Optimal operation of hybrid-SITs under a SBO accident

Nuclear Engineering and Design 297 (2016) 136–147

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Optimal operation of hybrid-SITs under a SBO accident In Seop Jeon a , Sun Heo b , Hyun Gook Kang a,∗ a Department of Nuclear and Quantum Engineering, Korea Advanced Institute of Science and Technology, 291 Daehak-ro, Yuseong-gu, Daejeon 305-701, Republic of Korea b Central Research Institute, Korea Hydro & Nuclear Power Co., 70 Yuseong-daero 1312 beon-gil, Yuseong-gu, Daejeon 305-343, Republic of Korea

h i g h l i g h t s • • • •

Operation strategy of hybrid-SIT (H-SIT) in station blackout (SBO) is developed. There are five main factors which have to be carefully treated in the development of the operation strategy. Optimal value of each main factor is investigated analytically and then through thermal-hydraulic analysis using computer code. The optimum operation strategy is suggested based on the optimal value of the main factors.

a r t i c l e

i n f o

Article history: Received 5 October 2015 Received in revised form 27 November 2015 Accepted 30 November 2015

a b s t r a c t A hybrid safety injection tank (H-SIT) is designed to enhance the capability of pressurized water reactors against high-pressure accidents which might be caused by the combined accidents accompanied by station blackout (SBO), and is suggested as a useful alternative to electricity-driven motor injection pumps. The main purpose of the H-SIT is to provide coolant to the core so that core safety can be maintained for a longer period. As H-SITs have a limited inventory, their efficient use in cooling down the core is paramount to maximize the available time for long-term cooling component restoration. Therefore, an optimum operation strategy must be developed to support the operators for the most efficient H-SIT use. In this study, the main factors which have to be carefully treated in the development of an operation strategy are first identified. Then the optimal value of each main factor is investigated analytically, a process useful to get the basis of the global optimum points. Based on these analytical optimum points, a thermal-hydraulic analysis using MARS code is performed to get more accurate values and to verify the results of the analytical study. The available time for long-term cooling component restoration is also estimated. Finally, an integrated optimum operation strategy for H-SITs in SBO is suggested. © 2015 Elsevier B.V. All rights reserved.

1. Introduction The Fukushima accident was not able to be managed properly due in part to a lack of effective mitigation systems and strategies against a station blackout (SBO) accident (Yang, 2014). The use of passive systems in nuclear power plants (NPP) has been

Abbreviations: SIT, safety injection tank; H-SIT, hybrid safety injection tank; SBO, station blackout; NPP, nuclear power plant; RCS, reactor coolant system; PAFS, passive auxiliary feedwater system; LOCA, loss of coolant accident; POSRV, pilot operated safety relief valve; MARS, multi-dimensional analysis of reactor safety; SG, steam generator; PCCT, passive condensation cooling tank; APR+, Advanced Power Reactor Plus; SAMG, severe accident management guideline; CET, core exit temperature. ∗ Corresponding author. Tel.: +82 423503830; fax: +82 423503810. E-mail addresses: [email protected] (I.S. Jeon), [email protected] (S. Heo), [email protected] (H.G. Kang). http://dx.doi.org/10.1016/j.nucengdes.2015.11.038 0029-5493/© 2015 Elsevier B.V. All rights reserved.

suggested as an alternative to active systems, as passive systems do not require an external energy source and their installation can increase the diversity of NPP accident mitigation strategies (Song and Kim, 2014). Recent research for developing passive systems and operation strategies, such as an integrated passive safety system, has been carried out to enhance plant safety in the nuclear field (Chang et al., 2006, 2013; Cherubini et al., 2008). General passive systems and strategies however have a critical limitation, especially for passive injection systems. As these systems use gravity as their driving force (Buchner and Fabian, 1994), it is difficult to inject coolant in a passive way in high-pressure conditions, and thus depressurization is needed to inject coolant to the reactor coolant system (RCS). High-pressure passive injection is essential to mitigate SBO accidents effectively. The passive auxiliary feedwater system (PAFS) is the primary system used for residual heat removal. Since PAFS relies on natural circulation in the primary coolant system and steam

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Fig. 1. Outline of an H-SIT system.

condensation in the water tank, it is designed to be operated even in an SBO accident (Kim et al., 2010). If both PAFSs fail, depressurization of the RCS is necessary for low-pressure injection by normal safety injection tanks (SITs) (Liu et al., 2015). This strategy however causes a loss of RCS inventory which may result in limited natural circulation in the primary coolant system when the PAFSs are restored. In that sense, if RCS inventory can be maintained during core cool down by high-pressure injection, it increases the diversity of mitigation means. Thus, a hybrid safety injection tank (H-SIT) that can cover not only low-pressure but also high-pressure passive injection was invented. The H-SIT was originally planned to be integrated into an Advanced Power Reactor Plus (APR+) (Kwon and Park, 2013) but can be used in any pressurized water reactor. This system is specialized for the mitigation of high-pressure accidents, such as SBO accidents, as it is a passive system that can inject coolant even in high-pressure conditions. Generally, the H-SIT system can inject water using the pressure from nitrogen gas as a conventional SIT in low-pressure accidents, such as large- and medium-break loss of coolant accidents (LOCA). Additionally, the H-SIT system can also inject water using gravitational force in high-pressure accidents. If a high-pressure accident occurs, the pressure of each H-SIT is equalized with RCS pressure through equalizing pipes, thus allowing the H-SITs to inject water by gravitational force. It is assumed that four H-SITs are installed in the target plant. Each has a 2.5 in diameter equalizing pipe and operates at around pilot operated safety relief valve (POSRV) open pressure, 160 bar. Fig. 1 shows a conceptual layout of the H-SIT system. In case of H-SIT operation signal, it is automatically generated thus human error probability is not considered for H-SIT operation. Restoration of AC power or PAFSs is the only way to achieve long-term cooling in an SBO condition. If AC power is restored, feed-and-bleed operation can be performed using safety injection pumps for long-term cooling (Kim et al., 2014) and if PAFSs are restored, the core can be cooled by natural circulation in the RCS. The restoration of these components, however, takes time. Previous research shows the probability of component restoration changes

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according to how much available time can be secured (Volkanovski and Proˇsek, 2013). Longer restoration times lead to a higher probability of component restoration. Therefore, as H-SITs have a limited inventory, their operation has to be supported by the best operation strategy in order to use the inventory effectively for cooling down the core as long as possible. In a previous study (Jeon and Kang, 2015), an operation strategy was developed focusing on the mitigation of accidents by the combined use of H-SIT and active systems, which is inappropriate in SBO. In this study, we focus on finding a global optimum of H-SIT operation under an SBO accident. First the characteristics of the components and accident situations requiring the use of H-SITs are analyzed in detail. Then an analytical study is performed based on the results from the first analysis to get the basis of the global optimum points among all possibilities. Based on these analytical optimum points, an analysis using computer code is performed to get more accurate values and to verify the results of the analytical study. Finally, a novel operation strategy is developed based on the results of a thermal-hydraulic analysis by using MARS (multi-dimensional analysis of reactor safety) ver. 1.3 (Jeong et al., 1999), which was developed by the Korea Atomic Energy Research Institute (KAERI) by integrating the one-dimensional RELAP/MOD3 with the multi-dimensional COBRA-TF code. The input decks of the APR+ and H-SIT were provided by Korea Hydro & Nuclear Power. In Section 2.1, the main factors necessary to consider for operation strategy development are identified. In Section 2.2, the optimal value of each main factor is estimated by analytical and theoretical investigation. In Section 3, optimal values are estimated and verified through the thermal-hydraulic analysis. Finally, in Section 4, an H-SIT optimum operation strategy is suggested. 2. Analytical study to develop optimum operation strategy An SBO accident is initiated by a total loss of both offsite and onsite AC power. Following this accident, the reactor trips, the main feed water system terminates, and the charging pump stops. When the water level of the steam generator (SG) is lower than the post-trip SG level, PAFS starts to work. PAFS has enough capacity to cool the reactor core by itself in an accident situation, thus if PAFS works well, H-SIT operation is not needed. The use of HSIT is needed when PAFSs or the refill of the passive condensation cooling tank (PCCT) for long-term cooling fails. The PAFS system has many valves and if those valves fail to make a proper water path, PAFS will not be available immediately. Or external shock may cause troubles in PAFS piping or water tanks. The PAFS system has a big tank for its heat sink and can only operate for 8 h due to the limited inventory of this tank. For long-term operation, operators have to refill the tanks. If they fail to do that, PAFS operates for 8 h only. This situation is considered as PAFS refill failure in our analysis. Originally, H-SIT was constructed to prevent the progression of an accident into a severe accident, the probability of which increases dramatically if the core is uncovered. Thus, the purpose of the H-SIT is to protect against the uncovering of the core in order to ensure core safety. In this study, seal LOCA is no longer considered as a phenomenon in SBO because, in APR+, the standstill seal is applied to prevent seal LOCA (Darnowski et al., 2015). 2.1. Identification of main factors to develop H-SIT operation strategy To develop the operation strategy, in this section, the main factors are identified based on the H-SIT heat removal equation. As the main function of the H-SIT is to remove heat from the

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reactor core, the operation strategy has to be focused on effective heat removal. Hence, we have to express the heat removal process systematically by developing an H-SIT heat removal equation. The equation is expressed based on the following critical principles. First, to maintain core safety, the amount of heat removal from the core has to be larger than the amount of decay heat generation, as shown in Eq. (1).





d(t) dt ≤

ht (t) dt

(1)

where d(t) is the amount of decay heat generation in unit time, and ht (t) is the amount of heat removal in the core in unit time. The change of decay heat generation can be easily calculated given only the time (Lamarsh and Baratta, 2001). The amount of heat removal from the core also continuously changes over time; however the change in this amount is related with many other variables. Thus, Eq. (2) is derived to express the heat removal phenomena clearly. Based on Eq. (2), we know that three critical time variables exist to calculate the heat removal amount from the core. These are the coolant injection mass rate from H-SIT, temperature of H-SIT, and evaporation mass rate in the core. In this equation, thermal capacity of the reactor component structures is not considered because the temperature of all component structures inside the reactor will have already reached the almost saturated water temperature by the time H-SIT operation is needed. Thus potential impact of the thermal capacity of the reactor component structures is very small. ht (t) = mi (t) × Cp × (Tv − Tsit (t)) + me (t) × fg

(2)

where mi (t) is mass of injected water of H-SIT in unit time, me (t) is mass of evaporated water of H-SIT in unit time, Cp is specific heat of water, Tv is evaporating temperature, Tsit (t) is temperature of coolant which is injected from the H-SIT in unit time, and fg is vaporization energy. Based on Eqs. (1) and (2), four critical variables important to develop the operation strategy are identified: amount of decay heat, temperature of H-SIT, injection mass rate from H-SIT, and evaporation mass of the coolant. As these heat removal equations are functions of time, the relation of H-SIT cooling capacity to initiation timing becomes clear. The amount of decay heat generation is closely related with the condition of the PAFSs. If both PAFSs fail from the beginning, H-SIT must be initiated in an early stage for decay heat removal. Thus the decay heat generation rate when H-SIT starts to operate is high. Whereas, if PAFSs fail due to PCCT refill failure, the H-SIT initiation time is moved back because one or two PAFSs can cool down the core for a period of time. In that sense, the number of PAFSs operating before the PCCT refill failure is an important factor to develop the operation strategy. Generally, it is assumed that PAFS operate for only 8 h without PCCT refill (Cheon and Kim, 2010). The temperature of H-SIT coolant is also one of the critical variables; in Eq. (2), if Tsit increases, Tv − Tsit decreases thus mi (t) has to increase in order to satisfy Eq. (1). Tsit is related with the amount of hot water flow from the pressurizer and the amount of H-SIT inventory. Hot water flow from the pressurizer is considered as a constant and the inventory of the H-SIT can be calculated based on the injection flow rate. Therefore, in order to set the optimal H-SIT injection rate, H-SIT temperature should be considered. The injection mass flow rate of each individual H-SIT cannot be controlled as they are operated by gravitational force, and it is almost constant because of the fluidic device in the H-SITs (Chu et al., 2008). Hence the flow rate can be controlled by changing the number of H-SITs in operation or making an overlap between operations. The operation order can also affect the injection mass flow rate as each H-SIT is in a different location and therefore has

a different length of equalizing pipe. These differences in length have an effect on the pressure balance between the RCS and the H-SITs because when the pressure is equalized through the equalizing pipe, the pressure can drop due to friction. For a long equalizing pipe, a large pressure drop occurs leading to a decrease in H-SIT injection performance. This performance is closely related with injection flow rate. Evaporation mass is a decay heat-related variable and is also related to the injection mass flow rate. If the injection mass rate increases, evaporation mass rate decreases because of the specific heat of cold water from the H-SIT. Concerning core safety, if the evaporation mass is higher than the injection mass, the existing coolant of the core has to be used, eventually leading to core uncover. Therefore, the relationship between the injection mass rate and the evaporation rate should be considered carefully and systemically. As a result, based on these critical variables, the five main factors necessary to develop the operation strategy are defined. These are, namely, the number of PAFSs used simultaneously for 8 h, the number of H-SITs operating simultaneously, the overlap percentage between operations, the initiation timing, and the operation order. 2.2. Optimal value estimation through analytical study In the previous section, five main factors were identified. The optimum value of all factors should be analytically estimated to best develop the operation strategy. Generally, optimal values can be estimated more accurately by thermal-hydraulic code, as the computer code continually calculates the value of the variables every second, including subtle changes. An analytical approach, however, has an advantage to show a more logical tendency according to the amount of variable change, not focused on one specific value. Therefore, an analytical approach is preferentially performed in this section to get the basis of the global optimum points among all possible situations. In this section, before we estimate the optimal values, the five main factors should be divided into two groups based on their dependency on the decay heat generation rate, as the optimum values can vary according to any change in the initial accident condition. The decay heat generation rate at the time when the H-SITs start to operate is a representative indicator to show any change in the initial condition. Especially in SBO, the decay heat generation rate (as a time function) at H-SIT initiation time can only change through a change in the H-SIT initiation time. This initiation time can be altered by changing the number of PAFSs in operation before the H-SITs initiate. Thus this dependency on decay heat generation shows whether the optimum value of the factors change or not, when the number of PAFS in operation changes. Generally, initiation timing and operation order are independent factors of the number of PAFSs in simultaneous operation, so their optimal values can be estimated without any consideration of initial condition changes. These factors always have the same optimal value so are easily estimated. Whereas the optimal value of the injection mass rate can change according to the decay heat generation rate, so the optimal value of the number of H-SITs operating simultaneously and the overlap percentage between operations of each H-SIT can vary according to a change in the number of PAFS in operation. These factors are also correlated to each other and so are considered together to develop the operation strategy. Therefore, we need a specific estimation methodology to find the optimal value for these factors. 2.2.1. Optimal value of independent factors 2.2.1.1. H-SIT initiation timing. Initiation timing is related with the effective use of core coolant. When PCCT refill fails, RCS pressure

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Fig. 2. Liquid fraction of ejection steam through the POSRV according to H-SIT initiation timing.

and temperature increase because of the secondary heat sink loss, so the POSRV should be opened to decrease RCS temperature and pressure. In this process, saturated steam is ejected through the POSRV. This is the ideal situation for decay heat removal. When, however, the POSRV opens, the pressure of the RCS dramatically decreases, leading to core and pressurizer level increase, until finally, the pressurizer becomes full and ejects hot water directly rather than saturated steam. This decreases the efficiency of the HSITs as this hot water cannot be further used to remove decay heat by evaporation. In this situation, if the H-SITs initiate before the pressurizer reaches full level, the inventory of the core increases when the pressurizer becomes full. That means the pressurizer will be at full level for a relatively long time, so more high-temperature water will be ejected through the POSRV. This is the important reason why H-SIT coolant cannot be used effectively when they initiate early. Therefore, initiation timing should be delayed as long as possible. Fig. 2 presents the liquid fraction of the steam ejected through the POSRV according to H-SIT initiation timing, calculated using MARS code. In this graph, SG WR 25% means that the operator initiates the H-SIT when SG wide range level is 25%. If the liquid fraction is 100%, only hot water is released through the POSRV. In this study, the latest timing for operation of H-SIT is considered as the time when the upper plenum level is 0%, as this means the core level is above the fuel. If the fuel is uncovered, the temperature of the core increases extremely fast and can exceed the severe accident management guideline (SAMG) entry condition without any mitigation action by the operator, meaning the accident situation progresses into a severe accident. Thus core uncover is not considered in this study. As the author mentioned in Section 1, HSIT is initiated automatically thus any human error or risk caused by late operation of H-SIT (= small amount of available time for H-SIT operation) is not needed to consider. Therefore, theoretically, a 0% upper plenum level is the best point for H-SIT initiation timing. 2.2.1.2. Operation order. Differences in H-SIT efficiency according to operation order come from the differing lengths of the equalizing pipes. As previously mentioned, if the equalizing pipe is long, a large pressure drop occurs which decreases H-SIT injection performance. Generally, different amount of pressure drop according to different pipe length is caused by the friction with the additional pipe length. Moreover, if equalizing pipe is long, there are many bending points

on the pipe because equalizing pipe of H-SIT cannot be designed as a straight due to circle shape of containment and arrangement with other components. For those reasons, operation order affects to injection performance of H-SIT. To do this analysis, the H-SITs are distinguished according to the length of their equalizing pipes. If HSIT(1) has the longest equalizing pipe and H-SIT(4) has the shortest, their highest-to-lowest performance should be H-SIT(4) – H-SIT(3) – H-SIT(2) – H-SIT(1). When an accident occurs, the reactor trips and decay heat starts to decrease. Considering the decrease of the decay heat generation rate, the H-SIT with the best performance should be used first. Then H-SIT(4) – H-SIT(3) – H-SIT(2) – H-SIT(1) is the best order for effective use. If the H-SITs are used in reverse order, the injection rate should be increased in order to make up for the low cooling capacity of H-SIT(1). 2.2.2. Optimal value of dependent factors The number of H-SITs operating simultaneously and the overlap percentage between operations are the most difficult and complex variables to determine optimal values for on account of their dependencies and correlation. In order to understand the dependency of the injection mass rate (operation number and overlap percentage) on the decay heat generation rate, first we have to clarify the H-SIT heat removal phenomena as the injection mass rate is directly related to the amount of heat removal. The amount of heat removal by the H-SITs can be called H-SIT cooling capacity for convenience. The cooling capacity is calculated by using an integral calculus in Eq. (2), as shown in Eq. (3).



t2

Ht =

mi (t) × Cp × (Tv − Tsit (t)) + me (t) × fg dt

(3)

t0

where Ht is the total cooling capacity of core, t0 is the time when HSIT starts to operate, and t2 is the time when core exit temperature exceeds SAMG entry condition. Although Eq. (3) appears simple, calculating the cooling capacity is not easy because from H-SIT initiation, temperature (Tsit (t) and evaporation mass (me (t)) can change continuously and also, in an actual accident situation, the coolant injected by the H-SITs and the originally existing coolant in the core are used to cool down the core in no particular order. To solve these difficulties, we make some reasonable assumptions. In this study, H-SIT coolant is assumed to be used preferentially to make the calculation easier, so the purpose of H-SIT operation is to cool down the core without consumption of

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existing core coolant. Existing coolant is used after the four H-SITs are dried out. Thus, Eq. (3) can be rewritten as Eqs. (4)–(6) because if time exceeds t1 , mi (t) should be zero. Based on this assumption, the total amount of core inventory does not decrease until t1 . Eq. (6) is not considered in this study as it does not relate to H-SIT operation. Ht = H1 + H2



(4)

t1

H1 =

mi (t) × Cp × (Tv − Tsit (t)) + me (t) × fg dt

(5)

me (t) × fg dt

(6)

t0



t2

H2 = t1

where H1 is the total cooling capacity of H-SIT, H2 is the total cooling capacity of existing coolant in core, and t1 is the time when H-SIT is dried out. In this study, finally, the maximum H-SIT cooling capacity is used because this study focuses on the H-SIT operation with maximum performance. Thus, the maximum H-SIT cooling capacity is expressed as Eq. (7). For this equation, another assumption that is the H-SIT injection mass all evaporates perfectly is used. Based on the results of Section 2.2.1.1 this assumption is actually not true, but if we consider that the H-SITs operate when the upper plenum level is 0%, the amount of released coolant through the POSRV without evaporation is negligible. Therefore, term of evaporation is changed to term of injection rate from H-SIT.



t1

Hsit =

mi (t) × Cp × (Tv − Tsit (t)) + mi (t) × fg dt

(7)

t0

Fig. 4. Amount of maximum cooling capacity of one H-SIT according to H-SIT level.

where Hsit is the total maximum cooling capacity of H-SIT. Rate of temperature increase of H-SIT coolant can be calculated by considering the injection flow rate and hot steam flow from the pressurizer and this study calculates the rate of temperature increase of the H-SIT coolant using the point model analysis even though there would be temperature stratification in the H-SIT tank. Because consideration of temperature stratification is not needed for our analytical study, as our calculations are focused on the total heat removal amount, not the heat removal rate per second. If the temperature stratification model is used to calculate the cooling capacity, at the beginning, a large amount of coolant is injected with initial temperature (= low temperature) which removes relatively more decay heat compared to the last moment, when H-SIT coolant removes relatively less heat removal on account of heat concentration at the top of the coolant due to temperature stratification. In point of total heat removal amount, however, these two phenomena cancel out thus this will have zero net effect when compared with the point model. Therefore, point model is used for this calculation. Rate of temperature increase of H-SIT coolant is expressed as Eq. (8). In this study, it is assumed that RCS pressure is 160 bar because the POSRV operates at and maintains RCS pressure at this value. Of course, RCS pressure has small fluctuations around 160 bar because of different set points of POSRV opening and closing, but the enthalpy of the saturated steam at these different set points is not significantly different. Tsit =

Fig. 3. H-SIT coolant temperature according to H-SIT level.

mpzr × hpzr Cp × (m0 − mi0 )

(8)

Tsit is the rate of temperature increase of H-SIT coolant, mpzr is the injection flow rate of hot steam from the pressurizer, hpzr is the enthalpy of hot steam from the pressurizer, m0 is the initial mass of H-SIT, and mio = Injection mass flow rate of one H-SIT After arbitrarily setting the injection flow rate of one H-SIT and pressurizer injection flow rate, the change in temperature is calculated and presented in Fig. 3.

Using Eqs. (7) and (8), maximum cooling capacity can be calculated. This cooling capacity is shown as a curve in Fig. 4. Based on the equations, if the H-SIT injection flow rate increases, the capacity curve will move up, and if the flow rate decreases, the capacity curve will move down. If mass flow is high enough, decay heat can be removed using only one H-SIT because the total max cooling capacity of one HSIT during operation is higher than the total decay heat generation. Fig. 5 shows the max cooling capacity under high injection mass flow. 0 s is the initiation time of H-SIT operation and the black line at 2800 s represents the time when the H-SIT is dried out. For analysis, the decay heat generation rate is calculated by using MARS code in the condition with one PAFS operating for 8 h. If Area A ≥ Area B is satisfied, the core can be cooled down by using one H-SIT. If the injection flow rate is insufficient, the decay heat generation rate is larger than the max cooling capacity, thus we have to increase the number of H-SITs used or overlap their operation. Fig. 6 shows the max cooling capacity under low mass flow. In this figure, (decay heat generation rate) − (H-SIT maximum cooling capacity) is always negative. That means the existing coolant of the core should be used, resulting in core uncover. To identify the optimal injection flow rate for a real accident situation, the injection flow rate of each H-SIT and the injection flow from the pressurizer are preferentially calculated using MARS code. Based on the results, the injection flow rate of each H-SIT is 14 kg/s and pressurizer flow is 1.5 kg/s. Considering the results of the analytical study, when one PAFS is used for 8 h and only one HSIT is in operation, we have to increase injection flow by more than 19 kg/s. Fig. 7a shows the total amount of remaining cooling capacity according to injection mass flow. If two PAFSs are used for 8 h, injection mass flow over 18.4 kg/s is sufficient for accident mitigation. Fig. 7b shows the amount of total remaining cooling capacity according to mass flow when two PAFSs are used for 8 h. Based on

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Fig. 5. Maximum cooling capacity of one H-SIT with high flow rate under specific mass flow.

Fig. 6. Maximum cooling capacity of one H-SIT with low flow rate under specific mass flow.

Fig. 7. Total amount of remaining H-SIT cooling capacity according to injection mass flow.

these results, even if two PAFSs are used before H-SIT initiation, the injection mass flows sufficient for cooling from a single H-SIT in both cases is not much different as the decay heat generation rate in both cases is not much different.

If the remaining capacity (total max H-SIT capacity − total decay heat generation) is at or above zero, the core is safe in both cases because the injection mass is sufficient to remove decay heat. However, in view of efficiency, any remaining capacity larger than zero

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Fig. 8. Cooling capacity of all H-SITs under specific mass flow.

is not ideal, as this implies that H-SIT coolant is excessively injected in comparison with the minimum necessary amount to cool down the core. If excessive coolant is injected (mi − me is very high), hot water may be ejected in liquid state rather than hot steam when the POSRV opens. Further, the coolant can get stuck in other places such as a hot leg due to water slug formation (Kordyban and Ranov, 1970). Accordingly, the ideal flow rate will result in zero remaining cooling capacity. If the remaining capacity is negative, the injection mass is insufficient to remove the decay heat and must be increased. As explained previously, there are two ways to increase injection mass: increase the number of H-SITs operating from the beginning, or overlap H-SIT operation. If injection flow rate must be significantly increased, it is preferable to increase the number of H-SITs in operation. If only a slight increase is necessary, overlapping the H-SITs in operation is sufficient. When H-SIT start times are staggered, the overlap between two H-SITs results in similar cooling capacity as when they initiate simultaneously. As shown in Fig. 8, two H-SITs overlap during A1, A2, and A3. In these areas, there is positive remaining capacity, whereas there is a negative remaining capacity in B1, B2, B3, and B4. Thus, if the sum of A1, A2, A3 ≥ the sum of B1, B2, B3, B4, the core is safe until the H-SITs are dried out. Considering the maximum efficiency discussed previously, the sum of A1, A2, A3 = the sum of B1, B2, B3, B4 is used to calculate the optimal overlap percentage. Overlapping operation can increase the injection flow rate slightly. If, however, the overlap percentage reaches 66%, the injection flow rate is similar to when two H-SITs operate from the beginning without overlap. Thus if an overlap percentage of greater than 66% is required, increasing the number of H-SITs is recommended. This case can be called a dual overlap, with two H-SITs initiating simultaneously and overlapping with the remaining two H-SITs. 66% is obtained through the average flow rate calculation. If the injection flow rate of one H-SIT is m˛ , then the rate of two H-SITs is 2m˛ . Fig. 9 demonstrates these injection flow rates with an operation overlap of 50%. In Fig. 9, the average mass flow rate is 1.6m˛ from dividing total injection mass by total injection time. Based on Eq. (11), if the average injection flow rate is over 2m˛ , the overlap percent k has to be larger than 66%. Eq. (11) is derived as follows: mi =

g t

(9)

where mi is an averaged mass flow rate from H-SIT, g is water mass of one H-SIT, and t is the total Injection time until an H-SIT is dried out. Averaged mass flow rate =

Total water mass of four H-SITs Total injection time of four H-SITs (10)

Fig. 9. Average mass injection rate of H-SITs according to time.

Total water amount of four H-SITs is 4g and total injection time of four H-SITs is 4t if there is no overlap. When an overlapping operation is used, total injection time will decrease. Based on the figure below, overlap is performed during (k/100)t in three ranges thus total injection time can be expressed as 4t − (3k/100)t. Averaged mass flow rate =

4g = 4t − (3k/100)t



4 4 − 0.03k



× mi (11)

where k is an overlap percentage of H-SIT. In this study each H-SIT injection flow rate is assumed to be equivalent because of their same design characteristics. Based on Fig. 7a and b, the H-SITs should be overlapped even when the PAFSs have operated for 8 h. To calculate the optimal overlap percentage, an analytical study is carried out with novel methodology shown in Fig. 8 using the matlab program. Fig. 10a and b shows the total amount of remaining cooling capacity of the H-SITs according to the overlap percentage. Based on the results of the analytical study, at least a 34% overlap percentage is needed to prevent core uncover when one PAFS is used for 8 h. Thus, the H-SITs should be used by overlapping two by at least 34%. If both PAFSs are used for 8 h, the minimum overlap percentage is 31%. This is similar to the case with one PAFS in operation, as the decay heat generation rate of these two cases is not much different. When both PAFSs fail, if one H-SIT is used from the beginning, the H-SITs should be overlapped by more than 74%; thus we have to consider two H-SITs used from the beginning. In this case, the HSITs should overlap by 4.6% to maintain core safety. Fig. 11a and b shows the total amount of remaining cooling capacity of the H-SITs when both PAFSs fail.

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Fig. 10. Total amount of remaining H-SIT cooling capacity according to overlap percentage when one or two PAFSs are available.

Fig. 11. The total amount of remaining H-SIT cooling capacity according to overlap percentage when both PAFSs fail.

3. Optimal value estimation using computer code In this section, an analysis by thermal-hydraulic code is performed to get more accurate and realistic optimum values of the main factors and to verify the results estimated by the analytical study. The available time for the restoration of the components without entry into a severe accident condition is also estimated by MARS code simulation. This study assumes that the PAFSs have been operating for 8 h and the code calculation stops when the core exit temperature (CET) exceeds the SAMG entry condition at 650 ◦ C (Park and Hong, 2011), as the purpose of H-SIT operation is to prevent the progression of an accident into a severe accident. The analysis to determine the optimal overlap percentage is performed under three conditions depending on the number of PAFS in operation, as the optimal overlap percentage can change according to the amount of decay heat generation. 3.1. Identification of initiation timing First, an analysis by code is performed to find the optimal initiation timing of the H-SITs. Based on various initiation timings, the analysis determines the time when the CET exceeds the SAMG entry condition (the limitation for the analysis) or in other words, the available time for the restoration of the long-term cooling components. Then optimal initiation timing is selected by comparing the amounts of time. For this analysis, operation order is assumed to be 4-3-2-1, overlap percentage is 0% and core uncover is not considered. Results are presented in Table 1.

Table 1 Time when CET exceeds SAMG entry condition according to H-SIT initiation timings. Initiation timing

Time when CET exceeds SAMG entry condition (Available time for restoration)

When PAFS stop When SG level is WR25% When POSRV open Upper plenum level is 50% Upper plenum level is 0%

41,212 s 41,016 s 52,251 s 52,540 52,895 s

Based on the results of analysis, initiation timing at 0% upper plenum level provides the longest available restoration time. This initiation timing is the same as the result of the theoretical study in Section 2.2.1.1. One critical problem is found when the initial H-SIT operates before the POSRV opens, related with Tsit . As previously discussed, when the pressurizer is at full level for a relatively long time a large amount of hot water from the pressurizer transports to the H-SIT. This maintains or increases the H-SIT water level, even as the H-SIT continues to inject water into the RCS. This phenomenon is shown in Fig. 12. As a result, the core temperature increases even though water is continuously injected by the H-SIT, as the cooling capacity dramatically decreases due to the hot water injection from the pressurizer. Fig. 13 shows the core temperature when the H-SIT operates before POSRV opening. All things considered, it should operate when the upper plenum level of the core is 0%.

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Fig. 12. Change of H-SIT level when H-SIT is operated before POSRV opens.

Fig. 13. Change of core exit temperature when H-SIT is operated before POSRV opens.

3.2. Identification of operation order Second, an analysis is performed using code to find the optimal H-SIT operation order. This analysis shows CET stability according to various operation orders, presented in Fig. 14 in four cases. As in Section 2.2.1.2, the H-SITs are numbered according to the length of the equalizing pipes, with H-SIT(1) having the longest pipe. Based on Fig. 14, if the H-SITs operate with a 4-3-2-1 order, the CET is the most stable when compared to all other cases. These results match the theoretical analysis in Section 2.2.1.2, where it was explained that the most effective use of H-SIT coolant comes from the H-SIT with the highest cooling capacity initiating first, which is H-SIT(4). Therefore, the 4-3-2-1 operation order should be used in the H-SIT operation strategy. 3.3. Identification of overlap percentage MARS code is used in this section to determine more accurate optimal overlap percentages and also to verify the results of the previous analytical study. In this code calculation, optimal overlap percentages gathered from the analytical study are used, and operation order is set to be 4-3-2-1 with initiation timing of 0%. Fig. 15a and b shows the CET with specific overlap percentages. When one PAFS is available for 8 h before H-SIT operation, 34% overlap leads to unstable CET. In this case the injection flow rate is not sufficient, as core uncover is not allowed during H-SIT operation to prevent the progression of an accident into a severe accident. Thus the overlap percentage should be increased. At 40% overlap,

the CET is very stable, with the longest restoration time of 49,470 s before the CET exceeds the SAMG entry condition. When two PAFSs operate for 8 h before the H-SIT initiates, overlap percentages of 31% and 35% result in CET instability, so should be increased to 40% to prevent core uncover. This result is quite different from the result of the analytical study because, in this case, coolant loss through the POSRV is relatively larger than the other cases. In the analytical study, coolant loss is assumed to be zero to make the calculations possible. Hence, 40% is again the optimum overlap percentage. If this optimum strategy is applied, the time when the CET exceeds the SAMG entry condition is 52,980 s. Fig. 16a–c shows the CET with specific overlap percentages when two PAFSs operate for 8 h before the H-SIT initiates. When both PAFSs fail before H-SIT initiation, if the H-SITs are used with 0% overlap, the CET is very unstable and exceeds the SAMG entry condition. If overlap percent is set to 4.6%, the CET is very stable, with a restoration time of 11,220 s before SAMG entry condition. Fig. 17a and b shows the CET when two H-SITs overlap with the remaining H-SITs by specific percentages.

4. The optimum operation strategy of H-SIT in SBO In SBO, H-SIT initiating conditions can be divided into three cases according to the number of PAFS in operation before the HSITs initiate, as the number of PAFS is the only way to change the H-SIT initiating conditions. The number of PAFS in operation affects H-SIT initiation time as it is closely related with the decay heat generation rate. As follows, in this study, an operation strategy is developed for these three cases. In each case, there are five main factors with infinite possible values thus the optimal value should be estimated among all possibilities. An operation strategy integrating all main factors and their optimal values is called the optimum operation strategy for each case. Finally the strategies of all three cases are merged into one optimum operation strategy for H-SIT in SBO, presented in Fig. 18. Based on the results of analysis, the optimum operation strategy of H-SIT is developed as follows. In SBO, it should initiate at an upper plenum level of 0% and operate in a 4-3-2-1 order in all three cases. An optimum overlap percentage of 40% was found in both cases with one or both PAFSs in operation prior to H-SIT initiation. With both PAFSs failure, dual H-SIT overlap is necessary with a 4.6% overlap percentage to properly cool down the core. With this optimum operation strategy, if both PAFSs are available for 8 h, up to 52,980 s of available time for safety component restoration without entry into the severe accident condition can be secured. If

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Fig. 14. Change of core exit temperature according to different operation orders.

Fig. 15. CET with H-SIT overlap and one PAFS operating for 8 h.

Fig. 16. CET with H-SIT overlap and two PAFSs operating for 8 h.

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Fig. 17. CET with dual H-SIT overlap and failure of both PAFSs.

Fig. 18. Diagram for the process of operation strategy development for H-SIT in SBO.

one PAFS is available, up to 49,470 s can be secured, and 11,220 s with no PAFS available. 5. Conclusion An optimum operation strategy for an H-SIT system in SBO was developed in this paper. In order to develop this operation strategy, five main factors were identified: the number of PAFSs in simultaneous operation before PCCT refill failure, the number of H-SITs in simultaneous operation, and the overlap percentage, initiation timing, and operation order of the H-SITs. Based on these main factors, optimum values were identified by analytical and theoretical studies. Results demonstrated that the H-SITs should initiate when the upper plenum level is 0%, and should operate in a 4-3-2-1 order. In case of the overlap percentage, it varies according to the number of PAFSs in operation for 8 h. With both PAFSs in operation before H-SIT initiation, the optimum overlap percent was found to be 31%, with a value of 34% for one PAFS in operation before H-SIT initiation. The results of these two cases are not much different as the decay heat generation rate in both cases is similar. When both PAFSs fail to operate, the result of the analytical study demonstrated the HSITs should overlap by 74%, as the decay heat generation rate during H-SIT operation was very high compared to the other cases. In this

case, with dual overlap of the H-SITs in simultaneous operation, a 4.6% overlap is sufficient to mitigate the accident. An analysis using MARS code was also performed to get accurate and realistic optimum values and to verify the results of the analytical study. Results also showed that the H-SITs should initiate at an upper plenum level of 0% and operate in a 4-3-2-1 order. An optimum overlap percentage of 40% was found in both cases with one or both PAFSs in operation prior to H-SIT initiation. With PAFSs failure, 4.6% was found to be the optimum overlap percentage. These represent the optimum operation strategy for an H-SIT system. Concerning the overlap percentages, the results from the MARS code are slightly different from the results of the analytical study on account of the many assumptions in the latter. However, the results of the analytical study are useful to specify the points for analysis using MARS code; the analytical study results have an important role in respect to giving a logical background to find the global optimum values of all possibilities of overlap percentages in this study. The results of the MARS code also showed the available time for safety component restoration without entry into the severe accident condition. If both PAFSs are available for 8 h, up to 52,980 s of available time can be secured. Up to 49,470 s can be secured with one PAFS available, and 11,220 s with no PAFS available.

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