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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 91 records · Page 5

Blockchain-Enabled Cyber-Secure Microgrid Control Using Consensus Algorithm

This paper proposes a distributed control method based on a consensus algorithm for distributed energy resources (DERs) using blockchain as a secure communication medium for cyber resilience. Each DER communicates with a local blockchain server that is maintained by the distributed ledger technology to allow for securely sharing local measurements among neighbouring assets to achieve the global control objectives, i.e., voltage and frequency regulation as well as accurate power sharing among the DERs, including collective grid-forming capability. To prove that the distributed control can retain system stability under a blockchain-induced variable communication delay, Lyapunov function-based stability analysis is carried out. This paper demonstrates the concept on an 11-bus test case developed in MATLAB Simulink, which has been modified from the IEEE 9-bus test case, to study dynamic operations of the five inverter-based DERs working with a blockchain-induced variable delay. The results validate the superior performance of the proposed control method, compared to heavily compromised operations of the other test cases without the security measure, affected by heavy communication delays and communication interruptions.

blockchains↗

Washington Clean Energy Fund: Energy Storage System Performance Test Plans and Data Requirements

This report documents the test plans, including detailed duty cycles, used in evaluating the technical performance of five energy storage systems (ESSs) sponsored by the Washington State Clean Energy Fund (CEF). These ESSs were installed at three participating utilities’ (Avista, Snohomish Public Utility District or SnoPUD, and Puget Sound Energy or PSE) designated sites. Under each test plan, a number of baseline and use case tests are defined. This report documents the test plan for each utility, including duty cycles, data and performance reporting requirements. Baseline tests defined in this report mainly focus on determining an initial or reference performance for each ESS, which may be compared with the performance at any later time to assess the state of health of the ESS. Parameter values of a given ESS obtained from baseline tests are applied for different modeling purposes and use case tests. The stored energy capacity test is the first test conducted in the baseline test program, which generates data to calculate round trip efficiency (RTE). The response time and ramp rate tests provide the time required for an ESS to change from zero to full charging/discharging rate and hence the ramp rate, which is important in understanding ESS performance for applications calling for fast response. Internal resistance testing of ESS cells is also conducted in conjunction with the response time and ramp rate tests. Finally, the baseline tests include frequency regulation (FR) and peak shaving (PS) tests based on real-world duty cycles. Upon completion of the baseline tests, use case tests are conducted at each of the storage sites with duty cycles developed to meet the site-specific criteria and conditions. The use cases are grouped according to their intended target benefits within the electric infrastructure topology (e.g., transmission versus distribution). Although an ESS may be located on the low-voltage side of a substation that provides power to a distribution feeder, a use case that addresses bulk power services could still be provided and would be grouped under the transmission or bulk-power benefits. Use cases for ESS applications deep into the distribution circuit would be categorized under the distribution system cases.

25 ENERGY STORAGE↗

WE-DE-201-04: Cross Validation of Knowledge-Based Treatment Planning for Prostate LDR Brachytherapy Using Principle Component Analysis

Purpose: To validate a knowledge-based algorithm for prostate LDR brachytherapy treatment planning. Methods: A dataset of 100 cases was compiled from an active prostate seed implant service. Cases were randomized into 10 subsets. For each subset, the 90 remaining library cases were registered to a common reference frame and then characterized on a point by point basis using principle component analysis (PCA). Each test case was converted to PCA vectors using the same process and compared with each library case using a Mahalanobis distance to evaluate similarity. Rank order PCA scores were used to select the best-matched library case. The seed arrangement was extracted from the best-matched case and used as a starting point for planning the test case. Any subsequent modifications were recorded that required input from a treatment planner to achieve V100>95%, V150<60%, V200<20%. To simulate operating-room planning constraints, seed activity was held constant, and the seed count could not increase. Results: The computational time required to register test-case contours and evaluate PCA similarity across the library was 10s. Preliminary analysis of 2 subsets shows that 9 of 20 test cases did not require any seed modifications to obtain an acceptable plan. Five test cases required fewer than 10 seed modifications or a grid shift. Another 5 test cases required approximately 20 seed modifications. An acceptable plan was not achieved for 1 outlier, which was substantially larger than its best match. Modifications took between 5s and 6min. Conclusion: A knowledge-based treatment planning algorithm for prostate LDR brachytherapy is being cross validated using 100 prior cases. Preliminary results suggest that for this size library, acceptable plans can be achieved without planner input in about half of the cases while varying amounts of planner input are needed in remaining cases. Computational time and planning time are compatible with clinical practice.

60 APPLIED LIFE SCIENCES↗

Hyperbolic Reformulation Approach to Enable Efficient Simulation of Groundwater Flow and Reactive Transport

We apply Cattaneo's relaxation approach to the one-dimensional coupled Boussinesq groundwater flow and advection-diffusion-reaction equations, commonly used in engineering applications to simulate contaminant transport in the subsurface. The diffusion-type governing equations are reformulated as a hyperbolic system, augmented by an equation that can be interpreted as a momentum balance. The hyperbolization enables an efficient unified computation of the primary variable and its gradients, for example piezometric head and unit discharge in the Boussinesq equation. An augmented Roe scheme is used to solve the hyperbolic system. The hyperbolized system of equations is studied in a set of steady state and transient test cases with idealized geometry. These test cases confirm the equivalence of the hyperbolic system to its original formulation. The larger time step size of the hyperbolic equation is verified theoretically by means of a stability analysis and numerically in the test cases. Finally, a reach-scale application of flow and transport across a river meander is considered. This application case shows that the performance of the hyperbolic relaxation approach holds for more realistic groundwater flow and transport problems, relevant to water resources management.

54 ENVIRONMENTAL SCIENCES↗

A Moving Embedded Boundary Approach for the Compressible Navier-Stokes Equations in a Block-Structured Adaptive Refinement Framework

A computational technique has been developed to perform compressible flow simulations involving moving boundaries using an embedded boundary approach within the block-structured adaptive mesh refinement (SAMR) framework of AMReX [1], [91], [92]. We leverage the SAMR capability to obtain quantitatively accurate results whilst using robust, second-order finite volume schemes. A conservative, unsplit, cut-cell approach is utilized and a ghost-cell approach is developed for computing the flux on the moving, embedded boundary faces. A third-order least-squares formulation has been developed to compute the wall velocity gradients, and was found to significantly improve the performance of the solver in terms of the quantitative comparison of surface quantities such as the skin friction coefficient. Various test cases are performed to validate the method, and compared with analytical, experimental, and other numerical results in literature. Inviscid and viscous test cases are performed that span a wide regime of flow speeds - acoustic (harmonically pulsating sphere), smooth flows (expansion fan created by a receding piston) and flows with shocks (shock-cylinder interaction, shock-wedge interaction, pitching NACA 0012 airfoil and shock-cone interaction). A closed system with moving boundaries - an oscillating piston in a cylinder, showed that the percentage error in mass within the system decreases with refinement, demonstrating that the numerical scheme is conservative with grid refinement, but is not discretely conservative. Viscous test cases involve that of a horizontally moving cylinder at Re = 40, an inline oscillating cylinder at Re = 100, and a transversely oscillating cylinder at Re = 185. The judicious use of adaptive mesh refinement with appropriate refinement criteria to capture the regions of interest leads to well-resolved flow features, and good quantitative comparison is observed with the results available in literature.

adaptive refinement↗

Vadose and Saturated Zone Flow and Transport Model Package Report for the Active Trenches of the Low-Level Burial Grounds, Hanford Site, Washington

This model package report (MPR) documents the development of the integrated vadose and saturated zone flow and transport model developed for the performance assessment of Trenches 31 and 34 in the low-level burial grounds (LLBGs). This modeling capability is intended for use in addressing the analysis requirements outlined in DOE O 435.1, Chg 1, Radioactive Waste Management1. The overall objective of the modeling effort is to provide a basis for making informed disposal decisions pertinent to Trenches 31 and 34. The purpose of the MPR is to document the development of the three-dimensional numerical vadose zone and saturated flow and transport model test case and evaluate its adequacy to support the LLBG performance assessment. The purpose is not to present results for DOE 435.1 decision making. The use of the model to perform base case and sensitivity analysis for the LLBG performance assessment, including inputs and results, is documented separately in subsequent environmental calculation files. This report discusses the development and translation of the conceptual model for flow and contaminant transport into the LLBG performance assessment three-dimensional numerical flow and transport model evaluated using the Subsurface Transport Over Multiple Phases (STOMP©) simulator. The development of representative geologic framework is described along with the implementation of waste release models used to represent contaminant release from waste disposed in the trenches. The report also provides the technical basis for specific model parameters and boundary conditions, along with description of modeling assumptions. This MPR includes certain calculations that are necessary to demonstrate the soundness of the model. Results provided by the model include vadose zone and saturated zone flow fields, and estimates of the possible future concentration in groundwater of technetium-99 and iodine-129 as example test cases. As an evaluation of the test cases, the model estimates of current vadose conditions are compared to available and analogous field and laboratory data, and compared to the results from the original performance assessment model (WHC-EP-0645, Performance Assessment for the Disposal of Low-Level Waste in the 200 West Area Burial Grounds 2 ). The features, events, and processes applicable to vadose zone and saturated zone flow and transport model are identified, and representative initial estimates for various parameters are documented. Note that the parameter estimates presented in this MPR are for illustration purposes, and may or may not reflect values selected for eventual performance assessment. Several key topical discussions (i.e., basis for recharge estimates, basis for vadose zone modeling, basis for saturated zone model development, and calibration) are included, which serve as the groundwork for confidence building for the groundwater pathway modeling and results. Numerical simulation results based on an example test case are included to illustrate the use of the combined saturated-unsaturated model in performance assessment calculations. Sensitivity and uncertainty results are not included in this MPR. Those results will be included in future environmental calculation files. The inclusion of the trapezoidal trench geometry and construction details in the finite difference grid introduces some gross simplifications regarding the trench and liner systems. The model test case presented in this MPR includes the assumption that the trench liner system does not affect flow through or around the trenches after the liner system is assumed to fail. This MPR also includes results of other test cases that involve alternate assumptions about how to incorporate the hydraulic effects of the trenches into the vadose zone of the model. These alternate cases do not attempt to account for the presence of the liner system after its assumed failure either. None of these cases is considered to be the base case at this time. Analysis and alternate cases that attempt to account for the presence of the liner system in greater detail, and its effect on flow through and around it, are to be documented in subsequent environmental calculation files. Depending on the results of those analyses and alternate cases, the eventual base case may involve more detailed inclusion of the effects of the liner system hydraulics.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Prototyping the BOPTEST Framework for Simulation-Based Testing of Advanced Control Strategies in Buildings

Advanced control strategies are becoming increasingly necessary in buildings in order to meet and balance requirements for energy efficiency, demand flexibility, and occupant comfort. Additional development and widespread adoption of emerging control strategies, however, ultimately require low implementation costs to reduce payback period and verified performance to gain control vendor, building owner, and operator trust. This is difficult in an already first-cost driven and risk-averse industry. Recent innovations in building simulation can significantly aid in meeting these requirements and spurring innovation at early stages of development by evaluating performance, comparing state-of-the-art to new strategies, providing installation experience, and testing controller implementations. This paper presents the development of a simulation framework consisting of test cases and software platform for the testing of advanced control strategies (BOPTEST - Building Optimization Performance Test). The objectives and requirements of the framework, components of a test case, and proposed software platform architecture are described, and the framework is demonstrated with a prototype implementation and example test case.

Blum, David↗

Creep, Fatigue, and Creep-Fatigue Testing of Alloy 709 Base Metal at ORNL (FY 2021)

The testing activities and research in support of ASME Code qualification of Alloy 709, an advanced austenitic steel, are being carried out at Oak Ridge National Laboratory (ORNL), Argonne National Laboratory, and Idaho National Laboratory. ORNL has been tasked to carry out a subset of the Code Case testing for creep rupture, fatigue and creep-fatigue. The focus of the FY 2021 Code Case testing on Alloy 709 base metal at ORNL includes (1) continuing the long-term creep rupture testing on ESR1100 and AOD1100; (2) adding ESR1150-AH to the creep Code Case testing matrix; and (3) continuing fatigue and creep-fatigue Code Case testing on ESR1150- AH. This report summarizes the status and the preliminary test results of FY 2021 planned Code Case testing at ORNL.

36 MATERIALS SCIENCE↗

Stochastic Particle Real Time Analyzer (SPARTA) Validation and Verification Suite

This report presents the test cases used to verify, validate and demonstrate the features and capabilities of the first release of the 3D Direct Simulation Monte Carlo (DSMC) code SPARTA (Stochastic Real Time Particle Analyzer). The test cases included in this report exercise the most critical capabilities of the code like the accurate representation of physical phenomena (molecular advection and collisions, energy conservation, etc.) and implementation of numerical methods (grid adaptation, load balancing, etc.). Several test cases of simple flow examples are shown to demonstrate that the code can reproduce phenomena predicted by analytical solutions and theory. A number of additional test cases are presented to illustrate the ability of SPARTA to model flow around complicated shapes. In these cases, the results are compared to other well-established codes or theoretical predictions. This compilation of test cases is not exhaustive, and it is anticipated that more cases will be added in the future.

97 MATHEMATICS AND COMPUTING↗

Stochastic Particle Real Time Analyzer (SPARTA) Validation and Verification Suite

This report presents the test cases used to verify, validate and demonstrate the features and capabilities of the first release of the 3D Direct Simulation Monte Carlo (DSMC) code SPARTA (Stochastic Real Time Particle Analyzer). The test cases included in this report exercise the most critical capabilities of the code like the accurate representation of physical phenomena (molecular advection and collisions, energy conservation, etc.) and implementation of numerical methods (grid adaptation, load balancing, etc.). Several test cases of simple flow examples are shown to demonstrate that the code can reproduce phenomena predicted by analytical solutions and theory. A number of additional test cases are presented to illustrate the ability of SPARTA to model flow around complicated shapes. In these cases, the results are compared to other well-established codes or theoretical predictions. This compilation of test cases is not exhaustive, and it is anticipated that more cases will be added in the future.

97 MATHEMATICS AND COMPUTING↗

Intelligent Hierarchical Resilient Operation of Distribution Systems: Implementation and Validation in a Power Hardware-in-the-Loop Simulation Testbed

This paper reports on the structure of a power hardware-in-the-loop (PHIL) simulation testbed that implements, tests, and validates a novel AI-based hierarchical resilient operation model for distribution systems. The testbed implements the central and distributed controllers of the hierarchical resilient operation model and integrates a Digital Real-Time Simulator (DRTS), protective relays, a Real-Time Automation Controller (RTAC), a Software Defined Network (SDN) switch, and a battery energy storage (BES) system. The testbed provides comprehensive real-time visualization and monitoring capability as an advanced situational awareness and operator interface solution. The IEEE 33-node system is used as a test case to test and validate the operation of the model in normal operation and recovery operation after major outages in a fully automated fashion.

Ganjkhani, Mehdi↗

Advanced Distributed Wind Turbine Controls Series: Part 3-Wind Energy in Grid-Connected Deployments – Microgrids, Infrastructure Resilience, and Advanced Controls Launchpad (MIRACL)

In recent years the technical ability and requirement for distributed wind turbines to provide grid support services beyond maximum energy production has increased. Ancillary services leveraged through advance controls of a wind turbine support grid reliability and resilience. One ancillary service that is significant to a grid-connected wind turbine deployment is fault ride through (FRT) in response to the voltage and frequency events in the power system. As part of the Microgrids, Infrastructure Resilience, and Advanced Controls Launchpad (MIRACL) this paper demonstrates, through desktop simulations, the wind turbine's FRT capabilities to support stable grid operation. We establish that the wind turbine models exceed FRT performance requirements stipulated in IEEE 1547-2018, regarding interconnection and interoperability of distributed energy resources. Utilizing a standalone CART2 (600 kW) wind turbine connected to the NREL's Flatirons Campus grid, we study voltage and frequency FRT utilizing various test cases. One of the test cases under study is a Category III voltage fault defined in IEEE 1547-2018 and derived from CA Rule 21. Some distributed wind turbines were unable to connect to the grid following the Rule 21 enforcement in California. Even if this is not a general requirement elsewhere, the grid codes might evolve in this direction. This study illustrates how a distributed wind turbine can provide some of these FRT services and enable a pathway toward a higher contribution of renewable energy in a distribution grid.

17 WIND ENERGY↗

SCALE 6.2 Lattice Physics Performance Assessment

The US Nuclear Regulatory Commission relies on the lattice physics analysis capabilities of the SCALE code system to perform confirmatory licensing analyses. Either SCALE lattice physics code—TRITON/NEWT or Polaris—can be used to generate cross section data used by the PARCS nodal core simulator for full-core neutronics calculations. This report presents an assessment of the accuracy of SCALE lattice physics codes for preparation of lattice physics data that are used to support simulator codes such as the NRC’s PARCS, for UO 2 -mixed oxide (MOX)/Zr fueled light water reactor (LWR) analyses. Due to the nature of lattice physics calculations, critical reactor experiment benchmarks cannot be modeled in explicit detail in a lattice physics code. However, this limitation does not mean that these measurement data are not usable for lattice physics studies. Therefore, either geometry approximations or axial buckling must be implemented to determine the critical water height. These modeling limitations have led to development of a three-phase assessment strategy. In the first phase, selected critical experiment benchmarks are modeled using the SCALE 3D continuous-energy (CE) Monte Carlo (MC) code KENO, which is the most rigorous neutron transport method available in SCALE, with no approximations in the spatial, angle, or energy treatments. Biases and statistical uncertainties in quantities of interest such as k eff and pin power distributions are determined by comparing CE KENO results to experimental data. This first phase in the accuracy assessment is to demonstrate and establish the use of CE KENO as a reference solution for the second phase. In the second phase, 14 numerical test suites are used to compare SCALE lattice physics calculations with CE KENO as a reference solution. In the third phase, SCALE lattice physics depletion calculations are performed, and the spent fuel isotopic results are compared with available radiochemical assay measurements. Isotopic measurement comparisons provide quantitative assessment of isotopic density distribution predictions with the depletion models in SCALE lattice physics codes. This report documents results for all test suites. The assessment was performed using standard production techniques unless otherwise noted. Both TRITON/NEWT and Polaris exhibited acceptable accuracy for most test cases. For the few test cases in which acceptable accuracy criteria were not met, further code and data development are planned. The computer codes used in this assessment are as follows: SCALE 6.2 rev19189 (pre-release of 6.2.1) was used for CE KENO, TRITON/NEWT and Polaris (PWR only) calculations; SCALE 6.2.2 was used for Polaris calculations to address several updates in support of support boiling water reactor (BWR) lattice geometries. For this work, there is no difference between SCALE 6.2.1 and SCALE 6.2.2 beyond the inclusion of the Polaris BWR analysis capability; The ENDF/B-VII.1 continuous energy and 252 group libraries deployed in SCALE 6.2 were generated with AMPX 6.2 that is distributed with SCALE.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

HDTS 2017.0 Testing and verification document

This report is a continuation of the series of Hunter Dose Tracking System (HDTS) Quality Assurance documents including (Foley and Powell, 2010; Dixon, 2012). In this report we have created a suite of automated test cases and a system to analyze the results of those tests as well as documented the methodology to ensure the field system performs within specifications. The software test cases cover all of the functions and interactions of functions that are practical to test. With the developed framework, if software defects are discovered, it will be easy to create one or more test cases to reproduce the defect and ensure that code changes correct the defect. These tests con rm HDTS version 2017.0 performs according to its specifications and documentation and that its performance meets the needs of its users at the Savannah River Site.

97 MATHEMATICS AND COMPUTING↗

A moist aquaplanet variant of the Held–Suarez test for atmospheric model dynamical cores

Abstract. A moist idealized test case (MITC) for atmospheric model dynamical cores is presented. The MITC is based on the Held–Suarez (HS) test that was developed for dry simulations on “a flat Earth” and replaces the full physical parameterization package with a Newtonian temperature relaxation and Rayleigh damping of the low-level winds. This new variant of the HS test includes moisture and thereby sheds light on the nonlinear dynamics–physics moisture feedbacks without the complexity of full-physics parameterization packages. In particular, it adds simplified moist processes to the HS forcing to model large-scale condensation, boundary-layer mixing, and the exchange of latent and sensible heat between the atmospheric surface and an ocean-covered planet. Using a variety of dynamical cores of the National Center for Atmospheric Research (NCAR)'s Community Atmosphere Model (CAM), this paper demonstrates that the inclusion of the moist idealized physics package leads to climatic states that closely resemble aquaplanet simulations with complex physical parameterizations. This establishes that the MITC approach generates reasonable atmospheric circulations and can be used for a broad range of scientific investigations. This paper provides examples of two application areas. First, the test case reveals the characteristics of the physics–dynamics coupling technique and reproduces coupling issues seen in full-physics simulations. In particular, it is shown that sudden adjustments of the prognostic fields due to moist physics tendencies can trigger undesirable large-scale gravity waves, which can be remedied by a more gradual application of the physical forcing. Second, the moist idealized test case can be used to intercompare dynamical cores. These examples demonstrate the versatility of the MITC approach and suggestions are made for further application areas. The new moist variant of the HS test can be considered a test case of intermediate complexity.

54 ENVIRONMENTAL SCIENCES↗

Comparison of Full-Field and Integrated CFD Convergence Based on Richardson Extrapolation

This work investigated the usefulness of Richardson extrapolation--based discretization error estimates across all points in a solution field to produce a spatial convergence field for a computational fluid dynamics (CFD) simulation. The presented work used previously developed methods for Richardson extrapolation to compute the convergence orders of a CFD simulation at all points of the base (coarsest) mesh solution. Three test cases of increasing complexity were considered: Poiseuille flow, incompressible flow around a sharp corner, and transonic flow over an RAE 2822 airfoil. These test cases highlighted the potential of the proposed method to identify error sources and their relation to the model system-response-quantity convergence orders. However, these test cases also revealed the immaturity of the proposed method stemming from the unreliability of computing observed convergence orders at single points. Nonetheless, the test cases highlighted that the observed convergence orders allow for a more accurate diagnosis of constructive and destructive error transport than mesh pair error estimates. In the long run, the proposed method can be a tool for developing efficient and advanced error management strategies like adaptive mesh refinement.

Weinmeister, Justin↗

Maxine Onsite: Estimating Dose from Chronic Atmospheric Radioactive Releases

Maxine Onsite: Developed to estimate dose to individuals who are working onsite but are not site employees. Follows the methodologies discussed in US NRC Regulatory Guides 1.109 and 1.111 to determine dose from a chronic atmospheric release. Determines the dose given relative air concentrations and deposition concentrations as input. We look at four locations onsite that may be accessed by members of the public. To show compliance with the EPA and DOE public dose limit of 10 mrem/yr, determining who is a member of the public or a worker onsite is necessary. SRS has defined a member of the public for NESHAPS and DOE O 458.1. Maxine Onsite runs on Microsoft Windows Operating System through a Microsoft Excel spreadsheet. Input from the user includes parameters that are variable such as air concentrations, and fixed, such as distance to the receptor and elemental iodine fraction. Maxine Onsite was developed from Maxine which is a program meant to calculate dose to the MEI via three pathways, external, inhalation, and ingestion. Maxine Onsite is meant for looking at the exposure through the external and inhalation pathways only, no local food production onsite. The ways that Maxine Onsite is used to calculate the dose to the MEI includes the following: - Determining the respective air concentration values at each location using distances from the release stack; - Breathing rates for the MEI; - Determining the amount of time the MEI is outside; - Determining the plume travel time. The following relative air and ground deposition values for proper execution of the spreadsheet come from MAXDOSE-SR and are needed to accurately determine the dose to the MEI: relative air concentration, relative air concentration decayed by 2.26 days, relative air concentration decayed and depleted for 8 days, and relative deposition. Test cases were designed, developed, and executed to determine the accuracy of Maxine Onsite, which were verified additionally through hand calculations. Several changes were made for testing, including varying air concentrations, distances, breathing rates, and shielding factors. Each test case was then verified through hand calculations to assure the accuracy of the calculated doses. The results from the test cases, as well as the default parameters, can be used for benchmarking Maxine Onsite in the future. Maxine Onsite performs as expected and produces correct and accurate results at each of the different locations onsite (TRL, B-Area Barracks, SRELCC, and Gunsite 51) for varying test cases. The input required by the user is minimal and includes the results of the dose to the MEI on the first page for ease of access. Future plans for Maxine Onsite include adding in the ingestion pathway and adding in atmospheric dispersion estimates to the spreadsheet.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗