A Heat Transfer Analysis of the Melting of Eutectic Alloys
Federal Authority for Nuclear Regulations
Melting and solidification of alloys is now studied in detail due to its commercial and technical potentialities. For example, zirconium alloys (zircaloy-2 and zircaloy-4) have become widely accepted structural material in nuclear power reactors today.
The phase change in alloys is a non-linear problem; having a moving boundary: the solid-liquid interface. The heat-transfer problem involves finding the location of the interface during the phase change process. From the position of the interface, the melting rate can then be determined.
Because alloys melt over a temperature range, there are two moving boundaries: the solidus line and the liquidus line.
Hence, the alloy melting problem is mathematically and physically more complex, and especially under the realistic condition of temperature-dependent thermos-physical properties.
This work analyzes the unidimensional heat transfer problem of the melting of a binary eutectic alloy under the realistic assumption of temperature dependent thermos-physical properties.
The mathematical model leads to a non-linear, boundary-value problem that has no analytic solution.
The problem is reduced to a system of first-order, initial-value ordinary differential equations that are then solved numerically.
The numerical solution gives the location of the solidus and liquidus lines, versus time. From the location-versus-time data, the melting rate is obtained as a function of time.
It is noticed that there is a time-delay before the two-phase zone appears, but that the zone width increases rapidly thereafter and becomes too appreciable to be neglected in alloy melting analysis.
The melting rate is noticed to be high at the early stage of the process, then drops rapidly with time.
The rate is observed to be much more sensitive to changes in latent heat and thermal conductivity than to changes in heat capacity.
A study on the effects of hydrogen content and peak temperature on threshold stress for hydride reorientation in Zircaloy-4 cladding
Hydride reorientation is one of the crucial degradation mechanisms of cladding integrity under dry storage conditions. Recently, it has been experimentally reported that the threshold stress triggering the reorientation depends on various factors synergistically such as temperature, thermal history, hydrogen content, thermal cycling, and stress biaxiality. In this study, the combined effects of the hydrogen content and peak temperature on the threshold stress were studied using ring tension tests with a Zircaloy-4 cladding tube. To simulate the thermo-mechanical history of the cladding during interim dry storage, pre-hydrided specimens with hydrogen concentrations up to 585 wppm were tested following a transient temperature from a peak temperature, 350 ℃ or 400 ℃ , to room temperature. Results show that the threshold stress reaches a minimum when the hydrogen content is the terminal solid solubility of dissolution (TSSD) at a given peak temperature. The minimum stress was found to be 52 MPa and 75MPa at 400 C and 350 C, respectively. With increasing hydrogen concentration, the threshold stress decreases in the regime of the solid solution state, whereas the stress steadily increases and then tends to saturate to a certain value in the regime of the supersaturated state. A qualitative model is presented to explain these findings on the basis of the mechanistic understanding of stress-driven hydrogen transport, memory effect, and radial hydride re-precipitation.
Cluster-Dynamics Modeling of Irradiated PWR Core Internals
Life extension of PWR beyond 40 years will expose austenitic steels of core internals to higher irradiation dose. Among the various degradation mechanisms occurring at high dose, the potential swelling of austenitic steel in PWR conditions is of special interest and several research programs are underway to get relevant experimental data.
This paper presents a model based on cluster-dynamics (CD) technique to describe the microstructural evolution of PWR internal steel under irradiation. The CD model, developed in the framework of Crescendo Code, simulates the coupled evolution of mixed helium-vacancy and interstitial clusters (cavity or bubble and Frank loops) as well as the evolution of dislocation network.
To calibrate the parameters of the model, a set of relevant post-irradiation experiments (PlE) of solution-annealed 304, 316 and cold-worked 316 is selected in the open literature. PIE data are based on Transmission Electron Microscopy (TEM) analysis and span a wide range of operational conditions : temperatures from 275 to 400°C, dose rates from 5.10-8 to 10-6 dpa/s and helium production rates from 0.2 to ~20 appm/dpa.
A single set of CD parameters is used to fit the entire 304 and 316 database, however an effective temperature-dependent bias for dislocation and loops was introduced to improve the fit of low and high temperature data. The predictions of the model and the fitted parameters are reasonably consistent with the microstructural database and follow some experimental trends reported in the literature. The role of helium in conditions relevant to PWR internal is found to be significant and leads to an increase of vacancy clusters density and swelling. The paper suggests areas of improvement in the model.
Disclosure of the Hydrogen Generation and Accumulation in Steel and Graphite Irradiated in Inert Environment
National Research Centre "Kurchatov Institute"
In traditional power engineering hydrogen may be one of the firstprimary source of equipment damage. This problem has high actuality for both nuclear and thermonuclear power engineering.
Our study of radiation-hydrogen embrittlement of the irradiated steel raises the question concerning the experimentally registered presence of unknown source of hydrogen and process of this hydrogen accumulation in steel irradiated in inert environment in research reactor. Later unexpectedly high hydrogen concentrations were detected in irradiated graphite. So alloying of steel and graphite by hydrogen in nuclear reactor takes place.
It is necessary to look for this source of hydrogen especially because unexpectedly hydrogen flakes of unknown origin were detected in reactor vessels of Belgian NPPs.
As a possible initial hypothesis about the enigmatical source of hydrogen one can propose protons generation during beta-decay of free neutrons inasmuch as protons detected by researches at nuclear reactors as witness of beta-decay of free neutrons.
Effect of Gamma-Irradiation Induced Degradation on Mechanical and Thermal properties of Polymeric Materials
Various polymeric materials are used in nuclear power plant as cable insulation and sealing part, and switch. However, these materials exposed to high energy radiation in normal operation and accident environment. To ensure the safety of nuclear power plants systems and survivability, understanding of degradation behavior caused by gamma radiation is important. In this study, to investigate the gamma irradiation induced degradation effects, fluoroelastomer (FKM), ethylene propylene diene monomer (EPDM), and nitrile butadiene rubber (NBR) samples were prepared to gamma irradiation tests at dose: 200, 400, 800, 1200, 1600, 2000 kGy. Mechanical (tensile strength, elongation at break, Shore A hardness), thermal properties (thermogravimetric analysis) and molecular analysis (Fourier transformed infrared spectroscopy) were conducted to investigate the gamma irradiation effects. The experimental results show hardening effects on polymeric samples and decreasing of thermal stability. The oxidized chemical bonds such as, C-O and C=O, in molecular structure increased as dose increases. Form FT-IR results, the carbonyl groups increased, and intensity of peak indicate the C-H bonds decreased with increasing of irradiation dose. These results indicate that free radicals are generated by scissioned bonds in molecular structure by high energetic gamma radiation, and theses free radicals react with scission bonds in structure and oxygen in the atmosphere, auto-oxidation phenomena. resulting in, damaged molecular crosslinked, and form unstable structure. The FKM had a significantly affected gamma radiation on mechanical properties and thermal stability than other polymeric materials. And 5% weight loss temperature from thermogravimetric curves decreased more significantly than EPDM and NBR due to dehydrofluorination reaction between hydrogen and fluorine form scissioned structure.