Thermal hydraulic analysis of the PWR with high uranium density accident tolerant fuels under accident transients with and without reactivity

Nuclear Engineering and Design 355 (2019) 110358

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Thermal hydraulic analysis of the PWR with high uranium density accident tolerant fuels under accident transients with and without reactivity Sihong He, Jiejin Cai

T

⁎

School of Electric Power, South China University of Technology, 510640 Guangzhou, China

A R T I C LE I N FO

A B S T R A C T

Keywords: Accident tolerant fuels Thermal hydraulic analysis Accident transients Reactivity feedback Pressurized water reactor

High uranium density accident tolerant fuel (ATF) with high economy and safety seems to be one of the most promising candidates to replace UO2 in future reactor. The thermal hydraulic analysis of the PWR loaded with high uranium density ATF fuels needs to be carried out to demonstrate this fuel performance. The thermal hydraulic performance of UN and UN+U3Si2 composites were evaluated in the PWR under unprotected complete loss of coolant flow accident (CLOFA) and reactivity initiated accident (RIA). The processes of CLOFA and RIA transients with and without reactivity were carried out using system code Relap5/Mod3.4, and the thermal hydraulic behaviors of UN and UN+U3Si2 composite under CLOFA and RIA transients were assessed by subchannel code COBRA-EN. The results show that UN and UN+U3Si2 fuels had more intensive negative reactivity feedback to further mitigate reactor power resulting in lower fuel temperature during CLOFA and RIA transients. The UN and UN+U3Si2 composites demonstrated better safety relative to UO2 because of higher minimal departure from nucleate boiling ratio (MDNBR) and lower peak fuel centerline temperature (PFCT). UN+U3Si2 composite performed better thermal hydraulic performance when compared to UN, but the safety margin may be lower due to low melting temperature of U3Si2.

1. Introduction The Fukushima accident had many important impacts on the development progress of nuclear energy safety, and after that accident tolerant fuel (ATF) materials get more and more concerns (Andersson et al., 2018). As pointed out by International Atomic Energy Agency (IAEA) comprehensive Fukushima report (IAEA, 2015), one of the most important reasons for the Fukushima accident occurrence was that people could not believe beyond design basic accident (BDBA) would happen with current reactor security protection measures. Fuel performance enhancement both in normal operating condition and accident transients can improve the ability of reactor accident resistance (Gu, 2018). To optimize reactor economy in normal operating condition and reactor safety in accident transients, ATF materials including fuel pellets and claddings had been studied to replace the traditional UO2-Zr system (Zinkle et al., 2014). The main motivation of development ATF concepts for severe accidents is to reduce both fuel centerline temperature and peak cladding temperature by enhancing thermal conductivity of fuel pellet materials and to decrease hydrogen generation by using high oxidation resistance of cladding materials (Terrani, 2018; Zhou and Zhou, 2018). A large amount of research of ATF characteristics has been published and is important to highlight. ATF cladding ⁎

materials include FeCrAl-alloy (Dryepondt et al., 2018; Kim et al., 2018; Yamamoto et al., 2015), SiC-based monomers and composite materials (Katoh et al., 2014; Wagih et al., 2018; Yang et al., 2018) and chromium-coated zirconium alloy (Brachet et al., 2019; Cheol Lee et al., 2019; Lee et al., 2019), etc. Besides, ATF fuel pellet materials primarily include UO2 with addition (BeO or SiC) (Cai et al., 2019; Liu and Zhou, 2017; Liu et al., 2016), fully ceramic micro-encapsulated (FCM) (Li et al., 2018; Qasim Awan et al., 2018), uranium nitride with uranium silicide (UN+U3Si2) (He et al., 2019; Ortega et al., 2016; White et al., 2017). The list is not complete, but it contains current experimental, modeling and simulation research achievements. In ATF concepts’ mid-term technologies predicting by the U.S. Department of Energy Office of Nuclear Energy, two high density fuels of UN and UN+U3Si2 were selected (Spencer et al., 2016). UN fuel pellet with high uranium density, high thermal conductivity and good fission products retention is one of the most promising candidates to replace UO2. However, the rapid oxidation in water and high temperature steam is a fatal weakness of UN (Johnson et al., 2016a). The silicide phase with high oxidation resistance is appended to improve the oxidation resistance of UN (Lopes et al., 2017). Therefore, triuranium disilicide (U3Si2) can enhance metal density and can provide an effective method to decrease the extreme sintering temperature needed for

Corresponding author. E-mail address: [email protected] (J. Cai).

https://doi.org/10.1016/j.nucengdes.2019.110358 Received 8 July 2019; Received in revised form 17 September 2019; Accepted 19 September 2019 0029-5493/ © 2019 Elsevier B.V. All rights reserved.

Nuclear Engineering and Design 355 (2019) 110358

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Fig. 1. Sketch of radial mesh for temperatures in a fuel rod.

Fig. 2. Modeling of the CPR1000 model in Relap5/Mod3.4 code. Table 1 Reactor parameters in Relap5/Mod3.4 code.

Table 2 Reactor core parameters in COBRA-EN code.

Parameter

Value

Parameter

Value

Reactor full power (MW) Hot-leg temperature (K) Cold-leg temperature (K) Reactor coolant system full load average temperature (K) Nominal pressurizer pressure (MPa) Steam generator secondary pressure (MPa) Reactor coolant flow (m3/h/loop) Main feed water temperature (K)

2895 603.2 566.1 583.15 15.5 6.71 23,372 499.15

Reactor core heat output (MW) Reactor coolant system pressure (MPa) Coolant temperature at core inlet (K) Mass flow rate (kg/s) Fuel assembly design Active fuel height (m) Number of fuel assembly Uranium rods per assembly

2895 15.5 565.8 13,500 17 × 17 3.658 157 264

densification of monolithic UN (Johnson et al., 2016b). UN+U3Si2 composite fuel pellet can perform higher uranium density and reaches 90% density at 1973 K (Ortega et al., 2016). Besides, performances of increasing the gap conductivity, reducing the fission gas release, abating the interaction between pellet and cladding are also improved (Wilson et al., 2018). The thermo-physical properties of UN+U3Si2 composite fuel spanning compositions of 10% to 40% volume fraction

U3Si2 is measured and impacts of sintering route for thermal diffusivity are also simulated (White et al., 2017). In this paper, UN and UN +U3Si2 with 10%, 20%, 30% and 40% volume faction of U3Si2 were conducted to simulation calculation. Although nuclear reactors have lots of designed safety barriers, various accident conditions, such as loss-of-coolant accident, loss-offlow accident, and reactivity initiated accident, may be occurred. 2

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Fig. 3. Three types of fuel pellets.

Fig. 4. Thermo-physical properties of fuel pellets and cladding used for this study (IAEA, 2008; White et al., 2017): (a) Thermal conductivity of fuel pellets; (b) Specific heat capacity of fuel pellets; (c) Thermal conductivity and specific heat capacity of Zr cladding; (d) Melting point temperature for several materials.

due to the changes of moderator density and fuel temperature during accident transients were in consideration. Furthermore, the reactivity feedback effect failure cases were conducted to obtain more sufficient thermal hydraulic evaluation of high uranium density ATF fuels. Additionally, the fuel-cladding gap conductance of ATF pellets was assumed higher than UO2 with consideration of the advantage of ATF fuel performance. This paper focused on analyzing the thermal hydraulic performance of UN and UN+U3Si2 composites in a typical 3-loop PWR under unprotected CLOFA and RIA transients. The changes of coolant flow rate

Thermal hydraulic performance under various accident transients is one of important factors to assess the accident resistance of ATF materials. In comparison with protected loss of flow accident analysis, there are limited analytical studies regarding unprotected loss of flow accident. Thus, unprotected complete loss of flow accident (CLOFA) and reactivity initiated accident (RIA) were performed to assess the thermal hydraulic behaviors of UN and UN+U3Si2 composites under accident transients. During accident transients, reactivity feedback effect is very important in calculating the reactor power and therefore has significant impact on thermal hydraulic parameters. The reactivity feedback effect 3

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Fig. 5. Power distributions for this study (Brown et al., 2014): (a) Axial power distributions of different pellets; (b) Radial power distributions of different pellets.

and reactor power under CLOFA and RIA transients were calculated by Relap5/Mod3.4 code. Then, the changes of coolant flow rate and power during CLOFA and RIA transients were applied for sub-channel analysis tool COBRA-EN code as initial calculation conditions. In comparison with system analysis Relap5/Mod3.4 code, sub-channel analysis COBRA-EN code can provide more accurate thermal hydraulic changes of reactor core. Further simulations and modeling can provide a better understanding for ATF thermal hydraulic performance and can be helpful for estimating the promising development direction. Thus, the results of this paper can show detail information and evaluation for thermal hydraulic characteristics of UN+U3Si2 composite fuel, benefiting for the further study and application of UN+U3Si2 composite fuel. The paper is organized as follow: The next section introduces the calculation models in Relap5/Mod3.4 code and COBRA-EN code. In Section 3, reactor models, thermo-physical properties of ATF fuels, and reactor core power distributions are introduced. The coolant flow rate and power parameters changes of two accident transients are presented in Section 4. The results of both unprotected CLOFA and RIA transients with and without reactivity feedback effect are showed in Section 5. Finally, the conclusion is summarized in Section 6.

Fig. 6. CLOFA transient with and without reactivity feedback: (a) Reactor core flow rate changed with time; (b) Reactor power changed with time; (c) Reactivity feedback changed with time.

2. Methodology Relap5/Mod3.4 code including reactor point kinetics model is the best system analysis tool suitable for the thermal hydraulic assessment of all transients and full range of postulated reactor accidents in light 4

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Fig. 7. RIA transient with and without reactivity feedback: (a) Reactor power changed without reactivity feedback; (b) Reactor power changed with reactivity feedback; (c) Reactivity changed without reactivity feedback; (d) Reactivity feedback changed with reactivity feedback.

conditions and event specifications of CLOFA and RIA transients for the thermal hydraulic analysis using COBRA-EN code. The sub-channel analysis COBRA-EN code was used for reactor core thermal-hydraulic analysis under accident transients. Fuel temperature, heat transfer process and flow state change were the most relevant issue in this study.

water reactors. This code has fully integrated, multi-dimensional thermal-hydraulic and kinetic modeling capability (Wang et al., 2013). The change of coolant flow rate in reactor core of CLOFA can be obtained by assumed all reactor coolant pumps stop due to loss of power. Besides, the reactor point kinetics model in Relap5/Mod3.4 code can calculate the changes of total reactor power with reactivity feedback effect under different accident transients. COBRA-EN code (Basile et al., 1999) allows “core analysis” and “sub-channel analysis” to be performed. In this paper, “sub-channel analysis” that concerns the detailed description of individual fuel rod bundles was considered, which could accurate calculate mass, energy and momentum conservation equations among coolant channels by Newton-Raphson iteration. COBRA-EN code can simulate the thermal hydraulic transient response for user-supplied changes of the power and the inlet temperature and the outlet pressure and the inlet mass flow rate with time (Noori-Kalkhoran et al., 2014). COBRA-EN code contains thermo-physical properties (thermal conductivity and specific heat capacity as a function of temperature) of the fuel materials (uranium dioxide and zircaloy) originally. The thermalhydraulic analysis about fuel performance was augmented by this work, which added models for additional materials including UN and UN +U3Si2 composites. These material properties were coded using Fotran and are described in Section 3. Relap5/Mod3.4 code can provide the time-dependent boundary

2.1. Point neutron kinetics model in Relap5/Mod3.4 code The reactor point kinetics model in Relap5/Mod3.4 code (Hamidouche and Bousbia-Salah, 2010) is the simplest model that can be used to compute the transient behavior of the neutron fission power in a nuclear reactor. The point neutron kinetics model embedded in this code is written as following Eq. (1):

[ρ (t ) − β ] n (t ) d n (t ) = + Λ dt

Nd

∑ λi Ci (t ) + S i=1

βf d Ci (t ) = i n (t ) − λi Ci (t ) i = 1, 2, ...,Nd dt Λ φ (t ) = n (t ) v

ψ (t ) = V ∑ φ (t ) f

5

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Fig. 8. Temperature profiles of ATF UN and UN+U3Si2 composite fuels under COLFA transient with and without reactivity feedback effect: (a) Peak fuel centerline temperature without reactivity feedback effect; (b) Peak cladding temperature without reactivity feedback effect; (c) Peak fuel centerline temperature with reactivity feedback effect; (d) Peak cladding temperature with reactivity feedback effect.

Pf (t ) = Qf ψ (t )

where r0 is the initial reactivity; rB is the bias reactivity; rsi is obtained from input tables defining ns curves as a function of time; Vci is nc control variables that can be user-defined as reactivity contributions; Rρ is a table defining reactivity as a function of the current moderator density of fluid ρi (t ) in the hydrodynamic volume i (density reactivity table); Wρi is the density volume weighting factor volume i ; Twi (t ) is the spatial density average moderator fluid temperature of volume i ; a wi is the volume fluid temperature coefficient for volume i ; nρ is the number of hydrodynamic volumes in the reactor core; RF is a table defining reactivity as a function of the heat structure volume average fuel temperature TFi (t ) in heat structure i (Doppler reactivity table); WFi is the fuel temperature heat structure weighting factor for heat structure i ; aFi is the heat structure temperature coefficient for heat structure i ; nF is the number of heat structure in reactor core. The separable model used two tables. One is defines reactivity as a function of moderator density and the other one defines reactivity as a function of average fuel temperature. Each effect of reactivity was assumed to be independent of the other effects, and total reactivity is the sum of individual effects.

Nd

β=

∑ βi ,

fi = βi / β

(1)

i=1

where t is time; n is neutron density; φ is neutron velocity; Ci is delayed neutron precursor concentration in group i ; β is effective delayed neutron fraction; Λ is prompt neutron generation time; ρ is reactivity; fi is fraction of delayed neutrons of group i ; βi is effective delayed neutron precursor yield of group i ; λi is decay constant of group i ; S is source rate density; ψ is fission rate; ∑f is macroscopic fission cross-section; Pf is immediate fission power; Qf is immediate fission energy per fission; V is volume; Nd is number of delayed neutron precursor groups. The reactivity in Eq. (1) can be calculated by using either separable or tabular models in Relap5/Mod3.4 code (Foad et al., 2018). The separable feedback model is selected for reactivity feedback in point reactor kinetics in this paper. The separable model defines reactivity as Eq. (2): n

n

n

r (t ) = r0 − rB + ∑i =s 1 rsi (t ) + ∑i =c 1 Vci (t ) + ∑i =ρ 1 [Wρi·R ρ (ρi (t))+ n

a wi ·Twi (t)]+ ∑i =F 1 [WFi·RF (TFi (t)) + aFi·TFi (t)]

(2) 6

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Qi − 1, i = −k ∂T / ∂r|r = ri − 1 is heat flow from (i − 1) to i , Qi + 1, i = k ∂T / ∂r|r = ri is heat flow from (i + 1) to i , k is thermal conductivity, Qi‴ is volumetric heat generation rate. Because power distribution of fuel pellet in the axial direction is a parabolic shape and power fraction of cladding is assumed to be uniformly distributed, the volumetric heat generation rate is described as Eq. (4): 2

Qi‴ =

QF ⎧ 1⎫ ⎛ r¯i ⎞ ⎤ 1 + η⎡ ⎢ RF ⎥ − 2 ⎬ VF ⎨ ⎝ ⎠ ⎣ ⎦ ⎩ ⎭ ⎜

⎟

(4)

where QF is power generated in the fuel per unit axial length, VF is fuel volume per unit axial length, RF is radius of a fuel pellet, η is a usersupplied fitting parameter. For “sub-channel analysis”, a fuel rod can face more than one channel. The heat transfer from the fuel to the flowing coolant is dominated by a full boiling curve. A full boiling curve can be divided into five heat transfer zones, including single-phase liquid forced convection, sub-cooled nucleate boiling, saturated nucleate boiling, transition and film boiling and single phase vapor forced convection. The heat transfer coefficients depend both on the cladding outer surface temperature and coolant temperature. If heat flux between cladding and coolant exceeds critical heat flux, the heat transfer regime would enter film boiling. To improve the calculation accuracy of heat transfer procedure, the heat transfer models applied in this work are verified empirical formulas. The heat transfer coefficients of different boiling curve regimes are introduced as following: The single-phase forced convention regime is characterized by Dittus-Boelter correlation. Dittus-Boelter correlation can be written as Eq. (5):

hT = 0.023Re0.8Pr 0.4 (k / Dh)

(5)

where hT is convective heat transfer coefficient, k is coolant thermal conductivity, Dh is equivalent hydraulic diameter, Re is Reynolds number, Pr is Prandtl number. Both sub-cooled and saturated nucleate boiling regimes are characterized by Thom and Dittus-Boelter correlations. Thom correlation is described as Eq. (6):

qT hom = 0.05358e P /630 (Tw − Tsat )2 Fig. 9. Minimal departure from nucleate boiling ratio of ATF UN and UN +U3Si2 composite fuels under COLFA transient with and without reactivity feedback effect: (a) Minimal departure nucleate boiling rate without reactivity feedback effect; (b) Minimal departure nucleate boiling rate without reactivity feedback effect.

where qT hom is heat flux calculated by Thom method, P is system pressure, Tw is temperature of the fuel rod surface, Tsat is coolant saturation temperature. Thom heat transfer coefficients and liquid phase forced convection are applied for HTC calculation in sub-cooled and saturated nucleate boiling, and can be presented as Eq. (7):

2.2. Heat transfer model in COBRA-EN code

hnb = hT + qT hom /(Tw − Tb)

The heat transfer model in COBRA-EN code (Chen et al., 2018) calculates the heat transfer from a heated wall to the coolant bulk, which implies a fuel heating model and a heat transfer model. For fuel heating model, the fuel pellet is divided into radial intervals of equal thickness and the cladding is divided into two computational points as respectively outer surface and internal surface of cladding. The view of radial mesh distribution representing a fuel rod is shown in Fig. 1. As the Fig. 1 shown, TN is the temperature on the cladding outer surface and TN − 1 and TN − 2 are the temperature at the cladding inner surface and at the pellet outer surface, N is the total number of radial nodes. The temperature Ti is computed at the radial location r¯i which is the volume-average radius of the node. The equation for the radial computational point temperature Ti is Eq. (3):

(ρCp V )

∂Ti = Qi − 1, i + Qi + 1, i + Qi‴ ∂τ

Vi

(6)

(7)

where hnb is nucleate boiling heat transfer coefficient, Tb is bulk coolant temperature. The critical heat flux is calculated by EPRI correlation presented in Eq. (8):

qCHF =

1 AFA − x in 0.0036 CFC Fg Fnu + (h − hin /0.0036qhfg )

A = 0.5328Pr 0.1212 (0.0036G )(−0.3040 − 0.3285 Pr) C = 1.6151Pr1.4066 (0.0036G )(0.4843 - 2.0749Pr)

(8)

where q CHF is the value of critical heat flux, FA , FC , Fg and Fnu are various correction factors for critical heat flux, x in is inlet flowing vapor quality, h is local enthalpy, hin is inlet enthalpy, q is local heat flux, hfg is vaporization enthalpy, G is coolant mass flux, Pr is critical pressure ratio. The HTC of film boiling can be described by Groeneveld 5.7 correlation as is presented in Eq. (9):

(3)

where ρ is fuel or cladding density, Cp is fuel or cladding specific heat, V is node volume, Ti is temperature at the computational point, 7

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Fig. 10. Coolant and vapor behaviors with and without reactivity feedback effect under CLOFA transient: (a) Average coolant temperature; (b) Average coolant density; (c) Average void fraction; (d) Core exit average coolant void fraction.

hfb = 0.052

kg Dh

Fig. 2 shows the three primary loops and a pressurizer of the CPR1000 nuclear power plant. The reactor pressure vessel is divided into fourteen control volumes that mainly represent the low plenum, the core inlet, the reactor core, the core outlet, the core bypass, the upper plenum and the upper head. The control volumes in primary loops include the hot and cold legs, the loop coolant main pumps, the main and auxiliary feed water systems, the accumulators, and safety injection tanks. Actuation of coolant main pumps including pumps shutdown and flow rate variations can be regulated by Relap5/Mod3.4 code control function. The initial reactor parameters of the CPR1000 normal operating conditions in Relap5/Mod3.4 code are presented in Table 1. In order to calculate the thermal hydraulic parameters of reactor core zone in greater detail, the reactor zone was divided into 10 axial sections and 9 radial rings. The geometric and thermal parameters as listed in Table 2 are the CPR1000 reactor core model in COBRA-EN code. The reactor core is composed of 157 fuel assemblies and active fuel height of each fuel rod is 3658 mm. To make a reasonable accurate estimate for reactor core thermal hydraulic behavior, 24 axial and 5 radial nodes were adequate after performing a mesh sensitivity analysis. All the coolant channels and fuel rods were divided into 24 equal intervals in axial direction and the fuel pellets were divided into 5 radial intervals of equal thickness.

1.26 1.06 Re0.688 hom Pr f / γ

⎡ ⎛ρ ⎞⎤ γ = 1.0 − 0.1 ⎢ (1 − x ) ⎜ l − 1⎟ ⎥ ρg ⎝ ⎠⎦ ⎣ Prf =

cpν μ ν kν

Re hom =

ρ GDh ⎡ ⎤ x + l (1 − x )⎥ ρg μg ⎢ ⎦ ⎣

(9)

where hfb is film boiling heat transfer coefficient, k g is thermal conductivity of saturated vapor, x is flowing vapor quality, ρl is saturated liquid density, ρg is saturated vapor density, cpν is specific heat of superheated vapor, μ ν is dynamic viscosity of superheated vapor, k ν is thermal conductivity of superheated vapor. 3. Simulation models and material properties 3.1. Reactor description A typical CPR1000 model (Wang et al., 2015) was selected as a reference reactor in this paper. CPR1000 is a pressurized light water reactor with three primary loops and is modeled in Relap5/Mod3.4. 8

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Fig. 10. (continued)

UN+U3Si2 composite fuel pellets for different volume fraction in this study were adopted from White et al. (2017)’s experimental values. Besides, the specific heat capacity of composite fuel pellets was the sum of weight fraction multiplied by the specific heat capacity of single component (UN) and additive (U3Si2). Obviously, the specific heat capacity of UN fuel pellet and UN +U3Si2 composite fuel pellets were lower than UO2 pellet, while the thermal conductivity of them are higher than UO2 pellet, as shown in Fig. 4 (a) and (b). Among nitride fuel pellets, both thermal conductivity and specific heat capacity of UN+U3Si2 composite pellets exceeded UN pellet. The thermal conductivity of 70%UN+30%U3Si2 composite after about 1073 K is higher than 80%UN+20%U3Si2 composite, because micro-cracks forming on cooling cause hysteresis in the thermal diffusivity curves. Moreover, the melting point temperature (1938 K) of U3Si2 was remarkable lower than UN (2953 K), shown in the inset of Fig. 4 (c). It is significant to append moderate volume fraction of U3Si2 for UN+U3Si2 composite to avoid too much low melting point. The safety margin of the ratio of the peak fuel temperature to the melting temperature may be lower for UN+U3Si2 composite.

3.2. Nitride fuels and material properties In mid- term technologies of ATF, UN and UN+U3Si2 were selected. For the analysis in this study, the paper will focus on three types of fuel pellets, UO2 fuel pellet, UN fuel pellet and UN+U3Si2 composite fuel pellet. But, cladding material of three types of fuel pellets was Zr-4, as shown in Fig. 3. The structure of fuel rod is shown in Fig. 1. For UN +U3Si2 composite fuel pellet, four ratios (90%UN+10%U3Si2, 80%UN +20%U3Si2, 70%UN+30%U3Si2, 60%UN+40%U3Si2 corresponded with the U3Si2 volume fraction of 10%, 20%, 30% and 40%, respectively) were investigated. The fuel pellet diameter (D) was 8.719 mm, Zr-4 cladding thickness (ts) was 0.572 mm and gas thickness (tg) was 0.082 mm, as shown in Fig. 3. The simulation will compare the performance of each ATF nitride fuel pellet against with UO2 fuel pellet. Fuel and cladding material properties include melting point, thermal conductivity and specific heat capacity. In this section, thermophysical properties of UO2 fuel pellet, UN fuel pellet, UN+U3Si2 composite fuel pellet (U3Si2 volume fraction of 10%, 20%, 30% and 40%) and Zircaloy-4 cladding were presented in Fig. 4. Thermo-physical properties of standard uranium dioxide (UO2) fuel pellet and Zircaloy-4 cladding and uranium nitride (UN) fuel pellet referred to IAEA’s theory manual (IAEA, 2008) for a complete description. The thermal conductivity values with the temperature range from 273 K to 1673 K of

3.3. Reactor core power distributions Power distribution in reactor core includes axial and radial power 9

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Fig. 11. Temperature profiles of ATF UN and UN+U3Si2 composite fuels under RIA transient with and without reactivity feedback effect: (a) Peak fuel centerline temperature without reactivity feedback effect; (b) Peak cladding temperature without reactivity feedback effect; (c) Peak fuel centerline temperature with reactivity feedback effect; (d) Peak cladding temperature with reactivity feedback effect.

and UN+U3Si2 composite fuels and accident transients with reactivity feedback effect can perform accurate and real simulation results. The coolant pumps in primary loops shutdown due to loss of power causes reactor coolant flow down and fuel rod temperature rising, and as a result of the loss of forced core flow. Reactor was normal operating condition before 10 s, and then three coolant pumps in three primary loops showed in Fig. 2 were stopped. The transient of normalized flow rate, normalized power and total reactivity under CLOFA condition evaluated by Relap5/Mod3.4 code is showed in Fig. 6. As Fig. 6 (a) presented, coolant flow rate in reactor core rapidly decreased to 50% at 25 s. With the assumption of reactivity feedback effect failure, the total reactor power maintained full power operation during CLOFA transient. A negative reactivity feedback effect and reactor power down appeared after COLFA, as shown in Fig. 6 (b and c). The coolant temperature increased and density decreased as vapor bubbles generated at cladding outer surface after the loss of flow, which led to the number of thermal neutron decreased and then power dropping. The total reactivity effect was the summation of negative coolant density reactivity and positive Doppler reactivity as average fuel temperature decreased. In comparison with UO2, the absolute reactivity of UN and UN+U3Si2 composite fuels was larger than UO2, and thereby the reactor power during CLOFA transient was lower than UO2. The possible reason for this result is that higher thermal conductivity of UN and UN+U3Si2 composite fuels can

distributions and is influenced by both fuel pellet and cladding materials. In this paper, cladding was the same and fuel pellet was different. The power distributions of UO2, UN and UN+U3Si2 were referred to Brown et al. (2014). The UN axial power distribution was similar UN +U3Si2. The radial power peaking factors of UN and UN+U3Si2 were lower than UO2 indicating more uniform radial power distributions. Among them, UN+U3Si2 fuel has the minimal radial peak power factor of 1.29. Axial power distributions and only radial power peaking factors were considered in Relap5/Mod3.4 code. Both axial and radial power distributions were considered in COBRA-EN code to gain a more precise thermal hydraulic analysis of reactor core.

4. CLOFA and RIA transients CLOFA and RIA transients that are two kinds of representative accident transients were studied in PWR. With reactor scram failure, CLOFA and RIA transients with and without reactivity feedback effect were performed to evaluate different thermal hydraulic performance between UO2 and high uranium density ATF fuels. The reactivity feedback effect induced by moderator density and average fuel temperature changes during accident transients had a significant influence on total reactor power. Therefore, accident transients without reactivity feedback effect can provide an extreme performance assessment for UN 10

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Fig. 13. The ratio of maximum peak fuel centerline temperature to fuel melting temperature for ATF UN and UN+U3Si2 composite fuels under normal operating condition and accident transients.

accidentally induced by a positive reactivity under various design conditions leading to reactor power surge. The RIA transient was hypothetically initiated by inducing a positive reactivity of $0.5 at 11 s and the positive reactivity was cancelled at 11.5 s. Fig. 7 shows the changes of the total reactivity and normalized reactor power under RIA transient with and without reactivity feedback effect using Relap5/ Mod3.4 code. Without reactivity feedback effect, the total reactivity changed with the assumption condition and the peak reactor power reached to near 220% of normal operating power, as presented in Fig. 7 (a and c). Although the total reactivity has been to $0.0 after RIA transient, the total reactor power was still higher than normal operating power about 6%. The reason is because reactor fission products decay power increased after RIA transient. As seen in Fig. 7 (b and d), the maximum positive reactivity only reached to near $0.33 due to negative Doppler reactivity, and thus the peak reactor power achieved near 160% of normal operating power. The total reactivity was impacted by negative Doppler reactivity because of the increase of average fuel temperature. Consequently, the total reactor power with reactivity feedback effect was near to normal operating power due to the regulating effect of negative reactivity during RIA transient. In addition, the peak reactor power of ATF UN and UN+U3Si2 composite fuels was also lower than UO2 as a result of larger negative reactivity effect.

Fig. 12. Minimal departure from nucleate boiling ratio of ATF UN and UN +U3Si2 composite fuels under RIA transient with and without reactivity feedback effect: (a) Minimal departure nucleate boiling rate without reactivity feedback effect; (b) Minimal departure nucleate boiling rate without reactivity feedback effect.

attain larger heat flux appreciably causing a large amount of vapor bubbles forming. Reactivity initiated accident belongs to design basic accident and is

Table 3 Fuel temperature and minimal MDNBR value of various fuels studied in this paper. Normal operating condition

Without reactivity feedback effect

With reactivity feedback effect

COLFA

COLFA

RIA

RIA

Fuel types

PFCT

PCT

MDNBR

PFCTa

PCTb

MDNBRc

PFCTa

PCTb

MDNBRc

PFCTd

PCTb

MDNBRc

PFCTa

PCTb

MDNBRc

UO2 UN 90%UN+10%U3Si2 80%UN+20%U3Si2 70%UN+30%U3Si2 60%UN+40%U3Si2

1563.3 913.2 883.4 888.4 891.6 898.5

620.6 620.2 619.9 619.9 619.9 619.9

1.722 1.803 1.843 1.840 1.843 1.843

2095.9 1225.5 1161.8 1165.8 1166.3 1172.4

963.1 950.8 912.6 912.6 912.6 912.6

0.611 0.639 0.655 0.655 0.655 0.655

1739.3 1017.0 987.0 991.7 994.5 1001.1

621.9 622.2 622.2 622.1 622.1 622.1

1.435 1.357 1.374 1.377 1.380 1.383

852.9 705.1 697.0 698.5 699.8 702.1

622.0 621.6 621.5 621.5 621.5 621.5

1.248 1.441 1.478 1.477 1.477 1.476

1662.5 970.9 949.2 945.8 948.8 955.5

621.6 621.4 621.5 621.3 621.3 621.3

1.512 1.546 1.519 1.573 1.575 1.577

a b c d

Maximum PFCT under accident transient (K). Maximum PCT under accident transient (K). Minimal MDNBR under accident transient. Minimal PFCT under accident transient (K). 11

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coolant flow rate decreased, the coolant temperature increased and coolant density decreased, as shown in Fig. 10. Average coolant temperature could not reach saturate temperature since reactor power reduced as a result of reactivity feedback effect. Therefore, in comparison with reactivity failure case, average void fraction in core and void fraction in core outlet was smaller causing slight decrease of average coolant density. The core exit average void fraction was near to 0.8, which means that reactor core under CLOFA transient was still submerged even with reactivity feedback effect and scram failure during simulation. Due to higher thermal conductivity and lower specific heat capacity of ATF UN and UN+U3Si2 composite fuels, without reactivity feedback effect, much heat can easily transfer to coolant from fuel rods leading to higher average void fraction. The coolant behaviors with reactivity feedback effect of UN and different UN+U3Si2 composites were similar and were better than UO2. The reason possibly is that the reactor power changes of them during CLOFA were similar and lower than UO2.

5. Reactor core thermal hydraulic behaviors under accident transients 5.1. CLOFA transient The temperature profiles with and without reactivity feedback effect under COLFA transient for ATF UN and UN+U3Si2 composite fuels calculated by COBRA-EN code are figured out in Fig. 8. The reactor core was under normal operating condition at the beginning and CLOFA transient happened at 10 s. Without reactivity feedback effect, reactor remained normal operating power accompanied with coolant flow rate decrease. Thus, peak fuel centerline temperature (PFCT) and peak cladding temperature (PCT) increased as coolant flow rate reduced, and fuel temperature reached new steady status finally, as seen in Fig. 8 (a and b). The temperature of coolant was over than saturation temperature to generate lots of bubbles, resulting in the heat stored in cladding not being able to transfer to coolant through vapor film. Therefore, the critical heat flux dropped appreciably and heat flux exceeded critical heat flux causing fast raises in fuel and cladding temperatures. The PFCT and PCT of ATF UN and UN+U3Si2 composite fuels after temperature escalation had an obvious reduction relative to UO2. Besides, the beginning time of PCT sudden soaring of ATF UN and UN+U3Si2 composite fuels was delayed about and 3.5 s and 6.1 s, respectively. This is because the lower temperature difference of ATF pellet and cladding, as a result that the heat flux gets smaller and slows the heat transfer rate from cladding to coolant. Therefore, the film boiling started time of ATF UN and UN+U3Si2 composite fuels was delayed. In comparison with reactivity feedback failure case, the PFCT reduced with the total reactor power decreasing during CLOFA transient, as seen in Fig. 8 (c). The PCT slightly increased due to coolant reducing conclusively (seen in Fig. 8 (d)). Since more uniform power distribution and lower reactor power during CLOFA transient, the PCT of ATF UN and UN+U3Si2 composite fuels was mildly lower than UO2 both in normal operating condition and accident transient. The PCT of different volume fraction UN+U3Si2 composites had little difference under the same condition. The reason for this result is that the coolant thermal parameters are similar (seen in Fig. 10) and reactor core power change as well as power distribution is identical (seen in Fig. 5 and Fig. 6), and there exists a layer of gas gap between the cladding and fuel pellet as a heat shield (seen in Fig. 1). The minimal departure from nucleate boiling ratio (MDNBR) with and without reactivity feedback effect under COLFA transient for ATF UN and UN+U3Si2 composite fuels utilizing COBRA-EN code are presented in Fig. 9. The DNBR value is defined as the ratio of the critical heat flux to the average heat flux and is an important thermal hydraulic parameter to assess reactor safety. The critical heat flux of cladding surface rapidly decreased as coolant mass reduced. Consequently, MDNBR values of reactivity feedback effect failure with unchanged reactor power were below 1.0 after about 15 s of CLOFA start, causing partial failure of fuel rods. With reactivity feedback effect, the heat flux of cladding surface decreased with reactor power decreased, and thus the MDNBR values decreased firstly because of coolant flow rate reduction and then increased due to power reduction. MDNBR values with protection of reactivity feedback effect were still higher than 1.0. Obviously, MDNBR values of ATF UN and UN+U3Si2 composite fuels were superior relative to UO2, as a result of higher critical heat flux. Various volume fraction UN+U3Si2 composites had the same MDNBR value because the heat flux between cladding and coolant was the same, and besides the MDNBR value was higher than UN with thermal conductivity improvement. The changes of coolant parameters during CLOFA transient have a significant influence on the calculation of fuel rod temperature and the evaluation of reactor security. Fig. 10 shows the changes of average coolant temperature, average coolant density, average void fraction and core exit average coolant void fraction under CLOFA transient with and without reactivity feedback effect simulated by COBRA-EN code. As the

5.2. RIA transient The temperature profiles and minimal departure nucleate boiling rates with and without reactivity feedback effect under RIA transient for ATF UN and UN+U3Si2 composite fuels calculated by COBRA-EN code are figured out in Fig. 11 and Fig. 12. The PFCT and PCT without reactivity feedback effect were higher than the PFCT and PCT with reactivity feedback effect because of higher peak power. In addition, after peak power, the PFCT and PCT without reactivity feedback effect were higher than normal operating temperature, and the PFCT and PCT with reactivity feedback effect, besides UO2, were lower than original. The changes of PFCT and PCT under RIA transient primarily lied on reactor power changes shown in Fig. 7. The PFCT value of different volume fraction UN+U3Si2 composites gradually increased with U3Si2 volume fraction increasing. Because RIA transient was very brief and peak power was not enough high, PCT slightly increased and MDNBR values were still within safety limit (seen in Fig. 12). In comparison with UO2, during RIA transient, the minimal MDNBR value of ATF UN and UN+U3Si2 composite fuels were higher with reactivity feedback effect and were lower without reactivity feedback effect. The possible reason for this situation is that the power increased too quickly and as a result the coolant could not timely reduce the fuel temperature due to the heat transfer delay, causing heat transfer deterioration on cladding surface. 5.3. Discussion Two kinds of representative reactor accident transients, CLOFA and RIA, were subjected to assess the thermal hydraulic behaviors of ATF UN and UN+U3Si2 composites. The CLOFA and RIA transients based on CPR1000 reactor model with and without reactivity feedback effect were simulated by Relap5/Mod3.4 code to provide initial conditions for thermal hydraulic calculated by COBRA-EN code. In Section 5.1, the ATF UN and UN+U3Si2 composite fuels exhibited excellent accident resistance under the COLFA transient with and without reactivity feedback effect. The coolant parameters without reactivity feedback effect were very nasty causing poor heat transfer. Thus, fuel temperature had a sudden soaring and then achieved new steady status under CLOFA transient. As coolant flow rate decreased, the negative reactivity due to fuel temperature rising and coolant density reducing can make reactor shutdown. With reactivity feedback protection mechanism, less steam formed in core, and consequently reactor can maintain stabilization and safety under CLOFA transient. The PFCT and PCT both with and without reactivity were lower and MDNBR values were higher, relative to UO2. The result of thermal hydraulic behaviors under RIA transient with and without reactivity feedback effect of ATF UN and UN +U3Si2 composite fuels was shown in Section 5.2. The positive reactivity effect caused reactor power increased resulting in fuel 12

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Acknowledgment

temperature increasing. The negative Doppler reactivity effect because of average fuel temperature increasing can effectively mitigate PFCT increasing and MDNBR reducing. A notable advantage of high thermal conductivity for UN+U3Si2 composites can obtain lower PFCT under RIA transient. However, with limited cooled capacity of coolant, too much high reactor power and higher thermal conductivity can cause higher heat flux from pellet to cladding leading to heat accumulation on cladding surface. Therefore, the PFCT of ATF fuels was lower, but MDNBR value was not higher under RIA transient without reactivity feedback effect. The maximum of PFCT and PCT and the minimal MDNBR under normal operating condition and accident transients, and particularly for the minimal PFCT of CLOFA with reactivity feedback effect, for several fuels studied in this paper are shown in Table 3. Thermal hydraulic behaviors of UN+U3Si2 composites were better than UN with consideration of the influence of thermo-physical properties and power distribution, as Table 3 presented. The PCT and MDNBR values of UN +U3Si2 composites were similar, because the difference of fuel behaviors, such as swelling, creep, fission gas release, among different UN +U3Si2 composites were not in consideration in this paper. Thus, it is difficult to confirm better volume fraction of U3Si2 for UN+U3Si2 composite. The safety margin of the ratio of maximum PFCT to corresponding melting temperature under normal operating condition and accident transients are shown in Fig. 13. The melting temperature of UN+U3Si2 composite was uncertain due to various sintered condition and process. Besides, there is not identified research to suggest a referred melting temperature of UN+U3Si2 composite. Therefore, the melting temperature of U3Si2 was selected as an assumption melting temperature of UN+U3Si2 composite for conservative evaluation. The larger safety margin can offer a reliable maintenance of reactor core integrity for ATF UN and UN+U3Si2 composite fuels. The security of UN may be the better due to high melting temperature, though the degradation rate of UN+U3Si2 composite is slower than UN in steam environment (Lopes et al., 2017). Thus, the volume fraction of U3Si2 of UN+U3Si2 composite is necessary to be carefully considered.

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6. Conclusions The advantages of higher thermal conductivity and more uniform power distribution for high uranium density ATF UN and UN+U3Si2 composite fuels can improve the heat transfer condition of reactor core causing lower fuel temperature and higher MDNBR value under normal operating condition, CLOFA and RIA transients. Without reactivity feedback effect, cladding surface of ATF UN and UN+U3Si2 composite fuels may cause heat transfer deterioration under RIA transient. In comparison with traditional UO2 fuel, ATF UN and UN+U3Si2 composite fuels had larger negative reactivity feedback effect resulting in lower reactor power under accident transients. Consequently, with reactivity feedback effect, ATF UN and UN+U3Si2 composite fuels showed better thermal hydraulic performance and reactor security under CLOFA and RIA transients. Besides, coolant density under CLOFA transient with reactivity feedback effect for ATF UN and UN+U3Si2 composite fuels was larger than UO2 and was not substantial reduction due to a small number of bubbles forming. UN+U3Si2 composite with reasonable adding U3Si2 could perform a satisfactory thermal hydraulic behaviors and the consequence of the accident was effectively mitigated relative to UN. In the future, at the mid-term technologies plan of ATFs, the research of high density fuels, such as UN+U3Si2 composite fuel and UN fuel, will be a hot pot. The fuel behaviors were not in consideration in this paper. To more comprehensive understanding of fuel characteristics, deeper and more precise researches have to be conducted and more accident transients should be in consideration. Declaration of competing interest The authors declare no conflict of interest. 13

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