Study of the impact of decay heat on the in-containment temperature and pressure evolution following a hypothetical severe accident in a SFR

Annals of Nuclear Energy 138 (2020) 107189

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Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene

Study of the impact of decay heat on the in-containment temperature and pressure evolution following a hypothetical severe accident in a SFR Parthkumar Rajendrabhai Patel a,b,⇑, A. John Arul b, G. Pandikumar b a b

Homi Bhabha National Institute, Mumbai, India Nuclear Systems Design Group, Indira Gandhi Centre For Atomic Research, Kalpakkam, India

a r t i c l e

i n f o

Article history: Received 14 May 2019 Received in revised form 22 July 2019 Accepted 31 October 2019

Keywords: Decay heat Temperature Pressure Containment Source term Radiation Gamma transport

a b s t r a c t We study the relative contribution of decay heat compared to sodium fire and solar radiation to the temperature and pressure evolution in the containment of a medium-size SFR following a postulated severe accident. This is an important problem for containment design concerning source term assessment. Sodium fire model, gamma transport of released radiation and solar heat flux model have been integrated to arrive at the results. Further, sensitivity studies are performed with respect to major dependent parameters. From the study, it is observed that decay heat contribution is significant as substantially higher values of pressure and temperature are sustained in the containment for a longer duration. This has implications for long term radiation release from the containment. The sensitivity study shows that in-containment release fraction, operating power and core inventory are the most sensitive parameters for the temperature and pressure rise in the containment. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction The safety goal of advanced reactors, for instance, as proposed for the Gen-IV reactors is to ensure that radioactivity release to the public that is not restricted to a small area and short duration are to be practically eliminated (Safety Design Criteria for Generation IV Sodium-Cooled Fast Reactor System, 2017). The activity release for an accident of very low frequency should only require a temporary evacuation over a small area (Safety Design Criteria for Generation IV Sodium-Cooled Fast Reactor System, 2017). To achieve such a goal, unless the reactor design itself is inherently shown to be immune to core meltdowns, reactor containment needs to be engineered to provide the required level of defense against the release of radionuclides (RNs) to the environment that would meet the criteria. The function of a containment structure is to isolate or provide a controlled barrier between the reactor and the environment during normal operating condition as well as during accident conditions (Design of Reactor Containment Systems for Nuclear Power Plants, 2008). The containment also has a protection function against external impact loads. This means that the containment must be designed to withstand impact, pressure and thermal loads

⇑ Corresponding author. E-mail address: [email protected] (P.R. Patel). https://doi.org/10.1016/j.anucene.2019.107189 0306-4549/Ó 2019 Elsevier Ltd. All rights reserved.

to retain structural integrity and also provide necessary leaktightness following severe accident conditions. To demonstrate the adequacy of structural strength and leak-tightness requirements from internal events, usually, a severe accident that would challenge the containment is postulated. Such a severe accident would fit into the description of the design extension condition as per the Gen-IV safety criteria. For the current generation of Sodium-cooled Fast Reactors (SFRs), Unprotected Loss of Flow Accident (ULOF) is one such bounding severe accident scenario chosen for safety demonstration. The containment would need to meet the leak-tightness and structural integrity requirements during a ULOFA such that the site boundary doses are within the regulatory limit, i.e., there are no long term effects, and if there are any short term restrictions, it is to be limited over only a small geographical area. For a given SFR design if the ULOFA occurrence frequency is not small such that it cannot be treated as practically eliminated, detailed analysis of the severe accident sequence and loading on containment structures is to be done to demonstrate the safety. To this end when the accident sequence evaluation is carried out, the major cause of containment thermal and pressure loading is due to the combustion of sodium ejected into the containment due to the energetic transient initiated by the ULOF accident. There is a well-established methodology to assess conservatively the severe accident generated work potential and consequent sodium release to the containment (Stepnewski et al., 1971;

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Nomenclature




/gav g

qg r

Ra

r1;i rg;i Rg!g0 s

s

As Aw dp g f ðcþbÞ w

f ðcþbÞ hcðp!gÞ hcw Hngc mg mp ms mw

Emissivity coefficient g th volume averaged group flux Air density ðkg=m3 Þ Stephen boltzmann constant (5:667  108 W=m2 :K4 ) Absorption cross-section (m1 ) One group cross section for ith reaction (m2 ) Cross-section for ith reaction for the g th energy group (m2 ) Scattering cross-section from group g to g0 (m1 ) Reactor cooling time (s) Area of sodium pool ðm2 Þ Area of containment wall surface ðm2 Þ Pool diameter (m) Fraction of released decay heat deposited in the containment atmosphere Fraction of released decay heat deposited in the containment wall structure Heat transport coeffcieint (sodium pool to gas) ðW=m2 KÞ Wall heat convection coeffcient ðW=m2 :KÞ Gas transport due to natural convection (m/s) 1 = 0:14 dDp ðGrScÞ8 Mass of containment air (kg) Mass of sodium in sodium pool Mass of sodium burnt (kg) Mass of containment wall structure (kg)

Chellapandi et al., 2003). Following this, many studies have been performed for estimating the thermal load due to sodium fire in the containment for SFRs (Tsai, 1980; Beiriger et al., 1973; Lebel et al., 2018; Lebel et al., 2018). However, there is no systematic study concerning the heat added by the released fission products to the containment. The decay heat addition to the containment environment is important in two respects. First, it contributes to the temperature and pressure increase in the containment (thermo-mechanical load and driving pressure for leak through containment) and second, it has a source term aspect, where the deposited RN can re-evaporate due to deposited heat (Denman et al., 2012; Wichner et al., 1984). This article deals with the first aspect of the decay heat in containment. Stepnewski et al. (1971) studied the effect of temperature rise in the containment due to decay heat contributed from the noble gases. However, the effect of other volatile and non-volatile RNs were neglected. In a study to assess the thermal and pressure loading of the SFR containment, Velusamy et al. (2011) have considered decay heat and solar radiation effects. However, the decay heat contributions from various RN groups and the release fractions are not mentioned. Further, since the quantity of volatile and non-volatile RNs released into the containment is a function of the reactor vessel to containment release fraction, the sensitivity of the impact to these uncertain release fractions needs to be studied as well. Additionally, as newer nuclear designs are attempted with inherent safety features such as reduced sodium void coefficient, molten fuel diversion devices to prevent re-criticality, the contribution due to decay heat could become the significant factor for the containment pressurization. In this study, a highly conservative bounding estimate and a less conservative estimate of the thermal and pressure loads are made to provide useful insights and data towards the design of RN and energy management systems in the containment. Further, the relative contribution of various groups of RN is also quantified. For accurate estimation of decay heat, reactor specific reaction cross-section database is generated

Pg Pressure inside containment (Pa) Qs Heat generation rate from sodium combustion Q conv ðp!gÞ Convection from sodium pool to gas Q rðp!gÞ Radiation from sodium pool to released aerosols Ta Ambient temperature (K) Tg Gas temperature (K) Sodium pool surface temperature (K) Ts Tw Containment wall temperature (K) V0 Containment volume ðm3 Þ Vi Volume of ith mesh of central SA (m3 ) Mass fraction of oxygen X O2 CDA Core Disruptive Accident D Diffusitivity of oxygen, 2:74  105 ðm2 =sÞ DORT Discrete Ordinate Transport code Gr Grashoff number LWR Light Water Reactor RCB Reactor Containment Building RN Radionuclide S Stoiciometric combustion ratio SA Sub-Assembly Sc Schmidt number SFR Sodium cooled Fast Reactor SGDHRS Safety Grade Decay Heat Removal System SPX Superphoenix ULOFA Unprotected Loss of Flow Accident

for ORIGEN2 (Croff et al., 1983) calculations. With conservative in-containment release fractions derived from various source term literature (Balard and Carluec, 1996; Powers et al., 2010; Grabaskas et al., 2016), the released decay heat in the containment is determined. This article is structured as follows: Section 2 describes reference reactor design and accident scenario. Section 3 briefly lists various possible thermal loadings in the containment and discusses assessment of conservative and realistic estimates of temperature and pressure evolution due to sodium fire, decay heat and solar radiation. Section 4 discusses sensitivity on temperature and pressure evolution due to different parameters like incontainment release fraction, operating power, burnup, different equilibrium core loading. Section 5 concludes our findings.

2. Description of the reference reactor and accident scenario 2.1. A brief description of the reference reactor For this study, a typical medium-sized, pool-type fast reactor core with a power of 1250 MWt (500 MWe) is chosen as reference reactor, which is a generic reactor broadly based on Prototype Fast Breeder Reactor (PFBR), India. The reference reactor is referred to as ‘Prototype Sodium-cooled Fast Reactor’ (PSFR) in this article. It is a pool type reactor with the reactor assembly consisting of the core, control assemblies and primary circuits immersed in a large sodium tank installed below ground level. It has a concrete containment of approximately 1 meter thick above the reactor. It is a two loop reactor with two primary pumps, two intermediate heat exchangers per secondary sodium loop. The secondary loops are connected to modular steam generators to drive the turbine generator. The inlet sodium temperature is 670 K, and outlet sodium temperature is 820 K. The detailed reactor parameter information is given in Arul et al. (2017). The reactor core consists of 180 fuel

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subassemblies (SA). For the calculation of decay heat, a peak burnup of 100 GWd/tHM is chosen. The reactor containment building has an available volume of 74,000 m3 . Design parameters and safety calculation results for PSFR are given in Table 1.

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analysis is performed to assess the impact of release fractions on containment temperature and pressure rise.

3. Thermal and pressure loadings in the containment 2.2. Accident scenario description Since the study is about the impact of decay heat on containment temperature rise and pressurisation, the following brief description is provided on the accident scenario considered as input for the analysis. The severe accident scenario considered for containment design is the unprotected loss of flow accident (ULOFA), possibly initiated due to loss of AC power to both the primary pumps and consequent loss of coolant flow through the core. Details of the accident scenario for a generic SFR is presented in Reynolds and Kress (1980), and for the SFR model studied here in Harish et al. (2009). Traditionally, to cope up with the complexity of accident progression, the accident has been conservatively divided into three calculation stages namely, pre-disassembly, transition and disassembly phases (Stepnewski et al., 1971). As per the calculations for the reference SFR, about 350 kg of sodium would be ejected to the containment where it reacts with oxygen resulting in temperature and pressure increase in the containment (Velusamy et al., 2011). The radionuclides would be released to the containment in different stages of the accident. For instance, the radionuclides in the fuel-clad gap would have been released to the cover gas sometime before the core melt bubble formation. This would predominantly contain almost all the noble gas inventory and a small fraction of the volatiles. This inventory in the cover gas together with the volatiles trapped in sodium (top layer) would be released instantaneously to the containment when the sodium slug compresses the cover gas and impacts the roof slab. However, the radionuclides released to the sodium during the core melt phase (either as aerosols in vapour bubbles or dissolved and suspended forms) may not have time to reach the top of sodium pool, when the sodium makes contact with the roof slab. However, some fraction of the RN transferred to the sodium would eventually be released to the containment through leak paths developed in the top shield. The release, retention and transport of radionuclides during the core melt and energetic core bubble expansion in the main vessel is a complex subject of investigation (Brunett et al., 2014), and there is considerable experimental and theoretical work being devoted to accurate modelling of the various phenomena. Considering the complexity of accident phenomena and the specifics during an accident the fraction of RN released can only be predicted to lie within a range. Hence, based on available quantitative and qualitative accident analysis information and data from published literature best-judged RN release fractions are arrived at to serve as input for containment decay heat input calculations. Because of uncertainty in the determination of the source term, sensitivity

Table 1 Design parameters of PSFR (Arul et al., 2017). Parameter

Value

Reactor power Fuel Coolant Max. Fuel burnup No of fuel SA Blanket material Primary system Coolant inlet temperature Coolant outlet temperature Volume of containment Average containment wall thickness

1250 MWt/500 MWe PuO2 ð21%=27%Þ-UO2 Sodium 100 GWd/tHM 180 Depleted UO2 Pool 670 K 820 K 74,000 m3 usable 1m

For an ULOF accident presented in Section 2, the containment can experience thermal loads from the following sources (Fig. 1) viz.,1) Sodium fire 2) Decay heat from the RN released to the containment 3) Heat dissipation from the sodium pipes 4) Heat addition from secondary fires due to other flammable material in the containment 5) Solar radiation 6) Conductive and convective heat transport from roof slab. If 350 kg is taken as the reference amount of sodium released for PSFR, sodium fire is the dominant contributor to containment pressurization (Velusamy et al., 2011). The peak temperature and pressure will depend on the mode of sodium fire such as pool, spray or mixed fire. During spray fire, since the sodium droplets react faster with the oxygen available in the containment due to higher effective surface area for the combustion compared to the pool fire, the temperature rise in the containment will be faster compared to sodium pool fire (Tsai, 1980). However, for the PSFR the sodium leak paths are such that the sodium release will have horizontal streamlines; further, these leak paths are located below thermal insulation. Since the spray droplet size is a parameter determining the rate of fire, and if very fine droplets are formed the case would closely correspond to an instantaneous fire. The other extreme for large droplets would be the case of a pool fire. Hence in this study, an instantaneous fire and pool fire cases are studied. As per typical scenario derived from the calculation, the ejected sodium will not have a significant fraction of the RN from the core. Noble gases would have been ejected just before Na release, and other volatile RN would be released gradually. However, to be conservative, it is assumed that with this released sodium a certain fraction of other RN will also get released uniformly into the containment. These RNs (except noble gases) get deposited on the containment structures through various removal mechanisms (like agglomeration, diffusion, gravitational sedimentation, inertial impaction, thermophoresis, condensation) with time. Some of these RN can also leak from the containment. Since the deposited radionuclides (to containment structure) and airborne RN will continue to emit decay heat, the effect of decay heat in containment needs to be studied. Apart from this, the secondary sodium pipelines and SGDHRS pipelines can also contribute in case of insulation failure during the accident. However, the contribution from secondary sodium pipelines and other SGDHRS pipelines is small, (0.1 MW) (Velusamy et al., 2011) and hence not studied further. Besides, containment also houses some amount of flammable material like oil for cooling primary sodium pump mechanical seals, hydrogen produced due to concrete sodium reaction, which can contribute to the thermal loads. With respect to oil, the piping that carries them are double walled like sodium pipelines and has seamless construction and hence not treated in this study. Hydrogen production from concrete is not considered as sodium release is contained in the reactor vessel top shield which is steel. The other significant heat load is from solar radiation which will contribute to the heating of containment walls in the absence of containment cooling. The temperature will rise during the day and cool off during the night and early morning and the effect will be cyclical as presented in Velusamy et al. (2011). In the present study, thermal loading due to solar radiation is included along with released decay heat. The subsequent sections present the evaluation of sodium fire, decay heat and solar contribution to containment thermal and pressure loading.

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Fig. 1. Various possible heat sources during postulated accident.

3.1. Temperature and pressure evolution in the containment

Pg V 0 ¼ nkT g

The temperature and pressure evolution in the containment due to various heat source can be given by following general conservation equation. The temperature evolution in the containment atmosphere is given as follows,

dPg dT g V 0 ¼ nk dt dt

mg ðC v Þg

dT g ¼ Q source  Aw r
w ðT 4g  T 4w Þ  Aw hcw ðT g  T w Þ dt

1 dPg 1 dT g ¼ Pg dt T g dt

ð1Þ

The heat balance equation for the containment wall can be given as below,

mw ðC p Þw

ð3Þ

dT w ¼ hcw Aw ðT g  T w Þ þ Aw r
g ðT 4g  T 4w Þ  hcw Aw ðT g  T a Þ dt ð2Þ

where Q source is the heat source in the containment as shown in Fig. 1. The pressure in the containment is derived from the ideal gas law,

where Pg is the pressure inside the containment. k is the boltzmann constant. V0 is the volume of the containment. n is the number of molecules in the containment volume V0 . To find the temperature and pressure rise for particular source, the Eqs. (1)–(3) are solved simultaneously by including appropriate heat source term in Eq. (1). The equations are solved using the finite difference method in the python; The code is named as PFIRE. The sodium fire module is based on SOFIRE-II one cell model (Beiriger et al., 1973) with the inclusion of decay heat and solar radiation module (Fig. 3). A

P.R. Patel et al. / Annals of Nuclear Energy 138 (2020) 107189

switch is provided which can calculate the temperature rise and pressure rise for particular heat source by removing the other heat source terms. 3.2. Sodium pool fire contribution The release of sodium in the containment can result in vigorous reaction with containment air and with the vapour content in the containment atmosphere. Since these reactions are exothermic, the heat released due to these reactions will lead to deposition of heat to containment structures and containment air. This leads to temperature and pressure rise in the containment atmosphere. From the sodium-oxygen reaction, two main reaction products can be formed viz., sodium mono-oxide and sodium peroxide. The reactions are as follows:


 i:e:; ; 27; 196; kg kJO2
 2Na þ O2 ! Na2 O2 þ 11; 280 kg ofkJ Na i:e:; 16; 123 kgkJO2 2Na þ 12 O2 ! Na2 O þ 9; 460

kJ kg of Na

The heat and mass transfer aspect of sodium combustion has been studied by various authors varying from lumped to multidimensional treatment (Beiriger et al., 1973; Peak et al., 1975; Miyake et al., 1991; Yamaguchi and Tajima, 2009; Lebel et al., 2018). However, the goal here is to compare the temperature and pressure rise due to the decay heat contribution with sodium fire contribution. Hence, the containment atmosphere and sodium pool are treated as lumped systems. For estimation of the containment air temperatures and pressure rise due to sodium fire, two approaches are considered viz., i) Assuming the combustion of the released sodium in the containment take places instantaneously ii) Sodium combustion as per the oxygen diffusion over the sodium pool surface, i.e. pool fire. Additionally, it is assumed here that the containment is leaktight which will give conservative estimates for excess pressures. Case-1: The instantaneous burning of all released sodium leads to conservative temperature estimates. To calculate the temperature rise due to instantaneous burning of all released sodium, the heat source term (Q source ) in Eq. (1) will be ðreleased sodium amountÞ  DHdðtÞ. Where DH is the heat of formation of sodium monoxide or sodium peroxide. Here DH taken as the heat of formation due to sodium peroxide, which will give conservative estimates for the temperature and pressure rise. For instantaneous combustion, the peak temperature in the containment is 346 K (Fig. 2a), the corresponding peak pressure rise in

5

the containment is ~15 kPa (Fig. 2b). The containment design pressure is in the range of 25 kPa. The temperature and pressure reach room temperature and atmospheric pressure after the 2-3 h. Case-2: The rate of sodium combustion depends on the oxygen concentration in the containment and the rate at which oxygen gets transported to the surface of the sodium pool through natural convection. The rate of sodium combustion can be given as (Beiriger et al., 1973),

  dms kg ¼ Hngc X O2 As qg S s dt

ð4Þ

The heat transfer from the sodium pool can occur through convective heat transfer between the sodium pool and containment atmosphere (Q conv ðp!gÞ ), radiative heat transfer from pool to released aerosols (Q rðp!gÞ ).

Q conv ðp!gÞ ¼ hcðp!gÞ ðT s  T g Þ

ð5Þ

Q rðp!gÞ ¼
p rðT 4s  T 4g Þ

ð6Þ

The conservation equation for the sodium pool temperature can be given as follows,

mp ðC p Þs

dT s ¼ Q s  Q conv ðp!gÞ  Q rðp!gÞ dt

ð7Þ

The temperature and pressure rise in the containment are calculated with the Eqs. (1)–(3). Where the heat source term (Q source ) in the Eq. (1) will be Q conv ðp!gÞ þ Q rðp!gÞ . The sodium pool fire model has been validated with the FAUNA 5, 6 and LTV test 4 experiments and the estimates are well within bounds. For the pool fire simulated using the PFIRE code, the peak temperature is 335 K (Fig. 2a), the corresponding peak pressure rise in the containment is around 12 kPa (Fig. 2b). The peak temperatures occur within 5 min of combustion. The containment temperature and pressure approach the room temperature and atmospheric pressure within an hour. 3.3. Decay heat contribution 3.3.1. Decay heat in core The RN released to the containment will continue to deposit the decay heat to the containment atmosphere and surfaces. To calculate the core inventory and decay heat, the computer code ORIGEN2 (Croff et al., 1983) was used. The detailed calculation flow is given in Fig. 3. To get an accurate estimate of decay heat, ORIGEN2’s one group reaction

Fig. 2. Temperature and pressure evolution in the containment (Approach-1: Instantaneous complete combustion of 350 kg sodium, Approach-2: Sodium combustion according to oxygen diffusion over sodium pool surface).

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cross-section library for fission products, actinides and activation product was updated using the ENDF/B-VII.1 data (Chadwick et al., 2011). The ENDF/B-VII.1 data is processed through NJOY code (Macfarlane et al., 2016); DTFR and NG COUP is used to generate 175 grouped cross-section in suitable format as input to the Discrete Ordinate Transport code (DORT) (Rhoades and Childs, 1988). The DORT generated flux is volume averaged and used to collapse the 175 grouped cross-section to one group cross section as required by ORIGEN2. For inventory calculations, only the central SA (sub-assembly) with peak burnup is considered. Therefore, the central SA region is axially divided into N (N = 60) equal meshes, and volume averaging for each group is done as follows:

XN /agv g ¼

i¼0 P

th

V i /i;g Vi

ð8Þ

Where i is i mesh in the R-Z geometry along the Z direction in the central SA. A python script takes the DORT volume averaged flux

and the 175 group cross section as input and generates reactor dependent one group cross section for each reaction i.e., (n,c), (n, a), (n, 2n), (n, 3n), (n, f), (n, p) and updated in place of the default LMFBR-100 cross-section database. The one group cross sections are determined as follows:

X175

r1;i ¼

g¼0

rg;i /g

/g

ð9Þ

The core inventory is calculated for core-1 central SA with the reactor irradiation time of 540 full power days (three irradiation cycles of 180 duration). The central SA inventory is scaled for whole core, which is a conservative estimate with respect to fission products as any increase due to spectrum change near core periphery is less than the decrease due to fall in total flux. The major decay heat contribution in the core is from the fission products (~95%), the actinides contribute only 5% (Fig. 4). From the fission product contribution, lanthanides and noble metals

Fig. 3. Flow of calculation for thermal and pressure loadings due to sodium fire, released decay heat contribution and solar radiation.

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contribute significantly, which is almost ~50% of the total decay heat in the core. The volatile groups (mainly Noble gases, Halogens, Alkali metals, Barium) contributes ~37% of total decay heat. 3.3.2. Decay heat in containment Given uncertainties in modelling in-containment source term for fast reactors (Kissane et al., 2013) and significant contribution from the volatiles (~37%) and lanthanides (~30%) to total decay heat, the conservative estimates for the in-containment release fraction is essential. In the absence of the mechanistic models for fast reactors that can calculate the realistic estimates of incontainment release fractions, a detailed literature review has been carried out. From the literature, various recommended in-vessel source terms for different fast reactors are compiled (Dinunno et al., 1962; Reactor Safety Study, 1975; Soffer et al., 1995; Balard and Carluec, 1996; Guntay et al., 1996) and from these release fractions, a conservative set of release fractions are chosen, which are given in Table 2. The grouping of the radionuclides is done as per NUREG-1465 (Soffer et al., 1995). From tellurium group, the release fraction for tellurium is taken as 0.1 instead of

Table 2 Release fraction for different radionuclide groups. Group

Elements

Designated release fractions

Noble Gases Halogen Alkali metals Tellurium group

Xe, Kr I, Br Cs, Rb * Te , Sb, Se

1 0.1 0.1

Barium Noble metals

Ba, Sr Ru, Rh, Pd, Mo, Tc, Co

Lanthanides

La, Zr, Nd, Eu, Nb, Pm, Pr, Sm, Y, Cm, Am Ce, Pu, Np

Cerium *

1  104 0.1 1  104 1  104 1  104

The release fraction for tellurium is taken as 0.1.

1  104 . This is because of larger spread of release fraction values (release fraction: 4:0  107 to 0.6) reported in both Light Water Reactor (LWR) and SFR source term literature (Dinunno et al., 1962; Reactor Safety Study, 1975; Soffer et al., 1995; Balard and Carluec, 1996; Guntay et al., 1996). These conservative set of release fractions are multiplied with the relevant element’s decay heat in the reactor core to obtain decay heat for that element in the containment (Fig. 3). Considering the release fraction provided in Table 2, the total decay heat released to the containment is found to be about 7.6 MWt (immediately after the release). Where the noble gas, volatile RNs (halogens, alkali metals, tellurium, barium), and non-volatile RNs contribution is 4.86, 2.74 and 0.004 MWt respectively, this corresponds to 63.9% of the noble gas, 26.9% volatiles and 9.3% of the non-volatiles in the total decay heat released in the containment (Fig. 5). To assess whether the thermal loading due to decay heat is significant compared to sodium pool fire, the power released due to sodium pool fire and released decay power in the containment are compared in Fig. 6. Here, the equivalent thermal power from the sodium fire is calculated from Eq. (4) and heat of formation of sodium monoxide/sodium peroxide (DH). At t = 0, the power released due to sodium fire is around ~11 MWt, whereas the decay power in the containment is about 7.6 MWt which is approximately 69% of power from sodium pool fire. After completion of sodium combustion (roughly 3 min), the energy due to the decay

Fig. 5. RN group wise decay heat contribution in containment at cooling time s = 0 s (The contribution from noble metals, lanthanides, cerium and others group is negligible).

Fig. 6. Equivalent thermal power due to decay heat and sodium pool fire in the containment (for sodium fire 40% Na2 O and 60% Na2 O2 is considered).

Fig. 4. RN group wise core decay heat contribution at cooling time

s = 0 s.

heat from RN dominates (~2 MWt after 20 min) and nearly stays constant at 1.5–1.6 MWt for a longer time. This sustained decay power can prolong the temperatures and pressures in the containment in the long term. To calculate the pressure and temperature rise in the containment due to decay heat the heat addition term due to released

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decay heat is added in Eqs. (1) and (2). After addition of the heat source term due to decay heat, the temperature evolution equations are as follows,

dT g ¼ Q source  Aw r
w ðT 4g  T 4w Þ  Aw hcw ðT g  T w Þ dt g þ f ðcþbÞ Q decay heat ðtÞ

mg ðC v Þg

ð10Þ

Where, the Q source is the source term due to sodium pool fire. The heat balance equation for the containment wall can be given as below,

dT w ¼ hcw Aw ðT g  T w Þ þ Aw r
g ðT 4g  T 4w Þ dt w  hcw Aw ðT w  T a Þ þ f ðcþbÞ Q decay heat ðtÞ

mw ðC p Þw

ð11Þ

g

where f ðcþbÞ is the fraction of decay heat deposited in the containw

ment atmosphere. f ðcþbÞ is the fraction of decay heat deposited in the containment wall structure. It is known that the total decay heat contribution from c and b decay is nearly 50% each (Todreas et al., 1993). The gamma rays travel through the atmosphere with only a small fraction of energy transferred to the containment atmosphere, and a higher fraction gets deposited to the walls. Whereas for beta rays, all the energy gets deposited in the containment atmosphere. Further, the energy absorbed in the containment atmosphere will depend on the RN suspended vs deposited fraction. To accurately determine the decay heat contribution in the containment air and containment w structure (fðgcþbÞ and f ðcþbÞ ) needs to be determined. However, due to the complexity in modelling of decay heat deposition in the containment, three cases are studied which provides a range of values covering best judged to conservative cases. Case-1: In the first case, it is assumed that all the decay heat released to the containment is transferred to the containment atmosphere. By applying release fraction in Table 2, it is found that despite the selective release of noble gas RN from the reactor vessel to the containment, the contribution of the gamma and beta nearly remain 50% each (at t = 0, i.e., sodium ejection). The temperature rise due to all released decay heat depositing to containment atmosphere is about 344 K (Fig. 7a), which is about 9 K higher than ‘only sodium fire’ case. The peak excess pressure is about 15 kPa (Fig. 7b) 3 kPa higher than peak pressures due to ‘only sodium fire’ case. These containment atmosphere temperatures and pressures are sustained for a longer time. Even after one hour the temperature and pressure in the containment atmo-

sphere are ~317 K and 6 kPa respectively, which is about 15 K and about 6 kPa higher than ‘only sodium fire’ case. Case-2: In the second case, gamma transport is performed to estimate the gamma energy deposition in the containment using gamma transport modelling with DORT code. With respect to beta rays, it is assumed that all of the beta energy is absorbed in the containment air. (Though some fraction of beta active RN would get deposited in the containment inner surfaces a significant fraction of the heat would eventually be transferred to the containment atmosphere). The containment is modelled as an equivalent cylinder of height of 55 m and a radius of 22 m neglecting any structures in the RCB. The DORT code requires 42 group gamma energy spectrum as an input to calculate gamma transport. It was found that, due to the unavailability of discrete or continuous gamma intensity spectrum for several RNs, the integrated 18 group gamma spectrum provided by ORIGEN2 results in only 23% of total decay heat from gamma contribution. This deficit of ~25% can result in incorrect 42 group gamma spectrum and significant uncertainty in the prediction. Hence, the ORIGEN2 generated gamma intensity cannot be used for this calculation. The radionuclide for which the continuous and discrete gamma intensity is available, the gamma strength is determined using gamma intensity and activity. For RN for which the continuous or discrete gamma intensity spectrum is not available, the following method is adopted: The detailed flow of calculation is given in Fig. 8. From the ENDF/B-VII.1 files (Chadwick et al., 2011), average beta and gamma energies are determined. From the average gamma and beta energies, average decay heat th

contribution from beta and gamma rays for i RN is determined. This beta and gamma decay heat contribution is used to calculate th

the gamma fraction for i RN. The product of the gamma fraction and activity is taken as the photon source at given average gamma energy. Based on this average energy, the 42 gamma groups are populated. The obtained gamma spectrum yields ~43% contribution to the total decay heat. The gamma energy spectrum obtained by this method is used for further calculations. From the DORT generated flux in the containment, the gamma heating contribution is calculated as follows:

Power deposited ðWÞ ¼

42 X g¼1

Rga /g Eg þ

42 X 42 X g¼1

0

0

Rg!g /g ðEg0  Eg Þ s

g 0 ¼1

Fig. 7. Temperature and pressure rise in containment due to different percent deposition of decay heat in the containment.

ð12Þ

9

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th

Fig. 8. Flow of calculation for generating 42 group gamma spectrum from ENDF/B-VII.1 without using ORIGEN2 (The legends are same as per Fig. 3), where i is i RN.

The axial and radial profile of heat deposited in containment at t = 0 is given in the Fig. 9. The Fig. 9a, shows axial gamma decay energy distribution at various radial points (i.e., containment centre axis, near containment walls, containment wall inner surface, containment wall outer surface). Since, most contribution in the containment air is constant, the graph is plotted from z = 49 m. The z = 54 to z = 55 m is the containment wall region. The Fig. 9b shows the radial gamma energy distribution at various axial points (i.e., near containment floor, containment centre radial plane, near containment roof, containment roof inner wall surface, containment roof outer wall surface). Since the gamma decay heat contribution in containment air remains constant, the plot starts from r = 19 m to r = 22 m, where r = 21 to r = 22 m is the concrete region. The gamma flux spatial distribution in the containment air remains almost uniform in the containment, and most of the gamma-ray energy gets deposited in the containment walls. The maximum heating in concrete is 6.26 kW/m3 , and in the air, it is 5 W/m3 . Which corresponds to a total of 0.37 MW decay heat deposition in the containment air and rest of ~4 MW is deposited in the concrete. Further, most of the decay heat deposited in concrete is in the first 1=3rd portion of the containment wall, and this does not increase the wall temperature significantly. However, beta energy deposited in the containment atmosphere leads to increase in the containment peak temperatures to 340 K which is 5 K more than ‘only sodium fire’ case (Fig. 7a: 50% b and 5% c contribution). The corresponding peak pressure is about 14 kPa which is 2 kPa more than ‘only sodium fire’ case.

From the Fig. 7a, it can be seen that even after one hour, the temperature difference between containment air temperature for ‘only sodium fire’ case and containment air temperature with decay heat (50% b and 5% c contribution) is 10 K. The corresponding excess pressures difference is about 4 kPa more than ‘only sodium fire’ case. These sustained temperatures and pressure can lead to a sustained leak of the radionuclide to the environment at lower leak rates. Case 3: The above DORT calculations for the deposition of decay heat in the containment atmosphere and containment walls have been performed assuming that no internal structures are present in the containment. However, containment houses many structures like various cells for equipment, beams, and cranes. Hence, despite low absorption in air, the gammas can be deposited in the containment via various structural surfaces. To account for this deposition, it is assumed that 20% decay heat in the containment atmosphere is added from the gamma contribution. For this case, peak temperature in the containment is 342 K which is 7 K more compared to ‘only sodium fire’ case (Fig. 7a: 50% b and 20% c contribution). The corresponding peak pressure in the containment ~14 kPa which is 3 kPa more than ‘only sodium fire’ case. After one hour, these temperatures are about 312 K, which is about 10 K more compared to ‘only sodium fire’ case. The corresponding pressure rise in containment is about 4.5 kPa which is about 4 kPa higher compared to ‘only sodium fire’ case. It has been observed that the temperature and pressure rise due to decay heat addition are proportionate. For example, the temper-

Fig. 9. Axial and radial profile of heating at various points on the walls and interior of RCB.

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ature rise due to 100% decay heat deposition is 9 K compared to the only sodium fire case, while the temperature rise due to 50% b and 5% c deposition in the containment leads to 5 K compared to the only sodium fire case. 3.4. Solar heat contribution During reactor operation, temperatures in the containment atmosphere will be controlled by containment ventilation and cooling system. After core disruptive accident, the containment will be isolated. In this case, the contribution of the solar heat source also needs to be studied. The solar radiation calculation is as follows. Eqs. (1)–(3) are solved in PFIRE section considering radiation, convection and conduction phenomena through the wall. The heat source Q solar is added in Eq. (2). These equations were solved using the finite differencing method. For the calculation of solar insolation of 1000 W=m2 is taken, which is peak flux during typical summer noon in Chennai (Shanmugam et al., 2006). The wall surface area for the heat transfer is taken as 12,000 m2 . The emissivity and absorptivity of the walls are taken 0.88 and 0.60 respectively (Cengel et al., 2007). For the calculation, it is assumed that all containment walls are exposed to solar radiation. This assumption will give conservative estimates since; the containment will be surrounded by the control building, fuel building and steam generator building. The solar flux is assumed to be available for 9.00 h to 17.00 h. Since, before 9 h and after 17 h the solar flux will not be available due to surrounding buildings. As shown in Fig. 10a, the initial spike in the containment atmosphere temperature is due to sodium fire. Later, for one day the temperature rise is dominated by the decay heat contribution. The temperature rise due to solar radiation is seen after one day. However, this temperature rise is much gradual; even after two days of CDA, the temperature rise due to solar radiation is about 1–2 K (compared to decay heat). After 5 days the temperature rise is about 5 K. The containment atmosphere attains equilibrium temperatures of about 318 K after 8–9 days. We conclude that since significant radiation release will happen in the first few hours of the accident, the solar radiation will not have a significant impact on nuclear radiation release. In PWR accidents the typical peak pressures are in the order of few bars. For a fast reactor the typical pressures in RCB during severe accidents are in the order of few kPa only. The inclusion of decay heat leads to about 17% increase in peak pressure and 7 K

increase in peak temperature (for 70% decay heat deposition in containment atmosphere). This increase is significant in FBR context, and cannot be neglected. Though these increases are not significant for structural aspect of the containment, the sustained pressures and temperature rise (3 kPa and 8 K respectively after two hours) are important from radiological aspect. From current analysis, the sustained excess pressure of 3 kPa (after 2 h) does lead to ~0.17%V/hr leak rate for longer duration (the leak rate is arrived from experimentally determined pressure to leak rate correlation: L = 5:2  104 DP0:72 ). For sodium fire only case, the excess pressure comes to atmospheric pressure within two hours. This lead to extra ~4%V release within 24 h to the environment. These releases can result in higher site boundary dose estimates. These results are evident that during containment design, the inclusion of decay heat is necessary to estimate the first 24 h temperature and pressures. For the long term, the containment temperatures will be driven by solar radiation. However solar radiation is unlikely to have an impact on the radiation release. 4. Sensitivity study The decay power deposited in the containment, in general, could depend on the core inventory, reactor operating power, peak burnup attained before the accident, core equilibrium configuration and in-containment release fractions. The sensitivity of the deposited decay power with respect to these parameters would be helpful to assess the impact of decay power for the new design of similar reactor and containment structures. In this section, the sensitivity of various parameters such as core inventory, reactor operating power, core equilibrium configuration at the time of the postulated accident and the effect of release fractions are studied. For all sensitivity calculations, 70% of incontainment released decay heat deposition is used as a reference case. It is found that the containment atmosphere temperatures due to decay heat deposition are independent of irradiation duration. This is because short term decay heat is an approximate function of the operating power only. For the containment volume increase of 4–16%, the peak temperatures decreases up to 1–4 K (Fig. 11a). The corresponding excess pressure varies from 14 to 12 kPa (Fig. 11b). However, the temperature and pressure become independent of volume change after 20 min and follows the same trend. Next, the impact of different operating powers is studied. As shown in Fig. 12a, 20%, 50% and 100% additional power from

Fig. 10. Comparison of temperature and pressure rise in the containment due to solar radiation and decay heat in the containment.

P.R. Patel et al. / Annals of Nuclear Energy 138 (2020) 107189

11

Fig. 11. Temperature and pressure evolution in the containment for different containment volume.

Fig. 12. Temperature and pressure loadings in the containment for different operating powers.

reference power is considered with constant release fraction as given in Table 2. The peak temperature rise due to the 20% power rise is 1 K, after one hour also the temperature rise is 1 K. Whereas 50% power rise leads to a peak temperature rise of 2–3 K, after an hour the temperature rise is 5 K. The 100% power rise leads to 6 K increase in the peak temperatures and 9 K increase after one hour (Fig. 12a). The corresponding increase in peak pressures are 0.5, 1, 2 kPa respectively for factor of 1.2, 1.5, 2 in operating power (Fig. 12b). For sensitivity study with respect to in-containment release fractions, different light water reactor (LWR) and SFR literature have been compiled (Table 3). These release fraction databases are tabulated according to NUREG-1465 element grouping. Although the Chernobyl accident resulted in the failure of its enclosure, the release fraction of Chernobyl is considered here for the comparison purpose. Further, it was found that for some fast reactors like MONJU, SNR, Superphoenix (SPX), the release fraction for some groups was not available. For these groups, the release fractions are assigned as 104 , since most of them are non-volatile elements. The NUREG-1465 has categorized different release phases (for ex: gap release phase, in-vessel release, ex-vessel release etc.) for a postulated accident; For each release phase was represented by

a release fraction in NUREG-1465. The in-containment release fractions are a combination of the gap release, in-vessel release and exvessel release (in-containment release from vessel to containment due to molten core penetration through reactor vessel), however, since for pool type fast reactors the ex-vessel release is the less probable event, two separate cases are considered for comparison in Table 3. Where one case considers ex-vessel for NUREG-1465 release fractions and other does not consider ex-vessel release fraction. The release fractions in TID-14844 and Chernobyl are environment source terms; The actual in-containment release fractions can be higher. The release fraction from SPX, Monju, SNR are for the instantaneous release phase (Balard and Carluec, 1996). Using these release fractions, the containment air temperatures are calculated. Here, it should be noted that, for the calculation of the in-containment released decay heat, PSFR core inventory is used for all the cases. As shown in Fig. 13a, the peak temperatures in RCB varies from 338 to 355 K, with highest for Chernobyl release fractions. The peak temperatures and pressures for different release fractions wide spread for different release fraction cases (spread: temperature: 17 K, pressure: 6 kPa). For a longer time, the temperature spread due to different release fraction is much higher. For

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P.R. Patel et al. / Annals of Nuclear Energy 138 (2020) 107189

Table 3 Release fraction recommended by different literature/countries tabulated as per NUREG-1465 grouping. The bold values are ones for which releases fraction were not available and assigned to 104 . Group

Elements

NUREG 1465 (Soffer et al., 1995)

TID 14844 (Dinunno et al., 1962)

SNR (Energetic) (Balard and Carluec, 1996)

Monju (Energetic) (Balard and Carluec, 1996)

SPX (Energetic) (Balard and Carluec, 1996)

Chernobyl (Guntay et al., 1996)

NUREG 1465 Without Ex-vessel release fraction (Soffer et al., 1995)

Noble gas Halogen Alkali metal Tellurium Barium group Noble metals

Xe, Kr I, Br Cs, Rb Te, Sb, Se Ba, Sr Ru, Rh, Pd, Mo, Tc, Co La, Zr, Nd, Eu, Nb, Pm, Pr, Sm, Y, Cm, Am Ce, Pu, Np U

1 0.6 0.6 0.3 0.12 0.005

1 0.5 0.01 0.01 0.01 0.01

1 0.5 0.5 0.5 1.70E02 1.00E04

1 0.1 0.1 0.1 1.00E04 1.00E04

1 5.00E09 5.00E05 4.00E07 3.00E03 1.00E04

1 0.5–0.6 0.22–0.44 0.1–0.6 0.035–0.045 0.035–0.06

1 0.3 0.3 0.05 0.02 0.0025

0.0055

0.01

1.00E04

1.00E04

1.00E04

3.50E02

0.0002

0.0052

0.01

1.00E04

1.00E04

1.00E04

3.50E02

0.0005

1.00E04

0.01

1.70E02

2.00E03

3.00E03

1.00E04

1.00E04

Lanthanides

Cerium U (Uranium)

Fig. 13. Temperature and pressure evolution in the containment for different release fraction recommended by literature.

example, after one hour the maximum temperature difference between Chernobyl and SPX is ~36 K. The corresponding pressure difference between Chernobyl and SPX is 10 kPa. The temperatures and pressures decrease slowly as the decay heat of RN in containment decay out depending on their inventory in the containment. After two hours this temperature and pressure difference is around 25 K and 8 kPa. The trend for the Monju is similar to that of the PSFR’s values (Fig. 7a: 70% decay heat deposited in the air) containment air temperatures. This is due to the similarity in in-containment release fraction for both cases. The peak temperatures in the containment are similar for the NUREG-1465 without consideration of ex-vessel release fraction and TID-14844. Interestingly, however, for longer times TID-14844 release fraction temperatures dominate. This is due to higher released fraction considered for lanthanides, and noble gases in TID-14844 compared to NUREG-1465 without exvessel. The temperatures due to SNR release fraction is higher than other fast reactor RN due to higher volatile contribution consideration. The corresponding pressures are shown in Fig. 13b. This widespread temperature and pressures suggest that the in-

containment release fraction (especially for halogen, alkali metals, noble metals and lanthanides) is a sensitive parameter for thermal and pressure loadings. These observations suggest that the accurate estimates of the in-containment release fraction, core inventory and reactor power are crucial to estimate the thermal and pressure load needed for containment design since these parameters can be deciding factors to establish the design pressure and design temperatures for the containment.

5. Conclusion A study of the impact of decay heat on the temperature and pressure rise in a medium size SFR containment under a severe accident condition in relation to the heat from sodium fire and solar flux is presented. Detailed models for the reactor source term, decay heat release and transport in the containment are used along with standard models for sodium fire and solar heat flux to evaluate the relative contributions. It is found that nuclear decay heat

P.R. Patel et al. / Annals of Nuclear Energy 138 (2020) 107189

makes a substantial contribution to the temperature and pressure evolution generated from burning of the sodium ejected during the accident. It is observed that compared to the increase in peak values of temperature and pressure, higher values of pressure and temperature are sustained in the containment atmosphere for longer durations due to the decay heat. For the reference reactor studied, with deposition of 70% decay heat in the containment atmosphere, the peak temperatures are found to be 7 K higher than that due to only sodium fire. The corresponding peak excess pressures are about 2 kPa higher than the peak excess pressure due to only sodium fire. But subsequently, say after one hour, the temperature and pressure are 10 K and 4 kPa respectively higher than the only sodium fire case. After the sodium fire is extinguished, the decay heat will be the dominant contributor to the thermal loadings in the containment up to one day, followed by heat addition from solar radiation. From the sensitivity study, it is found that the in-containment release fraction, operating power and the core inventory are the most sensitive parameters to the thermal loadings in the containment. It would be a interesting follow up study to characterize allowable containment leak rates that would meet the site boundary dose criteria given the range of containment loadings for a severe accident. Acknowledgment The assistance provided by the Department of Atomic Energy (DAE) and Director, Reactor Design Group (RDG), for this project is gratefully acknowledged. Authors acknowledge the contribution from Dr. D Sunil Kumar and Mr. Anupam Chakraborti who provided DORT generated gamma deposition in the RCB and axial flux profile for PSFR. References Arul, J., Kriventsev, V., Lebel, L., Batra, C., Ren, L., Yu, Y., Zhang, Y., Ruggieri, J.M., Girault, N., Scikor, M., Lee, W., Rtishchev, N., Herranz, L.E., Chang, J., Monti, S., Cass, K., 2017. Source term estimation for radioactivity release under severe accident scenarios in sodium cooled fast reactors: technical specification and approach. In: International Conference on Fast Reactors and Related Fuel Cycles: Next Generation Nuclear Systems for Sustainable Development. International Atomic Energy Agency, Yekaterinburg, Russian Federation, p. 16. Balard, F., Carluec, B., 1996. Evaluation of the LMFBR cover gas source term and synthesis of the associated R and D. In: Evaluation of Radioactive Materials and Sodium Fires in Fast Reactors, Japan.. Beiriger, P., Hopenfeld, J., Silberberg, M., Johnson, R., Baurmash, L., Koontz, R., 1973. SOFIRE II User Report, Technical Report AI-AEC-13055. Atomics International, Canoga Park, California. Brunett, A., Denning, R., Umbel, M., Wutzler, W., 2014. Severe accident source terms for a sodium-cooled fast reactor. Ann. Nucl. Energy 64, 220–229. Cengel, Y.A., 2007. Heat and Mass Transfer: A Practical Approach. McGraw-Hill, Boston. Chadwick, M., Herman, M., Oblozinsky`, P., Dunn, M.E., Danon, Y., Kahler, A., Smith, D.L., Pritychenko, B., Arbanas, G., Arcilla, R., et al., 2011. ENDF/B-VII. 1 nuclear data for science and technology: Cross sections, covariances, fission product yields and decay data. Nucl. Data Sheets 112, 2887–2996. Chadwick, M.B., Herman, M., Oblozˇinsky´, P., Dunn, M.E., Danon, Y., Kahler, A.C., Smith, D.L., Pritychenko, B., Arbanas, G., Arcilla, R., Brewer, R., Brown, D.A., Capote, R., Carlson, A.D., Cho, Y.S., Derrien, H., Guber, K., Hale, G.M., Hoblit, S., Holloway, S., Johnson, T.D., Kawano, T., Kiedrowski, B.C., Kim, H., Kunieda, S., Larson, N.M., Leal, L., Lestone, J.P., Little, R.C., McCutchan, E.A., MacFarlane, R.E., MacInnes, M., Mattoon, C.M., McKnight, R.D., Mughabghab, S.F., Nobre, G.P.A., Palmiotti, G., Palumbo, A., Pigni, M.T., Pronyaev, V.G., Sayer, R.O., Sonzogni, A.A., Summers, N.C., Talou, P., Thompson, I.J., Trkov, A., Vogt, R.L., van der Marck, S.C., Wallner, A., White, M.C., Wiarda, D., Young, P.G., 2011. ENDF/B-VII.1 nuclear data for science and technology: cross sections, covariances, fission product yields and decay data. Nucl. Data Sheets 112, 2887–2996. Chellapandi, P., Velusamy, K., Chetal, S.C., Bhoje, S.B., Lal, H., Sethi, V.S., 2003. Analysis for mechanical consequences of a core disruptive accident in prototype

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