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Nuclear Engineering and Technology 51 (2019) 60e72 Contents lists available at ScienceDirect Nuclear Engineering and Technology journal homepage: www.elsevier.com/locate/net Original Article Thermal-hydraulic study of air-cooled passive decay heat removal system for APRþ under extended station blackout Do Yun Kim a, Hee Cheon NO a, *, Ho Joon Yoon b, Sang Gyu Lim c a Korea Advanced Institute of Science & Technology (KAIST), Department of Nuclear and Quantum Engineering, 291 Daehak-ro, Yuseong-gu, Daejeon, 305701, Republic of Korea b Department of Nuclear Engineering, Khalifa University of Science, Technology & Research (KUSTAR), P.O. Box 127788, Abu Dhabi, United Arab Emirates c Korea Hydro and Nuclear Power Co.dCentral Research Institute, 70, 1312-gil, Yuseong-daero, Yuseong-gu, Daejeon, 34101, Republic of Korea a r t i c l e i n f o a b s t r a c t Article history: Received 1 May 2018 Received in revised form 21 August 2018 Accepted 12 September 2018 Available online 14 September 2018 The air-cooled passive decay heat removal system (APDHR) was proposed to provide the ultimate heat sink for non-LOCA accidents. The APDHR is a modified one of Passive Auxiliary Feed-water system (PAFS) installed in APRþ. The PAFS has a heat exchanger in the Passive Condensate Cooling Tank (PCCT) and can remove decay heat for 8 h. After that, the heat transfer rate through the PAFS drastically decreases because the heat transfer condition changes from water to air. The APDHR with a vertical heat exchanger in PCCT will be able to remove the decay heat by air if it has sufficient natural convection in PCCT. We conducted the thermal-hydraulic simulation by the MARS code to investigate the behavior of the APR þ selected as a reference plant for the simulation. The simulation contains two phases based on water depletion: the early phase and the late phase. In the early phase, the volume of water in PCCT was determined to avoid the water depletion in three days after shutdown. In the late phase, when the number of the HXs is greater than 4089 per PCCT, the MARS simulation confirmed the long-term cooling by air is possible under extended Station Blackout (SBO). © 2018 Korean Nuclear Society, Published by Elsevier Korea LLC. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Keywords: Air-cooled passive decay heat removal (APDHR) system Extended station blackout (SBO) Natural convection air cooling MARS simulation 1. Introduction Under any accidents accompanying with nuclear reactor shutdown, decay heat has to be removed for preserving the integrity of the nuclear reactor. Moreover, several passive design concepts have been investigated to remove decay heat even under the extended Station Blackout (SBO) after the Fukushima accident. In the Fukushima accident, off-site electricity supply was lost after the tsunami arrived, and it took at least 9 days to totally recover the offsite electricity supply [1]. Therefore, the passive safety system is essential for long-term cooling. In a decay heat removal system, the decay heat transferred to the steam generator (SG) results in the evaporation of feed-water. This generated steam must be condensed and supplied back, as feed-water, to the SG to continue the heat removal process. Hence it is important to find an effective solution to condense the steam. For example, the steam generator secondary emergency passive residual heat removal system (EPRHRs) has been suggested as a new * Corresponding author. E-mail address: hcno@kaist.ac.kr (H.C. NO). design for traditional generation II þ reactor CPR1000. The EPRHRs is designed to improve the safety and reliability of CPR1000 by completely or partially replacing traditional emergency water cooling system in the event of the station blackout or loss of heat sink accident [2,3]. There is also a valuable work about thermal hydraulic characteristics of a passive residual heat removal system for an integrated pressurized water reactor in ocean environment, not land state [4]. In Korea, Passive Auxiliary Feed-water System (PAFS) is suggested as one of the passive decay heat removal concepts. Steam generated in a SG flows into inclined heat exchangers (HXs), which are submerged in a water tank so-called Passive Condensate Cooling Tank (PCCT). Then the steam is condensed while the heat of the steam is transferred to the water in the PCCT. The capacity of the PAFS is designed to maintain hot shutdown condition for at least 8 h. If the water was not replenished after the PCCT was dried out, however, the decay heat could not be removed enough and the integrity of the nuclear reactor could not be ensured. Therefore, decay heat removal system without using water is needed in the environment where the water is short or not available for a long-term cooling under extended SBO. For the long-term decay heat removal without supplying off-site electricity and additional water, passively-operated air-cooled https://doi.org/10.1016/j.net.2018.09.006 1738-5733/© 2018 Korean Nuclear Society, Published by Elsevier Korea LLC. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/). D.Y. Kim et al. / Nuclear Engineering and Technology 51 (2019) 60e72 61 condenser, so-called APDHR, is suggested in this study. Up to three days after non-LOCA occurs, APDHR removes decay heat through the HXs submerged in PCCT like PAFS. However, the decay heat is eliminated through the air after three days when the water in the PCCT evaporates and the HXs are exposed to the air. We conducted the thermal-hydraulic simulation by the MARS code to investigate the behavior of the plant in a water cooling and an air cooling phase. Based on the simulations, design parameters, including the water volume in PCCT and the number of HXs, were determined. In addition, the long-term cooling capability of APDHR was investigated under the extended SBO. Condenser (ACC) is suggested. The ACC has a flexibility in the viewpoint of site selection because it is not dependent on the water supply. Moreover, the important point is that long-term cooling capability is ensured because the ultimate heat sink is an atmosphere and it is inexhaustible. Most of the existing ACC uses the finned HX with the narrow fin spacing to increase a heat transfer area and uses a fan to make air flow through the narrow air path of the finned HX surface. Despite the advantages of ACCs predominantly used, their main drawback is to utilize electricity for operating fans. If the fan worked with a normal electricity supply, ACC would give its best cooling capability. 2. The concept of the APDHR 2.2. The concept and the overall design of the APDHR 2.1. Background studies Therefore, innovative ACC should be developed, which operates in the way of natural convection for long-term cooling without fans using electricity. The innovative passive ACC is designed for cooling down the secondary side in non-LOCA without additional water supply nor electricity usage. It means that the decay heat can be eliminated for an indefinite period to ensure the safety of nuclear power plants. Fig. 2 shows the schematic of the Air-cooled Passive Decay Heat Removal (APDHR) system. The characteristics of the APDHR is that it utilizes both water cooling and air cooling for the decay heat removal. HXs of APDHR are initially submerged in PCCT like PAFS. In the early phase from the beginning of an accident, therefore, water in the PCCT cools down a large amount of steam coming from steam generators. It is the way to deal with the high decay heat in the early phase because the heat transfer rate using water is higher than that using air. However, the water in PCCT will be evaporated and the collapsed water level of the PCCT will decrease as time goes. Therefore, the size of the PCCT is designed to maintain the water cooling during three days after the accident, and then, an air path has been opened PAFS is one of the advanced safety features adopted in the APR þ that is intended to completely replace the conventional active Auxiliary Feed-Water System (AFWS). A schematic diagram is shown in Fig. 1 [5e7]. The PAFS cools the secondary side down and eventually removes the decay heat from the reactor core by adopting a natural convection mechanism condensing steam in nearly-horizontal U-tubes submerged inside the PCCT. The PCCT located outside the containment is designed to eliminate the decay heat for 8 h from the beginning of an accident [8e11]. Therefore, additional water should be replenished after 8 h for long-term cooling. It means that if the water was not supplied after the PCCT was dried out, however, the decay heat could not be removed enough and the integrity of the reactor core could not be ensured. Therefore, a decay heat removal system without using water is needed in the environment where the water is scarce or not available. For the solution of the water supply problem, Air-cooled Fig. 1. Schematic diagram of PAFS [5e7]. 62 D.Y. Kim et al. / Nuclear Engineering and Technology 51 (2019) 60e72 Fig. 2. Schematics of the APDHR in the early phase (Left) and the late phase (Right). for air to flow into the PCCT as shown in the right figure of Fig. 2. When the air flow path is opened due to the collapsed water level drop, the air keeps flowing into the PCCT and removing the decay heat indefinitely in the way of natural convection. Thus, the system can be operated without any external supply, including additional water to prevent the water depletion and electricity for using fans. Fig. 3 shows the cross-sectional view of the APDHR. An air baffle is located around the HXs. The role of the air baffle is to develop an air flow path efficiently by dividing cooling air intake part and heated air discharge part along the HXs. The HXs are located along the air baffle as a square ring type with several rows for the effective distribution of cooling air to each HXs. 3. Development of a MARS model for APDHR analysis 3.1. MARS nodalization for APDHR analysis Thermal hydraulic analysis of APDHR under extended SBO based on MARS code was performed to verify its long-term cooling capability in this paper. MARS is a realistic thermal hydraulic systems analysis code developed by KAERI with multi-dimensional analysis capability [12,13]. Fig. 4 shows the MARS nodalization of APRþ [14]. The APRþ is a Gen III þ reactor, the standard design of which is currently being developed in Korea [15]. The characteristics of the reactor are that it applies many passive safety design features to improve nuclear safety even under SBO. Therefore, APRþ was selected as a reference reactor in this study to check the long-term cooling capability of proposed APDHR, which is passively operated safety feature. The thermal power of APRþ is 4290MWt and ANS73 option that specifies the Proposed 1973 ANS Standard data was used for a decay heat curve in the MARS simulations [16]. Table 1 shows the thermal hydraulic parameters in the initial condition of APRþ [17]. The passive auxiliary feedwater system (PAFS) is one of the advanced safety features adopted in the APRþ, which is intended to completely replace the conventional active auxiliary feedwater system [10]. To simulate APDHR, we benchmarked the MARS nodalization for PAFS and the input was utilized with modifications reflecting the design parameters of APDHR. The right figure in Fig. 5 shows MARS nodalization of PAFS, and the left figure in Fig. 5 shows MARS nodalization of APDHR modified based on the MARS Nodalization of PAFS. The red circles in Fig. 5 indicated the same junction as the red circles in Fig. 4. In Figs. 4 and 5, J001 & J007 were the junctions from the steam generator to the steam supply line of Fig. 3. A cross-sectional view of the APDHR with the square ring type configuration of HXs. D.Y. Kim et al. / Nuclear Engineering and Technology 51 (2019) 60e72 63 Fig. 4. MARS nodalization of APRþ [14]. Table 1 Thermal hydraulic parameters in the initial condition [17]. Primary side Secondary side APDHR Parameters Initial condition Core power(100%)[MWth] PZR pressure [bar] Steam pressure [bar] Steam temperature [K] PCCT pressure [bar] PCCT temperature[K] 4290 155 70.3 559.15 1.01 313.15 the APDHR, and J083 & J089 represented the junctions where the condensate from the APDHR flowed back into the steam generator of APRþ. The part of PAFS, where the HXs and the PCCT were located, was mainly changed. Firstly, the inclination of HX was changed from nearly horizontal to vertical with 70 nodes. The length of the HXs where the heat transfer actually takes place was slightly increased from 8.4 m to 10 m. The steam supply line and the return line were nodalized with 94 and 104 nodes, respectively. In case of PCCT, it was divided one pipe and one annulus with multiple junctions. Each pipe and annulus was composed of 6 nodes. In the pipe, the HXs were located and the heat transfer took place, while the annulus was filled with water only. We checked that the effect of the cross-sectional area ratio between pipe and annulus on the heat transfer in the PCCT was insignificant. The specification of HXs and PCCT were shown in Table 2. The height of each PCCT nodes was changed as like the table because the specification of HX was changed. Therefore, in order to consider the modified design parameters, MARS nodalization of APDHR in the left figure of Fig. 5 have replaced the PCCT and HXs of PAFS that were marked by red box. The rest of components of PAFS, except PCCT and HXs, was used without modifications. The water level was maintained as the same with the level of PAFS, 10.5 m. In the left figure of Fig. 5, V030 & V032 were steam supply line from steam generator. V040 was Fig. 5. MARS nodalization of APDHR (left) and PAFS (right) [14]. 64 D.Y. Kim et al. / Nuclear Engineering and Technology 51 (2019) 60e72 Table 2 Design specifications of APDHR. HXs of APDHR PCCT Parameters Dimensions Outer/Inner diameter [mm] Length [m] Number of HXs per PCCT PCCT number Width x Height x Depth [m] Initial water level in PCCT [m] 50.9/44.8 10 3271e5451 2 14.4  14.4 x 15.2 10.5 tube inlet header. V050 was HXs. Condensation took place inside of V050, and water cooling and air cooling occurred outside of it. V090 & V092 were PCCT. V094 was pool outlet boundary which represented containment free volume. 3.2. Postulated accident scenario In order to check the cooling capability of APDHR under extended SBO, MARS simulation was conducted. The extended SBO scenario is described in Table 3. After the accident occurred, a reactor trip happen. And, all of the active safety systems using electricity, such as reactor coolant pumps (RCP), safety injection pumps (SIP), became disabled because electricity supply stopped. Then, main feed-water isolation and main steam line isolation also happened. Thus, all of the steam generated in SG flowed into APDHR system but turbine to be condensed passively. Especially, seal leakage was considered in this study to simulate the extended SBO scenario in Section 4.3. According to the State-ofthe-Art Reactor Consequence Analysis (SOARCA) report, when a loss of AC power occurs, RCP seal cooling systems no longer supplies cooling water, and primary coolant begins leaking along the RCP shaft through the mechanical seals [18]. Therefore we had to consider the seal leakage to check the long-term cooling capability of APDHR under the extended SBO. According to SOARCA report, the sensitivity of the seal leakage rate was investigated as follows. The nominal rate of the RCP seal leakage per RCP was 1.59L/s with a 79% likelihood for a small leakage, while it was 13.79L/s with a 20% likelihood for a large leakage at a full reactor pressure. Actually, the leakage rate subsequently changed in response to changes in primary system pressure, the primary system fluid subcooling at the RCP seal, and the primary system void fraction at the pump seal. However, the leakage rates was considered as a constant volumetric rate in a conservative manner in this study. In addition, they mentioned the RCP seal leakage has the attributes of a LOCA so seal leakage was simulated as a LOCA in this study. The seal leakage was located in the nodes right next to RCP. The leaked water-vapor mixture was discharged into the containment that was initially 1 bar and 40  C. 4. MARS analysis results 4.1. MARS simulation results in the early phase Firstly, MARS simulation was performed up to 3days when the HX of APDHR was totally or partially submerged in the water in PCCT. For the early phase simulation, the number of HXs should be selected. Heat removal in the early phase through the water in PCCT is more effective than the heat removal in the late phase through air cooling. Therefore, the required number of HXs was determined in the late phase, which was limiting condition. Firstly, we calculated the decay heat at three days after the reactor shutdown, and it was 23.85 MW, that is the 0.56% of the normal power of APRþ. In the late phase, the amount of decay heat should be removed through the APDHR for long-term cooling. When the operating range of SG is from 1 bar to 84 bar when main steam safety valves (MSSV) are opened, we assumed the temperature of SG was maintained constantly as the mean temperature of the saturation temperature of 1 bar and 84 bar. Based on the assumption, the temperature of SG was 199.6  C. Through the CFD simulation to calculate the air cooling heat transfer coefficient of APDHR as a function of SG temperature, 9.01W/m2K was determined as an air cooling heat transfer coefficient in the study for CFD-based design optimization for APDHR by Kim et al. [19]. Based on the SG temperature which is the external surface temperature of HXs and the air cooling heat transfer coefficient, the minimum a required number of HXs was 5451 per PCCT to remove the decay heat for long-term cooling. The selected number of HXs was conservative and maybe too large because we assume the heat removal rate through APDHR was constant due to fixed SG temperature, although the decay heat keeps decreasing as time goes in reality. Therefore, 5451 number of HXs were selected in the MARS simulation, and additional study related to the number of HXs will be conducted in Section 4.2. The inner and outer surface heat boundary conditions of HXs were the default convection boundary conditions of MARS. The MARS determines the heat transfer mode at each node based on the thermal-hydraulic lumped parameters such as fluid pressure, velocity, wall temperature. Then, MARS uses heat transfer correlations that are based on fully developed steady-state flow. An important factor that effects the magnitude of heat transfer coefficients, besides obvious parameters such as velocity, is the flow field or hydraulic geometry surrounding the surface. The correlation set appropriate for a specific surface depends on the hydraulic geometry of the adjacent fluid. Therefore, the correlation used depends on the hydraulic geometry in MARS. In our HX geometry, the following correlations in Fig. 6 were used to calculate the heat transfer for a specific mode [13]. Required water volume of PCCT was determined first through the sensitivity study. The left figure of Fig. 7 shows the collapsed water level of PCCT in the early phase. When we changed the water volume of PCCT, we enlarged the area of PCCT with fixed level of water in PCCT. Therefore, the initial level of three cases in Fig. 7 was 10.5 m in all cases. When the water volume in PCCT was 2,176 m3, the collapsed water level reached the lowest point of the HXs, and the elevation was 1.262 m from the bottom of PCCT. Therefore, 2,176 m3 of water per PCCT was selected in this study. In order to contain the amount of water, the width and the height of the PCCT was 14.4 m  14.4 m. The depth of the water was 10.5 m as mentioned in Section 3.2. The right figure of Fig. 7 shows decay heat and heat removal rate of APDHR after shutdown. The decay heat decreased drastically right after the shutdown, but gradually Table 3 The sequence of events for the MARS simulation. Time Incident Remarks 0 0.1 0.1e259,200s (0.1s - 3 days) 259,200e604,800s (3days e 7days) Reactor trip Seal leakage Early phase Late phase Initial incident (SBO) Seal leakage occurrence (RCP) Decay heat was removed through the water in PCCT Decay heat was removed by air-cooling due to the water depletion in PCCT D.Y. Kim et al. / Nuclear Engineering and Technology 51 (2019) 60e72 65 Fig. 6. MARS wall heat transfer correlations for default geometry [13]. decreased later. The heat removed from the APDHR was consistent with the tendency of the decay heat as shown in Fig. 7, except for the instability that occurred at the start of the operation of the APDHR. It shows the APDHR can remove the decay heat effectively in the early phase. Fig. 8 shows the pressure of core and SG. The increase of SG pressure before the abrupt decreasing at the beginning of the early phase occurred because the steam line valve from SG to APDHR was suddenly opened. When it opened, large amount of steam was abruptly flowed into APDHR with large mass flowrate due to large pressure difference between the SG and APDHR. However, the steam flowrate has been stable after 3,000s, and the decay power was abruptly decreased. Then, the decreasing rate became small and it was decreased slowly. Following the decay heat curve, the pressure of the core and SG were also decreased. The pressures were drastically decreased in 10,000s and they were almost constantly maintained as 16.8 bar and 1.7 bar for the core and the SG, respectively. During the early phase, the collapsed water levels in the core and the SG were checked as shown in Fig. 9. In case of the collapsed water level of core, it was maintained as 100% during the phase. It shows that the nuclear fuels in the core was fully submerged in the coolant of the primary loop during this phase. Therefore, the integrity of the core was preserved with the APDHR. In case of the collapsed water level of SG, it was decreased to 60% because the decay heat was drastically lowered right after shutdown. However, the level remained during the phase, and it means that the heat transfer between decay heat coming from the core and the heat removal through the APDHR was well balanced. It proved that the APDHR effectively removed the decay heat until three days. Fig. 8. Pressure of core and SG in the early phase. 4.2. MARS simulation results in the late phase with a constant heat flux boundary condition In the late phase, the water in the PCCT is depleted and the air flow path is opened. Therefore, decay heat is removed through natural convection air cooling in a passive way. To simulate the heat transfer phenomenon in the late phase, a constant heat flux boundary condition based on CFD calculation was applied to the external boundary condition of HXs. MARS code is the 1-D code, so it is not suitable to simulate natural convection of air because buoyancy effect, air velocity, and its flow direction are hard to be simulated by MARS and the results of the parameters by MARS may not be accurate. Hence, the heat transfer results by MARS on the natural convection of air side is not reliable. Therefore, the heat flux results from CFD were applied as a heat flux boundary condition on the air cooling side because of the accurate simulation of CFD for 3-D natural convection. The heat flux was calculated with constant HX wall temperatures. If we use the table type of HTRNRATE in MARS, the heat flux as a function of time can be applied as the form of a table [12]. In reality, the temperature of SG changes in real time, so the air cooling heat flux changes following the temperature change. However, we used the constant heat flux assuming the temperature of SG was 199.2  C as described in Section 4.1 for the screening process related to the number of HXs first. In this case, the natural Fig. 7. The collapsed water level of PCCT (Left) and decay heat compared with the heat removal rate through APDHR (Right) in the early phase. 66 D.Y. Kim et al. / Nuclear Engineering and Technology 51 (2019) 60e72 Fig. 10. PCT changes in the late phase. Fig. 9. The collapsed water levels in core and SG in the early phase. convection heat transfer coefficient was 9.01W/m2K, and the natural convection heat flux was 1383W/m2. In order to check the validity of the constant heat flux boundary condition in this Section, the realistic MARS simulation was performed following the change of SG temperature and the heat flux change in real time, and it is explained in Section 4.3. Based on the MARS input, we performed the MARS simulation for the late phase. If we only consider the decay heat at three days after the shutdown, 5451 number of HX were required as mentioned in Section 4.1. However, the less number of HXs was needed because the decay heat would be gradually reduced in reality. Therefore, the less number of 5451 was simulated as shown in Fig. 10. In case of the 3271 HXs which is the 60% of 5451, simulation was stopped due to peak cladding temperature (PCT) increase. This means that the removed heat through the number of HXs was insufficient compared to the decay heat. The heat transfer regime around nuclear fuel was saturated nucleate boiling, so the peak cladding temperature was dependent on core pressure. In the cases of 3271 and 3816 number of HXs, decay heat was not removed enough. Therefore, reactor core pressure of them was increased. If the pressure reached at 166.89 bar, safety valve in pressurizer has been opened, so the core pressure cannot exceed 166.89 bar. Therefore, the increase of peak cladding temperature (PCT) was stopped and flat temperature region around 600 K was observed in the cases of 3271 and 3816 number of HXs. Hence, HX number sensitivity study was conducted and approximately 4089 HXs which were the 75% of 5451 should have been needed at least, because the PCTs were tended to decrease at the end of their simulation in cases of more than 4089 HXs. It means the removed heat is larger than the decay heat. In case of the 5451 HXs, PCT was continuously decreased from the beginning of the late phase, and the simulation was stopped in 90,000s. The pressure of the condensate line located next to the HXs was decreased and finally reached to zero. Then the MARS simulation was failed. However, this was because we forcibly removed 1383 W/m2 of heat with a fixed heat flux boundary condition. In reality, if the pressure dropped, SG temperature would decrease and the heat transfer rate would decrease finally. Therefore, the decay heat will be reliably removed if there are more than 5451 HXs. Hence, not only PCT but also other parameters were investigated to make sure the number of HXs required for long-term cooling. Fig. 11 shows the SG pressure and level in the late phase. If the HXs were more than 4089 HXs, SG pressure was below the limit pressure, 84 bar that safety valve opened, because the heat removal rate was larger than the decay heat. However, if the HXs were less than the number, SG pressure was increased, and finally the safety valve opened. Because of the opening of the safety valve, the SG level became decreased. Therefore, the long-term cooling may not be ensured caused by the lack of water inventory of SG. As a result, 4089 HXs were the minimum required amount of HXs for reliably achieving the long-term decay heat removal. In this case, the peak pressure of SG was 54.7 bar. With the 4089 HXs, pressurizer (PZR) safety valves were opened at 166.9 bar in 150,000s, as shown in Fig. 12. And the PZR safety valve was closed when the core pressure became 145.2 bar after the discharge. Therefore, the PZR pressure repeated the rise and fall between the pressures until the decay heat became smaller than the removed heat by APDHR, and the peak pressure of the core was 166.9 bar. Despite the opening of the safety valve of PZR, the core level was maintained because of the safety injection by safety injection tank (SIT). SG level was maintained almost constantly as well because the SG safety valve was not opened. Therefore, water inventory of core and SG was sufficient, and it guaranteed that further cooling is possible with 4089 HXs. 4.3. MARS simulation results in the late phase with a realistic heat flux boundary condition So far, the air cooling heat flux applied in MARS simulations was constant and not changed in spite of the SG temperature change. Therefore, we tried to follow the SG temperature change as a function of time to simulate the actual situation. We reflected the SG temperature change to the heat flux boundary condition by iteration method. We utilized the empirical correlation of the air cooling heat flux as a function of temperature in APDHR as follows: 00 2 qAC ¼ 0:0076,TSG þ 3:94,TSG  2183:6 h . i W m2 (1) where TSG is a temperature of SG in the unit of K. The applicable range of the equation was from 373 K to 563 K, which was the operating temperature range of SG. The correlation resulted from CFD simulation for the air cooling in APDHR according to Kim et al. [19]. In the paper, the natural convection of air was simulated D.Y. Kim et al. / Nuclear Engineering and Technology 51 (2019) 60e72 67 Fig. 11. SG pressure (Top) and SG level (Bottom) in the late phase. when the temperature of SG changes. The computational domain for the CFD simulation of APDHR was benchmarked from the unit cell concept by Kim et al. [20]. Unit cell was only defined as some part of HX and surrounding air that showing representative phenomena occurring around the HX without simulating all the HXs in APDHR. By using the unit cell concept, we were able to reduce the computational loads for simulating all complex systems. We applied the heat transfer coefficient in a unit cell with a flat plate to a circular tube heat exchanger in this study. Fig. 13 shows the unit cell defined for CFD calculations. A unit cell was defined as a hexahedron, including air between HXs with its width was 0.5 cm. Thickness of the HX was 0.3 cm. The pitch 68 D.Y. Kim et al. / Nuclear Engineering and Technology 51 (2019) 60e72 Fig. 12. Pressure of core and SG (Left), and Core and SG levels (Right) in the late phase. Fig. 13. Unit cell geometry from top view (Left) and side view (Right) with boundary conditions. between HXs was determined as 20 cm through pitch sensitivity study. The length of the unit cell was 10 m the same as the height of the HX of APDHR. The material of the HX was stainless steel. According to Bae et al. [21], the operating steam condition of PAFS is 7.4 MPa and 290  C in the case of APRþ. Therefore, the same operating condition was applied to the wall temperature of the HXs. Ambient temperature was given as 46.11  C conservatively according to the AP1000 Design Control Document [22]. For the computational grids, Design Modeler in ANSYS Workbench 17.0 was used and ANSYS Fluent 17.0 was used as a solver. CFD calculation was performed under steady-state. We checked the Grashof numbers of each CFD simulations and they were in the range of 1012 < Gr < 2  1013 . Therefore, the natural convection flow regime covered in this study was turbulent because the Grashof number higher than 109 is considered as a turbulent in usual. The RNG k-epsilon model with enhanced wall treatment was used for the natural convection of air, and DO model was utilized for radiation heat transfer. The RNG k-epsilon model can apply the inclusion of buoyancy effects on epsilon and enhanced wall treatment for simulating the buoyancy-driven natural convection well. The RNG k-epsilon model was validated with the analytical solution for a natural convection heat transfer coefficient on a vertical flat plate introduced in the previous study (Kays et al., 2005) as follows: Fig. 14. The results of iteration for realistic SG temperature boundary condition in the late phase. D.Y. Kim et al. / Nuclear Engineering and Technology 51 (2019) 60e72 Fig. 15. Realistic heat flux boundary condition for the realistic SG temperature in the late phase. " Pr Nu ¼ 0:0295  6 1 þ 0:494Pr2=3 #1=15 Ra2=5 (2) The characteristic length of the Nu number in the correlation for vertical flat plate was the height of the vertical wall. By comparing with the correlation, the RNG k-epsilon model has correctly predicted the natural convection heat transfer coefficient within 5% error. Therefore, the RNG k-epsilon model was used in this study. Firstly, we conducted the MARS simulation with fixed heat flux, then it gave a SG temperature curve as a function of time. Then, we obtained a piecewise linear heat flux curve according to 69 the SG temperature using Eq. (1) and conducted second MARS simulation. After that, the new SG temperature curve resulted from the second simulation. Then, a new piecewise linear heat flux curve according to the second SG temperature curve was applied for the third MARS simulations. As the iteration process was repeated, our piecewise linear heat flux curve has become close to the real heat flux. Finally, the SG temperature that resulted from the realistic heat flux boundary condition has been also saturated realistically. Fig. 14 shows the SG temperature changes as the iteration was repeated, and the final result of the 9th iteration was the realistic SG temperature. Fig. 15 shows the realistic heat flux boundary condition for the realistic SG temperature. The SG temperature, which increased rapidly, reached a maximum around 100,000 s (1.1days after the air cooling was started). The sudden increase of SG temperature immediately after the start of air cooling was because the air cooling heat transfer rate was smaller than the water cooling in the early phase. After the SG temperature reached the peak of 499 K, it tended to gradually decrease. In addition, the time averaged mean temperature of the SG was 479.8 K. It was only 7 K higher than the initial SG temperature, 472.8 K, that was used as a constant in Section 4.2. It means that the constant heat flux boundary condition with a constant SG temperature was conservative in the viewpoint of the heat removal through APDHR because its heat removal performance was underrated than real. Therefore, less HXs was needed with the realistic heat flux boundary condition, because it reflected the heat removal increase due the SG temperature rise in this period. After applying the realistic SG temperature and the realistic heat flux boundary condition according to it, the PCT trend in the late phase was changed as shown in Fig. 16. The maximum value of the PCT was lowered from 551 K to 512 K, and the time to reach the maximum PCT was shortened. As a result of applying the realistic heat flux boundary condition, the peak pressure of core and SG was decreased as shown in Fig. 17. The peak pressures of core were 166.9 bar and 80 bar with constant Fig. 16. PCT changes with the realistic heat flux boundary condition in the late phase.