Methods of studying the effect of rough surfaces on reactivity in two-dimensional reactor physics problems

Highlights: • Approximations of small-scale interface and boundary perturbations. • Homotopy and homogenisation approximations were applied to cylindrical pincells. • Perturbations additionally applied to the Feinberg-Galanin method. • Perturbation methods provided a reasonable estimate at a lower computational cost. - Abstract: Rough and perturbed surfaces are examined in the field of reactor physics using homotopy, homogenisation and the Feinberg-Galanin method. The homotopy method allows a problem with a perturbed interface to be represented as an unperturbed problem with a modified boundary condition. Perturbation theory was applied to this method and the results were studied for the neutron transport equation, the neutron diffusion approximation and a hybrid ABH-diffusion approximation. The homogenisation of surface roughness in the fuel-moderator interface was also examined and compared to the homotopy approach. Finally, the effect of larger-scale geometric uncertainties was studied using the Feinberg-Galanin approach. The effectiveness of the methods is determined by examining the change in effective multiplication factor k_eff examined both directly and via the six-factor formula. Analytic solutions to approximations of perturbation theory differentials were capable of accurately predicting the change in k_eff when compared to numerical solutions. Examining a change in fuel pin radius of 20 µm, we find that for water moderated systems the overall change in $k_{\mathrm{eff}}$ is close to 70 pcm and for graphite systems it is 18 pcm. This shows that water and graphite moderated cores are sensitive to small changes in geometry.