Evaluation of heat-flux distribution at the inner and outer reactor vessel walls under the in-vessel retention through external reactor vessel cooling condition Academic research paper on "Chemical engineering"

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Original Article

EVALUATION OF HEAT-FLUX DISTRIBUTION AT THE INNER AND OUTER REACTOR VESSEL WALLS UNDER THE IN-VESSEL RETENTION THROUGH EXTERNAL REACTOR VESSEL COOLING CONDITION

JAEHOON JUNG*, SANG MO AN, KWANG SOON HA, and HWAN YEOL KIM

Severe Accident and PHWR Safety, Korea Atomic Energy Research Institute, 989-111 Daedeok-daero, Youseong-gu, Daejeon 305-353, Republic of Korea

ARTICLE INFO

ABSTRACT

Article history: Received 29 July 2014 Received in revised form 13 November 2014 Accepted 17 November 2014 Available online 21 January 2015

Keywords:

External reactor vessel cooling External wall heat flux In-vessel retention Severe accident two-dimensional conduction effect

Background: A numerical simulation was carried out to investigate the difference between internal and external heat-flux distributions at the reactor vessel wall under in-vessel retention through external reactor vessel cooling (IVR-ERVC).

Methods: Total loss of feed water, station blackout, and large break loss of coolant accidents were selected as the severe accident scenarios, and a transient analysis using the element-birth-and-death technique was conducted to reflect the vessel erosion (vessel wall thickness change) effect.

Results: It was found that the maximum heat flux at the focusing region was decreased at least 10% when considering the two-dimensional heat conduction at the reactor vessel wall. Conclusion: The results show that a higher thermal margin for the IVR-ERVC strategy can be achieved in the focusing region. In addition, sensitivity studies revealed that the heat flux and reactor vessel thickness are dominantly affected by the molten corium pool formation according to the accident scenario.

Copyright © 2015, Published by Elsevier Korea LLC on behalf of Korean Nuclear Society.

1. Introduction

Various safety systems are designed and adapted in nuclear power plants to prevent postulated accidents, to enhance the lifetime and economic benefit, and to increase public acceptance of the plants. Postulated severe core damage accidents have a high-threat risk for human health and the environment. Versatile measures have been suggested and applied to

mitigate severe accidents in nuclear power plants, as recently presented by Rempe et al. [1]. In-vessel corium retention (IVR) through the external reactor vessel cooling (ERVC) is known to be an effective method for maintaining the integrity of a reactor vessel during a severe accident in a nuclear power plant [2-4]. Under the IVR-ERVC conditions, it is necessary to ensure that the heat transfer from the reactor vessel wall to the coolant in the reactor cavity is sufficient to cool and

* Corresponding author. E-mail address: jh.jung@kaeri.re.kr (J. Jung).

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http:// creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. http://dx.doi.org/10.1016/j.net.2014.11.005

1738-5733/Copyright © 2015, Published by Elsevier Korea LLC on behalf of Korean Nuclear Society.

retain the molten corium inside the reactor vessel, especially for high-power reactors such as APR1400.

To evaluate the thermal margin for IVR-ERVC, the thermal load imposed on the external reactor vessel wall from the molten corium should be estimated correctly. Thermal behavior and loadings, that is, the thermal regime in the molten corium, have been extensively studied analytically to examine the feasibility of the IVR-ERVC strategy [5-8]. Previous studies assumed a fully developed molten pool, such as two- and three-layer models, in which the molten pool is separated into two or three metallic and oxidic layers. The natural convection phenomenon in each layer has been studied analytically and experimentally, and then the thermal load along the internal wall of the reactor vessel was estimated. In general, a focusing effect, which means that thermal load is focused on the light metallic layer [7], is taken into account as one of the important issues because it is related substantially to vessel failure due to the high-heat flux and low thermal margin.

In most previous studies, the thermal margin for IVR-ERVC has been conservatively evaluated with the thermal load imposed on the internal reactor vessel wall by ignoring the two-dimensional (2D) or three-dimensional heat conduction through the reactor vessel wall. That is, the heat flux on the external reactor vessel wall, which is the real contact surface with the coolant, was assumed to be the same as that on the internal wall from the molten corium pool as shown in Fig. 1. That is, q'n(6) was assumed to be equal to q'out(q), where 6 is the angle from the center of the reactor vessel bottom. However, if we consider the 2D conduction heat transfer through the reactor vessel wall, it is expected that there is some difference between the internal and the external wall heat-flux distributions because the generated heat from higher thermal load areas such as the focusing region can be removed from the lower heat-flux region. Accordingly, it is plausible that the 2D conduction heat transfer can provide the additional thermal margin for IVR-ERVC.

Water oulet, External gap

This paper is devoted to seeking the proper external heat-flux distribution for Korean advanced power reactor APR1400, using the IVR-ERVC strategy and considering the 2D conduction heat transfer. The results demonstrate that the 2D effect leads to a difference between the internal and external heat-flux distributions of the reactor vessel wall and provides an additional thermal margin. In addition, parametric studies have been performed to identify the parameters that control the external wall heat flux, and finally to improve the examination quality for the feasibility of IVR-ERVC strategy from an optimistic point of view.

2. Model

2.1. Model description

As shown in Fig. 1, the water from the in-containment refueling water storage tank is flooded into the reactor cavity under the IVR-ERVC conditions in APR1400, and the molten corium is relocated into the lower plenum, which is a conceptual schematic of the steady-state two-layered melt pool configuration [9]. Reactor vessel insulation for reducing the heat loss from the reactor vessel during normal operation plays an important role in IVR-ERVC to enhance the heat removal rate by generating a natural circulation flow between the reactor vessel wall and insulation with the water inlet, outlet, and steam outlet. In this study, a two-layer formation of the corium pool is assumed. Two layers are formed by a density difference in the lower plenum of the reactor vessel between the high-density oxidic layer of UO2 and ZrO2 and the low-density metallic layer of zirconium and stainless steel.

The heat flux from molten corium is dependent on the molten core formation. In other words, the heat generation rate of molten corium depends on the accident scenario. Although an extensive series of severe accident calculations is required to identify bounding transients, station blackout (SBO), large

Fig. 1 - Schematic diagram of the in-vessel retention through external reactor vessel cooling concept [8]. ICI: In-Core-Instrumentation.

Table 1 - Composition of molten corium and molten pool formation with severe accident scenarios for APR1400 [9].

Accident TLOFW SBO 9.6" LBLOCA

Reference time (s) 9,109 13,242 4,910

Decay heat (W) 4.63 x 107 4.14 x 107 5.18 x 107

Corium mass (kg) 1.957 x 105 1.929 x 105 1.67 x 105

UO2:ZrO2:Fe:Zr:B4C 57.84:9.30:25.55:5.98:1.33 57.44:9.85:25.92:5.60:1.19 64.25:1.68:29.94:2.81:1.32

Oxide layer

Depth (m) 1.67 1.67 1.45

Aspect ratio (H/R) 0.70 0.70 0.61

Pool angle (degree) 72.90 72.70 67.20

Metal layer

Depth (m) 0.59 0.58 0.54

Aspect ratio (H/R) 0.26 0.24 0.24

Pool angle (degree) 87.50 87.00 80.80

LBLOCA, large break loss of coolant accident; SBO, station blackout; TLOFW, total loss of feed water. Copyright holder: INEEL (Idaho National Engineering and Environmental Laboratory), 2005.

break loss of coolant accident (LBLOCA), and total loss of feed water (TLOFW) were selected for this simulation. The internal heat fluxes were obtained from Kim et al. [9]. In that study [9], the composition of molten corium and molten pool formation were calculated using the SCDAP/RELAP code and MATPRO code with severe accident scenarios for APR1400 (Table 1). Based on the information about molten corium, the heat-flux distributions in the internal reactor vessel wall were calculated for the selected cases using a lumped-parameter model. Fig. 2 shows the heat-flux change with angle for the selected accident scenarios, where the calculated heat flux was normalized by the area-averaged heat-flux value.

2.2. Numerical formulation

The conduction heat transfer from the molten corium to the external wall is governed by the following energy conservation equation:

9T k 2rT, „

---V2T = 0

ôt pc

where r, c, and k are the density, specific heat, conductivity, and temperature of the vessel medium, respectively. The

Fig. 2 - Molten corium pool heat fluxes with severe accident scenarios [9]. LBLOCA, large break loss of coolant accident; SBO, station blackout; TLOFW, total loss of feed water.

vessel medium, which is used for APR1400, is the SA508, Grade 3, Class 1. Thermal properties of the vessel medium strongly depend on the temperature. Here, thermal properties of the SA508 based on the American Society of Mechanical Engineers code were applied as shown in Fig. 3.

600 800 1,000 Temperature(oC)

1,000 1,200 1,400 1,600 1,800

Temperature(oC)

600 800

Temperature(oC)

1,000 1,200 1,400 1,600

Fig. 3 - Properties of SA508, Grade 3, Class 1. (A) Thermal conductivity; (B) specific heat; and (C) density.

Fig. 4 - Computational domain.

The computational domain was assumed to be having an axial symmetry as shown in Fig. 4. The dimensions in the computational domain for APR1400 are summarized in Table 2. The heat-flux distributions for the lower reactor vessel, which is located on A1 in Fig. 4, with the angle according to the chosen scenarios are given in Fig. 2.

A radiation heat transfer from the top surface of the light metallic layer was applied at the upper segment of the non-contacted part with the melt. Therefore, a heat-flux boundary condition on A2 can be expressed as follows:

qrad = seTmFd

where s, e, Tm, and Fd are the Stefan-Boltzmann constant, emissivity, molten core surface temperature, and configuration factor, respectively. We assumed that the emissivity on the top of the light metallic layer was 0.4 and the molten core surface was maintained at the melting temperature. The configuration factor [10] is given by:

F - V- 1 + H2 - R2

Fd " 2 V Pffi-ffiffi

r r oo

R = - = -= I. Z = 1 + H2 + R2 a r

Table 2 - APR1400 lower plenum information.

Vessel material SA508, Grade 3, Class 1

Melting temperature 1,501°C

Coolant Light water

Dimensions

Parameter Dimension (m)

S_SHELL_RAD 2.371

S_SHELL_THK 0.175

S_SHELL_OFF 0.369

C_SHELL_HGT 3.769

C_SHELL_THK 0.232

where h and r are the height and radius of the reactor vessel (Fig. 4), respectively. To calculate the external wall heat flux, the information about the outer wall temperature might be needed. For simplicity, the outer wall temperature on A3 was set to be 120°C due to the nucleate boiling condition, and the effects of convection and phase change are assumed to be negligible at the outer wall. The outer wall temperature would change due to the change of the coolant temperature with pressure. The effect of the wall temperature is discussed in the Sensitivity analysis and discussion section.

ANSYS Mechanics 14.5 (www.Ansys.com) was used to solve the transient conduction equation. An element-birth-and-death technique in the simulation was used to deactivate or reactivate selected elements in each case to reflect the vessel erosion (vessel wall thickness change) effect [11]. To achieve the element death, ANSYS cannot remove "killed" elements. Instead, it deactivates them. Element loads associated with deactivated elements are zeroed out of the load vector, but they still appear in the element list. Similarly, the conductivity and specific heat are set to infinity and zero for deactivated elements, which exceed the melting temperature in this simulation. The thickness of deactivated elements is not included in the wall thickness over the model.

To increase the numerical accuracy, a mesh-dependency test was performed. As a result, a4-mm mesh size was applied and the grid was made of 114,814 nodes in this finite-element model. The numerical simulations in the computational domain (Fig. 4) were used to determine the temperature distribution of the external reactor vessel. The work proceeded through the following steps: (1) Solve Equation 1 at t = t0, to find the temperature profile of the reactor vessel. (2) If each node temperature exceeds the melting temperature of the vessel material, then this node becomes a deactivated element by the element-death technique. (3) At t = to + At, treat the updated element information and

Fig. 5 - Temperature profiles with severe accident scenarios. (A) Total loss of feed water; (B) station blackout; and (C) 9.6" large break loss of coolant accident case.

solve Equation 1, and then apply the element-death technique. (4) Repeat Step 3 until there is no change in the temperature profile.

3. Results and discussion

3.1. Numerical results

The numerical results of temperature distributions of the reactor vessel are shown in Fig. 5. As mentioned in the Numerical formulation section, when the node temperature exceeds the melting temperature of the vessel material, that node is eliminated. It was observed that the wall thickness is thinner in the high-heat-flux region than in other regions,

such as the low-heat-flux region. Above the corium pool region, although the vessel wall is heated up by the radiation source from the top surface of the corium pool and conduction heat transfer from the corium pool heat source through the wall, the wall temperature cannot reach the melting temperature.

To investigate the effect of 2D conduction heat transfer within the vessel wall, the external heat-flux distributions were obtained in two ways. In the first method, we considered the 2D conduction effects. The external heat-flux distributions were obtained from the conduction equation at the external wall node based on the numerical results as follows:

00 i Twall-1 Twall

qwaii =k-^— (5)

where At is the mesh size of the computation domain. The second method determined the distribution of the external heat flux by dividing the internal heat flux by the ratio between the internal lower head area and the external lower head area, which is based on the assumption that the external heat-flux distribution is the same as the internal heat-flux distribution, i.e., one-dimensional conduction heat transfer was applied. The obtained heat fluxes were divided by the averaged internal heat flux to compare with the normalized heat fluxes.

The two methods yielded different heat-flux values and trends, as shown in Fig. 6. In the first method, more heat is removed through the low-heat-flux region on the lower vessel and the radiation heat-flux region due to the conduction heat transfer from the high-heat-flux region. Consequently, the maximum heat flux, which is located in the focusing region, decreases by about 20% compared with the maximum internal heat flux, whereas the maximum heat flux decreases by only 10% using the second method in the 9.6" LBLOCA case (Fig. 6C). This illustrates that the 2D conduction heat transfer could provide the additional thermal margin for the IVR-ERVC strategy. This result suggests that the calculated external heat transfer, which considers the 2D conduction on the wall, should be applied to analyze a thermal margin for the IVR-ERVC strategy.

It is also observed that the increase in the maximum heat flux from the molten corium pool results in an increase in the maximum heat-flux difference between the two methods. The result is straightforward because more heat is transferred by conduction through the vessel wall as the peak heat flux increases.

The wall thicknesses of the reactor vessel as a function of angle from the bottom of the reactor vessel were obtained as shown in Fig. 7. The reactor vessel thickness is about 17.5 cm. When the reactor vessel is in contact with the low-heat-flux region from the molten corium pool, melting reduces the wall by 30% of its initial thickness. However, when the reactor vessel is in contact with the high-heat-flux region, the wall ablation occurs due to the high value of the heat transfer coefficient, i.e., a focusing effect. In this case, melting reduces the thickness by 80% of its initial value. This effect is dominantly determined by the molten corium heat in the lower plenum of the reactor vessel. Because the maximum heat flux decreases by considering 2D conduction effects, it leads to a difference in the reactor vessel wall thickness. For example, the minimum wall thickness is about 25 mm on the focusing effect region using the first method, whereas it is 22 mm by the second method in the 9.6" LBLOCA case. This result also indicates that the 2D conduction heat transfer could provide a higher margin against vessel wall failure.

Fig. 6 - Distribution of external heat flux using two methods. (A) Total loss of feed water; (B) station blackout; and (C) 9.6" large break loss of coolant accident case.

3.2. Sensitivity analysis and discussion

The variations of external wall heat flux with other heat-transfer parameters (external wall temperature and emissiv-ity) were analyzed to identify the parameters that control the external wall heat flux.

The heat-flux distributions with the various emissivity values, which affect the boundary condition of A2, were

calculated considering the 2D conduction effect. Radiation energy could be changed by the components, which are located above the top of the surface of the molten core. Fig. 8 shows the changes in heat-flux distributions of the external reactor vessel with the emissivity for the TLOFW case. The external heat flux increases after 90°, but it was observed that the maximum heat flux and heat-flux distributions of the external reactor vessel at

Fig. 7 - Thickness of the reactor vessel wall with severe accident scenarios. (A) Total loss of feed water; (B) station blackout; and (C) 9.6 large break loss of coolant accident case.

the molten core segment are similar. It illustrates that the emissivity and the top surface of the molten corium are not affected, and the molten pool heat flux plays a key role in predicting the reactor vessel failure.

To calculate the external wall heat flux, information about the outer wall temperature might be needed. Under the IVR-ERVC conditions, nucleate boiling may occur along the outer surface of the vessel and then the temperature on the vessel outer surface would change along with both the nucleate boiling heat flux along angular locations and the saturation temperature of the coolant at a given pressure. Because information is limited about the local boiling curves for the conditions such as angle and pressure, the outer wall temperature should be assumed and its effect on the heat flux should be examined. The heat-flux distributions at different coolant temperatures were calculated using the first method as shown in Fig. 9. This graph shows that the distribution of heat flux is independent of the coolant temperature. The reason is that the temperature gradient on the reactor vessel, which determines the heat flux (Equation 5), slightly decreases even though the coolant temperature increases from 120°C to 200°C. It means that the coolant temperature slightly contributes to determining the heat-flux distributions of the external reactor vessel wall.

It was shown that a higher thermal margin for the IVR-ERVC strategy can be achieved in the high-heat-flux region by considering 2D conduction effects because the heat that is generated at the high-heat-flux region can be removed from the low-heat-flux region by the conduction heat transfer at the reactor vessel wall. Several numerical simulations with various parameters revealed that the maximum heat flux, which determines the thermal margins for the IVR-ERVC strategy, is most affected by the molten pool formation, which determines the internal heat flux on the lower plenum. The effects of the radiation heat transfer and the coolant temperature were not significant. The internal heat flux is strongly dependent on the accident scenario and core inventory, the crust formation at the top surface, and various combinations of pool depth. In a further study, a more detailed sensitivity analysis is necessary to evaluate the internal and external heat fluxes of a reactor vessel for improved

Fig. the

reactor vessel reliability, because there are many uncertainties (e.g., the material properties with temperature and melt pool formation in the lower plenum of the reactor vessel).

4. Conclusion

This paper addressed how to change the external wall heat-flux distribution of APR1400 under the IVR-ERVC conditions considering the 2D conduction effects. In making use of these results, the external reactor vessel heat fluxes have been calculated according to severe accident cases, which are SBO, LBLOCA, TLOFW, using ANSYS. It was found that the maximum heat flux of the external reactor vessel decreases at least 10% by considering 2D conduction heat transfer within the reactor vessel. This conclusion shows that this effect provides an additional thermal margin in the high-heat-flux region for the IVR-ERVC strategy. In addition, it revealed that the maximum heat flux of the external wall is most affected by the molten pool formation through several numerical simulations with various boundary conditions, which are the coolant temperature, the emissivity, and the internal heat flux. Because there are many uncertainties (e.g., the material properties with temperature and melt pool formation in the lower plenum of the reactor vessel), a more detailed sensitivity analysis is needed for a reliable reactor vessel during a severe accident.

Conflicts of interest

All contributing authors declare no conflicts of interest. Acknowledgments

This work was supported by the National Research Foundation of Korea grant funded by the Korean government (MEST; Grant No. 2012M2A8A4025885).

Appendix

Nomenclature

c Heat capacity of a material, J/kg/K

Fd Configuration factor

h Vessel height, m

k Thermal conductivity, W/m/K

q Heat flux, W/m2

r Radius of vessel, m

T Temperature, °C

t time, t

Greek symbols

e emissivity

r density, kg/m3

s Stefan-Boltzmann constant, W/m2/K4

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