The purpose of this thesis is to examine the accuracy of the RAPID (Real-Time Analysis for Particle Transport and In-situ Detection) eigenvalue algorithm based on a few problems from the ICSBEP (International Criticality Safety Benchmark Evaluation Project) Handbook. RAPID is developed based on the MRT (Multi-Stage Response-Function Transport) methodology and it uses the fission matrix (FM) method for performing eigenvalue calculations. RAPID has already been benchmarked based on several real-world problems including spent fuel pools and casks, and reactor cores. This thesis examines the accuracy of the RAPID eigenvalue algorithm for modeling the physics of problems with unique geometric configurations. Four problems were selected from the ICSBEP Handbook; these problems differ by their unique configurations which can effectively examine the capability of the RAPID code system. For each problem, a reference Serpent Monte Carlo calculation has been performed. Using the same Serpent model in the pRAPID (pre- and post-processing for RAPID) utility code, a series of fixed-source Serpent calculations are performed to determine spatially-dependent FM coefficients. RAPID calculations are performed using these FM coefficients to obtain the axially-dependent, pin-wise fission density distribution and system eigenvalue for each problem. It is demonstrated that the eigenvalues calculated by RAPID and Serpent agree with the experimental data within the given experimental uncertainty. Further, the detailed 3-D pin-wise fission density distribution obtained by RAPID agrees with the reference prediction by Serpent which itself has converged to less than 1% weighted uncertainty. While achieving accurate results, RAPID calculations are significantly faster than the reference Serpent calculations, with a calculation time speed-up of between 4x and 34x demonstrated in this thesis. In addition to examining the accuracy of the RAPID algorithm, this thesis provides useful information on the use of the FM method for simulation of nuclear systems. / Master of Science / In the modeling and simulation of nuclear systems, two parameters are of key importance: the system eigenvalue and the fission distribution. The system eigenvalue, known as kef f , is the ratio of neutron production from fission in the current neutron generation compared with the absorption and leakage of neutrons from the system in the previous neutron generation. When this ratio is equal to one, the system is critical and is a self-sustaining chain reaction. Knowledge of the fission distribution is important in the nuclear power industry, as it enables engineers to determine the best reactor core assembly configuration to maintain an even power distribution. Several methods have been developed over the years to effectively solve for a nuclear systems fission distribution and system eigenvalue. Aspects of both Monte Carlo and deterministic transport methods have been combined into RAPID’s MRT methodology. It is capable of accurately determining the system eigenvalue and fission distribution in real time. This thesis examines the accuracy of the RAPID algorithm using four unique problems from the ICSBEP handbook. These problems help us to test the limits of the FM method in RAPID through the modeling of small, unique geometric configurations not seen in large, uniformly configured power reactor cores and spent fuel pools. For comparison, each problem is modeled using the Serpent Monte Carlo code, an accurate code meant to serve as the industry standard for determination of the fission distribution of each problem. This model is then used to generate a set of FM coefficients for use in RAPID calculations. It is demonstrated that the eigenvalues calculated by RAPID and Serpent agree with the experimental data within the given experimental uncertainty. The fission distribution obtained by RAPID is also in agreement with the Serpent reference model. Finally, the RAPID eigenvalue calculation is significantly faster than the corresponding Serpent reference model, with speed-ups ranging from 4x to 34x demonstrated.

There is a significant need for 3-D steady-state and transient neutron transport formulations and codes that yield accurate, high-fidelity solutions with reasonable computing resources and time. These tools are essential for modeling innovative nuclear systems, such as next-generation reactor designs. The existing methods generally compromise heavily between accuracy and affordability in terms of computation times. In this dissertation, novel algorithms for simulation of reactor transient conditions have been developed and implemented into the RAPID code system. In addition, extensive computational verification and experimental validation of RAPID's steady-state and transient algorithms was performed, and a novel virtual reality system (VRS) web-application was developed for the RAPID code system. The new algorithms, collectively referred to as tRAPID, are based on the Transient Fission Matrix (TFM) methodology. By decoupling the kinetic neutron transport problem into two different stages (an accurate pre-calculation to generate a database and an on-line solution of linear partial differential equations) the method ensures the preservation of the highest level of accuracy while also allowing for high-fidelity modeling and simulation of nuclear reactor kinetics in a short time with minimal computing resources. The tRAPID algorithms have been computationally verified using several computational benchmarks and experimentally validated using the JSI TRIGA Mark-II reactor. In order to develop these algorithms, first the steady-state capabilities of RAPID have been successfully benchmarked against the GBC-32 spent fuel cask system, also highlighting issues with the standard eigenvalue Monte Carlo calculations that our code is capable of overcoming. A novel methodology for accounting for the movement of control rods in the JSI TRIGA reactor has been developed. This methodology, referred to as FM-CRd, is capable of determining the neutron flux distribution changes due to the presence of control rod in real-time. The FM-CRd method has been validated with successfully using the JSI TRIGA reactor. The time-dependent, kinetic capabilities of the new tRAPID algorithm have been implemented based on the Transient Fission Matrix (TFM) method. tRAPID has been verified and validated using the Flattop-Pu benchmark and reference calculations and measurements using the JSI TRIGA reactor. In addition to the main tRAPID algorithms development and benchmarking efforts, a new web-application for the RAPID Code System for input preparation and interactive output visualization was developed. VRS-RAPID greatly enhances the usability, intuitiveness, and outreach possibilities of the RAPID Code System. / Doctor of Philosophy / The simulation of the behavior of nuclear systems (such as power reactors) relies on the development of innovative software that allows for calculating nuclear-relevant quantities in support of the design, operation, and safety of said systems. Traditional codes are often very complex and need to rely on approximations and/or require a very large amount of time to perform even a single calculation. The RAPID Code System is based on a methodology that allows for pre-calculation of a database that can later be used to simulate nuclear systems in real-time while achieving high levels of accuracy. For this dissertation, several new algorithms for simulation of equilibrium and transient conditions of nuclear systems have been developed for the RAPID Code System. In particular, the main features and additions are the ability of simulating the insertion of control rods (devices that are used to control the fission chain reaction) in nuclear reactors and the ability of analyzing the kinetics of nuclear systems. This latter feature, in particular, is extremely important and difficult to simulate, as it involves the fast variation in time of the nuclear quantities under analysis. Finally, a Virtual Reality System (VRS) is embedded with RAPID for easy utilization of the code through a web-application. All these new algorithms and tools have been benchmarked and validated, against reference high-fidelity computational predictions and experimental data. This dissertation demonstrates RAPID's ability of achieving accurate high quality solutions in a rather short time.

Fuel burnup calculations provide material concentrations and intrinsic neutron and gamma source strengths as a function of irradiation and cooling time. Detailed, full-core 3D burnup calculations are critical for nuclear fuel management studies, including core design and spent fuel storage safety and safeguards analysis. For core design, specifically during refueling, full- core pin-wise, axially-dependent burnup distributions are necessary to determine assembly positioning to efficiently utilize fuel resources. In spent fuel storage criticality safety analysis, detailed burnup distributions enable best-estimate analysis which allows for more effective utilization of storage space. Additionally, detailed knowledge of neutron and gamma source distributions provide the ability to ensure nuclear material safeguards. The need for accurate and efficient burnup calculations has become more urgent for the simulation of advanced reactors and monitoring and safeguards of spent fuel pools. To this end, the Virginia Tech Transport Theory Group (VT3G) has been working on advanced computational tools for accurate modeling and simulation of nuclear systems in real-time. These tools are based on the Multi-stage Response-function Transport (MRT) methodology. For monitoring and safety evaluation of spent fuel pools and casks, the RAPID (Real-time Analysis for Particle transport and In-situ Detection) code system has been developed. This dissertation presents a novel methodology and algorithm for performing 3D fuel bur- nup calculations, referred to as bRAPID- Burnup with RAPID . bRAPID utilizes the existing RAPID code system for accurate calculation of 3D fission source distributions as the trans- port calculation tool to drive the 3D burnup calculation. bRAPID is capable of accurately and efficiently calculating assembly-wise axially-dependent fission source and burnup dis- tributions, and irradiated-fuel properties including material compositions, neutron source, gamma source, spontaneous fission source, and activities. bRAPID performs 3D burnup calculations in a fraction of the time required by state-of-the-art methodologies because it utilizes a pre-calculated database of response functions. The bRAPID database pre-calculation procedure, and its automation, is presented. The ex- isting RAPID code is then benchmarked against the MCNP and Serpent Monte Carlo codes for a spent fuel pool and the U.S. Naval Academy Subcritical Reactor facility. RAPID is shown to accurately calculate eigenvalue, subcritical multiplication, and 3D fission source dis- tributions. Finally, bRAPID is compared to traditional, state-of-the art Serpent Monte Carlo burnup calculations and its performance will be evaluated. It is important to note that the automated pre-calculation proceedure is required for evaluating the performance of bRAPID. Additionally, benchmarking of the RAPID code is necessary to understand RAPID's ability to solve problems with variable burnups distributions and to asses its accuracy. / Ph. D. / In a nuclear reactor, the energy released from a fission reaction, the splitting of an atomic nucleus into smaller parts, is harnessed to generate electricity. Nuclear reactors rely on fuel, typically comprised of uranium oxide (UO₂). While the reactor is operating and the fuel is being used, or “burned”, for power production it is undergoing numerous nuclear reactions, including fission, and radioactive decays which alter the material composition. Knowing the time evolution of fuel as it is burned in the reactor, i.e., concentration of isotopes and sources of radiation, is critical. Nuclear reactor designers and operators use this information to optimize power production and perform safety analysis of used nuclear fuel. By performing fuel burnup calculations, material concentrations and radiation source strengths are obtained as a function of time in an operating nuclear reactor. Using traditional computational techniques, these calculations are extremely time consuming and, for certain problems, can be difficult to obtain an accurate solution. Ideally, a reactor designer would like to know the three-dimensional (3D) distribution of material compositions and sources; however this level of detail would require an excessive amount of calculation time, therefore simplified models and assumptions are used. For the design of the new generation of nuclear reactors, and monitoring and safeguards analysis, this level of detail will be required in lieu of the availability of experimental facilities which do not currently exist. This dissertation presents a novel methodology and algorithm for performing accurate 3D fuel burnup calculations in real-time, referred to as bRAPID (Burnup with RAPID). bRAPID utilizes an existing nuclear software, RAPID (Real-time Analysis for Particle transport and In-situ Detection), developed in the Virginia Tech Transport Theory Group (VT3G), which has been shown to accurately solve time-independent nuclear calculations in significantly less time than traditional approaches. bRAPID is capable of accurately calculating 3D material and source distributions as a function of time in an operating nuclear reactor, and requires significantly less time and computational resources than traditional approaches. To ensure that bRAPID is relatively easy to use, a number of automated routines have been developed and are presented. RAPID is benchmarked against the traditional code systems MCNP (Monte Carlo N-Particle) and Serpent, both of which are widely used in the nuclear community, for a spent fuel storage pool and the U.S. Naval Academy subcritical nuclear reactor facility. RAPID is shown to accurately calculate system parameters (eigenvalue and subcritical multiplication factor) and 3D fission source distributions. Finally, bRAPID is compared to the traditional burnup approach, using the Serpent code system. bRAPID is shown to accurately calculate system parameters and 3D material and source distributions in significantly less time than the traditional approach.

This thesis presents a detailed analysis of the bRAPID (burnup for RAPID – Real Time Analysis for Particle transport and In-situ Detection) code system, and the implementation and validation of two new algorithms for improved burnup simulation. bRAPID is a fuel burnup algorithm capable of performing full core 3D assembly-wise burnup calculations in real time, through its use of the RAPID Fission Matrix methodology. A study into the effect of time step resolution on isotopic composition in Monte Carlo burnup calculations is presented to provide recommendations for time step scheme development in bRAPID. Two novel algorithms are implemented into bRAPID, which address: i) the generation of time-dependent correction factors for the fission density distribution in boundary nuclear fuel assemblies within a reactor core; ii) the calculation of pin-wise burnup distributions and isotopic concentrations. Time step resolution analysis shows that a variable time step scheme, developed to accurately characterize important isotope evolution, can be used to optimize burnup calculations and minimize computation time. The two new algorithms have been benchmarked against the Monte Carlo code system Serpent. Results indicate that the time-dependent boundary correction algorithm improves fission density distribution calculations by including a more detailed representation of boundary physics. The pin-wise burnup algorithm expands bRAPID capabilities to provide material composition data at the pin level, with accuracy comparable to the reference calculation. In addition, wall-clock time analyses show that burnup calculations performed using bRAPID with these novel algorithms require a fraction of the time of Serpent. / Master of Science / Fuel burnup modeling is an important aspect of nuclear reactor design that provides information about the energy extracted (called burnup) and isotopes created or used in the fuel of a reactor over time. A reactor core is a collection of fuel assemblies, and assemblies are simply a bundle of fuel pins, which contain nuclear fuel such as Uranium. The desire for accurate and fast computer codes to calculate fuel burnup rises each year as engineers working in reactor core design seek to arrange fuel assemblies in an optimal pattern to extract the most energy. State of the art burnup codes exist, however they have certain limitations due to their underlying methodologies. To satisfy this need, the bRAPID algorithm was developed by the Virginia Tech Transport Theory Group (VT³G). bRAPID is a new methodology capable of performing full core fuel burnup calculations in real time. bRAPID is able to calculate the criticality and burnup distribution of a reactor orders of magnitude faster than comparable algorithms, while addressing many of the shortcomings seen in other burnup codes. In this thesis, studies of standard burnup codes are conducted in order to aid in bRAPID analysis: first in the form of a detailed study of the reference Monte Carlo model used in this thesis, and secondly in an investigation of the effect of time step selection – or the time intervals used in burnup calculations – on isotope concentration. Both of these studies are conducted using the benchmark code system, Serpent, with the latter study providing useful insight that can be used for bRAPID database development. This thesis then presents two new algorithms for bRAPID that expand its capability and improve performance. First, an algorithm to more accurately simulate the boundary regions of the core – called the time dependent boundary correction algorithm – is presented and benchmarked. Next, an algorithm to expand bRAPID capability from assembly-wise to pin-wise burnup calculations is implemented and tested. These two algorithms are benchmarked against the Serpent Monte Carlo based burnup code.