the rod (with pellet) and the tube (without pellet). Then, the indirect turbulence induced force estimation theory is applied to the fuel rod, and some numerical and test results are discussed to verify the applicability of the suggested method.     

超临界压力下考虑密度脉动的湍流模型开发

目前超临界水传热数值程序中使用的湍流模型都是针对亚临界压力下常物性开发的,未考虑密度脉动。超临界水的物性随温度变化显著,密度脉动对湍流模型的贡献很大,不可忽略。本文建立了考虑密度脉动的模拟方法,模拟方法中同时考虑了热膨胀系数的脉动。将建立的密度脉动模型用于AKN湍流模型中,并采用实验数据进行验证评价。评价结果表明,考虑密度脉动的湍流模型模拟得到的结果与实验值符合得更好。建议在以后的超临界水传热的湍流模拟中考虑密度脉动。     

The derivation and moments solution of approximate transport equations for the implantation of ions into amorphous targets

Commencing with the LSS integro-differential equation, an approximate transport equation is derived from which the moments of the range distribution may be obtained. The resulting equation set is known as the Kent Range ALgorithm (KRAL). The method for numerical solution of these equations, when written as a set of coupled second order ordinary differential equations (ODEs) of the initial value type, is then outlined. Solution is achieved by recasting the equation set in the form of first order ODEs designed for iterative solution. The technique used is an iterative refinement (or residual correction) procedure and the set of first order ODEs is called the Kent Optimised Range ALgorithm (KORAL). Finally, the first three moments from KORAL, first and second order PRAL codes and the full transport equation code KUBBIC-91 are compared with Monte Carlo data obtained from a TRIM code modified to treat targets of infinite extent. Comparisons are performed using consistent nuclear and electronic energy loss models.     

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.     

氢气安全分析软件CYCAS的研发及初步验证

基于计算流体力学方法进行了三维氢气安全分析软件CYCAS的自主研发,采用隐式连续欧拉-任意拉格朗日欧拉方法求解三维、可压、非定常的Navier-Stokes方程组。CYCAS通过求解多组分的质量守恒方程描述多组分气体的扩散和混合,气流中的水蒸气相变行为采用均相平衡模型模拟,而壁面上的相变行为采用Chilton-Colburn相似假设,湍流模拟选用了代数湍流模型和k-ε湍流模型。采用喷射实验HYJET和国际标准测试题ISP23对CYCAS进行了初步验证,计算结果与实验值吻合良好。     

Modified k-ε model for two-phase turbulent jets

A modified k-ε model is proposed for two-phase turbulent jets which takes into account the additional dissipation of turbulent kinetic energy by the dispersed phase. Within the context of the two-phase averaged equation for the turbulent kinetic energy of the continuous phase, a constitutive relation is proposed for the additional dissipation of turbulence. The additional dissipation effect was modeled using a transfer function, which relates the fluctuations of the dispersed phase with the fluctuations of the continuous phase, integrating over the turbulence energy spectrum. A further improvement to the theory considers that dissipation only occurs when the eddies are bigger than the particles. Therefore a cutoff frequency is proposed and for big particles or bubbles dissipation may become negligible. The model is inserted in an Eulerian computational fluid dynamics code. The results are compared with data available in the literature for an air-particle jet. The results agree with the data within the range of experimental error. Comparisons were also made without including dissipation effects and it was concluded that the dissipation due to eddy-particle interactions is significant and should be included in a general two-phase k-ε model.     

Development of a generalized coalescence and breakup closure for the inhomogeneous MUSIG model

In the present study we propose new coalescence and breakup closures for the inhomogeneous MUltiple bubble Size Group (MUSIG) model. The major purpose is to consider bubble coalescence and breakup due to different mechanisms in turbulent gas–liquid mixtures and to develop a generally applicable constitutive model for CFD applications. For bubble coalescence the new model includes coalescence due to turbulence, laminar shear, wake-entrainment and eddy-capture. Bubble breakup mechanisms encompass turbulent fluctuation, laminar shear and interfacial slip velocity. The new model was implemented in the commercial CFD software (CFX-12.0) and applied to the case of turbulent air–water mixtures in a large vertical pipe (DN 200). Simulation results for the evolution of bubble size distributions were compared to the standard closure model of Luo and Svendsen (1996) and Prince and Blanch (1990) as well as the experimental data of TOPFLOW test facility. Better prediction is accomplished by the proposed new model.     

Development of local-scale high-resolution atmospheric dispersion model using large-eddy simulation. Part 4: turbulent flows and plume dispersion in an actual urban area

We have developed a local-scale high-resolution atmospheric dispersion model using large-eddy simulation (LOHDIM-LES) to assess the safety at nuclear facilities and to respond to emergency situations resulting from accidental or deliberate releases of radioactive materials (e.g., a terrorist attack in an urban area). In Part 1, the unsteady behavior of a plume dispersing over a flat terrain was successfully simulated. In Parts 2 and 3, LESs of turbulent flows and plume dispersion around an isolated building and in building arrays with different obstacle densities were performed, which showed the basic performance comparable to wind tunnel experimental technique. In this study, we apply the LES model to turbulent flows and plume dispersion in an actual urban area. Although some of the turbulence and dispersion characteristics are quantitatively different from the wind tunnel experimental data, the distribution patterns are generally similar to those of the experiments. It is concluded that our LES model simulates reasonably the unsteady behavior of turbulent flows and plume dispersion even for complex heterogeneous urban areas.     

Modeling free surface flows relevant to a PTS scenario: Comparison between experimental data and three RANS based CFD-codes. Comments on the CFD-experiment integration and best practice guideline

This paper presents some results concerning a benchmark for stratified two-phase flows conducted in the frame of the European Platform for NUclear REactor SIMulations (NURESIM). This benchmark relies on the FZD slug flow experiment performed in the horizontal air/water channel (HAWAC). For this benchmark special experimental arrangements have been taken in order to be able to properly model the boundary and initial conditions with CFD. A picture sequence recorded with a high-speed camera was used as reference for comparison with the simulations. For this benchmark, three different codes have been tried out. CFX was used with a turbulent two-fluid model in which a special turbulence damping function was implemented in the specific dissipation rate of the turbulent kinetic energy. This allowed a good qualitative representation of the slug dynamics, even though quantitative comparison were less successful because of difficulties in modeling the inlet instabilities. The VOF approach in its laminar and turbulent form was also tried out through the FLUENT code and was found to be inappropriate for those conditions due to the high velocity slip between phases. Moreover, NEPTUNE_CFD was tested with a newly implemented model allowing free surface location and the computation of momentum transfer across this interface. This Large Interface Model (LIM) is able to detect “stratified cells” from the other and so that appropriate closure law can be applied. With this model, the results agreed well with experimental data qualitatively and quantitatively. This benchmark experience also allowed us to draw basis recommendations for a best practice guideline in numerical simulation related to free surface flows in nuclear thermal hydraulics.     

Two-phase flow patterns in turbulent flow through a dose diffusion pipe

A numerical investigation is carried out for turbulent particle-laden flow through a dose diffusion pipe for a model reactor system. A Lagrangian stochastic Monte-Carlo particle-tracking approach and the averaged Reynolds equations with a k– turbulence model, with a two-layer zonal method in the boundary layer, are used for the disperse and continuous phases. The flow patterns coupled with the particle dynamics are predicted. It is observed that the coupling of the continuous phase with the particle dynamics is important in this case. It was found that the geometry of the throat significantly influences the particle distribution, flow patterns and length of the recirculation region. The accuracy of the simulations depends on the numerical prediction and correction of the fluid phase velocity during a characteristic time interval of the particles. A numerical solution strategy for the computation of two-way momentum coupled flow is discussed. The three test cases show different flow features in the formation of a recirculation region behind the throat. The method will be useful for the qualitative analysis of conceptual designs and their optimisation.     

Simulating large-scale bubble plumes using various closure and two-phase turbulence models

Large-scale, bubbly plumes have been simulated by a commercial CFD code using various models and correlations for the interfacial forces between the phases and for bubble-induced turbulence. Steady-state simulation results are compared with time-average plume behaviour obtained from a novel experimental series on large-scale bubble plumes. Numerical effects like e.g. numerical scheme and grid dependence are examined and the important issue of plume fluctuations is addressed. It is shown that it is necessary to include an appropriate model for the lateral interfacial forces like lift and turbulent dispersion to obtain the correct spreading of the plume observed experimentally. Including those and using standard drag coefficient, the agreement with the experiments is reasonable. The different two-phase turbulence models are either inappropriate or have very little influence on the simulation results, which do not predict the gas velocity everywhere in the plume correctly.