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The development of a three-dimensional transient CFD model for predicting cooling ability of spent fuel pools
Applied Thermal Engineering 50 (2013) 496e504
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
The development of a three-dimensional transient CFD model for predicting cooling ability of spent fuel pools Tzu-Chen Hung a, *, Vijay K. Dhir b, Bau-Shei Pei c, Yen-Shu Chen d, Fengjee P. Tsai e a
Department of Mechanical Engineering, National Taipei University of Technology, 1, Sec. 3, Chung-hsiao E. Rd., Taipei, Taiwan Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, USA c Department of Engineering and System Science, National Tsing Hua University, Hsinchu, Taiwan d Nuclear Engineering Division, Institute of Nuclear Energy Research, Taoyuan County, Taiwan e Cool-tec Co., Rancho Palos Verdes, CA, USA b
h i g h l i g h t s < A CFD model has been developed to simulate spent fuel pool (SFP). < SFP cooling capability of a nuclear station was verified by the model. < Current SFP configuration satisfies the regulations under normal operation. < An inappropriate layout of fuel without external cooling might cause local boiling.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 13 September 2011 Accepted 26 June 2012 Available online 14 July 2012
The objective of this research is to develop a numerical model for the evaluation of the cooling capability of spent fuel pool (SFP) in removing decay heat. Computational fluid dynamics (CFD) approach has been applied to develop a three-dimensional two-phase thermal hydraulic model. To simplify the analysis, the pressure drop of the coolant flowing through the fuel region in the pool is modeled as a porous-medium. The geometry as well as the boundary conditions of SFP of second nuclear power plant in Taiwan has been employed as sample to be analyzed and simulated numerically. The results show that the current configuration has enough cooling capability to meet the licensing regulations under normal operation and most kinds of conditions. In the case of extremely inappropriate layout of spent fuel arrangement, the computed results illustrate that slight local saturation on fuel rods may occur unless external cooling system is supplied. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Spent fuel pool Decay heat Computational fluid dynamics Local boiling
1. Introduction Nuclear policies and the use of nuclear energy have caused profound public concerns and conflicts worldwide. On March 11 of 2011, an earthquake of magnitude 9.0 with following ruinous tsunami caused the loss of adequate cooling capability to the reactors and spent fuel pool of Fukushima Daiichi nuclear plant in Japan. Accordingly, the issues of nuclear safety have attracted great public’s attention, and the safety of spent fuels has been in the spot issue among all the safety concerns. The spent fuels are not reprocessed in many countries, and wet storage has been the predominant mode of storage. Before permanent disposal of spent fuel, reprocess of waste, or residues of
* Corresponding author. Tel.: þ886 2 2771 2171x2021. E-mail address: [email protected] (T.-C. Hung). 1359-4311/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.applthermaleng.2012.06.042
transmutation or by other means are developed, spent fuels are in general stored for extended periods in SFPs [1]. The evaluation of the safety of spent fuels stored in the framework of the existing facility becomes of vital importance in accessing the magnitude of effects following a nuclear accident. Normally, nuclear power plant stores the spent fuels in a pool, which is located outside of the primary containment with sufficient cooling water. To authors’ knowledge, cooling study has not been extensively studied due to that SFP was not categorized as safety grade issue. Kaliatka et al. presented the results of loss of heat removal accidents in SFPs of Ignalina nuclear power plant (NPP) [2]. The analysis was performed by employing system thermal hydraulic code RELAP5 [3] and codes for severe accidents ATHLET [4] and ASTEC [5]. In addition to the concern in heat removal capacity, the pool water constituents have also been analyzed and electrochemical potential (ECP) measured in water samples drawn from different locations of the pool [6]. Aghoyeh and Khalafi [7]
T.-C. Hung et al. / Applied Thermal Engineering 50 (2013) 496e504
Nomenclature A B Cp D g h heff hfg hm k L Nu Num p P Ppeak Qh Qm Ra Ram
area (m2) specific buoyancy force, (m/s2) specific heat, (J/kg-K) mass diffusivity, (m2/s) Gravity, (m/s2) enthalpy, (J/kg) effective heat-transfer coefficient, (W/m2-K) latent heat, (J/kg) mass-convective-transfer-coefficient, (m/s) thermal conductivity, (W/m-K) characteristic length of the pool surface, (m) Nusselt number, Nu ¼ hL/k analogous Nusselt number of mass transfer, Nu ¼ hmL/D pressure, (N/m2) power generated from the fuels, (W) peak power generated from the fuels, (W) heat transferred via convection, (W) heat transferred via mass transfer (W) Rayleigh number; Ra ¼ rbgDTL3/ma analogous Rayleigh number of mass transfer, Ram ¼ rbgDTL3/mD
presented a design of make-up water system for optimal water supply and its chemical properties in SFP to provide proper cooling water throughout the storage time. The characteristics of activated carbon purifier, anionic, cationic and mixed-bed ion-exchangers have been determined. Park et al. investigated the seismic isolation for SFP [8]. They built a three-dimensional model using finite element method was presented for the analysis of the fluidstructure-isolator systems in time domain. Their study indicates that careful selection of mechanical properties of the isolators with a lower limit on the effective frequency can effectively reduce the dynamic responses of SFP and enhance the stability of stored spent fuel assemblies against earthquake. Dry-storage system is another effective long-term storage solution for lower-rate of decay heat spent fuel [9]. Through a passive cooling design, spent fuels can be stored in a safe and stable environment for at least 20 years. Several dry-storage systems were developed and analyzed for different kind of fuels at different power ratings. NAC-56 [10] is one of the examples. A three-dimensional CFD model was established and employed to investigate the heat removal characteristics by Tseng et al. [11]. Ko et al. used the ABAQUS/Explicit code [12] to analyze the seismic response of the dry storage facility. Nonetheless, dry storage cannot practically replace the spent fuel pool shortly after the fuel being removed from the reactor core. In a very recent study of Nimander [13], it has been found that the temperature difference between the heated air and ambient air is far too low for natural circulation of air to remove any significant amount of heat from the spent nuclear fuel pool in a worst case scenario. Air has too low density and specific heat to remove the heat generated by spent nuclear fuel shortly after it has been removed from the reactor core. In the study of Wang et al. [14], the safety analysis of the spent fuel pool for Chinshan NPP in Taiwan was performed by using both the system code TRACE [15] and CFD approach. The analysis result of TRACE and CFD are similar for the times to achieve the uncovering of the fuels by water and the metalewater reaction of the fuels after the cooling system failed. The 2D fuel bundle model was utilized to calculate the effective thermal conductivity for the
Re S T t ! V VOF
497
Reynolds number, Re ¼ ruL/m source term temperature, ( C) time, (h) resultant velocity, (m/s) volume fraction of liquid
Greek symbols void fraction ¼ 1 VOF permeability dynamic viscosity density, (kg/m3) viscous stress tensor Tij z, x, 4 represent any specific thermodynamic properties
a k m r
Subscripts i direction i f liquid phase s pool surface sat saturated g gas phase N atmosphere above SFP
porous media in the 3D spent fuel pool model. In their models, no detail mathematical model including either porosity or two-phase flow model was included. According to the regulation by Atomic Energy Commissions, Taiwan [16], when a reactor is on a scheduled refueling outage, fuel rods in the pressure vessel are removed from the reactor core after the reactor is shut down. In fact, it takes time to remove the fuel rods to SFP. The transportation time of the fuel rods to SFP is assumed to be 150 h with a power generation in this mode at approximately 0.36% of that while it is under a peak-load operation. The cooling system of the pool must be actuated before the peak temperature of the pool reaching 60 C. A comparative analysis in spent fuel re-racking designs can be found in documentation [17]. Once an accident occurs during a steady-state full load operation, the fuel rods in the reactor, as required by the regulations, have to be immediately removed to SFP. To provide enough cooling to the fuels, water level of the pool is required to be at least 3 m higher than the top of fuels in the pool, and no boiling is allowed. The most important issue of the simulations in this study is to find out the magnitude and location of peak temperature within the pool for a given configuration. It is essential to assure that the pool is operated without any violation of the regulations. Since the Computation Fluid Dynamics solving the conservation equations has become more efficient and robust due to the tremendous advancements of both software and hardware technologies in the past decades, It has emerged becoming a useful tool for engineering design and analysis. It has been previously successfully applied to various topics by the authors such as in passive enhancement of electronic cooling through geometric modification [18], phenomena of vortex induced vibration and heat transfer of a circular cylinder [19], the thermalehydraulic analysis for the passive decay heat removal of a sodium-cooled fast reactor [20]. For the nuclear applications, CFD has been applied to the fluidinduced vibration of the U-tube steam generator of a pressurized water reactor [21]. It also has been used to investigate thermalehydraulic characteristics of high temperature gas-cooled reactor during accident [22]. Therefore, CFD is employed to the spent fuel pool modeling in this study.
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The SFP geometry of Kuoshen nuclear power station was selected to create a CFD model to carry out the simulations. For the purpose of safety, temperature distributions and the location of peak temperature in the pool have been evaluated. In this study, a three-dimensional model including two-phase flow has been established to implement the simulations. The simulation results are presented and are expected to serve as a valuable reference in improving the cooling ability of SFPs. A three-dimensional transient CFD simulation tool with twophase flow model was developed. A configuration with normal cooling condition would be employed to validate the CFD model. Meanwhile the results from CFD simulation would be compared with the results of refueling outage with external cooling. The performance of passive heat removal with no external forced flow under the conditions of extremely inappropriate layout of spent fuel will be also simulated and investigated in the present study. 2. Mathematical model The geometry of SFP of Kuoshen power station is schematically shown in Fig. 1. For simplicity without sacrificing too much accuracy, it can be treated as a rectangular domain. The pool is 11 m long, 7.5 m wide and 11 m high. As shown, there are two inlets of cooling water located at the bottom of two opposite walls, and four outlets located at the top of the same two opposite walls. The region of fuel assemblies in the pool fills the bottom region of SFP with a height of 4.2 m. The fuel region is elevated to have its lower end 1 m above the pool bottom. Since the spent fuels release decay heat to the pool water, the flow within the pool is induced by the temperature-difference driven buoyancy, which is taken into consideration by the use of Boussinesq approximation. Heat absorbed by the pool water is then dissipated to the atmosphere above the top surface of the pool. The effective heat transfer coefficient is calculated by using empirical correlations to quantify the magnitude of heat loss. The governing equations describing the conservations of mass, momentum and energy are listed as:
vr vðrui Þ ¼ 0 þ vt vxi
It is necessary to deal with the governing equations for both single- and two-phase flows since liquidevapor phase change may occur in the pool. The region of two-phase flow is simulated by the homogeneous model [23,24]. A bulk pre-evaluation had been implemented before the homogeneous model was believed to be appropriately employed for two-phase simulations in the present study. The pre-evaluation for a single channel exhibited that the bulk quality is almost invisible. According to the simulation result of the most severe case from this study, the maximum local volume fraction of liquid (VOF) is about 0.95 (i.e. void fraction a ¼ 0.05), which corresponds to a quality of just only 3.15 105 for water under 1 atm. Boiling occurs only in limited local area. Meanwhile, the actual pressure around the depth of fuel is greater than 101 kPa with an associate saturated temperature being higher than 100 C. Above approach also provided another conservative concern to the study. It is therefore believed that homogeneous model is accurate enough to investigate the potential two-phase phenomena. For a pure substance, the “state” postulates that two independent, intensive thermodynamic properties are required to completely specify the state of the substance: z ¼ f(x,4). Its variation is hence represented as
dz ¼
vz vz dx þ df vf vx
The time and spatial dependent thermodynamic properties such as density, viscosity of the saturated fluid are calculated according to the local void fraction. The state of the fluid at any location, i.e., liquid phase or vapor phase, is determined based on the local value of enthalpy. If the enthalpy at any location is greater than that of saturated liquid, phase change occurs. The relation between enthalpy and temperature or dryness, x, can be determined as the following:
T ¼ h=Cpf if T < Tsat 0 B x ¼ @h 0
! vsij m Ci rj V j vðrui Þ ui ¼ Vi p þ þ pffiffiffiffi þ rBi þ V$ ruj ui þ ki ki vxi vt
(2)
vðrhÞ vðrui hÞ v vT k þQ ¼ þ vt vxi vxi vxi
(3)
ZTsat
B T ¼ @h
ZTsat
1 , C Cpf dT A hfg if T ¼ Tsat
(6)
1 , C Cpf dT hfg A Cpg if T>Tsat
(7)
T0
The amount of meshes in the domain for a three-dimensional fuel region will be unrealistically large if all the geometry details of the fuel assemblies are considered. Therefore, the flow resistance in the region of the fuel assemblies is simulated by approximating it as an anisotropic porous medium. According to the Darcy’s law, the pressure drop along y-direction, i.e. parallel to fuel rod, in a porous region is:
m. dp V ¼ ky dy
Fig. 1. Schematic of the spent fuel pool of Kuosheng power station.
(5)
T0
(1)
(4)
(8)
In which, a small value of permeability k corresponds to a large flow resistance. The flow velocity in the fuel region is in the range of 0e0.2 m/s. Via the simulations for the flow field within a subchannel amongst the fuel rods, a best-fit curve between Reynolds number and permeability is presented as k ¼ 1330Re0.97. Based on the flow condition, it can be found that the axial permeability, ky, has a value of about 103. As the fuel racks prevent any lateral flow, a very small value of permeability, i.e., 1010, is assumed for both kx and kz to ensure the flow is mainly in the vertical, y-direction.
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499
Fig. 2. Effective heat transfer coefficient vs. pool surface temperature under natural convection.
The thermal power of Kuosheng nuclear power station under normal operation is about 2940 MW. When the reactor is shut down, the heat generated in the fuel decays with time, and the best-fit curve of the decay heat obtained from the measured data is P ¼ P0 0.016323t0.3. In which, t is in hours and it represents the time after shut down. For conservatism, a higher P0 of 3000 MW is used in the analysis of this study. The spent fuels dissipate heat to the pool water and some of the heat may be releases to the atmosphere from the pool top water/air surface. To estimate the heat dissipation effect above the pool water, an effective heat transfer coefficient including both heat and mass transfer effects under natural convection has been developed in this study. Natural convection on the pool surface is induced by a change of density as temperature difference exists on the air/water interface. To calculate the external convection coefficient at the water surface of the pool, the empirical correlations from Fujii and Imura for natural convection [25] were used:
Fig. 4. Temperature variations of the hot spot, at the pool center, and the highest value on free surface of liquid at (a) 14th refueling outage and (b) full-core unload after 13th refueling outage.
Nu ¼ 0:54Ra1=4 ; 104 Ra 107
(9a)
Nu ¼ 0:15Ra1=3 ; 107 Ra 1011
(9b)
Then, the heat removal from the pool surface Qh can be calculated as:
Qh ¼ Nu
kAs ðTs TN Þ L
Fig. 3. Layouts of (a) the fuel with the associate decay heat at 14th refueling outage, and (b) the fuel when it is full-core unload after 13th refueling outage.
(10)
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In addition, due to the similarity between heat transfer and mass transfer, Goldstein et al. [26] developed an analogy and predicted Nusselt number based on mass diffusivity for mass transfer by substituting Prandtl number to Schmidt number. Therefore, the analogous mass transfer based Nusselt number can be expressed as the following: 1=4
(11a)
1=3
(11b)
Num ¼ 0:54Ram ; 104 Ram 107 Num ¼ 0:15Ram ; 107 Ram 1011
The mass transfer is associated with the evaporation of liquid water. Then, the heat removal from the pool surface via mass transfer can be calculated as:
. Qm ¼ Num hfg DðrN rs ÞAs L
(12)
Therefore, the effective heat transfer coefficient heff can be obtained from the combined effect of the heat and mass transfer across the top surface of the pool:
heff ¼
Qh þ Q m As ðTs TN Þ
equations for the fluxes through the surfaces of the control volume and possible volumetric sources. The second-order upwind difference method [28] was employed for discretization of the advective terms. The solver algorithm for the linearized systems of equations was ADI (Alternate Directions Implicit) method [29,30], which is a semi-iterative method solving the equations by maintaining full implicitness in one direction at each iteration step. The scheme employed in the present study to solve the pressure distribution is PISO (Pressure-Implicit with Splitting of Operators) developed by Issa et al. [31,32]. This method employs a series of sequential operations at each time step in which the discretized pressurelinked equation are solved in an alternating “predictorecorrector” fashion. A non-uniform structured grid system was generated. The density of the mesh is graded finer to areas located in regions of expected large velocity and temperature gradients in an effort to employ sufficient resolution to capture boundary-layer behavior with a reasonable accuracy in computation. The accuracy tests for
(13)
As stated above, the effective heat transfer coefficient is a function of temperature on the pool surface. Under the ambient conditions of 1 atm, 20 C, with the relative humidity of 20%, the variation the effective heat transfer coefficient with the pool surface temperature is shown in Fig. 2. The effective heat transfer coefficient exhibits a relatively greater capability in thermal energy removal. This is due to a non-linear proportionality constant between heat transfer and mass transfer under low temperature difference between the pool surface and the ambient. For the boundary conditions, no-slip condition is applied on all walls. 3. Numerical method The finite-volume approach was used to discretize the computation domain in this study [27]. The governing equations were integrated over each control volume. This leads to a set of algebraic
Fig. 5. Location of the new fuels.
Fig. 6. (a) Temperature ( C), (b) velocity, and (c) VOF distribution of SFP under current configuration.
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501
Fig. 7. Four layouts of new spent fuel arrangement.
hot spot temperature with various mesh amount associated with non-uniform grid distribution had been implemented for case of refueling outage with normal cooling by the use of a constant value of heat source. The deviation is within 3% under steady state between 125,000 and 512,000 grids. Convergence was achieved when the maximum sum of the normalized absolute residuals in all equations was reduced to a value less than 104 or the residuals drop three orders of magnitude from their initial value. 4. Results and discussion According to the licensing regulation, the water level of the pool must be 3 m higher than the top of the fuel region, which is set in the following analyses in order to implement the simulations including the worst case with no external water supply.
decay heat is transported to the top of the fuel region and then to the water surface. Due to the relatively lower efficiency in heat transfer from the water to the air, heat carried by the water stream is cumulated near the top free surface. This is why the temperature of water on free surface is higher than that at the pool center. The temperature of the hot spot is about 50 C and 30 C on the free surface of the pool. The results indicate the configuration under the present study would meet the requirements of licensing regulation that the peak temperature of the pool should not exceed 60 C. 4.1.2. Full-core unload with normal cooling As the regulation requires all fuel rods must be relocated to SFP while the power plant has an accident. The amount of decay heat is about 10.5 MW. The layout of the fuel in the pool is schematically shown as Fig. 3(b).
4.1. Spent fuel cooling with external flow 4.1.1. Refueling outage with normal cooling When a reactor is on a scheduled refueling outage, the fuel rods in the pressure vessel are removed after the reactor is shut down. Under normal operation, inlet water flow velocity is steadily given with 1 cm/s. No extra cooling facility is provided. CFD approach is employed to model SFP and simulate its thermal hydraulics characteristics. At 14th refueling outage, 157 rods of spent fuel were removed from reactor with the amount of decay heat being at 2.25 MW. The layout of the fuel is schematically shown as in Fig. 3(a). The variations of hot spot temperature, pool center temperature, and the highest surface liquid temperature with respect to time are shown in Fig. 4(a). In which, the location of the hot spot temperature is changed from time to time all along the simulation period. How could the temperature on the liquid surface be higher than that at the center of the pool? One reason is that the fuel rods are not located around the center region of the xez plane. Another reason is that the natural convection induced upward flow around the new fuel region intensifies after about 20 min. Therefore the
Fig. 8. VOF distribution of case (a).
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Fig. 9. (a) Temperature ( C), (b) velocity, and (c) VOF distributions of case (b).
As shown in Fig. 4(b), the results indicate that temperature distribution basically also becomes stable with minor fluctuation within expected time after the moving in of new fuel. The temperature of the hot spot and the free surface of the pool are about 80 C and 40 C, respectively. The results indicate that the peak temperature would be remained safety with the temperature lower than the saturated state. 4.2. Spent fuel cooling without external flow 4.2.1. Basic spent fuel arrangement The basic configuration of the new fuels which were moved into the pool from the reactor is shown in Fig. 5. The region filled by these fuels is the main heating region because the power generation from these fuels is larger than that of other fuels. Additionally, the old fuels, which have been in the pool for more than a month before core unloaded, are still generating heat. The locations occupied by the old fuels are adjacent to the new fuels. The simulation results after the new fuels placed in the pool for 6 h, including the distributions of temperature, velocity and VOF are shown in Fig. 6 for the center plane of the pool along the z-direction (z ¼ 3.5 m). The blocked region represents the location of the new fuels. As shown in Fig. 6(a), the temperature of the water entering the bottom of the fuel region is 75 C, and the water reaches saturation at the top of the fuel assembly. It can be observed that the main flow direction of the water is restricted in the y-direction inside the fuel region as shown in Fig. 6(b). This also concludes that the assumption of an anisotropic porous medium depicts a vertically-dominated flow field in the fuel region. As shown in
Fig. 6(c), VOF is less than 1 at the top of the fuel region. It means that liquidevapor phase change takes place here, and this could violate the regulation. From the simulation results, phase change may occur with the basic arrangement of the new fuels and this should be considered as an accident. 4.2.2. Another layout of new fuel arrangement In order to further verify the model and understand the cooling behavior of SFP, four layouts of fuel arrangement are proposed. As shown in Fig. 7(a), the new spent fuels are separated from other older fuel assemblies by loading on one side of the pool. Simulation results of this case show that phase change occurs within a more confined region as compared to the basic case with lower values of VOF (see Fig. 8). The cooling effect of the pool is rather reduced because the flow is blocked by the new fuels located adjacent to the wall. The flow is constricted by the pool wall. With the reduction of convection, water is not able to distribute the decay heat uniformly to the whole pool. This makes a higher degree of vaporization on the top of the new fuel region. As shown in Fig. 7(b), the new spent fuels are arranged to equally locate adjacent to two opposite walls of the pool. The
Table 1 Results of different arrangement. Layout
Basic case
a
b
c
d
100
100
100
(See Fig. 7) Highest temperature in the pool ( C) Average temperature of the surface ( C) Lowest VOF
100 97.05 0.946
100 94.99 0.901
93.87 0.97
92.74 0.897
93.57 0.956 Fig. 10. Variations of maximum pool temperatures of various fuel layouts.
T.-C. Hung et al. / Applied Thermal Engineering 50 (2013) 496e504 Table 2 Simulation results for the conservative cases. Cases
Condition Water level above fuel region (m) Highest temp. in the pool ( C) Average temp. of the surface ( C) Lowest VOF
e
f
g
Refueling outage 3
Full-core discharge 3
Full-core discharge 2
63
100
100
45 1
83.56 0.951
98.8 0.933
simulated results of temperature, velocity, and VOF distributions are shown in Fig. 9. The numerical results are presented for the center plane in the x-direction, i.e., the plane at x ¼ 5.5 m. As compared to Case (a), flow convection is less restricted and heat transfer is more efficient in the pool. As a result, the degree of phase change is also lower and the regions of two-phase are also reduced. The un-symmetric distributions in stream vectors, temperature, and VOF are caused by the flow instability during the transient and that is approximately varied periodically. Similarly, simulations for Cases (c) and (d) were obtained in the same fashion. The highest temperatures, average temperatures of the pool surface, and the lowest values of VOF are listed in Table 1. By comparing the lowest values of VOF, the performance of Case (b) has the best performance among all the cases under investigation as far as the phase change is concerned. Furthermore, Case (b) gives the longest time for the maximum pool temperature to reach saturation as shown in Fig. 10. Above finding reveals that the decay heat of the spent fuels could be difficultly removed solely via natural convection in existing configuration of SFP. Other approaches in enhancing heat removal such as an external supply of cooling water may become necessary. For a more conservative consideration, it can be assumed that the water level is reduced to 2 m above the fuel region in order to yield more adverse consequences. Under the current configuration of the spent fuels, the results with reduced water depth are shown in Table 2. Case (e) represents the condition of a refueling outage; Cases (f) and (g) represent the conditions of a full-core discharge. The water level of case (e) and (f) is assumed to be 3 m above the fuels while the water level is assumed to be 2 m above the fuels for Case (g). By comparing Cases (e) and (f), since the fuels of the fullcore discharge have much higher in heat generation, the temperature of Case (f) is higher than that of Case (e). With the reduction of pool water, the cooling ability of the pool decreases. Thus, the VOF values decrease, representing greater void fraction, with the lower water level. 5. Conclusion A three-dimensional two-phase CFD model has been successfully developed to simulate the thermalehydraulic behavior of the spent-fuel pool. In this study, SFP of the Kuoshen power station is employed for study. The simulation implemented with the worst situation, in which fuels under full-core discharge are assumed to be moved into SFP, and the external cool system is assumed failed. To present the pressure drop of the flow passing through the fuels, the effective permeability is calculated from Darcy’s law for porous medium, which simplified the fuel region. The effective convective coefficient on the pool surface is also modeled based on the empirical correlations. From the computation results, the current configuration of spent fuel layout in a SFP has an enough cooling capability to meet
503
the licensing regulations under normal operation conditions. However, local boiling would occur on the surface of the spent fuels with the current configuration of spent fuel layout if the event is beyond the regulation with no application of an external cooling system. To enhance the understanding of the cooling effect of the pool, four different layouts were considered and simulated in this study. It is found that to the arrangement of locating the new spent fuels on two opposite sides of the pool has a better improvement. However, the enhancement is marginal and there still exists local boiling. If the water level is less than 3-m higher than the fuels, the water temperature increases and the VOF value becomes lower. Although the arrangement of the fuels can improve the cooling effect of SFP, an external cool system is still required to prevent the occurrence of local boiling. Acknowledgements This research work has been supported by the National Science Council, Taiwan, R.O.C. under the grants of NSC 98-2221-E-027085-MY3 and NSC-100-2623-E-027-001-NU. The authors also highly appreciate Mr. C.W. Hsiao for his valuable assistance in the numerical approaches. References [1] D. Bodansky, Nuclear Energy e Principles, Practices, and Prospects, second ed., Springer, New York, 2005, pp. 253e290. [2] A. Kaliatka, V. Ognerubov, V. Vileiniskis, Analysis of the processes in spent fuel pools of Ignalina NPP in case of loss of heat removal, Nucl. Eng. Des. 240 (2010) 1073e1082. [3] C.D. Fletcher, R.R. Schultz, RELAP5/MOD3 Code Manual User’s Guidelines, NUREG/CR-5535, Idaho National Lab., 1992. [4] A.B. Wahba, International activities for the analysis of the TMI-2 accident with special consideration of ATHLET calculations, Nucl. Eng. Des. 118 (1990) 43e53. [5] J.P. Van Dorsselaere, C. Seropian, P. Chatelard, F. Jacq, J. Fleurot, P. Giordano, N. Reinke, B. Schwinges, H.J. Allelein, W. Luther, The ASTEC integral code for severe accident simulation, Nucl. Technol. 165 (3) (2009) 293e307. [6] V. Kain, P.K. De, K. Agarwal, P. Seetharamaih, Environmental degradation of materials during wet storage of spent nuclear fuels, J. Mater. Eng. Perform. 9 (3) (2000) 317e323. [7] R.G. Aghoyeh, H. Khalafi, Design of make-up water system for Tehran research reactor spent nuclear fuels storage pool, Nucl. Eng. Des. 240 (2010) 2532e2537. [8] J.H. Park, H.M. Koh, J.K. Kim, Seismic isolation of pool-type tanks for the storage of nuclear spent fuel assemblies, Nucl. Eng. Des. 199 (2000) 143e154. [9] US NRC, Standard Review Plan for Dry Cask Storage Systems. NUREG-1536 (1997). [10] NAC International Inc., Final Safety Analysis Report for the UMS Universal Storage System, Rev. 5 (2005). [11] Y.S. Tseng, J.R. Wang, F.P. Tsai, Y.H. Cheng, C.K. Shih, Thermal design investigation of a new tube-type dry-storage system through CFD simulations, Ann. Nucl. Energy 38 (2011) 1088e1097. [12] Y.Y. Ko, S.Y. Hsua, C.H. Chen, Analysis for seismic response of dry storage facility for spent fuel, Nucl. Eng. Des. 239 (2009) 158e168. [13] F. Nimander, Investigation of Spent Nuclear Fuel Pool Coolability, Master Dissertation, Royal Institute of Technology, Stockholm, Sweden, August (2011). [14] J.R. Wang, H.T. Lin, Y.S. Tseng, C.K. Shih, Application of TRACE and CFD in the spent fuel pool of Chinshan nuclear power plant, Appl. Mechanics and Materials 145 (2012) 78e82. [15] U.S. NRC, in: TRACE V5.0 Theory Manual, Division of Safety Analysis, Office of Nuclear Regulatory Research, 2010. [16] Atomic Energy Council, Regulations and Safety Report of Spent Fuel Pool. Taiwan (1990). [17] Atomic Energy Council, Safety Review Report on Maanshan Unit 1 & 2 Reracking Application (1995). NRD/LRS-8601, Taiwan, March. [18] T.C. Hung, C.S. Fu, Conjugate heat transfer analysis for the passive enhancement of electronic cooling through geometric modification in a mixed convection domain, Numer. Heat Tranf. A-Appl. 35 (5) (1999) 519e535. [19] S.K. Wang, T.C. Hung, G.W. Lin, B.S. Pei, Numerical simulations for the phenomena of vortex induced vibration and heat transfer of a circular cylinder, Numer. Heat Tranf. A-Appl. 45 (7) (2004) 1e18. [20] T.C. Hung, V.K. Dhir, J.C. Chang, S.K. Wang, CFD modeling and thermalhydraulic analysis for the passive decay heat removal of a sodium-cooled fast reactor, Nucl. Eng. Des. 241 (2011) 425e432.
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[21] Yuh-Ming Ferng, Han-Jou Chang, CFD investigating the impacts of changing operating conditions on the thermalehydraulic characteristics in a steam generator, Appl. Thermal Engineering 28 (2008) 414e422. [22] Y.M. Ferng, C.T. Chen, CFD investigating thermalehydraulic characteristics and hydrogen generation from graphite-water reaction after SG tube rupture in HTR-10 reactor, Appl. Thermal Engineering 31 (2011) 2430e2438. [23] G.B. Wallis, One-Dimensional Two-Phase Flow, McGraw-Hill, 1969, p. 17. [24] A. Ambros, C. Chalons, F. Coquel, E. Godlewski, F. Lagoutiere, P.A. Raviart, N. Seguin, The coupling of homogeneous models for two-phase flows, Int. J. on Finite Volumes 4 (1) (2007) 1e39. [25] T. Fujii, H. Imura, Natural convection heat transfer from a plate with arbitrary inclination, Int. J. Heat Mass Transf. 15 (1972) 755e767. [26] R.J. Goldstein, E.M. Sparrow, D.C. Jones, Natural convection mass transfer adjacent to horizontal plates, Int. J. Heat Mass Transf. 16 (1973) 1025.
[27] S.V. Patankar, Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing Corporation, Taylor & Francis Group, New York, 1980. [28] T.J. Barth, D. Jespersen, The Design and Application of Upwind Schemes on Unstructured Meshes, Technical Report AIAA-89-0366, AIAA 27th Aerospace Sciences Meeting, Reno, Nevada, U.S., 1989. [29] D.W. Peaceman, H.H. Rachford, The numerical solution of parabolic and elliptic differential equations, J. Soc. Ind. Appl. Math. 3 (1955) 28e41. [30] J. Douglas, On the numerical integration of v2u/vx2þv2u/vy2¼vu/vt by implicit methods, J. Soc. Ind. Appl. Math. 3 (1955) 42e65. [31] R.I. Issa, B. Ahmadi-Befrui, K.R. Beshay, A.D. Gosman, Solution of the implicit discretized reacting flow equations by operator-splitting, J. Comput. Phys. 93 (1991) 388e410. [32] R.I. Issa, A.D. Gosman, A.P. Watkins, The computation of compressible and incompressible recirculating flows by a non-iterative implicit scheme, J. Comput. Phys. 62 (1986) 66e82.
Contents lists available at SciVerse ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
The development of a three-dimensional transient CFD model for predicting cooling ability of spent fuel pools Tzu-Chen Hung a, *, Vijay K. Dhir b, Bau-Shei Pei c, Yen-Shu Chen d, Fengjee P. Tsai e a
Department of Mechanical Engineering, National Taipei University of Technology, 1, Sec. 3, Chung-hsiao E. Rd., Taipei, Taiwan Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, USA c Department of Engineering and System Science, National Tsing Hua University, Hsinchu, Taiwan d Nuclear Engineering Division, Institute of Nuclear Energy Research, Taoyuan County, Taiwan e Cool-tec Co., Rancho Palos Verdes, CA, USA b
h i g h l i g h t s < A CFD model has been developed to simulate spent fuel pool (SFP). < SFP cooling capability of a nuclear station was verified by the model. < Current SFP configuration satisfies the regulations under normal operation. < An inappropriate layout of fuel without external cooling might cause local boiling.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 13 September 2011 Accepted 26 June 2012 Available online 14 July 2012
The objective of this research is to develop a numerical model for the evaluation of the cooling capability of spent fuel pool (SFP) in removing decay heat. Computational fluid dynamics (CFD) approach has been applied to develop a three-dimensional two-phase thermal hydraulic model. To simplify the analysis, the pressure drop of the coolant flowing through the fuel region in the pool is modeled as a porous-medium. The geometry as well as the boundary conditions of SFP of second nuclear power plant in Taiwan has been employed as sample to be analyzed and simulated numerically. The results show that the current configuration has enough cooling capability to meet the licensing regulations under normal operation and most kinds of conditions. In the case of extremely inappropriate layout of spent fuel arrangement, the computed results illustrate that slight local saturation on fuel rods may occur unless external cooling system is supplied. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Spent fuel pool Decay heat Computational fluid dynamics Local boiling
1. Introduction Nuclear policies and the use of nuclear energy have caused profound public concerns and conflicts worldwide. On March 11 of 2011, an earthquake of magnitude 9.0 with following ruinous tsunami caused the loss of adequate cooling capability to the reactors and spent fuel pool of Fukushima Daiichi nuclear plant in Japan. Accordingly, the issues of nuclear safety have attracted great public’s attention, and the safety of spent fuels has been in the spot issue among all the safety concerns. The spent fuels are not reprocessed in many countries, and wet storage has been the predominant mode of storage. Before permanent disposal of spent fuel, reprocess of waste, or residues of
* Corresponding author. Tel.: þ886 2 2771 2171x2021. E-mail address: [email protected] (T.-C. Hung). 1359-4311/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.applthermaleng.2012.06.042
transmutation or by other means are developed, spent fuels are in general stored for extended periods in SFPs [1]. The evaluation of the safety of spent fuels stored in the framework of the existing facility becomes of vital importance in accessing the magnitude of effects following a nuclear accident. Normally, nuclear power plant stores the spent fuels in a pool, which is located outside of the primary containment with sufficient cooling water. To authors’ knowledge, cooling study has not been extensively studied due to that SFP was not categorized as safety grade issue. Kaliatka et al. presented the results of loss of heat removal accidents in SFPs of Ignalina nuclear power plant (NPP) [2]. The analysis was performed by employing system thermal hydraulic code RELAP5 [3] and codes for severe accidents ATHLET [4] and ASTEC [5]. In addition to the concern in heat removal capacity, the pool water constituents have also been analyzed and electrochemical potential (ECP) measured in water samples drawn from different locations of the pool [6]. Aghoyeh and Khalafi [7]
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Nomenclature A B Cp D g h heff hfg hm k L Nu Num p P Ppeak Qh Qm Ra Ram
area (m2) specific buoyancy force, (m/s2) specific heat, (J/kg-K) mass diffusivity, (m2/s) Gravity, (m/s2) enthalpy, (J/kg) effective heat-transfer coefficient, (W/m2-K) latent heat, (J/kg) mass-convective-transfer-coefficient, (m/s) thermal conductivity, (W/m-K) characteristic length of the pool surface, (m) Nusselt number, Nu ¼ hL/k analogous Nusselt number of mass transfer, Nu ¼ hmL/D pressure, (N/m2) power generated from the fuels, (W) peak power generated from the fuels, (W) heat transferred via convection, (W) heat transferred via mass transfer (W) Rayleigh number; Ra ¼ rbgDTL3/ma analogous Rayleigh number of mass transfer, Ram ¼ rbgDTL3/mD
presented a design of make-up water system for optimal water supply and its chemical properties in SFP to provide proper cooling water throughout the storage time. The characteristics of activated carbon purifier, anionic, cationic and mixed-bed ion-exchangers have been determined. Park et al. investigated the seismic isolation for SFP [8]. They built a three-dimensional model using finite element method was presented for the analysis of the fluidstructure-isolator systems in time domain. Their study indicates that careful selection of mechanical properties of the isolators with a lower limit on the effective frequency can effectively reduce the dynamic responses of SFP and enhance the stability of stored spent fuel assemblies against earthquake. Dry-storage system is another effective long-term storage solution for lower-rate of decay heat spent fuel [9]. Through a passive cooling design, spent fuels can be stored in a safe and stable environment for at least 20 years. Several dry-storage systems were developed and analyzed for different kind of fuels at different power ratings. NAC-56 [10] is one of the examples. A three-dimensional CFD model was established and employed to investigate the heat removal characteristics by Tseng et al. [11]. Ko et al. used the ABAQUS/Explicit code [12] to analyze the seismic response of the dry storage facility. Nonetheless, dry storage cannot practically replace the spent fuel pool shortly after the fuel being removed from the reactor core. In a very recent study of Nimander [13], it has been found that the temperature difference between the heated air and ambient air is far too low for natural circulation of air to remove any significant amount of heat from the spent nuclear fuel pool in a worst case scenario. Air has too low density and specific heat to remove the heat generated by spent nuclear fuel shortly after it has been removed from the reactor core. In the study of Wang et al. [14], the safety analysis of the spent fuel pool for Chinshan NPP in Taiwan was performed by using both the system code TRACE [15] and CFD approach. The analysis result of TRACE and CFD are similar for the times to achieve the uncovering of the fuels by water and the metalewater reaction of the fuels after the cooling system failed. The 2D fuel bundle model was utilized to calculate the effective thermal conductivity for the
Re S T t ! V VOF
497
Reynolds number, Re ¼ ruL/m source term temperature, ( C) time, (h) resultant velocity, (m/s) volume fraction of liquid
Greek symbols void fraction ¼ 1 VOF permeability dynamic viscosity density, (kg/m3) viscous stress tensor Tij z, x, 4 represent any specific thermodynamic properties
a k m r
Subscripts i direction i f liquid phase s pool surface sat saturated g gas phase N atmosphere above SFP
porous media in the 3D spent fuel pool model. In their models, no detail mathematical model including either porosity or two-phase flow model was included. According to the regulation by Atomic Energy Commissions, Taiwan [16], when a reactor is on a scheduled refueling outage, fuel rods in the pressure vessel are removed from the reactor core after the reactor is shut down. In fact, it takes time to remove the fuel rods to SFP. The transportation time of the fuel rods to SFP is assumed to be 150 h with a power generation in this mode at approximately 0.36% of that while it is under a peak-load operation. The cooling system of the pool must be actuated before the peak temperature of the pool reaching 60 C. A comparative analysis in spent fuel re-racking designs can be found in documentation [17]. Once an accident occurs during a steady-state full load operation, the fuel rods in the reactor, as required by the regulations, have to be immediately removed to SFP. To provide enough cooling to the fuels, water level of the pool is required to be at least 3 m higher than the top of fuels in the pool, and no boiling is allowed. The most important issue of the simulations in this study is to find out the magnitude and location of peak temperature within the pool for a given configuration. It is essential to assure that the pool is operated without any violation of the regulations. Since the Computation Fluid Dynamics solving the conservation equations has become more efficient and robust due to the tremendous advancements of both software and hardware technologies in the past decades, It has emerged becoming a useful tool for engineering design and analysis. It has been previously successfully applied to various topics by the authors such as in passive enhancement of electronic cooling through geometric modification [18], phenomena of vortex induced vibration and heat transfer of a circular cylinder [19], the thermalehydraulic analysis for the passive decay heat removal of a sodium-cooled fast reactor [20]. For the nuclear applications, CFD has been applied to the fluidinduced vibration of the U-tube steam generator of a pressurized water reactor [21]. It also has been used to investigate thermalehydraulic characteristics of high temperature gas-cooled reactor during accident [22]. Therefore, CFD is employed to the spent fuel pool modeling in this study.
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The SFP geometry of Kuoshen nuclear power station was selected to create a CFD model to carry out the simulations. For the purpose of safety, temperature distributions and the location of peak temperature in the pool have been evaluated. In this study, a three-dimensional model including two-phase flow has been established to implement the simulations. The simulation results are presented and are expected to serve as a valuable reference in improving the cooling ability of SFPs. A three-dimensional transient CFD simulation tool with twophase flow model was developed. A configuration with normal cooling condition would be employed to validate the CFD model. Meanwhile the results from CFD simulation would be compared with the results of refueling outage with external cooling. The performance of passive heat removal with no external forced flow under the conditions of extremely inappropriate layout of spent fuel will be also simulated and investigated in the present study. 2. Mathematical model The geometry of SFP of Kuoshen power station is schematically shown in Fig. 1. For simplicity without sacrificing too much accuracy, it can be treated as a rectangular domain. The pool is 11 m long, 7.5 m wide and 11 m high. As shown, there are two inlets of cooling water located at the bottom of two opposite walls, and four outlets located at the top of the same two opposite walls. The region of fuel assemblies in the pool fills the bottom region of SFP with a height of 4.2 m. The fuel region is elevated to have its lower end 1 m above the pool bottom. Since the spent fuels release decay heat to the pool water, the flow within the pool is induced by the temperature-difference driven buoyancy, which is taken into consideration by the use of Boussinesq approximation. Heat absorbed by the pool water is then dissipated to the atmosphere above the top surface of the pool. The effective heat transfer coefficient is calculated by using empirical correlations to quantify the magnitude of heat loss. The governing equations describing the conservations of mass, momentum and energy are listed as:
vr vðrui Þ ¼ 0 þ vt vxi
It is necessary to deal with the governing equations for both single- and two-phase flows since liquidevapor phase change may occur in the pool. The region of two-phase flow is simulated by the homogeneous model [23,24]. A bulk pre-evaluation had been implemented before the homogeneous model was believed to be appropriately employed for two-phase simulations in the present study. The pre-evaluation for a single channel exhibited that the bulk quality is almost invisible. According to the simulation result of the most severe case from this study, the maximum local volume fraction of liquid (VOF) is about 0.95 (i.e. void fraction a ¼ 0.05), which corresponds to a quality of just only 3.15 105 for water under 1 atm. Boiling occurs only in limited local area. Meanwhile, the actual pressure around the depth of fuel is greater than 101 kPa with an associate saturated temperature being higher than 100 C. Above approach also provided another conservative concern to the study. It is therefore believed that homogeneous model is accurate enough to investigate the potential two-phase phenomena. For a pure substance, the “state” postulates that two independent, intensive thermodynamic properties are required to completely specify the state of the substance: z ¼ f(x,4). Its variation is hence represented as
dz ¼
vz vz dx þ df vf vx
The time and spatial dependent thermodynamic properties such as density, viscosity of the saturated fluid are calculated according to the local void fraction. The state of the fluid at any location, i.e., liquid phase or vapor phase, is determined based on the local value of enthalpy. If the enthalpy at any location is greater than that of saturated liquid, phase change occurs. The relation between enthalpy and temperature or dryness, x, can be determined as the following:
T ¼ h=Cpf if T < Tsat 0 B x ¼ @h 0
! vsij m Ci rj V j vðrui Þ ui ¼ Vi p þ þ pffiffiffiffi þ rBi þ V$ ruj ui þ ki ki vxi vt
(2)
vðrhÞ vðrui hÞ v vT k þQ ¼ þ vt vxi vxi vxi
(3)
ZTsat
B T ¼ @h
ZTsat
1 , C Cpf dT A hfg if T ¼ Tsat
(6)
1 , C Cpf dT hfg A Cpg if T>Tsat
(7)
T0
The amount of meshes in the domain for a three-dimensional fuel region will be unrealistically large if all the geometry details of the fuel assemblies are considered. Therefore, the flow resistance in the region of the fuel assemblies is simulated by approximating it as an anisotropic porous medium. According to the Darcy’s law, the pressure drop along y-direction, i.e. parallel to fuel rod, in a porous region is:
m. dp V ¼ ky dy
Fig. 1. Schematic of the spent fuel pool of Kuosheng power station.
(5)
T0
(1)
(4)
(8)
In which, a small value of permeability k corresponds to a large flow resistance. The flow velocity in the fuel region is in the range of 0e0.2 m/s. Via the simulations for the flow field within a subchannel amongst the fuel rods, a best-fit curve between Reynolds number and permeability is presented as k ¼ 1330Re0.97. Based on the flow condition, it can be found that the axial permeability, ky, has a value of about 103. As the fuel racks prevent any lateral flow, a very small value of permeability, i.e., 1010, is assumed for both kx and kz to ensure the flow is mainly in the vertical, y-direction.
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499
Fig. 2. Effective heat transfer coefficient vs. pool surface temperature under natural convection.
The thermal power of Kuosheng nuclear power station under normal operation is about 2940 MW. When the reactor is shut down, the heat generated in the fuel decays with time, and the best-fit curve of the decay heat obtained from the measured data is P ¼ P0 0.016323t0.3. In which, t is in hours and it represents the time after shut down. For conservatism, a higher P0 of 3000 MW is used in the analysis of this study. The spent fuels dissipate heat to the pool water and some of the heat may be releases to the atmosphere from the pool top water/air surface. To estimate the heat dissipation effect above the pool water, an effective heat transfer coefficient including both heat and mass transfer effects under natural convection has been developed in this study. Natural convection on the pool surface is induced by a change of density as temperature difference exists on the air/water interface. To calculate the external convection coefficient at the water surface of the pool, the empirical correlations from Fujii and Imura for natural convection [25] were used:
Fig. 4. Temperature variations of the hot spot, at the pool center, and the highest value on free surface of liquid at (a) 14th refueling outage and (b) full-core unload after 13th refueling outage.
Nu ¼ 0:54Ra1=4 ; 104 Ra 107
(9a)
Nu ¼ 0:15Ra1=3 ; 107 Ra 1011
(9b)
Then, the heat removal from the pool surface Qh can be calculated as:
Qh ¼ Nu
kAs ðTs TN Þ L
Fig. 3. Layouts of (a) the fuel with the associate decay heat at 14th refueling outage, and (b) the fuel when it is full-core unload after 13th refueling outage.
(10)
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In addition, due to the similarity between heat transfer and mass transfer, Goldstein et al. [26] developed an analogy and predicted Nusselt number based on mass diffusivity for mass transfer by substituting Prandtl number to Schmidt number. Therefore, the analogous mass transfer based Nusselt number can be expressed as the following: 1=4
(11a)
1=3
(11b)
Num ¼ 0:54Ram ; 104 Ram 107 Num ¼ 0:15Ram ; 107 Ram 1011
The mass transfer is associated with the evaporation of liquid water. Then, the heat removal from the pool surface via mass transfer can be calculated as:
. Qm ¼ Num hfg DðrN rs ÞAs L
(12)
Therefore, the effective heat transfer coefficient heff can be obtained from the combined effect of the heat and mass transfer across the top surface of the pool:
heff ¼
Qh þ Q m As ðTs TN Þ
equations for the fluxes through the surfaces of the control volume and possible volumetric sources. The second-order upwind difference method [28] was employed for discretization of the advective terms. The solver algorithm for the linearized systems of equations was ADI (Alternate Directions Implicit) method [29,30], which is a semi-iterative method solving the equations by maintaining full implicitness in one direction at each iteration step. The scheme employed in the present study to solve the pressure distribution is PISO (Pressure-Implicit with Splitting of Operators) developed by Issa et al. [31,32]. This method employs a series of sequential operations at each time step in which the discretized pressurelinked equation are solved in an alternating “predictorecorrector” fashion. A non-uniform structured grid system was generated. The density of the mesh is graded finer to areas located in regions of expected large velocity and temperature gradients in an effort to employ sufficient resolution to capture boundary-layer behavior with a reasonable accuracy in computation. The accuracy tests for
(13)
As stated above, the effective heat transfer coefficient is a function of temperature on the pool surface. Under the ambient conditions of 1 atm, 20 C, with the relative humidity of 20%, the variation the effective heat transfer coefficient with the pool surface temperature is shown in Fig. 2. The effective heat transfer coefficient exhibits a relatively greater capability in thermal energy removal. This is due to a non-linear proportionality constant between heat transfer and mass transfer under low temperature difference between the pool surface and the ambient. For the boundary conditions, no-slip condition is applied on all walls. 3. Numerical method The finite-volume approach was used to discretize the computation domain in this study [27]. The governing equations were integrated over each control volume. This leads to a set of algebraic
Fig. 5. Location of the new fuels.
Fig. 6. (a) Temperature ( C), (b) velocity, and (c) VOF distribution of SFP under current configuration.
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Fig. 7. Four layouts of new spent fuel arrangement.
hot spot temperature with various mesh amount associated with non-uniform grid distribution had been implemented for case of refueling outage with normal cooling by the use of a constant value of heat source. The deviation is within 3% under steady state between 125,000 and 512,000 grids. Convergence was achieved when the maximum sum of the normalized absolute residuals in all equations was reduced to a value less than 104 or the residuals drop three orders of magnitude from their initial value. 4. Results and discussion According to the licensing regulation, the water level of the pool must be 3 m higher than the top of the fuel region, which is set in the following analyses in order to implement the simulations including the worst case with no external water supply.
decay heat is transported to the top of the fuel region and then to the water surface. Due to the relatively lower efficiency in heat transfer from the water to the air, heat carried by the water stream is cumulated near the top free surface. This is why the temperature of water on free surface is higher than that at the pool center. The temperature of the hot spot is about 50 C and 30 C on the free surface of the pool. The results indicate the configuration under the present study would meet the requirements of licensing regulation that the peak temperature of the pool should not exceed 60 C. 4.1.2. Full-core unload with normal cooling As the regulation requires all fuel rods must be relocated to SFP while the power plant has an accident. The amount of decay heat is about 10.5 MW. The layout of the fuel in the pool is schematically shown as Fig. 3(b).
4.1. Spent fuel cooling with external flow 4.1.1. Refueling outage with normal cooling When a reactor is on a scheduled refueling outage, the fuel rods in the pressure vessel are removed after the reactor is shut down. Under normal operation, inlet water flow velocity is steadily given with 1 cm/s. No extra cooling facility is provided. CFD approach is employed to model SFP and simulate its thermal hydraulics characteristics. At 14th refueling outage, 157 rods of spent fuel were removed from reactor with the amount of decay heat being at 2.25 MW. The layout of the fuel is schematically shown as in Fig. 3(a). The variations of hot spot temperature, pool center temperature, and the highest surface liquid temperature with respect to time are shown in Fig. 4(a). In which, the location of the hot spot temperature is changed from time to time all along the simulation period. How could the temperature on the liquid surface be higher than that at the center of the pool? One reason is that the fuel rods are not located around the center region of the xez plane. Another reason is that the natural convection induced upward flow around the new fuel region intensifies after about 20 min. Therefore the
Fig. 8. VOF distribution of case (a).
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Fig. 9. (a) Temperature ( C), (b) velocity, and (c) VOF distributions of case (b).
As shown in Fig. 4(b), the results indicate that temperature distribution basically also becomes stable with minor fluctuation within expected time after the moving in of new fuel. The temperature of the hot spot and the free surface of the pool are about 80 C and 40 C, respectively. The results indicate that the peak temperature would be remained safety with the temperature lower than the saturated state. 4.2. Spent fuel cooling without external flow 4.2.1. Basic spent fuel arrangement The basic configuration of the new fuels which were moved into the pool from the reactor is shown in Fig. 5. The region filled by these fuels is the main heating region because the power generation from these fuels is larger than that of other fuels. Additionally, the old fuels, which have been in the pool for more than a month before core unloaded, are still generating heat. The locations occupied by the old fuels are adjacent to the new fuels. The simulation results after the new fuels placed in the pool for 6 h, including the distributions of temperature, velocity and VOF are shown in Fig. 6 for the center plane of the pool along the z-direction (z ¼ 3.5 m). The blocked region represents the location of the new fuels. As shown in Fig. 6(a), the temperature of the water entering the bottom of the fuel region is 75 C, and the water reaches saturation at the top of the fuel assembly. It can be observed that the main flow direction of the water is restricted in the y-direction inside the fuel region as shown in Fig. 6(b). This also concludes that the assumption of an anisotropic porous medium depicts a vertically-dominated flow field in the fuel region. As shown in
Fig. 6(c), VOF is less than 1 at the top of the fuel region. It means that liquidevapor phase change takes place here, and this could violate the regulation. From the simulation results, phase change may occur with the basic arrangement of the new fuels and this should be considered as an accident. 4.2.2. Another layout of new fuel arrangement In order to further verify the model and understand the cooling behavior of SFP, four layouts of fuel arrangement are proposed. As shown in Fig. 7(a), the new spent fuels are separated from other older fuel assemblies by loading on one side of the pool. Simulation results of this case show that phase change occurs within a more confined region as compared to the basic case with lower values of VOF (see Fig. 8). The cooling effect of the pool is rather reduced because the flow is blocked by the new fuels located adjacent to the wall. The flow is constricted by the pool wall. With the reduction of convection, water is not able to distribute the decay heat uniformly to the whole pool. This makes a higher degree of vaporization on the top of the new fuel region. As shown in Fig. 7(b), the new spent fuels are arranged to equally locate adjacent to two opposite walls of the pool. The
Table 1 Results of different arrangement. Layout
Basic case
a
b
c
d
100
100
100
(See Fig. 7) Highest temperature in the pool ( C) Average temperature of the surface ( C) Lowest VOF
100 97.05 0.946
100 94.99 0.901
93.87 0.97
92.74 0.897
93.57 0.956 Fig. 10. Variations of maximum pool temperatures of various fuel layouts.
T.-C. Hung et al. / Applied Thermal Engineering 50 (2013) 496e504 Table 2 Simulation results for the conservative cases. Cases
Condition Water level above fuel region (m) Highest temp. in the pool ( C) Average temp. of the surface ( C) Lowest VOF
e
f
g
Refueling outage 3
Full-core discharge 3
Full-core discharge 2
63
100
100
45 1
83.56 0.951
98.8 0.933
simulated results of temperature, velocity, and VOF distributions are shown in Fig. 9. The numerical results are presented for the center plane in the x-direction, i.e., the plane at x ¼ 5.5 m. As compared to Case (a), flow convection is less restricted and heat transfer is more efficient in the pool. As a result, the degree of phase change is also lower and the regions of two-phase are also reduced. The un-symmetric distributions in stream vectors, temperature, and VOF are caused by the flow instability during the transient and that is approximately varied periodically. Similarly, simulations for Cases (c) and (d) were obtained in the same fashion. The highest temperatures, average temperatures of the pool surface, and the lowest values of VOF are listed in Table 1. By comparing the lowest values of VOF, the performance of Case (b) has the best performance among all the cases under investigation as far as the phase change is concerned. Furthermore, Case (b) gives the longest time for the maximum pool temperature to reach saturation as shown in Fig. 10. Above finding reveals that the decay heat of the spent fuels could be difficultly removed solely via natural convection in existing configuration of SFP. Other approaches in enhancing heat removal such as an external supply of cooling water may become necessary. For a more conservative consideration, it can be assumed that the water level is reduced to 2 m above the fuel region in order to yield more adverse consequences. Under the current configuration of the spent fuels, the results with reduced water depth are shown in Table 2. Case (e) represents the condition of a refueling outage; Cases (f) and (g) represent the conditions of a full-core discharge. The water level of case (e) and (f) is assumed to be 3 m above the fuels while the water level is assumed to be 2 m above the fuels for Case (g). By comparing Cases (e) and (f), since the fuels of the fullcore discharge have much higher in heat generation, the temperature of Case (f) is higher than that of Case (e). With the reduction of pool water, the cooling ability of the pool decreases. Thus, the VOF values decrease, representing greater void fraction, with the lower water level. 5. Conclusion A three-dimensional two-phase CFD model has been successfully developed to simulate the thermalehydraulic behavior of the spent-fuel pool. In this study, SFP of the Kuoshen power station is employed for study. The simulation implemented with the worst situation, in which fuels under full-core discharge are assumed to be moved into SFP, and the external cool system is assumed failed. To present the pressure drop of the flow passing through the fuels, the effective permeability is calculated from Darcy’s law for porous medium, which simplified the fuel region. The effective convective coefficient on the pool surface is also modeled based on the empirical correlations. From the computation results, the current configuration of spent fuel layout in a SFP has an enough cooling capability to meet
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the licensing regulations under normal operation conditions. However, local boiling would occur on the surface of the spent fuels with the current configuration of spent fuel layout if the event is beyond the regulation with no application of an external cooling system. To enhance the understanding of the cooling effect of the pool, four different layouts were considered and simulated in this study. It is found that to the arrangement of locating the new spent fuels on two opposite sides of the pool has a better improvement. However, the enhancement is marginal and there still exists local boiling. If the water level is less than 3-m higher than the fuels, the water temperature increases and the VOF value becomes lower. Although the arrangement of the fuels can improve the cooling effect of SFP, an external cool system is still required to prevent the occurrence of local boiling. Acknowledgements This research work has been supported by the National Science Council, Taiwan, R.O.C. under the grants of NSC 98-2221-E-027085-MY3 and NSC-100-2623-E-027-001-NU. The authors also highly appreciate Mr. C.W. Hsiao for his valuable assistance in the numerical approaches. References [1] D. Bodansky, Nuclear Energy e Principles, Practices, and Prospects, second ed., Springer, New York, 2005, pp. 253e290. [2] A. Kaliatka, V. Ognerubov, V. Vileiniskis, Analysis of the processes in spent fuel pools of Ignalina NPP in case of loss of heat removal, Nucl. Eng. Des. 240 (2010) 1073e1082. [3] C.D. Fletcher, R.R. Schultz, RELAP5/MOD3 Code Manual User’s Guidelines, NUREG/CR-5535, Idaho National Lab., 1992. [4] A.B. Wahba, International activities for the analysis of the TMI-2 accident with special consideration of ATHLET calculations, Nucl. Eng. Des. 118 (1990) 43e53. [5] J.P. Van Dorsselaere, C. Seropian, P. Chatelard, F. Jacq, J. Fleurot, P. Giordano, N. Reinke, B. Schwinges, H.J. Allelein, W. Luther, The ASTEC integral code for severe accident simulation, Nucl. Technol. 165 (3) (2009) 293e307. [6] V. Kain, P.K. De, K. Agarwal, P. Seetharamaih, Environmental degradation of materials during wet storage of spent nuclear fuels, J. Mater. Eng. Perform. 9 (3) (2000) 317e323. [7] R.G. Aghoyeh, H. Khalafi, Design of make-up water system for Tehran research reactor spent nuclear fuels storage pool, Nucl. Eng. Des. 240 (2010) 2532e2537. [8] J.H. Park, H.M. Koh, J.K. Kim, Seismic isolation of pool-type tanks for the storage of nuclear spent fuel assemblies, Nucl. Eng. Des. 199 (2000) 143e154. [9] US NRC, Standard Review Plan for Dry Cask Storage Systems. NUREG-1536 (1997). [10] NAC International Inc., Final Safety Analysis Report for the UMS Universal Storage System, Rev. 5 (2005). [11] Y.S. Tseng, J.R. Wang, F.P. Tsai, Y.H. Cheng, C.K. Shih, Thermal design investigation of a new tube-type dry-storage system through CFD simulations, Ann. Nucl. Energy 38 (2011) 1088e1097. [12] Y.Y. Ko, S.Y. Hsua, C.H. Chen, Analysis for seismic response of dry storage facility for spent fuel, Nucl. Eng. Des. 239 (2009) 158e168. [13] F. Nimander, Investigation of Spent Nuclear Fuel Pool Coolability, Master Dissertation, Royal Institute of Technology, Stockholm, Sweden, August (2011). [14] J.R. Wang, H.T. Lin, Y.S. Tseng, C.K. Shih, Application of TRACE and CFD in the spent fuel pool of Chinshan nuclear power plant, Appl. Mechanics and Materials 145 (2012) 78e82. [15] U.S. NRC, in: TRACE V5.0 Theory Manual, Division of Safety Analysis, Office of Nuclear Regulatory Research, 2010. [16] Atomic Energy Council, Regulations and Safety Report of Spent Fuel Pool. Taiwan (1990). [17] Atomic Energy Council, Safety Review Report on Maanshan Unit 1 & 2 Reracking Application (1995). NRD/LRS-8601, Taiwan, March. [18] T.C. Hung, C.S. Fu, Conjugate heat transfer analysis for the passive enhancement of electronic cooling through geometric modification in a mixed convection domain, Numer. Heat Tranf. A-Appl. 35 (5) (1999) 519e535. [19] S.K. Wang, T.C. Hung, G.W. Lin, B.S. Pei, Numerical simulations for the phenomena of vortex induced vibration and heat transfer of a circular cylinder, Numer. Heat Tranf. A-Appl. 45 (7) (2004) 1e18. [20] T.C. Hung, V.K. Dhir, J.C. Chang, S.K. Wang, CFD modeling and thermalhydraulic analysis for the passive decay heat removal of a sodium-cooled fast reactor, Nucl. Eng. Des. 241 (2011) 425e432.
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