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CFD analysis of flow field in a 5 × 5 rod bundle with multi-grid
Annals of Nuclear Energy xxx (2016) xxx–xxx
Contents lists available at ScienceDirect
Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
CFD analysis of flow field in a 5 5 rod bundle with multi-grid Songbai Cheng a, Huandong Chen b, Xiaoying Zhang a,⇑ a b
Sino-French Institute of Nuclear Engineering & Technology, Sun Yat-Sen University, Tang-Jia-Wan, Zhuhai 519-082, PR China School of Electric Power, South China University of Technology, Wushan, Guangzhou 510-640, PR China
a r t i c l e
i n f o
Article history: Received 22 March 2016 Received in revised form 19 September 2016 Accepted 30 September 2016 Available online xxxx Keywords: 5 5 rod bundle Multi-grid Flow field Heat transfer CFD analysis
a b s t r a c t In order to understand the characteristics of flow field in a fuel bundle with multi-grid, in this paper detailed CFD analyses were performed against a 5 5 rod bundle with two spacer grids and one mid span mixing grid. To represent the actual grid as accurately as possible, in our calculation the grids are described as a structure of stripe, dimple, spring, and mixing vane. Based on the calculated results, characteristics of flow field at different channels along the length of fuel assembly, flow information at important specific sites as well as the influence of mixing vane geometry (namely its deflection angle and vane length) are investigated and compared. It is shown that the upstream grid has no remarkable impact on the flow field formed at its downstream grids if the cross flow is sufficiently developed. Both the spacer grid and mid span mixing grid are verifiable to play an important role in changing the flow behavior and enhancing the heat transfer among the bundle channels. In addition to the mixing vane, the structure of dimple and spring is also observable to have some impact on the local flow field at the grids. The performed analyses in this work suggest that increasing the deflection angle and length of mixing vanes will lead to much strengthened mixing performance and enhance the local heat transfer, along with an appropriately increased pressure drop simultaneously. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Fuel assembly is one of the critical parts involved in reactor core, while the grids are important structures to fix the fuel rod bundle. In general, there are two types of grids that are widely used in Pressurized Water Reactors (PWRs), namely the pure supporting grid and the mixing vane grid. The pure supporting grid is shorter and does not have any mixing vanes while the mixing vane grid, which can be further divided into the spacer grid and mid span mixing grid, is comparatively longer and comprises a group of mixing vanes. Since the mixing vane is expectable to play an important role in enhancing the cross flow and heat transfer, motivated by providing useful evidence to improve the design of fuel assembly (esp. enhancing the grid mixing performance and local heat transfer among the bundle channels), during the past decades extensive studies were performed. Liu et al. (2012) tested the effect of several turbulent models on the convective heat transfer coefficient at the downstream of a 5 5 spacer grid and confirmed that the SST k–x model would be the best turbulence model for CFD simulations of fuel assembly.
⇑ Corresponding author. E-mail addresses: [email protected], [email protected] (X. Zhang).
Based on investigations on the impact of spacer grid on convective heat transfer, Holloway et al. (2008) proposed a general formula to estimate the convective heat transfer coefficient in the downstream of a grid. Navarro and Santos (2011) analyzed the axial flow rate and pressure drop in a downstream of 5 5 spacer grid using the CFX code. Ikeda et al. (2006) studied the cross and axial flow characteristics as well as the location of Departure Nucleate Boiling (DNB) in the downstream of a 5 5 spacer grid at high temperature and pressure conditions. Especially, during their calculations, aside from the mixing vane, the dimple was also simulated. Elvis and Hassan (2012) calculated the flow velocity in a downstream of one single spacer grid and compared their results with experimental data available; while Chang et al. (2008) studied the flow characteristics under different mixing-vane structures. In addition to the flow characteristics at the downstream of a single grid, studies on the flow behavior at the upstream of a grid can be also found. For example, by using the CFX code, Xiong et al. (2005), Tian et al. (2008) and Chen et al. (2009) investigated the characteristics of axial and cross flow velocities in both the upstream and downstream regions of different rod bundles (2 2 or 5 5) respectively. However, it should be pointed out that for all the literatures listed above, only a single grid is employed, which evidently should not be the fact encountered in reactor core conditions. In addition,
http://dx.doi.org/10.1016/j.anucene.2016.09.053 0306-4549/Ó 2016 Elsevier Ltd. All rights reserved.
Please cite this article in press as: Cheng, S., et al. CFD analysis of flow field in a 5 5 rod bundle with multi-grid. Ann. Nucl. Energy (2016), http://dx.doi. org/10.1016/j.anucene.2016.09.053
2
S. Cheng et al. / Annals of Nuclear Energy xxx (2016) xxx–xxx
the geometry of a real mixing vane grid is more complicated as compared to the geometries used in the above studies. For example, aside from the stripe and mixing vane, a spacer grid should contain parts of dimple and spring. Noting the potential importance of those parts on the flow field, Gandhir and Hassan (2011) and Conner et al. (2011) independently studied the flow characteristics of a 5 5 rod bundle (with one grid), in which a relatively complete structure of the grid including the spring and dimple was used. By using the Fluent code, Gao and Li (2013) even investigated the flow and heat-transfer characteristics in a 2 2 rod bundle with up to seven grids. Nevertheless, it should be emphasized again that the knowledge regarding the flow field in a complete grid structure, especially under a multi-grid condition, is still rather insufficient. In addition, information regarding the mixing performance at the cross section of such a condition is even scarce. Focusing on these aspects, in this work characteristics of the flow field (including both the axial and lateral directions) and heat-transfer in a 5 5 fuel assembly with 3 grids (two spacer grids and one mid span mixing grids) is studied by using the Fluent code. In addition to the mixing vane and stripe, a complete structure of the grid including the spring and dimple is modeled. In Section 2, after the determination of calculated geometry and model, the validity of such geometry and model is checked and compared with past experimental data reported with a single grid at cold conditions (Cheng et al., 2007; Wang et al., 2001). As for Section 3, detailed analyses and discussion of our target calculations at working conditions of PWRs are performed. Knowledge and evidence from this work will be utilized for improved core design of PWRs (esp. the fuel assembly) in China in the near future.
even consistent to that of the spacer grid. However, it should be pointed out that, compared to the spacer grid, the height of the mid span mixing grid is about 0.55 times shorter. As noted in Section 1, a 5 5 fuel rod bundle with two spacer grids and one mid span mixing grid (see Fig. 2) will be employed for analyses in this work. From Fig. 2, it can be clearly seen that the first and third ones are spacer grids, while the middle one is the mid span mixing grid. ICEM CFD 14.0 software is utilized to generate meshes. To achieve sufficient flow information for the followed analyses in Section 3, as shown in Fig. 3, a calculation domain (65 65 1120 mm in dimensions), ranging from the upstream of the first grid to the downstream of the third grid, is taken. Structured hexahedral meshes are used at the bundle channels away from the grids, while tetrahedral meshes are used at the grids where the geometry is quite complicated. To study the sensitivity of mesh size, four mesh sizes ranging from 0.5 mm to 4 mm have been tested. The detailed comparison of those mesh sizes on calculations are shown in Table 1. Considering the balance of result difference and solution time, a mesh size of 1 mm was set for CFD calculation in the following analyses. A non-slip boundary is set at the periphery area of the calculation domain as well as the surface of the fuel rods and 3 grids. At the exit of fuel assembly, a pressure balance boundary condition is assumed. As for the turbulence model, the SST k–x model, as suggested by previous investigators (Liu et al., 2012), is adopted. A high resolution scheme is used for the advection term. Also, the RMS model is chosen for evaluating the residual error with an error limit set to be 105.
2. Calculated geometry and model
As mentioned above, to check the validity of the determined geometry and model, in this part calculations with a single spacer grid under the cold condition (namely without any heat release from the fuel rod) is performed and compared with existing experimental data measured by Wang et al. (2001) and Cheng et al. (2007). In such a condition, the flow velocity (U) and temperature of coolant (water) at the entrance of the calculation domain are assumed to be 6.79 m/s and 298 K, respectively. Fig. 4 illustrates the cross section chosen for comparative analyses, while the detailed comparisons of the lateral and axial flow velocities at those sections are depicted in Figs. 5 and 6 respectively. It is easily observable that despite some slight deviation which is possibly due to the smoothness of some local structures (e.g. the dimple and spring) in our calculated geometry, a respectable agreement between the calculated results and experimental measurement provided by Wang et al. (2001) and Cheng et al.
2.1. Determination of calculated geometry and model Fig. 1 depicts the schematic view of a typical spacer grid. It is evident that the stripes are the base and frame of the grid. The mixing vanes, located on the top of a grid, are used to enhance the cross flow and heat transfer between neighboring channels. Typically, double vanes exist on the middle stripes, while single vane lies on the peripheral stripes. The dimple is an arc body located on the top and bottom of a stripe, while the springs are fixed along the interior of a stripe. Both of them are used to fix the fuel rod. The structure of the mid span mixing grid, as compared to the spacer grid, is quite similar, except the lack of spring. Moreover, the distribution and orientation of the mixing vane are
2.2. Verification of determined geometry and model
dimple Stripe
dimple
Fig. 1. Schematic view of a typical spacer grid.
Fig. 2. Schematic view of the 5 5 fuel assembly.
Please cite this article in press as: Cheng, S., et al. CFD analysis of flow field in a 5 5 rod bundle with multi-grid. Ann. Nucl. Energy (2016), http://dx.doi. org/10.1016/j.anucene.2016.09.053
S. Cheng et al. / Annals of Nuclear Energy xxx (2016) xxx–xxx
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Fig. 3. Calculated geometry and meshes.
Table 1 Sensitivity analysis of mesh size. Maximum mesh size (mm)
Mesh number
Du * u0:5
Dw * w0:5
Solution time (min)
0.5 1 2 4
11283877 8086472 7208496 6702348
0 3.18% 4.94% 7.15%
0 2.55% 4.83% 6.92%
350 264 236 178
*
Du and Dw are the maximum difference of axial and lateral velocities respectively (as compared to a mesh size of 0.5 mm), while u0:5 and w0:5 are the axial and lateral velocities at a mesh size of 0.5 mm.
Fig. 4. Cross-section used for comparative analysis.
(2007) can be achieved, as a result to some degree enhancing our confidence for future target investigations in Section 3.
3. Result of analyses As aforementioned, in order to understand the characteristics of flow field in a 5 5 fuel assembly with three grids, in this section some target calculations under typical PWR working conditions will be performed. The calculated pressure is 15.5 MPa, while the temperature and flow velocity of coolant at the entrance are assigned to be 573 K and 1 m/s, respectively. A non-uniform distribution of heat power at the radial section, as shown in Fig. 7, is
assumed. As for the axial direction, a cosine distribution, with its half-length being the peak heat power, is given at each fuel rod. To facilitate the following analyses, four channels named center, middle, side and corner ones (see Fig. 7), are defined. 3.1. Flow characteristics at different channels Fig. 8 shows the change of pressure drop at different channels along the fuel-rod length, in which the location of the three grids is marked with dotted lines. We can confirm that the pressure values at the four channels are almost overlapped. There is a sharp pressure drop at the three grids, as compared to the regions which are away from grids. In addition, it is seen that when the flow is about to leave a grid, a small pressure rise is observable, which we believe should be caused by the increase of flow area and loss of kinetic energy. Fig. 9 shows the change of fluid temperature at different channels along the fuel-rod length. It can be seen that, whatever the channels are, due to the heating from the fuel rod, the fluid temperature tends to be generally increasing along the axial direction. In addition, it is confirmable that the temperature is decreasing from the center to the corner, which obviously should be due to the non-uniform power distribution at the cross section as depicted in Fig. 7. Also, a slight decrease at each grid is observable. The potential reasons we believe should be resulted from the deteriorated heat-transfer caused by potential block of flow at the grids, the dispersion of flow at the grid border as well as the heat absorption by the grids. By making further comparisons between different grids, it is evident that the temperature increase at the first grid, as compared to others, is rather lower, which obviously should be caused by the cosine distribution of power along the axial direction. Fig. 10 shows the change of cross velocity at the four channels along the fuel-rod length. It is easily seen that an evident cross flow is observable at the three grids. In addition, it is evident that the cross velocity tends to be decreasing when the flow is leaving the grids. Also, we can confirm that the cross velocity is decreasing from the center channel to the corner. By making comparisons between different grids, it is further observable that the cross flow at the first grid seems to be comparatively mild. Although more elaborate investigations might be preferable, we believe the rather limited inflow in the lateral direction at the first grid should be the primary reason. This point is supportable as well by the less difference of cross velocities between the second and third grids since after the first grid the cross flow might be already developed to some degree. The above analyses suggest that the upstream grid would have no remarkable impact on the flow field formed at its downstream grids if the cross flow has been sufficiently developed.
Please cite this article in press as: Cheng, S., et al. CFD analysis of flow field in a 5 5 rod bundle with multi-grid. Ann. Nucl. Energy (2016), http://dx.doi. org/10.1016/j.anucene.2016.09.053
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Fig. 5. Dimensionless lateral flow velocity (u/U) in verification test.
Fig. 6. Dimensionless axial flow velocity (w/U) in verification test.
3500
center channel middle channel side channel corner channel
3000 2500
P(Pa)
2000 1500 1000 500 0 -0.4
Fig. 7. Radial heat power distribution of the 5 5 fuel assembly.
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
z(m) Fig. 8. Change of pressure drop at four channels.
Fig. 11 shows the change of axial flow velocity at different channels along the fuel-rod length. One can find that whatever the flow channels and grids are, due to the variation of flow area caused by the grid, the axial velocity tends to be rising rapidly when the flow enters the grid and decrease soon as the flow is going to leave the grid. Similarly, the axial velocity is confirmable to be decreasing from the center channel to the corner ones. By making comparisons with Fig. 10, a similar profile between different grids seems to be observable, which actually should not be surprising since the lateral and axial velocities are counter connected. 3.2. Flow characteristics at specific sites The streamlines at the exit of the first spacer grid and the mid span mixing grid are depicted in Figs. 12 and 13, respectively. It
is seen that at the exit of the spacer grid, due to the cross flow formed between the neighboring channels, relatively larger complete vortexes, with their major axis being consistent to the stretching direction of the mixing vane, are generally observable. In addition, we can further find that, because of the dimple and spring, several smaller vortexes tend to appear near the larger vortex. As for the mid span mixing grid, due to a similar structure of the mixing vane as mentioned above, no much difference of the streamline distribution at its exit can be observed (Fig. 13). However, as compared to the spacer grid, we can find that the main vortex at the exit of the mid-span-mixing grid seems to be a bit oblate, which evidently should be due to the much shortened grid height and vane length. Another point observable is that, the small vortex
Please cite this article in press as: Cheng, S., et al. CFD analysis of flow field in a 5 5 rod bundle with multi-grid. Ann. Nucl. Energy (2016), http://dx.doi. org/10.1016/j.anucene.2016.09.053
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5
620
610
T(K)
600
590
center channel middle channel side channel corner channel
580
570 -0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
Fig. 12. Streamline at the exit of spacer grid.
z(m) Fig. 9. Change of fluid temperature at four channels.
Fig. 13. Streamline at the exit of mid span mixing grid.
Fig. 10. Change of cross velocity at the four channels.
Fig. 11. Change of axial velocity at the four channels.
in Fig. 13 seems to be more difficult to be formed, as compared to Fig. 12, which again should be caused by the less local structures (e.g. spring) in the mid span mixing grid. To fully investigate the turbulence characteristics of the spacer grid, the contour map of cross and axial velocities at its 1/4 exit section is depicted in Fig. 14. One can see that a symmetrical characteristics of cross velocity tends to appear near the dual mixing vanes (namely areas a and b). The direction of the cross velocity
is orthogonal to the stretching direction of the mixing vane, which might be due to the fact that the dual mixing vanes tend to form a positive pressure zone along its vane-stretching direction and form a negative pressure zone at the orthogonal direction, as a result forcing the cross flow to move orthogonally. Also, from Fig. 14, we can observe an obvious cross flow near the single mixing vane (see area c). However, it should be mentioned that the magnitude of the cross flow velocity near the single mixing vane is much smaller than that near the dual mixing vanes. Further, from Fig. 14 we can confirm that the values of the axial velocity near the mixing vanes are closely dependent on the lateral velocity, i.e. higher cross velocity leads to smaller axial velocity, and vice versa. Fig. 15 shows the vector graph of flow velocity near different local structures including the double spring, single spring and dimple. One can find that both the double and single springs tend to prevent continuous cross-flow between neighboring channels. The cross flow at the two sides of double springs seems to be symmetrical, while at a condition of single spring no symmetrical distribution can be observed. As for the dimple, a noticeable impact on the cross flow is observable. The dimple tends to make the cross flow symmetrical along the diagonal of one channel in area I, and leave away from the convex to the stripe perpendicularly in area II. 3.3. Influence of mixing vane geometry on mixing performance In order to investigate the mixing performance of mixing vane geometry, here some calculations with four deflection angles and five vane lengths are performed. The four deflection angles are u = 25°, 31°, 37° and 43°, and the five lengths of mixing vane are L = 0.8L0, 0.9L0, L0, 1.1L0 and 1.2L0, where u = 25° and L0 are typical
Please cite this article in press as: Cheng, S., et al. CFD analysis of flow field in a 5 5 rod bundle with multi-grid. Ann. Nucl. Energy (2016), http://dx.doi. org/10.1016/j.anucene.2016.09.053
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a b
c
(a) Cross velocity
(b) Axial velocity Fig. 14. Flow velocity at the exit of spacer grid.
spring I II
spring
double spring
single spring
dimple
Fig. 15. Velocity vector near three typical local structures.
design parameters of mixing vanes in PWR fuel assembly. In order to quantitatively judge the mixing performance, a mixing coefficient b is defined as following (Cheng et al., 2007):
b¼
j ju ¼ C 0:2 Re0:12 W
is the average lateral velocity at each cross section, W is the where u entrance velocity (namely 1.0 m/s), and C and Re are constant and the Reynolds number respectively. Fig. 16 shows the mixing coefficient along the length of fuel assembly with different deflection angles. It is evident that the mixing coefficient tends to increase significantly at the three grids, and bigger deflection angles will result in larger b values. The total pressure drop along the whole length of fuel assembly with different deflection angles is illustrated in Fig. 17. It is seen that the pressure drop increases slightly with the increasing of deflection angles. The maximum difference of pressure drop is about 10% when the deflection angle changes from 25° to 43°. Figs. 18 and 19 depict the mixing coefficient and pressure drop along the length of fuel assembly with different vane lengths. Again, it is clear that the mixing coefficient seems to be increasing when the vane length increases. As for the pressure drop, we can find that when the vane length is less than L0, the pressure drop seems to have no significant difference; however, when the vane length changes to 1.1 L0 or 1.2 L0, an observable difference can be found. Based on the above parametric analyses, it can be summarized that increasing the deflection angle and vane length will lead to
Fig. 16. Mixing coefficient with different deflection angles.
enhanced mixing performance and local heat transfer. However, on the other hand, the flow resistance or pressure drop will be increased simultaneously. Therefore, for a specific application, more detailed analyses might be necessary in order to determine the most appropriate vane geometry.
Please cite this article in press as: Cheng, S., et al. CFD analysis of flow field in a 5 5 rod bundle with multi-grid. Ann. Nucl. Energy (2016), http://dx.doi. org/10.1016/j.anucene.2016.09.053
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Fig. 17. Pressure drop with different deflection angles.
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performed against a 5 5 rod bundle with two spacer grids and one mid span mixing grid. Compared to previous investigators, a much complete structure of the mixing grid including the stripe, mixing vane, dimple and spring was simulated in a multi-grid condition. Especially, sufficient attention was paid on the cross flow. From the detailed analyses performed, we found that both the spacer grid and mid span mixing grid are confirmable to play an important role in changing the flow behavior and enhancing the heat transfer along the fuel-rod length. The upstream grid has no remarkable impact on the flow field formed at its downstream grids if the cross flow is developed sufficiently. The distribution of fluid temperate is consistent with the axial and lateral power distributions imposed. In addition to the mixing vane, the local structure of dimple and spring is also observable to have an evident impact on the cross flow formed at the grids. Compared to the upstream spacer grid, possibly due to a much shortened grid height, the main vortex at the mid-span-mixing grid seems to be more oblate, while for the local small vortex, it tends to be less easy to be formed at the mid-span mixing grid due to the insufficiency of local structures (e.g. spring). The performed analyses regarding the geometry of the mixing vane suggest that increasing the deflection angle and stretching length of the vane will lead to much strengthened mixing performance and local heat transfer, along with appropriate increase of pressure drop simultaneously, as a result suggesting that a suitable mixing-vane geometry (e.g. neither too long nor too short in vane length) should be determined for a specific situation. Acknowledgements This work was supported by several research projects in China including the National Natural Science Foundation of China (Nos. 51376065, 51176052), Guangdong Key Scientific Project (No. 2013B010405004) and the Fundamental Research Funds for the Central Universities (No. 15lgjc29). References
Fig. 18. Mixing coefficient with different vane lengths.
Fig. 19. Pressure drop with different vane lengths.
4. Concluding remarks Motivated to provide useful information for improved design of fuel assembly of PWRs in China, in this work CFD analyses were
Chang, S.K., Moon, S.K., Baek, W.P., Choi, Y.D., 2008. Phenomenological investigations on the turbulent flow structures in a rod bundle array with mixing devices. Nucl. Eng. Des. 23 (8), 600–609. Chen, W.H., Zhang, H., Zhu, L., Xiong, W.Y., 2009. Research on application of CFD method in thermal-hydraulic performance analysis of rod bundle grid. Nucl. Power Eng. 30 (5), 34–38 (in Chinese). Cheng, X., Kuang, B., Yang, Y.H., 2007. Numerical analysis of heat transfer in supercritical water cooled flow channels. Nucl. Eng. Des. 23 (7), 240–252. Conner, Michael E., Baglietto, E., Elmahdi, Abdelaziz M., 2011. CFD methodology and validation for single-phase flow in PWR fuel assemblies. Nucl. Eng. Des. 24 (9), 2088–2095. Elvis, E.D., Hassan, Y.A., 2012. Experimental benchmark data for PWR rod bundle with spacer-grids. Nucl. Eng. Des. 25 (3), 396–405. Gandhir, A., Hassan, Y., 2011. RANS modeling for flow in nuclear fuel bundle in pressurized water reactors. Nucl. Eng. Des. 24 (1), 4404–4408. Gao, Y., Li, X., 2013. Numerical simulation of single-phase flow in a PWR foursubchannel model with overall length. J. Harbin Eng. Univ. 34 (3), 1–6 (in Chinese). Holloway, M., Beasley, D.E., Conner, M.E., 2008. Single-phase convective heat transfer in rod bundles. Nucl. Eng. Des. 238, 848–858. Ikeda, K., Makino, Y., Hoshi, M., 2006. Single-phase CFD applicability for estimating fluid hot-spot locations in a 5 5 fuel rod bundle. Nucl. Eng. Des. 236 (11), 1149–1154. Liu, C.C., Ferng, Y.M., Shih, C.K., 2012. CFD evaluation of turbulence models for flow simulation of the fuel rod bundle with a spacer assembly. Appl. Therm. Eng. 40, 389–396. Navarro, M.A., Santos, A.A.C., 2011. Evaluation of a numeric procedure for flow simulation of a 5 5 PWR rod bundle with a mixing vane spacer. Prog. Nucl. Energy 53 (8), 1190–1196. Tian, R.F., Mao, X.H., Wang, X.J., 2008. Study on 3-D flow field in 5 5 rod bundles with spacer grids. Nucl. Power Eng. 29 (5), 48–51 (in Chinese). Wang, K.I., Dong, S.O., Tae, H.C., 2001. Flow analysis for optimum design of mixing vane in a PWR fuel assembly. J. Korean Nucl. Soc. 33 (3), 327–338. Xiong, W.Y., Chen, B.D., Xiao, Z.J., 2005. 3-D flow field of rod bundles with spacer grids. At. Energy Sci. Technol. 39 (4), 326–329 (in Chinese).
Please cite this article in press as: Cheng, S., et al. CFD analysis of flow field in a 5 5 rod bundle with multi-grid. Ann. Nucl. Energy (2016), http://dx.doi. org/10.1016/j.anucene.2016.09.053
Contents lists available at ScienceDirect
Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
CFD analysis of flow field in a 5 5 rod bundle with multi-grid Songbai Cheng a, Huandong Chen b, Xiaoying Zhang a,⇑ a b
Sino-French Institute of Nuclear Engineering & Technology, Sun Yat-Sen University, Tang-Jia-Wan, Zhuhai 519-082, PR China School of Electric Power, South China University of Technology, Wushan, Guangzhou 510-640, PR China
a r t i c l e
i n f o
Article history: Received 22 March 2016 Received in revised form 19 September 2016 Accepted 30 September 2016 Available online xxxx Keywords: 5 5 rod bundle Multi-grid Flow field Heat transfer CFD analysis
a b s t r a c t In order to understand the characteristics of flow field in a fuel bundle with multi-grid, in this paper detailed CFD analyses were performed against a 5 5 rod bundle with two spacer grids and one mid span mixing grid. To represent the actual grid as accurately as possible, in our calculation the grids are described as a structure of stripe, dimple, spring, and mixing vane. Based on the calculated results, characteristics of flow field at different channels along the length of fuel assembly, flow information at important specific sites as well as the influence of mixing vane geometry (namely its deflection angle and vane length) are investigated and compared. It is shown that the upstream grid has no remarkable impact on the flow field formed at its downstream grids if the cross flow is sufficiently developed. Both the spacer grid and mid span mixing grid are verifiable to play an important role in changing the flow behavior and enhancing the heat transfer among the bundle channels. In addition to the mixing vane, the structure of dimple and spring is also observable to have some impact on the local flow field at the grids. The performed analyses in this work suggest that increasing the deflection angle and length of mixing vanes will lead to much strengthened mixing performance and enhance the local heat transfer, along with an appropriately increased pressure drop simultaneously. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Fuel assembly is one of the critical parts involved in reactor core, while the grids are important structures to fix the fuel rod bundle. In general, there are two types of grids that are widely used in Pressurized Water Reactors (PWRs), namely the pure supporting grid and the mixing vane grid. The pure supporting grid is shorter and does not have any mixing vanes while the mixing vane grid, which can be further divided into the spacer grid and mid span mixing grid, is comparatively longer and comprises a group of mixing vanes. Since the mixing vane is expectable to play an important role in enhancing the cross flow and heat transfer, motivated by providing useful evidence to improve the design of fuel assembly (esp. enhancing the grid mixing performance and local heat transfer among the bundle channels), during the past decades extensive studies were performed. Liu et al. (2012) tested the effect of several turbulent models on the convective heat transfer coefficient at the downstream of a 5 5 spacer grid and confirmed that the SST k–x model would be the best turbulence model for CFD simulations of fuel assembly.
⇑ Corresponding author. E-mail addresses: [email protected], [email protected] (X. Zhang).
Based on investigations on the impact of spacer grid on convective heat transfer, Holloway et al. (2008) proposed a general formula to estimate the convective heat transfer coefficient in the downstream of a grid. Navarro and Santos (2011) analyzed the axial flow rate and pressure drop in a downstream of 5 5 spacer grid using the CFX code. Ikeda et al. (2006) studied the cross and axial flow characteristics as well as the location of Departure Nucleate Boiling (DNB) in the downstream of a 5 5 spacer grid at high temperature and pressure conditions. Especially, during their calculations, aside from the mixing vane, the dimple was also simulated. Elvis and Hassan (2012) calculated the flow velocity in a downstream of one single spacer grid and compared their results with experimental data available; while Chang et al. (2008) studied the flow characteristics under different mixing-vane structures. In addition to the flow characteristics at the downstream of a single grid, studies on the flow behavior at the upstream of a grid can be also found. For example, by using the CFX code, Xiong et al. (2005), Tian et al. (2008) and Chen et al. (2009) investigated the characteristics of axial and cross flow velocities in both the upstream and downstream regions of different rod bundles (2 2 or 5 5) respectively. However, it should be pointed out that for all the literatures listed above, only a single grid is employed, which evidently should not be the fact encountered in reactor core conditions. In addition,
http://dx.doi.org/10.1016/j.anucene.2016.09.053 0306-4549/Ó 2016 Elsevier Ltd. All rights reserved.
Please cite this article in press as: Cheng, S., et al. CFD analysis of flow field in a 5 5 rod bundle with multi-grid. Ann. Nucl. Energy (2016), http://dx.doi. org/10.1016/j.anucene.2016.09.053
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S. Cheng et al. / Annals of Nuclear Energy xxx (2016) xxx–xxx
the geometry of a real mixing vane grid is more complicated as compared to the geometries used in the above studies. For example, aside from the stripe and mixing vane, a spacer grid should contain parts of dimple and spring. Noting the potential importance of those parts on the flow field, Gandhir and Hassan (2011) and Conner et al. (2011) independently studied the flow characteristics of a 5 5 rod bundle (with one grid), in which a relatively complete structure of the grid including the spring and dimple was used. By using the Fluent code, Gao and Li (2013) even investigated the flow and heat-transfer characteristics in a 2 2 rod bundle with up to seven grids. Nevertheless, it should be emphasized again that the knowledge regarding the flow field in a complete grid structure, especially under a multi-grid condition, is still rather insufficient. In addition, information regarding the mixing performance at the cross section of such a condition is even scarce. Focusing on these aspects, in this work characteristics of the flow field (including both the axial and lateral directions) and heat-transfer in a 5 5 fuel assembly with 3 grids (two spacer grids and one mid span mixing grids) is studied by using the Fluent code. In addition to the mixing vane and stripe, a complete structure of the grid including the spring and dimple is modeled. In Section 2, after the determination of calculated geometry and model, the validity of such geometry and model is checked and compared with past experimental data reported with a single grid at cold conditions (Cheng et al., 2007; Wang et al., 2001). As for Section 3, detailed analyses and discussion of our target calculations at working conditions of PWRs are performed. Knowledge and evidence from this work will be utilized for improved core design of PWRs (esp. the fuel assembly) in China in the near future.
even consistent to that of the spacer grid. However, it should be pointed out that, compared to the spacer grid, the height of the mid span mixing grid is about 0.55 times shorter. As noted in Section 1, a 5 5 fuel rod bundle with two spacer grids and one mid span mixing grid (see Fig. 2) will be employed for analyses in this work. From Fig. 2, it can be clearly seen that the first and third ones are spacer grids, while the middle one is the mid span mixing grid. ICEM CFD 14.0 software is utilized to generate meshes. To achieve sufficient flow information for the followed analyses in Section 3, as shown in Fig. 3, a calculation domain (65 65 1120 mm in dimensions), ranging from the upstream of the first grid to the downstream of the third grid, is taken. Structured hexahedral meshes are used at the bundle channels away from the grids, while tetrahedral meshes are used at the grids where the geometry is quite complicated. To study the sensitivity of mesh size, four mesh sizes ranging from 0.5 mm to 4 mm have been tested. The detailed comparison of those mesh sizes on calculations are shown in Table 1. Considering the balance of result difference and solution time, a mesh size of 1 mm was set for CFD calculation in the following analyses. A non-slip boundary is set at the periphery area of the calculation domain as well as the surface of the fuel rods and 3 grids. At the exit of fuel assembly, a pressure balance boundary condition is assumed. As for the turbulence model, the SST k–x model, as suggested by previous investigators (Liu et al., 2012), is adopted. A high resolution scheme is used for the advection term. Also, the RMS model is chosen for evaluating the residual error with an error limit set to be 105.
2. Calculated geometry and model
As mentioned above, to check the validity of the determined geometry and model, in this part calculations with a single spacer grid under the cold condition (namely without any heat release from the fuel rod) is performed and compared with existing experimental data measured by Wang et al. (2001) and Cheng et al. (2007). In such a condition, the flow velocity (U) and temperature of coolant (water) at the entrance of the calculation domain are assumed to be 6.79 m/s and 298 K, respectively. Fig. 4 illustrates the cross section chosen for comparative analyses, while the detailed comparisons of the lateral and axial flow velocities at those sections are depicted in Figs. 5 and 6 respectively. It is easily observable that despite some slight deviation which is possibly due to the smoothness of some local structures (e.g. the dimple and spring) in our calculated geometry, a respectable agreement between the calculated results and experimental measurement provided by Wang et al. (2001) and Cheng et al.
2.1. Determination of calculated geometry and model Fig. 1 depicts the schematic view of a typical spacer grid. It is evident that the stripes are the base and frame of the grid. The mixing vanes, located on the top of a grid, are used to enhance the cross flow and heat transfer between neighboring channels. Typically, double vanes exist on the middle stripes, while single vane lies on the peripheral stripes. The dimple is an arc body located on the top and bottom of a stripe, while the springs are fixed along the interior of a stripe. Both of them are used to fix the fuel rod. The structure of the mid span mixing grid, as compared to the spacer grid, is quite similar, except the lack of spring. Moreover, the distribution and orientation of the mixing vane are
2.2. Verification of determined geometry and model
dimple Stripe
dimple
Fig. 1. Schematic view of a typical spacer grid.
Fig. 2. Schematic view of the 5 5 fuel assembly.
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Fig. 3. Calculated geometry and meshes.
Table 1 Sensitivity analysis of mesh size. Maximum mesh size (mm)
Mesh number
Du * u0:5
Dw * w0:5
Solution time (min)
0.5 1 2 4
11283877 8086472 7208496 6702348
0 3.18% 4.94% 7.15%
0 2.55% 4.83% 6.92%
350 264 236 178
*
Du and Dw are the maximum difference of axial and lateral velocities respectively (as compared to a mesh size of 0.5 mm), while u0:5 and w0:5 are the axial and lateral velocities at a mesh size of 0.5 mm.
Fig. 4. Cross-section used for comparative analysis.
(2007) can be achieved, as a result to some degree enhancing our confidence for future target investigations in Section 3.
3. Result of analyses As aforementioned, in order to understand the characteristics of flow field in a 5 5 fuel assembly with three grids, in this section some target calculations under typical PWR working conditions will be performed. The calculated pressure is 15.5 MPa, while the temperature and flow velocity of coolant at the entrance are assigned to be 573 K and 1 m/s, respectively. A non-uniform distribution of heat power at the radial section, as shown in Fig. 7, is
assumed. As for the axial direction, a cosine distribution, with its half-length being the peak heat power, is given at each fuel rod. To facilitate the following analyses, four channels named center, middle, side and corner ones (see Fig. 7), are defined. 3.1. Flow characteristics at different channels Fig. 8 shows the change of pressure drop at different channels along the fuel-rod length, in which the location of the three grids is marked with dotted lines. We can confirm that the pressure values at the four channels are almost overlapped. There is a sharp pressure drop at the three grids, as compared to the regions which are away from grids. In addition, it is seen that when the flow is about to leave a grid, a small pressure rise is observable, which we believe should be caused by the increase of flow area and loss of kinetic energy. Fig. 9 shows the change of fluid temperature at different channels along the fuel-rod length. It can be seen that, whatever the channels are, due to the heating from the fuel rod, the fluid temperature tends to be generally increasing along the axial direction. In addition, it is confirmable that the temperature is decreasing from the center to the corner, which obviously should be due to the non-uniform power distribution at the cross section as depicted in Fig. 7. Also, a slight decrease at each grid is observable. The potential reasons we believe should be resulted from the deteriorated heat-transfer caused by potential block of flow at the grids, the dispersion of flow at the grid border as well as the heat absorption by the grids. By making further comparisons between different grids, it is evident that the temperature increase at the first grid, as compared to others, is rather lower, which obviously should be caused by the cosine distribution of power along the axial direction. Fig. 10 shows the change of cross velocity at the four channels along the fuel-rod length. It is easily seen that an evident cross flow is observable at the three grids. In addition, it is evident that the cross velocity tends to be decreasing when the flow is leaving the grids. Also, we can confirm that the cross velocity is decreasing from the center channel to the corner. By making comparisons between different grids, it is further observable that the cross flow at the first grid seems to be comparatively mild. Although more elaborate investigations might be preferable, we believe the rather limited inflow in the lateral direction at the first grid should be the primary reason. This point is supportable as well by the less difference of cross velocities between the second and third grids since after the first grid the cross flow might be already developed to some degree. The above analyses suggest that the upstream grid would have no remarkable impact on the flow field formed at its downstream grids if the cross flow has been sufficiently developed.
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Fig. 5. Dimensionless lateral flow velocity (u/U) in verification test.
Fig. 6. Dimensionless axial flow velocity (w/U) in verification test.
3500
center channel middle channel side channel corner channel
3000 2500
P(Pa)
2000 1500 1000 500 0 -0.4
Fig. 7. Radial heat power distribution of the 5 5 fuel assembly.
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
z(m) Fig. 8. Change of pressure drop at four channels.
Fig. 11 shows the change of axial flow velocity at different channels along the fuel-rod length. One can find that whatever the flow channels and grids are, due to the variation of flow area caused by the grid, the axial velocity tends to be rising rapidly when the flow enters the grid and decrease soon as the flow is going to leave the grid. Similarly, the axial velocity is confirmable to be decreasing from the center channel to the corner ones. By making comparisons with Fig. 10, a similar profile between different grids seems to be observable, which actually should not be surprising since the lateral and axial velocities are counter connected. 3.2. Flow characteristics at specific sites The streamlines at the exit of the first spacer grid and the mid span mixing grid are depicted in Figs. 12 and 13, respectively. It
is seen that at the exit of the spacer grid, due to the cross flow formed between the neighboring channels, relatively larger complete vortexes, with their major axis being consistent to the stretching direction of the mixing vane, are generally observable. In addition, we can further find that, because of the dimple and spring, several smaller vortexes tend to appear near the larger vortex. As for the mid span mixing grid, due to a similar structure of the mixing vane as mentioned above, no much difference of the streamline distribution at its exit can be observed (Fig. 13). However, as compared to the spacer grid, we can find that the main vortex at the exit of the mid-span-mixing grid seems to be a bit oblate, which evidently should be due to the much shortened grid height and vane length. Another point observable is that, the small vortex
Please cite this article in press as: Cheng, S., et al. CFD analysis of flow field in a 5 5 rod bundle with multi-grid. Ann. Nucl. Energy (2016), http://dx.doi. org/10.1016/j.anucene.2016.09.053
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5
620
610
T(K)
600
590
center channel middle channel side channel corner channel
580
570 -0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
Fig. 12. Streamline at the exit of spacer grid.
z(m) Fig. 9. Change of fluid temperature at four channels.
Fig. 13. Streamline at the exit of mid span mixing grid.
Fig. 10. Change of cross velocity at the four channels.
Fig. 11. Change of axial velocity at the four channels.
in Fig. 13 seems to be more difficult to be formed, as compared to Fig. 12, which again should be caused by the less local structures (e.g. spring) in the mid span mixing grid. To fully investigate the turbulence characteristics of the spacer grid, the contour map of cross and axial velocities at its 1/4 exit section is depicted in Fig. 14. One can see that a symmetrical characteristics of cross velocity tends to appear near the dual mixing vanes (namely areas a and b). The direction of the cross velocity
is orthogonal to the stretching direction of the mixing vane, which might be due to the fact that the dual mixing vanes tend to form a positive pressure zone along its vane-stretching direction and form a negative pressure zone at the orthogonal direction, as a result forcing the cross flow to move orthogonally. Also, from Fig. 14, we can observe an obvious cross flow near the single mixing vane (see area c). However, it should be mentioned that the magnitude of the cross flow velocity near the single mixing vane is much smaller than that near the dual mixing vanes. Further, from Fig. 14 we can confirm that the values of the axial velocity near the mixing vanes are closely dependent on the lateral velocity, i.e. higher cross velocity leads to smaller axial velocity, and vice versa. Fig. 15 shows the vector graph of flow velocity near different local structures including the double spring, single spring and dimple. One can find that both the double and single springs tend to prevent continuous cross-flow between neighboring channels. The cross flow at the two sides of double springs seems to be symmetrical, while at a condition of single spring no symmetrical distribution can be observed. As for the dimple, a noticeable impact on the cross flow is observable. The dimple tends to make the cross flow symmetrical along the diagonal of one channel in area I, and leave away from the convex to the stripe perpendicularly in area II. 3.3. Influence of mixing vane geometry on mixing performance In order to investigate the mixing performance of mixing vane geometry, here some calculations with four deflection angles and five vane lengths are performed. The four deflection angles are u = 25°, 31°, 37° and 43°, and the five lengths of mixing vane are L = 0.8L0, 0.9L0, L0, 1.1L0 and 1.2L0, where u = 25° and L0 are typical
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a b
c
(a) Cross velocity
(b) Axial velocity Fig. 14. Flow velocity at the exit of spacer grid.
spring I II
spring
double spring
single spring
dimple
Fig. 15. Velocity vector near three typical local structures.
design parameters of mixing vanes in PWR fuel assembly. In order to quantitatively judge the mixing performance, a mixing coefficient b is defined as following (Cheng et al., 2007):
b¼
j ju ¼ C 0:2 Re0:12 W
is the average lateral velocity at each cross section, W is the where u entrance velocity (namely 1.0 m/s), and C and Re are constant and the Reynolds number respectively. Fig. 16 shows the mixing coefficient along the length of fuel assembly with different deflection angles. It is evident that the mixing coefficient tends to increase significantly at the three grids, and bigger deflection angles will result in larger b values. The total pressure drop along the whole length of fuel assembly with different deflection angles is illustrated in Fig. 17. It is seen that the pressure drop increases slightly with the increasing of deflection angles. The maximum difference of pressure drop is about 10% when the deflection angle changes from 25° to 43°. Figs. 18 and 19 depict the mixing coefficient and pressure drop along the length of fuel assembly with different vane lengths. Again, it is clear that the mixing coefficient seems to be increasing when the vane length increases. As for the pressure drop, we can find that when the vane length is less than L0, the pressure drop seems to have no significant difference; however, when the vane length changes to 1.1 L0 or 1.2 L0, an observable difference can be found. Based on the above parametric analyses, it can be summarized that increasing the deflection angle and vane length will lead to
Fig. 16. Mixing coefficient with different deflection angles.
enhanced mixing performance and local heat transfer. However, on the other hand, the flow resistance or pressure drop will be increased simultaneously. Therefore, for a specific application, more detailed analyses might be necessary in order to determine the most appropriate vane geometry.
Please cite this article in press as: Cheng, S., et al. CFD analysis of flow field in a 5 5 rod bundle with multi-grid. Ann. Nucl. Energy (2016), http://dx.doi. org/10.1016/j.anucene.2016.09.053
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Fig. 17. Pressure drop with different deflection angles.
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performed against a 5 5 rod bundle with two spacer grids and one mid span mixing grid. Compared to previous investigators, a much complete structure of the mixing grid including the stripe, mixing vane, dimple and spring was simulated in a multi-grid condition. Especially, sufficient attention was paid on the cross flow. From the detailed analyses performed, we found that both the spacer grid and mid span mixing grid are confirmable to play an important role in changing the flow behavior and enhancing the heat transfer along the fuel-rod length. The upstream grid has no remarkable impact on the flow field formed at its downstream grids if the cross flow is developed sufficiently. The distribution of fluid temperate is consistent with the axial and lateral power distributions imposed. In addition to the mixing vane, the local structure of dimple and spring is also observable to have an evident impact on the cross flow formed at the grids. Compared to the upstream spacer grid, possibly due to a much shortened grid height, the main vortex at the mid-span-mixing grid seems to be more oblate, while for the local small vortex, it tends to be less easy to be formed at the mid-span mixing grid due to the insufficiency of local structures (e.g. spring). The performed analyses regarding the geometry of the mixing vane suggest that increasing the deflection angle and stretching length of the vane will lead to much strengthened mixing performance and local heat transfer, along with appropriate increase of pressure drop simultaneously, as a result suggesting that a suitable mixing-vane geometry (e.g. neither too long nor too short in vane length) should be determined for a specific situation. Acknowledgements This work was supported by several research projects in China including the National Natural Science Foundation of China (Nos. 51376065, 51176052), Guangdong Key Scientific Project (No. 2013B010405004) and the Fundamental Research Funds for the Central Universities (No. 15lgjc29). References
Fig. 18. Mixing coefficient with different vane lengths.
Fig. 19. Pressure drop with different vane lengths.
4. Concluding remarks Motivated to provide useful information for improved design of fuel assembly of PWRs in China, in this work CFD analyses were
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Please cite this article in press as: Cheng, S., et al. CFD analysis of flow field in a 5 5 rod bundle with multi-grid. Ann. Nucl. Energy (2016), http://dx.doi. org/10.1016/j.anucene.2016.09.053