Sensitivity Analysis of the TRIGA IPR-R1 Reactor Models Using the MCNP Code

2.1. TRIGA IPR-R1 Configurations

As described before, the differences between the models are in the geometry detailing. These models have the same materials composition obtained from [8] and they were configured according to the characteristics of TRIGA IPR-R1 [7]. In both models, the core was configured in the MCNP5 using a cylinder that contains water, fuel elements, radial reflectors, central tube, control rods, and neutron source. Each rod has a coordinate value. In these models, the rods were filled according to their individual characteristics. Around the core is the rotary rack with adequate groove to insert the samples to irradiation. The reactor was configured inside the pool where water surrounds the core and the rotary rack.

In the simulations, Dimension  1 has the geometric values of previous studies [8, 9] and Dimension  2 presents the geometric values of the technical report [10]. Table 1 shows the core elements dimensions of the simulated models and information about criticality calculation simulations.

2.2. Evaluated Neutronic Parameters

To the sensitivity analyses, the neutronic parameters evaluated were the effective multiplication factor (k_eff), the reactivity (ρ), and the thermal and total neutron flux in central thimble as described in detail in the next subsections.

3.1. Reactivity Analysis

Table 2 presents the standard deviation (σ_ST) and relative error (R) to the k_eff calculated by MCNP5 code. In addition, it shows the computation time (CT) for each case. According to [12], the values are reliable when the relative error R < 0.10. Table 2 shows that the relative error is around 0.011% and, therefore, the calculated k_eff values are acceptable. In addition, Table 2 shows that Cases  3 and 4 (configured with Model  2) present CT bigger than those for Cases  1 and 2 (configured with Model  1). This behaviour is due to Model  2 presenting more detailed geometry than Model  1. The MCNP code spends more time to follow particles in detailed geometries due to the increase of the number of surfaces and volumes. The code tracks particles through the geometry; it calculates the intersection of a track’s trajectory with each bounding surface and finds the minimum positive distance to an intersection. MCNP finds the correct cell that the particle will enter by checking the sense of the intersection point for each surface listed for the cell. When a complete match is found, MCNP has found the correct cell on the other side and the transport continues [12]. Therefore, a large number of surfaces will spend more computational time.

Table 3 presents the values of k_eff, ρ, Δk_eff, and Δρ when the shim, safety, or regulating rod is totally inserted into core. This table shows these parameters to four studied cases and to experimental data (ED). The k_eff1 represents the effective multiplication factor to all control rods withdrawn and k_eff2 is the effective multiplication factor due to only one of the control rods (shim, safety, or regulating) inserted into the core.

The investigated cases have the same behaviour when the shim, the safety, or the regulating rod is inserted in the reactor core (see Table 3). In these cases, the insertion of shim rod induces the highest Δk_eff, while the insertion of regulating rod causes the smallest Δk_eff. In this way, the shim rod presents the highest Δρ while the regulating rod presents the lower value of Δρ. On the other hand, for the safety and shim rods the Δk_eff and Δρ values are similar. The difference between the behaviours of such rods is due to their positions in the core. The regulating rod is located in the periphery of the core while the safety and shim rods are positioned near to the core centre. The simulated cases present the same behaviour of the experimental data.

Comparing Cases  1 and 2 (Model  1) or Cases  3 and 4 (Model  2), Cases  1 and 3 (Dimension  1) present the lowest value of the analysed difference. In comparison with the experimental data, Dimension  1 presents values of k_eff and ρ slightly overestimated while Dimension  2 presents values slightly underestimated.

As shown in Table 1, the fuel radius of aluminium element for Dimension  2 is smaller than for Dimension  1. Moreover, the central zirconium radius of stainless steel element in Dimension  2 is higher than in Dimension  1. These differences cause small decreasing of fissile material in the reactor core reducing the values of k_eff and ρ parameters. Furthermore, Dimension  1 presents outer radius of active core higher than Dimension  2. Then, the active core in Cases  1 and 3 presents more water volume than in Cases  2 and 4. As the water is a moderator material, its largest volume in Cases  1 and 3 causes probably an increase in the thermal fission. Consequently, Cases  1 and 3 presented k_eff values increased in comparison with Cases  2 and 4.

Although Cases  1 and 3 as well as Cases  2 and 4 have the same dimensions, Cases  3 and 4 have more detailed geometry (Model  2) which presents grid plates and control rods guide tube. In Cases  1 and 2 (Model  1), the volume of these elements is filled with water. Therefore, Model  1 presents water volume bigger than Model  2. As the water is a moderator material, Cases  1 and 2 (Model  1) have k_eff value bigger than Cases   3 and 4 (Model  3) (see Table 4).

Figures from 1 up to 3 show the evolution of the Δρ for 39 axial positions of the shim, safety, and regulation control rods, respectively. In the figures, the zero position (“0”) represents total withdraw and the thirty-nine position (“39”) represents total insertion of control rods. As mentioned before, (3) was applied to calculate the control rods reactivity worth (Δρ) to each of the 39 axial positions where the relative error of Δρ is around 4.9 × 10⁻⁴. As it can be observed in the figures, the evolution of the Δρ presented the expected behaviour for all the simulated cases: as the control rods are inserted in the reactor core, the reactivity variations (Δρ) increase. In agreement with the values presented in the Table 3, the shim and safety rods produce bigger reactivity worth (Figures 1 and 2) than the regulating rod (Figure 3) due to its radial core position. According to the Figures 1 and 2, the shim and safety rods provide around 2600 pcm each, while the regulating rod (Figure 3) provides about 500 pcm Δρ total.

3.2. Neutron Flux Analysis in the Central Thimble

Figures 4 and 5 present thermal and total neutron fluxes, respectively, along the axial thimble positions for the four cases and for each case of control rod insertion. The ordinate axis represents the neutron flux values divided by 10¹² and the abscissa axis represents the axial central thimble positions. As the central thimble was partitioned in 56 cylindrical cells in the model, the horizontal axis shows 56 positions from “–28” (bottom) up to “28” (top).

According to [12] the flux value is reliable when the relative error R < 0.10. In the simulated cases, the relative error of the estimated flux values is around 1%. Therefore, the calculated neutron flux values are statistically acceptable.

As it can be verified in Figures 4 and 5, the behaviour of the neutron flux distributions presents the typical “bell-shape.” For the simulated cases, there are some small differences in the flux values where the biggest difference is 7.5%.

As it was analyzed previously, the shim and the safety rods moving cause the biggest Δρ (see Table 3). Consequently, the insertion of such rods will produce the higher flux reduction. This behaviour was verified in the simulated cases (see Figures 4 and 5); in spite of the effect of this control rods insertion, the flux depression is very small. In addition, Table 5 presents the average total flux value in the middle of central thimble where the smallest flux values are of shim and safety rods inserted.