Thermal performance of a concrete cask: Methodology to model helium leakage from the steel canister

Annals of Nuclear Energy 108 (2017) 229–238

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Thermal performance of a concrete cask: Methodology to model helium leakage from the steel canister J. Penalva ⇑, F. Feria, L.E. Herranz CIEMAT, Unit of Nuclear Safety Research, Avda. Complutense, 40, Madrid 28040, Spain

a r t i c l e

i n f o

Article history: Received 21 November 2016 Received in revised form 31 March 2017 Accepted 9 April 2017 Available online 12 May 2017 Keywords: Dry storage cask Depressurization CFD simulation

a b s t r a c t Concrete cask storage systems used in dry storage allocate spent fuel within containers that are usually filled with helium at a certain pressure. Potential leaks from the container would result in a cooling degradation of fuel that might jeopardize fuel integrity if temperature exceeded a threshold value. According to ISG-11, temperatures below 673 K ensure fuel integrity preservation. Therefore, the container thermal response to a loss of leaktightness is of utmost importance in terms of safety. In this work, a thermo-fluid dynamic analysis of the canister during a loss of leaktightness has been performed. To do so, steady-state and transient Computational Fluid Dynamics (CFD) simulations have been carried out. Likewise, it has been developed two methodologies capable of estimating peak fuel temperatures and heat up rates resulting from a postulated depressurization in a dry storage cask. One methodology is based on control theory and transfers functions, and the other methodology is based on a linear relationship between the inner pressure and the maximum temperature. Both methodologies have been verified through comparisons with CFD calculations. The period of time to achieve the temperature threshold (673 K) is a function of pressure loss rate and decay heat of the fuel stored in the container; in case of a fuel canister with 30 kW the period of time to reach the thermal limit takes between half day (fast pressure loss) and one week (slow pressure loss). In case of a 15% reduction of the decay heat, the period of time to achieve the thermal limit increase up to a few weeks. The results highlight that casks with heat loads below 20 kW would never exceed the thermal threshold (673 K). Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction A concrete cask is an alternative system for storing spent fuel. As other options, it has to guarantee the cooling of fuel assemblies as one of the main objectives to meet. This requirement is of primary importance to fuel integrity preservation and, from the regulatory point of view, if clad temperature is below the prescribed limit of 673 K (USNRC, 2003) intact claddings should not get damaged during dry storage. In this frame, the thermo-fluid dynamics of spent fuel storage casks is a key aspect in safety analyses. Some casks designs rely on helium (He) over normal pressure to provide effective convective cooling to fuel during dry storage. As it is mentioned in the ISG-25 (USNRC, 2010), the pressure loss of the canister housing the spent fuel could degraded the cooling capacity of the system. In recent years, Takeda et al. (2008), Toriu et al. (2013) and Liu et al. (2015) have been studying the thermal effect of a helium gas leak in the canister. Takeda et al. (2008) studied ⇑ Corresponding author. E-mail address: [email protected] (J. Penalva). http://dx.doi.org/10.1016/j.anucene.2017.04.049 0306-4549/Ó 2017 Elsevier Ltd. All rights reserved.

experimentally this effect in two types of canisters, Reinforced Concrete cask (RC) and Concrete Filled Steel cask (CFS). They found that temperatures of the center of the top and bottom canister surface changed remarkably during the helium gas leak. Toriu et al. (2013) developed and verified a 2D computational method to predict the change of the temperature distributions around the canister boundaries. Liu et al. (2015) developed a 3D steady state model of a vertical dry storage cask with different canister inner pressure to perform a thermal analysis. A number of studies have proved the capability of Computational Fluid Dynamics (CFD) to accurately predict the thermal evolution of fuel in dry storage casks (Heng et al., 2002; Zigh and Solis, 2008; Lee et al., 2009; Holtec International, 2010; Tseng et al., 2011 and Herranz et al., 2015). Nonetheless, this modeling approach requires many computing resources and its application in long transients is still a challenge. The aim of the present paper is to thermally characterize the spent fuel response to a postulated depressurization of the canister of a dry storage cask through the fuel peak temperatures and heatup rates. To do so, two approximated methodologies are proposed

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Nomenclature A

a

b cS cs,max K K1 m Pabs Pg Pg,0 q Q Qmax q1 q2 qS R2 Ri

q

T T0 THe

Area Fitting parameter (553.21 kPa/kPab) Exponent of the potential function (0.028 s
1) Sound velocity Maximum sound velocity Flow coefficient Steady state gain of the system Mass Absolute pressure Pressure gauge Initial pressure gauge Decay heat Volume flow Maximum volume flow Heat rejected to the environment by natural convection Heat rejected to the environment by natural convection and radiation Heat deposited by the solar radiation Regression coefficient Individual gas constant Density Maximum temperature Initial maximum temperature Helium average temperature

T1 t t0 tPf tTf

sT sP

V

Steady state maximum temperature Time Starting time Final pressure time Final temperature time Thermal time constant Pressure loss time constant Volume

Acronyms BPGs Best Practice Guidelines CFD Computational Fluid Dynamics CFS Concrete Filled Steel cask DO Discrete Ordinates HI-STORM Holtec International Storage and Transfer Operation Reinforced Module MPC Multi-Purpose Canister NDT Non-Destructive Testing RC Reinforced concrete cask SCC Stress Corrosion Cracking SSM Steady State Methodology TF Transfer Function

to avoid expensive 3D transient calculations. Comparisons set with specific transient Computational Fluid Dynamics (CFD) calculations verify the capability of the approaches here proposed. Moreover, a thermal analysis has been carried out, whereby it has been observed thermal differences between normal and atmospheric inner pressure. 2. Global approximation 2.1. Scenario description The dry storage system considered in this work is a vertical concrete cask, in which the spent fuel assemblies are placed in a multipurpose canister (MPC) that is embedded inside a metal and concrete overpack. It is commonly used for storing spent fuel (Hanson et al., 2012). A detailed description can be found in Herranz et al. (2015). Stress corrosion cracking (SCC) may weaken the welding seams of the MPC up to developing micro-cracks, often too small to be detected by conventional non-destructive testing (NDT) methods (EPRI, 2011). This is the main scenario addressed in the present work by assuming a helium leak from the MPC through a narrow pathway. 2.2. Conceptual approach Fig. 1 shows the qualitative thermal evolution of a pressure loss transient in the canister. Under normal conditions, pressure level is steady. At t0 helium leaks and pressure falls down to ambient pressure. Such pressure decrease causes a substantial reduction of He density that decreases the gas heat capacity, so that He remaining in the cask heats up. Given the thermal inertia of the system, the thermal transient is always slower or equal than the pressure one. In other words, at the time pressure hits atmospheric values (tPf), He is still heating up and it will take some time to reach an asymptotic behavior (tTf).

Fig. 1. Conceptual pressure and thermal evolution in a spent fuel canister during a postulated pressure loss.

3. Tools In order to develop the methodologies previously cited it has been necessary to perform some CFD calculations and to develop an equation that describes the pressure evolution in a fuel canister during a pressure loss. It is worth to noting that to derive this equation it has been used some CFD calculations.

3.1. CFD calculations The approach adopted to develop an engineering methodology that describes the maximum fuel temperature during gas leak is based on 3D thermo-fluid dynamics calculations. These calculations have been carried out with the CFD Fluent 16.0 code.

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The simulations performed with Fluent 16.0 fulfilled the CFD Best Practice Guidelines (BPGs) of the US Nuclear Regulatory commission (USNRC, 2014). A thorough description of the modelling done in Fluent 16.0 is given by Herranz et al. (2015). It is worth to note that the validation of the thermal results is not possible due to the lack of actual data from the storage system studied. Instead, the 3D CFD model verification has been done by comparing to Holtec International estimates (Holtec International, 2010). Furthermore, in the appendix, it has been performed a thermal analysis of the cask studied under normal and atmospheric MPC inner pressure. 3.2. Pressure evolution One of the main features of a transient in a complex system such as a dry storage cask is the time length. An estimation of the characteristic depressurization time has been performed. To do so, it has been supposed that the helium inside the canister follows the ideal gas law (P abs V ¼ m Ri T He ). The derivative of ideal gas law with respect to time, t, at constant volume is written as:

dPabs dm T He m dT He Ri ¼ þ Ri dt V dt dt V

ð1Þ

As it can be observed in this equation, the pressure variation in the canister depends directly on the mass loss from the leakage and the gas temperature variation. The mass flow can be expressed like:

dm Pabs ðtÞ ¼
qðtÞ Q ðtÞ ¼
Q ðtÞ: dt Ri T He

ð2Þ

In this case the leakage volumetric flow, Q, is limited by the sound velocity in the medium, cs, as a maximum flow speed through the leakage spot. The sound velocity can be defined as a function of the gas temperature, thus, the maximum sound velocity, cs,max, is function of the maximum gas temperature (cs,max = 1270 m/s). Consequently, the maximum volumetric flow through a leakage is given by

Q max ðtÞ ¼ K A cs;max

ð3Þ

where K is the flow coefficient (2/3 for a perfectly circular hole). It is worth noting that these values increase the velocity of depressurization. Substituting the maximum volumetric flow into Eq. (2), it will be transformed to

dm Pabs ðtÞ ¼
K A cs;max dt Ri T He

ð4Þ

On the other hand, in order to approximate the gas temperature variation (second term of Eq. (1)), first it has been correlated the gas temperature with the pressure. Fig. 2 shows the helium average temperature as function of the inner pressure. In this figure the helium average temperature comes from steady state CFD simulations at different inner pressure, from normal condition to atmospheric pressure. The decay heat simulated is the maximum heat allowed in the cask. Therefore, this choice maximizes the gas temperature variation and hence, it increases the depressurization rate. It can be observed that the helium temperature follows a potential function (R2 = 0.98): In this figure the helium average temperature comes from steady state CFD simulations at different inner pressure, from normal condition to atmospheric pressure. The decay heat simulated is the maximum heat allowed in the cask. Therefore, this choice maximizes the gas temperature variation.

T He ¼ a P
b abs

ð5Þ

Fig. 2. Helium average temperature as a function of inner pressure.

The derivative of the Eq. (5) with respect to time, it is written down.

dT He dPabs ¼
a bP
b
1 abs dt dt

ð6Þ

Substituting Eq. (4) and Eq. (6) into Eq. (1), it is obtained:

dPabs K A cs;max m dPabs ¼
Pabs
Ri abP
b
1 abs V dt V dt

ð7Þ

Furthermore, substituting Eq. (5) into the ideal gas law and expressed as a function of the mass, it is then:

m¼

Pabs V V ¼ Ri T a Ri P
b
1 abs

ð8Þ

Finally, substituting Eq. (8) into Eq. (7), the differential equation for the depressurization can be expressed as

1 dPabs K A cs;max ¼
Pabs dt Vð1 þ bÞ

ð9Þ

Solving the differential equation, it is obtained an expression of the gauge pressure as a function of time; it can be written as

Pg ðtÞ ¼ Pg;0 e
K

A cs;max t=v ð1þbÞ

ð10Þ

As it can be observed, v ð1 þ bÞ=K A cs;max is the pressure loss time constant, sP. This equation is similar to the expression defined in DIN EN 1330-08 (DIN, 1998), but in the Eq. (10) it has been taken into account the gas temperature variation. In this connection, it should be said that the gas temperature variation only appears in b (0.028 s
1). It is worth to note that the smaller sP the faster pressure loss.

Pg ðtÞ ¼ Pg;0 e
t=sP

ð11Þ

As an example, Fig. 3 displays the evolution of pressure for a micro-fissure of 100 mm in a canister. In this case, the pressure loss time constant is around 16 days. It is worth to note that evolution of pressure is a very slow process (around 3 months to reach the steady state). In CFD codes the calculation time is much higher than the real time. Therefore, the time required to make a 3D model of the entire scenario would be impractical and expensive. In addition, each 3D study would be specific, so that any change in the crack dimensions would need an additional run. 4. Methodologies In this work, it has been developed two methodologies. The first one has been called Transfer Function (TF) methodology and it has been founded in the control theory; this is an interdisciplinary

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Fig. 3. Pressure evolution for a micro-fissure of 100 mm.

branch of engineering and mathematics that deals with the behavior of dynamical systems. It has been analyzed the thermal behavior of the cask during a pressure loss, and it has been obtained a relationship between maximum fuel temperature and canister inner pressure evolution. Finally, this pressure evolution is replaced by the Eq. (11). The second methodology has been called Steady State Methodology (SSM) and it has been based on a correlation between steady state temperature, decay heat and inner pressure; this correlation is based on CFD simulations. Assuming that the pressure loss is very slow, it can be assumed that the instantaneous temperature is similar to the steady state temperature. 4.1. Transfer function methodology As transient 3D calculations are computationally expensive, an approximate approach is to focus on the clad maximum temperature and find a correlation with the instantaneous pressure inside the canister during the loss of leaktightness transient. The control theory (Ogata, 2001) allows achieving it. The cask has been simplified to a linear system, in which a relation exists between the input, DP(t), and the output, DT(t), where the input is the difference between initial and transient inner pressures, Pg,0-Pg(t), and the output signal is the difference between the clad transient peak temperature and the initial one, T(t)-T0. The differential equation describing the system behavior is (Ogata, 2001):

sT

dDTðtÞ þ DTðtÞ ¼ K 1 DPðtÞ dt

ð12Þ

The system is characterized by the value of the coefficients sT and K1. Where, sT is the thermal time constant and K1 is the steady state gain of the system. These coefficients are independent of the input signal. Alternatively, instead of trying to find the solution in the time domain, each time-dependent variable and the differential equation can be transformed to a different variable domain in which the solutions can be obtained in a more straightforward way; then, an inverse transform would translate the solution into the time domain. The transform used in these cases is the Laplace transformation. The Fig. 4 shows the block diagram of the system in the time (up) and in Laplace (down) domains.

Fig. 4. Block diagram in the time (up) and in Laplace (down) domains.

Applying the Laplace transform to Eq. (12), it can be rewritten as.

ðsT s þ 1 ÞDTðsÞ ¼ K 1 DPðsÞ

ð13Þ

The transfer function in the Laplace domain is

HðsÞ ¼

DTðsÞ K1 ¼ DPðsÞ sT s þ 1

ð14Þ

The input signal used in the system analysed is the step function of amplitude DPS (Heaviside step function). In the Laplace domain this input signal is DP(s) = DPS/s. Then the output signal can be written as:

DTðsÞ ¼

DP S K 1 sðsT s þ 1Þ

ð15Þ

To separate the components of Eq. (15) it has been used the partial fraction expansion. Thus, the output signal become

DTðsÞ ¼

DP S K 1 DP S K 1
s s þ 1=sT

ð16Þ

The inverse Laplace transform of Eq. (16) gives (Ogata, 2001)

DTðtÞ ¼ ð1
e
t=sT ÞDPS K 1

ð17Þ

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Fig. 7. Comparison between the Fluent 16.0 simulation and the TF for a fast pressure loss process and q = 20 kW.

Fig. 5. DT(t) after a sudden pressure change (30 kW).

Table 1 Initial pressure gauge and temperature, thermal time constant and gain of the system for 20 and 30 kW. q (kW)

Pg,0 (kPa)

T0 (K)

sT (h)

K1

20 30

372.65 434.32

520.31 621.48

35.94 29.01

0.41 0.3

Fig. 8. T1 as a function of the inner pressure (q = 30 kW).

Fig. 6. Comparison between the Fluent 16.0 simulation and the TF for a fast pressure loss process and q = 30 kW.

The output has an initial value DT(t = 0) = 0, and this asymptotically approaches DT(t) = DT1 as t ? 1.

DTðt ! 1Þ ¼ DPS K 1 ¼ DT 1

ð18Þ

Then the gain of the system is:

K1 ¼

DT 1 DP S

ð19Þ

On the other side, it is necessary to know the thermal time constant to characterize the system. One way to perform this is to equalize the elapsed time and the thermal time constant (t = sT), thus the Eq. (17) become

DTðt ¼ sT Þ ¼ ð1
e
1 ÞDT 1 ¼ 0:632DT 1

ð20Þ

Therefore, when the elapsed time is equal to the thermal time constant the output achieves 63.2% of its total change. To determine the thermal time constant, it is necessary to carry out a tran-

Fig. 9. T1 under normal operation and atmospheric pressure conditions for different decay heat (between 30 and 10 kW).

sient simulation, where the system (cask) is exposed to a step input. (i.e., the pressure changes suddenly from normal to atmospheric pressure). Fig. 5 shows the results obtained for a spent fuel decay heat of 30 kW. The value of the thermal time constant is 29.01 h. Thus, the evolution of the maximum fuel temperature can be written as

TðtÞ ¼ ð1
e
t=sT ÞK 1 DPðtÞ þ T 0

ð21Þ

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Fig. 10. Pg,0 as a function of the decay heat.

Fig. 11. Comparison between the SSM and the TF for a slow (a), medium (b) and fast (c) pressure loss process (q = 30 kW).

Finally, using Eqs. (11) and (21) the evolution of the maximum fuel temperature can be written as

TðtÞ ¼ ð1
e
t=sT Þð1
e
t=sP ÞK 1 Pg;0 þ T 0

ð22Þ

It should be pointed out that the first exponential term is related to the thermal inertia, whose characteristic time is around one day and it is a function of the decay heat. The second exponential term is associated to the gas leak, whose characteristic time mainly depends on the size and form of the crack; for the crack considered before (perfectly circular hole of 100 lm) it is around

16 days, as previously cited. In this case the peak temperature evolution is dominated by the gas leak term, because the pressure time constant is 13 times higher than the thermal one. These constants are equals when the crack is around 360 lm. Table 1 shows the thermal time constant, the steady state gain of the system, the initial pressure gauge and the initial temperature, for two different decay heats (20 and 30 kW). It is worth noting that the thermal time constant is higher for 20 kW than for 30 kW; in other words, a decay heat increase means a quicker system response. Contrarily, the system gain grows nearly 30% in the 20 kW case with respect to the 30 kW ones; namely, temperature

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Fig. 12. Thermal evolutions in a canister with a 100 mm pore for different decay heat (between 30 and 10 kW) estimate with the methodologies (TF and SSM).

Fig. 13. Thermal evolutions in a canister with 30 kW of decay heat for different pores (between 200 and 50 mm) estimate with the methodologies (TF and SSM).

rise is bigger for 20 kW (around 11%). This can be explained by the different impact of the loss of efficiency of convection and the higher contribution of conduction and radiation at atmospheric pressure. In others words, the radiation heat transfer is proportional to the difference of temperatures to fourth powers, therefore, the radiation heat transfer enhances when the temperature difference increases. It is worth to note that the thermal time constant and the steady state gain could be used in any pressure evolution (Ogata, 2001). To demonstrate the reasonable behavior of the control function developed, its results have been compared to those coming from Fluent 16.0 transient calculations for a fast depressurization transient. Fig. 6 and Fig. 7 show the comparison between the Fluent 16.0 simulation and the transfer function (TF) in a fast pressure loss process for a decay heat of 30 and 20 kW, respectively. As it can be seen, in the Fluent 16.0 simulation the system has an initial delay of 1.2 and 1.4 h for 30 and 20 kW, respectively. The discrepancy produced by the delay is reduced with time during the first 24 h. 5. Steady state methodology 5.1. Correlation of steady state temperature In this case, it has been supposed that the pressure transient is very slow. Then, the maximum fuel temperature achievable at any pressure would be that of a steady state. By using Fluent 16.0 cal-

culations, steady state temperatures (T1) can be correlated with MPC inner pressure (Pg) and fuel decay heat (q). Thus, an analytical database of T1, Pg and q has been built to develop such a correlation. First, a few steady state simulations at different Pg but same q (q = 30 kW) have been conducted (Fig. 8). As observed, in the pressure range of interest in this study, a straight line captures reasonably the calculated trend. In other words, a stored fuel with a 30 kW decay power would experience a temperature increase of roughly 0.32 K per each pressure unit in case that canister leaked (i.e., 0.32 K/kPa). Second, steady state simulations with variable decay heats between 30 and 10 kW, under both normal operation and atmospheric pressure conditions, have been carried out. Fig. 9 shows the steady state fuel maximum temperature obtained in each case. It can be observed that under operating conditions the temperature increase corresponding to the different decay heat in the canister is nearly the same (about 10 K/kW); however, at atmospheric conditions such sensitivity decreases with power increase (i.e., 14 K/kW between 10 and 15 kW; and 8 K/kW between 25 and 30 kW). The reason under this different behavior at different pressures is the efficiency loss of convection at atmospheric pressure and, as a consequence, the major role played by thermal radiation. Finally, the dependence of the initial pressure gauge, Pg,0, with q (Fig. 10), allows correlating both variables in a quite simple way,

Pg;0 ¼ 6:16q þ 249:35

ð23Þ

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10kW 6 q 6 30kW

10 kW 6 q 6 30 kW That in turn highlights the relation of maximum clad temperature with pressure and decay heat (note that this expression is defendable just in the range explored in the present study):

T 1 ðq; Pg Þ ¼ 454:46 þ 10:35q
0:35Pg

0kPa 6 Pg 6 Pg;0 ðqÞ The correlation regression coefficient, R2, is 0.994. The expression consists of: a heavy independent term, which is the highest contribution under the conditions explored; the second term representing the heating effect, whose significance decreases along with efficiency of thermal energy dissipation mechanisms (either convection at high pressure or thermal radiation at near atmospheric pressures). It is noteworthy that the cooling term upper limit is bounded by the initial internal pressure that, in turn, it is a function of the decay heat (as shown in Eq. (23)). 5.2. Evolution of the maximum fuel temperature

The steady state methodology (SSM) has been compared with a transfer function (TF), which has been verified by CFD simulations previously. As mentioned above, the TF could be used in any pressure evolution (Ogata, 2001). Fig. 11 shows the comparison between the SSM and a TF for a slow (a), medium (b) and fast (c) pressure loss process. As it can be seen, in the slow and medium pressure loss the estimates of both approaches are quite close to each other. However, in the fast pressure loss significant discrepancies are observed. Anyhow, the SSM approach yields a conservative value of the maximum temperature, due to the fact that the kind of fitting chosen in the Eq. (24) does not encompass the entire role played by thermal radiation at high temperature (high heat load and low inner pressure). 6. Application

During the depressurization the transient maximum temperature of the fuel, T(t), is always less than the maximum steady state, T1, for a fixed pressure. However, when the variation of the pressure is a very slow process (e.g., micro-fissure of 100 mm (EPRI, 2011)) both temperatures can be approximated:

ð25Þ

Thus, using Eqs. (11), (23)–(25) the evolution of the maximum fuel temperature can be written as

Tðq; tÞ ¼ 454:46 þ 10:35q
0:35ð6:16q þ 249:35Þe
t=sP

5.3. Verification of the steady state methodology

ð24Þ

10kW 6 q 6 30kW

TðtÞ  T 1

tP0

ð26Þ

In this section an application of the methods showed above (SSM and TF) is shown. Given the key role played by cladding temperature, the focus is placed on this variable. Fig. 12 shows the fuel maximum temperature evolution for different decay heat (between 30 and 10 kW) but with the same pore (100 mm) estimate with both methodologies (TF and SSM). As it is shown, the temperature threshold (673 K) is only achieved when the decay heat is at or over 20 kW; in other words, when total power in the canister is less than 20 kW, the thermal limit will not be ever reached. As expected, for higher powers the time to reach the threshold is the shorter.

Fig. A1. Cask axial temperature (K) distribution (h = 0°) for normal (a) and atmospheric (b) MPC inner pressure (q = 30 kW).

J. Penalva et al. / Annals of Nuclear Energy 108 (2017) 229–238

Fig. 13 shows the fuel maximum temperature evolution for different pores (between 200 and 50 mm) but with the same decay heat of (30 kW) estimate with both methodologies (TF and SSM). As it is shown, the time to achieve the temperature threshold (673 K) is very sensitive to changes in the pore size.

7. Final remarks The present work has developed two alternative methodologies to predict thermal transients in case of a postulated loss of leak-

237

tightness in the spent fuel canister of a concrete cask for dry storage. However, despite being a low-probability scenario it is safetysignificant. One approximation is based on control theory (TF) and the other one is based on estimating steady states at different pressures (SSM), from the one at normal operating conditions down to atmospheric pressure. Steady state temperatures have been estimated through modeling the 3D thermo-fluid dynamics with Fluent 16.0. The TF methodology has been verified through comparisons with transient CFD simulations and the SSM has been verified through comparisons with TF approach. By applying the methodologies, a number of insights into the scenario investigated have been found:  The time to achieve the temperature threshold (673 K) is a function of the pressure loss rate and the decay heat stored in the container.  In case of a fuel canister with 30 kW, the time to achieve the thermal limit takes between half day (fast pressure loss) and one week (slow pressure loss). A decay heat reduction of just a 15% extends the time to go over the thermal threshold to a few weeks.  Canister housing spent fuel decay heat below 20 kW would never go over the thermal limit set by regulation.  Pore size is a determining factor of the grace time until reaching the regulatory thermal threshold.

Acknowledgments Fig. A2. Temperature axial profile at center fuels, for normal and atmospheric MPC inner pressure (q = 30 kW).

The authors wish to thank ENRESA, particularly F.J. Fernandez, for the technical discussions held and the financial support.

Fig. A3. MPC external wall temperature (K) distribution for normal (a) and atmospheric (b) MPC inner pressure (q = 30 kW).

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Fig. A4. Percentage of radiant and convective heat flux receives by the MPC inner surface for different inner pressures (q = 30 kW).

Appendix I: Thermal analysis The cask temperature distribution in a longitudinal section at 0° (azimuthal coordinates) for normal (a) and atmospheric (b) MPC inner pressure with the same decay heat (q = 30 kW) is presented in Fig. A.1. As it can be seen, the maximum fuel temperatures are 621.48 and 756.47 K for normal and atmospheric MPC inner pressure, respectively. However, even more outstanding than the expected temperature difference is the temperature distribution inside the canister. Whereas under normal conditions the peak clad temperature is reached in a quite local spot (z = 4.2 m) and there are not sharp radial thermal gradients, once at ambient pressure the peak temperature extends over a broad region (around 1 m long) of the central fuel assembly and show notable radial thermal gradients even with the neighbors fuel assemblies. These major differences clearly point out the convection efficiency loss at atmospheric pressure; in other words, convection causes a sort of uniform cooling of spent fuels, whereas thermal radiation works mainly from the honeycomb surface and its effect decreases with depth into the canister (i.e., the more peripheral a fuel assembly is, the better it is cooled). Temperature maps are further explored in the Fig. A2. This Figure shows the temperature axial profile at center fuels, for normal and atmospheric MPC inner pressure (q = 30 kW). The most outstanding observation is that the profiles are quite different. The normal pressure profile is characteristic of a vertical flow dominated by convection, the temperature increases linearly in the vertical direction along the active region since the gas heat-up is not trade off by the higher gas velocity at the upper regions of the fuel assemblies. However, the atmospheric pressure profile resembles that of a solid with internal heat generation dominated by conduction-convection. In an only conduction system the temperature is proportional to the square of characteristic length. It is worth to note that the He temperature increases 232 and 125 K

for normal and atmospheric MPC inner pressure, respectively. Furthermore, the difference between both simulations rapidly grows until the maximum (265 K) at z = 1.4 m. The Fig. A.3 presents the MPC external wall temperature distribution (K) for normal (a) and atmospheric (b) MPC inner pressure with the same decay heat (q = 30 kW). As it can be seen, at normal pressure the temperature is function of the height while at atmospheric pressure the temperature is function of the height and the azimuthal coordinate. It happens because the convection homogenizes the temperature while the inner radiation is function of the fuel basket geometry and this is azimuthally heterogeneous. Also, it is worth to note that the upper lid surface temperature distributions are quite similar but 10 K below at atmospheric inner pressure. The Fig. A.4 shows the percentage of radiant and convective heat flux received by the MPC inner surface for different inner pressures and with the same decay heat (q = 30 kW). As it can be seen the radiant heat flux becomes more important as the inner pressure becomes smaller. In other words, at normal pressure the MPC inner heat dissipation is dominated by the natural convection, and at low inner pressure the MPC inner heat dissipation is dominated by the radiation. References DIN, 1998. DIN EN 1330-8, Zerstörungsfreie Prüfung – Terminologie – Teil 8: Begriffe der Dichtheitsprüfung; Dreisprachige Fassung. EPRI, 2011. Welding and Fabrication Influence on Stress Corrosion Cracking (SCC). Lake Louise, Alberta, Canada, ATI-CSC-11. Hanson, B., Alsaed, H., Stockman, C., Enos, D., Meyer, R., Sorenson, K., 2012. Gap Analysis to Support Extended Storage of used Nuclear Fuel. PNNL-20509. Heng, X., Zuying, G., Zhiwei, Z., 2002. A numerical investigation of natural convection heat transfer in horizontal spent-fuel storage cask. Nucl. Eng. Des. 213, 59–65. Herranz, L.E., Penalva, J., Feria, F., 2015. CFD analysis of a cask for spent fuel dry storage: model fundamentals and sensitivity studies. Ann. Nucl. Energy 76, 54– 62. Holtec International, 2010. FSAR, Final Safety Analysis Report for the HI-STORM 100 Cask System, Holtec Report No. HI-2002444, rev 8. Downloaded from . Lee, J.C., Choi, W.S., Bang, K.S., Seo, K.S., Yoo, S.Y., 2009. Thermal-fluid flow analysis and demonstration test of a spent fuel storage system. Nucl. Eng. Des. 239, 551– 558. Liu Y., Tsai H.-C. Nutt M., 2015. Monitoring Helium Integrity in Welded Canisters. ASME Pressure Vessel and Piping Conference, Boston, MA. July 19–23, 2015. Ogata, K., 2001. Modern Control Engineering. Prentice Hall, Englewood Cliffs, New Jersey. Takeda, H., Wataru, M., Shirai, K., Saegusa, T., 2008. Development of the detecting method of helium gas leak from canister. Nucl. Eng. Des. 238, 1220–1226. Toriu D., Ushijima S., Takeda H., 2013 Development of monitoring system of helium leakage from canister. GLOBAL 2013. In: International Nuclear Fuel Cycle Conference – Nuclear Energy at a Crossroads. RN:45085399. Tseng, Y.S., Wang, J.R., Tsai, F.P., Cheng, Y.H., Shih, C., 2011. Thermal design investigation of a new tube-type dry storage system through CFD simulations. Ann. Nucl. Energy 38, 1088–1097. USNRC, 2003. Spent Fuel Project Office, Interim Staff Guidance N° 11, Revision 3 (ISG-11, rev 3). USNRC, 2010. Spent Fuel Project Office, Interim Staff Guidance N° 25 (ISG-25). USNRC, 2014. Best practice guidelines for the use of CFD in Nuclear Reactor Safety Applications. NEA/CSNI/R(2014) 11. Zigh, A., Solis, J., 2008. Computational Fluid Dynamics Best Practice Guidelines in Analysis of Storage Dry Cask, US Nuclear Regulatory Commission. MS-T10K08.