Theoretical Derivation and MCNP5-Based Comparative Study of Neutron flux density Distribution in Annular Reactors

摘要: To bridge the theoretical gap in the analysis of neutron flux density distributions within annular reactors, this study derives closed-form solutions for the neutron flux density under critical conditions based on the monoenergetic neutron diffusion equation and validates them using MCNP5 simulations. The study categorizes annular reactors into three types according to inner radius: Type A ($a > 27\,\text{cm}$), where the inner neutron flux density approaches zero, is modeled using zero-flux boundary conditions at both inner and outer radii; Type B ($a < 7\,\text{cm}$), resembling cylindrical reactor characteristics, assumes zero neutron current at the core axis; Type C (7--27 cm), representing a transitional state, introduces a novel hybrid-weight model. A homogeneous annular core model was established in MCNP5 (referencing a typical reactor outer diameter of $b = 1.61\,\text{m}$) to simulate neutron flux density distributions under critical conditions and compare them with the theoretical results after normalization. Results show that: For Type A, the average relative error between theoretical and simulated flux in the active region ($r = a \to b$) is 23.77\%, indicating strong agreement; For Type B, the theoretical solution matches the zeroth-order Bessel distribution of cylindrical reactors, with an average error of 23.54\%. However, for inner diameters greater than 5 cm, errors increase significantly; For Type C, the hybrid-weight model (with weights obtained via cubic polynomial fitting, $R^2 = 0.861 - 0.875$) effectively captures transitional flux behavior. In the 8--12 cm range, the relative error is lowest (10.77\%--15.19\%). Eigenvalue analysis further reveals a monotonic relationship between $Br \times b$ and the radius ratio $a/b$. When $a/b > 0.6$, neutron leakage increases sharply. This study fills a theoretical gap in modeling neutron flux density distributions in annular reactors and provides a robust foundation for geometry-based optimization in reactor core design.