Neutronics Analyses of a NERVA-derived NTP Reactor Core using Nodal Diffusion Codes

Nuclear Thermal Propulsion (NTP) systems offer twice the specific impulse over modern chemical systems, resulting in a significant travel time reduction necessary for enabling long duration space missions. NTP core neutronics analyses typically rely on Monte Carlo (MC) codes, which are computationally expensive and can be prohibitive to use in transient simulations. To reduce the computational burden of advanced analysis, Light Water Reactors (LWRs) are traditionally modeled using reduced order methods that follow a standard two-step approach in which cross sections are pre-generated for each unique assembly and fed into the deterministic core simulator. Previous to the work performed in this thesis, the extent of reduced order modeling for NTP reactors has been through the use of SPH-corrected deterministic transport. [1] As such, the primary goal of this thesis is to demonstrate a framework for NTP analysis that is better aligned with the conventional methods widely used in the commercial power industry. In the approach investigated in this work, few-group macroscopic cross sections are generated using a single, full core MC simulation and input into a nodal diffusion code, DYN3D, to obtain the multiplication factor and spatial power distribution. Through several 1D and 2D sensitivity analyses, various homogenization techniques are investigated and complied into a single successful sequence that is applied to a realistic NERVA-derived NTP core model. To ensure that the MC solution is reproduced by the diffusion solver, discontinuity factors (DFs) are generated using a Jacobian-Free Newton Krylov (JFNK) iterative scheme and applied as equivalence correction parameters to the full core homogenous solution. The development of the JFNK method is not an originality to this thesis; however, the verification of the DFs it produces is an aspect of this work. Verification of the JFNK-generated DFs is performed using the semi-analytical NEM-based solution to the intranodal homogeneous flux, yielding NEM-derived DFs that are guaranteed to preserve the heterogenous reaction rates, average flux and net currents. Using multiple SMR test cases, comparisons between the two methods of DF generation show excellent agreement in both the corrected homogenous flux and eigenvalue, as well as the actual values of the surface DF ratios. The last section of results depicts the adapted homogenization sequence applied to a 2D radial slice of the NTP core demonstrating that the homogenous power profile from DYN3D yields near perfect agreement (<.25% maximum relative error) with the reference power profile only when complemented by the JFNK-generated DFs. Further reduction of the residual error can be achieved when the reflector nodes are homogenized in lumped configuration. A final subsection of results presents a practical approach to modeling NTP cores using a hybrid 2D fuel + 3D reflector homogenization scheme, resulting in a corrected power profile with an average absolute error of less than 0.2%.