Towards a more realistic MELCOR model for a dry cask for spent nuclear fuel. Part I: sensitivity studies.

The United States (US) Department Of Energy (DOE) has addressed the thermal analysis of the Spent Nuclear Fuel (SNF) stored within a dry cask system as a matter of high priority. In this regard, it is of utmost importance that simulation tools effectively reproduce the general thermal behavior of the modelled cask, including heat exchange and removal. Temperature distribution in the different components of the system is usually the focus of performed thermal analyses. In particular, attention is paid to the maximum temperature reached in the fuel cladding, namely the Peak Cladding Temperature (PCT). Within this framework, the present paper is the first of a two-paper series aimed at developing a more accurate model for the HI-STORM 100S cask. The dry cask in question is modelled and its behavior is simulated by means of the MELCOR code (version 2.2.18019). Stressing the need for a more realistic model rather than a conservative one, this paper reports the efforts undertaken to evaluate the influence of some specific modelling choices on the PCT. The study of the cask performance is therefore conducted taking into consideration three main factors: the axial power distribution in the Fuel Assembly (FA), the flow losses in the air gap between the internal canister and the external overpack, and the conductivity of the overpack concrete.


Introduction
In response to Spent Fuel Pools (SFPs) reaching their maximum capacity and considering the delays in the construction of final repositories, dry casks have gained popularity worldwide as a valid alternative for the safe storage of Spent Nuclear Fuel (SNF).In this regard, several dry cask designs have been proposed and licensed: a list of dry storage systems approved by U.S. NRC is provided in [1].Regardless of their design characteristics, compliance with regulatory requirements as reported in 10CFR72 [2] must be guaranteed.In particular, the maximum temperature reached in the fuel cladding, namely the Peak Cladding Temperature (PCT), must not exceed the temperature limits (673.15K and 843.15K for normal and off-normal/accidental conditions, respectively) in order to ensure the safety of the system [3].In this regard, the thermal analysis of SNF stored within a dry cask system is addressed as high priority by U.S. Department Of Energy (DOE) [4].
Within this framework, many studies have been carried out in the past 40 years to thermally characterize various types of dry casks.Different classes of computer codes have been employed, with Computational Fluid Dynamic (CFD) tools being the most adopted ones nowadays [5][6][7][8][9].However, previous studies proved that the MELCOR code [10,11] is able to reproduce the general behavior of the modelled cask in both normal operating condition and also when considering more challenging boundary conditions.
Continuing along this path, the present paper is the first of a two-paper series aimed at creating a more accurate model for the largely used HI-STORM 100S system [12].In particular, pointing to a more realistic model rather than a conservative one, the influence of some modelling choices on the PCT is evaluated, taking into account three main factors: the axial power distribution in the FA, the flow losses in the air gap between the internal metallic canister and the external concrete-based overpack, and the conductivity of the concrete itself.As a first step, a comparison is made between the results, in terms of both PCT and its location, obtained considering a uniform axial power distribution and an axial power profile typical of Pressurized Water Reactor (PWR) fuel assemblies.Secondly, attention is paid to a more precise characterization of the flow losses in three different locations: air inlet, annular air channel, and air outlet.In particular, the complexity of inlet and outlet geometry seems to indicate the need for an improved definition of the flow losses, and consequently of the air mass flow rate, in order to reproduce the correct heat extraction capacity.Finally, a sensitivity study on the conductivity of the concrete is reported.Considering the multitude of plain concretes available and their different composition, an attempt is made to quantify the influence of different values of concrete conductivity on the PCT value.

Sensitivity Studies
As said before, the system addressed in this work is the HI-STORM 100S, the detailed description of which is reported in [12].However, for the sake of clarity, few information are reported hereafter.
As it can be seen in Figure 1, the SNF is stored within a sealed metallic Multi-Purpose Canister (MPC) filled with 99.995% pure Helium.The canister is, in turn, housed within a concrete-based overpack.The MPC ensures confinement, whilst the overpack acts as radiation shielding.The cooling of the SNF is, instead, achieved through the combination of three mechanisms: the thermosiphon effect of the Helium inside the MPC, the natural circulation of the external air in the channel between the MPC and the overpack, and the radiative exchange from the MPC to the overpack walls.The external wall of the overpack is, in turn, cooled down by convective heat exchange with the environment.
The MPC can contain a different number of Fuel Assemblies (FAs) depending on the design.The one considered in the present analysis is the MPC-32, that houses 32 PWR 17x17 FAs, with a decay power of 30.0 kW.The entire system has been modelled with the MELCOR code (version 2.2.18019), that is originally developed for the simulation of Severe Accident (SA) scenarios.The model is described in [13,14]; however, few details will be reported in the following in relation to the performed sensitivity studies.

Axial Power Profile
The "core" region (representing the spent FAs within the MPC) is depicted in MELCOR through radial rings and axial levels, the combination of which results in the definition of cells.For each cell the amounts of fuel, cladding, and other components' masses have to be defined together with their hydraulic diameters, flow areas, boundary surfaces, etc, as requested in [10].
In the original model, a uniform axial power profile was employed, as a first approach, for the 8 (out of 12) axial levels containing the fuel.However, for a more realistic model, a non-uniform axial power profile has to be employed to take into account fuel operating history.
For this reason, the first sensitivity study is devoted to the evaluation of the influence of a nonuniform axial profile for the "core" region in the MPC.The considered profile has a shape peculiar to the majority of PWR FAs: relatively flat in the central section (with peak burnup of 1.1/1.2times the FA average burnup) and significantly steep at the ends (with burnup of 0.5/0.6 times the assembly average), as it can be seen from Figure 2.More specifically, the profile (as proposed in [15]) has been exploited to obtain the "relative power density" for each axial level in the MELCOR model, as reported in Table 1.

Loss Coefficients in the air channel
As shown in Figure 3, the annular air channel is modelled in MELCOR with 8 Control Volumes (CVs), connected by means of 7 vertical Flow Paths (FPs).Two additional horizontal FPs are meant to represent the flow of air entering or leaving the channel.For each FP, a loss coefficient, K, is defined and then used by the code to determine the pressure drop, across the FP, due to form losses.In the original model, it was decided to keep default values, and loss coefficients for the FPs in the air channel were imposed as 1.0.However, a better characterization of the loss coefficients is needed to take into account the geometry of the system, with particular attention to the slightly more complex shape of inlet and outlet ducts connecting the environment with the annular space.
Considering what said, the second sensitivity study deals with a more realistic definition of the form losses in the air channel, with particular focus on three locations: air inlet, vertical (annular) channel, and air outlet.
Bearing in mind that form losses are usually linked to bends, changes in the flow area, valves, etc., a relatively low loss coefficient (K=0.1) has been selected for the FPs associated with the annular channel.On the contrary, higher loss coefficients have been considered for the FPs linked to the air inlet and outlet.More precisely, considering the presence, in the real cask, of 4 inlet and 4 outlet openings, and taking into account that, for sharp entrances or exits, the loss coefficients are between 0.5 and 1.0 [16], K values of 2.0 and 4.0 have been deemed appropriate for the analysis.
A summary of the values employed for each sensitivity study is reported in Table 2.

Concrete Conductivity
The overpack presents a sandwich structure composed of a thick core region made of plain concrete and two thin external layers of carbon steel.This means that the heat reaching the inner metallic wall of the overpack (by radiative exchange from the MPC or by convective exchange with the air in the channel) is almost completely transferred to the concrete.At this point, the heat transfer within the concrete wall is driven by two main factors: the thickness of the wall (that is 0.7 m) and the concrete thermal conductivity (that in the original model is imposed equal to 1.4 W/m-K, as in [6]).However, considering the multitude of plain concretes available and taking into account that the conductivity is dependent, among others, on the composition of the concrete itself, it is worth to make an attempt to evaluate the influence (if any) of different values of concrete conductivity on the PCT and, more generally, on thermal behavior of the system.For this sensitivity study, after a literature review [17][18][19], two "extreme" values have been taken into account: a lower bound of 0.7 W/m-K, and upper bound of 2.1 W/m-K.Higher values have not been considered, since they are usually attributed to reinforced concrete.

Results
Results from the performed sensitivity studies are reported in the following subsections, one for each considered factor: power profile, loss coefficients in the air channel and concrete conductivity.Simulations outcomes will be presented mainly in terms of PCT; however, axial temperature profiles will be displayed and discussed, when needed.

Axial Power Profile
For what concerns the maximum cladding temperature, the use of the axial power profile in the "core" region results in a modest reduction of the PCT value: in fact, a decrease of 2 K is calculated (630.5 K for the base case, 628.5 K when considering the non-uniform axial power profile).The location of the PCT is the same i.e., the upper part (11 th axial level) of the central FAs.However, as it can be seen in Figure 4, the addition of the axial power profile has a localized effect: following the shape of the burnup distribution, the temperatures in the upper and lower ends are slightly lower, whilst higher temperatures are calculated for the central part of FAs.

Flow Losses in the air channel
The variation of loss coefficients in the FPs associated with the air channel causes a change in the mass flow rates.As it is reported in Table 3, the highest mass flow rate is associated as expected with the case "FlowLosses 2", in which the loss coefficients are minimized.Case "FlowLosses 3", on the other hand, presents a mass flow rate similar to the "BaseCase", even with a quite different assessment of loss coefficients.Mass flow rate for case "FlowLosses 1" is, instead, in between the other two cases.
The change in the mass flow rates is reflected in the temperatures of both the air channel and the fuel, since the ability to extract heat from the canister changes in turn.As it can be seen in Figure 5, trends are the same, but lower temperatures are calculated in all three cases.Observing the profile for the fuel, the ΔT with respect to "BaseCase" is at its minimum in the lower part, and it increases moving upward towards the hottest section of the FAs.The same behavior can be noticed for the air in the annular channel; however, maximum ΔT is a bit more pronounced.
As expected, the lowest temperatures are connected with the highest mass flow rate ("FlowLosses 2"), for which differences of 15 K and 20 K (with respect to the "BaseCase") are calculated for the PCT and the maximum air temperature, respectively.On the contrary, temperatures for case "FlowLosses 3" are almost the same as in the "BaseCase".

Concrete Conductivity
As it can be seen in Figure 6 (left), the thermal conductivity of the concrete has almost no influence on the PCT or even on the temperature, at any axial level.This confirms that the main mechanisms for the extraction of the heat from the canister are the convective heat exchange in the air channel and, to a less extent, the radiative heat transfer from the canister wall to the overpack wall.However, concrete conductivity has an impact on the temperatures of the concrete overpack itself.As it can be observed in Figure 6 (right), a smaller ΔT between internal (hotter) and external (colder) concrete walls is linked to a higher thermal conductivity.On the contrary, the case with the lowest thermal conductivity shows a higher ΔT.This is consistent with the physical meaning of the thermal conductivity, that is the rate at which the material can transfer heat, either by receiving it from a hotter material or by passing it to a colder one.
The case with the lowest thermal conductivity is also the one with the highest temperature.However, temperatures are still below the limit as reported in [12], that is 422 K for normal operation.

Conclusions
The aim of the work is the creation of a more accurate and realistic model for the HI-STORM 100S system.In this framework, the present paper reports the efforts made in the evaluation of the influence of some modelling choices on the thermal response of the system, and particularly on the PCT, being a key parameter for the safe storage of SNF within a dry cask.
From the performed sensitivity studies, some insights can be drawn: • The employment of a non-uniform axial power profile has a localized effect: in fact, it affects mainly the fuel.Whilst there is no major impact on the PCT (only a 2K reduction), a change, even if limited, can be observed in the shape of the axial temperature profile: in fact, following the shape of the burnup distribution, the temperatures in the upper and lower ends are slightly lower, whilst a bit higher temperatures are calculated for the central part of FAs.• The sensitivity study shows that a reduction of 15 K (with respect to the "BaseCase") is foreseen for the PCT when considering low loss coefficients in the FPs associated to the air channel.As a consequence, a proper definition of the loss coefficients in the air channel is of utmost importance for the correct reproduction of the heat extraction from the fuel.• The thermal conductivity of the concrete has almost no influence on the PCT.This corroborate the idea that the main heat removal mechanisms from the canister are the convective heat exchange in the air channel and, to a less extent, the radiative heat transfer from the canister wall to the overpack wall.However, as expected, temperatures in the concrete layer of the overpack are influenced by the concrete conductivity values.In short, chosen parameters, taken individually, seem to have an influence on the thermal behavior of the cask.However, a further step needs to be done to investigate their conjoint influence.This will be proposed in Part II, where findings from the presented sensitivity studies will be leveraged to set up a more realistic MELCOR model for the HI-STORM 100S cask.

Figure 3 .
Figure 3. Sketch of the Air Channel Nodalization.

Table 1 .
Relative Power Density for each axial level in MELCOR.