Quasi-Diffusion Method with 3-D Cross Sections for TREAT Core Analysis

The conventional two-step neutronics method used to perform full-core reactor neutronics simulation has been used successfully for light water reactor steady-state and transient analysis. The first step in the method is to generate assembly homogenized few-group cross sections from a lattice transport calculation at the anticipated range of core conditions. The resulting cross sections are then used in the second step to calculate the whole-core flux distribution using nodal diffusion methods. However, when applying this method to small reactors or some experimental reactors such as the Transient Reactor Test (TREAT) Facility, the bias from approximations used in the conventional two-step method can become significant. A large source of error can be the cross sections that are generated from the assembly calculations with reflective boundary conditions since interassembly neutron leakages in small reactors can be significant. Another source of error can be the presence of large void regions such as in the TREAT core. In the work here, the shortcomings of the two-step method were addressed by using the quasi-diffusion method with cross sections obtained from a whole-core three-dimensional Monte Carlo simulation. For the nonvoid region, the group-averaged cross sections were obtained directly from Monte Carlo simulation results, and the directional diffusion coefficients were generated from flux-weighted transport cross sections and the Edington factors directly from the angular flux distribution from the Monte Carlo results. Discontinuity factors were also used in the nodal solution to preserve the neutron currents between nodes based on the Monte Carlo results. For the void region, the directional diffusion coefficients were optimized to minimize the magnitude of the discontinuity factors and thereby mitigate potential numerical problems in the quasi-diffusion method for full-core simulations. The numerical results from the TREAT core steady-state and transient analysis show that the quasi-diffusion method can reproduce the Monte Carlo whole-core results in steady state and that the transient results are in good agreement with experimental measurements.