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Thermal stratification and mixing in a Nordic BWR pressure suppression pool
Annals of Nuclear Energy 132 (2019) 442–450
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Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Thermal stratification and mixing in a Nordic BWR pressure suppression pool Ignacio Gallego-Marcos ⇑, Dmitry Grishchenko, Pavel Kudinov Royal Institute of Technology (KTH), Division of Nuclear Engineering, Stockholm, Sweden
a r t i c l e
i n f o
Article history: Received 3 October 2018 Received in revised form 22 April 2019 Accepted 27 April 2019
Keywords: Sparger Relief vales Steam injection Condensation CFD Effective momentum
a b s t r a c t The pressure suppression pool of a Nordic Boiling Water Reactor (BWR) serves as a heat sink to condense steam from the primary coolant system in normal operation and accident conditions. Thermal stratification can develop in the pool when buoyancy forces overcome the momentum created by the steam injection. In this case, hot condensate forms a hot layer at the top of the pool, reducing the pool cooling and condensation capacity compared to mixed conditions. The Effective Heat Source and Effective Momentum Source (EHS/EMS) models were previously proposed to model the large-scale pool behavior during a steam injection. In this work, we use CFD code of ANSYS Fluent with the EHS/EMS models to simulate the transient behavior of a Nordic BWR pool during a steam injection through spargers. First, a validation against a Nordic BWR pool test with complete mixing is presented. Prediction of the pool behavior for other possible injection scenarios show that stratification can occur at prototypic steam injection conditions, and that the hot layer temperature above the injection point can be non-uniform. In cases with significant steam condensation inside the sparger pipes, the 95 °C pool temperature limit for the Emergency Core Cooling System (ECCS) pumps was reached 7 h after the beginning of the blowdown. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction The Pressure Suppression Pool (PSP) of a Boiling Water Reactor (BWR) is a large heat sink used to limit the containment pressure by condensing steam released form primary coolant system (Pershagen, 1994). In Loss-Of-Coolant Accident (LOCA) steam is injected through blowdown pipes, connected the drywell volume, while multi-hole spargers connected to the primary circuit are used in both normal operation and accidents. Depending on the steam injection conditions, buoyancy forces can overcome the momentum induced by the steam condensation and result in thermal stratification, i.e. accumulation of hot condensate in the upper layers of the pool. Having a thermally stratified pool is of a safety concern since larger pool surface temperature leads to higher containment pressures compared to completely mixed pool conditions. An example of such behavior can be found in the Fukushima Daiichi Unit 3 accident, during the operation of the Reactor Core Isolation Condenser (RCIC) (Mizokami et al., 2013, 2016). Based on a mixed pool assumption, lumped parameter codes underestimated the maximum pressure ⇑ Corresponding author. E-mail addresses: [email protected] (I. Gallego-Marcos), (D. Grishchenko), [email protected] (P. Kudinov). https://doi.org/10.1016/j.anucene.2019.04.054 0306-4549/Ó 2019 Elsevier Ltd. All rights reserved.
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by about 160 kPa, whereas assuming stratification led to a much better agreement (Pellegrini, 2016). The PSP is also a source of water for the Emergency Core Cooling System (ECCS) and containment spray. In case when the pool surface temperature reaches a certain threshold, operators are expected to stop the ECCS in order to avoid pump cavitation, even if electricity and coolant are available (Störningshandboken, 2003). A reliable safety analysis for the design and licensing purposes requires adequate predictive capabilities for modeling of thermal stratification and mixing induced by a steam injection. To enable such prediction, Li and Kudinov (2010) introduced the concepts of the Effective Heat Source (EHS) and Effective Momentum Source (EMS) models. The premise of these models is that the averaged heat and momentum sources induced by the steam condensation determine the large-scale pool circulation and temperature distribution. These sources can be added to any CFD-type code to predict the large scale pool circulation using a single-phase liquid solver. This approach improves the computational efficiency compared to modelling two-phase flow, which would be unaffordable for a long-term transient in a large-scale pool. EHS/EMS models have been developed and validated for blowdown pipe condensation regimes of chugging and complete condensation inside the pipe (Li et al., 2014a, 2014b, 2018; Villanueva et al., 2015; GallegoMarcos et al., 2018b), and for the oscillatory bubble regimes
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appearing in spargers (Gallego-Marcos et al., 2018a, 2019; Gallego, submitted). The goal of this work is to apply the developed models for the prediction of full-scale Nordic BWR PSP behavior during a steam injection through spargers. In this design, the spargers inject steam a few meters above the floor into an annular pool of about 8–10 m depth. Since this configuration can lead to stratification, the pool volume below the injection point is usually neglected in safety analysis calculations. In this paper we show that (i) the model predictions agree well with the results of a test carried out in the PSP of a Nordic BWR, where steam injected through a single sparger led to complete mixing of the pool in the vertical and azimuthal directions; and that (ii) stratification can develop at different (more prototypic) steam injection conditions with a larger number of spargers. Results of the analysis suggest that assuming a homogeneous temperature distribution in the hot layer above steam injection point is far from being a conservative assumption for determining pool top surface temperature. The simulation of the PSP is done using the CFD code of ANSYS Fluent 17.0 with the EHS/EMS developed in (Gallego-Marcos et al., 2019) and the effective momentum correlations proposed in (Gallego, submitted). Section 3 addresses the pool behavior when injecting through the spargers of the 311 system (used in the Nordic BWR test) and Section 4 of the 314 Automatic Depressurization System (ADS). In Section 5, a simple correlation is proposed to predict the steam mass fluxes which will lead to complete steam condensation inside the sparger pipe.
C ¼ 4:28 T 0:35
443
ð2Þ
where DT is the subcooling (saturation minus pool temperature). The sonic experiments performed in SEF were all done at a similar steam mass fluxes of 320 kg/(m2s). At these conditions, the C coefficient was not observed to be strongly dependent on the subcooling. Instead, it observed to remain relatively constant, suggesting a correlation of the type
C G¼320
kg=ðm2 sÞ
¼ 0:84
ð3Þ
It should be noted that Eqs. (2) and (3) are only strictly valid within the ranges where they were calibrated. 3. Spargers of the 311 system The 311 spargers are typically used during the start-up of the reactor to clear water from the main steam lines by blowing it into the pool. Their geometry is similar to the spargers used in the PPOOLEX and PANDA experiments (Gallego-Marcos et al., 2018a). Therefore, the models developed in (Gallego-Marcos et al., 2019) are expected to be applicable. Similarities are the chamfered injection holes of 10 mm diameter, the pitch to diameter ratio of 5 in the vertical direction, and the area ratio between sparger pipe and injection hole area of 0.38. The differences are the total number of holes: 9 rings with 7 holes in the BWR and 4 rings with 8 holes in PPOOLEX and PANDA. 3.1. Modeling of the Nordic BWR pool test
2. Effective momentum sources The EMS was measured in the Separate Effect Facility (SEF) for a wide range of prototypic steam injection conditions of a Nordic BWR sparger (Gallego, submitted). Empirical correlations for the effective momentum source Meff were developed based on
M eff ¼ C qs Ai U 2s
ð1Þ
where qs is the steam density (function of the steam temperature and hydro-static pressure of the pool at the injection holes level), Ai the total injection hole area, U s the steam velocity at the injection holes and C a non-dimensional coefficient, which represents the effect of the condensation regime. In sub-sonic regimes (steam mass flux GK300 kg/(m2s)) the C coefficient was obtained in (Gallego, submitted) as
The test performed in a Nordic BWR was done by injecting steam through a single sparger of the 311 system. The data measured during the transient was the steam temperature inside the sparger T 0 , which varied between 200 and 250 °C, and the total _ s , which was maintained constant at 3.5 kg/s. mass flow rate m These conditions lead to a sonic flow with a mass flux of about 800 kg/(m2s). Thus, Eqs. (1) and (3) were used to determine the effective momentum (Gallegos submitted). The case setup for the CFD model used to simulate the PSP transient was the same as presented in (Gallego-Marcos et al., 2019). That is, single-phase RANS approach using the k-Omega BSL model with modified buoyancy term. The effective heat and momentum boundary conditions were also assumed to be non-homogeneous, with a jet profile given by an expansion coefficient K = 40 and a downwards injection angle a = 10° (Gallego-Marcos et al., 2018a,
Fig. 1. Mesh used for the BWR PSP transient, (a) over-view and (b) detail of the sparger mesh and the non-conformal transition to the rest of the pool.
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Fig. 2. Geometry of the 314 and 311 spargers and location of the equivalent heat and momentum sources added to the CFD simulations: ( ) heat sources due to steam condensation inside the pipe and ( ) heat and momentum sources due to steam condensation at the injection holes. Sizes of the source regions are in millimeters. The values of 384 mm and 336 mm in the 314 and 311 sparger, respectively, are the vertical length covered by the injection holes. Note that in the CFD simulations the sparger is represented with a wall and the sources are placed in the liquid pool (i.e. flow inside the sparger is not modelled).
2019) (Fig. 2). The sources were added with User Defined Functions (UDF). Additional turbulence sources that can be induced by steam condensation were not modeled in the condensation region. An over-view of the PSP geometry is presented in Fig. 1a. The total water volume is about 3300 m3 and the pool depth 9.8 m. The 4.3 m tall tunnel for access to the lower drywell (central cylindrical volume in Fig. 1a) was included in the model in order to assess if it can affect the development of thermal stratification. The sparger was located at about 140° from the tunnel, submerged 6.9 m into the pool (2.9 m above the pool bottom) at 600 mm distance from the outer wall. The size of the EHS/EMS region was estimated by maintaining the ratio of the vertical length covered by the injection holes to the EMS region height, estimated to be 2.6 in the PANDA experiments (see Figs. 13 and 15 in GallegoMarcos et al., 2018a) and the CFD simulations from (GallegoMarcos et al., 2019). Based on this ratio, the condensation region height of the 311 sparger becomes 135 mm (Fig. 2). In the radial direction, the sources were applied over a 40 mm distance, similar to what was used in the CFD simulations presented in (GallegoMarcos et al., 2019). The mesh dimensions were determined by the mesh sensitivity study done in (Gallego-Marcos et al., 2019). The vertical cell size below the sparger was kept to 25 mm to capture the sharp temperature gradients across the thermocline. The number of cells in the azimuthal direction of the sparger was set to 128 to minimize the diffusion of the sparger jets. The mesh was done independently for two separate volumes: a 1.2 1.2 9.8 m volume around the sparger and another one for the rest of the pool. The interfaces between these two volumes were non-conformal, allowing a
reduction of the number of cells in the azimuthal direction as shown in (Fig. 1b). The non-conformal interfaces were treated with the Matching option, which corresponds to completely overlapping faces. To reduce interpolation errors, the grid lines in the vertical direction were kept at the same level in both volumes. Nonconformal was preferred over a tetra-mesh transition since the quality of the tetra elements was too low and expected to induce larger errors than the interpolation. Comparison between the Nordic BWR test and simulation is presented in Fig. 3a. Good agreement was obtained in terms of mean temperature and mixed conditions above 4.3 m. In the test, the lowest TC measuring the PSP temperature was located 4.3 m above the floor. Therefore, it was unclear whether the bottom part of the pool was colder. The simulations showed that, below this level, only minor stratification develops in the KD sector, which is the region close to the lower drywell tunnel (Fig. 3b). The experimental data suggests a larger temperature differences at the KD sector (see line at 8.3 m in Fig. 3a). However, it is difficult to assess such differences with only one measurement point, especially since the uncertainty of the measurement was not available. Based on these results, we can conclude that a large enough single-source of momentum can induce mixing of the PSP. The PPOOLEX and PANDA experiments with sparger used to validate the EHS/EMS models were all designed with alternating stratification and mixing phases (Gallego-Marcos et al., 2018a, 2019). This enabled an efficient validation since parameters such as the thermocline location or erosion velocity could be closely compared. The complete mixing transient of the Nordic BWR test prevents such comparisons. Moreover, a complete mixing transient
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Fig. 3. Pool temperature evolution (a) measured in the Nordic BWR test (—) and obtained with Fluent (▬) and (b) temperature profile obtained with Fluent at different sectors and elevations of the PSP.
can be well predicted using any momentum above a certain level. For these reasons, the validation presented in this work can only be considered preliminary. Further validations against plant tests involving stratification and mixing phases should be done as such data becomes available. 3.2. Pool behavior at lower flow rates We now assume a steam injection of 0.3 kg/s through the same sparger as the one used in the PSP test. This leads to a sub-sonic steam mass flux of 70 kg/(m2s) for which Eqs. (1) and (2) were used to determine the effective momentum (Gallego, submitted). It should be noted that no plant data was available at these conditions. Thus, the results presented in this section are only the CFD predictions. The pool behavior obtained with these conditions led to thermal stratification (Fig. 4). However, since the lowest thermocouples at the PSP are located 4.3 m above the floor, the operator would not notice development of the cold layer located at about 2 m. These results suggest that adding more thermocouples in the PSP would be important for adequate diagnostics of the pool state for operator’s decisions. Once the steam injection started, the side of the pool opposite to the sparger began to show significant temperature increases after about 30 min (see sectors KA and KD in Fig. 4b). After this time, temperature differences in the azimuthal direction were observed to be very small (Fig. 5). The transport of heat from the
(a)
sparger vicinity to the rest of the pool is caused by buoyancy forces, which tend to align the hot layer perpendicular to the gravity vector. Hot liquid rising from the sparger was first spread along the top of the pool and then propagated down until the level of stratification reached at the sparger vicinity. Some of the simulations of Fukushima Daiichi Unit 3 presented in (Pellegrini, 2016) were performed with a suppression pool subdivided only in the azimuthal direction. The results presented in this work show that vertical stratification has a larger effect on the long-term pool temperature evolution than the small temperature differences in the azimuthal direction. Thus, it is suggested to include vertical sub-divisions.
4. Spargers of the 314 system In this section, we consider more prototypic steam injection conditions with multiple spargers of the 314 system and demonstrate that thermal stratification can develop in the pool. The spargers of the ADS (314) system are used to control the reactor vessel pressure. There are a total of 64 sparger pipes of DN 150 mm, each with an injection hole area about 3 times larger than the ones in the 311 system. The 314 spargers have an upper ring of downward facing holes, known as the Load Reduction Ring (LRR), and radially outwards holes at the sparger head (Fig. 2). The LRR is located about 2.5 m above the sparger bottom. The steam injection is controlled with 16 relief vales located at the main steam
(b)
Fig. 4. Pool temperature evolution predicted with Fluent during a 0.3 kg/s steam injection through a single 311 sparger. (a) Locations where TCs are located in the PSP and (b) at different sectors and elevations of the PSP.
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Fig. 5. Pool temperature field at t = 14 h obtained in the simulation with 0.3 kg/s steam injection through a single 311 sparger. The vertical lines denote the location of the TC measurements found in the plant, which are located at 8.3 and 4.3 m.
lines, each one feeding 4 spargers. Thus, the minimum number of spargers through which steam can be injected is 4. The simulations were run assuming 3.5 and 9 kg/s steam injection through different numbers of the 314 spargers. The 3.5 kg/s flow rate was selected to show the effect of sparger geometry by comparing to the plant test from Section 3. The flow rate of 9 kg/s represents the core decay heat that can be expected 6 h after reactor shutdown (assuming ANS 5.1 decay heat curve for a 3000 MWth reactor after 4 years of operation). Since the temperature differences in the azimuthal direction were observed to be very small in the simulation from Section 3.2, symmetry boundary conditions were used to reduce the computational domain. That is, a 11.25° slice for 64 spargers, 45° for 16, and 180° for 4 (Fig. 6). The flow distribution between the LRR and sparger head was estimated using GOTHIC code (GOTHIC Thermal Hydraulic Analysis Package, 2014) and assuming a constant pool temperature of 15 °C (Table 1). We can see that, for a given steam flow rate, increasing the number of spargers leads to more steam condensation inside the sparger pipes. This is due to the larger surface area available for condensation. The pool temperature of 15 °C used in the GOTHIC simulations provides conservative results in terms of thermal stratification development, which is the purpose of analysis in this paper. As the transient progresses and the temperature in the pool increases, the condensation inside the pipe and flow distribution between the LRR and sparger head can change. There-
Fig. 6. Mesh used in the Fluent simulations of a steam injection through the 314 spargers. Non-conformal mesh was used at the boundary between the two sparger volumes and the rest of the pool. The cell sizes in the sparger volumes are the same as the one presented in Fig. 1b. Only difference is that the vertical cell size was kept to 25 mm in all the pool, not only below the sparger injection point.
fore, further development of the EHS/EMS models should be focused on the development of a simplified (1D) model to predict the heat and flow distribution during run-time based on the pool temperature distribution. The effective momentum induced by the steam condensation was estimated with Eqs. (1) and (2) (Gallego, submitted). These sub-sonic correlations were calibrated for the condensation regimes between 70 and 175 kg/(m2s). Application of (1) and (2) to lower steam mass fluxes is an extrapolation, which can over or underestimate the resulting momentum. For instance, there is a possibility that chugging can develop at steam mass fluxes lower than about 70 kg/(m2s). Further separate effect experimental studies would be needed for development and validation of the models in all relevant to plant conditions regimes. 4.1. Simulation results The results obtained injecting 3.5 kg/s of steam are presented in Figs. 7and 9. In the case with 64 spargers all steam was condensed inside the sparger pipes. The uniform heat distribution along the topmost 2.9 m of submerged pipe wall led to a temperature gradient in the hot layer. A similar profile was observed in the low steam injection phases of the PPOOLEX experiments with blowdown pipe (Li et al., 2014a). This gradient led to rapidly increasing pool surface temperatures, which reached 95 °C in 7.7 h. At this point operator would be instructed to shutdown the ECCS. The
Table 1 Flow distribution through the 314 spargers when injecting a total steam flow rate of 3.5 and 9.0 kg/s into a 15 °C water pool. Simulation results obtained with GOTHIC. # spargers
Steam condensation inside pipe
LRR
Sparger head
Steam flow [kg/s]
Steam flux [kg/(m2s)]
Steam flow [kg/s]
Steam flux [kg/(m2s)]
Total steam flow rate = 3.5 kg/s 64 100% 16 44% 4 15.5%
0 1.96 2.10
0 38 165
0 0 0.86
0 0 19
Total steam flow rate = 9.0 kg/s 64 67% 16 23% 4 3.1%
3.00 4.88 2.63
15 96 207
0 2.01 6.06
0 11 134
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Fig. 7. Pool temperature fields 6 h after the beginning of a steam injection of 3.5 kg/s through (a) 64 (b) 16 and (c) 4 spargers of the 314 system.
injection through 16 spargers allowed a fraction of the steam to be pushed through the LRR holes. The stronger circulation induced by the LRR led to more homogeneous temperature distribution in the hot layer, reducing substantially the pool surface temperature compared to the 64 case. In the 4 sparger case steam was injected through the LRR and sparger head. Pool mixing was achieved through a strong downwards flow pattern induced by the LRR jets. The results obtained with 9 kg/s of steam are presented in Figs. 8 and 10. The observed thermal stratification suggests that the increased momentum source at larger steam mass flows was not sufficient to overcome the buoyance force creased by the heat source. In the case with 64 spargers, a significant amount of heat was released at the LRR outlet, resulting in a more uniform temperature distribution compared to the case with all steam condensing inside the pipe (Fig. 7a). The ECCS shutdown temperature limit was reached after 6.7 h. In the case with 16 spargers the LRR jets were initially able to reach the bottom of the pool. However, as the transient progressed, buoyancy forces reduced the jet penetration depth, which resulted in formation of a cold layer with larger temperature than the initial 15 °C. The case with 4 spargers led to pool mixing. Here the momentum at the sparger head was larger than in
447
Fig. 8. Pool temperature fields 6 h after the beginning of a steam injection of 9 kg/s through (a) 64 (b) 16 and (c) 4 spargers of the 314 system.
the case with 3.5 kg/s and 4 spargers. Still, mixing was achieved with the same downwards flow induced by the LRR. These results suggest that the orientation of the sparger head holes reduces the effectiveness of mixing since certain injection conditions could deflect the downwards LRR flow radially when reaching the sparger head, preventing it from reaching the pool bottom. 4.2. Discussion The presented results suggest that thermal stratification development cannot be excluded in prototypic plant conditions. To some extent, operators can enhance pool mixing by closing some of the spargers. However, a more robust solution would be changing the sparger design to increase the ratio between integral momentum and heat sources created by the steam injection. Accidents such as Station Black Out (SBO) are expected to be the most likely to present thermal stratification. In design basis accidents such as LOCA the pool could be mixed through the recirculation pumps and strainers of the Residual Heat Removal System (RHR). However, in most BWR designs the RHR system was not specifically designed to mix the pool. Its mixing capability depends
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Fig. 9. Evolution of the pool surface temperature and vertical temperature profiles during a steam injection of 3.5 kg/s through the 314 spargers. Data taken at the center of the domain.
on the location of the pumps and strainers, liquid momentum induced by these, strength of pool stratification, etc. (Puustinen et al., 2010). For example, in some Nordic BWRs the RHR pumps and strainers are all located a few meters above the pool bottom (between 2 and 7 m, depending on the design (Störningshandboken, 2003). This increases the probability of developing a cold layer below them due to the absence of momentum sources in this region.
The results presented in Section 4 show that the case with complete steam condensation inside the sparger pipe leads to much stronger stratification and larger pool surface temperatures compared to the cases with steam injection through sparger holes. The conditions leading to this regime can be computed with most thermal hydraulic codes. Nevertheless, we propose a simple correlation that can be used for an efficient estimation of such conditions. The total heat transfer between the steam inside the pipe and the water of the pool can be computed with
DT 1 lnðr o =ri Þ 1 þ þ Ao h o 2pls k Ai hi
Q 2 hfg p4d
ð5Þ
obtained by equating the injected steam flow rate and the condensed steam flow rate Q =hfg . The outer heat transfer coefficient ho can be computed using the correlation for free convection on a vertical plate (Churchill and Chu, 1975);
0
5. Steam condensation inside the sparger pipe
Q¼
Gmax ¼
12
kL B 0:387Ra1=6 C L ho ¼ @0:825 þ 8=27 A ls 9=16 1 þ ð0:492=PrL Þ
valid for vertical cylinders with D=L > 35=Gr1=4 L . This is a conservative assumption since nucleate boiling could also occur at the outer pipe surface. Inside the cylinder, two-phase heat transfer coefficients caused by a turbulent condensate film can be calculated with Eq. (7) when the steam velocity is low enough to make shear effects between steam and liquid unimportant (Incropera and DeWitt, 1996).
ð4Þ
where h is the heat transfer coefficient, A the area, ls the pipe submergence depth, DT the steam minus liquid temperature, and sub-indices o and i the outer and inner sides of the sparger pipe, respectively. The maximum steam mass that can be completely condensed inside the pipe can be computed with
ð6Þ
hi
m
1=3 2 L =g kL
! ¼
8 1:47 > > > > > Re 1=3 > < d
Red 6 30
Red 30 < Red 6 1800 > > 1:09Re1:22 5:2 > > > Re > d : Red > 1800 8750 þ 58Pr0:5 Re0:75 253 L d ð7Þ
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449
Fig. 10. Evolution of the pool surface temperature and vertical temperature profiles during a steam injection of 9 kg/s through the 314 spargers. Data taken at the center of the domain.
The Reynolds number in Eq. (7) is related to the flow rate of _ dL . We will estimate it assuming that condensed liquid in the film m all the steam condenses inside the pipe
2 _ dL 4G pd =4 4m Gd Red ¼ ¼ lL pd lL pd lL
ð8Þ
Solutions of Eqs. (4) to (8) for prototypic ranges of submergence depth ls , liquid temperature T L , steam temperature T S , and pipe diameter d are presented in Fig. 11. The limiting factor for the heat transfer was observed to be the heat convection at the pool side, giving Q ho Ao DT. Assuming constant water properties and neglecting the 0.825 factor in Eq. (6) gives Q / dls DT ðT w T L Þ1=3 . The pipe wall temperature on the liquid side T w requires a few iterand ations while solving Eqs. (4)–(8). Assuming ðT w T L Þ1=3 T 1=2 L adding the resulting Q to Eq. (5) gives a linear relation with Gmax which can be fitted by Eq. (9) and is compared to the full model predictions in Fig. 11.
Gmax 1:7 104
pffiffiffiffiffi ls DT T L d
ð9Þ
Respectively, for a given steam mass flux, the minimum pipe length lmin needed to completely condense the steam is
lmin
Gd 4
1:7 10
pffiffiffiffiffi T TL
ð10Þ
The analytical estimate proposed for Gmax is quite rough. However, it enables a quick assessment of the validity of different assumptions regarding pool mixing or stratification. For example,
Fig. 11. Maximum steam mass flux that can be condensed inside the pipe ( model, Eqs. (4)–(8) and ( ) Eq. (9).
) full
application of Eq. (9) to the 64 sparger and 3.5 kg/s case from Table 1 gives a Gmax = 3.9 kg/(m2s). The injection conditions of 3.5 kg/s through 64 spargers of 150 mm diameter give a
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G = 3.1 kg/(m2s), showing that significant condensation inside the pipe can be expected (i.e. large pool surface temperatures). Eq. (9) should be further validated against experimental data obtained at prototypic sparger injection conditions. 6. Conclusions The pressure suppression pool behavior in a BWR has been simulated using CFD and previously developed EHS/EMS models for a steam injection through spargers. The modeling approach was validated against a full scale pool test data in a Nordic BWR. Then, the pool behavior was predicted for different (more prototypic) steam flow rates and number of active spargers. Development of thermal stratification was observed at such conditions. Specific conclusions and recommendations are summarized below. The assumption that the pool temperature is homogeneously distributed above the injection holes is not conservative. Complete condensation inside the pipe can lead to much larger pool surface temperatures due to the development of a temperature gradient in the hot layer. As an example, injection of 3.5 kg/s and 9 kg/s through 64 spargers leads to complete condensation, reaching the 95 °C limit about 7.7 and 6.7 h respectively after the initiation of the steam injection. The downward injection of the Load Reduction Ring (LRR), originally designed to reduce loads on piping structures at the beginning of the blowdown, is effective in promoting mixing of the pool. The radial injection at the sparger head can deflect the downward flow created by LRR and thus decrease the mixing effectiveness. The spatial resolution of temperature measurements in the pool might be insufficient for the correct interpretation of pool mixing/stratified state by the operator. At least one TC located close to the pool bottom would be useful for operators. A combination of design optimization and changes in operator actions (such as decreasing number of open spargers) can help in providing pool mixing. No significant temperature differences are observed in the azimuthal direction of the annular pool, even when injecting steam through a single sparger at low steam mass fluxes. This would enable reducing the number of TCs in the pool required to address its condition. Assumptions of azimuthal stratification are not recommended for modeling in system/thermal–hydraulic codes. A single correlation to estimate the minimum steam mass flux needed to avoid complete condensation inside the pipe is proposed. This can be used to (i) assess the validity of different assumptions on the pool behavior and to (ii) determine the number of safety relief values that the operator should open when discharging steam into the pool. Further development of the computational tools would require separate effect experiments performed with the LRR, and integral experiments combining the LRR and sparger head. The effective momentum should be further measured at steam mass fluxes below 70 kg/(m2s), where chugging might develop. Although this regime increases structural loads, it could promote mixing, as observed in previous experiments with blowdown pipes. Acknowledgements The authors are grateful to Maria Agrell, Anna Ryman and Oddbjörn Sandervåg from the Swedish Radiation Safety Authority
(Strålsäkerhetsmyndigheten, SSM) for the discussions and to SSM for financial support for this project. We would also like to thank Berth Arbman from Oskarshamns KraftGrupp (OKG) for his comments and information on the Nordic BWR test with sparger and Walter Villanueva from KTH Royal Institute of Technology for the discussions on the simulation results. The simulations were performed on resources provided by the Swedish National Infrastructure for Computing (SNIC) at PDC Centre for High Performance Computing (PDC-HPC). The authors are grateful to the PDC-HPC staff for assistance concerning the implementation aspects in making the code run on the PDC-HPC resources. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.anucene.2019.04.054. References Churchill, S.W., Chu, H.H.S., 1975. Correlating equations for laminar and turbulent free convection from a vertical plate. Int. J. Heat Mass Transfer 18, 1323–1329. Gallego-Marcos, I., Kudinov, P., Villanueva, W., Puustinen, M., Räsänen, A., Tielinen, K., Kotro, E. Effective momentum induced by steam condensation in the oscillatory bubble regime. Submitted to Nucl. Eng. Des. Gallego-Marcos, I., Kudinov, P., Villanueva, W., Kapulla, R., Paranjape, S., Paladino, D., Laine, J., Puustinen, M., Räsänen, A., 2018a. Pool stratification and mixing during a steam injection through spargers. Part 1: analysis of the PPOOLEX and PANDA experiments. Nucl. Eng. Des. 337, 300–316. Gallego-Marcos, I., Villanueva, W., Kudinov, P., 2018b. Modelling of pool stratification and mixing induced by steam injection through blowdown pipes. Ann. Nucl. Energy 112, 624–639. Gallego-Marcos, I., Kudinov, P., Villanueva, W., Kapulla, R., Paranjape, S., Paladino, D., Laine, J., Puustinen, M., Räsänen, A., 2019. Pool Stratification and Mixing Induced by Steam Injection through Spargers: CFD modelling of the PPOOLEX and PANDA experiments. Nucl. Eng. Des. 347, 67–85. GOTHIC Thermal Hydraulic Analysis Package, Version 8.1(QA). EPRI, Palo Alto, CA: 2014. Incropera, F.P., DeWitt, D.P., 1996. Fundamentals of heat and mass transfer. John Wiley & Sons. Section, p. 10.8.. Li, H., Kudinov, P., 2010. Effective Approaches to Simulation of Thermal Stratification and Mixing in a Pressure Suppression Pool. OECD/NEA & IAEA Workshop CFD4NRS-3, Bethesda, MD, USA, September 14–16, 2010. Li, H., Villanueva, W., Kudinov, P., 2014a. Approach and development of effective models for simulation of thermal stratification and mixing induced by steam injection into a large pool of water. Sci. Technol. Nucl. Install. Article ID 108782. Li, H., Villanueva, W., Puustinen, M., Laine, J., Kudinov, P., 2014b. Validation of effective models for simulation of thermal stratification and mixing induced by steam injection into a large pool of water. Sci. Technol. Nucl. Install. Article ID 752597. Li, H., Villanueva, W., Puustinen, M., Laine, J., Kudinov, P., 2018. Thermal stratification and mixing in a suppression pool induced by direct steam injection. Ann. Nucl. Energy 111, 487–498. Mizokami, S., Yamanaka, Y., Watanabe, M., Honda, T., 2013. State of the art MAAP analysis and future improvements on TEPCO Fukushima-Daiichi NPP accident. Proceedings of 15th international conference on Nuclear Reactor ThermalHydraulics (NURETH-15). Pisa, Italy, paper 536. Mizokami, S., Yamada, D., Honda, T., Yamauchi, D., Yamanaka, Y., 2016. Unsolved issues related to thermal-hydraulics in the suppression chamber during Fukushima Daiichi accident progressions. J. Nucl. Sci. Technol. 53 (5), 630–638. Pellegrini, M. et al., 2016. Benchmark study of the accident at the Fukushima Daiichi NPS: best-estimate case comparison. Nucl. Technol. 196 (2), 198–210. Pershagen, B., 1994. Light Water Reactor Safety. Pergamon Press. Section 8.1. Puustinen, M., Laine, J., Räsänen, A., Kotro, E., 2010. Mixing tests with an RHR nozzle in PPOOLEX. Nordic Nucl. Saf. Res., NKS-383 Störningshandboken BWR, 2003. SKI Rapport 03:02 (In Swedish). Statens Kärnkraftinspektion. Villanueva, W., Li, H., Puustinen, M., Kudinov, P., 2015. Generalization of experimental data on amplitude and frequency of oscillations induced by steam injection into a subcooled pool. Nucl. Eng. Des. 295, 155–161.
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Thermal stratification and mixing in a Nordic BWR pressure suppression pool Ignacio Gallego-Marcos ⇑, Dmitry Grishchenko, Pavel Kudinov Royal Institute of Technology (KTH), Division of Nuclear Engineering, Stockholm, Sweden
a r t i c l e
i n f o
Article history: Received 3 October 2018 Received in revised form 22 April 2019 Accepted 27 April 2019
Keywords: Sparger Relief vales Steam injection Condensation CFD Effective momentum
a b s t r a c t The pressure suppression pool of a Nordic Boiling Water Reactor (BWR) serves as a heat sink to condense steam from the primary coolant system in normal operation and accident conditions. Thermal stratification can develop in the pool when buoyancy forces overcome the momentum created by the steam injection. In this case, hot condensate forms a hot layer at the top of the pool, reducing the pool cooling and condensation capacity compared to mixed conditions. The Effective Heat Source and Effective Momentum Source (EHS/EMS) models were previously proposed to model the large-scale pool behavior during a steam injection. In this work, we use CFD code of ANSYS Fluent with the EHS/EMS models to simulate the transient behavior of a Nordic BWR pool during a steam injection through spargers. First, a validation against a Nordic BWR pool test with complete mixing is presented. Prediction of the pool behavior for other possible injection scenarios show that stratification can occur at prototypic steam injection conditions, and that the hot layer temperature above the injection point can be non-uniform. In cases with significant steam condensation inside the sparger pipes, the 95 °C pool temperature limit for the Emergency Core Cooling System (ECCS) pumps was reached 7 h after the beginning of the blowdown. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction The Pressure Suppression Pool (PSP) of a Boiling Water Reactor (BWR) is a large heat sink used to limit the containment pressure by condensing steam released form primary coolant system (Pershagen, 1994). In Loss-Of-Coolant Accident (LOCA) steam is injected through blowdown pipes, connected the drywell volume, while multi-hole spargers connected to the primary circuit are used in both normal operation and accidents. Depending on the steam injection conditions, buoyancy forces can overcome the momentum induced by the steam condensation and result in thermal stratification, i.e. accumulation of hot condensate in the upper layers of the pool. Having a thermally stratified pool is of a safety concern since larger pool surface temperature leads to higher containment pressures compared to completely mixed pool conditions. An example of such behavior can be found in the Fukushima Daiichi Unit 3 accident, during the operation of the Reactor Core Isolation Condenser (RCIC) (Mizokami et al., 2013, 2016). Based on a mixed pool assumption, lumped parameter codes underestimated the maximum pressure ⇑ Corresponding author. E-mail addresses: [email protected] (I. Gallego-Marcos), (D. Grishchenko), [email protected] (P. Kudinov). https://doi.org/10.1016/j.anucene.2019.04.054 0306-4549/Ó 2019 Elsevier Ltd. All rights reserved.
[email protected]
by about 160 kPa, whereas assuming stratification led to a much better agreement (Pellegrini, 2016). The PSP is also a source of water for the Emergency Core Cooling System (ECCS) and containment spray. In case when the pool surface temperature reaches a certain threshold, operators are expected to stop the ECCS in order to avoid pump cavitation, even if electricity and coolant are available (Störningshandboken, 2003). A reliable safety analysis for the design and licensing purposes requires adequate predictive capabilities for modeling of thermal stratification and mixing induced by a steam injection. To enable such prediction, Li and Kudinov (2010) introduced the concepts of the Effective Heat Source (EHS) and Effective Momentum Source (EMS) models. The premise of these models is that the averaged heat and momentum sources induced by the steam condensation determine the large-scale pool circulation and temperature distribution. These sources can be added to any CFD-type code to predict the large scale pool circulation using a single-phase liquid solver. This approach improves the computational efficiency compared to modelling two-phase flow, which would be unaffordable for a long-term transient in a large-scale pool. EHS/EMS models have been developed and validated for blowdown pipe condensation regimes of chugging and complete condensation inside the pipe (Li et al., 2014a, 2014b, 2018; Villanueva et al., 2015; GallegoMarcos et al., 2018b), and for the oscillatory bubble regimes
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appearing in spargers (Gallego-Marcos et al., 2018a, 2019; Gallego, submitted). The goal of this work is to apply the developed models for the prediction of full-scale Nordic BWR PSP behavior during a steam injection through spargers. In this design, the spargers inject steam a few meters above the floor into an annular pool of about 8–10 m depth. Since this configuration can lead to stratification, the pool volume below the injection point is usually neglected in safety analysis calculations. In this paper we show that (i) the model predictions agree well with the results of a test carried out in the PSP of a Nordic BWR, where steam injected through a single sparger led to complete mixing of the pool in the vertical and azimuthal directions; and that (ii) stratification can develop at different (more prototypic) steam injection conditions with a larger number of spargers. Results of the analysis suggest that assuming a homogeneous temperature distribution in the hot layer above steam injection point is far from being a conservative assumption for determining pool top surface temperature. The simulation of the PSP is done using the CFD code of ANSYS Fluent 17.0 with the EHS/EMS developed in (Gallego-Marcos et al., 2019) and the effective momentum correlations proposed in (Gallego, submitted). Section 3 addresses the pool behavior when injecting through the spargers of the 311 system (used in the Nordic BWR test) and Section 4 of the 314 Automatic Depressurization System (ADS). In Section 5, a simple correlation is proposed to predict the steam mass fluxes which will lead to complete steam condensation inside the sparger pipe.
C ¼ 4:28 T 0:35
443
ð2Þ
where DT is the subcooling (saturation minus pool temperature). The sonic experiments performed in SEF were all done at a similar steam mass fluxes of 320 kg/(m2s). At these conditions, the C coefficient was not observed to be strongly dependent on the subcooling. Instead, it observed to remain relatively constant, suggesting a correlation of the type
C G¼320
kg=ðm2 sÞ
¼ 0:84
ð3Þ
It should be noted that Eqs. (2) and (3) are only strictly valid within the ranges where they were calibrated. 3. Spargers of the 311 system The 311 spargers are typically used during the start-up of the reactor to clear water from the main steam lines by blowing it into the pool. Their geometry is similar to the spargers used in the PPOOLEX and PANDA experiments (Gallego-Marcos et al., 2018a). Therefore, the models developed in (Gallego-Marcos et al., 2019) are expected to be applicable. Similarities are the chamfered injection holes of 10 mm diameter, the pitch to diameter ratio of 5 in the vertical direction, and the area ratio between sparger pipe and injection hole area of 0.38. The differences are the total number of holes: 9 rings with 7 holes in the BWR and 4 rings with 8 holes in PPOOLEX and PANDA. 3.1. Modeling of the Nordic BWR pool test
2. Effective momentum sources The EMS was measured in the Separate Effect Facility (SEF) for a wide range of prototypic steam injection conditions of a Nordic BWR sparger (Gallego, submitted). Empirical correlations for the effective momentum source Meff were developed based on
M eff ¼ C qs Ai U 2s
ð1Þ
where qs is the steam density (function of the steam temperature and hydro-static pressure of the pool at the injection holes level), Ai the total injection hole area, U s the steam velocity at the injection holes and C a non-dimensional coefficient, which represents the effect of the condensation regime. In sub-sonic regimes (steam mass flux GK300 kg/(m2s)) the C coefficient was obtained in (Gallego, submitted) as
The test performed in a Nordic BWR was done by injecting steam through a single sparger of the 311 system. The data measured during the transient was the steam temperature inside the sparger T 0 , which varied between 200 and 250 °C, and the total _ s , which was maintained constant at 3.5 kg/s. mass flow rate m These conditions lead to a sonic flow with a mass flux of about 800 kg/(m2s). Thus, Eqs. (1) and (3) were used to determine the effective momentum (Gallegos submitted). The case setup for the CFD model used to simulate the PSP transient was the same as presented in (Gallego-Marcos et al., 2019). That is, single-phase RANS approach using the k-Omega BSL model with modified buoyancy term. The effective heat and momentum boundary conditions were also assumed to be non-homogeneous, with a jet profile given by an expansion coefficient K = 40 and a downwards injection angle a = 10° (Gallego-Marcos et al., 2018a,
Fig. 1. Mesh used for the BWR PSP transient, (a) over-view and (b) detail of the sparger mesh and the non-conformal transition to the rest of the pool.
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Fig. 2. Geometry of the 314 and 311 spargers and location of the equivalent heat and momentum sources added to the CFD simulations: ( ) heat sources due to steam condensation inside the pipe and ( ) heat and momentum sources due to steam condensation at the injection holes. Sizes of the source regions are in millimeters. The values of 384 mm and 336 mm in the 314 and 311 sparger, respectively, are the vertical length covered by the injection holes. Note that in the CFD simulations the sparger is represented with a wall and the sources are placed in the liquid pool (i.e. flow inside the sparger is not modelled).
2019) (Fig. 2). The sources were added with User Defined Functions (UDF). Additional turbulence sources that can be induced by steam condensation were not modeled in the condensation region. An over-view of the PSP geometry is presented in Fig. 1a. The total water volume is about 3300 m3 and the pool depth 9.8 m. The 4.3 m tall tunnel for access to the lower drywell (central cylindrical volume in Fig. 1a) was included in the model in order to assess if it can affect the development of thermal stratification. The sparger was located at about 140° from the tunnel, submerged 6.9 m into the pool (2.9 m above the pool bottom) at 600 mm distance from the outer wall. The size of the EHS/EMS region was estimated by maintaining the ratio of the vertical length covered by the injection holes to the EMS region height, estimated to be 2.6 in the PANDA experiments (see Figs. 13 and 15 in GallegoMarcos et al., 2018a) and the CFD simulations from (GallegoMarcos et al., 2019). Based on this ratio, the condensation region height of the 311 sparger becomes 135 mm (Fig. 2). In the radial direction, the sources were applied over a 40 mm distance, similar to what was used in the CFD simulations presented in (GallegoMarcos et al., 2019). The mesh dimensions were determined by the mesh sensitivity study done in (Gallego-Marcos et al., 2019). The vertical cell size below the sparger was kept to 25 mm to capture the sharp temperature gradients across the thermocline. The number of cells in the azimuthal direction of the sparger was set to 128 to minimize the diffusion of the sparger jets. The mesh was done independently for two separate volumes: a 1.2 1.2 9.8 m volume around the sparger and another one for the rest of the pool. The interfaces between these two volumes were non-conformal, allowing a
reduction of the number of cells in the azimuthal direction as shown in (Fig. 1b). The non-conformal interfaces were treated with the Matching option, which corresponds to completely overlapping faces. To reduce interpolation errors, the grid lines in the vertical direction were kept at the same level in both volumes. Nonconformal was preferred over a tetra-mesh transition since the quality of the tetra elements was too low and expected to induce larger errors than the interpolation. Comparison between the Nordic BWR test and simulation is presented in Fig. 3a. Good agreement was obtained in terms of mean temperature and mixed conditions above 4.3 m. In the test, the lowest TC measuring the PSP temperature was located 4.3 m above the floor. Therefore, it was unclear whether the bottom part of the pool was colder. The simulations showed that, below this level, only minor stratification develops in the KD sector, which is the region close to the lower drywell tunnel (Fig. 3b). The experimental data suggests a larger temperature differences at the KD sector (see line at 8.3 m in Fig. 3a). However, it is difficult to assess such differences with only one measurement point, especially since the uncertainty of the measurement was not available. Based on these results, we can conclude that a large enough single-source of momentum can induce mixing of the PSP. The PPOOLEX and PANDA experiments with sparger used to validate the EHS/EMS models were all designed with alternating stratification and mixing phases (Gallego-Marcos et al., 2018a, 2019). This enabled an efficient validation since parameters such as the thermocline location or erosion velocity could be closely compared. The complete mixing transient of the Nordic BWR test prevents such comparisons. Moreover, a complete mixing transient
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445
Fig. 3. Pool temperature evolution (a) measured in the Nordic BWR test (—) and obtained with Fluent (▬) and (b) temperature profile obtained with Fluent at different sectors and elevations of the PSP.
can be well predicted using any momentum above a certain level. For these reasons, the validation presented in this work can only be considered preliminary. Further validations against plant tests involving stratification and mixing phases should be done as such data becomes available. 3.2. Pool behavior at lower flow rates We now assume a steam injection of 0.3 kg/s through the same sparger as the one used in the PSP test. This leads to a sub-sonic steam mass flux of 70 kg/(m2s) for which Eqs. (1) and (2) were used to determine the effective momentum (Gallego, submitted). It should be noted that no plant data was available at these conditions. Thus, the results presented in this section are only the CFD predictions. The pool behavior obtained with these conditions led to thermal stratification (Fig. 4). However, since the lowest thermocouples at the PSP are located 4.3 m above the floor, the operator would not notice development of the cold layer located at about 2 m. These results suggest that adding more thermocouples in the PSP would be important for adequate diagnostics of the pool state for operator’s decisions. Once the steam injection started, the side of the pool opposite to the sparger began to show significant temperature increases after about 30 min (see sectors KA and KD in Fig. 4b). After this time, temperature differences in the azimuthal direction were observed to be very small (Fig. 5). The transport of heat from the
(a)
sparger vicinity to the rest of the pool is caused by buoyancy forces, which tend to align the hot layer perpendicular to the gravity vector. Hot liquid rising from the sparger was first spread along the top of the pool and then propagated down until the level of stratification reached at the sparger vicinity. Some of the simulations of Fukushima Daiichi Unit 3 presented in (Pellegrini, 2016) were performed with a suppression pool subdivided only in the azimuthal direction. The results presented in this work show that vertical stratification has a larger effect on the long-term pool temperature evolution than the small temperature differences in the azimuthal direction. Thus, it is suggested to include vertical sub-divisions.
4. Spargers of the 314 system In this section, we consider more prototypic steam injection conditions with multiple spargers of the 314 system and demonstrate that thermal stratification can develop in the pool. The spargers of the ADS (314) system are used to control the reactor vessel pressure. There are a total of 64 sparger pipes of DN 150 mm, each with an injection hole area about 3 times larger than the ones in the 311 system. The 314 spargers have an upper ring of downward facing holes, known as the Load Reduction Ring (LRR), and radially outwards holes at the sparger head (Fig. 2). The LRR is located about 2.5 m above the sparger bottom. The steam injection is controlled with 16 relief vales located at the main steam
(b)
Fig. 4. Pool temperature evolution predicted with Fluent during a 0.3 kg/s steam injection through a single 311 sparger. (a) Locations where TCs are located in the PSP and (b) at different sectors and elevations of the PSP.
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Fig. 5. Pool temperature field at t = 14 h obtained in the simulation with 0.3 kg/s steam injection through a single 311 sparger. The vertical lines denote the location of the TC measurements found in the plant, which are located at 8.3 and 4.3 m.
lines, each one feeding 4 spargers. Thus, the minimum number of spargers through which steam can be injected is 4. The simulations were run assuming 3.5 and 9 kg/s steam injection through different numbers of the 314 spargers. The 3.5 kg/s flow rate was selected to show the effect of sparger geometry by comparing to the plant test from Section 3. The flow rate of 9 kg/s represents the core decay heat that can be expected 6 h after reactor shutdown (assuming ANS 5.1 decay heat curve for a 3000 MWth reactor after 4 years of operation). Since the temperature differences in the azimuthal direction were observed to be very small in the simulation from Section 3.2, symmetry boundary conditions were used to reduce the computational domain. That is, a 11.25° slice for 64 spargers, 45° for 16, and 180° for 4 (Fig. 6). The flow distribution between the LRR and sparger head was estimated using GOTHIC code (GOTHIC Thermal Hydraulic Analysis Package, 2014) and assuming a constant pool temperature of 15 °C (Table 1). We can see that, for a given steam flow rate, increasing the number of spargers leads to more steam condensation inside the sparger pipes. This is due to the larger surface area available for condensation. The pool temperature of 15 °C used in the GOTHIC simulations provides conservative results in terms of thermal stratification development, which is the purpose of analysis in this paper. As the transient progresses and the temperature in the pool increases, the condensation inside the pipe and flow distribution between the LRR and sparger head can change. There-
Fig. 6. Mesh used in the Fluent simulations of a steam injection through the 314 spargers. Non-conformal mesh was used at the boundary between the two sparger volumes and the rest of the pool. The cell sizes in the sparger volumes are the same as the one presented in Fig. 1b. Only difference is that the vertical cell size was kept to 25 mm in all the pool, not only below the sparger injection point.
fore, further development of the EHS/EMS models should be focused on the development of a simplified (1D) model to predict the heat and flow distribution during run-time based on the pool temperature distribution. The effective momentum induced by the steam condensation was estimated with Eqs. (1) and (2) (Gallego, submitted). These sub-sonic correlations were calibrated for the condensation regimes between 70 and 175 kg/(m2s). Application of (1) and (2) to lower steam mass fluxes is an extrapolation, which can over or underestimate the resulting momentum. For instance, there is a possibility that chugging can develop at steam mass fluxes lower than about 70 kg/(m2s). Further separate effect experimental studies would be needed for development and validation of the models in all relevant to plant conditions regimes. 4.1. Simulation results The results obtained injecting 3.5 kg/s of steam are presented in Figs. 7and 9. In the case with 64 spargers all steam was condensed inside the sparger pipes. The uniform heat distribution along the topmost 2.9 m of submerged pipe wall led to a temperature gradient in the hot layer. A similar profile was observed in the low steam injection phases of the PPOOLEX experiments with blowdown pipe (Li et al., 2014a). This gradient led to rapidly increasing pool surface temperatures, which reached 95 °C in 7.7 h. At this point operator would be instructed to shutdown the ECCS. The
Table 1 Flow distribution through the 314 spargers when injecting a total steam flow rate of 3.5 and 9.0 kg/s into a 15 °C water pool. Simulation results obtained with GOTHIC. # spargers
Steam condensation inside pipe
LRR
Sparger head
Steam flow [kg/s]
Steam flux [kg/(m2s)]
Steam flow [kg/s]
Steam flux [kg/(m2s)]
Total steam flow rate = 3.5 kg/s 64 100% 16 44% 4 15.5%
0 1.96 2.10
0 38 165
0 0 0.86
0 0 19
Total steam flow rate = 9.0 kg/s 64 67% 16 23% 4 3.1%
3.00 4.88 2.63
15 96 207
0 2.01 6.06
0 11 134
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Fig. 7. Pool temperature fields 6 h after the beginning of a steam injection of 3.5 kg/s through (a) 64 (b) 16 and (c) 4 spargers of the 314 system.
injection through 16 spargers allowed a fraction of the steam to be pushed through the LRR holes. The stronger circulation induced by the LRR led to more homogeneous temperature distribution in the hot layer, reducing substantially the pool surface temperature compared to the 64 case. In the 4 sparger case steam was injected through the LRR and sparger head. Pool mixing was achieved through a strong downwards flow pattern induced by the LRR jets. The results obtained with 9 kg/s of steam are presented in Figs. 8 and 10. The observed thermal stratification suggests that the increased momentum source at larger steam mass flows was not sufficient to overcome the buoyance force creased by the heat source. In the case with 64 spargers, a significant amount of heat was released at the LRR outlet, resulting in a more uniform temperature distribution compared to the case with all steam condensing inside the pipe (Fig. 7a). The ECCS shutdown temperature limit was reached after 6.7 h. In the case with 16 spargers the LRR jets were initially able to reach the bottom of the pool. However, as the transient progressed, buoyancy forces reduced the jet penetration depth, which resulted in formation of a cold layer with larger temperature than the initial 15 °C. The case with 4 spargers led to pool mixing. Here the momentum at the sparger head was larger than in
447
Fig. 8. Pool temperature fields 6 h after the beginning of a steam injection of 9 kg/s through (a) 64 (b) 16 and (c) 4 spargers of the 314 system.
the case with 3.5 kg/s and 4 spargers. Still, mixing was achieved with the same downwards flow induced by the LRR. These results suggest that the orientation of the sparger head holes reduces the effectiveness of mixing since certain injection conditions could deflect the downwards LRR flow radially when reaching the sparger head, preventing it from reaching the pool bottom. 4.2. Discussion The presented results suggest that thermal stratification development cannot be excluded in prototypic plant conditions. To some extent, operators can enhance pool mixing by closing some of the spargers. However, a more robust solution would be changing the sparger design to increase the ratio between integral momentum and heat sources created by the steam injection. Accidents such as Station Black Out (SBO) are expected to be the most likely to present thermal stratification. In design basis accidents such as LOCA the pool could be mixed through the recirculation pumps and strainers of the Residual Heat Removal System (RHR). However, in most BWR designs the RHR system was not specifically designed to mix the pool. Its mixing capability depends
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Fig. 9. Evolution of the pool surface temperature and vertical temperature profiles during a steam injection of 3.5 kg/s through the 314 spargers. Data taken at the center of the domain.
on the location of the pumps and strainers, liquid momentum induced by these, strength of pool stratification, etc. (Puustinen et al., 2010). For example, in some Nordic BWRs the RHR pumps and strainers are all located a few meters above the pool bottom (between 2 and 7 m, depending on the design (Störningshandboken, 2003). This increases the probability of developing a cold layer below them due to the absence of momentum sources in this region.
The results presented in Section 4 show that the case with complete steam condensation inside the sparger pipe leads to much stronger stratification and larger pool surface temperatures compared to the cases with steam injection through sparger holes. The conditions leading to this regime can be computed with most thermal hydraulic codes. Nevertheless, we propose a simple correlation that can be used for an efficient estimation of such conditions. The total heat transfer between the steam inside the pipe and the water of the pool can be computed with
DT 1 lnðr o =ri Þ 1 þ þ Ao h o 2pls k Ai hi
Q 2 hfg p4d
ð5Þ
obtained by equating the injected steam flow rate and the condensed steam flow rate Q =hfg . The outer heat transfer coefficient ho can be computed using the correlation for free convection on a vertical plate (Churchill and Chu, 1975);
0
5. Steam condensation inside the sparger pipe
Q¼
Gmax ¼
12
kL B 0:387Ra1=6 C L ho ¼ @0:825 þ 8=27 A ls 9=16 1 þ ð0:492=PrL Þ
valid for vertical cylinders with D=L > 35=Gr1=4 L . This is a conservative assumption since nucleate boiling could also occur at the outer pipe surface. Inside the cylinder, two-phase heat transfer coefficients caused by a turbulent condensate film can be calculated with Eq. (7) when the steam velocity is low enough to make shear effects between steam and liquid unimportant (Incropera and DeWitt, 1996).
ð4Þ
where h is the heat transfer coefficient, A the area, ls the pipe submergence depth, DT the steam minus liquid temperature, and sub-indices o and i the outer and inner sides of the sparger pipe, respectively. The maximum steam mass that can be completely condensed inside the pipe can be computed with
ð6Þ
hi
m
1=3 2 L =g kL
! ¼
8 1:47 > > > > > Re 1=3 > < d
Red 6 30
Red 30 < Red 6 1800 > > 1:09Re1:22 5:2 > > > Re > d : Red > 1800 8750 þ 58Pr0:5 Re0:75 253 L d ð7Þ
I. Gallego-Marcos et al. / Annals of Nuclear Energy 132 (2019) 442–450
449
Fig. 10. Evolution of the pool surface temperature and vertical temperature profiles during a steam injection of 9 kg/s through the 314 spargers. Data taken at the center of the domain.
The Reynolds number in Eq. (7) is related to the flow rate of _ dL . We will estimate it assuming that condensed liquid in the film m all the steam condenses inside the pipe
2 _ dL 4G pd =4 4m Gd Red ¼ ¼ lL pd lL pd lL
ð8Þ
Solutions of Eqs. (4) to (8) for prototypic ranges of submergence depth ls , liquid temperature T L , steam temperature T S , and pipe diameter d are presented in Fig. 11. The limiting factor for the heat transfer was observed to be the heat convection at the pool side, giving Q ho Ao DT. Assuming constant water properties and neglecting the 0.825 factor in Eq. (6) gives Q / dls DT ðT w T L Þ1=3 . The pipe wall temperature on the liquid side T w requires a few iterand ations while solving Eqs. (4)–(8). Assuming ðT w T L Þ1=3 T 1=2 L adding the resulting Q to Eq. (5) gives a linear relation with Gmax which can be fitted by Eq. (9) and is compared to the full model predictions in Fig. 11.
Gmax 1:7 104
pffiffiffiffiffi ls DT T L d
ð9Þ
Respectively, for a given steam mass flux, the minimum pipe length lmin needed to completely condense the steam is
lmin
Gd 4
1:7 10
pffiffiffiffiffi T TL
ð10Þ
The analytical estimate proposed for Gmax is quite rough. However, it enables a quick assessment of the validity of different assumptions regarding pool mixing or stratification. For example,
Fig. 11. Maximum steam mass flux that can be condensed inside the pipe ( model, Eqs. (4)–(8) and ( ) Eq. (9).
) full
application of Eq. (9) to the 64 sparger and 3.5 kg/s case from Table 1 gives a Gmax = 3.9 kg/(m2s). The injection conditions of 3.5 kg/s through 64 spargers of 150 mm diameter give a
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G = 3.1 kg/(m2s), showing that significant condensation inside the pipe can be expected (i.e. large pool surface temperatures). Eq. (9) should be further validated against experimental data obtained at prototypic sparger injection conditions. 6. Conclusions The pressure suppression pool behavior in a BWR has been simulated using CFD and previously developed EHS/EMS models for a steam injection through spargers. The modeling approach was validated against a full scale pool test data in a Nordic BWR. Then, the pool behavior was predicted for different (more prototypic) steam flow rates and number of active spargers. Development of thermal stratification was observed at such conditions. Specific conclusions and recommendations are summarized below. The assumption that the pool temperature is homogeneously distributed above the injection holes is not conservative. Complete condensation inside the pipe can lead to much larger pool surface temperatures due to the development of a temperature gradient in the hot layer. As an example, injection of 3.5 kg/s and 9 kg/s through 64 spargers leads to complete condensation, reaching the 95 °C limit about 7.7 and 6.7 h respectively after the initiation of the steam injection. The downward injection of the Load Reduction Ring (LRR), originally designed to reduce loads on piping structures at the beginning of the blowdown, is effective in promoting mixing of the pool. The radial injection at the sparger head can deflect the downward flow created by LRR and thus decrease the mixing effectiveness. The spatial resolution of temperature measurements in the pool might be insufficient for the correct interpretation of pool mixing/stratified state by the operator. At least one TC located close to the pool bottom would be useful for operators. A combination of design optimization and changes in operator actions (such as decreasing number of open spargers) can help in providing pool mixing. No significant temperature differences are observed in the azimuthal direction of the annular pool, even when injecting steam through a single sparger at low steam mass fluxes. This would enable reducing the number of TCs in the pool required to address its condition. Assumptions of azimuthal stratification are not recommended for modeling in system/thermal–hydraulic codes. A single correlation to estimate the minimum steam mass flux needed to avoid complete condensation inside the pipe is proposed. This can be used to (i) assess the validity of different assumptions on the pool behavior and to (ii) determine the number of safety relief values that the operator should open when discharging steam into the pool. Further development of the computational tools would require separate effect experiments performed with the LRR, and integral experiments combining the LRR and sparger head. The effective momentum should be further measured at steam mass fluxes below 70 kg/(m2s), where chugging might develop. Although this regime increases structural loads, it could promote mixing, as observed in previous experiments with blowdown pipes. Acknowledgements The authors are grateful to Maria Agrell, Anna Ryman and Oddbjörn Sandervåg from the Swedish Radiation Safety Authority
(Strålsäkerhetsmyndigheten, SSM) for the discussions and to SSM for financial support for this project. We would also like to thank Berth Arbman from Oskarshamns KraftGrupp (OKG) for his comments and information on the Nordic BWR test with sparger and Walter Villanueva from KTH Royal Institute of Technology for the discussions on the simulation results. The simulations were performed on resources provided by the Swedish National Infrastructure for Computing (SNIC) at PDC Centre for High Performance Computing (PDC-HPC). The authors are grateful to the PDC-HPC staff for assistance concerning the implementation aspects in making the code run on the PDC-HPC resources. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.anucene.2019.04.054. References Churchill, S.W., Chu, H.H.S., 1975. Correlating equations for laminar and turbulent free convection from a vertical plate. Int. J. Heat Mass Transfer 18, 1323–1329. Gallego-Marcos, I., Kudinov, P., Villanueva, W., Puustinen, M., Räsänen, A., Tielinen, K., Kotro, E. Effective momentum induced by steam condensation in the oscillatory bubble regime. Submitted to Nucl. Eng. Des. Gallego-Marcos, I., Kudinov, P., Villanueva, W., Kapulla, R., Paranjape, S., Paladino, D., Laine, J., Puustinen, M., Räsänen, A., 2018a. Pool stratification and mixing during a steam injection through spargers. Part 1: analysis of the PPOOLEX and PANDA experiments. Nucl. Eng. Des. 337, 300–316. Gallego-Marcos, I., Villanueva, W., Kudinov, P., 2018b. Modelling of pool stratification and mixing induced by steam injection through blowdown pipes. Ann. Nucl. Energy 112, 624–639. Gallego-Marcos, I., Kudinov, P., Villanueva, W., Kapulla, R., Paranjape, S., Paladino, D., Laine, J., Puustinen, M., Räsänen, A., 2019. Pool Stratification and Mixing Induced by Steam Injection through Spargers: CFD modelling of the PPOOLEX and PANDA experiments. Nucl. Eng. Des. 347, 67–85. GOTHIC Thermal Hydraulic Analysis Package, Version 8.1(QA). EPRI, Palo Alto, CA: 2014. Incropera, F.P., DeWitt, D.P., 1996. Fundamentals of heat and mass transfer. John Wiley & Sons. Section, p. 10.8.. Li, H., Kudinov, P., 2010. Effective Approaches to Simulation of Thermal Stratification and Mixing in a Pressure Suppression Pool. OECD/NEA & IAEA Workshop CFD4NRS-3, Bethesda, MD, USA, September 14–16, 2010. Li, H., Villanueva, W., Kudinov, P., 2014a. Approach and development of effective models for simulation of thermal stratification and mixing induced by steam injection into a large pool of water. Sci. Technol. Nucl. Install. Article ID 108782. Li, H., Villanueva, W., Puustinen, M., Laine, J., Kudinov, P., 2014b. Validation of effective models for simulation of thermal stratification and mixing induced by steam injection into a large pool of water. Sci. Technol. Nucl. Install. Article ID 752597. Li, H., Villanueva, W., Puustinen, M., Laine, J., Kudinov, P., 2018. Thermal stratification and mixing in a suppression pool induced by direct steam injection. Ann. Nucl. Energy 111, 487–498. Mizokami, S., Yamanaka, Y., Watanabe, M., Honda, T., 2013. State of the art MAAP analysis and future improvements on TEPCO Fukushima-Daiichi NPP accident. Proceedings of 15th international conference on Nuclear Reactor ThermalHydraulics (NURETH-15). Pisa, Italy, paper 536. Mizokami, S., Yamada, D., Honda, T., Yamauchi, D., Yamanaka, Y., 2016. Unsolved issues related to thermal-hydraulics in the suppression chamber during Fukushima Daiichi accident progressions. J. Nucl. Sci. Technol. 53 (5), 630–638. Pellegrini, M. et al., 2016. Benchmark study of the accident at the Fukushima Daiichi NPS: best-estimate case comparison. Nucl. Technol. 196 (2), 198–210. Pershagen, B., 1994. Light Water Reactor Safety. Pergamon Press. Section 8.1. Puustinen, M., Laine, J., Räsänen, A., Kotro, E., 2010. Mixing tests with an RHR nozzle in PPOOLEX. Nordic Nucl. Saf. Res., NKS-383 Störningshandboken BWR, 2003. SKI Rapport 03:02 (In Swedish). Statens Kärnkraftinspektion. Villanueva, W., Li, H., Puustinen, M., Kudinov, P., 2015. Generalization of experimental data on amplitude and frequency of oscillations induced by steam injection into a subcooled pool. Nucl. Eng. Des. 295, 155–161.