1 Introduction
Generally, there are supporting columns (SCs), core instrument measuring columns, control rod guide tubes (CRGTs), and other components in the upper plenum of a typical pressurized water reactor (PWR). The coolant flowing upward in the reactor core needs to redirect in the upper plenum and to distribute to several hot legs. Therefore, the coolant flow conditions are very complicated. The highly unstable turbulent flow applies a lateral force on the control rod assemblies, causing the vibration and wear between the control rod assemblies and control rod guide cards. In addition, the presence of transverse forces affects the falling speed of control rod assemblies under emergency shutdown conditions, thus threatening the reactor safety. More importantly, the core arrangement and refueling strategy in PWR lead to a significantly higher coolant temperature in the core center region than in the core peripheral region, with a maximum coolant temperature difference of about 30 K.
The high temperature coolant from fuel assemblies (FAs) in the core central area will flow to the top of the upper plenum, and then redirect to the horizontal flow into the hot legs through a long zigzag flow path imposed by SCs and CRGTs with sufficient mixing, while the low temperature coolant from the core peripheral FAs goes straight to the hot legs with a shorter residence time and less mixing. Thus, inadequate mixing of coolant with a certain temperature distribution in the upper plenum leads to a heterogeneous temperature distribution that continues in the hot legs. The coolant temperature distribution in the hot legs and the limited temperature measurement points will lead to errors in coolant temperature measurement, which affects the accuracy of core power prediction. Therefore, it is useful to conduct a detailed computational fluid dynamics (CFD) study on the temperature distributions in the hot legs. In fact, the studies of coolant mixing phenomena are very common and critical in the nuclear reactor thermal hydraulic study with the development of CFD technology these years [1–4].
Actually, series of studies on the flow and heat transfer characteristics in the reactor pressurized vessel (RPV) of PWR could be found. Xu et al. [5–7] performed series of detailed CFD simulations on flow features in the lower plenum of the typical PWRs using the Code_Saturne, which is free, open-source software developed and released by EDF. Some meaningful conclusions could be used for future structure design and optimization of flow diffusers. Philippe et al. [8] built the 1/5 scale Rossendorf coolant mixing (ROCOM) experimental facility based on the upper plenum of European pressurized water reactor (EPR), which includes all the SCs, CRGTs, and internal control components. The experimental results show that, at the core outlet, the flowrates in FAs near the four hot legs are significantly higher than the average value mainly due to the hot leg suction effect, while the flowrates in FAs in the core central region are lower. The CRGTs greatly affect the flowrates of the FAs and the flowrates in the FAs with CRGTs are significantly higher than those without CRGTs. Xu et al. [9] compared the transverse flow strength at the core outlet of AP1000 with other types of Westinghouse reactors using CFD software. The simulation results show that the coolant transverse velocity in the reactor core increases along the height direction and the maximum coolant horizontal velocity is not higher than 1/10 of the axial velocity.
Kao et al. [10] built a detailed CFD model of 1/4 CRGT using the STAR-CCM+ and calculated the flow distributions inside the CRGT. The simulation results show that about 81% of the coolant flow through the large windows at the bottom of guide tubes. Chiang et al. [11] predicted the distribution of temperature in the reactor core with the versatile internals and component program for reactors, EPRI (VIPRE) subchannel code and compared the results of the numerical simulation with the actual measured values. Then, the subchannel analysis results were used as the boundary conditions of CFD simulations for the upper plenum and hot legs coolant mixing study in the typical PWR. The results show that the high temperature in the core central regions flows upward and then enters the upper region of the hot legs, while the low temperature coolant in the surrounding FAs is entrained into the recirculation area, then flows into the lower part of the hot legs.
Cheng et al. [12] simulated the coolant flow in the upper plenum and dome of Maanshan reactor using CFD software, and found that the high temperature coolant entering the dome through the gap was only 2.12% of the total flow. Wu et al. [13] also conducted a detailed CFD simulation for the Maanshan reactor and the calculation region included the core outlet, upper plenum and hot legs. The results showed that the flow in the CRGT was weak, and the shear stress on the wall of CRGT was mainly concentrated in the lower part with large windows. There is a largescale vortex at the lower corner of upper plenum opposite to the hot legs, while there are no vortices at the lower corner below the hot legs.
Martinez and Galpin [14] modeled the main circuit of EPR, including the primary side of steam generator, cold legs, lower plenum, reactor core, upper plenum and hot legs using the commercial CFD software STAR-CD with the realizable k-ε (k stands for the turbulence kinetic energy while ε stands for the turbulence dissipation rate) turbulence model under the condition of steady-state operation. The simulation results of lateral velocity inside the hot legs agreed well with the experiment data. Defossez et al. [15] studied the flow paths of coolant in the hot legs using the CFD software. The simulation results showed that the k-ε turbulence model and the Speziale, Sarkar and Gatski (SSG) Reynolds stress model could accurately predict the mixing phenomenon and tangential velocity distributions in the hot legs.
Prasser and Kliem [16] conducted an experimental study with the construction of a 1/5 scale test facility ROCOM based on the KONVOI reactor. The saline water was injected into different FAs and the wire mesh sensors were used to measure the coolant temperature distributions at the core outlet and hot legs. The results showed that the maximum temperature difference at the reactor core outlet is about 44.3 K which decreases to about 10.3 K after sufficient mixing in the upper plenum. Hofmann et al. [17] simulated the surface pressure of control rods in the presence or absence of transverse flow using the N3S code so as to study the influence of transverse flow on the rod dropping time.
Actually, there are various types of PWR with unique internal structure in service currently, and different types of reactor design have their own characteristics. For example, there are large windows on CRGTs in M310 and AP1000, while there are no windows on the surface of CRGTs of EPR. The upper plenum in VVER contains two perforated barrel shells and SCs. The different designs of upper plenum structures lead to different coolant flow and temperature mixing characteristics, as well as different flow distributions at the core outlet. In this paper, three types of widely adopted upper plenum in the current commercial PWRs are selected, which are named TYPE 1, TYPE 2, and TYPE 3. A transverse and systematic comparative study of the influences of different upper plenum structures on the thermal hydraulic phenomena is studied deliberately. Some qualitative and quantitative flow and heat transfer features in the upper plenum and hot legs are obtained, providing important reference for future advanced PWR design.
2 Geometry description
As mentioned above, the corresponding descriptions of the upper plenum named TYPE 1, TYPE 2, and TYPE 3 in the current commercial PWRs are summarized in Table 1.
Tab.1 Three typical types of internal structures in upper plenum of PWRs |
| Types | Description | Similar adoption in current PWRs |
|---|---|---|
| TYPE 1 | SCs and CRGTs with two large windows | M310, AP1000, etc. |
| TYPE 2 | SCs and CRGTs without windows | EPR, etc. |
| TYPE 3 | Two parallel perforated barrel shells and CRGTs | VVER, etc. |
Many commercial PWRs, such as AP1000 and M310, adopt the design concept of TYPE 1 upper plenum. The schematic diagram of a typical PWR with TYPE 1 upper plenum is shown in Fig. 1(a). The upper core plate prevents the core from hydraulic suspension and hold the CRGTs and SCs. There are 157 coolant holes, of which 69 are square holes with round fillets which correspond to the position of CRGTs. The rest of the holes are round in shape [18]. There are 69 CRGTs and 42 SCs. The CRGT is a square tube with fillets, which houses the rod cluster assembly and several control rod guide cards between the control rod guide plate and upper core plate. There are two large windows on each side of the lower part of the CRGTs. The SC is a cylinder tube with reversed truncated cone at the top as a connection to the control rod tube guide plate and with four-foot bracket at the bottom as a connection to the upper core plate. The hole through the SCs allows the passage of in-core measurement probe.
After the coolant flows out of the core, it enters the upper plenum through the core upper plates. The existence of core upper plate narrows the flow area and thus the coolant accelerates significantly [19]. Depending on different positions of the FAs, part of the coolant flows directly into the upper plenum, exerting impacts on the bottom of SCs, and turns to the transverse flow at a high velocity. The rest of the coolant enters the CRGT, most of which flows out from the windows at the CRGT, approximately 15% of the coolant flow out through the gaps between the control rod guide cards and the CRGTs, and only a tiny part flow upward into the dome [20].
For TYPE 2 upper plenum, the typical application is the EPR Nuclear Power Plant (NPP), which is an evolutionary PWR designed by Framatome ANP, a jointly-owned subsidiary of AREVA and Siemens. TYPE 2 upper plenum consists of the reactor core control assembly (RCCA) guides which are located in the central region and SCs which are located in the peripheral area around the RCCAs as the passage channel for in-core measurement probes [21]. The RCCA guides are similar to the CRGTs of TYPE 1 upper plenum. The main difference is that the there is no window in the RCCAs, but there is only a gap between the bottom of RCCAs and core upper plates, through which the coolant can flow into the upper plenum. The schematic of TYPE 2 upper plenum internals is demonstrated in Fig. 1(b).
The series of VVER nuclear reactor system employs TYPE 3 upper plenum which is a four-loop pressurized water reactor designed in Russia. The design of the core upper plenum in this type of PWR, which adopts two concentric perforated barrels encompassing CRGTs [22], is completely different from the previous two types. Since there are no open windows on the surface of CRGTs, most of the coolant enters the upper plenum through the holes in the upper core plate.
Since there are no holes in the CRGTs, a small amount of coolant entering the CRGTs flows upward into the dome. The proportion of this part is low; therefore, it has little influence on the temperature distribution inside the upper plenum. The perforated barrels are located in TYPE 3 upper plenum, enclosing all the SCs and CRGTs inside, and the holes in the barrel are small in diameter but large in number. The barrel is far away from the core outlet, but it weakens the influence of hot legs on the pressure distribution in the core. The coolant passes through the holes in the barrel and enters the space between the perforated first and second barrel at a higher velocity. The coolant is mixed and the temperature is homogenized further.
Compared with the holes in the core barrel, the number of holes in the perforated barrel is larger and the cross-section area is smaller. Therefore, small vortices are generated in the part between two perforated barrels [23]. These vortices have less influences on the flow distribution at the core outlet and large influences on the temperature distribution in the hot legs. The layout of the internal of TYPE 3 upper plenum is depicted in Fig. 1(c).
3 Methodology
It is unpractical to reconstruct all the details in the upper plenum in CFD calculations, because the required number of cells and computational resources is beyond the capabilities of current computers. Therefore, the necessary geometry simplifications should be done on the premise of guaranteeing the accuracy of results. In addition, to ensure the comparability of CFD calculation results of different types of upper plenums, the original designs were adapted to the BORA experimental facility, a methodology similar to that in Ref. [24]. BORA is a mock-up experimental facility of four-loop typical PWR with a 1/5 scale, as illustrated in Fig. 2.
3.1 Core modeling
The fluid and computational domain of RPV upper internals was divided into two parts. The first part is the upper half core generated with structured mesh and the second part is the upper plenum including four hot legs generated with tetrahedral mesh. The upper half core was divided into nine volumes which are delimited by the top and bottom edges of the grids. Therefore, the cells are aligned with edges of grids. The details are exhibited in Fig. 3. To consider the confining effect introduced by the upper nozzle walls, walls without thickness is introduced, as displayed in Fig. 4. The joining face with the upper plenum is set on the bottom surface of the upper core plate. The nodes of the two parts on the joining face are conformal to avoid the numerical interpolation error. The core contains numerous fuel rod pins and several mixing and spacer grids with a complex geometry which is unfeasible to consider their detailed shape for limited computing resources. Therefore, the blockage effect caused by the FA was introduced by a head loss term in the momentum equation which is introduced in Ref. [24].
3.2 Upper plenum modeling
TYPE 1 upper plenum contains 42 SCs, 69 CRGTs with two large windows on each side of CRGT. The internals inside the CRGT which include control rod guide cards and control rods are ignored, and the internal space above the upper large windows is replaced by solid because the flowrate that goes through the CRGT to the dome is negligible compared with the flow going out through the windows. The simplified SCs and CRGTs are plotted in Fig. 5 and the layout of SCs and CRGTs inside TYPE 1 upper plenum is shown in Fig. 6.
For TYPE 2 upper plenum, there are 69 RCCAs located in the central region and 16 SCs located in the peripheral region. The brackets at the lower end of RCCAs and normal SCs are deleted as presented in Fig. 7. The layout of the internals inside TYPE 2 upper plenum is shown in Fig. 8.
Compared with TYPE 1 and TYPE 2 upper plenums, the main characteristic of TYPE 3 upper plenum is the existence of two concentric perforated barrels. The number and diameter of coolant holes in the barrels can be referred to that in VVER-1000. To reduce the required number of cells, the size of coolant holes in the perforated barrels is enlarged and the number is reduced while the total flow area is kept the same with the original design. The details of the two types of perforated barrels are given in Fig. 9.
In addition, the SCs and RCCAs are kept the same as those in TYPE 2. Hence, the result differences between TYPE 3 and TYPE 2 are caused by the two-layer perforated barrels only. The detailed geometry and layout of TYPE 3 upper plenum internals is portrayed in Fig. 10. The mesh details of three types of upper plenum are shown in Fig. 11.
3.3 Boundary conditions and model settings
The inlet condition is very important for the thermal hydraulic phenomena in the upper plenum. For the convenience of comparing the effect of different types of upper plenum on the core outlet flowrate, a uniformly distributed volumetric flowrate of 0.4 m3/s is applied at the upper half core inlet, i.e., the middle plane of the core. The temperature difference of different FAs are the cause of temperature heterogeneity in the hot legs. The temperature field derives from the sub-channel analysis code COBRA-EN with a maximum temperature difference of 26.4°C at the inlet. The inlet temperature field is shown in Fig. 12. All wall surfaces are set to be adiabatic and the scalable wall function is used. The transient calculation is launched with Code_Saturne using the shear-stress transport (SST) k-ω turbulence model with a time step of 0.005 s and a total physical flow time of 15 s. The flow fields are time averaged over the last 8 s. The fluid properties and model settings are listed in Table 2.
Tab.2 Boundary conditions and model settings |
| Variable | Value |
|---|---|
| Pressure/MPa | 15.5 |
| Density/(kg·m-3) | 726.5 |
| Dynamic viscosity/(Pa·s) | 8.85e-5 |
| Thermal conductivity/(W·m-1·K-1) | 0.562 |
| Specific heat/(kJ·kg-1·K-1) | 5.46 |
| Inlet temperature | Temperature map |
| Volumetric flow rate/(m3·s-1) | Uniform inlet (0.4) |
| Outlet | Free outlet |
| Upper half core region | Head loss term |
| Turbulence model | k-ω SST |
| Turbulence intensity at inlet | 5% |
| Time step/s | 0.005 |
| Spatial mean courant number | ~5 |
| Calculated flow time/s | 15 |
Nuclear reactor core consists of more than ten thousand fuel rods and spacer grids with a complex geometry. It is unrealistic and unnecessary to construct core geometry details in view of the unimportance of the flow phenomena inside the reactor core in this paper.
3.4 Mesh independence study
A series of meshes are tested for each geometry to analyze mesh sensitivity. The flowrate distribution at the core outlet is used as the mesh independent criteria. Take the TYPE 1 upper plenum for example, five sets of meshes were tested and the cell numbers are M1 = 8.80 million, M2 = 15.40 million, M3 = 19.68 million, M4 = 27.36 million, and M5 = 48.26 (Mi stands for the ith set of meshes) respectively. The normalized flowrate of each FA at the core outlet was obtained and the result using 48.26 million-cell mesh was used as the reference. The R2 difference between Mi and largest mesh M5 was defined as where 193 is the total number of FAs. As shown in Fig. 13, the R2 difference between M4 and M5 is below 10-4. Therefore, for TYPE 1 geometry, the result using a mesh of no less than M4 = 27.36 million cells is regarded as the mesh independent solution. The final meshes for three types of upper plenums consist of 27.36 million, 17.24 million, and 30.74 million cells respectively.
4 Results and discussion
The differences of flowrate distributions at the core outlet and temperature fields in the hot legs were compared for the three types of upper plenums. As shown in Fig. 14, due to the presence of large windows in the CRGTs in TYPE 1 upper plenum, the flow distribution at the core outlet presents a checkerboard distribution, which signifies that the CRGTs enhances the suction effect of the hot leg at the core outlet and SCs suppresses the suction effect. There is no window on the surface of CRGTs in TYPE 2 upper plenum, which results in the fact that the maximum coolant flowrate is located in the corner of the reactor core outlet near the nozzle of hot legs, and the flowrate below the average appears in the core central region with an elliptical distribution. The presence of two concentric perforated barrels in TYPE 3 upper plenum results in a circular flow distribution at the core outlet. The peripheral FAs have higher flowrates, while the lower flowrate FAs are at the core central area. In terms of flowrate distribution heterogeneity at the core outlet, TYPE 1 upper plenum is the largest while TYPE 3 upper plenum is the smallest, which suggests that the perforated barrels decrease the hot leg suction compared to the other two types of upper plenum internals. Generally, the flowrate rises with the horizontal distance of the FA location to the center of the core, as shown in Fig. 15. The outlet flow distributions of FAs are at the core vertical and horizontal lines, as shown in Fig. 16. The outlet flowrates in all three types of reactor cores present the lowest flowrate in the central part and the highest flowrate in the peripheral part. The flowrate in the core outlet of adjacent FAs with TYPE 1 upper plenum has a large difference. The flowrate in the vertical direction is significantly higher than that in the horizontal direction with TYPE 2 upper plenum. The flowrates at the outlet of FAs in the two directions have a consistent variation with TYPE 3 upper plenum, which suggests that the presence of two perforated core barrels eliminates the dominance of the suction effect induced by the arrangement of the hot legs.
The wall surface temperatures and coolant temperatures inside the three types of upper plenums are shown in Figs. 17 and 18. The hot coolant from the central core reaches the top face of TYPE 1 upper plenum with an elliptic shape before entering the upper close part of the two adjacent hot legs while the low temperature coolant stays in the surrounding region. The coolant temperature in TYPE 2 upper plenum increases with height. The temperature distribution in TYPE 3 upper plenum is similar to that in TYPE 2 upper plenum, but the proportion of high temperature coolant is much higher than that in the other two types of upper plenums.
The coolant tangential velocity distributions inside the hot legs, in which totally five planes were selected (shown in Fig. 19), are presented in Fig. 20. As the coolant flows from the upper plenum into the hot legs, the flow area decreases abruptly. The coolant from different directions mixs in the hot legs, leading to a complex flow condition, and the maximum tangential velocity appears near the inner wall of the hot legs. As the coolant flows down along the hot legs, the magnitude of the tangential velocity decreases. The internal tangential velocity of the hot legs with TYPE 1 upper plenum manifests that the coolant forms two rotating flows in the opposite directions, which rotates together around the axis of the hot legs with TYPE 2 upper plenum. Of all types of upper plenum, the tangential velocity at the initial cross section is the largest with TYPE 3 upper plenum, because the outer perforated barrel is close to the hot legs. As it flows downstream, it develops into two swirls of rotating fluid, which rotate around the axis of the hot legs with TYPE 3 upper plenum.
The temperature distributions in the hot legs with the three types of upper plenums are shown in Fig. 21. Due to the spatial arrangement of the hot legs, the high temperature coolant enters the part of upper area in the adjacent two hot legs with TYPE 1 and TYPE 2 upper plenums. However, it occupies the upper part of the hot legs completely due to the complete filling with high temperature coolant in the top of TYPE 3 upper plenum.
The temperature fields at the initial cross sections of the hot legs are the most heterogeneous, and the temperature heterogeneity decreases gradually as the coolant moves downstream along the hot legs. The development of temperature fields in the hot legs is mainly affected by the coolant tangential velocity. As the coolant moves downstream, the position of the hot coolant and cold coolant in the hot legs with TYPE 1 upper plenum remain unchanged. However, it rotates around the axis of hot legs with TYPE 2 and TYPE 3 upper plenums. Since the coolant tangential velocity in the hot legs with TYPE 3 upper plenum is the largest, the speed of temperature homogenization is the fastest of the three types of upper plenums.
5 Conclusions
In this paper, CFD models of three types of upper plenums in the current typical PWRs were established. The flow distributions at the core outlet and the upper plenum, and the temperature heterogeneity inside the hot legs with TYPE 1, TYPE 2, and TYPE 3 were obtained and analyzed. The main findings are listed as follows:
The flowrate difference at the core outlet with TYPE 1 upper plenum is the largest of the three types of upper plenum, but it is the smallest with TYPE 3 upper plenum. The CRGTs with large windows enhance the suction effect of the hot legs at the core outlet and enlarge the flowrate difference. However, the two-layer perforated barrels in upper plenum reduce the heterogeneity of flowrate difference at the core outlet. The flowrate distributes in a checkerboard pattern at the core outlet with TYPE 1 upper plenum, but it appears in an elliptical and circular pattern for TYPE 2 and TYPE 3 upper plenum respectively.
The distribution and development of tangential velocity inside the hot leg is highly dependent on the upper plenum internals. Although the tangential velocities at the initial cross section of the hot leg with different types upper plenums are in chaos, they develop in different ways. A pair of counter-rotating swirls develop inside the hot leg of TYPE 1 upper plenum, while a swirl rotating basically around hot leg axis generated inside that of TYPE 2 upper plenum and a pair of counter-rotating swirls revolves around the hot leg axis gradually form inside TYPE 3 hot leg.
Although the temperature distributions at the initial cross-section of the hot legs with the three types of upper plenums are similar, the high-temperature coolant occupies the upper part and low-temperature coolant takes the lower part of the hot leg, but their developments are determined by their unique transverse velocity. The coolant with different temperatures remains the same position as it is at the initial cross section of the hot legs with the TYPE 1 upper plenum, but the coolant revolves around the hot leg axis with the TYPE 2 and TYPE 3 upper plenums. The highest transverse velocity of TYPE 3 hog leg leads to the fastest temperature homogenization speed.