A parametric analysis of heat transfer in composite nuclear fuels

The composite nuclear fuel described in this paper consists of a heat generating fuel matrix containing cylindrical metal and fibers uniformly aligned throughout the matrix. Exact analytical solutions were found for temperature distributions in the fiber and matrix for a composite cell modeled as concentric cylinders. A parametric study is presented of composite overall thermal conductivities and temperature distributions as a function of fiber-to-matrix conductivity ratios, cell length-to-radius ratios, and fiber-to-cell radius ratios. For composite cells in which length-to-radius ratios exceed 10, axial temperature distributions may be calculated assuming a homogeneous material.     

Applications of fault detection and diagnosis methods in nuclear power plants: A review

Nuclear power industries have increasing interest in using fault detection and diagnosis (FDD) methods to improve safety, reliability, and availability of nuclear power plants (NPP). A brief overview of FDD methods is presented in this paper. FDD methods are classified into model-based methods, data-driven methods, and signal-based methods. While practical applications of model-based methods are very limited, various data-driven methods and signal-based methods have been applied for monitoring key subsystems in NPPs. In this paper, six areas of such applications are considered. They are: instrument calibration monitoring, instrumentation channel dynamic performance monitoring, equipment monitoring, reactor core monitoring, loose part monitoring, and transient identification. The principles of using FDD methods in these applications are explained and recent studies of advanced FDD methods are examined. Popularity of FDD applications in NPPs will continuously increase as FDD theories advance and the safety and reliability requirement for NPP tightens     

A heat transfer model for volumetrically heated nuclear debris beds

The thermal response of a fixed porous volumetrically heated debris bed is analyzed. The Modified Dispersion-Concentric Model (D-C model) is used in the analysis of forced flow cooling through a volumetrically heated fixed porous debris bed. The fundamental equations are based on the assumptions of dispersed plug flow and concentric intra-particle temperature profiles. The model is theoretically sound provided that a large axial effective fluid thermal dispersion coefficient is assumed. The fundamental equations are rather simple and can be easily solved in terms of temperature profiles for the solid and fluid phases. The theoretical model for the temperature profile for the fluid phase in the subcooled liquid region and in the superheated vapor region compares well with existing experimental measurements.     

非能动余热排出热交换器流动和传热数值模拟

非能动余热排除系统(Passive Residual Heat Removal system,PRHR)是非能动核电厂的重要安全设施,在全厂断电事故下,大部分的堆芯衰变热是通过PRHR热交换器传递至内置换料水箱(In-containment Refueling Water Storage Tank,IRWST)。但PRHR热交换器属于大型非稳态换热器,其传热机理十分复杂。基于PRHR系统的重要性和复杂性,有必要研究PRHR系统的流动和传热特性。利用计算流体动力学(Computational Fluid Dynamics,CFD)软件针对非能动堆芯冷却系统试验装置中的PRHR系统进行建模计算,分析了PRHR热交换器及IRWST的流动和传热特性,发现IRWST内部沿垂直高度上呈现明显的温度分层现象,温度沿水平方向的分布趋于均匀;IRWST内部的流动主要是沿着C型传热管竖直段向上流动,流速逐渐增大,但在两相阶段,水箱上部区域流动明显增强;C型传热管上部水平段和竖直段上部区域的换热系数要明显高于其它区域,且在上部水平段与竖直段连接弯管处换热系数最大,在两相阶段,上部区域的换热系数明显增大。     

A multiparticle Monte Carlo simulation of temperature noise and heat transfer in turbulent flow

Temperature fluctuations generated by turbulent mixing in flowing sodium, downstream of a specified temperature profile, are modelled by a Monte Carlo technique. Multiparticle batches are used to permit dissipation processes to be simulated. The model is validated against measurements made in pipe- and jet-flow experiments performed in sodium-loop facilities.     

Experimental study on flow pattern and heat transfer of inverted annular flow

Experimental results are presented on flow pattern and heat transfer in the regions from inverted annular flow to dispersed flow in a vertical tube using freon R-113 as a working fluid at atmospheric pressure to discuss the correspondence between them. Axial distributions of heat transfer coefficient are measured and flow patterns are observed. The heat transfer characteristics are divided into three regions and a heat transfer characteristics map is proposed. The flow pattern changes from inverted annular flow (IAF) to dispersed flow (DF) through inverted slug flow (ISF) for lower inlet velocities and through agitated inverted annular flow (AIAF) for higher inlet velocities. A flow pattern map is obtained which corresponds well with the heat transfer characteristic map.     

Liquid metal heat transfer in heat exchangers under low flow rate conditions

The present paper describes the liquid metal heat transfer in heat exchangers under low flow rate conditions. Measured data from some experiments indicate that heat transfer coefficients of liquid metals at very low Péclet number are much lower than what are predicted by the well-known empirical relations. The cause of this phenomenon was not fully understood for many years. In the present study, one countercurrent-type heat exchanger is analyzed using three, separated countercurrent heat exchanger models: one is a heat exchanger model in the tube bank region, while the upper and lower plena are modeled as two heat exchangers with a single heat transfer tube. In all three heat exchangers, the same empirical correlation is used in the heat transfer calculation on the tube and the shell sides. The Nusselt number, as a function of the Péclet number, calculated from measured temperature and flow rate data in a 50 MW experimental facility was correctly reproduced by the calculation result, when the calculated result is processed in the same way as the experiment. Finally, it is clarified that the deviation is a superficial phenomenon which is caused by the heat transfer in the plena of the heat exchanger.     

圆柱形带反射层反应堆的数值传热计算

在结构化和非结构化网格中,采用有限容积方法,数值计算带有反射层(反射层布置分为轴向、径向和复合双向三种情况)的圆柱形反应堆的物理和热特性。首先采用单组法数值求解堆芯和反射层中的热中子注量率密度,并同其精确解相比较,验证彼此的正确性;然后用类似法确定堆内两区中热中子产生的热功率分布规律,并进行数值传热计算。所有结果都与没有反射层的反应堆(裸堆)状况进行比较,并且得到具有参考价值的结果。     

Analysis of heat transfer and flow characteristics in turbulent impinging jet

Jet impingement technique is characterized by a high heat removal capability. As such it has been proposed as a cooling method for the helium cooled divertor, a high-heat flux component of the future fusion reactor called DEMO. Since power plant efficiency depends on the divertor’s heat removal capability it has to meet certain demands, i.e. high-heat transfer and low pressure drop.In this paper local heat transfer and flow characteristics of an axis-symmetric impinging jet are analyzed numerically using the RANS approach and eddy viscosity type SST turbulence model. Turbulence models and heat transfer predictions are validated on the free jet impingement experiment (Baughn and Shimizu, 1989). Since the numerical results are affected by the turbulence model the influence of the turbulent production is investigated in particular.The validated numerical model is further applied to analyze the effect of the nozzle inlet shape on the heat removal capability and pressure drop in the confined impinging jet. Two different nozzle inlet parameters are tested; chamfer angle θ and chamfer depth L_ch. The numerical results are compared with the experimental data (Brignoni and Garimella, 2000).     

Finite element analysis of steady-state nonlinear heat transfer problems

A method of analysis and the associated computer program are presented for the purpose of solving steady-state nonlinear heat transfer problems in two-dimensional structures. The nonlinearity arises from the dependence of the thermal conductivities on temperature as well as from the presence of rediative heat transfer between parts of the structure. The problem is formulated in terms of an integral of conductivity and solved in an iterative way via the finite element concept. Several examples are given to illustrate the validity and practicality of the suggested solution technique.     

Two-phase flow and boiling heat transfer in two vertical narrow annuli

Experimental study associated with two-phase flow and heat transfer during flow boiling in two vertical narrow annuli has been conducted. The parameters examined were: mass flux from 38.8 to 163.1 kg/m² s; heat flux from 4.9 to 50.7 kW/m² for inside tube and from 4.2 to 78.8 kW/m² for outside tube; equilibrium mass quality from 0.02 to 0.88; system pressure from 1.5 to 6.0 MPa. It was found that the boiling heat transfer was strongly influenced by heat flux, while the effect of mass velocity and mass quality were not very significant. This suggested that the boiling heat transfer was mainly via nucleate boiling. The data were used to develop a new correlation for boiling heat transfer in the narrow annuli. In the two-phase flow study, the comparison with the correlation of Chisholm [Chisholm, D., 1967. A theoretical basis for the Lockhart–Martinelli correlation for two-phase flow. Int. J. Heat Mass Transfer 10, 1767–1778] and Mishima and Hibiki [Mishima, K., Hibiki, T., 1996. Some characteristics of air–water two-phase flow in small diameter vertical tubes. Int. J. Multiphase Flow 22, 703–712] indicated that the existing correlations could not predict the two-phase multiplier in the narrow annuli well. Based on the experimental data, a new correlation was developed.     

A study of the unsteady flow and heat transfer in the reflooding of water reactor cores

In the event of a loss-of-coolant accident in a water-cooled reactor, the primary consideration is terminating the clad temperature excursion caused by release of the stored and decay heat in the fuel. This requires that emergency coolant injection systems reflood the reactor core.For certain break positions, the pressure loss incurred by venting steam partially offsets the hydrostatic head available to drive flow through the core. Flow oscillations can also be set up due to the fluid inertia and vapour compressibility.The present paper reports the results of an extensive series of experiments performed on unstable reflooding, covering wall temperatures up to 1000°C and reflooding rates typical of reactor values. Measurements are reported of quenching rates, oscillation frequencies and pre-quench heat transfer.It is shown, except for a short initial period of violent oscillations, that the rewetting rate and pre-quench heat transfer, for a given mass flow rate, are relatively unaffected by the presence of oscillations. The average pre-quench heat transfer coefficient is shown to vary as (water mass flow rate)ⁿ where n = 0.5–0.7, consistent with available world data.Theory and experiments also show that there is a critical value of outlet loss coefficient, for a given power level, where no further advance of the quench front can occur, the back pressure completely offsetting the available driving head for core reflooding. This value is much greater than the outlet loss coefficient for typical reactor designs, thus ensuring core reflooding. The critical loss coefficient is suggested as the relevant parameter for scaling purposes.A new theoretical model for the oscillations is derived which is shown to predict the oscillation frequencies of all available data. It is also shown that the frequency and damping are only weakly dependent on: upper plenum flow area, size of vapour space, effective inertia of water oscillating and pressure, and are independent of the outlet loss coefficient.     

The flow and heat transfer characteristics of turbulent flow in typical rod bundles in ocean environment

The flow and heat transfer characteristic of turbulent flow in typical 4 and 7 rod bundles in ocean environment is investigated theoretically. In ocean environment, the periodic variation of secondary flow in 7 rod bundles is not obvious. Because of the velocity oscillation, there is a periodic heat accumulation on the tube wall. And the restriction of the channel wall on the rolling motion is considerable. In 7 rod bundles, because of the restriction of the channel wall, the effect of the additional force perpendicular to flowing direction is limited, and the turbulent flowing and heat transfer is mainly determined by the axial turbulent intensity and inlet velocity. However, in the 4 rod bundles, the restriction of the channel wall is small. The effect of the additional force perpendicular to flowing direction on the flowing and heat transfer is significant. And the additional force perpendicular to flowing direction can also affect the Reynolds stress.     

Revisiting the resolution requirements for turbulence simulations in nuclear heat transfer

Direct numerical simulations (DNSs) require the resolution of all relevant turbulence scales in space and time, whereas large eddy simulations (LESs) need only to resolve the dominant energy carrying large scales. Important influences from physics and numerics on the small-scale resolution are discussed. Quantitative criteria for turbulent flows are re-evaluated. Experience shows, resolving the microscales is usually by far not achieved in DNS; this is less relevant than the adequate resolution of the anisotropic coherent fine flow structures. These structures depend on the flow type, so that general criteria cannot be given. Resolving the large scales is a serious problem. When the computational domain covers only part of the flow domain, the large-scale resolution is coupled to the artificial boundary conditions for open boundaries. Each measure and criteria have to be carefully considered to ensure that the simulations meet the expectations. Special emphasis is given to liquid metal flows because related nuclear applications are often in the transition range between LES and DNS of the temperature field. A new model is given to predict local turbulent Prandtl numbers for subgrid scale heat flux modeling. It covers the required most important influences: local resolution, a local turbulence parameter, and Reynolds and Prandtl numbers.     

Effects of flow obstacles on film boiling heat transfer

The effect of flow obstacles on film boiling heat transfer in a vertical upward tube is investigated experimentally using R134a as a coolant. The results show that flow obstacles enhance heat transfer downstream of the obstacle and promote rewetting to occur in this region. The rewetting zone is found to increase with a decrease in quality at the obstacle location, and with an increase in mass flux, but the effect of pressure is inconclusive. The rewetting effect is strongest near the obstacle location, and weakens with distance from the obstacle, i.e. at locations axially downstream from the obstacle and circumferentially away from the obstacle. The characteristic time is found to be a good correlating factor to characterize the effect of mass flux. The prediction from the post-dryout look-up table, after applying the appropriate fluid-to-fluid modeling technique, is in reasonable agreement with the experimental results.     

Modeling of three-dimensional steady state non-linear heat transfer in CANDU nuclear fuel

Modeling and analysis of three-dimensional steady-state heat transfer in a CANDU6¹ nuclear fuel rod are presented in this paper. A special three-dimensional finite element, developed through combining the nine-node two-dimensional isoparametric finite element and the Fourier series, is employed to model the temperature distribution in the pellets and the sheath. To achieve high accuracy and a high convergence rate, the temperature-dependent thermal conductivity matrices of UO₂ and Zircaloy are allowed to vary with spatial coordinates in the same manner as temperature within a finite element. The non-linear algebraic equations of nodal temperatures are formulated using the Galerkin method and solved using the iteration approach. A computer code, , which contains the finite element modeling and solution schemes described in this paper, was developed for heat transfer analysis of nuclear fuel rods. Numerical simulation results obtained using have shown excellent agreement with other independent solutions.