A two-component equilibrium-diffusion limit

The equilibrium-diffusion limit of the radiative transfer equations is characterized by a medium that is optically thick and diffusive for photons of all frequencies. In reality, this condition is almost never met because the transport medium tends to be optically thin for photons of sufficiently high frequency. Motivated by this fact, we derive a new asymptotic limit of the radiative transfer equations that is characterized by two photon components: one for which the medium is optically thick and diffusive, and the other for which the medium is extremely optically thin. In this limit, the leading-order material temperature satisfies a time-dependent diffusion equation, and the leading-order radiation intensity for the optically thick photons is given by the Planck function evaluated at the leading-order material temperature, but the radiation intensity for the optically thin photons is zero through first order. The O(ϵ²) radiation intensity for the optically thin photons satisfies a quasi steady-state transport equation with zero interaction terms and a Planck emission term that depends upon the leading-order material temperature. We also discuss alternative scalings associated with the two-component limit that are characterized by stronger coupling between the material and the optically thin component.     

A simplified technique for shakedown limit load determination

In this paper, a simplified technique is presented to determine the shakedown limit load of a structure using the finite element method. The simplified technique determines the shakedown limit load without performing lengthy time consuming full elastic-plastic cyclic loading simulations or conventional iterative elastic techniques. Instead, the shakedown limit load is determined by performing two analyses namely: an elastic analysis and an elastic-plastic analysis. By extracting the results of the two analyses, the shakedown limit load is determined through the calculation of the residual stresses developed within the structure. The simplified technique is applied and verified using two bench mark shakedown problems namely: the two-bar structure subjected to constant axial force and cyclic thermal loading, and the Bree cylinder subjected to constant internal pressure and cyclic high temperature variation across its wall. The results of the simplified technique showed very good correlation with the, analytically determined, Bree diagrams of both structures. In order to gain confidence in the simplified technique, the shakedown limit loads output by the simplified technique are used to perform full elastic-plastic cyclic loading simulations to check for shakedown behavior of both structures.     

Studies on diffusion and natural convection of two-component gases

A primary-pipe rupture accident is one of the design-based accidents of a high-temperature engineering test reactor (HTTR), which is being developed at JAERI. When the primary pipe ruptures, air is expected to enter into the reactor core from the breach by molecular diffusion and natural convection. In order to investigate the process of air ingress during the early stage of the primary-pipe rupture accident, experimental and analytical studies are performed on the conjugate phenomenon of the transient molecular diffusion and natural convection of a two-component gas mixture in two test sections, a reverse-U-shaped tube and a test model simulating simply the reactor. One-dimensional basic equations for continuity and momentum conservation are numerically solved to obtain a concentration change of gas species and an initiation time of a natural circulation of pure nitrogen in the reverse-U-shaped tube. Moreover, a modified numerical solution is proposed to reduce the computing time. A one-dimensional flow net work model is employed to calculate the transport process of air in the test model simulating the reactor. The calculated results agree well with the experimental ones on the concentration change of gas species and the initiation time of the natural circulation of pure nitrogen or pure air.     

Choking flow modeling with mechanical non-equilibrium for two-phase two-component flow

A mechanistic model which considers the mechanical non-equilibrium is described for two-phase choking flow. The choking mass flux is obtained from the momentum equation with the definition of choking. The key parameter for the mechanical non-equilibrium is a slip ratio. The dependent parameters for the slip ratio are identified. In this research, the slip ratio which is defined in the drift flux model is used to identify the impact parameters on the slip ratio. Because the slip ratio in the drift flux model is related to the distribution parameter and drift velocity, the adequate correlations depending on the flow regime are introduced in this study. In this mechanistic modeling approach, the choking mass flow rate is expressed by the function of pressure, quality and slip ratio. The developed model is evaluated by comparing with the air–water experimental data to eliminate the thermal effect. The comparison of predicted choking model for mechanical non-equilibrium with other experimental data in high quality region (up to 80%) is quite reasonable with a small error.     

The creep strain limit experiment

A Euratom sponsored irradiation of HTR annular compacts manufactured by the Dragon Project and Belgonuclèaire has been carried out in the BR-2 reactor to support the tubular interacting fuel element concept. The purpose of this experiment was the investigation of the behaviour of annular compacts under peak stresses and peak strain conditions and the study of the failure mechanism. The post-irradiation examination showed that the rupture of the compacts by interaction did not lead to particle breakage and that the broken compacts had one fracture only and remained in contact with the inner spine. This indicated that no significant variations of temperatures and heat split between the two coolant surfaces of a tubular interacting fuel element should be expected if the compacts happen to break during irradiation.     

ITER operating limit definition criteria

The operating limits and conditions (OLCs) are operating parameters and conditions, chosen among all system/components, which, together, define the domain of the safe operation of ITER in all foreseen ITER states (operation, maintenance, commissioning). At the same time they are selected to guarantee the required operation flexibility which is a critical factor for the success of an experimental machine such as ITER. System and components that are important for personnel or public safety (safety important class, SIC) are identified considering their functional importance in the overall plant safety analysis. SIC classification has to be presented already in the preliminary safety analysis report and approved by the licensing authority before manufacturing and construction.OLCs comprise the safety limits that, if exceeded, could result in a potential safety hazard, the relevant settings that determine the intervention of SIC systems, and the operational limits on equipment which warn against or stop a functional deviation from a planned operational status that could challenge equipment and functions. Some operational conditions, e.g. in-Vacuum Vessel (VV) radioactive inventories, will be controlled through procedures. Operating experience from present tokamaks, in particular JET, and from nuclear plants, is considered to the maximum possible extent.This paper presents the guidelines for the development of the ITER OLCs with particular reference to safety limits.     

Nickel solubility limit in liquid lead-bismuth eutectic

In the framework of the Accelerator-Driven System (ADS), the Pb-Bi eutectic can be used as spallation target for neutron production. The Pb-Bi flow in contact with the ADS structural steels, T 91 (Fe-9Cr martensitic steel) and 316L (Fe-17Cr-10Ni austenitic steel), can dissolve the main steel components: iron, chromium and nickel. According to literature, in low oxygen containing Pb-Bi, the dissolution rates of 316L depend, at least, on the nickel solubility limit as it dissolves preferentially in the Pb-Bi alloy. Consequently, the determination of this physico-chemical data in the temperature range of the ADS operating conditions (350-450 °C) is needed for the prediction of the corrosion rates in ADS.The nickel solubility limit in Pb-Bi is available in the literature from 400 °C to 900 °C but not for lower temperatures. However, the Ni-Bi phase diagram leads one to suppose that the nickel solubility limit law changes for lower temperatures. Consequently in this study, two experimental techniques have been implemented for the determination of the nickel solubility limit at low temperatures. The first one is performed from 400 °C to 500 °C using the Laser Induce Breakdown Spectroscopy (LIBS). The LIBS technique permits to obtain in situ measurements directly performed on liquid Pb-Bi. This characteristic is very interesting as it allows to monitor on line the concentration of the dissolved impurities in the liquid coolant. However, this technique is still under development and optimization on liquid Pb-Bi medium. The second technique is ICP-AES. This technique, commonly used to analyze alloys composition, is interesting as it permits a global analysis of a Pb-Bi sample. Moreover, the measurement made by ICP-AES is very reliable, very accurate and optimized for such analyses. However, this technique is ex situ; this is its main disadvantage. Experiments using ICP-AES were performed from 350 °C to 535 °C. The two techniques lead to the same solubility limit in their common temperature range. However, the experiment using ICP-AES technique revealed a change in the nickel solubility law for the temperatures lower than 415 °C. Consequently, this study recommends the use of two solubility limits relations, which take into account these results, as well as the literature results: the solubility limits laws of Martynov and Rosenblatt. The nickel solubility limit can thus be expressed as: for the temperature range: 330-415 °C. This law is the empirical solubility law obtained in this study at the low temperature range. for 415-900 °C temperature range. This law is the linear regression made on the overall experimental points available in literature and in this study. According to the Martynov studies, it seems reliable up to 900 °C.     

A parametric study on pressure–temperature limit curve using 3-D finite element analyses

In order to operate a reactor pressure vessel (RPV) safely, it is necessary to keep the pressure–temperature (P–T) limit during the heatup and cooldown process. While the ASME Code provides the P–T limit curve for safe operation, this limit curve has been prepared under conservative assumptions. In this paper, the effects of conservative assumptions involved in the P–T limit curve specified in the ASME Code Sec. XI were investigated. Three different parameters, the crack depth, the cladding thickness and the cooling rate, were reviewed based on 3-D finite element analyses. Also, the constraint effect on P–T limit curve generation was investigated based on J–T approach. It was shown that the crack depth and constraint effect change the safety region in P–T limit curve dramatically, and thus it is recommended to prepare a more precise P–T limit curve based on finite element analysis to obtain P–T limit for safe operation of a RPV.     

Even-parity finite-element transport methods in the diffusion limit

We use an asymptotic analysis to investigate the behavior of continuous finite-element-method (CFEM) discretizations of the even-parity transport equation, in problems containing optically thick diffusive regions. Our first interesting result is that we can analyze the entire family of even-parity CFEMs, and can do so in three dimensions on an arbitrarily-connected grid. (Previous asymptotic analyses have been restricted to specific discretizations, either in slab geometry or in XY geometry on a rectangular grid.) We show that every even-parity CFEM transport solution satisfies a corresponding CFEM discretization of the correct diffusion equation in the diffusion limit, which is a highly desirable property. We further show that this solution is subject to a Dirichlet boundary condition given by a cosine (|n·Ω|) weighting of the incident intensity. We show that this boundary condition, which is less accurate than we would like, means that in certain problems the transport solution in a diffusive region can be more than a factor of two greater than the correct solution. We also show that the CFEM transport solution can be incorrect in non-diffusive regions that are adjacent to diffusive regions, no matter how fine the spatial grid is in the non-diffusive region. We give numerical results from slab geometry verifying the predictions of our analysis.     

Evaluation of anelasticity and plastic creep limit for alloy 800

The elevated temperature tensile, anelastic and creep properties of a precipitation strengthened Ni---Cr austenitic steel (alloy 800) have been evaluated with respect to LMFBR application. These properties have been estimated and formulated for small strains and temperatures on the order of 823 K. It has been shown that despite suppression of the in-service stresses to beneath the alloy's yield strength, plastic deformation will occur at such temperatures and the stress below which plastic strain is effectively zero (plastic creep limit) is negligible for a reactor life time. The plastic creep limit at a given time and temperature markedly depends on the degree of precipitation hardening or prior cold deformation for alloy 800. The contribution from anelastic deformation is less than 0.05% and only becomes important for strict dimensional control and constrained parts.