Abstract

The decay heat removal system (DHRS) for the European sodium-cooled fast reactor (ESFR) concept consists of three cooling systems, which provide highly reliable, redundant, and diversified decay heat removal functions. Two of the systems provide a strong line of defense, whereas the third system provides long term-heat removal. This third DHR system, DHRS-3, involves in separating oil, and water-cooled loops integrated in the reactor pit serves the purpose of the safety vessel. It is expected that the proposed DHR concept enables a robust demonstration of the practical elimination of the prolonged loss of the decay heat removal function. For its confirmation, detailed numerical analysis is needed as a basis for further investigation. Supporting this approach, the current evaluation with means of computational fluid dynamic (CFD) provides a preliminary thermal analysis of the capability of the oil cooling system in the reactor to be used for residual heat removal in the pit in case of emergency. For the evaluation, different heat flux values are assumed at the vessel wall to examine the range of the resulting temperatures. The temperature of the main vessel wall should be below 800 °C. Furthermore, a sodium leakage at 500 °C into the reactor pit is assumed. The concrete structure is below 70 °C.

1 Introduction

The European sodium-cooled fast reactor (ESFR) is a large pool-type oxide fueled sodium-cooled fast reactor (SFR) concept, which has been developed within the Euratom FP7 project CP-ESFR [1]. To improve the Safety of the ESFR concept, new safety provisions have been proposed within the Euratom Horizon 2020 ESFR-SMART project [2], considering safety objectives envisaged for generation-IV reactors and the update of European and international safety frameworks taken after the Fukushima accident. The proposed measures aim at enhancing safety and improving the robustness of the safety demonstration to the level of the requirements for the generation-IV reactors [3]. The safety goals for generation IV reactors require excelling in safety and reliability, the reduction of the likelihood and degree of reactor core damage, and the elimination of the need for offsite emergency response. In the order to meet these goals, innovative safety concepts are needed in all areas of safety design of the fundamental safety functions. Beside a highly reliable and robust plant protection system, highly reliable heat removal systems for assuring adequate cooling of safety relevant components and structures and effective options for dealing with severe accidents need to be implemented [4].

With regard to decay heat removal (DHR), the design objective is to achieve the practical elimination of the prolonged complete failure of the decay heat removal function, which may cause severe core damage and the failure of the reactor coolant boundary. In order to achieve the safety design goals, a highly reliable, redundant, and diversified decay heat removal concept needs to be implemented and a robust demonstration of the practical elimination of this prolonged complete failure needs to be accomplished.

Various concepts for decay heat removal systems (DHRSs) exist both for past reactor designs and for concepts currently under development typically based on auxiliary cooling systems involving direct reactor cooling, primary reactor cooling, intermediate reactor cooling, reactor vessel cooling, and steam generator cooling connected to one or more ultimate heat sinks. Current designs aim at passive decay heat removal systems using natural convection for heat removal from the reactor pool to ultimate heat sink for pool type concepts.

The DHRS for the ESFR concept consists of three cooling systems, namely, DHRS-1, DHRS-2, and DHRS-3, which are described in detail in Refs. [5,6]. These three DHR systems are expected to provide two strong lines of defense (DHRS-1 and DHRS-2) with a decay heat removal capacity of about 36 MW and a weak line of defense (DHRS-3) with a lower capacity. Considerations are also given to redundancy and simplicity of plant operation. The proposed set of DHRS provides good confidence in the possibility of the global system to meet the criteria of safety of the generation-IV reactors.

The DHRS-3 is a part of the safety innovation related to the replacement of the safety vessel with a reactor pit which is able to provide improved operational and safety functions of both the decay heat removal system and the containment function. With this innovation, the aim is to discard the safety vessel and to keep its safety functions, i.e., containment of the primary sodium in case of the reactor vessel leak without reduction of the primary sodium free level below the intermediate heat exchanger (IHX) windows, by modifying the reactor pit geometry and by using the metallic liner on the reactor pit surface. In addition, this approach provides options to implement a new decay heat removal option within the reactor pit.

The DHRS-3 consists of several independent oil/water systems to ensure redundancy and is installed between the primary vessel and the liner. It is used both for cooling the reactor pit in normal operation and for DHR function when needed. The removal of the safety vessel that shields the heat removal substantially increases the DHR capabilities of the DHRS-3. In order to confirm the DHR capacity of the DHRS-3 system, detailed numerical studies are being performed. The focus of this paper is the computational fluid dynamic (CFD) analysis of the design of the DHRS-3 using a three-dimensional model of the reactor pit. This paper describes the overall design of the reactor pit, including the preliminary parametric calculations of temperature distributions for various design scenarios.

The efficiency of the oil cooling system is evaluated. A representative part of the reactor pit structure is modeled. The heat path is from the reactor vessel wall through a gap, an insulation layer into a concrete structure. The heat sinks of the modeled part of the pit are the oil cooling system and the ambience at the outer wall of the structure. The oil cooling system is situated at the metal liner, which is mounted along the insulation layer in the gap region. A simplified case is used for verification with an analytical solution. Furthermore, it is shown that the oil cooling system is capable of removing heat from the structure and maintain the temperature below 70 °C. At nominal conditions, about 3 MW have to be removed at a top cooling temperature of approximately 200 deg. This CFD computation provides a preliminary thermal analysis of the capability of the oil cooling system in the reactor to be used for residual heat removal pit in case of an emergency. For evaluation, different heat flux values are assumed at the vessel wall to examine the range of the resulting temperatures. The temperature of the main vessel wall should be below 800 °C. Furthermore, a sodium leakage at 500 °C into the reactor pit is assumed. The concrete structure should be below 70 °C.

2 European Sodium-Cooled Fast Reactor Concept

2.1 System Layout.

The ESFR concept has been developed within the Euratom FP7 CP-ESFR project (2009–2013), considering past European experience in SFR technology, in particular, the French SPX2 project and European Fast Reactor project which both involved a wider European cooperation. For both projects, the operational experience of the Superphenix reactor SPX [5] provided valuable inputs to improve safety, reliability, in-service inspection, and repair as well as economics.

The ESFR concept is a large pool type industrial sodium fast reactor of 1500 MWel/3600 MWth. The design objectives for ESFR include simplification of structures, improved in-service inspection and repair capabilities, reduction of risks related to sodium fires and to the water/sodium reaction, improved fuel maintenance, core catcher with the capability for a whole core discharge, and improved robustness against external hazards [2]. The ESFR core is composed of two zones of inner and outer fuel assemblies and three rows of reflectors. There are two independent control rod assembly systems with additional passive reactivity insertion mechanisms. The core design aims at a fuel management scheme with a flexible breeding and minor actinide burning strategy.

The ESFR concept is based on options already considered in previous and existing pool sodium fast reactors, with several potential improvements regarding safety, inspection, and manufacturing. Particular attention is also given to compactness. The reactor vessel is cooled with sodium (submerged weir) and is surrounded by a reactor pit which replaces the safety vessel including all its function for normal operations and accident conditions. The reactor vault can be inspected for maintenance.

2.2 Decay Heat Removal System.

The main design objective for the DHR system is to practically eliminate the prolonged loss of the decay heat removal function. In order to achieve this objective, three independent DHR systems have been implemented (see Fig. 1). The three systems are redundant: six loops for the DHRS-1, six secondary loops for the DHRS-2, and several oil circuits for the DHRS-3. All these systems have a high degree of passivity and are easy to operate. They are forgiving and admitting significant grace periods due to the high thermal inertia provided by the large volume of the subcooled sodium. This global high thermal inertia allows the temperature to increase only slowly, thus providing grace periods in order of several days before a critical temperature is reached.

Fig. 1
ESFR-SMART secondary and primary systems with the DHR systems
Fig. 1
ESFR-SMART secondary and primary systems with the DHR systems
Close modal

The first DHR system, DHRS-1, is provided by sodium/air heat exchangers connected to each IHX. These loops replace the direct reactor cooling system in the previous design and have various advantages such as avoiding additional roof penetrations and maintaining cold column in the IHXs [2].

The second DHR system, DHRS-2, is provided by cooling the steam generator modules by air in natural or forced convection through hatch openings, as is done in the Phénix reactor, providing the heat sink for the secondary loop.

The third DHR system, DHRS-3, is implemented in the reactor pit with two independent cooling circuits, one with an oil heat exchanger brazed on the liner and the other one with water inside the concrete. The water loop is capable of maintaining temperatures of the whole pit below 70 °C. Due to the removal of the safety vessel, the DHRS-3 which is directly attached to the liner is expected to be more efficient and to assure a large part of the decay heat removal close to 100%.

It should be noted that the operation of the DHR systems is expected to be simple for the operator. After the reactor was shut down, the secondary loops very easily ensure the decay heat removal through the steam generator. In the event of loss of the water supply to the steam generators, the operator opens the windows of the steam generator casings, the DHRS-2, ensuring the secondary sodium cooling thanks to the natural convection of the air around these steam generators. During this time, the DHRS-3 oil heat removal system in front of the reactor vessel ensures a non-negligible complement. It is designed to ensure this function alone after about three days. If these circuits become unavailable, the operator opens the windows of sodium/air heat exchangers of the DHRS-1. The natural convection of secondary sodium in this loop then allows the DHR in a completely passive way by maintaining a column of the cold primary sodium in the IHX and thus a good natural convection of primary sodium through the core.

3 Reactor Pit

3.1 Design Detail.

One of the main innovative approaches to the safety design of the ESFR concept concerns the replacement of the safety vessel with the reactor pit that aims to improve the operational and safety functions of both the decay heat removal systems and the containment [4]. All existing SFRs have a safety vessel around the main vessel [7]. The function of this safety vessel is to confine the primary sodium in case of the main vessel leakage, so as to avoid lowering of the primary sodium free level below the inlet windows of the intermediate heat exchangers and thus providing an efficient natural convection through the core. In case of the main vessel leakage, the reactor is not recoverable and the core must be unloaded. Due to the need to wait for reduction of the residual power of the assemblies, this handling could take a significant duration (i.e., higher than 1 year) especially in the ESFR-SMART design without external sodium storage. The safety vessel must, therefore, remain filled with sodium for a long time. The potential danger in these conditions is that the reactor pit is not designed to withstand a sodium leak from this safety vessel. Moreover, this safety vessel leak would also lead to interruption of the core cooling by natural convection, leading to a very difficult overall situation [8].

A number of measures have been taken to prevent leakage of the safety vessel, such as a slight overpressure between the two vessels to detect a possible leak and the choice of different materials to avoid a common failure mode on corrosion. It is recalled that it is a problem of corrosion on welds that led to the leakage of the Superphenix storage drum vessel and that this leak was taken up by the safety vessel of this storage drum [7].

The scenarios of vessel leakage are diverse, from corrosion leakage to leakage on a severe accident with mechanical energy release. This leads to high uncertainties in the temperatures and leakage rates, which make it difficult to demonstrate the safety vessel mechanical strength against the corresponding thermal shocks. Moreover, the French licensing authority requires considering double leakages in order to verify that the situation that does not lead to the cliff-edge effect in terms of radiological releases to the environment. This demonstration was required after the SPX external sodium storage leak. It is particularly required if the core unloading is high.

The safety vessel is a proven option, especially demonstrated during the incident at the Superphenix storage drum [7], and is adopted in all existing fast reactors. However, the evolution of safety standards leads us to look at other options where its functions could be directly taken over by a reactor pit capable of withstanding a sodium leak and, thus, a long-term mitigation situation. It was an option that had already been looked at in the EFR project with a vessel anchored in the pit and was later abandoned for reasons of feasibility and design difficulties.

The proposed design of the reactor pit is composed of the following domains (Fig. 2):

Fig. 2
Detail of the reactor pit design
Fig. 2
Detail of the reactor pit design
Close modal
  • A mixed concrete/metal structure with a water cooling system inside the concrete supports the thick metal slab to which the reactor vessel is attached. Together with the reactor roof, it provides a sealed containment which must keep its integrity in all the cases of normal or accidental operations.

  • Inside the concrete/metal structure, blocks of insulating materials (nonreactive with sodium) are installed. Alumina is selected as a reference material for the insulation blocks. A conventional insulation layer could be considered in future to increase insulation effects (outside the scope of this paper).

A metallic liner is placed on the surface of the insulation blocks. The gap between the reactor vessel and the liner must be small enough (350 mm was chosen) to avoid the decrease in the primary sodium free level below the IHX windows in case of sodium leakage from the reactor vessel. During normal operations, the primary sodium free level is 1350 mm below the roof. In case of primary sodium leak, about 300 m3 of sodium will leave the reactor vessel to fill the gap and the new equilibrium free level of the primary sodium will be about 3070 mm below the reactor roof. With this level of sodium inside the primary circuit, there is still a 1090 mm sodium level above the upper IHX openings, which allows a sodium inflow into the IHX and a good natural convection and core cooling. If the sodium temperature decreases to 180 °C, the volume of remaining sodium will decrease of about 205 m3 due to the change in the density, and it would cause the sodium level to go down to around 50 mm above the IHX entry bottom. Furthermore, the natural convection remains possible.

  • The oil cooling system is installed next to or even inside the liner.

  • Finally, a special concrete with alumina (aluminous concrete) which could withstand, without significant chemical reaction with sodium, a leakage of the liner could be used between the liner and the insulation (blocks of alumina).

3.2 Description of the DHRS-3.

The DHRS-3 consists of two independent active cooling systems located in the reactor pit (see Fig. 2):

  • The oil cooling system (DHRS-3.1) is close to the liner. The oil under forced convection can remove the heat transferred by radiation from the reactor vessel at high temperature. Conversely to water, the adopted synthetic oil is resistant to high temperatures above 300 °C and reacts with sodium without producing hydrogen. As an example, the commercial oil called “Therminol SP” [4] can be used in normal operations at temperatures up to 315 °C.

  • The water cooling system (DHRS-3.2) for the concrete cooling is installed in the concrete and aims at maintaining the concrete temperature under 70 °C in all possible situations, even if the oil system is lost.

Both oil and water circuits work during the normal operation and have to maintain the concrete temperature below 70 °C. This margin is intended to ensure the concrete integrity and to protect it from thermal degradation. A few days after the reactor was shut down, the oil cooling system alone has to be able to remove all the decay heat generated by the fuel. In case of a reactor vessel leak and loss of the oil system, the water system should be able to remove the decay heat generated by the core and to maintain the concrete below 70 °C.

3.3 Design-Basis Scenario.

The reactor pit is designed considering the following three main scenarios:

  • Scenario 1: Normal operation: The main vessel temperature is at about 400 °C. The operation of the oil cooling system is sufficient to maintain the correct thermal conditions in the pit (i.e., less than 70 °C for the concrete of the mixed structures).

  • Scenario 2: Operation in exceptional decay heat removal regime: The safety studies should be taken into account for exceptional situations of successive losses of decay heat removal systems. In this case, in exceptional situations of categories 3 and 4, the reactor vessel is allowed to reach a temperature of 650 °C. The two cooling systems (oil and water) must make it possible to maintain the concrete temperature below 70 °C while playing an important role in the decay heat removal (in this study, only the oil cooling system is taken into account; further publication is following).

  • Scenario 3: Operation in accident situation of sodium leakage: In a situation of little leak, vigorous sodium cooling is possible with the redundant and available DHRS to bring the sodium to a temperature corresponding to the handling temperature (180 °C). Therefore, the maximum temperature of the sodium in the gap should not exceed 200 °C. The demonstration of the oil cooling system availability in case of reactor vessel leakage is difficult, and we assume as hypothesis that the oil cooling system is no longer available. The operation of the water cooling system alone must be sufficient to maintain the concrete temperature below 70 °C (further publication).

It has to be noted that further studies need to be performed, taking in account a leakage due (or combined) with a high thermal transient (e.g., due to failure of the DHR system) and if the failure is due to a severe accident.

4 Computational Fluid Dynamic Computation of the Reactor Pit Structure Heat Transfer

The aim of this CFD computation is the evaluation of the steady-state heat transfer from the ESFR primary vessel through the reactor pit structure. The primary vessel is surrounded by a gas-filled gap, a metal liner, an insulation layer, and a concrete structure. The outside surface of the concrete structure is in contact with the ambience that is defined as one of the heat sinks for this evaluation. The other heat sink for this evaluation is the cooling system. The pit structure is simplified as one segment, an elementary cell. In the solids, heat conduction is assumed.

Two cases are applied for this computation. First, the goal is to keep the temperature at the main vessel wall below 800 °C in case of emergency by the application of the reactor pit cooling system. Second, a sodium leakage into the pit is assumed and the heat of the hot liquid metal is directly applied to the liner and the gap is not modeled.

The calculations were performed using the high-performance CFD software tool ansyscfx. It is a parallelized code based on the applied finite volume technique [9].

4.1 The Computational Model.

The steady-state model is defined to compute the heat transfer from the primary vessel through the gap, through the insulation layer, and through the concrete structure. The reactor pit is divided into several axial sections, and the computational analysis can be performed for a representative section. The drawing of the geometry for one section, the “elementary cell” of the reactor pit structure, is shown in Fig. 3. The resulting model geometries for the two cases are shown in Fig. 4.

Fig. 3
Drawing of an “elementary cell” of the reactor pit
Fig. 3
Drawing of an “elementary cell” of the reactor pit
Close modal
Fig. 4
The CFD model for an “elementary cell” of the reactor pit: (a) case one and (b) case two
Fig. 4
The CFD model for an “elementary cell” of the reactor pit: (a) case one and (b) case two
Close modal

The geometry for case one is shown in Fig. 4(a). The heat source is the outside of the reactor vessel wall (red). Constant heat flux is applied as the boundary condition. The gap (white) between the primary vessel and the liner (cyan) is considered as vacuum for those computations to minimize the computation time. There, only heat transfer due to radiation is taken into account. The cooling system in the liner consists of vertical oil pipes (blue; the coolant is not modeled, and constant temperature is applied at the inner pipe surfaces). For the radiation model, the liner surface toward the gap is simplified as a part of a cylindrical surface, and the cooling pipes are modeled at the inside of the liner instead. Along the liner is an insulation layer (yellow). The water cooling system (magenta) in the concrete (gray) structure is not modeled for this case.

The geometry for case two is shown in Fig. 4(b). The gap is not modeled, and the temperature of the liquid metal is applied directly on the liner surface (red). Constant temperature is applied as the boundary condition. For this case, the insulation layer (yellow) is assumed to be at least partly soaked by liquid metal and damaged. Heat conduction parameters of concrete are applied here. The oil cooling system (blue) in the liner (cyan) and the water cooling system in the concrete structure (gray) consist of vertical pipes (magenta; the coolant is not modeled, and constant temperature is applied at the inner pipe surfaces).

The domains for the computational model in Fig. 4 are (λ is the thermal conductivity):

  • The metal liner, steel (blue); λ = 60.5 W/m K.

  • The insulation layer (yellow); case one: λ = 0.04 W/m K and case two: λ = 1.4 W/m K.

  • The concrete structure (gray); λ = 1.4 W/m K.

The boundary conditions in Fig. 4 are as follows:

  • The heat sources are at the left (red); case one: fixed heat flux at the reactor vessel wall, up to 0.1 MW/m; case two: constant temperature at 500 °C.

  • The main heat sinks are the cooling systems (constant temperature at the inner side of the cooling channels); the oil cooling system in the metal liner (blue; −196 °C to 200 °C), and the water cooling system in the concrete structure (magenta; 50 °C).

  • The outside ambience of the concrete structure (black surface at the right; Ta = 50 °C, k = 6 W/m K).

  • The other outer surfaces are defined as symmetric.

The model for case one has been verified by a comparison of the computational results to an analytical solution for heat flow from the vessel toward the ambience without cooling. The maximum deviation of the temperature profile is less than 1% of the order of magnitude and considered to be acceptable for this simple and fast-solution oriented computational model.

4.2 Maximum Sustainable Heat Flux at the Reactor Vessel Wall.

Figure 5(a) displays computational results for the temperature at the main vessel wall as a function of the local heat flux. In the near vacuum of the gap, the heat transfer takes place by means of radiation, from the vessel wall toward the metal liner, where the cooling system is located. For computational evaluation, different cooling temperatures are assumed in the range of −196 °C (e.g., liquid nitrogen) and 200 °C (assumed maximum oil cooling temperature for normal operation). In one of the cases, the temperature at the entire backside of the metal liner is set to be −196 °C to overcome the effects defined by the location of the piping. Figure 5(a) clearly shows that within the current range, the cooling temperature has little influence on the intensity of the heat transfer and, consequently, on the capability of the cooling system. Due to the Stefan–Boltzmann law, the total radiant heat energy emitted from a surface is proportional to the fourth power of its absolute temperature. Hence, the hot side defines the intensity of the heat transfer as long as the cool side is of “sufficiently low” temperature. This is obviously the case here. Consequently, the cooling effect depends on the radiant heat transfer at the reactor wall which is clearly the limiting factor. As visible in Fig. 5(a), the wall heat flux must be kept well below qw = 30 kW/m2 to maintain a reactor vessel wall temperature below Tw = 800 °C.

Fig. 5
Resulting temperatures for different oil cooling temperatures at the liner Tcl. (a) Temperature at the reactor vessel wall as a function of the heat flux. (b) Temperature at the gap side of the cooled metal liner (for a vessel wall heat flux of 100 kW/m2) (*for this case, the entire backside of the liner is cooled).
Fig. 5
Resulting temperatures for different oil cooling temperatures at the liner Tcl. (a) Temperature at the reactor vessel wall as a function of the heat flux. (b) Temperature at the gap side of the cooled metal liner (for a vessel wall heat flux of 100 kW/m2) (*for this case, the entire backside of the liner is cooled).
Close modal

The resulting temperatures at the inner surface of the cooled liner are shown in Fig. 5(b) for a heat flux of 100 kW/m2. The temperature distribution follows the local heat removal effect imposed by the location of the tubes of the cooling system. As expected the temperature in the vicinity of the cooling pipes reaches lower values than in the remote areas. For demonstration, cooling of the entire backside of the metal liner is assumed for one of the cases. There the temperature is kept at −196 °C, and consequently, the local overheating is much lower than in the other cases. However, this case clearly shows the minor influence of the parameters of the cooling system on the heat removal capacity since the radiation at the reactor vessel wall is the limiting factor.

4.3 Reactor Heat Balance in the First 1.5 h After the Trip.

A simple estimation can give a rough idea about the potential temperature development in the vessel after a reactor trip if only the discussed oil cooling system in the reactor pit remains in operation. The residual power [9] expected after a reactor trip can be expressed as
Pr=6.48×103P0[t0.2(t+T0)0.2]
(1)

as shown in Fig. 6. Hereby, P0 = 3600 MW is the nominal reactor power and the operation time is T0 = 2100 days (T0 and t in effective full power days). The estimated resulting heat flux at the vessel wall is qw = Pr/A with the heat transfer surface A =1189 m2.

Fig. 6
Residual power and the resulting heat flux at the reactor vessel wall as a function of time
Fig. 6
Residual power and the resulting heat flux at the reactor vessel wall as a function of time
Close modal

As discussed in Sec. 4.2, the heat flux at the reactor vessel wall must be below qw = 30 kW/m2 to limit the wall temperature to 800 °C. As shown in Fig. 6(b) (solid blue line), the heat flux drops below this value at about 1.5 h after the reactor trip (note that transient effects and local overheating in the core cannot be considered by this model). The residual reactor power at 1.5 h is Pr ≈ 36 MW (about 1% of the nominal power). Integration of the residual power (solid red line in Fig. 6(b)) for this time window results in about Q =69 MWh and in an average power of about Pa = 46 MW (dashed red line in Fig. 6(b)) [10,11].

4.4 Cooling of the Concrete Structure in Case of Sodium Leakage.

In case of sodium leakage, the gap between the main vessel and the metal liner is assumed to be flooded with liquid sodium at 500 °C. This defines the boundary condition (constant temperature) at the outer surface of the metal liner. The insulation layer between the liner and the concrete is assumed to be (partly) soaked and significantly damaged; heat conduction parameters for concrete have been assumed here. At the right-hand side, ambient conditions have been assumed, as defined above. As shown in Fig. 4, two cooling systems are available, one at the metal liner (the oil cooling system) and an additional cooling system embedded into the concrete structure (the water cooling system). The number of oil cooling pipes at the liner is defined with the piping number np; the cooling system in the concrete structure is equipped with np −1 pipes, i.e., always one less than that at the liner. For a parameter study, the piping number np is steadily increased, along with the temperatures for both cooling systems, for the liner and for the structure (Tcl and Tcs).

Figure 7 shows the computational results for the temperature distribution in the elementary cell with four cooling pipes at the liner on the left and three cooling pipes in the concrete structure. At the liner, a temperature of 500 °C is realized for the boundary condition. The adjacent domain (the damaged insulation layer) is treated as the concrete for this study, and consequently, no pronounced temperature gradients are visible between the domains. Furthermore, the temperature is below the required limit of 70 °C for the concrete on the right-hand side of the cooling pipes (dark blue area); this is the majority of the concrete structure.

Fig. 7
Temperature in the elementary cell with np = 4 cooling pipes for the liner (Tcl = 200 °C) and np − 1 = 3 cooling pipes in the concrete structure (Tcs = 50 °C). The yellow lines serve as probe lines for Fig. 8.
Fig. 7
Temperature in the elementary cell with np = 4 cooling pipes for the liner (Tcl = 200 °C) and np − 1 = 3 cooling pipes in the concrete structure (Tcs = 50 °C). The yellow lines serve as probe lines for Fig. 8.
Close modal

Figure 8 displays the temperature profiles versus the x-axis defined along the yellow probe lines on Fig. 7; the piping number is np = 4, and the temperature for the structure cooling is Tcs = 50 °C. The temperature for the liner cooling is assumed in a range of −196 °C < Tcl < 500 °C (the case for Tcl = 200 °C corresponds to Fig. 7). Again, it can be seen that for this case, the concrete temperature mostly remains below the limit of 70 °C on the right-hand side of the structure cooling pipes. Furthermore, it can be seen that the oil cooling system in the liner is of low efficiency. Despite the huge range of cooling temperature, the effect is minor. This can be explained by the proximity of the heat source. The structure cooling system is located well away from the heat source and, therefore, much more efficient at 50 °C than the other one at −196 °C. Consequently, for the cooling of the concrete temperature in case of sodium leakage, the cooling system in the concrete is significantly more effective than the one at the liner.

Fig. 8
Temperature in the structure along the x-coordinate (following the yellow probe lines on Fig. 7); the liner is at the left, the ambience at the right. The concrete structure is on the right-hand side of the vertical line (gray, dotted). The horizontal line (red, dashed) refers to the temperature limit of 70 °C for the concrete. The red circle is the probe point for Fig. 9(b).
Fig. 8
Temperature in the structure along the x-coordinate (following the yellow probe lines on Fig. 7); the liner is at the left, the ambience at the right. The concrete structure is on the right-hand side of the vertical line (gray, dotted). The horizontal line (red, dashed) refers to the temperature limit of 70 °C for the concrete. The red circle is the probe point for Fig. 9(b).
Close modal

Figure 9 shows a parameter study concerning three parameters, namely, the number of cooling pipes np and the temperatures of both cooling systems at the liner Tcl and within the concrete structure Tcs. The performance of the cooling systems can be compared. In Fig. 9(a), the maximum temperature in the concrete structure is shown (at the interface between the concrete and the damaged insulation) if only the oil cooling at the liner is applied. Again, the low efficiency of the liner cooling system is obvious; even in a hypothetical (and not realistic) case of a cooling at Tcl = −196 °C and with six vertical liner cooling pipes, the maximum concrete temperature remains above 200 °C. Figure 9(b) shows the temperature of the concrete at x =1.3 m (probe location, red circle in Fig. 8(a)). The case np = 1 (which results in np −1 = 0: no cooling pipes in the concrete) corresponds to the case presented in Fig. 9(a) where the concrete temperature is in the magnitude of 300 °C. The other profiles show the concrete temperature at a moderate structure cooling temperature of Tcs = 50 °C and for the increasing number of structure cooling pipes; the temperatures are significantly lower. Again, the capacity of the structure cooling system is shown.

Fig. 9
Maximum concrete temperature Tc,max and the concrete temperature at as a function of the liner cooling temperature Tcl and the piping number np; without cooling of the structure and different structure cooling temperatures Tcs
Fig. 9
Maximum concrete temperature Tc,max and the concrete temperature at as a function of the liner cooling temperature Tcl and the piping number np; without cooling of the structure and different structure cooling temperatures Tcs
Close modal

5 Conclusion

This paper summarizes a short computational evaluation of the capability and limitations of the reactor pit cooling systems to be used for residual heat removal. The cooling systems are designed for cooling of the reactor pit structure during normal operations. Two cooling systems are applied, the one at the liner and the other inside the concrete structure.

The model is steady-state, two-dimensional, defined as a representative cell, applying cylindrical symmetry. Two cases are assumed for the modeling. In the first case, a fixed heat flux is assumed at the vessel wall. The gap between the primary vessel and the metal liner is assumed to be practically evacuated. The heat transfer takes place by means of radiation from the vessel through the gap toward a cooled metal liner. In a second case, sodium leakage into the gap is assumed. The heat source is at the metal liner of the gap with a constant sodium temperature.

For the first case, the computational results show that the limiting factor for the heat removal is the radiation at the reactor vessel wall, the hot side of the gap between the vessel and the metal liner. The temperature of the cooling system plays almost no role (in the relevant range). For a heat flux at the reactor vessel wall below 30 kW/m2, the temperature of the wall is expected to remain below the limit of 800 °C. About 1.5 h after the reactor trip, the residual power is about 1% of the nominal power and the heat flux is expected to be sufficiently low to fulfill the discussed cooling requirement. After that period of time, the cooling system is, in principle, capable of coping with the residual heat.

For the second case, it could be shown that the oil cooling system at the metal liner cannot operate with sufficient performance since it is too close to the heat source. The second cooling system is embedded within the concrete structure and applying water as a coolant can fulfill the task. This system can operate at moderate cooling temperatures in the magnitude of 50 °C. However, it can be shown that the number of cooling pipes must be increased. Four cooling pipes per elementary cell are needed to keep the temperature of the concrete structure below the prescribed 70 °C.

Acknowledgment

The research leading to these results has received funding from the Euratom research and training programme 2014–2018 under Grant Agreement No. 754501.

Funding Data

  • H2020 Euratom (Funder ID: 10.13039/100010687; Grant No. 754501).

Nomenclature

     
  • A =

    heat transfer surface at the reactor vessel wall, m2

  •  
  • k =

    heat transfer coefficient, W/m K

  •  
  • np =

    piping number (for cooling systems)

  •  
  • Pa =

    average residual power, MW

  •  
  • Pr =

    residual power after trip, MW

  •  
  • P0 =

    nominal thermal reactor power, MW

  •  
  • Q =

    energy, MWh

  •  
  • qw =

    reactor vessel wall heat flux, kW/m2

  •  
  • t =

    time, d; h

  •  
  • Ta =

    ambient temperature, °C

  •  
  • Tc =

    concrete temperature, °C

  •  
  • Tc,max =

    maximum concrete temperature, °C

  •  
  • Tcl =

    cooling temperature at the liner (oil circuit), °C

  •  
  • Tcs =

    cooling temperature in the (concrete) pit structure, °C

  •  
  • Tl =

    liner temperature, °C

  •  
  • Tw =

    reactor vessel wall temperature, °C

  •  
  • T0 =

    reactor operation time (effective full power days), d

  •  
  • x =

    coordinate, m

  •  
  • y =

    coordinate, m

  •  
  • z =

    coordinate, m

Greek Symbol

    Greek Symbol
     
  • λ =

    thermal conductivity, W/m K

Subscripts or Superscripts

    Subscripts or Superscripts
     
  • a =

    ambient, average

  •  
  • c =

    concrete

  •  
  • cl =

    cooling of liner

  •  
  • cs =

    cooling of structure

  •  
  • el =

    electrical

  •  
  • l =

    liner

  •  
  • max =

    maximum

  •  
  • p =

    pipe

  •  
  • r =

    residual

  •  
  • th =

    thermal

  •  
  • w =

    wall

  •  
  • 0 =

    nominal

Acronyms and Abbreviations

    Acronyms and Abbreviations
     
  • CFD =

    computational fluid dynamics

  •  
  • CP =

    competitive project

  •  
  • DHR =

    decay heat removal

  •  
  • DHRS =

    decay heat removal system

  •  
  • ESFR =

    European sodium-cooled fast reactor

  •  
  • FP7 =

    Frame Program 7

  •  
  • IHX =

    intermediate heat exchanger

  •  
  • SFR =

    sodium-cooled fast reactor

  •  
  • SPX =

    Superphénix (nuclear reactor)

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