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Local effect model development for the steam generator three dimensional thermal hydraulics analysis code
Annals of Nuclear Energy 136 (2020) 107020
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Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Local effect model development for the steam generator three dimensional thermal hydraulics analysis code Xi Wang a, Mingjun Wang a,⇑, Ge Wu b, Jing Zhang a, Suizheng Qiu a,⇑, G.H. Su a, Wenxi Tian a a b
State Key Laboratory of Multiphase Flow in Power Engineering, Department of Nuclear Science and Technology, Xi’an Jiaotong University, Xi’an 710049, China Nuclear Power Institute of China, Chengdu, China
a r t i c l e
i n f o
Article history: Received 24 April 2019 Received in revised form 4 August 2019 Accepted 29 August 2019
Keywords: Model development Steam generator Local effect CFD
a b s t r a c t The thermal hydraulic characteristics of steam generator secondary side in pressurized water reactor has been always a research hot point in the literatures. The detailed three dimensional thermal hydraulic parameters distribution in steam generator is very important for the reactor safety and economy. A three-dimensional two-phase analysis program STAF for the secondary side of steam generator has been developed by NuTheL at Xi’an Jiaotong University. The program is based on porous medium model and four-equation drift flow model. It can simulate the flow and heat transfer characteristics of steam generator. However, due to the limitation of porous medium model, STAF are not functional to obtain the local velocity distribution near the supporting plate and anti-vibration bars, which are very important for fouling deposition and flow vibration analysis. In this paper, the local detailed thermal hydraulic characteristics near steam generator supporting plate and anti-vibration bars are studied. The local flow field is obtained and the influence range and degree of local components on the velocity distribution is analyzed. The supporting plate and anti-vibration bars analysis model was developed and implemented into the STAF code. Results show that the improved code could predict the local velocity variations compared with the original code. This work is meaningful for the function promotion of steam generator thermal hydraulic code STAF. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction As the key equipment to connect the primary and secondary loops of pressurized water reactor (PWR), the steam generator plays the role of pressure boundary and heat transfer boundary in the primary loop. Because the pressure difference between the primary and secondary loops is very large (Zhao et al., 2019; Zhang et al., 2018), and the fluid in the primary loop contains highly radioactive substances, the integrity of heat transfer tube of steam generator must be guaranteed during operation. In large PWR nuclear power plants, the steam generator usually contains thousands of heat transfer pipes, and at the same time, a number of supporting plates and a number of anti-vibration bars are set up respectively in the straight and bend areas of heat transfer pipes, so the structure is very complex. The geometric shapes of these two local structures are shown in Fig. 1. In summary, the detailed three-dimensional thermal hydraulic parameters distributions in the steam generator are of great significance to the safe ⇑ Corresponding authors. E-mail addresses: [email protected] (M. Wang), [email protected]. edu.cn (S. Qiu). https://doi.org/10.1016/j.anucene.2019.107020 0306-4549/Ó 2019 Elsevier Ltd. All rights reserved.
operation of the steam generator and the economy of the whole nuclear power plant. In the early stage of reactor design, the steam generator was only considered as a component connecting the primary and secondary loops, usually being analyzed with zero-dimensional or one-dimensional methods. As researchers gradually expand their research focus to equipment safety analysis, the study of threedimensional thermal and hydraulic characteristics of steam generators has become very crucial. Due to the large volume and high thermal power of the steam generator, it is difficult to carry out the real scale experimental research. Therefore, most researchers first chose the numerical simulation method to study the thermal and hydraulic characteristics of steam generator. CNRL developed the THIRST program for AECL in 1991 (Carver et al., 1981; Pietralik et al., 1998). By solving the mixture flow model based on porous media model in three-dimensional cylindrical coordinates, the three-dimensional two-phase flow and heat transfer characteristics of steam generator under steady state conditions were obtained. CEA developed and validated the threedimensional thermo-hydraulic characteristic analysis program GENEPI for U-tube steam generator (Soussan and Grandotto, 1998), which uses zero-equation turbulence model to solve the
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Fig. 1. Local structure geometric shapes.
effective viscosity of two-phase fluid and Lellouche-Zolotar drift flow model to solve the slip velocity between phases (Lellouche and Zolotar, 1982). In 1984, EPRI introduced the CFD program ATHOS for the analysis of three-dimensional thermo-hydraulic characteristics of the secondary side of UTSG and OTSG (Singhal et al., 1984). This program can solve the mixture flow and threeequation drift flow model based on porous medium model, and can simulate various components of common steam generator. At the same time, in order to verify the accuracy of the program, the research of relevant experiments is also essential, but the scale test is usually used. The FRIGG circuit is designed and constructed by ASEA-ATOM and other research institutions (Nylund, 1970; Nylund et al., 1968). The circuit includes rod bundle area, steamwater separator, descending section, pump and connecting pipeline. The void fraction is measured by gamma ray. Although the experiment is based on boiling water reactor, the test data can be used to verify the steam generator program. In order to verify the thermal and hydraulic characteristics of Westinghouse F steam generator, Westinghouse and EPRI established MB-2 test bench (Young et al., 1984; Singhal et al., 1984). The test piece is a 1% power scale model test piece of Westinghouse F type steam generator. The material parameters, geometric parameters, thermal and hydraulic parameters are the same as those of F type steam generator. The nuclear reactor thermal hydraulic Lab. (NuTheL) at Xi’an Jiaotong University studied the local single-phase and two-phase flow and heat transfer characteristics outside the heat transfer tube of pressurized water reactor steam generator at atmospheric pressure (Tian et al., 2016; Zhang et al., 2017; Zhang et al., 2019). The heat transfer capacity and flow resistance of straight and elbow tube bundles under different working conditions were obtained. On the basis of the above numerical simulation and experimental research, the NutheL developed a three-dimensional two-phase thermal-hydraulic analysis STAF program for the secondary side of steam generator (Cong et al., 2013; Cong et al., 2014; Fang et al., 2020.). The porous medium model and four equation drift flow model are used to calculate the coupled heat transfer between the primary and secondary sides of the steam generator, especially the characteristics of the subcooled boiling and saturated boiling stages, and obtain the three-dimensional parameter distribution in the steam generator. Although the STAF program has been able to calculate and analyze the distribution of thermal and hydraulic parameters of steam generator on the whole, it still has some limitations. Because the porous medium model is used to simplify the heat transfer tube region, the influence of supporting plate and anti-vibration bars
on the local flow field cannot be obtained. This part of the influence is very important for the analysis of fouling deposition (Rummens et al., 2004; Srikantiah and Chappidi, 2000) and flow-induced vibration (Nakamura et al., 2011; Mohany and Janzen, 2009) in steam generator. Therefore, it is necessary to analyze the structure of supporting plate and anti-vibration bars in the tube bundle area of steam generator. But at present, there are few related studies. Cizelj et al. simulated the flow field and temperature field around a heat transfer tube near the supporting plate by ABAQUS software (Cizelj et al., 1995). Li and Sun of Harbin Engineering University have studied the thermohydraulic parameters of U-tube of steam generator with supporting plate by CFX (Li et al., 2013; Sun and Yang, 2013). Based on the above information, it is necessary to carry out local modeling and calculation for the supporting plate area and anti-vibration bars area in the secondary side of the steam generator, analyze the change of local flow field, extract threedimensional velocity distribution from the simulation results, so as to modify the overall calculation. In this paper, the local flow fields in the supporting plate and anti-vibration bars regions are modeled and calculated respectively. The local velocity field distribution is obtained. The influence of the supporting plate and anti-vibration bars structures on the local flow field is analyzed. The method of adding the influence of the local structure on the flow field to the overall calculation is proposed, and the overall calculation is revised accordingly. 2. Local effect model development method 2.1. Local effect model As mentioned above, in the three-dimensional two-phase simulation of the secondary side of the steam generator, the STAF program can calculate the flow characteristics and heat transfer characteristics of the steam generator. However, due to the limitation of the porous medium model, the STAF program can only add a local pressure drop to the supporting plate, which cannot reflect the influence of the supporting plate and the anti-vibration strip on the local velocity. In the analysis of fouling deposition and flow-induced vibration of steam generator, these local velocity distributions are important input conditions. In order to improve the function of STAF program, this study was carried out to modify the local velocity field. In this research, firstly, three-dimensional modeling and numerical simulation are carried out for the region near the supporting plate and anti-vibration strip, and the local flow field is
X. Wang et al. / Annals of Nuclear Energy 136 (2020) 107020
obtained. Then, the influence of local components on velocity is analyzed, and the influence range and degree are calculated. In addition, this study also proposes a model of adding local effects to the overall calculation. The main steps are to determine the impact grid, read the local speed, calculate the impact speed, store and output by user-defined memory. Finally, according to the above model, the local velocity correction of the threedimensional steam generator analysis program STAF is carried out. The local impact model developed in this study not only considers the influence of local velocity, but also does not waste computing resources where there are no local components.
2.2. Mathematic model In the part of local flow field calculation in this paper, because the calculation region is modeled according to the real geometric structure with no simplification, so the required mathematical models are three conservation equations and turbulence equations, and no additional equations are needed. In the integral revision part, because the overall framework of STAF program has not been modified, the mathematical model is consistent with the original mathematical model of STAF. The mathematical model of local calculation is as follows. Mass equation:
@ ! ðq Þ þ r ðqm v m Þ ¼ 0 @t m
ð1Þ
Momentum equation: @ ð @t
qm ! v m Þ þ r ðqm ! v m! v m Þ ¼ rp þ r ½lm ðr! v m þ r! v m Þ T
n P ! ! ! ! þqm g þ F þ r ð ak qk v dr;k v dr;k Þ k¼1
ð2Þ Energy equation: n n X @ X ! ðak qk Ek Þ þ r ðak v k ðqk Ek ÞÞ ¼ r ðkejf rTÞ þ SE @t k¼1 k¼1
ð3Þ
Turbulence equation:
qm kÞ þ r ðqm um kÞ ¼ r
@ ð @t
qm eÞ þ r ðqm um eÞ ¼ r
@ ð @t
h
i
lm þ rlkt rk þ Gk qm e
h
ð4Þ
i
lm þ rlet re þ ke ðC e1 Gk C e2 qm eÞ
3. Analysis of local flow field in supporting plate region 3.1. Three-dimensional CFD modeling In steam generator, the supporting plate generally exists in the triangular tube bundle area with the structure of trifoliate plum orifice plate to support the tube bundle. In this paper, in order to obtain the influence of the supporting plate on the local flow field, it is necessary to select the area near the supporting plate as the research object. According to the principle of symmetry, the flow passages enclosed by three heat transfer tubes are selected as the research object. The middle of the calculation area is the supporting plate area, and a distance is taken along the flow direction. The final geometric model is shown in Fig. 2. The established geometric model needs to be meshed. Due to the regularity of computational regions, integrated structural grid generation can be carried out. At the same time, grid independence study should be considered during the CFD application in nuclear thermal hydraulic research, which has been regarded as the guideline (Wang et al., 2017; Wang et al., 2018). Because the mathematical model of local simulation is standard, the grid independent scheme can be obtained by calculating the grid models with different number of grids under simple single-phase and steady-state conditions. The relationship between the inlet and outlet pressure drop and the number of grids is shown in Fig. 3. It can be seen that when the number of grids is 640000, the grid scheme is the independent one. The final grid model is shown in Fig. 4. In order to ensure the accuracy of the calculation, it is necessary to make reasonable settings in the calculation. It mainly includes physical parameters, boundary conditions and so on. In this paper, it is necessary to set the physical parameters of water and steam under the operating conditions of steam generator. In the boundary conditions, the inlet is set as the velocity inlet and the outlet is set as the pressure outlet, and the velocity, temperature, void fraction and turbulence parameters are set according to the relevant data. In addition to the inlet and outlet, the pipe wall and the supporting plate are set as the wall, and the other surfaces are set as the symmetrical surface. In addition, the main consideration in this part is the velocity field. The primary and secondary side heat transfer has little effect on the local velocity, which can be ignored.
3.2. Results analysis Through accurate local geometric modeling and numerical calculation of the supporting plate and the adjacent tube bundle area,
ð5Þ
lt ¼ Cl qem k
2
ð6Þ
! ! ! T Gk ¼ lt r um r um þ r um
ð7Þ !
v m is the ! velocity of mixture; p is pressure, lm is the viscosity of mixture, g is ! gravitational acceleration, F is the body force of the mixture, ak is ! the volume fraction of the k phase, v dr;k is velocity of mixture flow weighted by relative mass of phase k; Ek is the enthalpy of the k phase, keff is the effective heat conductivity, T is temperature, SE is an additional energy source term; k is turbulent pulsating kinetic energy, rk is Prandtl number of pulsating kinetic energy, e is dissipation rate, C is empirical coefficient. where, q is density, and subscript m represents mixture;
3
Fig. 2. Supporting plate geometric model.
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calculated, as shown in Fig. 6. Cross-flow velocity and downstream velocity are defined as follows: Cross-flow velocity:
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
v crossflow ¼ v 2x þ v 2y
ð8Þ
Downstream velocity:
v downstream ¼ v z
Fig. 3. Grid independence study.
Fig. 4. Supporting plate grid model.
the distribution of thermal and hydraulic parameters of the flow field in this area is obtained. Because the main purpose of this study is to obtain the velocity field distribution, analyze the influence of the supporting plate structure on the local flow field, and use it to modify the overall calculation, the velocity field near the supporting plate structure is mainly selected for analysis, and the streamline is drawn as shown in Fig. 5. As can be seen from Fig. 5, when the fluid flows through the supporting plate area, there is an obvious cross-flow velocity and a significant increase in the downstream velocity, which can indicate the influence of the supporting plate structure on the local flow field. However, relative to the tube bundle area before and after the support plate, the change of velocity concentrates near the support plate structure, while the fluid velocity in the tube bundle area has no change in size and direction compared with the inlet velocity. In order to quantitatively describe the influence of supporting plate on velocity field, further processing and analysis of velocity distribution are needed. By calculating the average parameters of a section, the weighted average values of the required physical quantities (such as velocity, pressure, etc.) on a section can be obtained. In order to quantitatively analyze the influence area of the supporting plate on the local flow field in the axial part, the distribution curves of the cross-section average cross-flow velocity and the cross-section average parallel-flow velocity along the axial direction are
ð9Þ
where, v x and v y are a group of velocity components perpendicular to the heat transfer tube and perpendicular to each other; v z is the velocity component parallel to the heat transfer tube. As can be seen from Fig. 6, when the fluid flows in the tube bundle area in front of the supporting plate, the average cross-flow velocity of the cross-section is constant at 0, which indicates that there is no cross-flow of the fluid in the area. At the entrance section and exit section of the supporting plate, there is a peak value of cross-flow velocity, which is due to the influence of the supporting plate structure and the change of the flow area, resulting in the change of the direction of fluid flow in the supporting plate, so there will be a peak value of cross-flow velocity. In the tube bundle area downstream of the supporting plate, the cross-flow velocity is gradually stabilized to 0, which indicates that the flow of fluid is gradually stable after passing through the supporting plate, and the cross-flow gradually disappears. It can also be seen from the results that when the fluid flows in the tube bundle area in front of the supporting plate, the average downstream velocity of the cross section is constant, which is the initial inflow velocity. In the area of supporting plate, the peak value of downstream velocity occurs, which is due to the influence of supporting plate structure, the flow area decreases, and the downstream velocity inevitably increases. There is a minimum downstream velocity near the exit section of the supporting plate, which is caused by the local vortices when the fluid flows out of the supporting plate. In the downstream tube bundle area of the supporting plate, the downstream velocity gradually stabilizes and maintains the inflow velocity before the supporting plate. According to the above analysis, we can know that the influence of the supporting plate on the local flow field mainly concentrates near the supporting plate structure, but has little influence on the front and rear tube bundle area, which is also consistent with the conclusion obtained by the qualitative analysis of the streamline diagram. In order to determine the magnitude of the influence area more accurately, the criterion for determining whether the supporting plate has an effect on the local flow field is defined artificially. For cross-flow velocity, the cross-flow velocity at the front and back of the supporting plate is greater than 10% of the peak velocity at the front and back of the supporting plate, respectively, as the criteria for judging the influence of the supporting plate. For the downstream velocity, the difference between the downstream velocity and the incoming velocity is greater than 10% as the criterion for judging the influence of the supporting plate. Finally, the influence range of the supporting plate structure on the local flow field can be quantitatively obtained. In order to avoid the influence of flow conditions on the conclusion, the calculation of different inlet velocities and different void fractions was carried out, and the analysis was carried out. The influence range did not change significantly. Therefore, it can be considered that the influence range of the supporting plate structure on the local flow field is independent of the flow conditions under the premise of determining the geometrical structure. In order to apply the influence of supporting plate on local velocity to the correction of local velocity field in STAF program, it is necessary to determine the influence degree of supporting plate on velocity within the influence range. Considering that STAF program uses porous medium model to simplify the tube bundle
X. Wang et al. / Annals of Nuclear Energy 136 (2020) 107020
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Fig. 5. Streamline distribution near the supporting plate.
Fig. 6. Distribution of the cross-flow/downstream velocity along the axial direction.
area, the grid size of the tube bundle area is relatively large compared with the thickness of the supporting plate. As the input condition of fouling deposition and flow vibration analysis, the two components of the cross flow velocity perpendicular to the heat transfer tube and the downstream velocity along the direction of the heat transfer tube are most needed. In this paper, the velocity components of cross-flow velocity and along-flow velocity are directly used to describe the velocity correction in the supporting plate area. For cross-flow velocity, the ratio of average velocity to inflow velocity is calculated as two correction factors in the grid before and after the support plate. For the downstream velocity, the ratio of the average velocity of the calculation range to the incoming velocity is used as the correction factor in the mesh before and after the supporting plate. In order to avoid the influence of flow conditions, multi-condition calculations with different flow velocities and different void fractions were carried out and analyzed. The data under different working conditions are shown in Table 1. As can be seen from the table, the correction factor obtained does not change significantly, which is also because the influence of the supporting plate structure on the local flow field is independent of the flow conditions. Based on the above analysis, the influence range and correction factors of the supporting plate on the local flow field are determined respectively, which can be used to modify the local velocity field of STAF program.
4. Analysis of local flow field in anti-vibration bars region 4.1. Three-dimensional CFD modeling Similar to the supporting plate, in the bend section of the steam generator tube bundle, a number of anti-vibration bars are inserted to restrict the tube bundle. In this paper, in order to obtain the effect of anti-vibration bars on local flow field, we need to select the bend area as the research object, establish the geometric model of the bend area without anti-vibration bars and with antivibration bars respectively, and carry out the corresponding meshing. The geometric model is shown in Fig. 7. In the direction perpendicular to the paper surface, it contains only one layer of fluid between two adjacent rows of heat transfer tubes. Correspondingly, only one anti-vibration bar in each group is in the calculation area (six groups, one in each group, so there are six in all.).
4.2. Results analysis Through precise local geometric modeling and numerical calculation of the bend area without and with anti-vibration bars, the distribution of thermal and hydraulic parameters under the two structures is obtained. In this paper, the influence of antivibration bar on velocity is analyzed and the velocity vector diagram is drawn.
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Table 1 Correction factors under different working conditions. Working condition
No. 1
Inlet velocity(m/s) Cross-flow velocity(m/s)* Cross-flow correction factor* Downstream velocity(m/s) Downstream correction factor
0.90 0.22 0.24 1.66 1.84
No. 2 0.08 0.09
2.70 0.68 0.25 4.97 1.84
No. 3 0.25 0.09
5.50 1.38 0.25 10.13 1.84
No. 4 0.50 0.09
8.80 2.21 0.25 16.20 1.84
No. 5 0.81 0.09
11.00 2.76 0.25 20.25 1.84
1.03 0.09
* Note: The cross-flow velocity has two peaks at the inlet and outlet of the supporting plate, respectively. Therefore, there are two values for cross-flow velocity and crossflow correction factor in each case.
Fig. 7. Bend area without/with anti-vibration bars geometric model.
In the bend area, the local area of a row of pipe bundles is selected as the research object. The velocity vector diagram of the area under two different structures is shown in Fig. 8. As can be seen from the results, the fluid velocity in this area does not fluctuate much without anti-vibration bar structure. Under the structure of anti-vibration strip, when the fluid flows through the antivibration strip, the cross-flow velocity is obvious, and the alongflow velocity is obviously increased. The comparison between them can show the influence of anti-vibration bar structure on local flow field. At the same time, the anti-vibration strip has a small influence
on the flow field, which is concentrated in the area near several groups of anti-vibration strips, which is the same as the effect of the supporting plate on the local flow field. Therefore, in order to quantitatively describe the influence of anti-vibration bar on flow field, the anti-vibration bar area is simplified, and the local area near a single anti-vibration bar in the bend area is selected for calculation, and the velocity distribution is analyzed. As shown in Fig. 9, a geometric model for calculating the local flow field of a single anti-vibration bar is presented. The influence of anti-vibration bar on local flow field can be quantitatively
Fig. 8. Velocity vector diagram of bend area without/with anti-vibration bars.
X. Wang et al. / Annals of Nuclear Energy 136 (2020) 107020
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stabilizes after passing through the anti-vibration bar, and the cross-flow gradually disappears. In addition, when the fluid flows in the bundle area before and after the anti-vibration bar, the average cross-sectional downstream velocity is stable at the inflow velocity. In the anti-vibration strip region, the downstream velocity peaks. These results are similar to the effect of the supporting plate on the local flow field. According to the above analysis, we can know that the influence of anti-vibration bars on the local flow field are mainly concentrated in the vicinity of anti-vibration bars structure, but have little influence on the front and rear tube bundles. Similar to the analysis of supporting plate area, the criteria for determining the influence range of anti-vibration strip area are defined, and the influence range and correction factors are calculated for the correction of local velocity field. Fig. 9. Geometric model of local flow near a single anti-vibration bar.
analyzed by selecting this area for calculation. Similar to the supporting plate, the local velocity can also be decomposed into two components parallel to and vertical to the anti-vibration bar. Fig. 10 is a local velocity vector map of the region. It can be seen from the results that the velocity and direction of the fluid flow through the anti-vibration strip area have obvious changes. In the area of the tube bundle before and after the anti-vibration bar, the velocity of the fluid is the same as that of the incoming flow. The cross-flow and downflow velocities are defined to obtain the distribution of cross-section average cross-flow velocities and downflow velocities along the length of tube bundles, and the curves in Fig. 11 are obtained. It can be seen from the results that when the fluid flows in the area of the tube bundle in front of the anti-vibration bar, the average cross-flow velocity of the cross-section is constant at 0, which indicates that there is no cross-flow in the area. At the entrance and exit of the anti-vibration strip, the cross-flow velocity has a peak value, which is due to the influence of the anti-vibration strip structure and the change of the flow area, resulting in the change of the flow direction of the fluid at the position, so the peak value of the cross-flow velocity will occur. However, in the downstream bundle area of the anti-vibration bar, the cross-flow velocity gradually stabilizes to 0, which indicates that the flow of fluid gradually
5. Local velocity field correction According to the influence range and factors of local velocity in support plate area and anti-vibration strip area obtained above, the local velocity field can be corrected in STAF program. Specific operations are as follows: Firstly, according to the influence range and the mesh size of the calculation model, the partially affected mesh is judged and marked. Secondly, the initial speed in the affected grid is read. In the vicinity of the supporting plate, the initial velocity is along the direction of the tube bundle, which is the same as that of the downstream velocity. In the vicinity of the antivibration bar, the initial velocity is not vertical to the antivibration bar, so it needs to be decomposed into normal and tangential directions. Finally, the velocity correction factor is added to the velocity field. In the vicinity of the supporting plate, the cross-flow influencing factor multiplied by the initial velocity is the new cross-flow velocity, and the downstream influencing factor multiplied by the initial velocity is the new downstream velocity. In the vicinity of the anti-vibration bar, the initial normal velocity is multiplied by the cross-flow correction factor and the downstream correction factor respectively, and the velocity is synthesized with the initial tangential velocity to obtain the corrected velocity. In STAF program, the revised velocity is stored in user-defined variables, and the velocity field distribution before or after the revised output can be manually selected. In order to reflect the velocity difference between the original STAF program and the modified STAF program, a line along bundle direction is selected to extract the secondary side velocity and draw the curve. The velocity distribution along the axis before and after correction is shown in Fig. 12. It can be seen that the revised results can better show the influence of local components on local velocity in the supporting plate and anti-vibration strip area. 6. Conclusion
Fig. 10. Velocity vector diagram near a single anti-vibration bar.
Aiming at the local components of steam generator, a series of high fidelity CFD analysis in the supporting plate and antivibration strip area were performed respectively. The accurate local thermal-hydraulic parameter distributions were achieved and the local velocity field was analyzed. The quantitatively analyses of the influence range and degree of supporting plate and anti-vibration strip on local velocity distribution were obtained. The local effect indicated parameter, namely correction factors of cross-flow and along-flow velocity, was defined and obtained. Then the local effect correction factors were applied in the STAF program, which is a three dimensional steam generator thermal hydraulic code developed by NuTheL at Xi’an Jiaotong University. Compared with the code before improvement, the modified code
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Fig. 11. Distribution of the cross-flow/downstream velocity along the axial direction.
Fig. 12. Velocity difference between original program and modified program.
shows great advantages and it can reflect the influence of supporting plate and anti-vibration strip on local flow field obviously. The modified STAF code can be used to analyze steam generator more accurately, and provide input conditions for fouling deposition and flow-induced vibration analysis. Acknowledgment This research has been supported by National Natural Science Foundation of China (No. 11705139). Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.anucene.2019.107020. References Carver, M., Carlucci, L., Inch, W., 1981. Thermal-hydraulics in Recirculating Steam Generators. THIRST Code User’s Manual. Chalk River. Atomic Energy of Canada Ltd., Ontario, Canada. Cizelj, L., Dvorsek, T., Petelin, S., 1995. On the distribution of temperatures in steam generator tubes at tube support plate intersections. The 2nd Regional Meeting on Nuclear Energy in Central Europe, Sep 11-14, 1995. Nuclear Society of Slovenia, Portoroz, Slovenia, pp. 276–282.
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X. Wang et al. / Annals of Nuclear Energy 136 (2020) 107020 Singhal, A.K., Keeton, L.W., Przekwas, A.J., et al., 1984. ATHOS3: A Computer Program For Thermal-Hydraulic Analysis of Steam Generators. Volume 1: Mathematical and physical models and method of solution. Cham of North America Incorporated, Palo Alto, CA, USA. Singhal, A.K., Keeton, L.W., Przekwas, A.J., et al., 1984. ATHOS3: A Computer Program for Thermal-Hydraulic Analysis of Steam Generators. Volume 4: Applications. Cham of North America Incorporated, Palo Alto, CA, USA. Soussan, D., Grandotto, M., 1998. An eddy viscosity model for flow in a tube bundle. Canadian Nuclear Society, Toronto, ON, Canada. Srikantiah, G., Chappidi, P.R., 2000. Particle deposition and fouling in PWR steam generators. Nucl. Eng. Des. 200 (1–2), 285–294. Sun, B., Yang, Y., 2013. Numerically investigating the influence of tube support plates on thermal-hydraulic characteristics in a steam generator. Appl. Therm. Eng. 51 (1–2), 611–622. Tian, W.X., Zhang, K., Hou, Y.D., Zhang, Y.P., Qiu, S.Z., Su, G.H., 2016. Hydrodynamics of two-phase flow in a rod bundle under cross-flow condition. Ann. Nucl. Energy 91, 206–214. Wang, Mingjun, Bai, Leyuan, Wang, Lianfa, et al., 2017. Thermal hydraulic and stress coupling analysis for AP1000 Pressurized Thermal Shock (PTS) study under SBLOCA scenario. Appl. Therm. Eng. 122, 158–170.
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Wang, Mingjun, Fang, Di, Xiang, Yan, et al., 2018. Study on the coolant mixing phenomenon in a 45 degrees T junction based on the thermal-mechanical coupling method. Appl. Therm. Eng. 144, 600–613. Young, M.Y., Takeuchi, K., Mendler, O.J., et al., 1984. Prototypical Steam Generator Transient Testing Program: Test Plan/Scaling Analysis. Westinghouse Electric Corporation, Pittsburgh, Pennsylvania, USA. Zhang, Jing, Chen, Ronghua, Wang, Mingjun, Tian, Wenxi, Guanghui, Su., Qiu, Suizheng, 2018. A code development for leak before break (LBB) leakage from supercritical to subcritical conditions. Prog. Nucl. Energy 103, 217–228. Zhang, Jing, Hao, Yu., Wang, Mingjun, Yinwei, Wu., Tian, Wenxi, Qiu, Suizheng, Guanghui, Su., 2019. Experimental study on the flow and thermal characteristics of two-phase leakage through micro crack. Appl. Therm. Eng. 156, 145–155. Zhang, K., Hou, Y.D., Tian, W.X., 2017. Experimental investigations on single-phase convection and steam-water two-phase flow boiling in a vertical rod bundle. Exp. Therm Fluid Sci. 80, 147–154. Zhao, Xiaohan, Wang, Mingjun, Chen, Chong, Wang, Xi, Haoran, Ju, Tian, Wenxi, Qiu, Suizheng, Su, G.H., 2019. Three-dimensional study on the hydraulic characteristics under the steam generator (SG) tube plugging operations for AP1000. Prog. Nucl. Energy 112, 63–74.
Contents lists available at ScienceDirect
Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Local effect model development for the steam generator three dimensional thermal hydraulics analysis code Xi Wang a, Mingjun Wang a,⇑, Ge Wu b, Jing Zhang a, Suizheng Qiu a,⇑, G.H. Su a, Wenxi Tian a a b
State Key Laboratory of Multiphase Flow in Power Engineering, Department of Nuclear Science and Technology, Xi’an Jiaotong University, Xi’an 710049, China Nuclear Power Institute of China, Chengdu, China
a r t i c l e
i n f o
Article history: Received 24 April 2019 Received in revised form 4 August 2019 Accepted 29 August 2019
Keywords: Model development Steam generator Local effect CFD
a b s t r a c t The thermal hydraulic characteristics of steam generator secondary side in pressurized water reactor has been always a research hot point in the literatures. The detailed three dimensional thermal hydraulic parameters distribution in steam generator is very important for the reactor safety and economy. A three-dimensional two-phase analysis program STAF for the secondary side of steam generator has been developed by NuTheL at Xi’an Jiaotong University. The program is based on porous medium model and four-equation drift flow model. It can simulate the flow and heat transfer characteristics of steam generator. However, due to the limitation of porous medium model, STAF are not functional to obtain the local velocity distribution near the supporting plate and anti-vibration bars, which are very important for fouling deposition and flow vibration analysis. In this paper, the local detailed thermal hydraulic characteristics near steam generator supporting plate and anti-vibration bars are studied. The local flow field is obtained and the influence range and degree of local components on the velocity distribution is analyzed. The supporting plate and anti-vibration bars analysis model was developed and implemented into the STAF code. Results show that the improved code could predict the local velocity variations compared with the original code. This work is meaningful for the function promotion of steam generator thermal hydraulic code STAF. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction As the key equipment to connect the primary and secondary loops of pressurized water reactor (PWR), the steam generator plays the role of pressure boundary and heat transfer boundary in the primary loop. Because the pressure difference between the primary and secondary loops is very large (Zhao et al., 2019; Zhang et al., 2018), and the fluid in the primary loop contains highly radioactive substances, the integrity of heat transfer tube of steam generator must be guaranteed during operation. In large PWR nuclear power plants, the steam generator usually contains thousands of heat transfer pipes, and at the same time, a number of supporting plates and a number of anti-vibration bars are set up respectively in the straight and bend areas of heat transfer pipes, so the structure is very complex. The geometric shapes of these two local structures are shown in Fig. 1. In summary, the detailed three-dimensional thermal hydraulic parameters distributions in the steam generator are of great significance to the safe ⇑ Corresponding authors. E-mail addresses: [email protected] (M. Wang), [email protected]. edu.cn (S. Qiu). https://doi.org/10.1016/j.anucene.2019.107020 0306-4549/Ó 2019 Elsevier Ltd. All rights reserved.
operation of the steam generator and the economy of the whole nuclear power plant. In the early stage of reactor design, the steam generator was only considered as a component connecting the primary and secondary loops, usually being analyzed with zero-dimensional or one-dimensional methods. As researchers gradually expand their research focus to equipment safety analysis, the study of threedimensional thermal and hydraulic characteristics of steam generators has become very crucial. Due to the large volume and high thermal power of the steam generator, it is difficult to carry out the real scale experimental research. Therefore, most researchers first chose the numerical simulation method to study the thermal and hydraulic characteristics of steam generator. CNRL developed the THIRST program for AECL in 1991 (Carver et al., 1981; Pietralik et al., 1998). By solving the mixture flow model based on porous media model in three-dimensional cylindrical coordinates, the three-dimensional two-phase flow and heat transfer characteristics of steam generator under steady state conditions were obtained. CEA developed and validated the threedimensional thermo-hydraulic characteristic analysis program GENEPI for U-tube steam generator (Soussan and Grandotto, 1998), which uses zero-equation turbulence model to solve the
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Fig. 1. Local structure geometric shapes.
effective viscosity of two-phase fluid and Lellouche-Zolotar drift flow model to solve the slip velocity between phases (Lellouche and Zolotar, 1982). In 1984, EPRI introduced the CFD program ATHOS for the analysis of three-dimensional thermo-hydraulic characteristics of the secondary side of UTSG and OTSG (Singhal et al., 1984). This program can solve the mixture flow and threeequation drift flow model based on porous medium model, and can simulate various components of common steam generator. At the same time, in order to verify the accuracy of the program, the research of relevant experiments is also essential, but the scale test is usually used. The FRIGG circuit is designed and constructed by ASEA-ATOM and other research institutions (Nylund, 1970; Nylund et al., 1968). The circuit includes rod bundle area, steamwater separator, descending section, pump and connecting pipeline. The void fraction is measured by gamma ray. Although the experiment is based on boiling water reactor, the test data can be used to verify the steam generator program. In order to verify the thermal and hydraulic characteristics of Westinghouse F steam generator, Westinghouse and EPRI established MB-2 test bench (Young et al., 1984; Singhal et al., 1984). The test piece is a 1% power scale model test piece of Westinghouse F type steam generator. The material parameters, geometric parameters, thermal and hydraulic parameters are the same as those of F type steam generator. The nuclear reactor thermal hydraulic Lab. (NuTheL) at Xi’an Jiaotong University studied the local single-phase and two-phase flow and heat transfer characteristics outside the heat transfer tube of pressurized water reactor steam generator at atmospheric pressure (Tian et al., 2016; Zhang et al., 2017; Zhang et al., 2019). The heat transfer capacity and flow resistance of straight and elbow tube bundles under different working conditions were obtained. On the basis of the above numerical simulation and experimental research, the NutheL developed a three-dimensional two-phase thermal-hydraulic analysis STAF program for the secondary side of steam generator (Cong et al., 2013; Cong et al., 2014; Fang et al., 2020.). The porous medium model and four equation drift flow model are used to calculate the coupled heat transfer between the primary and secondary sides of the steam generator, especially the characteristics of the subcooled boiling and saturated boiling stages, and obtain the three-dimensional parameter distribution in the steam generator. Although the STAF program has been able to calculate and analyze the distribution of thermal and hydraulic parameters of steam generator on the whole, it still has some limitations. Because the porous medium model is used to simplify the heat transfer tube region, the influence of supporting plate and anti-vibration bars
on the local flow field cannot be obtained. This part of the influence is very important for the analysis of fouling deposition (Rummens et al., 2004; Srikantiah and Chappidi, 2000) and flow-induced vibration (Nakamura et al., 2011; Mohany and Janzen, 2009) in steam generator. Therefore, it is necessary to analyze the structure of supporting plate and anti-vibration bars in the tube bundle area of steam generator. But at present, there are few related studies. Cizelj et al. simulated the flow field and temperature field around a heat transfer tube near the supporting plate by ABAQUS software (Cizelj et al., 1995). Li and Sun of Harbin Engineering University have studied the thermohydraulic parameters of U-tube of steam generator with supporting plate by CFX (Li et al., 2013; Sun and Yang, 2013). Based on the above information, it is necessary to carry out local modeling and calculation for the supporting plate area and anti-vibration bars area in the secondary side of the steam generator, analyze the change of local flow field, extract threedimensional velocity distribution from the simulation results, so as to modify the overall calculation. In this paper, the local flow fields in the supporting plate and anti-vibration bars regions are modeled and calculated respectively. The local velocity field distribution is obtained. The influence of the supporting plate and anti-vibration bars structures on the local flow field is analyzed. The method of adding the influence of the local structure on the flow field to the overall calculation is proposed, and the overall calculation is revised accordingly. 2. Local effect model development method 2.1. Local effect model As mentioned above, in the three-dimensional two-phase simulation of the secondary side of the steam generator, the STAF program can calculate the flow characteristics and heat transfer characteristics of the steam generator. However, due to the limitation of the porous medium model, the STAF program can only add a local pressure drop to the supporting plate, which cannot reflect the influence of the supporting plate and the anti-vibration strip on the local velocity. In the analysis of fouling deposition and flow-induced vibration of steam generator, these local velocity distributions are important input conditions. In order to improve the function of STAF program, this study was carried out to modify the local velocity field. In this research, firstly, three-dimensional modeling and numerical simulation are carried out for the region near the supporting plate and anti-vibration strip, and the local flow field is
X. Wang et al. / Annals of Nuclear Energy 136 (2020) 107020
obtained. Then, the influence of local components on velocity is analyzed, and the influence range and degree are calculated. In addition, this study also proposes a model of adding local effects to the overall calculation. The main steps are to determine the impact grid, read the local speed, calculate the impact speed, store and output by user-defined memory. Finally, according to the above model, the local velocity correction of the threedimensional steam generator analysis program STAF is carried out. The local impact model developed in this study not only considers the influence of local velocity, but also does not waste computing resources where there are no local components.
2.2. Mathematic model In the part of local flow field calculation in this paper, because the calculation region is modeled according to the real geometric structure with no simplification, so the required mathematical models are three conservation equations and turbulence equations, and no additional equations are needed. In the integral revision part, because the overall framework of STAF program has not been modified, the mathematical model is consistent with the original mathematical model of STAF. The mathematical model of local calculation is as follows. Mass equation:
@ ! ðq Þ þ r ðqm v m Þ ¼ 0 @t m
ð1Þ
Momentum equation: @ ð @t
qm ! v m Þ þ r ðqm ! v m! v m Þ ¼ rp þ r ½lm ðr! v m þ r! v m Þ T
n P ! ! ! ! þqm g þ F þ r ð ak qk v dr;k v dr;k Þ k¼1
ð2Þ Energy equation: n n X @ X ! ðak qk Ek Þ þ r ðak v k ðqk Ek ÞÞ ¼ r ðkejf rTÞ þ SE @t k¼1 k¼1
ð3Þ
Turbulence equation:
qm kÞ þ r ðqm um kÞ ¼ r
@ ð @t
qm eÞ þ r ðqm um eÞ ¼ r
@ ð @t
h
i
lm þ rlkt rk þ Gk qm e
h
ð4Þ
i
lm þ rlet re þ ke ðC e1 Gk C e2 qm eÞ
3. Analysis of local flow field in supporting plate region 3.1. Three-dimensional CFD modeling In steam generator, the supporting plate generally exists in the triangular tube bundle area with the structure of trifoliate plum orifice plate to support the tube bundle. In this paper, in order to obtain the influence of the supporting plate on the local flow field, it is necessary to select the area near the supporting plate as the research object. According to the principle of symmetry, the flow passages enclosed by three heat transfer tubes are selected as the research object. The middle of the calculation area is the supporting plate area, and a distance is taken along the flow direction. The final geometric model is shown in Fig. 2. The established geometric model needs to be meshed. Due to the regularity of computational regions, integrated structural grid generation can be carried out. At the same time, grid independence study should be considered during the CFD application in nuclear thermal hydraulic research, which has been regarded as the guideline (Wang et al., 2017; Wang et al., 2018). Because the mathematical model of local simulation is standard, the grid independent scheme can be obtained by calculating the grid models with different number of grids under simple single-phase and steady-state conditions. The relationship between the inlet and outlet pressure drop and the number of grids is shown in Fig. 3. It can be seen that when the number of grids is 640000, the grid scheme is the independent one. The final grid model is shown in Fig. 4. In order to ensure the accuracy of the calculation, it is necessary to make reasonable settings in the calculation. It mainly includes physical parameters, boundary conditions and so on. In this paper, it is necessary to set the physical parameters of water and steam under the operating conditions of steam generator. In the boundary conditions, the inlet is set as the velocity inlet and the outlet is set as the pressure outlet, and the velocity, temperature, void fraction and turbulence parameters are set according to the relevant data. In addition to the inlet and outlet, the pipe wall and the supporting plate are set as the wall, and the other surfaces are set as the symmetrical surface. In addition, the main consideration in this part is the velocity field. The primary and secondary side heat transfer has little effect on the local velocity, which can be ignored.
3.2. Results analysis Through accurate local geometric modeling and numerical calculation of the supporting plate and the adjacent tube bundle area,
ð5Þ
lt ¼ Cl qem k
2
ð6Þ
! ! ! T Gk ¼ lt r um r um þ r um
ð7Þ !
v m is the ! velocity of mixture; p is pressure, lm is the viscosity of mixture, g is ! gravitational acceleration, F is the body force of the mixture, ak is ! the volume fraction of the k phase, v dr;k is velocity of mixture flow weighted by relative mass of phase k; Ek is the enthalpy of the k phase, keff is the effective heat conductivity, T is temperature, SE is an additional energy source term; k is turbulent pulsating kinetic energy, rk is Prandtl number of pulsating kinetic energy, e is dissipation rate, C is empirical coefficient. where, q is density, and subscript m represents mixture;
3
Fig. 2. Supporting plate geometric model.
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calculated, as shown in Fig. 6. Cross-flow velocity and downstream velocity are defined as follows: Cross-flow velocity:
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
v crossflow ¼ v 2x þ v 2y
ð8Þ
Downstream velocity:
v downstream ¼ v z
Fig. 3. Grid independence study.
Fig. 4. Supporting plate grid model.
the distribution of thermal and hydraulic parameters of the flow field in this area is obtained. Because the main purpose of this study is to obtain the velocity field distribution, analyze the influence of the supporting plate structure on the local flow field, and use it to modify the overall calculation, the velocity field near the supporting plate structure is mainly selected for analysis, and the streamline is drawn as shown in Fig. 5. As can be seen from Fig. 5, when the fluid flows through the supporting plate area, there is an obvious cross-flow velocity and a significant increase in the downstream velocity, which can indicate the influence of the supporting plate structure on the local flow field. However, relative to the tube bundle area before and after the support plate, the change of velocity concentrates near the support plate structure, while the fluid velocity in the tube bundle area has no change in size and direction compared with the inlet velocity. In order to quantitatively describe the influence of supporting plate on velocity field, further processing and analysis of velocity distribution are needed. By calculating the average parameters of a section, the weighted average values of the required physical quantities (such as velocity, pressure, etc.) on a section can be obtained. In order to quantitatively analyze the influence area of the supporting plate on the local flow field in the axial part, the distribution curves of the cross-section average cross-flow velocity and the cross-section average parallel-flow velocity along the axial direction are
ð9Þ
where, v x and v y are a group of velocity components perpendicular to the heat transfer tube and perpendicular to each other; v z is the velocity component parallel to the heat transfer tube. As can be seen from Fig. 6, when the fluid flows in the tube bundle area in front of the supporting plate, the average cross-flow velocity of the cross-section is constant at 0, which indicates that there is no cross-flow of the fluid in the area. At the entrance section and exit section of the supporting plate, there is a peak value of cross-flow velocity, which is due to the influence of the supporting plate structure and the change of the flow area, resulting in the change of the direction of fluid flow in the supporting plate, so there will be a peak value of cross-flow velocity. In the tube bundle area downstream of the supporting plate, the cross-flow velocity is gradually stabilized to 0, which indicates that the flow of fluid is gradually stable after passing through the supporting plate, and the cross-flow gradually disappears. It can also be seen from the results that when the fluid flows in the tube bundle area in front of the supporting plate, the average downstream velocity of the cross section is constant, which is the initial inflow velocity. In the area of supporting plate, the peak value of downstream velocity occurs, which is due to the influence of supporting plate structure, the flow area decreases, and the downstream velocity inevitably increases. There is a minimum downstream velocity near the exit section of the supporting plate, which is caused by the local vortices when the fluid flows out of the supporting plate. In the downstream tube bundle area of the supporting plate, the downstream velocity gradually stabilizes and maintains the inflow velocity before the supporting plate. According to the above analysis, we can know that the influence of the supporting plate on the local flow field mainly concentrates near the supporting plate structure, but has little influence on the front and rear tube bundle area, which is also consistent with the conclusion obtained by the qualitative analysis of the streamline diagram. In order to determine the magnitude of the influence area more accurately, the criterion for determining whether the supporting plate has an effect on the local flow field is defined artificially. For cross-flow velocity, the cross-flow velocity at the front and back of the supporting plate is greater than 10% of the peak velocity at the front and back of the supporting plate, respectively, as the criteria for judging the influence of the supporting plate. For the downstream velocity, the difference between the downstream velocity and the incoming velocity is greater than 10% as the criterion for judging the influence of the supporting plate. Finally, the influence range of the supporting plate structure on the local flow field can be quantitatively obtained. In order to avoid the influence of flow conditions on the conclusion, the calculation of different inlet velocities and different void fractions was carried out, and the analysis was carried out. The influence range did not change significantly. Therefore, it can be considered that the influence range of the supporting plate structure on the local flow field is independent of the flow conditions under the premise of determining the geometrical structure. In order to apply the influence of supporting plate on local velocity to the correction of local velocity field in STAF program, it is necessary to determine the influence degree of supporting plate on velocity within the influence range. Considering that STAF program uses porous medium model to simplify the tube bundle
X. Wang et al. / Annals of Nuclear Energy 136 (2020) 107020
5
Fig. 5. Streamline distribution near the supporting plate.
Fig. 6. Distribution of the cross-flow/downstream velocity along the axial direction.
area, the grid size of the tube bundle area is relatively large compared with the thickness of the supporting plate. As the input condition of fouling deposition and flow vibration analysis, the two components of the cross flow velocity perpendicular to the heat transfer tube and the downstream velocity along the direction of the heat transfer tube are most needed. In this paper, the velocity components of cross-flow velocity and along-flow velocity are directly used to describe the velocity correction in the supporting plate area. For cross-flow velocity, the ratio of average velocity to inflow velocity is calculated as two correction factors in the grid before and after the support plate. For the downstream velocity, the ratio of the average velocity of the calculation range to the incoming velocity is used as the correction factor in the mesh before and after the supporting plate. In order to avoid the influence of flow conditions, multi-condition calculations with different flow velocities and different void fractions were carried out and analyzed. The data under different working conditions are shown in Table 1. As can be seen from the table, the correction factor obtained does not change significantly, which is also because the influence of the supporting plate structure on the local flow field is independent of the flow conditions. Based on the above analysis, the influence range and correction factors of the supporting plate on the local flow field are determined respectively, which can be used to modify the local velocity field of STAF program.
4. Analysis of local flow field in anti-vibration bars region 4.1. Three-dimensional CFD modeling Similar to the supporting plate, in the bend section of the steam generator tube bundle, a number of anti-vibration bars are inserted to restrict the tube bundle. In this paper, in order to obtain the effect of anti-vibration bars on local flow field, we need to select the bend area as the research object, establish the geometric model of the bend area without anti-vibration bars and with antivibration bars respectively, and carry out the corresponding meshing. The geometric model is shown in Fig. 7. In the direction perpendicular to the paper surface, it contains only one layer of fluid between two adjacent rows of heat transfer tubes. Correspondingly, only one anti-vibration bar in each group is in the calculation area (six groups, one in each group, so there are six in all.).
4.2. Results analysis Through precise local geometric modeling and numerical calculation of the bend area without and with anti-vibration bars, the distribution of thermal and hydraulic parameters under the two structures is obtained. In this paper, the influence of antivibration bar on velocity is analyzed and the velocity vector diagram is drawn.
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X. Wang et al. / Annals of Nuclear Energy 136 (2020) 107020
Table 1 Correction factors under different working conditions. Working condition
No. 1
Inlet velocity(m/s) Cross-flow velocity(m/s)* Cross-flow correction factor* Downstream velocity(m/s) Downstream correction factor
0.90 0.22 0.24 1.66 1.84
No. 2 0.08 0.09
2.70 0.68 0.25 4.97 1.84
No. 3 0.25 0.09
5.50 1.38 0.25 10.13 1.84
No. 4 0.50 0.09
8.80 2.21 0.25 16.20 1.84
No. 5 0.81 0.09
11.00 2.76 0.25 20.25 1.84
1.03 0.09
* Note: The cross-flow velocity has two peaks at the inlet and outlet of the supporting plate, respectively. Therefore, there are two values for cross-flow velocity and crossflow correction factor in each case.
Fig. 7. Bend area without/with anti-vibration bars geometric model.
In the bend area, the local area of a row of pipe bundles is selected as the research object. The velocity vector diagram of the area under two different structures is shown in Fig. 8. As can be seen from the results, the fluid velocity in this area does not fluctuate much without anti-vibration bar structure. Under the structure of anti-vibration strip, when the fluid flows through the antivibration strip, the cross-flow velocity is obvious, and the alongflow velocity is obviously increased. The comparison between them can show the influence of anti-vibration bar structure on local flow field. At the same time, the anti-vibration strip has a small influence
on the flow field, which is concentrated in the area near several groups of anti-vibration strips, which is the same as the effect of the supporting plate on the local flow field. Therefore, in order to quantitatively describe the influence of anti-vibration bar on flow field, the anti-vibration bar area is simplified, and the local area near a single anti-vibration bar in the bend area is selected for calculation, and the velocity distribution is analyzed. As shown in Fig. 9, a geometric model for calculating the local flow field of a single anti-vibration bar is presented. The influence of anti-vibration bar on local flow field can be quantitatively
Fig. 8. Velocity vector diagram of bend area without/with anti-vibration bars.
X. Wang et al. / Annals of Nuclear Energy 136 (2020) 107020
7
stabilizes after passing through the anti-vibration bar, and the cross-flow gradually disappears. In addition, when the fluid flows in the bundle area before and after the anti-vibration bar, the average cross-sectional downstream velocity is stable at the inflow velocity. In the anti-vibration strip region, the downstream velocity peaks. These results are similar to the effect of the supporting plate on the local flow field. According to the above analysis, we can know that the influence of anti-vibration bars on the local flow field are mainly concentrated in the vicinity of anti-vibration bars structure, but have little influence on the front and rear tube bundles. Similar to the analysis of supporting plate area, the criteria for determining the influence range of anti-vibration strip area are defined, and the influence range and correction factors are calculated for the correction of local velocity field. Fig. 9. Geometric model of local flow near a single anti-vibration bar.
analyzed by selecting this area for calculation. Similar to the supporting plate, the local velocity can also be decomposed into two components parallel to and vertical to the anti-vibration bar. Fig. 10 is a local velocity vector map of the region. It can be seen from the results that the velocity and direction of the fluid flow through the anti-vibration strip area have obvious changes. In the area of the tube bundle before and after the anti-vibration bar, the velocity of the fluid is the same as that of the incoming flow. The cross-flow and downflow velocities are defined to obtain the distribution of cross-section average cross-flow velocities and downflow velocities along the length of tube bundles, and the curves in Fig. 11 are obtained. It can be seen from the results that when the fluid flows in the area of the tube bundle in front of the anti-vibration bar, the average cross-flow velocity of the cross-section is constant at 0, which indicates that there is no cross-flow in the area. At the entrance and exit of the anti-vibration strip, the cross-flow velocity has a peak value, which is due to the influence of the anti-vibration strip structure and the change of the flow area, resulting in the change of the flow direction of the fluid at the position, so the peak value of the cross-flow velocity will occur. However, in the downstream bundle area of the anti-vibration bar, the cross-flow velocity gradually stabilizes to 0, which indicates that the flow of fluid gradually
5. Local velocity field correction According to the influence range and factors of local velocity in support plate area and anti-vibration strip area obtained above, the local velocity field can be corrected in STAF program. Specific operations are as follows: Firstly, according to the influence range and the mesh size of the calculation model, the partially affected mesh is judged and marked. Secondly, the initial speed in the affected grid is read. In the vicinity of the supporting plate, the initial velocity is along the direction of the tube bundle, which is the same as that of the downstream velocity. In the vicinity of the antivibration bar, the initial velocity is not vertical to the antivibration bar, so it needs to be decomposed into normal and tangential directions. Finally, the velocity correction factor is added to the velocity field. In the vicinity of the supporting plate, the cross-flow influencing factor multiplied by the initial velocity is the new cross-flow velocity, and the downstream influencing factor multiplied by the initial velocity is the new downstream velocity. In the vicinity of the anti-vibration bar, the initial normal velocity is multiplied by the cross-flow correction factor and the downstream correction factor respectively, and the velocity is synthesized with the initial tangential velocity to obtain the corrected velocity. In STAF program, the revised velocity is stored in user-defined variables, and the velocity field distribution before or after the revised output can be manually selected. In order to reflect the velocity difference between the original STAF program and the modified STAF program, a line along bundle direction is selected to extract the secondary side velocity and draw the curve. The velocity distribution along the axis before and after correction is shown in Fig. 12. It can be seen that the revised results can better show the influence of local components on local velocity in the supporting plate and anti-vibration strip area. 6. Conclusion
Fig. 10. Velocity vector diagram near a single anti-vibration bar.
Aiming at the local components of steam generator, a series of high fidelity CFD analysis in the supporting plate and antivibration strip area were performed respectively. The accurate local thermal-hydraulic parameter distributions were achieved and the local velocity field was analyzed. The quantitatively analyses of the influence range and degree of supporting plate and anti-vibration strip on local velocity distribution were obtained. The local effect indicated parameter, namely correction factors of cross-flow and along-flow velocity, was defined and obtained. Then the local effect correction factors were applied in the STAF program, which is a three dimensional steam generator thermal hydraulic code developed by NuTheL at Xi’an Jiaotong University. Compared with the code before improvement, the modified code
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Fig. 11. Distribution of the cross-flow/downstream velocity along the axial direction.
Fig. 12. Velocity difference between original program and modified program.
shows great advantages and it can reflect the influence of supporting plate and anti-vibration strip on local flow field obviously. The modified STAF code can be used to analyze steam generator more accurately, and provide input conditions for fouling deposition and flow-induced vibration analysis. Acknowledgment This research has been supported by National Natural Science Foundation of China (No. 11705139). Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.anucene.2019.107020. References Carver, M., Carlucci, L., Inch, W., 1981. Thermal-hydraulics in Recirculating Steam Generators. THIRST Code User’s Manual. Chalk River. Atomic Energy of Canada Ltd., Ontario, Canada. Cizelj, L., Dvorsek, T., Petelin, S., 1995. On the distribution of temperatures in steam generator tubes at tube support plate intersections. The 2nd Regional Meeting on Nuclear Energy in Central Europe, Sep 11-14, 1995. Nuclear Society of Slovenia, Portoroz, Slovenia, pp. 276–282.
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