- Email: [email protected]
SMR code using a simple correlation for subcooled boiling flow prediction
Annals of Nuclear Energy xxx (2016) xxx–xxx
Contents lists available at ScienceDirect
Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Technical note
Improvement of TASS/SMR code using a simple correlation for subcooled boiling flow prediction Young Jong Chung ⇑, Hyungjun Kim, Kyoo Hwan Bae Korea Atomic Energy Research Institute, 989-111 Daedeokdaero, Yuseong, Daejeon 34057, Republic of Korea
a r t i c l e
i n f o
Article history: Received 28 April 2016 Received in revised form 23 September 2016 Accepted 27 September 2016 Available online xxxx Keywords: TASS/SMR SMART Subcooled boiling condition Critical enthalpy Energy partitioning
a b s t r a c t SMART, which was an advanced integral type small modular PWR, was developed by KAERI (Kim et al., 2014). To analyze the thermal hydraulic phenomena including behaviors at the SMART specific components, the TASS/SMR code which can predict a heat transfer for various thermal hydraulic conditions, has been developed. Information of the void distribution in a subcooled boiling flow is important in predicting the inception of a two-phase flow and an onset of the critical heat flux condition. The TASS/SMR code adopts an energy partitioning method and a critical enthalpy correlation determining a point of net vapor generation for subcooling conditions. A range of the subcooling degree investigated is 1.5–50.6 K to validate the method for a subcooled boiling flow prediction. The TASS/SMR code predicts well the void distribution along the height for the subcooled boiling flow conditions compared with the experimental data. The predicted location of the onset of void generation is simulated well at most investigated conditions and delayed slightly at the very high subcooling condition. Ó 2016 Published by Elsevier Ltd.
1. Introduction SMART (System-Integrated Modular Advanced ReacTor), which was an advanced integral type small modular PWR (Pressurized Water Reactor), was developed by KAERI (Kim et al., 2014). The main components such as the steam generators (SGs) and reactor coolant pumps (RCPs) are located in the reactor pressure vessel (RPV), as shown in Fig. 1. It has a compact size compared to a conventional PWR, and can produce an electricity of 100 MW, or an electricity of 90 MW and a desalinated water of 40,000 tons per day, concurrently. The performance and safety of the SMART plant should be analyzed using a system analysis code. To analyze the thermal hydraulic phenomena at the SMART plant, the TASS/SMR code, which can predict a heat transfer for various thermal hydraulic conditions in the core has been developed (Lee et al., 2009). With increasing heat flux, bubbles generated in the fuel aggregate heat transfer in the core and form a transient vapor film, which lead to a sharp rise of the fuel surface temperature. This is called a departure from nucleate boiling (DNB). The rapid increase of the fuel surface temperature leads to the fuel surface damage. A void distribution in a subcooled boiling flow is important in predicting an inception of a two-phase flow and an onset of the critical heat flux condition. The subcooled boiling is the early stage of the ⇑ Corresponding author.
departure from nucleate boiling, which is a key phenomenon related to a nuclear reactor safety (Okawa et al., 2007; Zhang et al., 2015). Many models are developed to predict the void distribution under a subcooled boiling flow. The void distributions assuming the simple relation of local vapor quality to the thermal equilibrium qualities was developed at the point of net vapor generation (Saha and Zuber, 1974). Research activities for a subcooled boiling flow at low pressures have been done focused on the safety analysis of research reactors operation with atmospheric pressure (Bibeau and Salcudean, 1994; Rogers et al., 1987; Tu and Yeoh, 2002), and an improvement of best estimate system analysis code (Koncar and Mavko, 2003). Multi-dimensional calculations were carried out to predict the void fraction in a subcooled boiling flow (Kljenak and Mavko, 2006; Krepper and Rzehak, 2011). These models were generally mechanistic models compared with conventional one-dimensional models. In addition, Bosma et al. (2004) showed that subcooled nucleate boiling occurring at a core region in the pressurized water reactors caused the accumulation of boron compounds on fuel surfaces that led to an unexpected deviation in axial power distribution. Lo (1996) proposed population balance equations for the CFD code to take into account a non-uniform bubble size distribution in two-phase flows. Recently, an interfacial area transport and bubble number density transport equations were applied, respectively, into CFD codes for the prediction of subcooled boiling flows (Yao and Morel, 2004; Yeoh and Tu, 2005).
E-mail address: [email protected] (Y.J. Chung). http://dx.doi.org/10.1016/j.anucene.2016.09.048 0306-4549/Ó 2016 Published by Elsevier Ltd.
Please cite this article in press as: Chung, Y.J., et al. Improvement of TASS/SMR code using a simple correlation for subcooled boiling flow prediction. Ann. Nucl. Energy (2016), http://dx.doi.org/10.1016/j.anucene.2016.09.048
2
Y.J. Chung et al. / Annals of Nuclear Energy xxx (2016) xxx–xxx
Energy conservation
ICI Nozzles
A
@ @ ðqm em Þ þ xf hg þ ð1 xf Þhl W m ¼ q_ w @t @x
ð5Þ
A
@ @ ðaqg hg Þ þ ðxf hg W m Þ ¼ Cg hsg þ q_ wg þ q_ ig @t @x
ð6Þ
Control Rod Drive Mechanism Pressurizer
Here, Reactor Coolant Pump
Core Support Barrel Feedwater Nozzle Flow Mixing Header Ass’y Core
Fig. 1. Schematic diagram for the SMART reactor vessel.
The use of CFD codes has been recently extended to analyze a multi-dimensional two-phase flow to improve the limitation of one-dimensional analysis code. An accurate simulation of a subcooled boiling flow is important for the performance, and safety of nuclear power plants (Yun et al., 2012). However, a one dimensional system analysis is widely used to analyze the overall system behaviors of nuclear power plants for various conditions including accidents. In the present work, a simple model to predict subcooled boiling flow is examined in the TASS/SMR code, which was developed to analyze thermal hydraulic phenomena for the integral reactor, SMART. 2. Implementation of subcooled boiling model The TASS/SMR code was developed for an analysis of the design based accidents in an integral type reactor reflecting the characteristics of the SMART design (Chung et al., 2015). The governing equations are six one-dimensional conservation variables to predict a two-phase condition well. Mass conservation
@ @ ½ð1 aÞql þ ½ð1 xf ÞW m ¼ Cg @t @x ! @ @ qn xf W m ¼ 0 A ðaqn Þ þ @t @x qg
A
ð1Þ ð2Þ ð3Þ
Momentum conservation
" !# ! x2f ð1 xf Þ2 @ Wm @ W 2m A þ þ @t A @x aqg ð1 aÞql A ¼ A
@P W m jW m j W m jW m j K f U2 Kg þ qm aext A @x 2q l A 2qm A
qm em ¼ aðqs es þ qn en Þ þ ð1 aÞql el
ð8Þ
aqg aqg ð1 aÞql þ vrA qm qm W m
v r ¼ vg v l
Upper Guide Structure
@q @W m A mþ ¼0 @t @x
ð7Þ
xf ¼
Steam Nozzle
Steam Generator
qm ¼ aðqs þ qn Þ þ ð1 aÞql
ð9Þ ð10Þ
where q W, A, a, v, P, e, and h denote density, mass flow rate, area, void fraction, velocity, pressure, internal energy and enthalpy, respectively. Also, subscript m, r, g, n, and l denote mixture, relative, gas, non-condensable and liquid, respectively. It is also assumed that a non-condensable gas is a thermal equilibrium between a gas and steam, and distributes homogeneously. Considering a subcooled boiling flow, a vapor phase and liquid phase coexist at different temperatures. Thus, the governing equations describing thermal non-equilibrium and non-homogeneous velocity should be implemented to model a subcooled boiling flow. In TASS/SMR code, a subcooled boiling is implemented in the wall evaporation model (q_ w ; and q_ wg in Eqs. (5) and (6)), which determines the wall evaporation rate using a heat flux partitioning and the drift flux model, which determines the differential velocity between the steam and liquid phases (Chexal and Lellouche, 1991). Heat flux partitioning assumes that a total heat transferred from a heated wall is partitioned into a latent heating and a sensible heating of bulk fluid. A critical enthalpy correlation determining the point of net vapor generation is adopted to improve a void distribution prediction under a subcooled boiling flow. Saha and Zuber introduces that a critical enthalpy for a bubble detachment is function of a fixed Nusselt number at low flow rate and fixed Stanton number at high flow rate (Saha and Zuber, 1974). These equations are modified since the trend of the bulk liquid temperature at the onset of significant void is opposite those predicted by Saha and Zuber’s correlation (Rogers et al., 1987). The data cited by Saha and Zuber were fitted to two correlations depending on the Peclet number of 52000 (Ha, 2004).
hcr ¼
8 0:124 < hsat St Pe C pf f
:
sat hf
0:0287
St Pe1:08 C pf 918:525
for Pe P 52000 for Pe < 52000
ð11Þ
where St, Pe and Cpf are the Peclet number, Stanton number, and liquid specific heat, respectively. In the TASS/SMR code, the critical enthalpy for the onset of subcooled boiling is adopted Eq. (11). 3. Validation of subcooled boiling model The developed subcooled boiling model in the TASS/SMR code is validated. The simulations have been performed and the results are compared with the experimental data. The selected experimental data are the KIT and FRIGG test results (Kalitvianski, 2000; Gingrich, 2007). 3.1. KIT subcooled boiling test
ð4Þ
The test section of the KIT has a pipe with an inner diameter of 11.7 mm or 12.23 mm with a constant height of 1.5 m, and is
Please cite this article in press as: Chung, Y.J., et al. Improvement of TASS/SMR code using a simple correlation for subcooled boiling flow prediction. Ann. Nucl. Energy (2016), http://dx.doi.org/10.1016/j.anucene.2016.09.048
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Y.J. Chung et al. / Annals of Nuclear Energy xxx (2016) xxx–xxx
heated by an electrical alternate current. Preliminary heated water is supplied to the inlet of the pipe at some steady state conditions. The experimental data used for the validation are shown in Table 1. The absolute instrumental uncertainty of the void fraction is ±0.03. The inlet flow to the test section and the pressure of the upper plenum are given as the boundary conditions. The modeling of the test section is shown in Fig. 2. The nodalization of the test facility has 23 nodes. The active tube region consists of 20 nodes, and the subcooled water is put into node 23 for the test section simulation. Figs. 3–8 show the local void distribution along the height for various degrees of subcooling, pressures, heat fluxes, and mass fluxes. The degree of subcooling is an important parameter in the test matrix. Since the degree of subcooling at an inlet of the test section affects the location at an onset of net vapor generation for the given boundary conditions. Generally, the void fraction increases the increase in heat flux or decrease in mass flux under the same pressure conditions. Fig. 3 shows the void distribution under the nearly saturated water conditions and the void fraction increases along the height. The TASS/ SMR code with and without the subcooled boiling model predicts the void distribution well because the degree of subcooling is very small (1.5 K). Figs. 4 and 5 show the void distribution with different degrees of subcooling, and mass flux at the same pressure and heat flux. The location of the onset of void generation is delayed under the high subcooling conditions. The TASS/SMR code with the subcooled boiling model predicts well or over-estimates slightly the experimental data. However, the code without the subcooled boiling model does not predict a void generation at the lower part, which is a subcooled boiling flow region. In this case, the code predicts a void generation when the water temperature reaches a saturation temperature at the given pressure. Figs. 6 and 7 represent the void distribution at the different pressures (6.8 and 10.8 MPa) under the similar degree of subcooling temperature. The trend of the TASS/SMR simulation is nearly the same as those of the previous results. Fig. 8 shows the void distribution at the highly subcooled condition (50.6 K) for the high pressure, heat flux, and mass flux conditions. The code with the subcooled boiling model predicts properly along the height, and the onset of the void generation location is about 0.6 m. However, the code without the subcooled boiling model predicts a delay in the onset location, which is about 0.95 m and the increasing rate is over-predicted after the water temperature reaches the saturated temperature. 3.2. FRIGG subcooled boiling test The FRIGG facility provided the capability for testing the full height Marviken fuel bundle under both forced and natural circulation conditions. The test section featured 36 identical rods having a diameter of 13.8 mm arranged in concentric rings of 6, 12, and 18 rods each with the diameter of 0.1595 m and the height of 4.375 m. The facility was designed to measure the void profile along the test section. All of the tests were performed at approximately 5 MPa. For the tests used to validate, the rod power is 1500 and 4415 kW to validate the TASS/SMR code as shown in Table 2. Sub-
Fig. 2. Nodalization of the KIT test section for TASS/SMR code.
cooled nucleate boiling occurred at most of the bundle, giving rise to an increasing void fraction along the height. The inlet flow to the test section and the pressure at the test section outlet are given as the boundary conditions. The modeling of the test section is similar to the nodalization of the KIT test. The nodalization of the test facility has 13 nodes. For the test section, the fuel bundle region consists of 10 nodes, and the subcooled water is supplied to the inlet node. Figs. 9 and 10 show the local void distribution along the test section for the different subcooling temperatures at the same pressure and power. Fig. 11 shows the void distribution at the high
Table 1 Initial conditions for KIT test. Test No.
P (MPa)
q00 (W/cm2)
G (kg/m2 s)
Subcooling (K)
6" 12; 5" 38; 12-
4.442 4.413 4.413 6.806 10.817 10.797
43.729 43.729 43.147 113.823 42.798 171.833
973 1969 969 1975 967 2109
1.5 8.7 15.3 17.9 19.1 50.6
", ;, - denote linear increase, decrease, and constant for the axial power distribution, respectively.
Please cite this article in press as: Chung, Y.J., et al. Improvement of TASS/SMR code using a simple correlation for subcooled boiling flow prediction. Ann. Nucl. Energy (2016), http://dx.doi.org/10.1016/j.anucene.2016.09.048
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Y.J. Chung et al. / Annals of Nuclear Energy xxx (2016) xxx–xxx
1.0
1.0
Experiment w/o subcooled boiling model w subcooled boiling model
Experiment w/o subcooled boiling model w subcooled boiling model
0.8
0.6
Void fraction (-)
Void fraction (-)
0.8
0.4
0.2
0.6
0.4
0.2
0.0
0.0 0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.0
1.4
0.2
0.4
Fig. 3. Void distributions at 1.5 K subcooling (KIT).
1.0
1.2
1.4
1.0
Experiment w/o subcooled boiling model w subcooled boiling model
0.8
Experiment w/o subcooled boiling model w subcooled boiling model
0.8
0.6
Void fraction (-)
Void fraction (-)
0.8
Fig. 6. Void distributions at 17.9 K subcooling (KIT).
1.0
0.4
0.2
0.0
0.6
0.4
0.2
0.0 0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0.0
0.2
0.4
Height (m)
0.6
0.8
1.0
1.2
1.4
Height (m)
Fig. 4. Void distributions at 8.7 K subcooling (KIT).
Fig. 7. Void distributions at 19.1 K subcooling (KIT).
1.0
1.0
Experiment w/o subcooled boiling model w subcooled boiling model
0.8
Experiment w/o subcooled boiling model w subcooled boiling model
0.8
0.6
Void fraction (-)
Void fraction (-)
0.6
Height (m)
Height (m)
0.4
0.2
0.0
0.6
0.4
0.2
0.0 0.0
0.2
0.4
0.6
0.8
1.0
1.2
Height (m) Fig. 5. Void distributions at 15.3 K subcooling (KIT).
1.4
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Height (m) Fig. 8. Void distributions at 50.6 K subcooling (KIT).
Please cite this article in press as: Chung, Y.J., et al. Improvement of TASS/SMR code using a simple correlation for subcooled boiling flow prediction. Ann. Nucl. Energy (2016), http://dx.doi.org/10.1016/j.anucene.2016.09.048
Y.J. Chung et al. / Annals of Nuclear Energy xxx (2016) xxx–xxx Table 2 Initial conditions for FRIGG test. Test No.
P (MPa)
Power (kW)
W (kg/s)
Subcooling (K)
313005 313007 313020
4.98 5.00 4.97
1500 1500 4415
15.85 15.85 16.55
3.7 11.7 22.4
Experiment w/o subcooled boiling model w subcooled boiling model
Void Fraction (-)
0.8
0.6
0.4
0.2
0.0 0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Height (m) Fig. 9. Void distributions at 3.7 K subcooling (FRIGG).
1.0
Experiment w/o subcooled boiling model w subcooled boiling model
0.8
Void Fraction (-)
power and subcooling temperature. The TASS/SMR code with the subcooled boiling model predicts the void distributions well for each case. However, the code without the subcooled boiling model does not predict the void generation in the subcooled boiling region. 4. Conclusions
1.0
A one dimensional system analysis code, TASS/SMR, having the SMART specific models, was developed to simulate the thermal hydraulic phenomena at the SMART plant. The subcooled boiling flow was a key phenomenon related to the nuclear reactor safety because a void distribution in a subcooled boiling flow was important in predicting the inception of a two-phase flow and onset of critical heat flux condition. The TASS/SMR code adopted a critical enthalpy correlation and an energy partitioning method determining the point of net vapor generation to predict the subcooled boiling phenomenon. A range of the subcooling degree investigated was 1.5–50.6 K. This range was included all possible degrees of subcooling, which could be occurred at the accidents on the SMART plant. It was shown that the TASS/SMR code with the subcooled boiling model predicted the void distribution well for the subcooled boiling flow conditions compared with the experimental data. The predicted location of the onset of void generation was shown well at most investigated conditions and delayed slightly at the very high subcooling condition. Acknowledgement This research was supported by the National Research Foundation of Korea (NRF) grant funded from the Korea government (MSIP) (No. 2016M2C6A1930041).
0.6
0.4
References
0.2
0.0 0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
4.5
5.0
Height (m) Fig. 10. Void distributions at 11.7 K subcooling (FRIGG).
1.0
Experiment w/o subcooled boiling model w subcooled boiling model
0.8
Void Fraction (-)
5
0.6
0.4
0.2
0.0 0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Height (m) Fig. 11. Void distributions at 22.4 K subcooling (FRIGG).
Bibeau, E.L., Salcudean, M., 1994. Subcooled void growth mechanism and prediction at low pressure and low velocity. Int. J. Multiph. Flow 20, 837–863. Bosma, J.T., Deshon, J., Epperson, K.R., Kennamore, P., Secker, J.R., Young, M.Y., 2004. A comprehensive method for assessing fuel performance risks due to crud deposition. In: Proceedings of the 2004 International Meeting on LWR Fuel Performance. Paper 1061. Chexal, B., Lellouche, G., 1991. The Chexal-Lellouche void fraction correlation for generalized applications. NSAC-139. EPRI. Chung, Y.J., Kim, S.H., Lim, S.W., Bae, K.H., 2015. TASS/SMR code improvement for small break LOCA applicability at an integral type reactor, SMART. Nucl. Eng. Des. 295, 221–227. Gingrich, C., 2007. TRACE V5.0 assessment manual Appendix B: Separate Effect Tests – FRIGG Tests. USNRC, 481–517. Ha, H.S., 2004. Development of the subcooled boiling model using a computer tool with the drift-flux model (MS.D. thesis). Korea Advanced Institute of Science and Technology (KAIST), Rep. of Korea. Kalitvianski, V., 2000. Qualification of CATHARE 2 V1.5 REV.6 on subcooled boiling experiments (KIT test). SMTH/LMDS/EM/2000-030, CEA. Kim, K.K., Lee, W.J., Choi, S., Kim, H.R., Ha, J., 2014. SMART: The first licensed advanced integral reactor. J. Energy Power Eng. 8, 94–102. Kljenak, I., Mavko, B., 2006. Simulation of void fraction profile evolution in subcooled nucleate boiling flow in a vertical annulus using a bubble-tracking approach. Heat Mass Transfer 42, 552–561. Koncar, B., Mavko, B., 2003. Modeling of low-pressure subcooled flow boiling using the RELAP5 code. Nucl. Eng. Des. 220, 255–273. Krepper, E., Rzehak, R., 2011. CFD for subcooled flow boiling: Simulation of DEBORA experiments. Nucl. Eng. Des. 241, 3851–3866. Lee, S.W., Kim, Y.H., Chung, Y.J., 2009. Development and steady state level experimental validation of TASS/SMR core heat transfer model for the integral reactor SMART. Ann. Nucl. Energy 36, 1039–1048. Lo, S., 1996. Application of Population Balance to CFD Modelling of Bubbly Flow via the MUSIG Model. AEA Technology. AEAT-1096. Okawa, T., Kubota, H., Ishida, T., 2007. Simultaneous measurement of void fraction and fundamental bubble parameters in subcooled flow boiling. Nucl. Eng. Des. 237, 1016–1024. Rogers, J.T., Salcudean, M., Abdullah, Z., McLeod, D., Poirier, D., 1987. The onset of significant void in up-flow boiling of water at low pressure and velocities. Int. J. Heat Mass Transf. 30 (11), 2247–2260.
Please cite this article in press as: Chung, Y.J., et al. Improvement of TASS/SMR code using a simple correlation for subcooled boiling flow prediction. Ann. Nucl. Energy (2016), http://dx.doi.org/10.1016/j.anucene.2016.09.048
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Saha, P., Zuber, N., 1974. Point of net vapor generation and vapor void fraction in subcooled boiling. In: Proceedings of the 5th International Heat Transfer Conference, pp. 175–179. Tu, J.Y., Yeoh, G.H., 2002. On numerical modeling of low pressure subcooled boiling flows. Int. J. Heat Mass Transf. 45, 1197–1209. Yao, W., Morel, C., 2004. Volumetric interfacial area prediction in upward bubbly two-phase flow. Int. J. Heat Mass Transf. 47, 307–328.
Yeoh, G.H., Tu, J.Y., 2005. A unified model considering force balances for departing vapour bubbles and population balance in subcooled boiling flow. Nucl. Eng. Des. 235, 1251–1265. Yun, B., Splawski, N., Lo, S., Song, C., 2012. Prediction of a subcooled boiling flow with advanced two-phase flow models. Nucl. Eng. Des. 253, 351–359. Zhang, R., Cong, T., Tian, W., Qiu, S., Su, G., 2015. Effects of turbulence models on forced convection subcooled boiling in vertical pipe. Ann. Nucl. Energy 80, 293–302.
Please cite this article in press as: Chung, Y.J., et al. Improvement of TASS/SMR code using a simple correlation for subcooled boiling flow prediction. Ann. Nucl. Energy (2016), http://dx.doi.org/10.1016/j.anucene.2016.09.048
Contents lists available at ScienceDirect
Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Technical note
Improvement of TASS/SMR code using a simple correlation for subcooled boiling flow prediction Young Jong Chung ⇑, Hyungjun Kim, Kyoo Hwan Bae Korea Atomic Energy Research Institute, 989-111 Daedeokdaero, Yuseong, Daejeon 34057, Republic of Korea
a r t i c l e
i n f o
Article history: Received 28 April 2016 Received in revised form 23 September 2016 Accepted 27 September 2016 Available online xxxx Keywords: TASS/SMR SMART Subcooled boiling condition Critical enthalpy Energy partitioning
a b s t r a c t SMART, which was an advanced integral type small modular PWR, was developed by KAERI (Kim et al., 2014). To analyze the thermal hydraulic phenomena including behaviors at the SMART specific components, the TASS/SMR code which can predict a heat transfer for various thermal hydraulic conditions, has been developed. Information of the void distribution in a subcooled boiling flow is important in predicting the inception of a two-phase flow and an onset of the critical heat flux condition. The TASS/SMR code adopts an energy partitioning method and a critical enthalpy correlation determining a point of net vapor generation for subcooling conditions. A range of the subcooling degree investigated is 1.5–50.6 K to validate the method for a subcooled boiling flow prediction. The TASS/SMR code predicts well the void distribution along the height for the subcooled boiling flow conditions compared with the experimental data. The predicted location of the onset of void generation is simulated well at most investigated conditions and delayed slightly at the very high subcooling condition. Ó 2016 Published by Elsevier Ltd.
1. Introduction SMART (System-Integrated Modular Advanced ReacTor), which was an advanced integral type small modular PWR (Pressurized Water Reactor), was developed by KAERI (Kim et al., 2014). The main components such as the steam generators (SGs) and reactor coolant pumps (RCPs) are located in the reactor pressure vessel (RPV), as shown in Fig. 1. It has a compact size compared to a conventional PWR, and can produce an electricity of 100 MW, or an electricity of 90 MW and a desalinated water of 40,000 tons per day, concurrently. The performance and safety of the SMART plant should be analyzed using a system analysis code. To analyze the thermal hydraulic phenomena at the SMART plant, the TASS/SMR code, which can predict a heat transfer for various thermal hydraulic conditions in the core has been developed (Lee et al., 2009). With increasing heat flux, bubbles generated in the fuel aggregate heat transfer in the core and form a transient vapor film, which lead to a sharp rise of the fuel surface temperature. This is called a departure from nucleate boiling (DNB). The rapid increase of the fuel surface temperature leads to the fuel surface damage. A void distribution in a subcooled boiling flow is important in predicting an inception of a two-phase flow and an onset of the critical heat flux condition. The subcooled boiling is the early stage of the ⇑ Corresponding author.
departure from nucleate boiling, which is a key phenomenon related to a nuclear reactor safety (Okawa et al., 2007; Zhang et al., 2015). Many models are developed to predict the void distribution under a subcooled boiling flow. The void distributions assuming the simple relation of local vapor quality to the thermal equilibrium qualities was developed at the point of net vapor generation (Saha and Zuber, 1974). Research activities for a subcooled boiling flow at low pressures have been done focused on the safety analysis of research reactors operation with atmospheric pressure (Bibeau and Salcudean, 1994; Rogers et al., 1987; Tu and Yeoh, 2002), and an improvement of best estimate system analysis code (Koncar and Mavko, 2003). Multi-dimensional calculations were carried out to predict the void fraction in a subcooled boiling flow (Kljenak and Mavko, 2006; Krepper and Rzehak, 2011). These models were generally mechanistic models compared with conventional one-dimensional models. In addition, Bosma et al. (2004) showed that subcooled nucleate boiling occurring at a core region in the pressurized water reactors caused the accumulation of boron compounds on fuel surfaces that led to an unexpected deviation in axial power distribution. Lo (1996) proposed population balance equations for the CFD code to take into account a non-uniform bubble size distribution in two-phase flows. Recently, an interfacial area transport and bubble number density transport equations were applied, respectively, into CFD codes for the prediction of subcooled boiling flows (Yao and Morel, 2004; Yeoh and Tu, 2005).
E-mail address: [email protected] (Y.J. Chung). http://dx.doi.org/10.1016/j.anucene.2016.09.048 0306-4549/Ó 2016 Published by Elsevier Ltd.
Please cite this article in press as: Chung, Y.J., et al. Improvement of TASS/SMR code using a simple correlation for subcooled boiling flow prediction. Ann. Nucl. Energy (2016), http://dx.doi.org/10.1016/j.anucene.2016.09.048
2
Y.J. Chung et al. / Annals of Nuclear Energy xxx (2016) xxx–xxx
Energy conservation
ICI Nozzles
A
@ @ ðqm em Þ þ xf hg þ ð1 xf Þhl W m ¼ q_ w @t @x
ð5Þ
A
@ @ ðaqg hg Þ þ ðxf hg W m Þ ¼ Cg hsg þ q_ wg þ q_ ig @t @x
ð6Þ
Control Rod Drive Mechanism Pressurizer
Here, Reactor Coolant Pump
Core Support Barrel Feedwater Nozzle Flow Mixing Header Ass’y Core
Fig. 1. Schematic diagram for the SMART reactor vessel.
The use of CFD codes has been recently extended to analyze a multi-dimensional two-phase flow to improve the limitation of one-dimensional analysis code. An accurate simulation of a subcooled boiling flow is important for the performance, and safety of nuclear power plants (Yun et al., 2012). However, a one dimensional system analysis is widely used to analyze the overall system behaviors of nuclear power plants for various conditions including accidents. In the present work, a simple model to predict subcooled boiling flow is examined in the TASS/SMR code, which was developed to analyze thermal hydraulic phenomena for the integral reactor, SMART. 2. Implementation of subcooled boiling model The TASS/SMR code was developed for an analysis of the design based accidents in an integral type reactor reflecting the characteristics of the SMART design (Chung et al., 2015). The governing equations are six one-dimensional conservation variables to predict a two-phase condition well. Mass conservation
@ @ ½ð1 aÞql þ ½ð1 xf ÞW m ¼ Cg @t @x ! @ @ qn xf W m ¼ 0 A ðaqn Þ þ @t @x qg
A
ð1Þ ð2Þ ð3Þ
Momentum conservation
" !# ! x2f ð1 xf Þ2 @ Wm @ W 2m A þ þ @t A @x aqg ð1 aÞql A ¼ A
@P W m jW m j W m jW m j K f U2 Kg þ qm aext A @x 2q l A 2qm A
qm em ¼ aðqs es þ qn en Þ þ ð1 aÞql el
ð8Þ
aqg aqg ð1 aÞql þ vrA qm qm W m
v r ¼ vg v l
Upper Guide Structure
@q @W m A mþ ¼0 @t @x
ð7Þ
xf ¼
Steam Nozzle
Steam Generator
qm ¼ aðqs þ qn Þ þ ð1 aÞql
ð9Þ ð10Þ
where q W, A, a, v, P, e, and h denote density, mass flow rate, area, void fraction, velocity, pressure, internal energy and enthalpy, respectively. Also, subscript m, r, g, n, and l denote mixture, relative, gas, non-condensable and liquid, respectively. It is also assumed that a non-condensable gas is a thermal equilibrium between a gas and steam, and distributes homogeneously. Considering a subcooled boiling flow, a vapor phase and liquid phase coexist at different temperatures. Thus, the governing equations describing thermal non-equilibrium and non-homogeneous velocity should be implemented to model a subcooled boiling flow. In TASS/SMR code, a subcooled boiling is implemented in the wall evaporation model (q_ w ; and q_ wg in Eqs. (5) and (6)), which determines the wall evaporation rate using a heat flux partitioning and the drift flux model, which determines the differential velocity between the steam and liquid phases (Chexal and Lellouche, 1991). Heat flux partitioning assumes that a total heat transferred from a heated wall is partitioned into a latent heating and a sensible heating of bulk fluid. A critical enthalpy correlation determining the point of net vapor generation is adopted to improve a void distribution prediction under a subcooled boiling flow. Saha and Zuber introduces that a critical enthalpy for a bubble detachment is function of a fixed Nusselt number at low flow rate and fixed Stanton number at high flow rate (Saha and Zuber, 1974). These equations are modified since the trend of the bulk liquid temperature at the onset of significant void is opposite those predicted by Saha and Zuber’s correlation (Rogers et al., 1987). The data cited by Saha and Zuber were fitted to two correlations depending on the Peclet number of 52000 (Ha, 2004).
hcr ¼
8 0:124 < hsat St Pe C pf f
:
sat hf
0:0287
St Pe1:08 C pf 918:525
for Pe P 52000 for Pe < 52000
ð11Þ
where St, Pe and Cpf are the Peclet number, Stanton number, and liquid specific heat, respectively. In the TASS/SMR code, the critical enthalpy for the onset of subcooled boiling is adopted Eq. (11). 3. Validation of subcooled boiling model The developed subcooled boiling model in the TASS/SMR code is validated. The simulations have been performed and the results are compared with the experimental data. The selected experimental data are the KIT and FRIGG test results (Kalitvianski, 2000; Gingrich, 2007). 3.1. KIT subcooled boiling test
ð4Þ
The test section of the KIT has a pipe with an inner diameter of 11.7 mm or 12.23 mm with a constant height of 1.5 m, and is
Please cite this article in press as: Chung, Y.J., et al. Improvement of TASS/SMR code using a simple correlation for subcooled boiling flow prediction. Ann. Nucl. Energy (2016), http://dx.doi.org/10.1016/j.anucene.2016.09.048
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Y.J. Chung et al. / Annals of Nuclear Energy xxx (2016) xxx–xxx
heated by an electrical alternate current. Preliminary heated water is supplied to the inlet of the pipe at some steady state conditions. The experimental data used for the validation are shown in Table 1. The absolute instrumental uncertainty of the void fraction is ±0.03. The inlet flow to the test section and the pressure of the upper plenum are given as the boundary conditions. The modeling of the test section is shown in Fig. 2. The nodalization of the test facility has 23 nodes. The active tube region consists of 20 nodes, and the subcooled water is put into node 23 for the test section simulation. Figs. 3–8 show the local void distribution along the height for various degrees of subcooling, pressures, heat fluxes, and mass fluxes. The degree of subcooling is an important parameter in the test matrix. Since the degree of subcooling at an inlet of the test section affects the location at an onset of net vapor generation for the given boundary conditions. Generally, the void fraction increases the increase in heat flux or decrease in mass flux under the same pressure conditions. Fig. 3 shows the void distribution under the nearly saturated water conditions and the void fraction increases along the height. The TASS/ SMR code with and without the subcooled boiling model predicts the void distribution well because the degree of subcooling is very small (1.5 K). Figs. 4 and 5 show the void distribution with different degrees of subcooling, and mass flux at the same pressure and heat flux. The location of the onset of void generation is delayed under the high subcooling conditions. The TASS/SMR code with the subcooled boiling model predicts well or over-estimates slightly the experimental data. However, the code without the subcooled boiling model does not predict a void generation at the lower part, which is a subcooled boiling flow region. In this case, the code predicts a void generation when the water temperature reaches a saturation temperature at the given pressure. Figs. 6 and 7 represent the void distribution at the different pressures (6.8 and 10.8 MPa) under the similar degree of subcooling temperature. The trend of the TASS/SMR simulation is nearly the same as those of the previous results. Fig. 8 shows the void distribution at the highly subcooled condition (50.6 K) for the high pressure, heat flux, and mass flux conditions. The code with the subcooled boiling model predicts properly along the height, and the onset of the void generation location is about 0.6 m. However, the code without the subcooled boiling model predicts a delay in the onset location, which is about 0.95 m and the increasing rate is over-predicted after the water temperature reaches the saturated temperature. 3.2. FRIGG subcooled boiling test The FRIGG facility provided the capability for testing the full height Marviken fuel bundle under both forced and natural circulation conditions. The test section featured 36 identical rods having a diameter of 13.8 mm arranged in concentric rings of 6, 12, and 18 rods each with the diameter of 0.1595 m and the height of 4.375 m. The facility was designed to measure the void profile along the test section. All of the tests were performed at approximately 5 MPa. For the tests used to validate, the rod power is 1500 and 4415 kW to validate the TASS/SMR code as shown in Table 2. Sub-
Fig. 2. Nodalization of the KIT test section for TASS/SMR code.
cooled nucleate boiling occurred at most of the bundle, giving rise to an increasing void fraction along the height. The inlet flow to the test section and the pressure at the test section outlet are given as the boundary conditions. The modeling of the test section is similar to the nodalization of the KIT test. The nodalization of the test facility has 13 nodes. For the test section, the fuel bundle region consists of 10 nodes, and the subcooled water is supplied to the inlet node. Figs. 9 and 10 show the local void distribution along the test section for the different subcooling temperatures at the same pressure and power. Fig. 11 shows the void distribution at the high
Table 1 Initial conditions for KIT test. Test No.
P (MPa)
q00 (W/cm2)
G (kg/m2 s)
Subcooling (K)
6" 12; 5" 38; 12-
4.442 4.413 4.413 6.806 10.817 10.797
43.729 43.729 43.147 113.823 42.798 171.833
973 1969 969 1975 967 2109
1.5 8.7 15.3 17.9 19.1 50.6
", ;, - denote linear increase, decrease, and constant for the axial power distribution, respectively.
Please cite this article in press as: Chung, Y.J., et al. Improvement of TASS/SMR code using a simple correlation for subcooled boiling flow prediction. Ann. Nucl. Energy (2016), http://dx.doi.org/10.1016/j.anucene.2016.09.048
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Y.J. Chung et al. / Annals of Nuclear Energy xxx (2016) xxx–xxx
1.0
1.0
Experiment w/o subcooled boiling model w subcooled boiling model
Experiment w/o subcooled boiling model w subcooled boiling model
0.8
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Void fraction (-)
Void fraction (-)
0.8
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0.0 0.0
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Fig. 3. Void distributions at 1.5 K subcooling (KIT).
1.0
1.2
1.4
1.0
Experiment w/o subcooled boiling model w subcooled boiling model
0.8
Experiment w/o subcooled boiling model w subcooled boiling model
0.8
0.6
Void fraction (-)
Void fraction (-)
0.8
Fig. 6. Void distributions at 17.9 K subcooling (KIT).
1.0
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0.0 0.0
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Height (m)
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Height (m)
Fig. 4. Void distributions at 8.7 K subcooling (KIT).
Fig. 7. Void distributions at 19.1 K subcooling (KIT).
1.0
1.0
Experiment w/o subcooled boiling model w subcooled boiling model
0.8
Experiment w/o subcooled boiling model w subcooled boiling model
0.8
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Void fraction (-)
Void fraction (-)
0.6
Height (m)
Height (m)
0.4
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0.0
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0.2
0.0 0.0
0.2
0.4
0.6
0.8
1.0
1.2
Height (m) Fig. 5. Void distributions at 15.3 K subcooling (KIT).
1.4
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Height (m) Fig. 8. Void distributions at 50.6 K subcooling (KIT).
Please cite this article in press as: Chung, Y.J., et al. Improvement of TASS/SMR code using a simple correlation for subcooled boiling flow prediction. Ann. Nucl. Energy (2016), http://dx.doi.org/10.1016/j.anucene.2016.09.048
Y.J. Chung et al. / Annals of Nuclear Energy xxx (2016) xxx–xxx Table 2 Initial conditions for FRIGG test. Test No.
P (MPa)
Power (kW)
W (kg/s)
Subcooling (K)
313005 313007 313020
4.98 5.00 4.97
1500 1500 4415
15.85 15.85 16.55
3.7 11.7 22.4
Experiment w/o subcooled boiling model w subcooled boiling model
Void Fraction (-)
0.8
0.6
0.4
0.2
0.0 0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Height (m) Fig. 9. Void distributions at 3.7 K subcooling (FRIGG).
1.0
Experiment w/o subcooled boiling model w subcooled boiling model
0.8
Void Fraction (-)
power and subcooling temperature. The TASS/SMR code with the subcooled boiling model predicts the void distributions well for each case. However, the code without the subcooled boiling model does not predict the void generation in the subcooled boiling region. 4. Conclusions
1.0
A one dimensional system analysis code, TASS/SMR, having the SMART specific models, was developed to simulate the thermal hydraulic phenomena at the SMART plant. The subcooled boiling flow was a key phenomenon related to the nuclear reactor safety because a void distribution in a subcooled boiling flow was important in predicting the inception of a two-phase flow and onset of critical heat flux condition. The TASS/SMR code adopted a critical enthalpy correlation and an energy partitioning method determining the point of net vapor generation to predict the subcooled boiling phenomenon. A range of the subcooling degree investigated was 1.5–50.6 K. This range was included all possible degrees of subcooling, which could be occurred at the accidents on the SMART plant. It was shown that the TASS/SMR code with the subcooled boiling model predicted the void distribution well for the subcooled boiling flow conditions compared with the experimental data. The predicted location of the onset of void generation was shown well at most investigated conditions and delayed slightly at the very high subcooling condition. Acknowledgement This research was supported by the National Research Foundation of Korea (NRF) grant funded from the Korea government (MSIP) (No. 2016M2C6A1930041).
0.6
0.4
References
0.2
0.0 0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
4.5
5.0
Height (m) Fig. 10. Void distributions at 11.7 K subcooling (FRIGG).
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Experiment w/o subcooled boiling model w subcooled boiling model
0.8
Void Fraction (-)
5
0.6
0.4
0.2
0.0 0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Height (m) Fig. 11. Void distributions at 22.4 K subcooling (FRIGG).
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Please cite this article in press as: Chung, Y.J., et al. Improvement of TASS/SMR code using a simple correlation for subcooled boiling flow prediction. Ann. Nucl. Energy (2016), http://dx.doi.org/10.1016/j.anucene.2016.09.048