*2.3.1 HELIOS*

HELIOS version 2.1.2 is a general *xy* coordinate deterministic transport code. Arbitrary geometry is created by user defined nodes, connected to form line segments, then closed to form the spatial mesh. The code supports property overlays, such as composition, temperature, and density. These overlays are mapped to each mesh in the arbitrary 2D geometry. Geometry-corrected resonance integrals are calculated on-the-fly for every spatial mesh of the arbitrarily heterogeneous

**Figure 2.** *KJRR-FAI fuel plate showing U-7Mo dispersion in Al-Si matrix.*

**Figure 3.**

*Profile view of the KJRR-FAI prototype fuel element.*

geometry description using the subgroup resonance treatment. HELIOS uses 49 groups derived from ENDF/B-VII. Very large and complex geometries are supported by subdividing the geometry into smaller subsystems. Each subsystem is solved explicitly via the collision probability (CP) transport solution, or method of characteristics (MOC), and then coupled with adjacent subsystems by sharing interface currents [6]. The angular dependence of the interface currents is discretized by a subdivision of outward/inward angles (i.e., a directional halfsphere). In the HELIOS model, all possible azimuthal directions crossing the interface are discretized into four equal sectors of equal weight. A HELIOS model containing the KJRR-FAI is provided in **Figure 4**.

From 20102015, the HELIOS code underwent extensive Verification and Validation (V&V) to elevate the software quality of HELIOS to Nuclear Quality—1 (NQA-1) [7, 8]. The HELIOS code replaced the neutron diffusion code, PDQ, for performing core reload analysis and associated safety calculations.

#### *2.3.2 MCNP*

MCNP uses the Monte Carlo method for solving particle (e.g., neutron and photon) transport in a continuous energy, angle, and three-dimensional space representation of the reactor core [9]. MCNP also makes use of ENDF/B-VII crosssection libraries. The Monte Carlo solution method represents particle interaction as probabilistic collisions between traveling particles and atomic nuclei. Therefore, the MCNP solution can be considered to be a near exact representation of reality to within the accuracy of the input nuclear interaction cross-section data. However, this level of solution fidelity comes at greater computational expense compared to a 2D deterministic code such as HELIOS.

MCNP 3D models, shown in **Figure 5**, of the ATR core with the KJRR-FAI loaded were developed for comparison with HELIOS. The MCNP model of an ATR fuel element consists of homogenized regions. The 19 fuel plates and associated coolant channels are homogenized into three radial regions. Each of these radial regions are partitioned into seven axial layers. Each axial layer is depleted separately during the depletion calculation. Though increases in computational speed is currently enabling 3D Monte Carlo solutions to be much cheaper, production calculations are still very time-consuming. Thus, the homogenization is done to reduce the required computational burden of resolving the geometry of every plate while still providing the desired level of accuracy for heating rates in the experiments. This is common practice when using MCNP to solve for heating rates in ATR experiments. *Core Reload Analysis Techniques in the Advanced Test Reactor DOI: http://dx.doi.org/10.5772/intechopen.103896*

**Figure 4.** *HELIOS model of ATR (cycle 158A) with the KJRR-FAI loaded in the northeast flux trap.*

Fuel depletion is solved using the ORIGEN2 code using the tallied neutron fluxes from each of the MCNP 21 regions. The ATR operating cycle is broken into discrete time-steps. MCNP solves for the one-group neutron flux and coalesced absorption and fission cross-sections in each of the 21 regions in each fuel element. These fluxes are passed to ORIGEN2. ORIGEN2 solves the Bateman equations to deplete the fuel. The depleted compositions are then passed back to MCNP.

MCNP is used to compute the axial peak-to-average peaking factor which is multiplied against HELIOS intra-plant powers during post-processing. The combination of the HELIOS 2D solution for every sub-plate region with the axial peak-toaverage factor for every fuel element allows the final predictive core performance calculations to provide adequate 3D information. Typically, many design evolutions of different fuel loading patterns, and OSCC and neck-shim withdrawal patterns are needed to demonstrate the cycle's operating requirements can be met while respecting all safety limits. HELIOS is used for these design evolutions with axial peak-to-average factors provided by MCNP in the final design calculation.

The MCNP code was also validated against extensive fission wire activation measurements made in the advanced test reactor critical (ATRC) facility [5, 10]. The ATRC facility is zero power replica of the ATR used for low-power activation

**Figure 5.** *MCNP model of ATR (cycle 158A) with the KJRR-FAI loaded in the northeast flux trap.*

analysis to verify power distributions and to measure the reactivity worth of experiments prior to being inserted into the ATR.
