Towards a more realistic MELCOR model for a dry cask for spent nuclear fuel. Part II: application.

Nowadays, a great deal of attention is devoted to the development of best-estimate models able to produce more realistic outcomes. This is also the case for system codes, such as MELCOR, that are being mostly used in a conservative way especially when dealing with the licensing process. The above-mentioned need for more realistic results is at the core of this two-paper series related to the creation of a more accurate MELCOR model for the HI-STORM 100S dry cask. The findings obtained from the sensitivity studies carried out in the Part I are leveraged to set up an improved MELCOR model, the characteristics of which are consistent with the typical features of Spent Nuclear Fuel (SNF), and with geometrical and material properties of the cask itself. The addition of an axial power profile in the Fuel Assembly (FA), the better characterization of the flow losses in the air gap between internal metallic canister and external concrete-based overpack, and the choice of an appropriate value for the concrete thermal conductivity, are taken into account conjointly in this Part II. The outcomes from the improved MELCOR simulation are reported mainly in terms of the Peak Cladding Temperature (PCT), being the variable under regulatory surveillance. However, in addition to PCT, calculated temperature profiles are displayed and compared against the ones resulting from the previous model.


Introduction
In the early days, highly conservative design and safety analyses were performed to compensate the lack of adequate knowledge and the limitations in the modelling of some physical phenomena.However, conservative assumptions and conservative computer codes do not always lead to conservative results: indeed, over-conservative analysis might produce misleading or even unrealistic results [1].For this reason, later on, with the development of improved simulation tools and with research programs filling in some knowledge gaps, a shift towards less conservative approaches was carried out.More realistic evaluations were foreseen also in the safety analysis of Emergency Core Cooling Systems (ECCS) [2].
Following this path, a number of studies were performed, during the past decades, to promote Best-Estimate (BE) analyses rather than conservative ones.In particular, Best Estimate Plus Uncertainty (BEPU) methodologies and their application in different areas, from thermal-hydraulics to Severe Accidents, have been largely investigated [3][4][5][6][7][8][9][10][11].Furthermore, another option beyond BEPU has been introduced in [12], where a realistic approach with BE computer codes, BE assumptions and BE initial and boundary conditions (with no request for an uncertainty assessment) is foreseen.
Considering what said above, the present paper (that is the second of a two-paper series) pursues the need for more realistic results, when evaluating the thermal performance of a dry storage system for Spent Nuclear Fuel (SNF).More precisely, an improved model for the HI-STORM 100S system [13] is set up starting from a previously developed model [14], created employing the MELCOR code [15,16] and verified against a Computational Fluid Dynamic (CFD) model of the same system [17].
The improved model has been obtained exploiting the findings of the sensitivity studies carried out in the Part I [18] of this two-paper series.In particular, the three addressed factors (namely the axial power profile for the Fuel Assembly (FA), the loss coefficients in the air gap between the internal metallic canister and the external concrete-based overpack, and the thermal conductivity of the concrete itself) have been taken into account conjointly in this Part II.Considering that the objective is to have a more accurate and realistic model, the three factors mentioned above have been characterized as to have consistency with the typical features of the SNF, and to be coherent with geometrical and material properties of the system itself.
Results will be presented in comparison with outcomes from the previous model.Being the thermal analysis of utmost importance for the safety of the system [19], temperature profiles of the main components of the cask will be reported, and the new safety margins addressed.

Modelling
The modelling choices for the improved MELCOR model are described in the following as well as the rationale behind each decision made.However, before moving to the modelling, a summary of the findings from the sensitivity studies performed in Part I are reported.

Recap of Part I
As said before, the sensitivity studies addressed in Part I involved three main factors: • the axial power profile for the FA; • the loss coefficients in the air channel between the internal metallic canister and the external concrete-based overpack; • the thermal conductivity of the concrete itself.As for the axial power profile, a non-uniform profile with a shape peculiar to the majority of the Pressurized Water Reactor (PWR) FAs were considered to take into account the fuel operating history.As a result, a slight variation in the axial temperature distribution of the fuel is observed, with a 10 K rise in temperature in the central zone of the FA and a little reduction at the extremities.As a consequence, the calculated maximum temperature reached in the fuel cladding, namely the Peak Cladding Temperature (PCT), presents a minor decrement (2 K).
For what concerns the loss coefficients in the air channel, three different cases were run: for all three of them, the loss coefficients for the Flow Paths (FPs) defined in the vertical (annular) channel were imposed as 0.1, whereas for inlet and outlet FPs three values were selected, one for each case (1.0, 2.0 and 4.0).The variation of the loss coefficients produces a change in the heat extraction capability: when the loss coefficients are at their minimum, mass flow rate in the air channel rises, and lower temperatures are calculated for both air in the channel and fuel.On the other hand, when considering high loss coefficients, results are almost the same as in the original model.With regard to the PCT, a 15 K reduction is shown for the case with the lower loss coefficients, as a consequence of an enhanced heat removal from the canister.
As regards the thermal conductivity of the concrete in the overpack, two "extreme" values (0.7 W/m-K and 2.1 W/m-K) were analyzed following a literature review [20][21][22] for plain concrete.As expected, simulation outcomes confirmed that the thermal conductivity of the concrete mainly affect the temperature in the overpack, whilst it has almost no impact on the PCT.

Modelling Choices
Starting from the model presented in [14], an improved MELCOR model for the HI-STORM 100S system is implemented.Considering the outcomes of the sensitivity studies in Part I and having in mind the creation of a model as consistent to the reality as possible, modelling choices were made as presented below: • Despite the impact of the addition of the axial power profile for the FA being localized at the fuel zone and limited in terms of temperature difference, it was decided in favour of it.
The decision is based on the idea of having a model as realistic as possible.In fact, the fuel axial power profile is non-uniform along the entire fuel life.In particular, for a PWR, the initial quasi-cosine shape for the axial power profile is eventually substituted by a flattened curve with sharp ends, as an indication of a fuel more burned in the central zone and less burned at the extremities.Moreover, a slightly higher axial power is observed in the lower part of the FA than at the top, due to differences in the moderator (water) density.
In • Having a lower PCT would be optimal in terms of increasing the safety margins.However, the case with the smallest values for the loss coefficients in the FPs (and, consequently, with the lowest PCT) was not chosen for the improved model: the loss coefficients selected for such case are deemed inadequate to represent the geometry of the channel and of the inlet and outlet ducts, especially.In fact, whilst a value of 0.1 is appropriate for a correct reproduction of the vertical flow of the air in the vertical annular gap between the external canister wall and the internal wall of the overpack, a value of 1.0 is not suitable for the proper representation of the form losses due to the combination of entrance/exit effects plus the direction changes.This is particularly true considering that the inlet and outlet FPs are meant to represent the actual 4 inlets and 4 outlets of the real cask.
For the above mentioned reason, the loss coefficients for inlet and outlet FPs have been imposed as 2.0.Table 2 summarizes the loss coefficients chosen for the improved model.• Notwithstanding the fact that concrete thermal conductivity seems to have almost no influence on the PCT, it still plays a role in the heat transfer within the overpack.However, since the only requirements for the plain concrete in the overpack are its density and its compressive strength [13], it was decided to not to employ any extreme value for its thermal conductivity and to leave it as in the original case (1.4 W/m-K).

Results
As said before, the thermal analysis is considered a fundamental part in the safety assessment of a dry storage for SNF.Therefore, in the following, results will be presented mainly in terms of temperatures for the various components, taking into account the regulatory limits as reported in [13,23].
Comparisons between the original and improved MELCOR models outcomes will be displayed.
In view of the safety importance of the maximum temperature in the fuel, the PCT is reported first.As it can be seen in Table 3, the two models agree on the location of the PCT, that is in the upper part (11 th axial level) of the central FAs.However, with the improved model, a reduction of around 11 K is foreseen, mostly due to the increased heat extraction by the air in the channel (that, in turn, is due to values chosen for the more realistic characterization of the loss coefficients in the air channel).This reduction in the PCT points to a broadening of the safety margins, with the maximum temperature being now more than 50 K lower than the regulatory limit for normal operating conditions (673.15 K).Some differences can be observed also in the axial temperature profile for the central (hotter) FAs (Figure 1), where the influence of the use of the axial power profile is visible in the shape of the axial temperature profile, with extremities presenting a reduction with respect to the original model.Even so, the effect of the axial power profile in the central zone of the FAs is counterbalanced by the effect of a higher heat extraction from the canister, and temperatures are almost identical to the original model.The effect of the larger heat removal capability of the air in the channel can be observed also in the axial temperature profiles for the canister wall and for the air channel itself.As it can be seen in Figure 2, lower temperatures are obtained with the improved model in all axial locations, with the ΔT between outcomes by the original model and the improved one increasing along the axial direction.In particular, a ΔT of almost 15 K is reported for the upper part of the steel canister, with the predicted maximum temperature (402.2K) being well below the maximum allowed temperature for the stainless stell in the canister in normal conditions (658.15K [13]).As for the air in the channel, instead, the air  Finally, to go a step further in the description of the performance of the system, attention is paid to the thermal behavior of the overpack.In Figure 3, the axial temperature profile of the concrete is displayed, for both the inner (hotter) and outer (colder) surfaces, together with the radial temperature profile within the overpack at the axial level corresponding to the PCT (11 th axial level).As it can be seen from the radial profile, there is almost no temperature drop within the thin carbon steel liners surrounding the thick concrete wall.On the other hand, a ΔT of 50 K and 60 K can be observed within the concrete for the improved and original models, respectively.The difference in the temperature profile is not due to the thermal conductivity of the concrete, that is the same for both simulations, but rather to the lower predicted temperatures at the inner side of the overpack as a result of the higher heat removal by natural convection in the air channel.

Conclusions
The present paper carries on with the work started in Part I, where a number of sensitivity studies was performed as a first step in the creation of a more realistic model for the HI-STORM 100S storage system for SNF.In this framework, the findings from Part I are leveraged to set up an improved MELCOR model, the essential trait of which is to be as representative as possible of the typical characteristics of the SNF and of the geometry of the system.To do so, a non-uniform axial power profile typical of a PWR FA has been implemented into the model, and the FPs associated with the air channel have been better characterized by imposing more suitable pressure loss coefficients.
Being temperatures of utmost importance for the safety of the cask system, the results have been analyzed mainly in terms of temperature profiles, paying attention to the limits imposed in the regulations.
A number of observations can be derived from the calculation outcomes: • A PCT of 619.3 K is obtained, with a safety margin of around 50 K with respect to the regulatory limit for normal conditions.The PCT value is 11 K lower than the one from the original calculation.The improved (and more realistic) BE model results in less conservative outcomes.• The axial temperature profile for the hotter FA is the expression of the combined effect of the presence of the axial power profile for the fuel and the increased heat removal from the air.Temperatures at the extremities are now lower than in the original case, as can be also inferred from the lower value of the PCT.• Trends in the axial temperature profile for the different components are the same as in the original model, but lower temperatures are foreseen.This behavior is, again, due to the higher heat removed through natural circulation of air in the channel.• The characterization of the loss coefficients in the air channel seems to play a major role in the thermal performance of the system.As mentioned above, results show that their values have a non-negligible influence on the capacity of the system to extract heat from the cask and, consequently, on the temperatures of any of the components of the system itself.• Maximum calculated temperatures for fuel cladding, stainless steel in the canister and concrete in the overpack are all well below the regulatory limits.Summarizing, it can be said that an improved (and more realistic) MELCOR model was implemented for the selected dry storage system.Being the proposed results consistent with the expected behavior of the system, the model seems suitable for the reproduction of its thermal performance, especially in cases in which no detailed fluid-dynamics analysis is needed.
Heat Transfer Conference (UIT 2023) Journal of Physics: Conference Series 2685 (2024) 012044 IOP Publishing doi:10.1088/1742-6596/2685/1/0120445 temperature rises moving upwards toward the hotter part of the canister, with the maximum reached temperature being more than 10 K below the one calculated in the original model.

Table 1 ,
the axial power values as entered in the MELCOR model are reported for each axial level containing fuel.Values are in agreement with what enounced above.

Table 1 .
Axial Power Profile for the Fuel as imposed in MELCOR.

Table 2 .
Loss Coefficients in the Air Channel.