Large-Scale Numerical Modeling of Melt and Solution Crystal Growth

We present an overview of mathematical models and their large-scale numerical solution for simulating different phenomena and scales in melt and solution crystal growth. Samples of both classical analyses and state-of-the-art computations are presented. It is argued that the fundamental multi-scale nature of crystal growth precludes any one approach for modeling, rather successful crystal growth modeling relies on an artful blend of rigor and practicality

Fundamental Science Investigations to Develop a 6-MV Laser Triggered Gas Switch for ZR: First Annual Report.

In October 2005, an intensive three-year Laser Triggered Gas Switch (LTGS) development program was initiated to investigate and solve observed performance and reliability issues with the LTGS for ZR. The approach taken has been one of mission-focused research: to revisit and reassess the design, to establish a fundamental understanding of LTGS operation and failure modes, and to test evolving operational hypotheses. This effort is aimed toward deploying an initial switch for ZR in 2007, on supporting rolling upgrades to ZR as the technology can be developed, and to prepare with scientific understanding for the even higher voltage switches anticipated needed for future high-yield accelerators. The ZR LTGS was identified as a potential area of concern quite early, but since initial assessments performed on a simplified Switch Test Bed (STB) at 5 MV showed 300-shot lifetimes on multiple switch builds, this component was judged acceptable. When the Z{sub 20} engineering module was brought online in October 2003 frequent flashovers of the plastic switch envelope were observed at the increased stresses required to compensate for the programmatically increased ZR load inductance. As of October 2006, there have been 1423 Z{sub 20} shots assessing a variety of LTGS designs. Numerous incremental and fundamental switch design modifications have been investigated. As we continue to investigate the LTGS, the basic science of plastic surface tracking, laser triggering, cascade breakdown, and optics degradation remain high-priority mission-focused research topics. Significant progress has been made and, while the switch does not yet achieve design requirements, we are on the path to develop successively better switches for rolling upgrade improvements to ZR. This report summarizes the work performed in FY 2006 by the large team. A high-level summary is followed by detailed individual topical reports

Permeability calculations in three-dimensional isotropic and oriented fiber networks

Hydraulic permeabilities of fiber networks are of interest for many applications and have been studied extensively. There is little work, however, on permeability calculations in three-dimensional random networks. Computational power is now sufficient to calculate permeabilities directly by constructing artificial fiber networks and simulating flow through them. Even with today’s high-performance computers, however, such an approach would be infeasible for large simulations. It is therefore necessary to develop a correlation based on fiber volume fraction, radius, and orientation, preferably by incorporating previous studies on isotropic or structured networks. In this work, the direct calculations were performed, using the finite element method, on networks with varying degrees of orientation, and combinations of results for flows parallel and perpendicular to a single fiber or an array thereof, using a volume-averaging theory, were compared to the detailed analysis. The detailed model agreed well with existing analytical solutions for square arrays of fibers up to fiber volume fractions of 46% for parallel flow and 33% for transverse flow. Permeability calculations were then performed for isotropic and oriented fiber networks within the fiber volume fraction range of 0.3%–15%. When drag coefficients for spatially periodic arrays were used, the results of the volume-averaging method agreed well with the direct finite element calculations. On the contrary, the use of drag coefficients for isolated fibers overpredicted the permeability for the volume fraction range that was employed. We concluded that a weighted combination of drag coefficients for spatially periodic arrays of fibers could be used as a good approximation for fiber networks, which further implies that the effect of the fiber volume fraction and orientation on the permeability of fiber networks are more important than the effect of local network structure