**3.1 Managing core reactivity for high worth tests**

Typically, ATR flux traps irradiate large volume experiments having high flux requirements. By definition, a flux trap is designed to 'trap' the excess flux from the surrounding fuel elements. This typically implies that the neutrons from the experiment do not greatly influence power production (or power distribution) in the ATR fuel elements. However, given the sheer quantity of fissile U-235 introduced by the KJRR-FAI, it became readily apparent that the KJRR-FAI could drive the northeast lobe power, rather than the northeast lobe driving the KJRR-FAI power. The thermal limits of the KJRR-FAI test could be exceeded unless the excess reactivity introduced by the KJRR-FAI could be managed. The KJRR-FAI test needed to be maintained at a power <2.3 MW to ensure its thermal margins could be met.

*Core Reload Analysis Techniques in the Advanced Test Reactor DOI: http://dx.doi.org/10.5772/intechopen.103896*

Several burnable poison options were investigated, but ultimately abandoned as this would interfere with the desired neutron flux environment.

It was decided that highly burned ATR fuel elements could be loaded into the northeast lobe to essentially "sponge" the reactivity introduced by the KJRR-FAI. However, even with the use of these highly burned fuel elements, the northeast quadrant of OSCCs would need to be rotated inwards to keep the northeast lobe at the desired 19 MW.1 Typically, the burnup distribution of the fuel elements is selected such that the OSCCs can be rotated relatively (though not exactly) evenly. Said differently, it is desirable to manage power distribution around the serpentine using the fissile content of the fuel elements, not by using the OSCCS for power shaping. This does not always happen in practice, but this is a general goal of the fuel reload analysis. **Figure 6** shows the localized power distribution for 10 regions per plate for every plate in the core for cycle 158A. The OSCC are in the startup position at 29 degrees.

Rotating the northeast control bank to nearly "all-in" acceptably suppressed the northeast lobe's power but unacceptably robbed the whole core of excess reactivity. This required adding fresh assemblies somewhere else in the core such that the requested cycle-length could be met.

#### **3.2 Updating power peaking factors**

Prior to HELIOS, the 2D Cartesian mesh version of PDQ was routinely used to predict core reactivity, lobe-power distribution, and localized plate power peaking. However, the axial component of power peaking had been incorporated via an empirical correlation assuming the ATR thermal flux was a "chopped" cosine shape. The fresh fuel axial peak-to-average ratio was 1.43. The bounding thermal-

#### **Figure 6.**

*The dimensionless point-to-average power density ratio for every fuel region in the HELIOS model for 'balanced' OSSCs at startup. Note, that the HELIOS 2D power density is corrected for axial power peaking using data from MCNP.*

<sup>1</sup> The 19 MW for the eight ATR fuel elements in the northeast lobe, not including the 2.3 MW power from KJRR-FAI.

hydraulic analysis for the ATR assumes this axial power shape, originally calculated by PDQ, as universal for every cycle. Changing the axial power shape requires an update to the ATR thermal-hydraulic safety analysis, or at minimum a calculation to assure that the existing safety limits are not challenged by the new axial shape.

Prior to the KJRR-FAI, the chopped-cosine rule was rigorously enforced by ensuring that new experiments would not cause a major deviation from the established axial power shape.2 An acceptance band is used to ensure that new tests would not violate the chopped cosine rule. Experiments that did not meet this criterion would require redesign if the chopped cosine rule could not be met. Typically, the MCNP code is used to design ATR experiments and used to predict the axial peak-to-average factor. If the MCNP analysis finds the axial peak-to-average power factor will likely be non-compliant to the chopped cosine rule, a measurement of the axial shape in the ATRC facility is considered to verify the calculated axial shape.

Note that the axial power peaking factor is significantly greater for the MCNP calculation with the KJRR-FAI in the northeast flux trap than it is for the chopped cosine rule. This is primarily contributed to the influence of the KJRR-FAI fuel loading being concentrated near the mid-plane, i.e., within 30 cm about coremidplane. The axial peak-to-average power factor was calculated using MCNP by tallying the power in the fuel every two inches when the ATR fuel elements are all assumed to be fresh. This calculation was repeated with a generic test configuration typically used as an experiment backup in the northeast flux trap, called the Large Irradiation Housing Assembly (LIHA). The LIHA consists of an arrangement of cobalt and aluminum rods and is considered a standard backup for the northeast flux trap when not in use. The axial peak-to-average power factor in fresh ATR fuel elements was found to be 1.5 when neighboring the KJRR-FAI and 1.4 when neighboring the LIHA. The MCNP tallied power profile for fresh ATR fuel elements adjacent to the KJRR-FAI versus the LIHA is shown in **Figure 7**.

Modifying the test design was not an option for the KJRR-FAI; thus, the empirical chopped cosine shape would need to be rederived. Furthermore, the evolution of this power shape considering depletion effects would need to be considered. Even without the significant axial distortion due to the KJRR-FAI, fuel naturally depletes preferentially at mid-plane due to geometric shape or buckling of the neutron flux. This axial variation in burnup, and hence fuel nuclide distribution, needs to be represented

**Figure 7.** *Comparison of the axial power shape in ATR fresh fuel (Fuel Element 5, Coolant Channel 2) computed using MCNP due to the KJRR-FAI versus the standard LIHA northeast flux trap configuration.*

<sup>2</sup> Control rods for gross reactivity control excluded from the ATR design as they would introduce an axial power tilt as a function of insertion depth. OSCCs could provide reactivity shim without significant change to localized power distribution, thus allowing constant flux conditions for the test locations [4].

*Core Reload Analysis Techniques in the Advanced Test Reactor DOI: http://dx.doi.org/10.5772/intechopen.103896*

in the HELIOS model (just as previously with the PDQ code). This axial burnup variation also impacts the axial power shape as represented in **Figure 8**.

Within the PDQ-based methodology, a three-dimensional extension of the "*x*�y" PDQ analysis was needed to compute the effect of the axial burnup shape on excess reactivity, axial power peaking, and axial burnup peaking. PDQ could be used to solve a 1D *r*-dimensional as well as a 2D *r*�*z* coordinate system. These two features were used together to calculate 1D and/or 2D reactivity biases and axial multipliers due to fuel burnup. To derive a generic peak-to-axial power factor, a single lobe is approximated by a right circular cylinder (RCC) comprised of a generic in-pile tube (IPT) encircled by eight fresh ATR fuel elements. These ATR fuel elements are represented by seven fueled concentric annuli with no side-plates. The modelled seven annuli represented fuel plates 1, 2, 3-4, 5-15, 16-17, 18, and 19, respectively. Each fueled annulus is represented by a homogenized cell containing water, aluminum, and UAlx fuel matrix. The RCC lobe is also recast as a 1D rdimensional model. Both the 1D r-dimensional and 2D *r*�*z* model are depleted at 60 MW for 50 days, or 3000 MW�days (MWD) of "lobe-exposure". The 2D/1D reactivity bias and the axial power peaking factor are then set to a polynomial fit as a function of lobe-energy.

The PDQ axial peak-to-average factor is provided in Eq. (1).

$$A(t) = \frac{P\_{\mathfrak{m}}(t)\zeta\_{V\_{\mathfrak{m}}}}{\sum P\_i(t)} = \frac{\mathcal{P}\_{\mathfrak{m}}(t)}{\mathcal{P}\_{\mathfrak{a}}(t)}\tag{1}$$

*P*<sup>m</sup> represents power at midplane. This is the average power for regions of fuel on core-midplane. *V*<sup>m</sup> is the volume of these regions. *P*<sup>i</sup> and *V*<sup>i</sup> represents the power and volume of all fuel mesh in the PDQ *r*�*z* model. Note that the cursive, ?, represents power density. Time, *t*, represents fuel burnup in units of MWD, referred to as lobe-exposure. The fuel element axial burnup peaking factor is then derived from the indefinite integral of the axial power peaking factor.

**Figure 8.** *Approximate axial power-to-average factors created as 2D/1D factors using the* r�z *PDQ RCC lobe model.*

The average power density of the simple r-z model is held constant; thus, this factor may be eliminated.

$$B(t) = \frac{\int\_0^t A(t) \, \mathrm{d}t}{\int\_0^t \mathrm{d}t} = \frac{1}{t} \int\_0^t A(t) \, \mathrm{d}t}{},\tag{3}$$

The behavior of *B*(*t*) with depletion can be represented with a simple polynomial. In fact, for the duration of only one cycle, it is essentially linear.

$$A(\mathbf{t}) = A\_0 + A\_1 t + A\_1 t^2 \dots A\_n t^n \tag{4}$$

From basic calculus, the power rule can then be used to find the antiderivative of *A*(*t*).

$$B(t) = \frac{1}{t} \left( A\_0 t + \frac{A\_1 t^2}{2} \dots \frac{A\_n t^{n+1}}{n+1} \right) \tag{5}$$

This process is simplistic but allows for accurate reproducibility of 3D power and burnup behaviors with burnup. This is true so long as power and burnup behavior in the x-y frame are separable from the axial-*z* frame. This is generally the case with ATR. This process was used to compute *A*(*t*) and *B*(*t*) for HELIOS using the MCNP code.

The beginning-of-cycle 3D/2D MCNP calculations occur just after the HELIOS fuel selection. With the core load pattern found, the MCNP 21-region model is created. The ORIGEN2 code is used to independently deplete each of the 21-regions assuming an approximate flux shape for an ATR fuel element. The depletion time is carried such that the sum of the 21 U-235 masses and the end of the depletion agrees with the U-235 inventory of that element used in the HELIOS model. The combination of 3D fuel nuclides, 3D experiment models, as well as OSCC and neck-shim positions as a function of burnup constitute the 3D MCNP model.

Unlike the 2D/1D peaking factor used in the PDQ methodology, the 3D/2D MCNP peaking factor may be derived for every fuel element. Here again, it is important to note that this method is very useful only when the *x*�*y* frame is separable from the axial frame. **Figure 9** shows the change in the axial

#### **Figure 9.**

*Comparison of axial peak-to-average factors in previously irradiated ATR fuel elements: power factor (a) and burnup factor (b).*
