A Level Set Method for Foam Expansion and Property Prediction
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Nuclear energy is one industry where aging of safety-related materials and components is of great concern. Many U.S. nuclear power plants are approaching, or have already exceeded, 40 years of age. Analysis comparing the cost of new plant construction versus long-term operation under extended plant licensing through 60 years strongly favors the latter option. To ensure the safe, reliable, and cost-effective long-term operation of nuclear power plants, many systems, structures, and components must be evaluated. Furthermore, as new analytical techniques and testing approaches are developed, it is imperative that we also validate, and if necessary, improve upon the previously employed Institute of Electrical and Electronic Engineers (IEEE) qualification standards originally written in 1974. Fortunately, this daunting task has global support, particularly in light of the new social and political climate surrounding nuclear energy in a post-Fukushima era.
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We are developing computational models to elucidate the expansion and dynamic filling process of a polyurethane foam, PMDI. The polyurethane of interest is chemically blown, where carbon dioxide is produced via the reaction of water, the blowing agent, and isocyanate. The isocyanate also reacts with polyol in a competing reaction, which produces the polymer. Here we detail the experiments needed to populate a processing model and provide parameters for the model based on these experiments. The model entails solving the conservation equations, including the equations of motion, an energy balance, and two rate equations for the polymerization and foaming reactions, following a simplified mathematical formalism that decouples these two reactions. Parameters for the polymerization kinetics model are reported based on infrared spectrophotometry. Parameters describing the gas generating reaction are reported based on measurements of volume, temperature and pressure evolution with time. A foam rheology model is proposed and parameters determined through steady-shear and oscillatory tests. Heat of reaction and heat capacity are determined through differential scanning calorimetry. Thermal conductivity of the foam as a function of density is measured using a transient method based on the theory of the transient plane source technique. Finally, density variations of the resulting solid foam in several simple geometries are directly measured by sectioning and sampling mass, as well as through x-ray computed tomography. These density measurements will be useful for model validation once the complete model is implemented in an engineering code.
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Polymer Degradation and Stability
All polymers are intrinsically susceptible to oxidation, which is the underlying process for thermally driven materials degradation and of concern in various applications. There are many approaches for predicting oxidative polymer degradation. Aging studies usually are meant to accelerate oxidation chemistry for predictive purposes. Kinetic models attempt to describe reaction mechanisms and derive rate constants, whereas rapid qualification tests should provide confidence for extended performance during application, and similarly TGA tests are meant to provide rapid guidance for thermal degradation features. What are the underlying commonalities or diverging trends and complications when we approach thermo-oxidative aging of polymers in such different ways? This review presents a brief status report on the important aspects of polymer oxidation and focuses on the complexity of thermally accelerated polymer aging phenomena. Thermal aging and lifetime prediction, the importance of DLO, property correlations, kinetic models, TGA approaches, and a framework for predictive aging models are briefly discussed. An overall perspective is provided showing the challenges associated with our understanding of polymer oxidation as it relates to lifetime prediction requirements.
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A selective literature review was conducted to assess whether currently available accelerated aging and original qualification data could be used to establish operational margins for the continued use of cable insulation and jacketing materials in nuclear power plant environments. The materials are subject to chemical and physical degradation under extended radiationthermal- oxidative conditions. Of particular interest were the circumstances under which existing aging data could be used to predict whether aged materials should pass loss of coolant accident (LOCA) performance requirements. Original LOCA qualification testing usually involved accelerated aging simulations of the 40-year expected ambient aging conditions followed by a LOCA simulation. The accelerated aging simulations were conducted under rapid accelerated aging conditions that did not account for many of the known limitations in accelerated polymer aging and therefore did not correctly simulate actual aging conditions. These highly accelerated aging conditions resulted in insulation materials with mostly inert aging processes as well as jacket materials where oxidative damage dropped quickly away from the air-exposed outside jacket surface. Therefore, for most LOCA performance predictions, testing appears to have relied upon heterogeneous aging behavior with oxidation often limited to the exterior of the cable cross-section a situation which is not comparable with the nearly homogenous oxidative aging that will occur over decades under low dose rate and low temperature plant conditions. The historical aging conditions are therefore insufficient to determine with reasonable confidence the remaining operational margins for these materials. This does not necessarily imply that the existing 40-year-old materials would fail if LOCA conditions occurred, but rather that unambiguous statements about the current aging state and anticipated LOCA performance cannot be provided based on original qualification testing data alone. The non-availability of conclusive predictions for the aging conditions of 40-year-old cables implies that the same levels of uncertainty will remain for any re-qualification or extended operation of these cables. The highly variable aging behavior of the range of materials employed also implies that simple, standardized aging tests are not sufficient to provide the required aging data and performance predictions for all materials. It is recommended that focused studies be conducted that would yield the material aging parameters needed to predict aging behaviors under low dose, low temperature plant equivalent conditions and that appropriately aged specimens be prepared that would mimic oxidatively-aged 40- to 60- year-old materials for confirmatory LOCA performance testing. This study concludes that it is not sufficient to expose materials to rapid, high radiation and high temperature levels with subsequent LOCA qualification testing in order to predictively quantify safety margins of existing infrastructure with regard to LOCA performance. We need to better understand how cable jacketing and insulation materials have degraded over decades of power plant operation and how this aging history relates to service life prediction and the performance of existing equipment to withstand a LOCA situation.
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