Study on the Influence of Ambient Temperature and RPV Temperature on Operation Performance of HTR-PM Reactor Cavity Cooling System ^†

Abstract

The High Temperature Gas-cooled Reactor (HTGR) is a Generation IV advanced nuclear reactor, which can realize inherent safety and prevent core melt. The Institute of Nuclear and New Energy Technology (INET) of Tsinghua University developed a commercial-scale 200 MWe High Temperature gas-cooled Reactor Pebble bed Module project (HTR-PM), which entered commercial operation on 6 December 2023. A passive Reactor Cavity Cooling System (RCCS) was designed for HTR-PM to export heat from the reactor cavity during normal operation and also in accident conditions, keeping the safety of the reactor pressure vessel (RPV) and reactor cavity. The RCCS of HTR-PM has been designed as three independent sets; the normal operation of two sets of RCCS can guarantee the safety of the PRV and reactor activity. The heat can be transferred from the RPV to the final heat sink atmosphere through thermal radiation and natural convection in the reactor cavity, and the natural circulation of water and air in the RCCS. The CAVCO code was developed by the INET to simulate the behavior of an RCCS. In this paper, assuming different RPV temperatures and different ambient temperatures, as well as assuming all or parts of the RCCS sets work, the performances of RCCS are studied by CAVCO to evaluate its operational reliability, so as to provide a reference for further optimization. The analysis results indicate that even under hypothetically extremely RPV temperatures, two sets of RCCS could effectively remove heat without causing water boiling or system failure. However, during the winter when ambient temperatures are low, particularly when the reactor operates at a lower RPV temperature, additional attention must be given to the operational safety of the system. It is crucial to prevent system failure caused by the freezing of circulating water and the potential cracking of water-cooling pipes due to freezing. Depending on the reactor status and ambient conditions, one or all three sets of RCCS may need to be taken offline. In addition, the maximum heat removal capacity of the RCCS with only two sets operational exceeds the design requirement of 1.2 MW. When the ambient temperature fluctuates significantly, it may be advisable to increase the number of available RCCS sets to mitigate the effect of abrupt changes in cooling water temperature on pipeline thermal stress.

1. Introduction

High Temperature Gas-cooled Reactors (HTGRs) are internationally listed as one of the reactor types that meet the technical requirements of the Generation IV advanced nuclear reactor, which have excellent inherent safety [1,2,3]. The HTGR uses helium gas with good chemical stability as a coolant and graphite with a large heat capacity as a moderator. In addition, the HTGR can achieve excellent high-temperature resistance by utilizing encapsulated particulate fuel elements; the reactor can naturally export residual heat without any external energy supply, thereby eliminating the possibility of a core melting accident. Even if an accident were to happen, it can effectively contain radioactive products and control the radiation level at a lower level [4].

The High Temperature Gas-cooled Reactor Pebble bed Module (HTR-PM) is the world’s first modular HTGR nuclear power plant (NPP) with inherent safety characteristics and significant commercial potential among the Generation IV advanced nuclear reactors. It was designed by the Institute of Nuclear and New Energy Technology (INET), Tsinghua University, and constructed in Shidao Bay, Rongcheng city, Shandong province, China. In HTR-PM, a Reactor Cavity Cooling System (RCCS) is designed to remove residual heat from the reactor core during both normal operation and accident conditions, thereby ensuring the safety of the reactor.

The design of an RCCS varies significantly across different types of HTGRs. In the United States’ Modular High Temperature Gas-cooled Reactor (MHTGR), the RCCS consists of cooling panels surrounding the Reactor Pressure Vessel (RPV) [5]. These panels, together with concentric hot/cold ductwork and inlet/outlet steel plenums, form a completely passive air-cooling system that is based on natural convection, with air circulating between the panels and the external environment. In Japan’s High Temperature Engineering Test Reactor (HTTR), the Vessel Cooling System (VCS) is composed of Cooling Water Panels (CWP) surrounding the RPV, which are installed on the inner surface of the concrete containment wall. Heat is transferred to the water-cooling loop primarily by thermal radiation and natural convection, and then ultimately dissipated to an external heat exchanger. The residual heat is transferred from the CWP to the cooling tower by a pump-driven water loop [6,7,8]. In South Africa’s Pebble Bed Modular Reactor (PBMR), the RCCS is a totally passive safety system based on a “water-steam” concept. The system relies mainly on natural circulation without active mechanical drives to remove heat [9,10].

In the HTR-PM, the RCCS operates based on the natural circulation of water and air to remove heat, without the need for an external energy input. Figure 1 shows the main components of the RCCS [11], which consists of three independent sets. The Water-Cooling Panel (WCP) is arranged on the inner layer of the reactor cavity with vertical WCPs welded on it. The heat can be transferred from the RPV to the WCP by radiation and natural convection. The heated water in the water-cooling pipes then flows upwards to the air cooler in the air-cooling tower and finally transfers the heat to the environment via natural air circulation. The design capability of the RCCS for each reactor module is 1.2 MW with a 3 × 50% redundancy design, which means that two sets working normally can meet the design requirements and effectively remove the heat [12].

In the simulations of the RCCS for the HTR-PM and the 10 MW High Temperature Gas-cooled Test Reactor (HTR-10), Zhang et al. derived a formula for calculating the view factors of two-dimensional radiative heat transfer within the cavity and established a mathematical model for calculating the radiative heat flux [13]. Wang et al. developed the TINTE-RHRS code by integrating an HTGR system analysis program with an RCCS model [14]. This software enables thermodynamic coupling between the reactor core and the RCCS, employing an overlapping domain decomposition coupling method to analyze the operational characteristics of the RCCS in the HTR-PM. Qin et al. established a two-dimensional model of the HTR-PM cavity using the CFD software Fluent to simulate both radiative and convective heat transfer within the cavity, thereby obtaining the temperature distribution of the concrete structures [11]. In addition, Qin et al. used the CFD software CFX to analyze the heat transfer behavior inside the air-cooling tower of the HTR-PM by solving the Reynolds-Averaged Navier–Stokes (RANS) equations combined with a turbulence model [15]. Zhao et al. developed a program in the C language to evaluate the transient characteristics of the RCCS for the HTR-10. The program analyzed the flow and heat transfer in the water circulation loop and the air-cooling tower, and its results were compared with experimental data [16]. Zhao et al. also developed a multi-scale CFD-system coupled code to simulate the transient behavior of the MHTGR’s RCCS during startup, demonstrating good agreement with experimental results [17].

In this paper, the operational characteristics of the RCCS are analyzed by the CAVCO code, which was developed by the INET, Tsinghua University, specifically for evaluating the performance of the HTGR’s RCCS [18,19,20]. The effects of RPV temperature and ambient temperature on the performance of the RCCS with varying numbers of sets available are analyzed. Particular attention is given to the potential failure model of the RCCS, for example, heat transfer deterioration due to boiling in a hot summer or at a high RPV temperature, and pipe rupture caused by freezing in a cold winter or at a low RPV temperature. These analyses aim to enhance the understanding and support the optimization of the system. The work presented in this paper proves that the RCCS can effectively remove residual heat to ensure reactor safety and provides insight for the safe operation of the RCCS.

2. Code and Model

The CAVCO code was developed by the INET to simulate the thermal–hydraulic behavior of the RCCS, which utilizes natural water circulation and natural air circulation to transfer heat, with the outer wall temperature of the RPV as a boundary condition. Furthermore, this code has also been coupled with the TINTE code, a system code developed by the Jülich Research Center, Germany, for the thermal–hydraulic and transient analysis of a pebble-bed HTGR, to analyze the impact of RCCS behavior on the reactor core and RPV. Figure 2a illustrates the calculation nodes of the RCCS in the CAVCO code: A-nodes represent the annular reactor cavity formed by the cylindrical RPV wall, the WCP, and the upper and lower insulation walls; A1–A15 and A43–A45 denote the outer insulation walls of the annular cavity, A16–A42 correspond to the WCP, A46–A90 represent the inner wall of the annular cavity (i.e., the outer surface of the RPV), and A91 and A92 refer to the bottom and top surfaces of the cavity (insulation wall). C-nodes represent the water circulation components, while B-nodes and D-nodes denote the walls of the water-cooling pipes and the air cooler pipes, respectively. C1–C27 represent the water inside the water-cooling pipes, C29–C46 represent the water inside the air cooler pipes, and C28 and C47 correspond to the rising and falling sections of the water flow, respectively. E-nodes represent the air-cooling tower section, where E19 is insulated, and the remaining nodes correspond to air nodes. In the calculation process, the temperature of A46–A90 (outer wall of RPV) and E20 (ambient temperature) are provided as boundary conditions.

During the calculation process, the temperature distribution along the outer wall of the RPV is defined as the heat source, while the ambient temperature serves as the cold source. The natural convection within the cavity between the RPV and the WCP is calculated using an empirical formula (Equation (1)), which is derived based on CFD simulation results. And radiative heat transfer is modeled based on radiation exchange among micro-elements within the annular cavity [21] (between the RPV and the WCP), excluding the pipe sections (Equations (2) and (3) [22]). Therefore, the number of operational RCCS sets does not influence the radiative view factor calculations of the heat transfer surfaces (Figure 2b). The meaning of each variable in the equation is provided in Table 3. In the real cavity, there is a narrow gas-filled gap between the WCP and the concrete wall on the outer side of the annular cylinder. In the simulation, this heat transfer through the gap is neglected because its contribution to the overall process is negligible. Once the panel absorbs the heat, it conducts the heat to the water-cooling pipes. It is assumed that the pipe temperature equals the temperature at its contact point with the steel panel. The approximate temperature distribution of the WCP is shown in Figure 3. The color distribution in the figure decreases gradually from red to orange to blue. The relationship between the temperature of the steel panel and that of the water-cooling pipes is shown in Equation (4), which is derived based on the thermal conductivity equation. In this equation, h_eff represents the equivalent heat transfer coefficient, $\overline{{\mathrm{T}}_{\mathrm{panel}}}$ represents the average temperature of the steel panel, and T_pipe represents the temperature of the water-cooling pipes.

Table 1. Effective thermal conductivity under different sets of operational RCCS. Reprinted from Ref. [1].

Set of RCCS	Sketch	h (W/(m2·K))
1		3λpδ/b2
2		3λpδ/(b12 − b1b2 + b22)
3		3λpδ/b2

shows the expressions for effective thermal conductivity under different operational configurations of the RCCS. In the expressions, δ refers to the thickness of the panel, and λ denotes the thermal conductivity of the panel material.

Q_c = −0.9799A_RPV∆t_c^1.3787R_c^0.7171e^{0.3896X + 0.0004∆T} × H_c(H_c + 0.3502)(H_c − 1.3714)

(1)

$${\mathrm{J}}_{\mathrm{k}}-\left(1 -{ \mathsf{\epsilon }}_{\mathrm{k}}\right){{\displaystyle \sum }}_{\mathrm{i}=1}^{\mathrm{N}}{\mathrm{J}}_{\mathrm{i}}{\mathrm{X}}_{\mathrm{k}-\mathrm{i}}{=\mathsf{\epsilon }}_{\mathrm{k}}{\mathsf{\sigma }\mathrm{T}}_{\mathrm{k}}^4$$

(2)

$${\mathrm{Q}}_{\mathrm{r},\mathrm{k}}={\displaystyle \frac{{\mathrm{A}}_{\mathrm{k}}{\mathsf{\epsilon }}_{\mathrm{k}}}{1-{\mathsf{\epsilon }}_{\mathrm{k}}}}\left({\mathsf{\sigma }\mathrm{T}}_{\mathrm{k}}^4-{ \mathrm{J}}_{\mathrm{k}}\right)$$

(3)

$$\mathrm{q}={\mathrm{h}}_{\mathrm{eff}}(\overline{{\mathrm{T}}_{\mathrm{panel}}}-{\mathrm{T}}_{\mathrm{pipe}})$$

(4)

The code employs a one-dimensional model to calculate the water and air circulation loop. The following assumptions are considered during the calculation process: due to the small temperature difference between the inlet and outlet water, the flow velocity is considered constant; therefore, the momentum equation of the fluid at each computational node is omitted under the assumption of constant velocity. Furthermore, the diffusion of heat along the temperature gradient is neglected when solving the fluid energy equation, given the relatively mild variation in water temperature along the flow direction. The governing equations for the loop calculation are shown in Equations (5) and (6):

$$\sum \mathsf{\rho }\mathrm{g}\mathsf{\Delta }\mathrm{H} = \sum {\displaystyle \frac{\mathsf{\lambda }\mathrm{l}}{\mathrm{d}}}{\displaystyle \frac{{\mathsf{\rho }\mathrm{u}}^2}{2}} + \sum {\displaystyle \frac{{\mathsf{\xi }\mathsf{\rho }\mathrm{u}}^2}{2}}$$

(5)

$${\mathsf{\rho }\mathrm{c}}_{\mathrm{p}}\mathrm{u}\partial \mathrm{T}/\partial {\mathrm{x}=\mathrm{q}}_{\mathrm{x}}{/\mathrm{A}}_{\mathrm{c}}$$

(6)

In the simulation, the variations in the heat transfer area are used to reflect the impact of different numbers of operating RCCS sets. The periodic temperature distribution of the water-cooling panel and the water-cooling pipes in the circumferential direction, and also the resulting non-uniform temperature distribution in the circumferential direction of the RPV, are not considered.

3. Results and Discussion

3.1. Calculation Condition

This study primarily evaluates the influence of RPV temperature, ambient temperature, and the number of operating RCCS sets on the system’s heat-carrying capacity and cooling water temperature. Additionally, potential failure modes of the system are analyzed, for example, heat transfer deterioration or pipe rupture caused by boiling or freezing of the water.

Table 2. Calculation conditions.

Case		RPV Temperature (K)	Ambient Temperature (K)	Set of RCCS
1		373.15	258.15/263.15/268.15/ 273.15/278.15/283.15/ 288.15/293.15/298.15/ 303.15/308.15	1/2/3
2		473.15
3		523.15
4		573.15
5		673.15
6	6-1	−100cos(2π × h/23.446) + 473.15	293.15
	6-2	−75cos(2π × h/23.446) + 473.15
	6-3	−50cos(2π × h/23.446) + 473.15
	6-4	−25cos(2π × h/23.446) + 473.15
	6-5	473.15

summarizes the operating conditions studied in this paper, and

Table 3. Variables.

Variable	Unit	Physical Significance
Ac	m2	Cross-sectional area of the pipe
ARPV	m2	Area of RPV
Ak	m2	Area of surface k
bp	kW	Intercept of the line
$c_p$	J/(kg∙K)	Specific heat capacity
d	m	Diameter of the pipe
g	m/s2	Gravitational acceleration
Hc		WCP height to annular cavity height ratio
heff	W/(m2∙K)	Equivalent heat transfer coefficient
Jk	W/m2	Net radiative heat transfer of surface k
kp	kW/K	Slope of the line
l	m	Length of the pipe
n		Operational sets of the RCCS
P	kW	Heat-carrying capacity
Qc	W	Natural convection heat power on the outer wall of the annular cavity
Qr,k	W	Net radiative heat transfer of surface k
qx	W/m	Linear heat rate
Rc		Ratio of inner and outer wall radius in the annular cavity
Ta	K	Ambient temperature
TRPV	K	RPV temperature
TWCP	K	WCP temperature
Tfreezing	K	Ambient temperature corresponding to the water zero point
Tboiling	K	Ambient temperature corresponding to the water boiling point
Tpipe	K	Temperature of the pipe wall
$\overline{{\mathrm{T}}_{\mathrm{panel}}}$	K	Average temperature of the steel panel
∆Tc	K	The difference between the highest and lowest temperatures on the RPV wall
∆tc	K	The average temperature difference between the inner and outer walls of the annular cavity
u	m/s	Velocity of the fluid
Xk-i		View factor from surface k to surface i
εk		Emissivity of surface k
σ	W/(m2·K4)	Stefan–Boltzmann constant
$\mathsf{\rho }$	kg/m3	Density
$\mathsf{\lambda }$		Friction factor
$\mathsf{\xi }$		Local loss coefficient
δ	m	Thickness of the panel
λp	W/(m·K)	Thermal conductivity of the panel

lists the main variables. For cases 1 through 5, the RPV temperature is assumed to be uniform along its height. In case 6, the RPV temperature follows a cosine distribution along the height direction, while the ambient temperature remains constant. The working pressure of the cooling water inside the water-cooling pipes is set at 0.3 MPa, corresponding to a saturation temperature of 131.4 °C. It is conservatively considered that the RCCS would fail completely, and the computation would terminate, once the outlet water temperature (node C28 in Figure 2a) reaches 130 °C.

3.2. Calculation Results

3.2.1. Heat-Carrying Capacity

Figure 4 illustrates the calculated heat-carrying capacity for cases 1 to 5. Figure 4a–c, respectively, correspond to different numbers of operating RCCS sets, with different colors representing different RPV temperatures. Some temperatures in the figure have no corresponding data points; this indicates system failure (cooling-water freezing or boiling) under the respective operating conditions.

It can be observed that the total heat-carrying capacity of the system is positively correlated with the RPV temperature and the number of operating RCCS sets, and negatively correlated with the ambient temperature. Moreover, the heat-carrying capacity of each individual set is positively correlated with the RPV temperature, but negatively correlated with both the ambient temperature and the number of operating RCCS sets. A large temperature difference between the heat source (RPV) and the cold source (ambient environment) enables the system to dissipate more heat. Therefore, the higher RPV temperatures and lower ambient temperatures result in greater total heat-carrying capacity, as well as increased average heat-carrying capacity per set. Although increasing the number of operating RCCS sets enhances the overall heat-carrying capacity of the system, it leads to a reduction in the average heat-carrying capacity of each set.

Furthermore, under identical RPV temperatures and numbers of operating RCCS sets, the relationship between heat-carrying capacity and ambient temperature is nearly linear (as shown by Equation (3)), indicating minimal sensitivity to ambient temperature variations. This indicates that the system’s heat-carrying capacity is predominantly influenced by the RPV temperature. This behavior can be attributed to the dominant heat transfer mechanism between the RPV and the WCP, which is thermal radiation. Since radiative heat transfer is proportional to the fourth power of absolute temperature, the heat transfer rate is mainly governed by the temperature of the hotter region (RPV).

Figure 5 shows the proportion of convection heat transfer within the cavity under different conditions. The thermal radiation dominates the heat transfer mechanism inside the reactor cavity, with convection contributing less than 20%. As the ambient temperature increases or the RPV temperature increases, the proportion of convective heat transfer decreases. This is because the variation in radiative heat transfer with temperature is significantly greater than that of convective heat transfer. Consequently, an increase in the RPV temperature leads to a higher share of radiative heat transfer and a corresponding decrease in convective heat transfer. Additionally, the more RCCS sets in operation, the higher the proportion of convective heat transfer. Under the same RPV temperature conditions, the temperature of the water-cooled pipes decreases. This results in an enhanced natural convection within the cavity, thereby increasing the proportion of convective heat transfer in the overall heat removal.

Equation (8) and Figure 6 further illustrate the influence of the ambient temperature variations on heat-carrying capacity. The ratio b_p/k_p serves as an indicator of this sensitivity; the smaller the value of b_p/k_p, the less pronounced the impact of ambient temperature variations on heat-carrying capacity. Figure 6 shows that b_p/k_p decreases with increasing RPV temperatures and numbers of operating RCCS sets. This negative correlation is because a higher RPV temperature enlarges the temperature difference between the RPV and the ambient temperature, thereby reducing the relative effect of ambient temperature changes on radiative heat transfer. At a constant RPV temperature, a larger number of operating RCCS sets corresponds to a larger heat exchange area, which enhances the heat-carrying capacity and improves the system’s adaptability to ambient temperature variations. Consequently, with more sets working normally, the ambient temperature variations have less effect on the heat-carrying capacity.

P = P(T_a, T_RPV, n) = k_pT_a + b_p

(7)

P(T_a + ∆T_a, T_RPV, n)/P(T_a, T_RPV, n) = (kP(T_a + ∆T_a) + b_p)/(k_pT_a + b_p)
= 1 + ∆T_a/(b_p/k_p + ∆T_a)

(8)

3.2.2. Cooling Water Temperature

Figure 7, Figure 8 and Figure 9 illustrate how the inlet and outlet temperatures of the cooling water vary under different ambient temperatures, numbers of operating RCCS sets, and RPV temperatures. It is observed that the inlet and outlet water temperatures exhibit a positive correlation with both ambient and RPV temperatures. When either the RPV or ambient temperature increases, the cooling water temperature also rises, and vice versa. In addition, inlet and outlet water temperatures show a negative correlation with the number of operating RCCS sets.

The temperature difference between the inlet and outlet of the cooling water is negatively correlated with both the ambient temperature and the number of operating RCCS sets, while it is positively correlated with the RPV temperature. It can be inferred that the temperature difference increases with the increase in heat-carrying capacity per set.

3.2.3. RPV Temperature Distribution

Figure 10 shows the RPV temperature under different operating conditions. The temperature distributions during normal operation and under Depressurized Loss of Forced Coolant (DLOFC) accident at 540,000 s were calculated by the DAYU3D code. The DAYU3D is a system analysis code independently developed by the INET for the HTGR [23,24,25]. It has been validated against the TINTE code [26], confirming its reliability and accuracy. DLOFC is a typical accident of the HTGR, which may result in the maximal fuel and RPV temperature [27,28]. The RPV temperature distribution under DLOFC conditions follows an approximate cosine pattern, consistent with case 6-1. During normal operation, the RPV temperature distribution remains relatively uniform along the vertical axis, with the value close to 200 °C. The RPV temperature’s axial cosine distribution is based on a fit to the DAYU3D’s computational result. This study investigates the influence of the RPV temperature distribution on the system’s heat-carrying capacity. A cosine-shaped temperature distribution is assumed, with varying amplitudes but a constant average temperature.

Figure 11 shows the total heat-carrying capacity, radiative heat transfer capacity, and convection heat transfer capacity of the system under the different RPV temperature distributions and numbers of operating RCCS sets. The greater the RPV temperature variation, the higher the system’s overall heat-carrying capacity. Since thermal radiation is the dominant heat transfer mechanism within the reactor cavity, the trend of total heat-carrying capacity closely mirrors that of radiative heat transfer. The thermal radiation capacity of a surface is proportional to the fourth power of its absolute temperature. Under the identical temperature variations in a certain surface, the increase in thermal radiation caused by a temperature rise is higher than the decrease caused by an equivalent temperature drop (Equation (9)). Consequently, at a constant average RPV temperature, a greater temperature difference among the RPV surfaces results in a higher overall thermal radiation capacity of the RPV surface, thereby enhancing the heat-carrying capacity of the system.

εσ[(T + ∆T)⁴ − T⁴] − εσ[T⁴ − (T − ∆T)⁴] = εσ(12T²∆T² + 2∆T⁴) > 0

(9)

3.2.4. Temperature Limit

Figure 12 shows the ambient temperature limits of the system under the different numbers of operational RCCS sets and RPV temperatures, with

Table 4. Equation between limit temperature and RPV temperature.

Set of RCCS	Equation
1	Tfreezing = 0.000114TRPV2 − 0.354TRPV + 379.903	Tboiling = 0.000416TRPV2 − 0.0199RPV + 444.231
2	Tfreezing = −0.000352TRPV2 − 0.187TRPV + 247.845	Tboiling = 0.000370TRPV2 − 0.0889TRPV + 415.496
3	Tfreezing = −0.000343TRPV2 + 0.228TRPV + 231.553	Tboiling = 0.000335TRPV2 − 0.112TRPV + 403.750

providing the fitting formula for these curves. The results indicate that, at a fixed RPV temperature, increasing the number of operating RCCS sets leads to a higher ambient temperature limit. This observation is consistent with the conclusion that the more operating RCCS sets result in a lower average cooling water temperature, which reduces the likelihood of reaching the boiling point and increases the risk of freezing at the same ambient temperature. In addition, it was found that higher RPV temperatures correspond to lower ambient temperature limits for the same number of operating sets. This is because, as the RPV temperature increases, the average cooling water temperature also increases, decreasing the likelihood of freezing and increasing the likelihood of boiling, which ultimately lowers the ambient temperature limit.

The heat-carrying capacity is also influenced by the temperature distribution of the RPV. Greater temperature non-uniformity enhances the total heat released from the reactor cavity. Using the average RPV temperature for calculations may underestimate the actual heat-carrying capacity, potentially leading to an overestimation of the ambient temperature at which system failure occurs. Therefore, for estimating the ambient temperature associated with boiling failure, the maximum PRV temperature should be used; conversely, for icing failure estimation, the average RPV temperature is recommended. This approach ensures a conservative estimation of the ambient temperature limit range.

4. Discussion

In the HTR-PM, the RCCS is designed such that two sets working normally can guarantee the heat-carrying capacity of 1.2 MW, keeping the RPV and cavity safe under accident conditions. The working pressure of the cooling water in the water-cooled pipes is 0.3 MPa.

The calculation results introduced in Section 3 show the influence of ambient temperature, RPV temperature, and the number of operational RCCS sets on the system’s operational characteristics and safety performance. These findings provide valuable insights for future design improvement, as well as optimization of operation and maintenance strategies. In this section, potential failure modes due to boiling or freezing of the water are further analyzed, along with possible mitigation measures. Additionally, the heat-carrying capacity of the HTR-PM RCCS is also discussed.

4.1. High Temperature Failure Analysis

The temperature of the RCCS cooling water rises with increasing ambient temperature and RPV temperature, and also increases when fewer RCCS sets are in operation. According to the HTR-PM design, the RPV temperature limits for normal operation and design basis accident (DBA) are set at 350 °C and 425 °C, respectively. The analyses indicate that in all DBAs and most beyond design basis accidents (BDBAs), the RPV temperature did not exceed 400 °C. Calculation results show that if two or three RCCS sets can work normally and the ambient temperature is below 40 °C, the outlet water temperature would not reach the boiling point at 0.3 MPa, which means the RCCS would not fail due to the heat transfer deterioration. Thus, the HTR-PM satisfied the design requirement of 3 × 50% redundancy during operation.

Based on the working principle of the RCCS, as well as the above analysis, it is crucial to prevent cooling water from boiling and subsequent heat transfer deterioration during hot summer conditions. Therefore, the continuous monitoring of RPV temperature, RCCS operating pressure, ambient temperature, and outlet water temperature is essential. If the outlet water temperature approaches the boiling point, increasing the system pressure is a feasible countermeasure.

Moreover, analysis results show that if only one RCCS set works, the system may be prone to failure under higher RPV or ambient temperature. Therefore, reactor operation with only a single RCCS set should not be permitted. In exceptional circumstances where only two sets are functional and the third is undergoing maintenance or repair, the reactor should be shut down if the maintenance or repair cannot be completed within the designated timeframe.

When curve-fitting equations (Table 4) are employed to estimate the ambient temperature at which system boiling failure occurs, using the average RPV temperature for calculations may result in an overestimation of the actual ambient temperature at failure. Instead, using the maximum RPV temperature leads to a more conservative estimation.

As discussed in Section 3.2.3, for cases with the same average temperature, a more non-uniform temperature distribution leads to a higher system heat load. Consequently, when employing empirical correlations (curve-fitting equations, Table 4) to estimate the ambient temperature at which system boiling failure occurs, the use of the average RPV temperature in the calculation may overpredict the actual failure ambient temperature. Instead, using the maximum RPV temperature leads to a more conservative estimation.

4.2. Low Temperature Failure Analysis

Based on the above analysis, it can be concluded that, compared with system failure caused by water boiling, cooling water freezing in the HTR-PM RCCS is more likely to occur and thus requires greater attention. This conclusion is also supported by HTR-PM operational experience. Freezing of cooling water may result in the rupture of water-cooling pipes, thereby disrupting the circulation of cooling water within the RCCS.

During winter operation, it is crucial to monitor the inlet water temperature closely and implement preventive measures when the temperature approaches the freezing point, for example, shutting down part or all of the RCCS sets, closing the air inlet door of the air-cooling tower, or applying insulation to the water pipes of the air cooler.

4.3. System Heat-Carrying Capacity

The actual heat-carrying capacity of the system is influenced by several factors, including the RPV temperature, ambient temperature, and the number of operating RCCS sets. The cavity transfers heat mainly through radiation, with natural convection contributing less than 16% of the total heat transfer. The heat-carrying capacity increases with the increase in RPV temperature, decreases with the increase in ambient temperature, and increases with the increase in operating RCCS sets. According to the calculation results, the RPV temperature has the most significant impact on the system’s heat-carrying capacity, whereas the ambient temperature and the number of operating RCCS sets have relatively minor effects. The relationship between heat-carrying capacity and ambient temperature is approximately linear. When the RPV temperature is high and multiple RCCS sets are in operation, the heat-carrying capacity is less sensitive to the variations in ambient temperature. In addition, there is a positive correlation between the heat-carrying capacity and the temperature difference between the inlet and outlet of the cooling water.

The temperature distribution across the RPV also influences the system’s heat-carrying capacity. When the average RPV temperature remains constant, a more uneven temperature distribution leads to increased thermal radiation emitted by the RPV, thereby enhancing the heat-carrying capacity of the RCCS. Therefore, approximating the system’s heat-carrying capacity using the average RPV temperature, rather than the actual temperature, may result in an underestimation. Employing the highest RPV temperature as the input temperature for calculation provides a more conservative approach.

In the case that ambient temperature fluctuations are significant, increasing the number of operating RCCS sets appropriately can help mitigate the impact of ambient temperature changes on the heat-carrying capacity, reduce cooling water temperature fluctuations, and minimize thermal stress on the pipelines.

In the HTR-PM design, the specified heat-carrying capacity of the RCCS with two sets in operation is 1.2 MW. According to the calculation results, the heat-carrying capacity of two RCCS sets can exceed 2 MW in normal operation, when the RPV exhibits a uniform temperature distribution above 400 °C (a scenario unlikely to occur in practice). The analysis results indicate that the current RCCS design of the HTR-PM meets and potentially exceeds the required performance standards.

In actual reactor operation, the RPV temperature is also affected by the operational characteristics of the RCCS. Therefore, in order to accurately determine the required design capacity of the RCCS and optimize associated costs, further coupled analysis of the reactor behaviors and RCCS behaviors is necessary.

5. Conclusions

The paper investigates the influence of ambient temperature, RPV temperature, and the number of operating RCCS sets on the system’s heat-carrying capacity and cooling water temperature. Furthermore, the limit of the ambient temperature under which the system can operate normally at various RPV temperatures and RCCS configurations is also analyzed. Based on the calculation results, the following conclusions can be drawn:

(1)

During normal operation of the HTR-PM, when the RPV temperature is maintained at a relatively low level, a single RCCS set is sufficient to ensure the safety of the reactor cavity. However, in certain accident scenarios involving emergency reactor shutdowns, the core and RPV temperatures may rise due to the decay heat and lack of forced cooling. In such cases, two RCCS sets can effectively remove the residual decay heat and keep the RPV and reactor cavity safe.

(2)

The RCCS may experience boiling or freezing of the cooling water during operation, potentially leading to heat transfer deterioration or even system failure. According to the calculation results, cooling-water boiling does not occur during normal operation of the reactor. However, under accident conditions with elevated RPV temperatures, it is essential to maintain an adequate number of operating RCCS sets to prevent boiling. Compared to boiling, the freezing of the cooling water and the resulting pipe rupture need more attention. Especially during the winter and at lower RPV temperatures, partial or full shutdown of the RCCS sets may be necessary to avoid freezing. Alternatively, closing the air inlet door of the air cooler to increase the cooling water temperature is also a feasible measure.

(3)

Heat transfer within the cavity primarily occurs through thermal radiation, with natural convection contributing less than 20% of the total heat transfer. The system’s heat-carrying capacity is predominantly determined by the RPV temperature and is positively correlated with the temperature difference between the inlet and outlet of cooling water. Additionally, the spatial distribution of the RPV temperature influences the heat transfer performance; a more uneven temperature distribution enhances the radiative heat emission from the RPV, thereby increasing the overall heat load of the system. Based on the analysis results and operation experience, it was found that the heat-carrying capacity of the RCCS of the HTR-PM exceeds the design requirement of 1.2 MW when two of three sets are operating normally.

(4)

Nevertheless, since the RPV temperature is also influenced by the operational characteristics of the RCCS, future studies should incorporate coupled simulations of the reactor, RPV, and RCCS behaviors. Such integrated analyses will enhance the understanding of RCCS performance and support further design optimization of the system.