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At least 1,261 records · Page 70

Full Scale 3D Computational Model of the Industrial -Scale Coal Fired Boiler Performance for Temperature Sensor Installation Guidance

Abstract Nearly 30% of the electricity is generated by using coal as the primary fuel in the US. One of the major concerns in coal-fired power plants is the failure of boiler tubes that leads to unscheduled maintenance and has a huge economical and societal impact. High temperature flue gas along with ash pass over the boiler tubes, which over time leads to tube failure. Therefore, developing temperature sensors for harsh environments and install them for temperature sensing and boiler tube lifetime prediction is an urgent need. On the side of sensor development, the location of the sensor installation is important for stable sensing performance and easy calibration. In this study, computational fluid dynamics and heat transfer modeling are adopted to establish a full-scale 3-dimensional model of a coal-fired boiler to investigate the flue gas temperature distribution within the boiler and identify the proper locations for sensor installation. We proposed three criteria to select the temperature sensor installation location: (1) select the boiler tube panel away from the sidewalls, (2) select the boiler tube section closer to the top wall of the boiler; and (3) select the boiler tube on the back of the boiler panel (not directly facing the flue gas flow). In these regions, the flue gas temperature is stable, providing an ideal environment for stable temperature sensing and calibration.

Gupta, Tanuj↗

Exascale Virtualized and Programmable Distributed Cyber Resource Control: Final Scientific Technical Report

Extreme-science drives the need for distributed exascale processing and communications that are carefully, yet flexibly, managed. Exponential growth of data for scientific simulations, experimental data, collaborative data analyses, remote visualization and GRID computing requirements of scientists in fields as diverse as high energy physics, climate change, genomics, fusion, synchrotron radiation, material science, medicine, and other scientific disciplines cannot be accommodated by simply applying existing transport protocols to faster pipes. Further, scientific challenges today demand diverse research teams, heightening the need for and increasing the complexity of collaboration. To address these issues within the network layer and physical layer, we have performed a number of research activities surrounding effective allocation and management of elastic optical network (EON) resources, particularly focusing on FlexGrid transponders. FlexGrid transponders support the opportunity to build Layer-1 connections at a wide range of bandwidths and to reconfigure them rapidly. The new flexibility supports complex new ways of using the physical layer that must be carefully managed and hidden from the scientist end-users. FlexGrid networks utilize flexible (or elastic) spectral bandwidths for each data link without using fixed wavelength grids. The flexibility in spectrum allocation brings many appealing features to network operations. Current networks are designed for the worst case impairments in transmission performance and the assigned spectrum is over-provisioned. In contrast, the FlexGrid networks can operate with the highest spectral efficiency and minimum bandwidth for the given traffic demand while meeting the minimum quality of transmission (QoT) requirement. Two primary focuses of our research are: (1) resource and spectrum allocation (RSA) for IP traffic over EONs, and (2) RSA for cross-domain optical networks. Previous work concentrates primarily on large file transfers within a single domain. Adding support for IP traffic changes the nature of the RSA problem: instead of choosing to accept or deny each request for network support, IP traffic is inherently elastic and thus lends itself to a bandwidth maximization formulation. We developed a number of algorithms that could be easily deployed within existing and new FlexGrid networks, leading to networks that better support scientific collaboration. Cross-domain RSA research is essential to support large-scale FlexGrid networks, since configuration information is generally not shared or coordinated across domains. The results presented here are in their early stages. They are technically feasible and practical, but still require coordination among organizations and equipment owners and a higher-layer framework for managing network requests.

42 ENGINEERING↗

PDEMOD: Software for control/structures optimization

Because of the possibility of adverse interaction between the control system and the structural dynamics of large, flexible spacecraft, great care must be taken to ensure stability and system performance. Because of the high cost of insertion of mass into low earth orbit, it is prudent to optimize the roles of structure and control systems simultaneously. Because of the difficulty and the computational burden in modeling and analyzing the control structure system dynamics, the total problem is often split and treated iteratively. It would aid design if the control structure system dynamics could be represented in a single system of equations. With the use of the software PDEMOD (Partial Differential Equation Model), it is now possible to optimize structure and control systems simultaneously. The distributed parameter modeling approach enables embedding the control system dynamics into the same equations for the structural dynamics model. By doing this, the current difficulties involved in model order reduction are avoided. The NASA Mini-MAST truss is used an an example for studying integrated control structure design.

Taylor, Lawrence W., Jr.↗

Comparative study of turbulence models in predicting hypersonic inlet flows

A numerical study was conducted to analyze the performance of different turbulence models when applied to the hypersonic NASA P8 inlet. Computational results from the PARC2D code, which solves the full two-dimensional Reynolds-averaged Navier-Stokes equation, were compared with experimental data. The zero-equation models considered for the study were the Baldwin-Lomax model, the Thomas model, and a combination of the Baldwin-Lomax and Thomas models; the two-equation models considered were the Chien model, the Speziale model (both low Reynolds number), and the Launder and Spalding model (high Reynolds number). The Thomas model performed best among the zero-equation models, and predicted good pressure distributions. The Chien and Speziale models compared very well with the experimental data, and performed better than the Thomas model near the walls.

Kapoor, Kamlesh↗

Comparative study of turbulence models in predicting hypersonic inlet flows

A numerical study was conducted to analyze the performance of different turbulence models when applied to the hypersonic NASA P8 inlet. Computational results from the PARC2D code, which solves the full two-dimensional Reynolds-averaged Navier-Stokes equation, were compared with experimental data. The zero-equation models considered for the study were the Baldwin-Lomax model, the Thomas model, and a combination of the Baldwin-Lomax and Thomas models; the two-equation models considered were the Chien model, the Speziale model (both low Reynolds number), and the Launder and Spalding model (high Reynolds number). The Thomas model performed best among the zero-equation models, and predicted good pressure distributions. The Chien and Speziale models compared wery well with the experimental data, and performed better than the Thomas model near the walls.

Kapoor, Kamlesh↗

Three-D Flow Analysis of the Alternate SSME HPOT TAD

This paper describes the results of numerical flow analyses performed in support of design development of the Space Shuttle Main Engine Alternate High Pressure Oxidizer Turbine Turn-around duct (TAD). The flow domain has been modeled using a 3D, Navier-Stokes, general purpose flow solver. The goal of this effort is to achieve an alternate TAD exit flow distribution which closely matches that of the baseline configuration. 3D Navier Stokes CFD analyses were employed to evaluate numerous candidate geometry modifications to the TAD flowpath in order to achieve this goal. The design iterations are summarized, as well as a description of the computational model, numerical results and the conclusions based on these calculations.

Kubinski, Cheryl A.↗

Concurrent Probabilistic Simulation of High Temperature Composite Structural Response

A computational structural/material analysis and design tool which would meet industry's future demand for expedience and reduced cost is presented. This unique software 'GENOA' is dedicated to parallel and high speed analysis to perform probabilistic evaluation of high temperature composite response of aerospace systems. The development is based on detailed integration and modification of diverse fields of specialized analysis techniques and mathematical models to combine their latest innovative capabilities into a commercially viable software package. The technique is specifically designed to exploit the availability of processors to perform computationally intense probabilistic analysis assessing uncertainties in structural reliability analysis and composite micromechanics. The primary objectives which were achieved in performing the development were: (1) Utilization of the power of parallel processing and static/dynamic load balancing optimization to make the complex simulation of structure, material and processing of high temperature composite affordable; (2) Computational integration and synchronization of probabilistic mathematics, structural/material mechanics and parallel computing; (3) Implementation of an innovative multi-level domain decomposition technique to identify the inherent parallelism, and increasing convergence rates through high- and low-level processor assignment; (4) Creating the framework for Portable Paralleled architecture for the machine independent Multi Instruction Multi Data, (MIMD), Single Instruction Multi Data (SIMD), hybrid and distributed workstation type of computers; and (5) Market evaluation. The results of Phase-2 effort provides a good basis for continuation and warrants Phase-3 government, and industry partnership.

Abdi, Frank↗

Transient Three-Dimensional Side Load Analysis of Out-of-Round Film Cooled Nozzles

The objective of this study is to investigate the effect of nozzle out-of-roundness on the transient startup side loads at a high altitude, with an anchored computational methodology. The out-of-roundness could be the result of asymmetric loads induced by hardware attached to the nozzle, asymmetric internal stresses induced by previous tests, and deformation, such as creep, from previous tests. The rocket engine studied encompasses a regeneratively cooled thrust chamber and a film cooled nozzle extension with film coolant distributed from a turbine exhaust manifold. The computational methodology is based on an unstructured-grid, pressure-based computational fluid dynamics formulation, and a transient inlet history based on an engine system simulation. Transient startup computations were performed with the out-of-roundness achieved by four different degrees of ovalization: one perfectly round, one slightly out-of-round, one more out-of-round, and one significantly out-of-round. The results show that the separation-line-jump is the peak side load physics for the round, slightly our-of-round, and more out-of-round cases, and the peak side load increases as the degree of out-of-roundness increases. For the significantly out-of-round nozzle, however, the peak side load reduces to comparable to that of the round nozzle and the separation line jump is not the peak side load physics. The counter-intuitive result of the significantly out-of-round case is found to be related to a side force reduction mechanism that splits the effect of the separation-line-jump into two parts, not only in the circumferential direction and most importantly in time.

Wang, Ten-See↗

Parallel Asynchronous Distributed-Memory Maximal Independent Set Algorithm with Work Ordering

The maximal independent set (MIS) graph problem arises in many applications such as computer vision, information theory, molecular biology, and process scheduling. The growing scale of graph data suggests the use of distributed memory hardware as a cost-effective approach to providing necessary compute and memory resources. Existing distributed memory parallel MIS algorithms rely on synchronous communication and use techniques such as subgraph computations. In this paper, we present an asynchronous distributed-memory parallel graph algorithm that relies on a virtual directed acyclic graph (DAG) that is created during the algorithm execution. We introduce two additional algorithms that save computations by ordering generated work. The first algorithm applies ordering globally to reduce computations, and the second algorithm applies ordering locally at the level of threads to minimize the synchronization overhead. We use two different implementations of Luby’s algorithm variants as baseline to compare the performance of the presented algorithms: (1) vertex-centric Luby A and Luby B implementations, and (2) the CombBLAS linear-algebra Luby A implementation. Results show that proposed algorithms outperform both implementations of Luby algorithms, especially in distributed execution. Furthermore, we show that for low-diameter graphs the algorithm that applies global ordering scales better than other algorithms and for high diameter graphs the original asynchronous algorithm and thread-level ordering algorithm show better performance.

maximal independent set (MIS), distributed memory ↗

Comparison of Mixing Characteristics for Several Fuel Injectors at Mach 8, 12, and 15 Hypervelocity Flow Conditions

CFD analysis is presented of the mixing characteristics and performance of three fuel injectors at flight Mach numbers of 8, 12, and 15. The Reynolds-averaged simulations (RAS) were carried out using the VULCAN-CFD solver. The high Mach number flow conditions match those of the experiments conducted as a part of the Enhanced Injection and Mixing Project (EIMP) at the NASA Langley Research Center. The EIMP aims to investigate scramjet fuel injection and mixing physics, improve the understanding of underlying physical processes, and develop enhancement strategies relevant to flight Mach numbers greater than 8. The injectors include a fuel placement device, a strut, and a fluidic vortical mixer, a ramp. These fuel injectors accomplish the necessary task of distributing and mixing fuel into the supersonic cross-flow, albeit via different strategies. For comparison, a flush-wall injector is also included. This type of injector generally represents the simplest method of introducing fuel into a scramjet combustor. The three injectors represent the baseline configurations of the EIMP experiments. The mixing parameters of interest, such as mixing efficiency and total pressure recovery, are computed from the RAS and compared for the three flight conditions and injector configurations. In addition to mixing efficiency and total pressure recovery, the combustion efficiency and thrust potential are also computed for the reacting simulations. Plotting the total pressure recovery and thrust potential as a function of mixing efficiency provides added insight into critical aspects of combustor performance as the flight condition and injector type are varied.

Shenoy, Rajiv R.↗

A multi-platform evaluation of the randomized CX low-rank matrix factorization in Spark

We investigate the performance and scalability of the randomized CX low-rank matrix factorization and demonstrate its applicability through the analysis of a 1TB mass spectrometry imaging (MSI) dataset, using Apache Spark on an Amazon EC2 cluster, a Cray XC40 system, and an experimental Cray cluster. We implemented this factorization both as a parallelized C implementation with hand-tuned optimizations and in Scala using the Apache Spark high-level cluster computing framework. We obtained consistent performance across the three platforms: using Spark we were able to process the 1TB size dataset in under 30 minutes with 960 cores on all systems, with the fastest times obtained on the experimental Cray cluster. In comparison, the C implementation was 21X faster on the Amazon EC2 system, due to careful cache optimizations, bandwidth-friendly access of matrices and vector computation using SIMD units. We report these results and their implications on the hardware and software issues arising in supporting data-centric workloads in parallel and distributed environments.

Gittens, Alex↗

OpenSHMEM Implementation of IOR Benchmark

The benchmarking effort within the Computational Research & Development Programs at the Oak Ridge National Laboratory (ORNL) seeks to design and enable High Performance Computing (HPC) benchmarks and test suites. The work described in this report is a part of the effort focusing on the comparison and analysis of OpenSHMEM implementations using the Interleave Or Random (IOR) software for benchmarking parallel file system using POSIX, MPIIO, or HDF5 interfaces. We describe the effort to emulate the MPIIO parallel collective capabilities in the IOR benchmark using OpenSHMEM communication. One development effort was in emulating the MPI derived datatype used in the read/write operations and in setting the file view. Another effort was in implementing an internal cache in OpenSHMEM distributed shared memory to facilitate global collective I/O operations. Experiments comparing collective I/O in MPIIO implementations with the OpenSHMEM implementations were performed on the SGI Turing Cluster and the Cray XK7 Titan supercomputer at the Oak Ridge Leadership Computing Facility (OLCF). The preliminary results suggest that on the Cray XK7 Titan, the MPIIO implementations obtained higher write performance and the OpenSHMEM version obtained slightly higher read performance. On the SGI Turing Cluster, the MPIIO implementations obtained slightly higher performance over the OpenSHMEM implementations on large files.

97 MATHEMATICS AND COMPUTING↗

Introduction to Special Section: Machine Learning for Image-based Geologic Interpretation

Image-based geological interpretation has been a labor-intensive and time-consuming process because it requires well-trained geoscientists to identify geological structures, features, and textures from various types of images. These images include scanning electron microscopic images, optical microscopic images, optical photos, resistivity images, seismic volumes, remote-sensing images, etc. With fast-evolving machine learning (ML) technology and computing power in recent decades, computers can achieve nearhuman-level to super-human-level performance with scalable high efficiency in the computer vision field. These technological revolutions facilitated image-based geological interpretation in petroleum exploration and production. For example, a fault picking method applied to 3-D seismic volume data using deep learning can achieve superior performance in comparison to conventional auto-picking methods. In addition, under the new normal of low oil prices, the petroleum industry seeks cost-effective strategies such as automating traditionally labor-intensive processes. Nevertheless, the potential of applying ML to geological image interpretation is still facing a few key challenges including data scarcity, data distribution, poor data and/or label quality, data leakage, learning algorithms, model architecture, training methodologies, testing and evaluation metrics, hyper-parameters optimization, model drift, production deployment, and the like.

58 GEOSCIENCES↗

The Pulsed Fission-Fusion (PUFF) Concept for Deep Space Exploration and Terrestrial Power Generation

This team is exploring a modified Z-pinch geometry as a propulsion system, imploding a liner of liquid lithium onto a pellet containing both fission and fusion fuel. The plasma resulting from the fission and fusion burn expands against a magnetic nozzle, for propulsion, or a magnetic confinement system, for terrestrial power generation. There is considerable synergy in the concept; the lithium acts as a temporary virtual cathode, and adds reaction mass for propulsion. Further, the lithium acts as a radiation shield against generated neutrons and gamma rays. Finally, the density profile of the column can be tailored using the lithium sheath. Recent theoretical and experimental developments (e.g. tailored density profile in the fuel injection, shear stabilization, and magnetic shear stabilization) have had great success in mitigating instabilities that have plagued previous fusion efforts. This paper will review the work in evaluating the pellet sizes and z-pinch conditions for optimal PuFF propulsion. Trades of pellet size and composition with z-pinch power levels and conditions for the tamper and lithium implosion are evaluated. Current models, both theoretical and computational, show that a z-pinch can ignite a small (~1 cm radius) fission-fusion target with significant yield. Comparison is made between pure fission and boosted fission targets. Performance is shown for crewed spacecraft for high speed Mars round trip missions and near interstellar robotic missions. The PuFF concept also offers a solution for terrestrial power production. PuFF can, with recycling of the effluent, achieve near 100% burnup of fission fuel, providing a very attractive power source with minimal waste. The small size of PuFF relative to today's plants enables a more distributed power network and less exposure to natural or man-made disruptions.

Adams, Robert↗

Minimizing Error Potential Using Computer Applications - 18498

Many Savannah River Site (SRS) liquid waste facility operations depend upon repetitive engineering calculations and operator actions. Although these calculations and actions are formalized in technical reports and paper procedures, they can still be vulnerable to data entry errors, calculation errors, equipment alignment errors, and occasional changes caused by different people performing these activities. Savannah River Remediation (SRR) is using computer automation to reduce these error precursors by standardizing repetitive calculations and by performing plant alignment checks for repetitive operation processes. Data entry can be automated, calculation methodologies can be standardized, and computers can check to see that predefined plant conditions exist before equipment operation. In addition to improving quality, the time required for these activities to generate technical reports, to perform independent reviews, and to perform equipment alignment checks can be significantly reduced. In the case of operator-performed calculations, error precursors involve distractions that can occur over a multi-page paper procedure, confusing displays and controls from equipment, mathematical errors, complacency, and unfamiliarity with the procedure among many others. Repetitive engineering calculations suffer from similar error precursors and are often compounded by high workloads, lack of proficiency, lack of standard methodology, mental shortcuts, and biases. Web-based computer applications can eliminate many of these precursors through standardization. Calculation methods are fixed, inputs are fixed, and computer checks can highlight potentially wrong inputs and outputs. Automated calculations are performed almost instantaneously once input is provided. Operators and engineers can spend more time focusing on the results than on the process to achieve the results. Similarly, when operators use repetitive procedures involving equipment manipulation, the same error precursors apply. Automated operation sequences and equipment checks can be programmed into the distributed control system to provide standard operating processes that reduce and eliminate error precursors. This paper describes how SRR incorporates Human Performance Improvement (HPI) principles when automating calculations and operation processes. Computer applications will be reviewed in detail, highlighting the software development life-cycle that includes requirements gathering, prototyping, design, development, testing, and implementation. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

MCNP6 Study of Spatial Fidelity Required for ROC Curve Convergence

The detection of special nuclear material at ports and borders is one of the primary missions of the Department of Homeland Security's (DHS) Domestic Nuclear Detection Office (DNDO). In support of this mission a large-scale modeling and simulation effort has been undertaken with the goal of providing a comprehensive tool-kit that addresses the complexity of problems involved with developing and maintaining technologies deployed to global nuclear detection architecture (GNDA) nodes. An important objective of DNDO's mission is to characterize detector system performance before deployment. In the effort to support this mission, the latest version of MCNP has been used to perform detectability studies of highly enriched uranium (HEU) to populate a database that will be used for the tool-kit. The characterization method used in the implementation of the database is the receiver operating characteristic (ROC). A ROC curve shows the limits of detectability of a given system as well as an overall metric of the efficacy of a detection system. This is accomplished by comparing total detector count distributions to the count distribution produced by background alone. For an in-depth explanation of the theory behind the MCNP production of ROC curves please refer to the paper, 'How To Use The Receiver Operating Characteristic Tally Option in MCNP6'. Building a useful database requires an expansive parameter space. The current tool-kit use nine parameters, which if varied with just 5 options each, results in nearly two million simulations to run. Depending on the set of parameters these simulations can take a few hours or a few weeks to complete. This computational cost necessitates the use of scaling algorithms to interpolate between the data contained in the database. The tool-kit employs a discrete event method to simulate the movement and detector response of special nuclear material (SNM) through a GNDA node. Given the nature of a discrete event simulation, constant motion of SNM must be split up in to discrete spatial detection points. The fidelity required of the spatial splitting to achieve a properly converged answer is investigated here for a neutron detection system. The detector used was a SNAP-3 neutron detector in front of a sphere of SNM in the presence of background radiation. A parameter study has been performed to determine the spatial fidelity required for ROC curve convergence for moving objects in a discrete event simulator. It appears that 5 points is the minimum number of detection points with 7 points needed for one of the parameter sets. The convergence worsens with increases to detection length but appears to improve with increasing detector distance. These results will help future work involving quantifying the accuracy based on given tolerances and parameters. (authors)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Generic hypersonic vehicle performance model

An integrated computational model of a generic hypersonic vehicle was developed for the purpose of determining the vehicle's performance characteristics, which include the lift, drag, thrust, and moment acting on the vehicle at specified altitude, flight condition, and vehicular configuration. The lift, drag, thrust, and moment are developed for the body fixed coordinate system. These forces and moments arise from both aerodynamic and propulsive sources. SCRAMjet engine performance characteristics, such as fuel flow rate, can also be determined. The vehicle is assumed to be a lifting body with a single aerodynamic control surface. The body shape and control surface location are arbitrary and must be defined. The aerodynamics are calculated using either 2-dimensional Newtonian or modified Newtonian theory and approximate high-Mach-number Prandtl-Meyer expansion theory. Skin-friction drag was also accounted for. The skin-friction drag coefficient is a function of the freestream Mach number. The data for the skin-friction drag coefficient values were taken from NASA Technical Memorandum 102610. The modeling of the vehicle's SCRAMjet engine is based on quasi 1-dimensional gas dynamics for the engine diffuser, nozzle, and the combustor with heat addition. The engine has three variable inputs for control: the engine inlet diffuser area ratio, the total temperature rise through the combustor due to combustion of the fuel, and the engine internal expansion nozzle area ratio. The pressure distribution over the vehicle's lower aft body surface, which acts as an external nozzle, is calculated using a combination of quasi 1-dimensional gas dynamic theory and Newtonian or modified Newtonian theory. The exhaust plume shape is determined by matching the pressure inside the plume, calculated from the gas dynamic equations, with the freestream pressure, calculated from Newtonian or Modified Newtonian theory. In this manner, the pressure distribution along the vehicle after body expansion surface is then determined. The aerodynamic modeling, the engine modeling, and the exhaust plume analysis are described in more detail. A description of the computer code used to perform the above calculations is given and an input/output example is then given. The computer code is available on a Macintosh floppy disk.

Chavez, Frank R.↗

Impact of Time Dependent Reactor and Sensor Physics on Core Power Synthesis

Online synthesis of the power distribution is critical in the operation and control of nuclear power reactors to ensure that the core is operating within safety margins, and to provide essential knowledge associated with the burnup of the fuel. In light water reactors (LWRs), power synthesis is achieved by using some a priori knowledge of the state of the reactor core and updating based on the signals coming from in-core sensors—namely, self-powered neutron detectors (SPNDs). This report aims to study the effects of fuel burnup and sensor degradation on the ability to accurately synthesize the power distribution in a LWR. Several modeling tools were used to simulate power synthesis based on the responses of SPNDs, with emitters made out of Rh or V. A representative pressurized water reactor low-enriched uranium (LEU) core was modeled using the Polaris/Purdue Advanced Reactor Core Simulator (PARCS) approach. The Monte Carlo N-Particle Transport 6 (MCNP6) code was used, as well, to calculate response functions between different segments of fuel to individual SPNDs; this is a crucial parameter for power synthesis. The Oak Ridge Isotope GENeration (ORIGEN) package in the Standardized Computer Analyses for Licensing Evaluation (SCALE) code was used to model the time-dependent isotopic transmutation in the SPND emitters. All these data were fed into a custom code that enacted the point-based iterative (PBI) method to simulate power synthesis. Developmental work was also performed on high-fidelity SPND models in the GEometry ANd Tracking 4 (Geant4) code, which enables higher-accuracy modeling of the current responses from SPNDs. In this work, five sets of time-dependent power synthesis test cases were conducted. In these test cases, systematic changes in the input conditions enabled an analysis of the effect of (1) slightly inaccurate a priori power distribution assumptions with respect to fuel burnup, (2) highly inaccurate a priori assumptions with respect to fuel burnup (such that burnup is not included in the a priori assumed distribution), and (3) differences between Rh and V SPNDs in terms of downstream consequences of the transmutation in the emitters. The authors discovered that one may permissibly have slightly inaccurate a priori assumptions of the fuel burnup (such that the level of burnup may be slightly under- or over-approximated by the accumulated burnup in approximately 9.3 full power days), but to not account for burnup at all in the a priori assumption leads to severe levels of error, approaching 25% at maximum. The authors also discovered that V SPNDs are extraordinarily robust in the low-enriched uranium fuel cycle considered in this modeling work, whereas Rh SPNDs undergo significant transmutation that can result in large errors in the synthesized power distribution.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗