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Study of perforated plate effect in horizontal WWER1000 steam generator
Nuclear Engineering and Design 256 (2013) 249–255
Contents lists available at SciVerse ScienceDirect
Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
Study of perforated plate effect in horizontal WWER1000 steam generator A. Safavi a , M.R. Abdi b , M. Aghaie c,∗ , M.H. Esteki d , A. Zolfaghair c , A.F. Pilevar a , A. Daryabak a a
Department of Engineering, Faculty of Advanced Sciences & Technologies, University of Isfahan, 81746-73441 Isfahan, Iran Department of Physics, Faculty of Science, University of Isfahan, 81746-73441 Isfahan, Iran c Engineering Department, Shahid Beheshti University, G.C., P.O. Box 1983963113, Tehran, Iran d Department of Biomedical, Faculty of Engineering, University of Isfahan, 81746-73441 Isfahan, Iran b
h i g h l i g h t s
Effect of perforated plate in steam distribution at top levels of SG is studied. The 3D numerical model of SG is prepared in ANSYS CFX. The interfacial functions for mass, momentum and energy transfer are prepared. The desired boundary conditions and marching method are implemented. The void fraction values are compared with experimental data.
a r t i c l e
i n f o
Article history: Received 28 May 2012 Received in revised form 18 December 2012 Accepted 19 December 2012
a b s t r a c t In this paper, the effect of perforated plate in horizontal steam generator (SG) has been studied. The injected feed water into the SG is cold and heavy, so it pulls down the fluid around the feed water injection pipeline. The perforated plate has been designed above tube bundles in the SG to relax this asymmetrically void generation. In this work, with consideration of the perforated plate and feed injection effects in tube side, it is illustrated that generated steam will be distributed in the top level of the SG homogeneously. Therefore, the steam collector contains high quality homogeneously distributed dry steam and the perforated plate prevents the water from ascending in the cold side containing cold collector and the steam from descending on the other side. In addition, it can be seen that without the perforated plate, the void fraction distribution becomes heterogeneous in the top level of the SG. In this analysis, the 3D numerical model of a large conventional WWER1000 steam generator in the nuclear industry has been presented. For the computational fluid dynamic (CFD) study of desired steam generator in ANSYS CFX, the SG geometry is prepared with details and interfacial relations of mass, momentum and heat transfer are defined by appropriate functions. In momentum source terms, the interfacial drag forces are defined with Ishii and Zuber model. An Euler–Euler approach is applied to modeling boiling heat transfer and condensation. Porosity model is applied to the primary side in which the tube bundles are not described in detail but they are modeled as sources of enthalpy and pressure loss. The primary side effect is modeled based on a 1D thermal heat source model. Finally, the importance of perforated plate is demonstrated and it shows that the results are in a good agreement with published and experimental data. © 2013 Elsevier B.V. All rights reserved.
1. Introduction Steam generator is a heat exchanger of pressurized water reactor (PWR) that nuclear power plant (NPP) uses to evaporate the secondary side water. A steam generator (SG) has a significant role in the operation of a pressurized water reactor power plant and the prolongation of its life cycle. The steam generator not only transfers thermal energy from the primary coolant to the secondary side,
∗ Corresponding author. Tel.: +98 21 22431595; fax: +98 21 29902546. E-mail address: m [email protected] (M. Aghaie). 0029-5493/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nucengdes.2012.12.010
but also prevents the release of radionuclide. The preservation of the complete separation between the primary and secondary loops is very important in order to avoid radioactive contamination of secondary loop and leak of coolant, as well. The investigations in the flow field of water and steam mixture on the secondary side of horizontal or vertical steam generator of the NPP are limited due to lack of large experimental devices, as well as the difficulties related to the measurements in the real NPPs. The two-phase flow in a complicated three-dimensional (3D) geometry is also very problematic in the field of computational fluid dynamics (CFD). Regarding importance of steam quality in power plant, the steam distribution in steam generators
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A. Safavi et al. / Nuclear Engineering and Design 256 (2013) 249–255
needs some detailed researches. The flow fluid studies about temperature and pressure of fluid would be very useful to manage power cycle thermal-hydraulic parameters, accident analysis and steam generator lifetime. The geometry of the secondary side of a steam generator is complicated for a detailed numerical simulation. Therefore, some simplifications are suggested with previous works. Stavanovic and Studovic (1999) have suggested using a model in which the tube bundles of the steam generator are considered as a porous media. They presented a simplified thermal-hydraulics model and a numerical procedure for the simulation and analysis of steady state nuclear power plant components. The porosity model presented by Stosic and Stevanovic (2002) simulated the secondary side of the steam generator. Groburov and Zorin (1994) reported a simple model of WWER1000 SG shell side two-phase flow within tube bundles. Kristof et al. (2008) presented the numerical model of WWER440 steam generator in fluent. The most important effect concerning the shell side flow in a secondary boiler is the unevenness of heating (Kristof et al., 2008). The WWER1000 type steam generator contains 10,978 tubes of 16 mm diameter bent in horizontal planes delivering high temperature primary circuit water. The enthalpy of the primary circuit coolant delivered to the secondary circuit water on the shell side of the pipes to the saturation temperature eventually evaporating it. The effect of the primary circuit on the secondary side is characterized with source terms of heat. Indeed, this term makes it possible to describe the heat transfer from the primary circuit to the secondary side. In this paper, the effect of perforated plate in horizontal steam generator (SG) has been studied. The injected feed water into the SG is cold and heavy, so it pulls down the fluid around the water injection system. Without the perforated plate, the void fraction distribution becomes more heterogeneous. In this work, with consideration of the perforated plate and feed injection effects in tube side, it illustrates that generated steam is distributed in the top level of the SG homogeneously. Therefore, the steam collector contains high quality homogeneously distributed dry steam and the perforated plate prevents the water from ascending in the cold side containing cold collector and the steam from descending on the other side. In the presented simulation, a complete 3D model of the horizontal WWER1000 steam generator has been prepared. The Euler–Euler multiphase model is used in computational fluid dynamics modeling of the secondary side. Consequently, equations for mass, momentum and enthalpy conservation will be solved for two phases. The numerical model involves the relevant interactions between the phases, drag forces and the mass transfer between the phases due to evaporation and condensation. The source terms are implemented into the ANSYS CFX code by using user-defined functions. The spatial distribution of the transferred heat flux is modeled by 1D thermo-hydraulic model. This model is constructed of a pipe from the primary side of the steam generator. Solving the Navier–Stokes equations numerically, the distribution of heat flux in the pipe will be gained. The 3D steam generator CFD modeling prepared numerical results for full load operating condition. The obtained results clearly illustrated the role of submerged perforated plate in the distribution of the void fraction and pressure losses in top levels of SG. Finally, it shows that the results are in a good agreement with published and experimental data. 2. Model description The role of SG in a PWR nuclear power plants is the heat transfer from the reactor cooling system, to the secondary side of the tubes containing feed water. Primary coolant receives heat passing through the core, and then flows through the steam generator, where it transfers heat to the secondary coolant water to make steam (Green and Hetsroni, 1995). Eventually, the steam drives a turbine connected to an electric generator to produce energy. The
coolant enters the hot leg from the reactor and circulates through the tube bundles of the SG and out of the cold leg into the coolant pumps suction line (Fig. 1). Heat is transferred through the wall of the tubes from the hot coolant, boils the water on the shell side, and generates steam. The feed water enters to SG just below the perforated plate and joints the water being circulated. It then flows upward by natural convection through the bundle absorbing heat, and leaves the tube bundles as a steam water mixture. The main components of the SG are (Fig. 1): • • • • •
Steam generator body Heat transfer tubes and primary coolant heads Feed water nozzle facility Perforated plate Inlet collector, outlet collector, steam collector, . . .
Feed water flows into the steam generator through a pipe 426 mm inside diameter, then through 16 collectors of 80 mm inside diameter, which are coupled to the distribution pipes. Each of these distribution pipes has 38 perforated pipes. Some are at the upper steam tubing elevation while another portion is over the perforated plate in order to balance the non-uniform steam generation. This is achieved by partial condensation of the voids in high steam areas. The perforated plate is a metal sheet with structured holes for steam ascending. The perforated plate has been designed above the tube bundles to relax asymmetrical void generation. The sheet prevents asymmetry circulation of feed water and helps to homogenous boiling of it. The design data for desired SG are shown in Table 1. 2.1. The ANSYS CFX model In this work, three-dimensional model of the steam generator is modeled in ANSYS CFX, and unstructured meshes are generated for numerical calculations. The detailed 3D model consists of about 4.5 million computational cells. There are 2.8 million computational cells in the simplified 3D model. In the simplified case, some details of minor importance will be ignored in order to reduce the number of cells. Using the converged results of the simplified model as initial condition for the finally improved model, the time of computation was reduced. The 3D SG model with all meshes is shown in Fig. 2. Time dependent numerical simulation has been carried out in every case with sufficient number of time steps to obtain converged solution. Indeed, the marching method is chosen for suitable convergence of results. In addition, to access the accurate superficial velocity of water and vapor, the effect of tube bundles should be considered. For this, the 2D model in ANSYS CFX has been developed. In this case, a section in the middle of steam generator, considering all tubes, has been simulated. 3. Governing equations The three dimensional CFD model used herein includes the continuity, momentum, and energy conservation equations. The general equations for the CFD analysis of the SG are defined as below (Ferng, 2007; Pattikangas et al., 2010; Wang et al., 2012): Conservation equations for phase q: Mass conservation :
∂ − → (˛q q ) + ∇ · (˛q q V q ) = Smass,q ∂t
Momentum conservation :
(1)
∂ − → − → − → (˛q q V q ) + ∇ · (˛q q V q V q ) = SM,q ∂t (2)
A. Safavi et al. / Nuclear Engineering and Design 256 (2013) 249–255
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Fig. 1. Horizontal steam generator description.
Energy conservation : Volume conservation :
∂ − → (˛q q hq ) + ∇ · (˛q q hq V q ) = SM,q ∂t
˛q = 1
(3) (4)
where ˛q is the volume fraction, q is the density, hq is the specific enthalpy and Vq is the velocity of phase q, (q = 1) for liquid, (q = 2) for vapor. The source term Smass,q on the right hand side is described as the mass transfer between the phases, either evaporation or condensation. The inter phase momentum transfer; lift force, and virtual mass force are described by the momentum source term SM,q on the right hand side of the momentum equation. Moreover, it includes the effects of the pressure gradient, gravitation, and turbulence. The right hand side of the energy equation is the energy source term SE,q including the interface heat exchange, the effects of turbulence and changing pressure. The source term in momentum conversation is (Pattikangas et al., 2010): − → − → → → S M,q = −˛q ∇ p + ∇ · − g + R pq q + ˛q q − − → − → − → − → + F CE,q + F lift,q + F vm,q + F DF,q
Fig. 2. Model of the secondary side of the steam generator.
(5)
where pressure is denoted by p and g is the gravitational acceler− → → ation, − q is the stress–strain tensor, R pq is the interface friction − → force, and F DF,q is the friction caused by the tubes of the primary − → circuit. F CE,q is the force related to momentum transfer which occurs between phases, when the mass transfer occurs. The effects − → − → of lift force F lift,q and the virtual mass force F vm,q are ignored. The gravitational force is the main force driving the mixture circulation. The main step to calculate properly the relative velocities between steam and water phase, and consequently the void
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Table 1 Steam generator design data. Description
Value
Steam flow (kg/s) Steam temperature (◦ C) Steam pressure (MPa) Feed water temperature (◦ C) Reactor coolant pressure (MPa) Inlet coolant temperature to SG (K) Outlet coolant temperature from SG (K) Hot coolant volume (m3 ) Pressure drop between steam collector and turbo-generator (Pa) Pressure drop between SG and steam collector (Pa) Feed water temperature with HP pre-heaters on (K) Feed water temperature with HP pre-heaters off (K) Thermal power (MW) Steam load (MPa) Live steam pressure (MPa) Live steam temperature (K) SG primary side pressure drop (MPa) SG secondary side pressure drop (MPa) Steam quality at steam generator outlet (%) Nominal secondary side level (m) Steam lines volume from SG to the steam collector (m3 ) Steam lines volume from the steam collector to the turbo-generator (m3 ) Upper level of the tubing (m) Length of a cylindrical part of the SG (m) SG ID (m) SG OD (m) Upper level of perforated plate (m) Number of primary side heads Volume of one SG head (m3 ) Total height of a head (m) Primary side volume (m3 ) Number of heat transfer tubes Average length of the tubes (m) Heat transfer tube OD (mm) Heat transfer tube ID (mm) Total cross-section area of heat transfer tubes (m2 ) Total heat transfer area (secondary side) (m2 ) Relative elevation of FW nozzle (m) Equivalent hydraulic diameter (secondary side) (mm) Distance between axes of rows (mm) Distance between tubes axes in a row (mm)
437 278.5 6.28 ± 0.2 220 15.7 ± 0.3 593.15 ± 3.5 559.15 ± 2.0 20.5 1 × 105
fCrossFlow p
0.3165 0.25 Rem
→ CCrossFlow =
fCrossFlow de
(8)
where de is the equivalent diameter. 4. Condensation and evaporation modeling
493.15 ± 5
The feed water injection is simulated by volumetric mass source considered near injection nozzles. The feed water, when injected into the SG, should be mixed with the boiling water. Evaporation occurs when the liquid enthalpy is higher than the liquid saturation enthalpy, i.e., h1 > h (h1 , h liquid and saturation enthalpies, respectively) whereas condensation occurs, when vapor is in contact with subcooled water, i.e., h1 < h . It means when a relatively small percentage of feed water is mixed with boiling water of the high vapor content, the liquid temperature of the mixture attains the saturation temperature. When the amount of initial feed water is going higher, the vapor content can completely be condensed and the temperature of the mixture going to be lower than the saturation temperature. The mixing can occur in the tube bundle in the same way, wherein the additional heat received from the heat exchanger pipes must be considered. So, in this section the coupled numerical models consists of preheating, condensation and heat exchange with the solid surface (Kristof et al., 2008). This process is implemented numerically using the multiphase model in CFX by solving energy equation.
437.15 ± 4 750 437.22 6.28 ± 0.2 551.65 0.133 0.1 <0.2 2.55 100 62 2.19 11.34 4 4.29 2.45 2 2.4 4 20.5 11,000 11.1 16 13 1.46
5. Solid to fluid heat transfer approximation
6.115 2.72 17.4 19 23
(6)
In this case, the viscous loss term has been neglected (Dq = 0). The CCrossFlow , cross flow friction loss coefficient for the bundle is acquired by combining the friction loss coefficient for a single tube, fCrossFlow , and the summation effect related to several tube layers. −n fCrossFlow = A Rem → CCrossFlow =
fCrossFlow =
2 × 105
fraction, is to predict the interfacial momentum transfer. The model for interfacial drag force, proposed by Ishii and Zuber (1979) is chosen. Pressure loss in the axial and perpendicular directions caused by the tube bundles are modeled by the porous media formulation. In this model, the drag force on the fluid phases consists of two parts: a viscous loss term proportional to flow velocity and an inertial loss term proportional to the square of the flow velocity. When the flow velocity is high, the linear term could often be neglected. In a tube bundle, which is an anisotropic porous medium, the pressure loss coefficients describing the friction forces are tensors, which are dependent on the direction (Pattikangas et al., 2010): 1 → − → − → − → − → − − → F DF,q = −q D q V q − q | V q | V q C q 2
where p is the pitch in the cross flow direction and Rem is calculated using the mixture (m) values. The values, which are chosen for the constant parameter are A = 3.29, n = 0.18 (Stavanovic and Studovic, 1999). In the direction parallel to the tube bundles, The Blasius correlation can be applied:
(7)
Shell side water circulation in the steam generator vessel is caused by heat flux received from the primary side and the consequential increase in the specific volume of the fluid. The heat flux from solid tube bundles to fluid is modeled on the basis of a 1D thermal hydraulic model. Heat transfer surface consists of 10,978 steel tubes 16 mm inside diameter made of steel. A simple heating pipe from the primary side that has been modeled is shown in Fig. 3. For calculating heat flux function, the following operation was considered. The water temperature at the inlet and the outlet were set 320 ◦ C and 290 ◦ C, respectively. Due to the fact that boiling occurs on the outer side of the pipe, the temperature on this side is fixed. The wall heat flux between primary coolant and the outer side of pipe in this model has been numerically measured, and the function approximating the distribution of heat flux has been constructed. The heat flux in the porous domain is described by Eq. (9). The li is the pipe length between each element and the hot collector. qi
kwatt m2
= 1410 exp(−4li )
(9)
6. Perforated plate modeling The perforated plate is a metal sheet with structured holes for steam ascending. The perforated plate is has been designed above the tube bundles. The metal sheet prevents asymmetrically circulation of feed water in sell side and helps to homogenous boiling of water. Also, the sheet could be considered as a moisture separator located above the tube bundles in steam generator. As mentioned the perforated plate has the constructed holes for steam transfer. In the holes modeling, the entities shall be complicated if the complete
A. Safavi et al. / Nuclear Engineering and Design 256 (2013) 249–255
Fig. 3. Model of one pipe from the primary side of steam generator.
Fig. 4. Streamlines in the SG.
Fig. 5. The effect of perforated plate in distribution of void fraction.
Fig. 6. The distribution of water temperature.
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A. Safavi et al. / Nuclear Engineering and Design 256 (2013) 249–255 Table 4 Comparison between the results of 3D-ANA code and ANSYS CFX.
Fig. 7. The distribution of vapor velocity. Table 2 Positions of transducers (Stavanovic and Studovic, 1999). Transducer
Distance (mm)
ϕ1 ,ϕ2 ,ϕ3 ,ϕ8 ,ϕ10 ,ϕ12 ,ϕ13 ,ϕ14 ϕ4 ,ϕ11 ,ϕ15 ,ϕ16 ,ϕ17 ,ϕ18 ϕ5 ,ϕ7
Between transducer
From perforated plate
1000 700 200
350 70 35
geometry is used for constructing the numerical model, accordingly it results in solving difficulties even in a high performance computing system. Hence, for the purpose of availing analysis, the actual perforated plate is replaced by the opening boundary conditions in ANSYS CFX. 7. Results Coolant enters the hot collector (inlet) from the reactor and circulates through the tubes and leaves SG from the cold collector (outlet) into the coolant pumps suction line (see Figs. 1 and 2). Heat is transferred through the walls of the tubes from the coolant, boils the water on the shell side, and generates steam. Near the inlet collector, temperature of the tube bundles and the consequential heat flux is higher than near the outlet collector. Uneven steam production, because of the spatial distribution of heat flux, is the driver of the shell side circulation illustrated in Fig. 4. As depicted in Fig. 4, a circulative cross flow occurs in the tube side. In this way,
3D-ANA code
ANSYS CFX
0.48 0.51 0.54 0.61 0.70 0.70 0.71 0.57 0.48 0.57 0.53 0.50 0.43
0.45 0.49 0.50 0.64 0.88 0.68 0.86 0.53 0.54 0.51 0.57 0.48 0.46
a circulation from the outlet collector to the inlet collector occurs because of density variation in their vicinity. Moreover, feed water injection and perforated plate have a major impact on the shell side circulation. The comparison between the results obtained with and without perforated sheet is showed in Fig. 5a and b. Without perforated plate with the fact that vapor generation in hot side is higher, the generated steam is placed on top levels of inlet collector side. As can be seen in Fig. 5a in this situation due to the fact that injected water is cold and heavy, it pulls down the fluid around the water injection system. The steam collector is faced with the heterogeneous void generation. This state causes the higher mixed circulative cross flow. Perforated plate prevents the water from ascending in the cold side due to the nature of this sheet. Because this sheet only allows the vapor to be passed, it causes the vapor distribution to become more homogenous. The distribution of water temperature is illustrated in Fig. 6. As can be seen, water temperature decreases away from the center of SG. The CFX-2D model was developed to investigate the velocity of vapor in the SG. In this model, the tube bundle has been considered in details. Around 10,000 pipes have been modeled and meshed. The superficial velocity evaluated by our two dimensional SG model is illustrated in Fig. 7. As can be seen, the vapor velocity reaches the peak at 0.72 m/s above the tube bundles, and in general, the velocity of vapor has been increased by receiving heat from the tube bundles. The results of numerical solution have been compared to the data measured at certain positions at the SG with the perforated plate of the Novoronezh Nuclear Power Plant. These data have been extracted from a paper published by Stavanovic and Studovic in 1999. The positions of measuring points are shown in Fig. 8 and Table 2.
Table 3 Comparison between numerical data and experimental data. Void
EXP.Ageev (1987)
EXP.Karppinen (1994)
STEG-01Melikhov et al. (1995)
Average of experimental data
ANSYS CFX
ϕ1 ϕ2 ϕ3 ϕ4 ϕ5 ϕ6 ϕ7 ϕ8 ϕ10 ϕ12 ϕ13 ϕ14 ϕ15
0.30 0.45 0.45 0.80 1.00 0.70 1.00 0.55 0.47 0.52 0.50 0.55 0.38
0.50 0.18 0.42 – – 1.00 0.98 0.48 – 0.54 0.15 0.56 –
0.55 0.63 0.54 – 0.84 0.77 0.89 0.55 0.56 0.51 0.63 0.54 –
0.45 0.42 0.47 0.80 0.92 0.82 0.96 0.53 0.52 0.52 0.43 0.55 0.41
0.45 0.49 0.50 0.64 0.88 0.68 0.86 0.53 0.54 0.51 0.57 0.48 0.46
A. Safavi et al. / Nuclear Engineering and Design 256 (2013) 249–255
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Fig. 8. Void measuring points (Stavanovic and Studovic, 1999).
8. Conclusion
References
In this analysis, the simulations have been shown the comparable results with reported experimental data. In Table 3, the numerical results are compared with the experimental data and Table 4 contains the comparison of calculated results with reported data (Stavanovic and Studovic, 1999). In these tables the evaluation points are depicted in Fig. 8 that these points are void measuring transducer positions. As seen, a good agreement between the results of the simulation in ANSYS CFX and experimental data or reported data has been achieved. Consequently, the estimated function for modeling heat source and momentum source are reliable. So, the presented method for approximations of heat transfer and momentum is compatible with the desired domain of fluid. It is demonstrated that the perforated plate in steam generator WWER1000 has an undeniable impact on the distribution of the void fraction in the steam generator. Results show the void fraction of vapor and the temperature of water in the environment of the hot collector have their maximum values without the perforated plate. Perforated plate consideration with related feed injection helps a homogenous void generation, this demonstrates the importance of perforated plate utilization. Finally, the steam velocity above the tube bundle reaches the velocity of 0.72 m/s and consequently, the tubes located above tube bundle will have more vibration. The study of vibration in tube bundles is the next interesting subject.
Ageev, A.G., 1987. Elektricheskie stancii, No. 6, 19. Ferng, Y.M., 2007. Investigation the distribution characteristics of boiling flow and released nuclide in the steam generator secondary side using CFD methodology. Ann. Nucl. Energy 34, 724–731. Green, S.J., Hetsroni, G., 1995. PWR steam generators. Int. J. Multiphase Flow 12 (Suppl.), 1–97. Groburov, V.I., Zorin, V.M., 1994. Computer modelling of water hydrodynamics of steam generator PGV-1000. Teploenergetika 5, 22–29. Ishii, M., Zuber, N., 1979. Drag coefficient and relative velocity in bubbly, droplet or particulate flows. AIChE J. 5, 843–855. Karppinen, F., 1994. Horizontal steam generators. In: Third Int. Sem., Lappeenranta, Sweden. Kristof, G., Szabo, K., Regert, T., 2008. Modeling of Boiling Water Flow in the Horizontal Steam Generator of the Paks Nuclear Power Plant. CFD.HU, Ltd., Budapest, Hungry. Melikhov, V.I., Melikhov, O.I., Nigmatulin, B.I., 1995. Two phase flow modeling and experimentation. Proc. Int. Conf. 1, 115. Pattikangas, T., Niemi, J., Hovi, V., 2010. CFD modeling of horizontal steam generators. 12.1 SGEN summary report. Stavanovic, V., Studovic, M., 1999. 3D modelling as a support to thermal-hydraulic safety analyses with standard codes. In: 7th International Conference on Nuclear Engineering, Tokyo, Japan. Stosic, M., Stevanovic, V., 2002. Advanced three-dimensional two-fluid porous media method for transient two-phase flow thermal-hydraulics in complex geometries. Numer. Heat Transfer B: Fund, 263–289. Wang, Z.L., Tian, W.X., Wu, Y.W., 2012. Numerical study on annular tube oncethrough steam generator using compressible flow model. Ann. Nucl. Energy 39, 49–55.
Contents lists available at SciVerse ScienceDirect
Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
Study of perforated plate effect in horizontal WWER1000 steam generator A. Safavi a , M.R. Abdi b , M. Aghaie c,∗ , M.H. Esteki d , A. Zolfaghair c , A.F. Pilevar a , A. Daryabak a a
Department of Engineering, Faculty of Advanced Sciences & Technologies, University of Isfahan, 81746-73441 Isfahan, Iran Department of Physics, Faculty of Science, University of Isfahan, 81746-73441 Isfahan, Iran c Engineering Department, Shahid Beheshti University, G.C., P.O. Box 1983963113, Tehran, Iran d Department of Biomedical, Faculty of Engineering, University of Isfahan, 81746-73441 Isfahan, Iran b
h i g h l i g h t s
Effect of perforated plate in steam distribution at top levels of SG is studied. The 3D numerical model of SG is prepared in ANSYS CFX. The interfacial functions for mass, momentum and energy transfer are prepared. The desired boundary conditions and marching method are implemented. The void fraction values are compared with experimental data.
a r t i c l e
i n f o
Article history: Received 28 May 2012 Received in revised form 18 December 2012 Accepted 19 December 2012
a b s t r a c t In this paper, the effect of perforated plate in horizontal steam generator (SG) has been studied. The injected feed water into the SG is cold and heavy, so it pulls down the fluid around the feed water injection pipeline. The perforated plate has been designed above tube bundles in the SG to relax this asymmetrically void generation. In this work, with consideration of the perforated plate and feed injection effects in tube side, it is illustrated that generated steam will be distributed in the top level of the SG homogeneously. Therefore, the steam collector contains high quality homogeneously distributed dry steam and the perforated plate prevents the water from ascending in the cold side containing cold collector and the steam from descending on the other side. In addition, it can be seen that without the perforated plate, the void fraction distribution becomes heterogeneous in the top level of the SG. In this analysis, the 3D numerical model of a large conventional WWER1000 steam generator in the nuclear industry has been presented. For the computational fluid dynamic (CFD) study of desired steam generator in ANSYS CFX, the SG geometry is prepared with details and interfacial relations of mass, momentum and heat transfer are defined by appropriate functions. In momentum source terms, the interfacial drag forces are defined with Ishii and Zuber model. An Euler–Euler approach is applied to modeling boiling heat transfer and condensation. Porosity model is applied to the primary side in which the tube bundles are not described in detail but they are modeled as sources of enthalpy and pressure loss. The primary side effect is modeled based on a 1D thermal heat source model. Finally, the importance of perforated plate is demonstrated and it shows that the results are in a good agreement with published and experimental data. © 2013 Elsevier B.V. All rights reserved.
1. Introduction Steam generator is a heat exchanger of pressurized water reactor (PWR) that nuclear power plant (NPP) uses to evaporate the secondary side water. A steam generator (SG) has a significant role in the operation of a pressurized water reactor power plant and the prolongation of its life cycle. The steam generator not only transfers thermal energy from the primary coolant to the secondary side,
∗ Corresponding author. Tel.: +98 21 22431595; fax: +98 21 29902546. E-mail address: m [email protected] (M. Aghaie). 0029-5493/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nucengdes.2012.12.010
but also prevents the release of radionuclide. The preservation of the complete separation between the primary and secondary loops is very important in order to avoid radioactive contamination of secondary loop and leak of coolant, as well. The investigations in the flow field of water and steam mixture on the secondary side of horizontal or vertical steam generator of the NPP are limited due to lack of large experimental devices, as well as the difficulties related to the measurements in the real NPPs. The two-phase flow in a complicated three-dimensional (3D) geometry is also very problematic in the field of computational fluid dynamics (CFD). Regarding importance of steam quality in power plant, the steam distribution in steam generators
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needs some detailed researches. The flow fluid studies about temperature and pressure of fluid would be very useful to manage power cycle thermal-hydraulic parameters, accident analysis and steam generator lifetime. The geometry of the secondary side of a steam generator is complicated for a detailed numerical simulation. Therefore, some simplifications are suggested with previous works. Stavanovic and Studovic (1999) have suggested using a model in which the tube bundles of the steam generator are considered as a porous media. They presented a simplified thermal-hydraulics model and a numerical procedure for the simulation and analysis of steady state nuclear power plant components. The porosity model presented by Stosic and Stevanovic (2002) simulated the secondary side of the steam generator. Groburov and Zorin (1994) reported a simple model of WWER1000 SG shell side two-phase flow within tube bundles. Kristof et al. (2008) presented the numerical model of WWER440 steam generator in fluent. The most important effect concerning the shell side flow in a secondary boiler is the unevenness of heating (Kristof et al., 2008). The WWER1000 type steam generator contains 10,978 tubes of 16 mm diameter bent in horizontal planes delivering high temperature primary circuit water. The enthalpy of the primary circuit coolant delivered to the secondary circuit water on the shell side of the pipes to the saturation temperature eventually evaporating it. The effect of the primary circuit on the secondary side is characterized with source terms of heat. Indeed, this term makes it possible to describe the heat transfer from the primary circuit to the secondary side. In this paper, the effect of perforated plate in horizontal steam generator (SG) has been studied. The injected feed water into the SG is cold and heavy, so it pulls down the fluid around the water injection system. Without the perforated plate, the void fraction distribution becomes more heterogeneous. In this work, with consideration of the perforated plate and feed injection effects in tube side, it illustrates that generated steam is distributed in the top level of the SG homogeneously. Therefore, the steam collector contains high quality homogeneously distributed dry steam and the perforated plate prevents the water from ascending in the cold side containing cold collector and the steam from descending on the other side. In the presented simulation, a complete 3D model of the horizontal WWER1000 steam generator has been prepared. The Euler–Euler multiphase model is used in computational fluid dynamics modeling of the secondary side. Consequently, equations for mass, momentum and enthalpy conservation will be solved for two phases. The numerical model involves the relevant interactions between the phases, drag forces and the mass transfer between the phases due to evaporation and condensation. The source terms are implemented into the ANSYS CFX code by using user-defined functions. The spatial distribution of the transferred heat flux is modeled by 1D thermo-hydraulic model. This model is constructed of a pipe from the primary side of the steam generator. Solving the Navier–Stokes equations numerically, the distribution of heat flux in the pipe will be gained. The 3D steam generator CFD modeling prepared numerical results for full load operating condition. The obtained results clearly illustrated the role of submerged perforated plate in the distribution of the void fraction and pressure losses in top levels of SG. Finally, it shows that the results are in a good agreement with published and experimental data. 2. Model description The role of SG in a PWR nuclear power plants is the heat transfer from the reactor cooling system, to the secondary side of the tubes containing feed water. Primary coolant receives heat passing through the core, and then flows through the steam generator, where it transfers heat to the secondary coolant water to make steam (Green and Hetsroni, 1995). Eventually, the steam drives a turbine connected to an electric generator to produce energy. The
coolant enters the hot leg from the reactor and circulates through the tube bundles of the SG and out of the cold leg into the coolant pumps suction line (Fig. 1). Heat is transferred through the wall of the tubes from the hot coolant, boils the water on the shell side, and generates steam. The feed water enters to SG just below the perforated plate and joints the water being circulated. It then flows upward by natural convection through the bundle absorbing heat, and leaves the tube bundles as a steam water mixture. The main components of the SG are (Fig. 1): • • • • •
Steam generator body Heat transfer tubes and primary coolant heads Feed water nozzle facility Perforated plate Inlet collector, outlet collector, steam collector, . . .
Feed water flows into the steam generator through a pipe 426 mm inside diameter, then through 16 collectors of 80 mm inside diameter, which are coupled to the distribution pipes. Each of these distribution pipes has 38 perforated pipes. Some are at the upper steam tubing elevation while another portion is over the perforated plate in order to balance the non-uniform steam generation. This is achieved by partial condensation of the voids in high steam areas. The perforated plate is a metal sheet with structured holes for steam ascending. The perforated plate has been designed above the tube bundles to relax asymmetrical void generation. The sheet prevents asymmetry circulation of feed water and helps to homogenous boiling of it. The design data for desired SG are shown in Table 1. 2.1. The ANSYS CFX model In this work, three-dimensional model of the steam generator is modeled in ANSYS CFX, and unstructured meshes are generated for numerical calculations. The detailed 3D model consists of about 4.5 million computational cells. There are 2.8 million computational cells in the simplified 3D model. In the simplified case, some details of minor importance will be ignored in order to reduce the number of cells. Using the converged results of the simplified model as initial condition for the finally improved model, the time of computation was reduced. The 3D SG model with all meshes is shown in Fig. 2. Time dependent numerical simulation has been carried out in every case with sufficient number of time steps to obtain converged solution. Indeed, the marching method is chosen for suitable convergence of results. In addition, to access the accurate superficial velocity of water and vapor, the effect of tube bundles should be considered. For this, the 2D model in ANSYS CFX has been developed. In this case, a section in the middle of steam generator, considering all tubes, has been simulated. 3. Governing equations The three dimensional CFD model used herein includes the continuity, momentum, and energy conservation equations. The general equations for the CFD analysis of the SG are defined as below (Ferng, 2007; Pattikangas et al., 2010; Wang et al., 2012): Conservation equations for phase q: Mass conservation :
∂ − → (˛q q ) + ∇ · (˛q q V q ) = Smass,q ∂t
Momentum conservation :
(1)
∂ − → − → − → (˛q q V q ) + ∇ · (˛q q V q V q ) = SM,q ∂t (2)
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Fig. 1. Horizontal steam generator description.
Energy conservation : Volume conservation :
∂ − → (˛q q hq ) + ∇ · (˛q q hq V q ) = SM,q ∂t
˛q = 1
(3) (4)
where ˛q is the volume fraction, q is the density, hq is the specific enthalpy and Vq is the velocity of phase q, (q = 1) for liquid, (q = 2) for vapor. The source term Smass,q on the right hand side is described as the mass transfer between the phases, either evaporation or condensation. The inter phase momentum transfer; lift force, and virtual mass force are described by the momentum source term SM,q on the right hand side of the momentum equation. Moreover, it includes the effects of the pressure gradient, gravitation, and turbulence. The right hand side of the energy equation is the energy source term SE,q including the interface heat exchange, the effects of turbulence and changing pressure. The source term in momentum conversation is (Pattikangas et al., 2010): − → − → → → S M,q = −˛q ∇ p + ∇ · − g + R pq q + ˛q q − − → − → − → − → + F CE,q + F lift,q + F vm,q + F DF,q
Fig. 2. Model of the secondary side of the steam generator.
(5)
where pressure is denoted by p and g is the gravitational acceler− → → ation, − q is the stress–strain tensor, R pq is the interface friction − → force, and F DF,q is the friction caused by the tubes of the primary − → circuit. F CE,q is the force related to momentum transfer which occurs between phases, when the mass transfer occurs. The effects − → − → of lift force F lift,q and the virtual mass force F vm,q are ignored. The gravitational force is the main force driving the mixture circulation. The main step to calculate properly the relative velocities between steam and water phase, and consequently the void
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Table 1 Steam generator design data. Description
Value
Steam flow (kg/s) Steam temperature (◦ C) Steam pressure (MPa) Feed water temperature (◦ C) Reactor coolant pressure (MPa) Inlet coolant temperature to SG (K) Outlet coolant temperature from SG (K) Hot coolant volume (m3 ) Pressure drop between steam collector and turbo-generator (Pa) Pressure drop between SG and steam collector (Pa) Feed water temperature with HP pre-heaters on (K) Feed water temperature with HP pre-heaters off (K) Thermal power (MW) Steam load (MPa) Live steam pressure (MPa) Live steam temperature (K) SG primary side pressure drop (MPa) SG secondary side pressure drop (MPa) Steam quality at steam generator outlet (%) Nominal secondary side level (m) Steam lines volume from SG to the steam collector (m3 ) Steam lines volume from the steam collector to the turbo-generator (m3 ) Upper level of the tubing (m) Length of a cylindrical part of the SG (m) SG ID (m) SG OD (m) Upper level of perforated plate (m) Number of primary side heads Volume of one SG head (m3 ) Total height of a head (m) Primary side volume (m3 ) Number of heat transfer tubes Average length of the tubes (m) Heat transfer tube OD (mm) Heat transfer tube ID (mm) Total cross-section area of heat transfer tubes (m2 ) Total heat transfer area (secondary side) (m2 ) Relative elevation of FW nozzle (m) Equivalent hydraulic diameter (secondary side) (mm) Distance between axes of rows (mm) Distance between tubes axes in a row (mm)
437 278.5 6.28 ± 0.2 220 15.7 ± 0.3 593.15 ± 3.5 559.15 ± 2.0 20.5 1 × 105
fCrossFlow p
0.3165 0.25 Rem
→ CCrossFlow =
fCrossFlow de
(8)
where de is the equivalent diameter. 4. Condensation and evaporation modeling
493.15 ± 5
The feed water injection is simulated by volumetric mass source considered near injection nozzles. The feed water, when injected into the SG, should be mixed with the boiling water. Evaporation occurs when the liquid enthalpy is higher than the liquid saturation enthalpy, i.e., h1 > h (h1 , h liquid and saturation enthalpies, respectively) whereas condensation occurs, when vapor is in contact with subcooled water, i.e., h1 < h . It means when a relatively small percentage of feed water is mixed with boiling water of the high vapor content, the liquid temperature of the mixture attains the saturation temperature. When the amount of initial feed water is going higher, the vapor content can completely be condensed and the temperature of the mixture going to be lower than the saturation temperature. The mixing can occur in the tube bundle in the same way, wherein the additional heat received from the heat exchanger pipes must be considered. So, in this section the coupled numerical models consists of preheating, condensation and heat exchange with the solid surface (Kristof et al., 2008). This process is implemented numerically using the multiphase model in CFX by solving energy equation.
437.15 ± 4 750 437.22 6.28 ± 0.2 551.65 0.133 0.1 <0.2 2.55 100 62 2.19 11.34 4 4.29 2.45 2 2.4 4 20.5 11,000 11.1 16 13 1.46
5. Solid to fluid heat transfer approximation
6.115 2.72 17.4 19 23
(6)
In this case, the viscous loss term has been neglected (Dq = 0). The CCrossFlow , cross flow friction loss coefficient for the bundle is acquired by combining the friction loss coefficient for a single tube, fCrossFlow , and the summation effect related to several tube layers. −n fCrossFlow = A Rem → CCrossFlow =
fCrossFlow =
2 × 105
fraction, is to predict the interfacial momentum transfer. The model for interfacial drag force, proposed by Ishii and Zuber (1979) is chosen. Pressure loss in the axial and perpendicular directions caused by the tube bundles are modeled by the porous media formulation. In this model, the drag force on the fluid phases consists of two parts: a viscous loss term proportional to flow velocity and an inertial loss term proportional to the square of the flow velocity. When the flow velocity is high, the linear term could often be neglected. In a tube bundle, which is an anisotropic porous medium, the pressure loss coefficients describing the friction forces are tensors, which are dependent on the direction (Pattikangas et al., 2010): 1 → − → − → − → − → − − → F DF,q = −q D q V q − q | V q | V q C q 2
where p is the pitch in the cross flow direction and Rem is calculated using the mixture (m) values. The values, which are chosen for the constant parameter are A = 3.29, n = 0.18 (Stavanovic and Studovic, 1999). In the direction parallel to the tube bundles, The Blasius correlation can be applied:
(7)
Shell side water circulation in the steam generator vessel is caused by heat flux received from the primary side and the consequential increase in the specific volume of the fluid. The heat flux from solid tube bundles to fluid is modeled on the basis of a 1D thermal hydraulic model. Heat transfer surface consists of 10,978 steel tubes 16 mm inside diameter made of steel. A simple heating pipe from the primary side that has been modeled is shown in Fig. 3. For calculating heat flux function, the following operation was considered. The water temperature at the inlet and the outlet were set 320 ◦ C and 290 ◦ C, respectively. Due to the fact that boiling occurs on the outer side of the pipe, the temperature on this side is fixed. The wall heat flux between primary coolant and the outer side of pipe in this model has been numerically measured, and the function approximating the distribution of heat flux has been constructed. The heat flux in the porous domain is described by Eq. (9). The li is the pipe length between each element and the hot collector. qi
kwatt m2
= 1410 exp(−4li )
(9)
6. Perforated plate modeling The perforated plate is a metal sheet with structured holes for steam ascending. The perforated plate is has been designed above the tube bundles. The metal sheet prevents asymmetrically circulation of feed water in sell side and helps to homogenous boiling of water. Also, the sheet could be considered as a moisture separator located above the tube bundles in steam generator. As mentioned the perforated plate has the constructed holes for steam transfer. In the holes modeling, the entities shall be complicated if the complete
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Fig. 3. Model of one pipe from the primary side of steam generator.
Fig. 4. Streamlines in the SG.
Fig. 5. The effect of perforated plate in distribution of void fraction.
Fig. 6. The distribution of water temperature.
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A. Safavi et al. / Nuclear Engineering and Design 256 (2013) 249–255 Table 4 Comparison between the results of 3D-ANA code and ANSYS CFX.
Fig. 7. The distribution of vapor velocity. Table 2 Positions of transducers (Stavanovic and Studovic, 1999). Transducer
Distance (mm)
ϕ1 ,ϕ2 ,ϕ3 ,ϕ8 ,ϕ10 ,ϕ12 ,ϕ13 ,ϕ14 ϕ4 ,ϕ11 ,ϕ15 ,ϕ16 ,ϕ17 ,ϕ18 ϕ5 ,ϕ7
Between transducer
From perforated plate
1000 700 200
350 70 35
geometry is used for constructing the numerical model, accordingly it results in solving difficulties even in a high performance computing system. Hence, for the purpose of availing analysis, the actual perforated plate is replaced by the opening boundary conditions in ANSYS CFX. 7. Results Coolant enters the hot collector (inlet) from the reactor and circulates through the tubes and leaves SG from the cold collector (outlet) into the coolant pumps suction line (see Figs. 1 and 2). Heat is transferred through the walls of the tubes from the coolant, boils the water on the shell side, and generates steam. Near the inlet collector, temperature of the tube bundles and the consequential heat flux is higher than near the outlet collector. Uneven steam production, because of the spatial distribution of heat flux, is the driver of the shell side circulation illustrated in Fig. 4. As depicted in Fig. 4, a circulative cross flow occurs in the tube side. In this way,
3D-ANA code
ANSYS CFX
0.48 0.51 0.54 0.61 0.70 0.70 0.71 0.57 0.48 0.57 0.53 0.50 0.43
0.45 0.49 0.50 0.64 0.88 0.68 0.86 0.53 0.54 0.51 0.57 0.48 0.46
a circulation from the outlet collector to the inlet collector occurs because of density variation in their vicinity. Moreover, feed water injection and perforated plate have a major impact on the shell side circulation. The comparison between the results obtained with and without perforated sheet is showed in Fig. 5a and b. Without perforated plate with the fact that vapor generation in hot side is higher, the generated steam is placed on top levels of inlet collector side. As can be seen in Fig. 5a in this situation due to the fact that injected water is cold and heavy, it pulls down the fluid around the water injection system. The steam collector is faced with the heterogeneous void generation. This state causes the higher mixed circulative cross flow. Perforated plate prevents the water from ascending in the cold side due to the nature of this sheet. Because this sheet only allows the vapor to be passed, it causes the vapor distribution to become more homogenous. The distribution of water temperature is illustrated in Fig. 6. As can be seen, water temperature decreases away from the center of SG. The CFX-2D model was developed to investigate the velocity of vapor in the SG. In this model, the tube bundle has been considered in details. Around 10,000 pipes have been modeled and meshed. The superficial velocity evaluated by our two dimensional SG model is illustrated in Fig. 7. As can be seen, the vapor velocity reaches the peak at 0.72 m/s above the tube bundles, and in general, the velocity of vapor has been increased by receiving heat from the tube bundles. The results of numerical solution have been compared to the data measured at certain positions at the SG with the perforated plate of the Novoronezh Nuclear Power Plant. These data have been extracted from a paper published by Stavanovic and Studovic in 1999. The positions of measuring points are shown in Fig. 8 and Table 2.
Table 3 Comparison between numerical data and experimental data. Void
EXP.Ageev (1987)
EXP.Karppinen (1994)
STEG-01Melikhov et al. (1995)
Average of experimental data
ANSYS CFX
ϕ1 ϕ2 ϕ3 ϕ4 ϕ5 ϕ6 ϕ7 ϕ8 ϕ10 ϕ12 ϕ13 ϕ14 ϕ15
0.30 0.45 0.45 0.80 1.00 0.70 1.00 0.55 0.47 0.52 0.50 0.55 0.38
0.50 0.18 0.42 – – 1.00 0.98 0.48 – 0.54 0.15 0.56 –
0.55 0.63 0.54 – 0.84 0.77 0.89 0.55 0.56 0.51 0.63 0.54 –
0.45 0.42 0.47 0.80 0.92 0.82 0.96 0.53 0.52 0.52 0.43 0.55 0.41
0.45 0.49 0.50 0.64 0.88 0.68 0.86 0.53 0.54 0.51 0.57 0.48 0.46
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Fig. 8. Void measuring points (Stavanovic and Studovic, 1999).
8. Conclusion
References
In this analysis, the simulations have been shown the comparable results with reported experimental data. In Table 3, the numerical results are compared with the experimental data and Table 4 contains the comparison of calculated results with reported data (Stavanovic and Studovic, 1999). In these tables the evaluation points are depicted in Fig. 8 that these points are void measuring transducer positions. As seen, a good agreement between the results of the simulation in ANSYS CFX and experimental data or reported data has been achieved. Consequently, the estimated function for modeling heat source and momentum source are reliable. So, the presented method for approximations of heat transfer and momentum is compatible with the desired domain of fluid. It is demonstrated that the perforated plate in steam generator WWER1000 has an undeniable impact on the distribution of the void fraction in the steam generator. Results show the void fraction of vapor and the temperature of water in the environment of the hot collector have their maximum values without the perforated plate. Perforated plate consideration with related feed injection helps a homogenous void generation, this demonstrates the importance of perforated plate utilization. Finally, the steam velocity above the tube bundle reaches the velocity of 0.72 m/s and consequently, the tubes located above tube bundle will have more vibration. The study of vibration in tube bundles is the next interesting subject.
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