Multidimensional gap conductance model for thermo-mechanical simulation of LWR fuel behavior using a virtual link element

In light water reactor (LWR) fuel, the modeling of the heat transfer across the gap between the fuel pellets and the protective cladding is essential to understanding the fuel behavior. Based on the Ross and Stoute model, the gap conductance that specifies the temperature gradient within the gap depends on the gap thickness, which is related to the mechanical behavior. A multidimensional gap conductance problem can be challenging in terms of convergence and nonlinearity. In this work, a virtual link gap (VLG) element has been proposed to resolve the convergence issue and nonlinear characteristic of multidimensional gap conductance. The elements that link the node of a pellet surface with the node of the cladding surface are virtually generated so as to transfer heat as a function of gap thickness at every iteration step. To evaluate the proposed methodology for the simulation of the gap conductance, a thermo-mechanical model has been established using ANSYS Parametric Design Language (APDL) for a preliminary study, and a 3D thermo-mechanical module using FORTRAN77 has been implemented. In terms of calculation accuracy and convergence efficiency, the proposed VLG model has been evaluated. As a result, the convergence criterion of the thermo-mechanical calculation considering the iteration characteristics of the VLG element has been proposed. To demonstrate the effect of the VLG model in a 3D simulation with the implemented thermo-mechanical module, the simulation results of a missing pellet surface (MPS) have been compared.     

Modeling of gap conductance for LWR fuel rods applied in the BISON code

ABSTRACT

A new gap conductance model is proposed in this study as a combination of Toptan’s model and the Ross-Stoute model. A variance-based sensitivity analysis is performed to understand how simulation results depend on all input parameters of the proposed model. Additionally, new modeling options (e.g. fill gas thermal conductivity, temperature jump distance, thermal accommodation coefficient, etc.) are added into the nuclear fuel performance code, BISON. The need for further investigation of the gap heat transfer between fuel and cladding in BISON motivated this study to evaluate its impact on the code’s predictions. New gap conductance modeling is proposed. A series of integral-effects validation tests is performed: (1) to demonstrate the impact of the proposed model on the code’s fuel temperature predictions at the beginning of life and through the reactor’s life; (2) to ensure that the proposed model is capable of accurately modeling gap heat transfer characteristics in real-world problems; and (3) to investigate the impact of the estimation of fission gas release on the fuel temperature predictions with the proposed model. The results indicate that the proposed gap conductance model improves BISON’s predictions.     

PECITIS-II, a computer program to predict the performance of collapsible clad UO2 fuel elements

The codes devised and used in India for the design of fuel for their Pressurized Heavy Water Reactor (PHWR) programme are described. The scheme includes the use of collapsible fuel cladding for improved neutron economy.This code is made with reference to collapsible clad UO₂ fuel elements. This evaluates sheath strain and fission gas pressure. The fuel expansion is calculated by a two zone model which assumes that above a certain temperature the UO₂ deforms plastically and below that temperature it cracks radially and behaves as an elastic solid; the plastic core is under compression. The pellet clad gap conductance is calculated by using a modified Ross and Stoute model considering the effects of fuel and clad thermal expansion, fission gas release, dilution of filler gas and irradiation swelling. Stress relaxation of the sheath and its effect on fuel sheath contact pressure is also considered for arriving at the end result.     

BEAF - a computer program for analysis of light water reactor fuel rod behavior

BEAF - a computer program for analysis of light water reactor fuel rod behavior was developed. The BEAF code, which is appropriate for on-line prediction of fuel rod behavior, can analyze fuel rod thermal and mechanical behaviors using the axisymmetric, plane strain approximation and finite difference method to realize a fast running time.In the mechanical analysis, a new cracked pellet compliance model is introduced, in which pellet cracking and crack healing, pellet initial relocation, modified elastic moduli of a cracked fuel pellet, and stress dependent hot pressing are considered. Adding to those capabilities, fission gas flow and diffusion in the fuel-clad gap are analyzed to take into account the slow fission gas dilution effect on the gap conductance during power ramp.     

Computational experience showing the influence of the fuel-to-sheath thermal conductance in reactor fuel temperature predictions

Employing the BACO [1] code, the influence of the pellet-sheath gap thermal conductance models on temperature predictions has been investigated. Four different models have been used for simulating the thermo-mechanical behavior of a reactor fuel element.     

3D finite element analysis of a nuclear fuel rod with gap elements between the pellet and the cladding

Nuclear fuel rods which comprises an important component of a nuclear power plant are composed of nuclear fuel and cladding. Simulating the nuclear fuel rod using a computer program is the universal method to verify its safety. The computer program used for this is called the fuel performance code. The main objective of this study is to simulate the nuclear fuel rod behavior considering the gap conductance using three-dimensional gap elements. Gap elements are used because, unlike other methods, this approach does not require special methods or other variables such as the Lagrange multiplier. In this work, a nuclear fuel rod has been simulated and the results are compared with the experimental results.     

Preliminary comparison of Samura code predictions with experimental fuel pin data

In this paper some examples of SAMURA analysis and modelling capabilities are presented. Here, we have compared SAMURA predictions with available experimental results particularly along the lines of the EPRI code evaluation project on the basis of few selected cases. Full evaluation of SAMURA is still under investigation and the results presented here are preliminary ones.The evaluation of thermal analysis models was performed with the aim of comparing SAMURA gap conductance model predictions with available fuel centreline temperature data. Overall modelling capabilities of SAMURA were evaluated with respect to only two cases studied by EPRI, i.e., the Maine Yankee Core 1 pins and the CC-7 experimental pins.The conclusion from the first part of these studies was that the cracked-pellet gap conductance model used in SAMURA provides temperature predictions that compare well with the experimental data. It was shown that the classical Ross and Stoute model generally overpredicted the fuel centreline temperature. As for the EPRI evaluation studies, it was concluded that within the limitations associated with a one-dimensional code such as SAMURA, its overall predictions bracketted the experimental fuel pin data in a reasonable manner, i.e., they were well within the range of predictions made by the four major codes evaluated by the EPRI program.     

Swelling and gas release in oxide fuels during fast temperature transients

A previously reported intergranular swelling and gas release model for oxide fuels has been modified to predict fission gas behavior during fast temperature transients. Under steady state or slowly varying conditions it has been assumed in the previous model that the pressure caused by the fission gas within the gas bubbles is in equilibrium with the surface tension of the bubbles. During a fast transient, however, net vacancy migration to the bubbles may be insufficient to maintain this equilibrium. In order to ascertain the net vacancy flow, it is necessary to model the point defect behavior in the fuel. Knowing the net flow of vacancies to the bubble and the bubble size, the bubble diffusivity can be determined and the long range migration of the gas out of the fuel can be calculated. The model has also been modified to allow release of all the gas on the grain boundaries during a fast temperature transient.The gas release predicted by the revised model shows good agreement to fast transient gas release data from an EBR-II TREAT H-3 (Transient Reactor Test Facility) test. Agreement has also been obtained between predictions using the model and gas release data obtained by Argonne National Laboratory from out-of-reactor transient heating experiments on irradiated UO₂. It was found necessary to increase the gas bubble diffusivity used in the model by a factor of thirty during the transient to provide agreement between calculations and measurements. Other workers have also found that such an increase is necessary for agreement and attribute the increased diffusivity to yielding at the bubble surface due to the increased pressure.     

Evaluation of Gap Heat Transfer between Boron Carbide Pellet and Cladding in Control Rod of FBR

Heat transfer across a gas gap between a boron carbide pellet and a cladding in FBR control rod has been experimentally investigated. The main purpose of this investigation is to present a calculational method for the gap heat transfer in order to improve accuracy of thermal design for the control rod with 0.5 mm gap width at a beginning of reactor operation.

Two types of tests have been carried out using simulated control rods. One is low temperature tests below 200°C. The test results indicated that the convective heat transfer has a negligible effect on the gap conductance when the Rayleigh number using the gap width as the characteristic length is below 0.1. The other is high temperature tests up to 600°C.

The results showed +10 to — 5% variations in the gap conductance data due to eccentricity between the pellet and the cladding. The prediction based on conduction and radiation heat transfers considering a thermal expansion and an eccentricity gave better results of gap conductance having a maximum difference of only 17% from the measured ones. Calculation in the radiation heat transfer used thermal emissivities. 0.85 for the boron carbide and 0.15 for the cladding, measured by infrared thermography.     

FRED fuel behaviour code: Main models and analysis of Halden IFA-503.2 tests

The FRED fuel rod code is being developed for thermal and mechanical simulation of fast breeder reactor (FBR) and light-water reactor (LWR) fuel behaviour under base-irradiation and accident conditions. The current version of the code calculates temperature distribution in fuel rods, stress-strain condition of cladding, fuel deformation, fuel-cladding gap conductance, and fuel rod inner pressure. The code was previously evaluated in the frame of two OECD mixed plutonium-uranium oxide (MOX) fuel performance benchmarks and then integrated into PSI's FAST code system to provide the fuel rod temperatures necessary for the neutron kinetics and thermal-hydraulic modules in transient calculations. This paper briefly overviews basic models and material property database of the FRED code used to assess the fuel behaviour under steady-state conditions. In addition, the code was used to simulate the IFA-503.2 tests, performed at the Halden reactor for two PWR and twelve VVER fuel samples under base-irradiation conditions. This paper presents the results of this simulation for two cases using a code-to-data comparison of fuel centreline temperatures, internal gas pressures, and fuel elongations. This comparison has demonstrated that the code adequately describes the important physical mechanisms of the uranium oxide (UOX) fuel rod thermal performance under steady-state conditions. Future activity should be concentrated on improving the model and extending the validation range, especially to the MOX fuel steady-state and transient behaviour.     

Effects gap heat transfer on LWR fuel behavior during an RIA transient: In-pile experimental results with helium and xenon fillet rods

Gap heat transfer characteristics and their effects on LWR fuel behavior during an RIA have been studied through the in-pile experiment with UO₂ pellet fuel rods. The report describes the experimental results obtained in the NSRR tests in which PWR type test fuel rods of helium and xenon filled as the gap gas have been irradiated in the pulse reactor, NSRR, to simulate the prompt heat up of RIAs. The relation between the cladding temperature history and the gap heat transfer conditions, and the effects of gap gas composition on fuel behavior and on the fuel failure threshold are discussed based on the in-pile experimental data.     

An approximate method for calculating the temperature distribution in gas-filled cracked fuel elements

Treating radial cracks by an idealized geometry in fuel elements containing a thermal source gradient, the temperature distribution throughout a cracked fuel element, its gaseous bonding gap, and its surrounding can is found by an approximate series expansion method. This approximation allows the cracked fuel zone to be described by a single series expansion rather than by a multizone approach and allows approximate satisfaction of the boundary conditions at the interfaces of the cracked fuel zone and both at the non-cracked fuel zone and at the can. The method allows for the temperature dependence of the fuel and that of the gas mixture in the cracks and bonding gap, and takes into account the effect of crack openings on gap conductance at the fuel-can interface. The temperature distribution, its mean and variance resulting from the stochastic distribution of radial crack locations, are found. The case of hairline radial cracks, the mean locations of which are azimuthally uniformly distributed, is used to illustrate the importance of cracks on the can temperature distribution and it is shown that their presence may lead to central fuel zone melting problems.     

Verification of FEMAXI-7 code by using irradiation test in Halden reactor for He-pressurization effect on FGR of BWR fuels under power transient

Power ramp test for He-pressurization effect on fission gas release (FGR) of about 42GWd/tUO₂ boiling water reactor (BWR) fuel rods was analyzed by the fuel performance code FEMAXI-7. The experimental data were obtained with the two rods, which were base irradiated in the Halden reactor for 12 years (IFA-409), then subjected to the power ramp tests (IFA-535) to investigate the He-pressurization effect. The FEMAXI-7 calculations were performed by inputting rod specifications and experimental conditions in both the baseand test irradiations. The results showed that the calculations reasonably followed the trends of measured cladding elongation and FGR during the power ramp test, depending on the pellet temperature and fission gas atoms diffusion rate. Based on the calculated results, the reason that no apparent He-pressurization effect was observed in the experiment was considered to be caused by insufficient gas communication during strong pellet–clad mechanical interaction (PCMI) and enhanced gap thermal conductance by the solid–solid contact due to gap closure.     

FEMAXI-III,a computer code for fuel rod performance analysis

This paper presents a method of fuel rod thermal-mechanical performance analysis used in the FEMAXI-III code. The code incorporates the models describing thermal-mechanical processes such as pellet-cladding thermal expansion, pellet irradiation swelling, densification, relocation and fission gas release as they affect pellet-cladding gap thermal conductance. The code performs the thermal behavior analysis of a full-length fuel rod within the framework of one-dimensional multi-zone modeling. The mechanical effects including ridge deformation is rigorously analyzed by applying the axisymmetric finite element method. The finite element geometrical model is confined to a half-pellet-height region with the assumption that pellet-pellet interaction is symmetrical. The 8-node quadratic isoparametric ring elements are adopted for obtaining accurate finite element solutions. The Newton-Raphson iteration with an implicit algorithm is applied to perform the analysis of non-linear material behaviors accurately and stably. The pellet-cladding interaction mechanism is exactly treated using the nodal continuity conditions. The code is applicable to the thermal-mechanical analysis of water reactor fuel rods experiencing variable power histories.     

COBRA-3M: A modified version of COBRA for analyzing thermal-hydraulics in small pin bundles

COBRA-3M, a modified version of COBRA computer code, is most suitable for the analysis of thermal-hydraulics in small pin bundles commonly used in in-reactor or out-of-reactor experiments. It includes detailed thermal models for the fuel pins and duct walls. It can handle nonuniform power distribution across the bundle and/or within a fuel pin. Temperature dependence of material properties and fuel-cladding gap conductance can be treated. Heat generation in the duct walls and the effect of heat loss to the surroundings can also be simulated. COBRA-3M has been used extensively in the design and analysis of TREAT and SLSF experiments.     

A model for analysis of fuel behaviour in transients

For many applications, analysis of fuel element behaviour must take non-linear thermal, and elasto-plastic effects into account. This is particularly true if the fuel undergoes large deformations and rapid temperature transients. To meet this need a multi-dimensional fuel model based on finite element stress and thermal analysis has been developed. The model is solved for the transient temperature distribution by a step-by-step time incremental procedure. The temperature is then introduced into the elasto-plastic analysis as a thermal load and stresses and deformations are calculated. A model for treatment of creep and a special element for the gap between fuel pellet and cladding is incorporated together with semi-empirical procedures for calculating fission gas release, fuel pellet to cladding heat transfer coefficients, etc.The fuel model has been compared with both analytical solutions and in-reactor experimental results. The observed and predicted results are in good agreement.     

三维燃料棒精细化模拟软件FUPAC3D与FUPAC的对比验证研究

为验证基于三维有限元分析平台建立的三维燃料棒精细化模拟软件FUPAC3D在分析评价压水堆燃料棒辐照-热-力耦合行为方面的能力和精度,本文给出了三维FUPAC3D软件采用的热学模型、燃料棒力学模型、裂变气体释放模型以及腐蚀模型,以华龙一号典型燃料棒参数和运行工况作为输入参数,分别使用三维FUPAC3D软件和已工程化应用的1.5维FUPAC软件进行建模分析,并针对2种软件在芯块和包壳温度、包壳应力与应变、芯块与包壳间间隙宽度的计算结果进行对比研究。研究结果表明,FUPAC3D软件与FUPAC软件具有相当的精度,FUPAC3D软件具备压水堆燃料棒辐照-热-力耦合行为的精细化模拟能力。      

Effects of background pressure on the arc characteristics of gas spark gap

Gas spark gap is widely used in any pulsed power system as the key element which directly determines its repetitive performance and output characteristics. Among many factors of threeelectrode gas spark gap, background pressure is of much importance in determining the gap performance parameters such as the delay and jitter, and relevant studies have been rarely performed. A magneto-hydrodynamic model of the arc in gas spark gap is built and the effects of background pressure on the arc characteristics are discussed in this paper. It is demonstrated that a higher background pressure may result in radial compression of the arc column, a higher arc voltage, and a lower declination rate of arc resistance in the first quarter cycle. Relevant simulation data would be helpful for the optimization of the design of gas spark gap.     

Numerical investigation of a heat transfer within the prismatic fuel assembly of a very high temperature reactor

The complex geometry of the hexagonal fuel blocks of the prismatic fuel assembly in a very high temperature reactor (VHTR) hinders accurate evaluations of the temperature profile within the fuel assembly without elaborate numerical calculations. Therefore, simplified models such as a unit cell model have been widely applied for the analyses and designs of prismatic VHTRs since they have been considered as effective approaches reducing the computational efforts. In a prismatic VHTR, however, the simplified models cannot consider a heat transfer within a fuel assembly as well as a coolant flow through a bypass gap between the fuel assemblies, which may significantly affect the maximum fuel temperature. In this paper, a three-dimensional computational fluid dynamics (CFD) analysis has been carried out on a typical fuel assembly of a prismatic VHTR. Thermal behaviours and heat transfer within the fuel assembly are intensively investigated using the CFD solutions. In addition, the accuracy of the unit cell approach is assessed against the CFD solutions. Two example situations are illustrated to demonstrate the deficiency of the unit cell model caused by neglecting the effects of the bypass gap flow and the radial power distribution within the fuel assembly.