Laminar flow induced deflections of stacked plates

Some research and power reactors such as the Engineering Test Reactor (ETR), the Materials Test Reactor (MTR) and the Shippingport Reactor have core designs which consist of parallel, flat or curved plate fuel assemblies. The fuel is contained in the thin plates which are separated by narrow channels through which coolant flows to remove heat generated within the plates. Since the plates are flexible, the coolant flowing through the channels causes the plates to deflect. At high coolant velocities large deflections have been observed causing the plates to deform plastically leading to structural failure or plate collapse. This work examines a single plate bounded by two channels and determines the static plate deflection as a function of plate, channel and flow parameters. The deflection is due to differences in pressure and flow velocity in the channels bounding the plate and also due to different channel dimensions caused by tolerance effects. The classical thin plate equations are used with a nonlinear hydrodynamic loading function expressing the external fluid forces on the plate surfaces.     

Flow-induced vibration and stability of an element model for parallel-plate fuel assemblies

Flow-induced vibration and stabilities of the parallel-plate assemblies are studied theoretically. A model of multi-parallel-beams joined with single-beam is adopted in the theoretical analysis of the natural vibration characteristics of the parallel-plate assemblies. The functions of the dry-modal mode are used as trial functions to solve the equations of the complex-modal mode by the variational method for the natural frequencies and modes of the wet modal. The critical flow velocity and destabilizing deflection are solved by the direct method and the variational method for the stability of the parallel-plate assemblies and the results of the two methods agree with each other. This paper discovers some systemic results from theoretical and numerical analysis, which offers several useful methods and data to the design and safe operation for the fuel element of nuclear reactors.     

Radiostability of fuel plates used in SM-2 reactor fuel elements

Conclusions The data cited imply a high structural and dimensional stability on the part of plate type fuel elements used in the SM-2 reactor. The linearity of the volume increase with burnup allows us to assess changes in the physical, hydraulic, and heat-transfer parameters of the core. We note that a process of layer separation resulting in a loss of pressuretightness sets-in in some fuel elements with 30% uranium burnup, and this could be involved in failures during cooling or cooldown. Checking out this last point would enable us to settle on a criterion for the limiting allowable burnup. It is highly probable that this criterion will be related to the physics of the reactor, rather than to the degree of radiation damage of the reactor materials.Translated from Atomnaya Énergiya, Vol. 24, No. 5, pp. 432–435, May, 1968.     

Effect of oxide layer growth on fuel temperature of mini fuel plates

The effect of the oxide layer formed on the mini fuel plates is studied to evaluate fuel centerline temperature. For a part of U-Mo fuel qualification program, mini fuel plates, double-stacked as upper and lower plates, will be irradiated in the HANARO reactor for four cycles. In the present study, fuel performance and thermal hydraulic behavior during irradiation are numerically investigated using the MCNP and TMAP codes. The power released from the mini fuel plates is estimated using the MCNP code. From the neutronic analysis results, it is observed that the lower plate at the BOC during the 1st cycle releases the highest power, and the power gradually decreases during the irradiation test. The growth of the oxide layer thickness during the irradiation test is predicted using many correlations with various pH values ranging from 5.0 to 7.0. The pH value in the HANARO reactor is controlled between 5.7 and 6.2, and the oxide layer thickness is predicted by the Boehmite model for these two pH values. The oxide layer thickness predicted using the other correlations are bounded by these two predicted values. The maximum oxide layer thickness at the end of irradiation is approx. 9 and 68 μm with pH of 5.7 and 6.2, respectively. The Pawel model with a rate factor of 16 predicts the maximum oxide layer as 25 μm. Using the predictions of the oxide layer thickness, the centerline fuel temperatures are evaluated using the TMAP code. The maximum fuel temperature is not observed when the power released from the fuel is the highest. Because the temperature rise through the oxide layer is significant, the oxide layer thickness must be considered in the fuel temperature evaluation. The oxide formation saturates with time, and the fuel reaches the maximum temperature at the end of the saturation. After the maximum fuel temperature is reached, it starts decreasing, because the power decreases.     

Nonlinear dynamic analysis of a stacked fuel column subjected to boundary motion

A method has been developed for analyzing the nonlinear dynamic response of a column consisting of stacked elements excited by boundary motions. The elements are constrained by dowel pins which restrict relative horizontal movement but allow vertical and rocking motions between elements. Two different models have been considered. In the first, the dowels are treated as rigid shear connectors, and equations of constraint are used in conjunction with Lagrange multipliers. In the second, the dowels are considered as flexible items. Horizontal slipping at the element-to-element interface is permitted, the Coulomb friction is considered at the contact point. Example problems were solved using both models, and numerical results are presented for the free vibrations of short columns and the boundary-excited response of tall columns.     

Displacement estimates of pipe elbows prior to plastic collapse loads

The non-differentiability of the plastic dissipation calculated through the Von-Mises yield function leads to convergence difficulties when using mathematical programming to solve Köiter's kinematical formulation of the classical limit analysis. This problem is avoided replacing the plastic dissipation by the strain energy of a fictitious viscoelastoplastic material with a nearly infinite Young modulus. Classical limit analysis can only give information about the limit load multiplier and the plastic collapse mechanism. Based on Zarka's method and using the finite element method and mathematical programming, it is possible to obtain not only the limit load but also an estimate of the elastoplastic displacements. This is very useful because construction codes usually impose limits on the electroplastic displacements. Some pipeline systems are examined using a 1-dimensional shell type finite element to illustrate the procedure. The results obtained are compared with simplified analytical solutions and with alternative numerical results using 2-dimensional shell elements and realistic materials.     

Calculational procedure for determining creep collapse of LWR fuel rods

Observed collapses in pressurized water reactor fuel rods have been attributed to the radiation enhanced creep of Zircaloy cladding into regions where separations in the fuel pellet stack have occurred. A computer code, COLAPX, has been written to determine the growth of ovality and the ultimate collapse of fuel rod cladding under reactor operating conditions. This paper describes the theoretical bases of this code, the finite element formulation used, the constitutive relations between the displacement fields and the element forces, and the radiation, temperature and stress dependent material model for creep of Zircaloy tubing. Comparisons of the creep rate predictions and of the ovality predictions with data from irradiated tubes and fuel cladding are presented.     

Characterization of plastic collapse load determination in circumferentially through-wall cracked elbows

The solutions of cracked elbow are shown to be excessively conservative and on occasion, non-applicable to the cases for which they are intended. The objective of the work described in this paper is to use the 3D non-linear finite element method (FEM) backed up with experimental results to determine the collapse limit load. Non-linear finite element analyses were performed considering both material and geometrical non-linearity using the advanced fracture analysis code WARP3D. Various alternative methods are used to determine plastic collapse loads based on the FEM calculated load–displacement curves. The predicted collapse loads are compared to collapse loads determined by available solutions and finally these are compared to experimental results. The work can be considered as the source of the benchmark data that helped to shape the engineering treatment of piping elbows in design codes.     

Leak-before-break and plastic collapse behaviour of statically indeterminate pipe system with circumferential crack

Much research has been carried out on Leak-Before-Break (LBB) behavior of pipes with cracks. However, most studies have been made on statically determinate pipe systems. Few studies have been made on LBB behavior of statically indeterminate pipe systems. Most pipe systems in nuclear power plants have supports and restraints, thus they can be considered as statically indeterminate pipe systems. From above points of view, LBB and plastic collapse behaviors of statically indeterminate pipe with circumferential crack and compliance were studied in this paper. A new method is proposed to analyze and evaluate the LBB and plastic collapse behavior of a statically indeterminate structure. The pipe system of which one end is clamped and the other is supported with compliance was analyzed. The main results obtained are as follows: (1) By combining the limit analysis theory and elastic–plastic fracture mechanics, the effects of crack size, compliance and fracture toughness on load deflection behaviors to failure and structural integrity of statically indeterminate pipe system have been analyzed quantitatively and easily. (2) When a crack grows in a statically indeterminate pipe before plastic collapse, load drop conditions can be derived quantitatively, as a function of J_IC, dJ/da, flow stress, crack size, pipe span length, compliance and flexural rigidity of the pipe. (3) The analytic method developed in this research is useful and convenient to evaluate the LBB and tearing instability behavior of a statically indeterminate pipe system. (4) LBB resolves easily for statically indeterminate pipes with a crack, even when it does not resolve for statically determinate pipes with the same crack. That results from the fact that bending moment redistribution during the fracture process occurs easily for statically indeterminate pipe systems, and its redistribution restrains plastic deformation of the cracked weak section.     

Spacers for fuel elements as structural anisotropic plates composed of cylindrical shells

The results of investigations concerning some problems of the spacers which are assumed to be structural anisotropic plates composed of cylindrical shells are presented. The problem of stresses due to the aero-hydrodynamic loads and the behaviour of the spacers in the interactions with fuel elements are considered: a method is developed whereby the state of stress in the mentioned plates can be computed. An application of the developed method — including its experimental verification — is shown. On the basis of experimental values the influence of the spacers on the effectiveness and on the reliability of the fuel element bundles is demonstrated.     

Microstructural analysis of MTR fuel plates damaged by a coolant flow blockage

In 1975, as a result of a blockage of the coolant inlet flow, two plates of a fuel element of the BR2 reactor of the Belgian Nuclear Research Centre (SCK•CEN) were partially melted. The fuel element consisted of Al-clad plates with 90% ²³⁵U enriched UAl_x fuel dispersed in an Al matrix. The element had accumulated a burn up of 21% ²³⁵U before it was removed from the reactor. Recently, the damaged fuel plates were sent to the hot laboratory for detailed PIE.Microstructural changes and associated temperature markers were used to identify several stages in the progression to fuel melting. It was found that the temperature in the center of the fuel plate had increased above 900-950 °C before the reactor was scrammed. In view of the limited availability of such datasets, the results of this microstructural analysis provide valuable input in the analysis of accident scenarios for research reactors.     

Modeling of irradiation-induced damage and failure behaviors of fuel foil/cladding interface in UMo/Zr monolithic fuel plates

Models to describe the damage and fracture behaviors of the interface between the fuel foil and cladding in UMo/Zr monolithic fuel plates were established and numerically implemented. The effects of the interfacial cohesive strength and cohesive energy on the irradiationinduced thermal-mechanical behaviors of fuel plates were investigated. The results indicated that for heterogeneously irradiated fuel plates:(1) interfacial damage and failure were predicted to be initiated near the fuel foil cor...     

Influence of flow stress choice on the plastic collapse estimation of axially cracked steam generator tubes

The influence of the choice of flow stress on the plastic collapse estimation of axially cracked steam generator (SG) tubes is considered. The plastic limit and collapse loads of thick-walled tubes with external axial semi-elliptical surface cracks are investigated by three-dimensional non-linear finite element (FE) analyses. The limit pressure solution as a function of the crack depth, length and tube geometry has been developed on the basis of extensive FE limit load analyses employing the elastic–perfectly plastic material behaviour and small strain theory. Unlike the existing solutions, the newly developed analytical approximation of the plastic limit pressure for thick-walled tubes is applicable to a wide range of crack dimensions. Further, the plastic collapse analysis with a real strain-hardening material model and a large deformation theory is performed and an analytical approximation for the estimation of the flow stress is proposed. Numerical results show that the flow stress, defined by some failure assessment diagram (FAD) methods, depends not only on the tube material, but also on the crack geometry. It is shown that the plastic collapse pressure results, in the case of deeper cracks obtained by using the flow stress as the average of the yield stress and the ultimate tensile strength, can become unsafe.     

Mechanical behaviors of the dispersion nuclear fuel plates induced by fuel particle swelling and thermal effect I: Effects of variations of the fuel particle volume fractions

A new method of modeling the in-pile mechanical behaviors of dispersion nuclear fuel elements is proposed. Considering the irradiation swelling together with the thermal effect, numerical simulations of the in-pile mechanical behaviors are performed with the developed finite element models for different fuel particle volume fractions of the fuel meat. The effects of the particle volume fractions on the mechanical performances of the fuel element are studied. The research results indicate that: (1) the maximum Mises stresses and equivalent plastic strains at the matrix increase with the particle volume fractions at each burnup; the locations of the maximum first principal stresses shift with increasing burnup; at low burnups, the maximum first principal stresses increase with the particle volume fractions; while at high burnups, the 20% volume fraction case holds the lowest value; (2) at the cladding, the maximum equivalent plastic strains and the tensile principal stresses increase with the particle volume fractions; while the maximum Mises stresses do not follow this order at high burnups; (3) the maximum Mises stresses at the fuel particles increase with the particle volume fractions, and the particles will engender plastic strains until the particle volume fraction reaches high enough.     

研究堆用U3Si2-Al燃料板的热稳定性试验

U3Si2-Al板状燃料组件是一种推广应用的新型燃料元件,在国内首次应用。燃料组件的各项性能,特别是热稳定性必须通过实验验证。通过对铀密度为3.02 g/cm3的U3Si2-Al燃料板的热稳定性试验,得到:热稳定性试验会使燃料板的体积略有增大;120℃及250℃的热循环下,燃料板无明显变形,表面无变化,400℃的热循环下,燃料板略有弯曲,个别芯体裸露的燃料板表面有起泡现象;循环温度越高,芯体中U3Si2颗粒开裂越严重等实验结论,为该燃料组件的结构设计、安全分析、加工工艺提供了关键参数,并为该组件的堆内运行提供了借鉴。     

Uranium-molybdenum nuclear fuel plates behaviour under heavy ion irradiation: An X-ray diffraction analysis

Heavy ion irradiation has been proposed for discriminating UMo/Al specimens which are good candidates for research reactor fuels. Two UMo/Al dispersed fuels (U-7 wt%Mo/Al and U-10 wt%Mo/Al) have been irradiated with a 80 MeV ¹²⁷I beam up to an ion fluence of 2 × 10¹⁷ cm⁻². Microscopy and mainly X-ray diffraction using large and micrometer sized beams have enabled to characterize the grown interaction layer: UAl₃ appears to be the only produced crystallized phase. The presence of an amorphous additional phase can however not be excluded. These results are in good agreement with characterizations performed on in-pile irradiated fuels and encourage new studies with heavy ion irradiation.     

压水堆吊篮下部防断支承组件流致振动分析

对秦山核电厂堆芯下腔流场、堆内下部防断支承组件振动特性及全组件的流致振动进行了分析,特别对旋涡脱落致振进行了定量分析.分析结果表明防断支承组件初始结构的整体转动振动的固有频率与旋涡脱落频率相差较大,发生大幅振动的可能性不大;只有当部分连接件松动,整体结构转动振动的固有频率下降时,才很有可能发生大幅振动.     

Calculating decay heat removal rates via natural circulation along variable heat flux reactor fuel plates

A recently developed integral technique is applied to natural convection cooling along test reactor fuel plates. The technique is demonstrated for water and air flow. In the case of air flow, the process is characterized by a large temperature rise along the fuel channel, thereby rendering the commonly applied Boussinesq approximation invalid. This case is a heat transfer problem of particular interest in accident analyses such as determining the level of decay heat dissipation possible, without exceeding the melting temperature of the fuel, subsequent to a hypothetical loss of primary coolant.     

传热管流致振动设计准则比较

蒸汽发生器是核反应堆中将一回路热量传递给二回路（水-蒸汽动力回路）的重要设备。二次侧流体冲刷引起的传热管振动是管壁疲劳、磨损直至破裂的主要原因之一。为确保传热管的结构完整,有必要对传热管开展流致振动设计与评价。针对传热管这样的圆柱形结构的流致振动设计与评价,有3种设计规范：GB/T151、TEMA、ASME。本文对3种设计规范中传热管流致振动的设计准则进行了比较,指出了相关准则和参数在计算上的差异以及对流致振动相关机制判定上的差异。选取某典型热交换器为算例,具体展现了3种设计规范对传热管流致振动评价结果的异同,给出了不同规范设计准则的选取对于表征流致振动的特征参数（如附加质量、固有频率、漩涡脱落频率、振幅等）计算结果带来的偏差,并对3种设计规范在工程应用中的保守性提出了参考性建议。结果表明：对不同参数,设计规范保守性不相同,TEMA计算频率相对更为保守,其他参数GB/T151较为保守,TEMA和ASME整体相对GB/T151更加宽容。