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At least 487 records · Page 27

Building Initial Dynamic System Models for Digital Twins of the Cryogenic Moderator System at the ORNL Spallation Neutron Source

This work describes the initial development of dynamic system models of the cryogenic moderator system (CMS) of the Spallation Neutron Source (SNS) at ORNL as a part of the ORNL LDRD funded project Building TRANSFORM to Accelerate Digital Twin Applications for Nuclear Systems, LOIS 10563. The goal of the work is to start the dynamic system modeling effort with the end goal of using them for real-time applications as digital twins. The CMS is a cryogenic liquid hydrogen flow loop that provides moderation of the neutrons that are generated by the SNS. For optimal neutron production, the CMS needs to maintain a steady and controlled density of cryogenic hydrogen in the moderator section thus requiring precise temperature and pressure control. Due to the varied time scales and system characteristics, control of the system is complex, and diagnostics are also difficult. Difficulty in accessing the flow loop during operations, limited instrumentation and unknown design details of the equipment combine to make the case for having sophisticated digital twin models of the system. Operationally the CMS also provides a strong use case for digital twins due to the constant need of optimization and for troubleshooting/diagnostics. The large amount of data collected which are freely available for using in building the model and verifying and validating the model also makes it a great candidate for a proof-of-concept for digital twins. The project extends ORNL's capacity of development and implementation of the open-source dynamic system modeling tool TRANSFORM for engineering design and digital twin/real-time applications. Specific system configuration data for the CMS have been gathered and an initial dynamic model was created in the TRANSFORM library using Dymola as the solution platform. Models of increasing complexity are created to demonstrate the need for a multi-layered approach in digital twin modeling depending on the scale and phenomena being focused on. The dynamic modeling is shown to bring the dynamic operational aspects to the design process for systems as well as serve as a digital twin to the hardware and allow for models to be tuned and compared against real time operational data. These aims should help to push forward strategic goals of application of digital twins and increase the impact of ORNL systems modeling capabilities with TRANSFORM/Modelica for various advanced energy systems.

42 ENGINEERING↗

Application of Multi-Satellite Precipitation Analysis to Floods and Landslides

Satellite data acquired and processed in real time now have the potential to provide the spacetime information on rainfall needed to monitor flood and landslide events around the world. This can be achieved by integrating the satellite-derived forcing data with hydrological models and landslide algorithms. Progress in using the TRMM Multi-satellite Precipitation Analysis (TMPA) as input to flood and landslide forecasts is outlined, with a focus on understanding limitations of the rainfall data and impacts of those limitations on flood/landslide analyses. Case studies of both successes and failures will be shown, as well as comparison with ground comparison data sets both in terms of rainfall and in terms of flood/landslide events. In addition to potential uses in real-time, the nearly ten years of TMPA data allow retrospective running of the models to examine variations in extreme events. The flood determination algorithm consists of four major components: 1) multi-satellite precipitation estimation; 2) characterization of land surface including digital elevation from NASA SRTM (Shuttle Radar Terrain Mission), topography-derived hydrologic parameters such as flow direction, flow accumulation, basin, and river network etc.; 3) a hydrological model to infiltrate rainfall and route overland runoff; and 4) an implementation interface to relay the input data to the models and display the flood inundation results to potential users and decision-makers. In terms of landslides, the satellite rainfall information is combined with a global landslide susceptibility map, derived from a combination of global surface characteristics (digital elevation topography, slope, soil types, soil texture, and land cover classification etc.) using a weighted linear combination approach. In those areas identified as "susceptible" (based on the surface characteristics), landslides are forecast where and when a rainfall intensity/duration threshold is exceeded. Results are described indicating general agreement with landslide occurrences. However, difficulties in comparing landslide event information (mostly from news reports) with the satellite-based forecasts are analyzed.

Adler, Robert↗

A CONDUCTION-BASED HEAT PIPE MODEL FOR ANALYZING THE ENTIRE PROCESS OF LIQUID-METAL HEAT PIPE STARTUP

The Heat Pipe-cooled Microreactor (HPM) is one of the micro nuclear reactor designs under active study at the U.S. Idaho National Laboratory. Among the major concerns of HPM research is to understand the startup behavior of the heat pipe-cooled system associated with the startup of the liquid-metal heat pipes initialing from frozen state. The startup of liquid-metal heat pipes typically involves a number of nonlinear mass and heat transport processes including the phase change from solid to liquid and vapor. Hence, it is still a huge challenge to simulate the liquid-metal heat pipe startup using conventional CFD methods and software. The major difficulties of numerical CFD modeling come from the phase-change process, multiphase interaction, microporous wick flow, and compressible gas dynamics that occur during startup of the liquid-metal heat pipes. This paper proposes a simplified conduction-based method to provide practical insights into the entire startup process of the liquid-metal heat pipes while mitigating the challenges of addressing all the complex physics. We discuss the theoretical basis and modeling assumptions to analyze the liquid-metal heat pipe startup from frozen state based solely on heat-conduction equations. Then, the proposed model is implemented into the commercial CFD software to verify the model performance. The model prediction results are discussed via the comparison with the experimental data obtained from sodium heat-pipe startup experiments.

42 ENGINEERING↗

Fluor Idaho's Technical and Programmatic Approach That Resolved the Problems with the Integrated Waste Treatment Unit - 19290

The Integrated Waste Treatment Unit (IWTU) is a facility designed to treat approximately 900,000 gallons of radioactive liquid waste, referred to as Sodium Bearing Waste (SBW). IWTU is a Fluidized Bed Steam Reforming process that will be used to treat the SBW to produce a granular sodium carbonate and sodium aluminate product. The product is planned to be managed as remote handled transuranic waste. Construction of the IWTU was completed in 2011 and Critical Decision 4 was achieved in 2012 with the expectation that the treatment of the SBW would be completed in 2012. However, process instabilities and equipment problems prevented the safe and reliable operation of the facility. All of the nonradiological tests of the IWTU had to be stopped prematurely because each time the IWTU was operated, the process would become unstable within a few days of initiating the operation. The instabilities were associated with the primary fluidized bed reaction vessel, the Denitration Mineralization Reformer (DMR). The instabilities included difficulties maintaining fluidization conditions and scale formation within the DMR. Design inadequacies and equipment reliability problems in other parts of the facility also hampered the testing the IWTU. The U.S. Department of Energy (DOE) awarded the Idaho Clean-up contract to Fluor Idaho (Fluor) in 2016. To resolve the issues with the IWTU, Fluor assembled a dedicated team to develop the technical and programmatic strategy to resolve the issues with the IWTU and get it operational. Fluor's approach has successfully resolved the primary issues with the IWTU. As a result of modifications of equipment and operating strategies implemented by Fluor, the core part of the IWTU process now works reliably when processing simulated Sodium Bearing Waste over a wide range of operating conditions. This paper describes Fluor's approach and summarize key steps in the process to resolve the issues with the IWTU. Fluor has used strong fundamentals including a first principles approach and unique program management techniques to solve the technical problems with the IWTU. The successful approach has provided renewed confidence in the IWTU process enabling the troubled project to move forward. Important factors in the success of the project include using a dedicated project team separate from the IWTU line organization, a Technical Review Group, the Chemistry Team and a diverse set of supporting contractors and National Laboratories. Fluor typically used multiple means to validate solutions before testing them in the IWTU. Fluor's successful full-scale demonstration runs of the IWTU confirm the process will reliably produce a compliant, treated waste product over a wide range of operating conditions.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Where did the tumor start? An inverse solver with sparse localization for tumor growth models

In this work, we present a numerical scheme for solving an inverse problem for parameter estimation in tumor growth models for glioblastomas, a form of aggressive primary brain tumor. The growth model is a reaction–diffusion partial differential equation (PDE) for the tumor concentration. We use a PDE-constrained optimization formulation for the inverse problem. The unknown parameters are the reaction coefficient (proliferation), the diffusion coefficient (infiltration), and the initial condition field for the tumor PDE. Segmentation of magnetic resonance imaging (MRI) scans drive the inverse problem where segmented tumor regions serve as partial observations of the tumor concentration. Like most cases in clinical practice, we use data from a single time snapshot. Moreover, the precise time relative to the initiation of the tumor is unknown, which poses an additional difficulty for inversion. We perform a frozen-coefficient spectral analysis and show that the inverse problem is severely ill-posed. We introduce a biophysically motivated regularization on the structure and magnitude of the tumor initial condition. In particular, we assume that the tumor starts at a few locations (enforced with a sparsity constraint on the initial condition of the tumor) and that the initial condition magnitude in the maximum norm is equal to one. We solve the resulting optimization problem using an inexact quasi-Newton method combined with a compressive sampling algorithm for the sparsity constraint. Our implementation uses PETSc and AccFFT libraries. We conduct numerical experiments on synthetic and clinical images to highlight the improved performance of our solver over a previously existing solver that uses standard two-norm regularization for the calibration parameters. The existing solver is unable to localize the initial condition. Our new solver can localize the initial condition and recover infiltration and proliferation. In clinical datasets (for which the ground truth is unknown), our solver results in qualitatively different solutions compared to the two-norm regularized solver.

97 MATHEMATICS AND COMPUTING↗

Some implications of reciprocity for two-way clock synchronization

The difficulties related to propagation perturbances in one-way and two-way methods for the synchronization of remote clocks are defined, and a possible means of circumventing these problems in the two-way method is suggested. In the two-way method, if signals are launched from two sources, A and B, then the two signals arriving at A and B will be displaced in arrival time by an amount that is equal to the difference in launch times of the two signals. Thus, the only condition to comparing clocks is that the medium be isotropic. The practice implementation of this is explored theoretically, in some detail, with respect to the Loran-C navigation system.

Jespersen, J. L.↗

Formal and heuristic system decomposition methods in multidisciplinary synthesis

The multidisciplinary interactions which exist in large scale engineering design problems provide a unique set of difficulties. These difficulties are associated primarily with unwieldy numbers of design variables and constraints, and with the interdependencies of the discipline analysis modules. Such obstacles require design techniques which account for the inherent disciplinary couplings in the analyses and optimizations. The objective of this work was to develop an efficient holistic design synthesis methodology that takes advantage of the synergistic nature of integrated design. A general decomposition approach for optimization of large engineering systems is presented. The method is particularly applicable for multidisciplinary design problems which are characterized by closely coupled interactions among discipline analyses. The advantage of subsystem modularity allows for implementation of specialized methods for analysis and optimization, computational efficiency, and the ability to incorporate human intervention and decision making in the form of an expert systems capability. The resulting approach is not a method applicable to only a specific situation, but rather, a methodology which can be used for a large class of engineering design problems in which the system is non-hierarchic in nature.

Bloebaum, Christina L.↗

Idiomatic Correctness-Checking via Julienne in Fortran 2023

This paper presents a unified approach to unit testing and runtime assertion checking using Fortran 2023. The paper describes the support for our approach in the Julienne framework. Julienne leverages recent Fortran standards to implement object-oriented design patterns, support testing parallel programs, and implement functional programming patterns in order to craft idioms inspired by natural-language expressions. The presented idioms employ novel operators to write expressions that evaluate to a test-diagnosis object encapsulating two components: (1) the test outcome or assertion outcome and (2) an automatically generated diagnostic string. Two other novel aspects of the approach include (1) the ability to enforce assertions inside pure procedures and (2) the ability to output rich diagnostic information inside pure procedures during error termination when assertions fail. The latter capability mitigates against a reason that Fortran programmers commonly cite for not writing pure procedures: difficulty obtaining useful program output inside pure procedures when debugging code. This paper demonstrates how the adoption of the proposed idioms leads naturally to a unifying theme across two otherwise disparate technologies: unit testing and runtime assertion checking. Finally, this paper describes the usage of the Julienne testing framework for writing unit tests and assertions in the Matcha high-performance computing application and the Fiats deep learning library.

Rouson, Damian↗

Smashing the Stovepipe: Leveraging the GMSEC Open Architecture and Advanced IT Automation to Rapidly Prototype, Develop and Deploy Next-Generation Multi-Mission Ground Systems

Satellite/Payload Ground Systems - Typically highly-customized to a specific mission's use cases - Utilize hundreds (or thousands!) of specialized point-to-point interfaces for data flows / file transfers Documentation and tracking of these complex interfaces requires extensive time to develop and extremely high staffing costs Implementation and testing of these interfaces are even more cost-prohibitive, and documentation often lags behind implementation resulting in inconsistencies down the road With expanding threat vectors, IT Security, Information Assurance and Operational Security have become key Ground System architecture drivers New Federal security-related directives are generated on a daily basis, imposing new requirements on current / existing ground systems - These mandated activities and data calls typically carry little or no additional funding for implementation As a result, Ground System Sustaining Engineering groups and Information Technology staff continually struggle to keep up with the rolling tide of security Advancing security concerns and shrinking budgets are pushing these large stove-piped ground systems to begin sharing resources - I.e. Operational / SysAdmin staff, IT security baselines, architecture decisions or even networks / hosting infrastructure Refactoring these existing ground systems into multi-mission assets proves extremely challenging due to what is typically very tight coupling between legacy components As a result, many "Multi-Mission" ops. environments end up simply sharing compute resources and networks due to the difficulty of refactoring into true multi-mission systems Utilizing continuous integration / rapid system deployment technologies in conjunction with an open architecture messaging approach allows System Engineers and Architects to worry less about the low-level details of interfaces between components and configuration of systems GMSEC messaging is inherently designed to support multi-mission requirements, and allows components to aggregate data across multiple homogeneous or heterogeneous satellites or payloads - The highly-successful Goddard Science and Planetary Operations Control Center (SPOCC) utilizes GMSEC as the hub for it's automation and situational awareness capability Shifts focus towards getting GS to a final configuration-managed baseline, as well as multi-mission / big-picture capabilities that help increase situational awareness, promote cross-mission sharing and establish enhanced fleet management capabilities across all levels of the enterprise.

GMSEC↗

Metrology for femtosecond pulsed x-ray heating in diamond anvil cell experiments at the European XFEL: Revisiting the iron phase diagram up to 150 GPa

The development of pulsed intense x-ray sources, such as free electron laser, offers new avenues for high pressure experiments. Here, we study the feasibility and metrology of x-ray heating in diamond anvil cells at the European x-ray free electron laser. This method enables one to volumetrically heat the sample while inhibiting chemical migration and probing the crystallographic structure of the sample throughout the heating with a high repetition rate. We focus our study on iron, whose phase diagram is well established up to 100 GPa, to explore the possibilities and limitations of this technique. We volumetrically heat iron samples at starting pressures ranging from 10 to 138 GPa, using the x-ray beam pulsed at 4.5 MHz in a serial pump-and-probe experimental design. Experimental challenges arise from temperature gradients within the sample, changes in temperature at the 100 ns timescale, the difficulty of direct temperature estimates, the effect of thermal pressure, and the presence of metastable crystallites due to rapid cycles of heating and cooling. Hence, we develop a multi-crystal-like data processing method that allows us to account for sample heterogeneity in probed conditions. We then calibrate our measurements using known physical properties of iron under pressure. Thermal pressure in our experiments increases from 4% of the isochoric prediction at 10 GPa to 23% at 138 GPa, and we show that our data are in agreement with most previous observations of iron in this pressure range. The method can now be implemented at higher pressures and temperatures and on materials with unknown phase diagrams.

Materials science↗

Ultrasonic inspection of carbon fiber reinforced plastic by means of sample-recognition methods

In the case of carbon fiber reinforced plastic (CFRP), it has not yet been possible to detect nonlocal defects and material degradation related to aging with the aid of nondestructive inspection method. An approach for overcoming difficulties regarding such an inspection involves an extension of the ultrasonic inspection procedure on the basis of a use of signal processing and sample recognition methods. The basic concept involved in this approach is related to the realization that the ultrasonic signal contains information regarding the medium which is not utilized in conventional ultrasonic inspection. However, the analytical study of the phyiscal processes involved is very complex. For this reason, an empirical approach is employed to make use of the information which has not been utilized before. This approach uses reference signals which can be obtained with material specimens of different quality. The implementation of these concepts for the supersonic inspection of CFRP laminates is discussed.

Bilgram, R.↗

Parallel Computational Environment for Substructure Optimization

Design optimization of large structural systems can be attempted through a substructure strategy when convergence difficulties are encountered. When this strategy is used, the large structure is divided into several smaller substructures and a subproblem is defined for each substructure. The solution of the large optimization problem can be obtained iteratively through repeated solutions of the modest subproblems. Substructure strategies, in sequential as well as in parallel computational modes on a Cray YMP multiprocessor computer, have been incorporated in the optimization test bed CometBoards. CometBoards is an acronym for Comparative Evaluation Test Bed of Optimization and Analysis Routines for Design of Structures. Three issues, intensive computation, convergence of the iterative process, and analytically superior optimum, were addressed in the implementation of substructure optimization into CometBoards. Coupling between subproblems as well as local and global constraint grouping are essential for convergence of the iterative process. The substructure strategy can produce an analytically superior optimum different from what can be obtained by regular optimization. For the problems solved, substructure optimization in a parallel computational mode made effective use of all assigned processors.

Gendy, Atef S.↗

Implementation of Implicit Adaptive Mesh Refinement in an Unstructured Finite-Volume Flow Solver

This paper explores the implementation of adaptive mesh refinement in an unstructured, finite-volume solver. Unsteady and steady problems are considered. The effect on the recovery of high-order numerics is explored and the results are favorable. Important to this work is the ability to provide a path for efficient, implicit time advancement. A method using a simple refinement sensor based on undivided differences is discussed and applied to a practical problem: a shock-shock interaction on a hypersonic, inviscid double-wedge. Cases are compared to uniform grids without the use of adapted meshes in order to assess error and computational expense. Discussion of difficulties, advances, and future work prepare this method for additional research. The potential for this method in more complicated flows is described.

Schwing, Alan M.↗

Interlaboratory Study: Testing Reproducibility of Solid Biofuels Component Identification Using Reflected Light Microscopy

Considering global market trends and concerns about climate change and sustainability, increased biomass use for energy is expected to continue. As more diverse materials are being utilized to manufacture solid biomass fuels, it is critical to implement quality assessment methods to analyze these fuels thoroughly. One such method is reflected light microscopy (RLM), which has the potential to complement and enhance current standard testing, leading to improving fuel quality assessment and, ultimately, preventing avoidable air pollution. An interlaboratory study (ILS) was conducted to test the reproducibility of biomass fuels component identification using a reflected light microscopy technique. The exercise was conducted on thirty photomicrographs showing biomass and various undesired components (like plastics or mineral matter), which were purposely added (by the ILS organizers) to contaminate wood pellets and charcoal-based grilling fuels. Forty-six participants had various levels of difficulty identifying the marked components, and as a result, the percentage of correct answers ranged from 52.2 to 94.4%. Among the most difficult components to distinguish were petroleum products and inorganic matter. Various reasons led to the misidentification, including insufficient morphological descriptions of the components provided to participants, ambiguities of the nomenclature, limitations of the analytical and exercise method, and insufficient experience of the participants. Overall, the results indicate that RLM has the potential to enhance the quality assessment of biomass fuels. However, they also demonstrate that the petrographic classification used in this exercise requires further refinement before it can be standardized. While a new simplified classification of solid biomass fuels components was created as an outcome of this study, future research is necessary to refine the nomenclature, develop a microscopic morphological description of the components, and verify the accuracy of component identification with a follow-up ILS.

biomass↗

A Three-Dimensional Variational Data Assimilation Scheme for the Regional Ocean Modeling System: Implementation and Basic Experiments

A three-dimensional variational data assimilation scheme for the Regional Ocean Modeling System (ROMS), named ROMS3DVAR, has been described in the work of Li et al. (2008). In this paper, ROMS3DVAR is applied to the central California coastal region, an area characterized by inhomogeneity and anisotropy, as well as by dynamically unbalanced flows. A method for estimating the model error variances from limited observations is presented, and the construction of the inhomogeneous and anisotropic error correlations based on the Kronecker product is demonstrated. A set of single observation experiments illustrates the inhomogeneous and anisotropic error correlations and weak dynamic constraints used. Results are presented from the assimilation of data gathered during the Autonomous Ocean Sampling Network (AOSN) experiment during August 2003. The results show that ROMS3DVAR is capable of reproducing complex flows associated with upwelling and relaxation, as well as the rapid transitions between them. Some difficulties encountered during the experiment are also discussed.

California coastal ocean↗

Toward Quantity-of-Interest Preserving Lossy Compression for Scientific Data

Today's scientific simulations and instruments are producing a large amount of data, leading to difficulties in storing, transmitting, and analyzing these data. While error-controlled lossy compressors are effective in significantly reducing data volumes and efficiently developing databases for multiple scientific applications, they mainly support error controls on raw data, which leaves a significant gap between the data and user's downstream analysis. This may cause unqualified uncertainties in the outcomes of the analysis, a.k.a quantities of interest (QoIs), which are the major concerns of users in adopting lossy compression in practice. In this paper, we propose rigorous mathematical theories to preserve four families of QoIs that are widely used in scientific analysis during lossy compression along with practical implementations. Specifically, we first develop the error control theory for univariate QoIs which are essential for computing physical properties such as kinetic energy, followed by multivariate QoIs that are more commonly used in real-world applications. The proposed method is integrated into a state-of-the-art compression framework in a modular fashion, which could easily adapt to new QoIs and new compression algorithms. Experiments on real-world datasets demonstrate that the proposed method provides faithful error control on important QoIs including kinetic energy, regional average, and isosurface without trials and errors, while offering compression ratios that are up to 4x of the compression ratios provided by state-of-the-art compressors.

Jiao, Pu↗

The Legislative and Regulatory Histories Related to Greater-Than-Class-C Low-Level Radioactive Waste - 18602

The history surrounding the legislative and regulatory developments regarding Greater-Than-Class C Low Level Radioactive Waste (GTCC LLW) is both interesting and complex. On October 25, 1978, the U.S. Nuclear Regulatory Commission (NRC) published an Advanced Notice of Proposed Rulemaking pertaining to the development of regulations for the land disposal of LLW. This regulation was one of the first undertaken by NRC since its inception pursuant to the Energy Reorganization Act of 1974. Given the problematic challenges that many States were facing with releases of radioactivity from waste disposal facilities at the time, the technical bases supporting this rulemaking were both forward-thinking and comprehensive. The rule included a waste classification system that was tiered in four waste classes: Class A, B, C and GTCC LLW. On December 27, 1982, the NRC finalized the requirements for disposing of these classes of radioactive waste in Title 10 of the Code of Federal Regulations, Part 61 (10 CFR 61). The NRC established the waste classification system to protect both members of the public and individuals that may someday inadvertently intrude in the waste placed in the disposal facility after expiration of the institutional control period. This waste classification was developed to ensure that radiation doses to members of the public and an inadvertent intruder would not exceed 0.25 mSv y{sup -1} (25 mrem y{sup -1}) or 5.0 mSv y{sup -1} (500 mrem y{sup -1}), respectively. At the time the regulation was promulgated, GTCC LLW was considered generally not suitable for near surface disposal. It was recognized that disposal of GTCC LLW would require disposal technologies having greater confinement capacity or protection than 'normal' near-surface disposal. In 1980 Congress enacted the Low-Level Waste Policy Act of 1980, as amended in 1985 (LLWPAA of 1985) that assigned responsibility of disposing of GTCC LLW generated in the commercial sector or owned or generated by the federal government to the U.S. Department of Energy (DOE). At the time States were having difficulties in developing disposal facilities within the time constraints mandated in the LLWPA of 1980. Therefore, Congress believed that if DOE was assigned responsibility of developing disposal facilities for GTCC LLW, then the States would be more likely to develop new LLW disposal facilities. Congress also assigned the NRC with the responsibility to license the disposal of GTCC LLW generated or owned by the federal government or by the commercial sector. Lastly, Congress changed the definition of LLW that had been defined in the LLWPA of 1980 removing the 'transuranic' exclusionary language. Four years later, on May 25, 1989, the NRC promulgated its regulation needed to implement the mandates specified in the LLWPAA of 1985. The NRC revised 10 CFR 61.55 specifying that the NRC was responsible for licensing the disposal of GTCC LLW. However, it inadvertently did not revise the definition of LLW needed to remove the 'transuranic' exclusionary language in this rulemaking consistent with the LLWPAA of 1985. This seemingly inconsequential omission was not discovered until a Petition for Rulemaking was filed in Texas in July 2014. Moreover, this omission has effectively orphaned waste with certain transuranic radionuclides with concentrations exceeding 100 nanocuries per gram (100 nCi/g). In December 2015, the NRC Commissioners directed its staff to move forward with a rulemaking to resolve this issue and to perform a regulatory analysis to determine whether or not an Agreement State can license the disposal of GTCC LLW pursuant to Section 274 of the Atomic Energy Act of 1954. The paper will discuss past and current legislation, rulemaking, and regulatory developments pertaining to resolving the transuranic waste discrepancy and providing a pathway to disposition GTCC LLW. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Taylor wave solution for a general equation of state

This document describes a solution procedure for calculating the Taylor wave behind an unsupported Chapman–Jouguet (CJ) detonation in planar, cylindrical, and spherical geometries given a general equation of state. The resulting semi-analytic solution can be utilized to examine new equation of state models for detonation products and during the verification of hydrodynamic codes. The governing partial differential equations are reduced to ordinary differential equations in both characteristic and self-similar forms. The first-order systems corresponding to each geometry are amenable to solution numerically using commonly available methods. A difficulty arises at the CJ point in radial coordinates where the similarity equations become singular. Two separate strategies are proposed to integrate the first-order system. The first one uses an asymptotic approximation near the CJ point that can be used to perturb the boundary conditions. The second one applies a change of variables which removes the singularity at the expense of an additional equation to be integrated. A test problem is provided for the Davis products equation of state to illustrate the qualitative features of the Taylor wave in each geometric configuration and compared with a Lagrangian hydrodynamics research code. A Python code listing gives an implementation using the SciPy library to assists users in generating the results.

97 MATHEMATICS AND COMPUTING↗