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CFD analysis of flow blockage phenomena in a LBE-cooled 19-pin wire-wrapped rod bundle
Nuclear Engineering and Design 344 (2019) 107–121
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CFD analysis of flow blockage phenomena in a LBE-cooled 19-pin wirewrapped rod bundle
T
⁎
Xiang Chai , Xiaojing Liu, Jinbiao Xiong, Xu Cheng School of Nuclear Science and Engineering, Shanghai Jiao Tong University, China
A R T I C LE I N FO
A B S T R A C T
Keywords: CFD Lead-bismuth eutectic Flow blockage accident Rod bundle Inter-channel mixing
Flow blockage accident is a severe accident. When fuel assembly is partially or totally blocked, the heat transfer between coolant and cladding is significant impaired due to a rapid decrease of coolant flow, which leads to a local increase of cladding and coolant temperature and possibly results in a release of fission products. A recirculation region is formed downstream the blockage and a temperature peak can be found in this region. In this paper, CFD modelling and simulation for a LBE-cooled 19-pin wire-wrapped bundle were carried out to consider the influence from the flow blockage on the rod surface temperature and cross flow. Three-dimensional flow and temperature distributions of LBE were obtained using commercial CFD software. The influence from the blockage area and its location was investigated as well as the axial length of blockages. It was found that flow blockages in the center of bundle result in a higher surface temperature while comparing with blockages in the side sub-channels. The cross flow between sub-channels through gaps has been evaluated and their dependency on the blockage area is also evaluated based on CFD simulation results.
1. Introduction Lead-cooled fast reactor (LFR), which is considered to be part of new generation of nuclear power plant designs has drawn a lot of attentions due to its good thermodynamic properties (Martelli et al., 2017), safety and closed fuel cycle. Due to the high heat removal capability, the pitch to diameter ratio (P/D) of the pin bundle is kept around 1.28 in the design of LFR which is smaller compared to PWR and BWR (1.30–1.33). Moreover, P/D of sodium fast reactor (1.16–1.23) is usually smaller than LFR in order to reduce pressure drop in LFR. Wire-wrapped spacers are provided over each fuel pin to avoid pin-to-pin contact and to guard the pin bundle against flow-induced vibration (Rasu et al., 2014). Flow blockage of coolant channels, which is a severe accident, may occur in fuel assembly. A partial blockage at the fuel assembly foot may be caused by foreign materials left during construction. Furthermore, the corrosion of the structural material is accelerated due to the high operating temperature of LFR and corrosion products as well as debris from failed fuel pins or broken wire may accumulate in the flow channels and results in an internal blockage, which can be even more dangerous (Bertini, 1980). In addition, deformation of cladding caused by radiation may also lead to a reduction of coolant flow area. When fuel assembly is partially or totally blocked, the heat transfer between coolant and cladding is significant impaired
⁎
due to a rapid decrease of coolant flow, which leads to a local increase of cladding and coolant temperature and possibly results in a release of fission products. However, flow blockage of coolant channels has negligible effect on the total mass flow rate and it is difficult for the protect system to detect the local effect caused by flow blockages. Hence, flow blockage accident is considered to be one of the important issues to be addressed for LFR fuel assembly and it is necessarily important to investigate the progression and underlying phenomenon caused by the flow blockage. However, it remains a great challenge to accurately assess the consequence of flow blockage accident due to the complex mechanism involved. In the past decades, a lot of researches have been carried out to investigate the flow and heat transfer process in a bare or wire-wrapped rod bundle. Experimental studies have been also carried out to investigate the flow properties in a 61-pin wire-wrapped fuel bundle based on MIR method in which water is chosen as the working medium (Nguyen et al., 2017; Goth et al., 2018). The pin and wire diameter are 15.9 mm and 3 mm, respectively. A large amount of experimental data is provided which includes ensemble-averaged velocity, root-meansquare fluctuating velocity, Reynolds stress, and integral length scales. Based on MIR method, it is also capable to visualize 3D vorticity isosurfaces and show the movement of vortical structures in the streamwise direction which were generated from shear layers of neighboring
Corresponding author. E-mail address: [email protected] (X. Chai).
https://doi.org/10.1016/j.nucengdes.2019.01.019 Received 10 August 2018; Received in revised form 15 January 2019; Accepted 17 January 2019 0029-5493/ © 2019 Elsevier B.V. All rights reserved.
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results indicated that the influence from porous blockage is found to be limited to the porous zone and a non-linear relationship between peak cladding temperature and the blockage porous was clearly indicated. A CFD study was carried out by Di Piazza et al. (2014) to analyze flow blockage phenomena in the lead-cooled fuel pin bundle of the ALFRED LFR DEMO without wire-wrapped spacer. In the simulation, the blockage area was placed at the beginning of the active region so that both local and global effects were considered. It was found that for large blockage, a temperature peak behind the blockage can be found in the recirculation region downstream the blockage while the lower mass flow rate in the blocked sub-channels leads to a temperature peak at the end of the active region for small blockage. This simulation also indicated that blockages greater than 15% could be detected by putting some thermocouples in the plenum region of the FA. Although lots of researches were carried out to investigate flow blockage in bundles, more investigations focus on simulating such blockage scenarios in plate-type assemblies with two-dimensional or three-dimensional method (Salama, 2012; Salama et al. (2015); Fan et al. (2015); Davari et al., 2015). Based on previous experimental and numerical studies, it was found that flow blockage accident may lead to a temperature peak behind the blockage or at the outlet which is dependent on the blockage area. Nevertheless most of work were carried out based on system codes like RELAP (Lu et al., 2009). Although some CFD studies have been carried out to show the influence from the blockage geometry, location and so on, the information about the inter-channel mixing downstream the blockage is still quite limited, especially for a rod bundle with wirewrapped spacer in which cross flows are greatly enhanced due to the rotation of wire. In this paper, RANS model is employed to predict the flow and heat transfer properties affected by flow blockage in a LBEcooled 19-pin wire-wrapped rod bundle. Based on this numerical configuration, blockage geometry and its location were systematically varied in a parametric study to consider their influence on the threedimensional flow and temperature distributions. The rod surface temperature is quantitatively investigated as well as the cross flow between sub-channels. The dependency of maximum temperature difference between blocked and unblocked cases was evaluated as well as the inter-channel mixing based on simulation results in which blockage geometry varies in a wide range.
rods (Nguyen et al., 2018; Vaghetto et al., 2018). Pacio et al. (2014, 2015, 2016, 2017) investigated the heat transfer characteristics in a 19pin rod bundle with grid spacer or wire-wrapped spacer. The obtained results can be also employed to prove the correctness of the numerical configuration. Due to the limitation of measurement, CFD method is a quite popular way which can provide a detailed profile of velocity and temperature inside the rod bundle. Based on these numerical methods, the influence from the secondary flow in the sub-channel was identified in which the influence from the turbulent Prandtl number is clearly clarified (Cheng and Tak, 2006). Although difficulties arise at the contacting point between wire-wrapped spacer which impairs the mesh quality, different methods have been proposed to mesh the geometry of rod bundle based on a general validation methodology which includes a detailed analysis of velocity, temperature and pressure loss (Merzari et al., 2012). Based on these efforts, the influence from the wirewrapped spacer on the flow and heat transfer properties is carefully investigated. And it has been found that the inter-channel mixing between neighboring sub-channels has been greatly enhanced and several correlations have been proposed to evaluate the transvers flow caused by the wire-wrapped spacer (Raj and Velusamy, 2016). For the design and safety assessment of flow blockage accident, a vast of studies which include both experimental and numerical studies have been carried out to investigate the flow blockage in a bare or wirewrapped rod bundle. In 1970s, experiments were carried out in Karlsruhe to investigate the influence from flow blockages on heat transfer process in the coolant channels (Kramer et al., 1979), especially the integrity of the fuel assembly (FA). It was concluded that the crosssection area occupied by channel blockage cannot be too high. A possible explanation for this phenomenon can be given based on the accumulation of corrosive products or foreign materials which is quite a slow process. A rapid decrease of coolant flow caused by channel blockage may not affect its neighboring fuel rods and the blockage can be detected by delayed neutron detection signal which will trigger the protection system to shut down the reactor. Due to the limitation of measurement, the information about the flow and heat transfer properties cannot be provided. In addition, the influence from the blockage is three-dimensional, which again makes the measurement and interpretation problematic, such as Ohtsubo and Uruwashi (1972), Kikuchi et al. (1977), Sudo and Osakabe (1983). With increasing computer power, the employment of the numerical approach has gained considerable attentions to investigate flow blockage accident. In 70s, Kirsch (Kirsch, 1974) theoretically evaluated the flow and heat transfer properties of sodium downstream the blockage with an assumption that the heat transfer is dominated by turbulent diffusion and molecular heat transfer can be neglected. It was found that the dimensionless temperature distribution in the recirculation region is independent of Reynolds and Prandtl number if Reynolds number is larger than 105. Han and Fontana (Han, 1977) summarized a comprehensive review on the experimental and analytical investigations of flow blockage accident in fuel assemblies of sodium cooled fast reactors performed in United States and Germany. An analytical approach was proposed to estimate the flow blockage effect. Jeong et al. (2005) investigated flow blockage accident in a subassembly of a liquid metal cooled reactor (LMR). In their analysis, in order to guarantee the design safety, turbulent mixing model was evaluated based on the experimental data of the Oak Ridge National Laboratory 19- pin bundle in which blockages with both high-flow and low-flow conditions are included. The turbulent mixing models suggested by Rehme (1992) and by Zhukov et al. (1994) were found to be appropriate for the description of the flow blockage in an LMR subassembly with which user selective constants are not needed anymore. Rasu et al. (2014) investigated three-dimensional flow and temperature fields within a 19-pin wire-wrapped fuel bundle of fast reactor with internal blockage. A porous blockage is considered in the simulation. Blockage geometry, its location and porosity were systematically varied in a parametric study to consider their influence on the coolant and cladding temperature. The simulation
2. Mathematical formulation
Axial Pitch
In the current study, RANS model is used to predict flow and heat transfer properties downstream the blockage in a LBE-cooled 19-pin wire-wrapped rod bundle. The main geometrical parameters of simulation domain is the same as the experimental work of Pacio et al. (2016, 2017). A schematic sketch of the cross-section of the simulation domain at the inlet is shown in Fig. 1. The geometry size of the simulation domain such as pitch P, diameter D, height H, apothem A are 10.49 mm, 8.2 mm, 870 mm and 24.65 mm, respectively. In order to consider the influence from the flow blockage on the three-dimensional
Fig. 1. Schematic diagram of a hexagonal 19-pin fuel assembly. 108
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temperature distribution in the solid region, the cladding is also included in the simulation. The inner diameter of cladding is set to 6.56 mm which is consistent with the experimental work (Pacio et al., 2017). The diameter of wire is 2.2 mm and its axial pitch is 328 mm. In the flow direction (upward), the wires follow a counter-clockwise spiral. The simulation domain has been discretized by unstructured meshes based on a sensitive analysis of grid resolution. In order to accurately capture the turbulent and heat transfer properties in the nearwall region, the value of y + is kept around 1 based on the prism layer mesher which creates the boundary layer elements necessary to resolve the momentum boundary layer. The mass flow rate and inlet temperature used in the simulation are 19.18 kg/s and 473.15 K, respectively. LBE flows upward in the rod bundle. More detailed descriptions of the experimental facility can be found in Pacio et al. (2016, 2017). Different blockage geometries are considered in the simulation. Both steel cladding wall and fluid region were included in the simulation region. A temperature-dependent thermo-physical property for LBE was adopted in the simulation. In the experimental study of Pacio et al. (2017), wire-wrapped spacer is employed to fix the position of the heated rod and this configuration introduces difficulties to generate the mesh. The contact point between the wire and rod introduces great difficulties to generate the mesh. In order to circumvent this problem, each helical wire is pushed toward its adjacent fuel rod around 0.1 mm without employing a circular fillet between cladding and wire. Hence, the wire and wall are considered in contact and merged with an angle of 11° as shown in Fig. 2, as suggested by Ranjan et al. (2010). This configuration leads to a small gap between each helical wire spacer and adjacent pin. This numerical configuration is obtained based on a sensitive analysis which provides a best compromise between the requirement of prediction accuracy and the wire contact angle. As discussed in the numerical work proposed by Merzari et al. (2012), RANS-based techniques are sufficient to provide an accurate simulation result of a wire-wrapped pin bundle. Due to its numerically economic, SST k-ω model is employed to investigate the flow and heat transfer properties downstream the blockage. If employing a temperature-dependent physical property, the system of averaged governing equations for the mass, momentum and energy is given in the steadystate form by:
∂ρUj ∂x j
∂x j
Fig. 4. Influence from the inlet velocity profile on rod surface temperature.
∂ (ρUj T )
=0
∂ (ρUi Uj )
Fig. 3. Typical mesh near the helical wire space.
∂x j
(1)
=−
∂P ∂ ⎛ ∂Ui ⎞ + ⎜μ ⎟ − ρgi ∂x i ∂x j ⎝ eff ∂x j ⎠
=
μ ∂T ⎞ ∂ ⎛⎛ μ + t⎞ ⎜ ⎟ ∂x j ⎝ ⎝ Pr Prt ⎠ ∂x j ⎠ ⎜
⎟
(3)
where U, T and P are velocity, temperature and pressure, respectively. Pr and Prt are Prandtl and turbulent Prandtl number, respectively. In order to close the modeling, the effective viscosity which is composed by laminar viscosity and turbulence viscosity is calculated as follows:
(2)
μeff = μ + μt
(4)
In the previous numerical studies of the forced convection flow in the rod bundle, different turbulence models are employed to evaluate the value of turbulent viscosity, such as k-ε model, shear stress transport model and so on. STAR-CCM + provides several two-equation models with corresponding wall function to predict the turbulent properties. In the current study, SST (Mentor) k-ω turbulence model with low y + wall treatment are adopted due to their robust, accuracy and computational efficiency as suggested by Hamman and Berry (Hamman and Berry, 2010). More details about the turbulence models and the corresponding wall treatment can be found in the user guide of STARCCM (CD-ADAPCO, 2012). The initial turbulent intensity is I set to 5% which is a default value of STAR-CCM. Based on turbulent intensity, turbulent kinetic energy is − − 3 evaluated by k = 2 (IU )2 in which U is the averaged coolant velocity. The hydraulic diameter of rod bundle is chosen as the characteristic length in the current study. The mass flow inlet is chosen as the boundary condition of inlet and the mass flow rate and inlet
Fig. 2. Top view of simulation domain including solid and fluid regions. 109
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Table 1 Test matrix adopted for the flow blockage computations. Case number
Block Type
Nblock
Axial Length [mm]
A [mm2]
Cross section
Case 0 Case 1
None Central
0 1
0 10
0 19.3705
See Fig. 1
Case 2
Central
2
10
38.7411
Case 3
Central
3
10
58.1116
Case 4
Central
4
10
77.4821
(continued on next page)
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Table 1 (continued) Case number
Block Type
Nblock
Axial Length [mm]
A [mm2]
Case 5
Central
6
10
116.2232
Case 6
Side
1
10
37.8287
Case 7
Side
2
10
75.6575
Case 8
Side
4
10
102.1293
Cross section
(continued on next page)
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Table 1 (continued) Case number
Block Type
Nblock
Axial Length [mm]
A [mm2]
Case 9
Corner
1
10
15.109
Case Case Case Case Case Case Case Case Case
Central Central Central Central Central Central Central Central Central
1 1 1 3 3 3 6 6 6
20 40 80 20 40 80 20 40 80
19.3705 19.3705 19.3705 58.1116 58.1116 58.1116 116.2232 116.2232 116.2232
10 11 12 13 14 15 16 17 18
Cross section
See See See See See See See See See
Case Case Case Case Case Case Case Case Case
1 1 1 3 3 3 5 5 5
temperature are set to 19.18 kg/s and 473.15 K, respectively. The boundary condition named “pressure outlet” is used for outlet. For other boundaries, the “wall” boundary is used. As discussed before, the steel cladding wall is considered in the simulation and hence, a uniform heat flux is applied to the inner surface of cladding with which the total heat power is nearly identical to the experimental value 197 kW. The default coefficients are employed in the numerical configuration and their values can be found in the manual of STAR-CCM (CD-ADAPCO, 2012). The total number of the meshes of coolant and cladding is around 42 million and 11 million, respectively. A typical mesh near the helical wire spacer can be found in Fig. 3. The simulation domain employed in the current study is consistent with the experimental facility proposed by Pacio et al. (2017). In order to prove the correctness of the numerical configuration employed in the current study, the experimental data which includes both rod surface temperature and coolant temperature are compared against the simulation results obtained in unblocked case. The different measurement levels are provided in the literature which include both inlet and fullydeveloped regions. Sensitive analysis of mesh is firstly carried out which includes three different mesh resolutions. The mesh number of fluid region is varied from 21 million to 42 million. The finest mesh is proved to be the best compromise between the requirement of prediction accuracy and computational efforts. Moreover, three different turbulence models are chosen in the sensitive analysis of turbulence model which includes k-ε model, realizable k-ε model and SST k-ω model. The root-mean-square errors of the predicted rod surface temperature and coolant temperature obtained by these three models are 1.65%, 1.46% and 1.38%, respectively. Hence, SST k-ω model is used in the current study. The influence from the boundary condition of inlet velocity is also investigated. The surface temperature of Rod 1 is circumferentially averaged and plotted against its axial position. As shown in Fig. 4, it is confirmed that the simulation results of rod surface temperature produced by a uniformed profile and a fully-developed profile are almost the same in an unblocked case.
profile at the inlet based on the mass flow rate. As the flow develops, a recirculation region is formed downstream the blockage which results in a temperature peak in both cladding and fluid regions. The Reynolds number Re and Prandtl number Pr at the inlet of simulation domain are 35,830 and 0.039, respectively. The hydraulic diameter dh of rod bundle is equal to 4.7362 mm. As discussed above, blockage geometry and its location have a great influence on the flow and heat transfer properties inside the fuel assembly. However, the knowledge of how to model blockage is still quite limited. A partial blockage at the inlet of fuel assembly may be most dangerous for the integrity of fuel assembly. With the progress of fast reactor, a filter is usually placed at the inlet of core in order to prevent solid particles from entering the fuel assembly. In this case, broken wires show a possible way to block sub-channels and cause an internal blockage. Hence, blockages formed of wire and located at the center of fuel assembly are considered in the current study. The material of blockage is set to stainless steel and its heat conductivity is set to λ = 9.248 + 0.01571T . In the current study, the fluid motion inside the blockage is not considered in the current study. In Table 1, the computational test matrix is reported with the following fields: case number, block type, number of blocked sub-channels (Nblock). The distance from the bottom surface of blockage to the inlet is set to 492 mm which is as 1.5 times as wire axial pitch. The blockage and cladding are combined together and named “solid region” in which the same material is employed. The vertical distance from the upper surface of blockage to its bottom surface is defined as its axial length. As discussed before, blockages may result in a lower mass flow rate in the blocked fuel assembly and leads to an increase of the bulk flow temperature. It has to be noted that the reduction of mass flow is not linear with the blockage area. In the current study, the reduction of mass flow rate due to the higher hydraulic resistance is not considered for the reason that the present work only focuses on the influence from the blockage on the coolant and cladding temperature. The influence from the mass flow rate can be estimated based on the system code (Davari et al., 2015) and it is beyond the scope of the current study.
3. Modeling of the blockage
4. Simulation and analysis of the thermal hydraulics in the rod bundle
The purpose of the current study is to compare the numerical results obtained in both blocked and unblocked cases which include both solid and fluid regions. The simulation is initialized with a constant velocity
In Fig. 5, a transverse plane perpendicular to the axial flow direction chosen to present the temperature distribution in both solid and fluid 112
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e)
a)
Case 0
b)
Case 1
c)
Case 3
d)
Case 5
Case 7
f)
Case 9
Fig. 5. Cross-sectional profiles of temperature in fluid and solid regions.
channels which are close to the blockage is obviously reduced due to a lower coolant temperature in side sub-channels. The existence of blockage drives coolant from the side channels to their neighboring channels and leads to a reduced temperature in these sub-channels. Fig. 6 shows velocity magnitude profiles in different cases. The chosen plane is the same as those in Fig. 5. The solid part is also included in these figures to show the locations of cladding and blockage. From these figures, it is indicated that generally the coolant velocity in the side sub-channels is much larger than that in the central subchannels due to a lower flow resistance and this phenomenon is consistent with the unperturbed case. Moreover, the existence of blockage shows an evidently influence on the coolant velocity. The coolant near the blockage flows backward due a sudden reduction of flow area,
regions. The distances from the selected plane to the bottom of blockage is set to 5 mm and this value corresponds to half of the axial length of blockage. The areas occupied by cladding and blockage are indicated as the dashed lines. From these figures, it is clearly shown that coolant temperature in sub-channels which are close to the blockages shows an obvious increase while the variance of coolant temperature in other sub-channels can be neglected if comparing with the unblocked case. Furthermore, the maximum temperature difference between blocked and unblocked cases can be found in the solid region for the reason that the cooling ability of LBE is much better than steel. When blockage area varies from 19.37 to 116.22 mm2, the maximum temperature increases almost 100 K. In contrast to central blockages, when side sub-channels are occupied as shown in Case 7, the coolant temperature in the sub113
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a)
Case 0
b)
Case 1
c)
Case 3
d)
Case 5
e)
Case 7
f)
Case 9
Fig. 6. Cross-sectional profiles of coolant axial velocity.
coolant regions. The maximum coolant temperature can be found in the region close the blockage. Furthermore, the influence from central blockages on the coolant temperature tends to vanish when the distance to the upper surface of blockage is larger than 10 times of hydraulic diameters. Coolant temperature in the neighboring sub-channels shows a similar profile comparing with the unblocked case. However, for the blockage in the side-channels, the influence from the blockage is still obvious even if it is far downstream of the blockage. The axial velocity profiles near the blockage are shown in Fig. 8. The chosen planes are the same as those in Fig. 7. A similar tendency can be observed in these figures. A typical recirculation region attached to the top surface of blockages can be found in all cases and these recirculation regions directly correspond to the high temperature regions
suggesting that a local hot peak of coolant can be found in this region due a slow movement of coolant. As shown above, the existence of blockage leads to a sudden reduction of flow area and recirculation regions can be found beside and downstream the blockage. Hence, several planes are chosen to present the axial velocity and temperature profiles affected by blockages. The selected planes are parallel to the flow direction and their locations can be found in Fig. 5. Both solid and coolant regions are included in the following figures. The areas occupied by blockages are also indicated as the dashed lines. A sudden reduction of flow area leads to a higher temperature value in both solid and coolant. The peak temperature in the solid region is much larger than that in the fluid region. As blockage area increases, a higher temperature can be expected in both solid and 114
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a)
Case 0
b)
Case 1
c)
Case 3
d)
Case 5
e)
Case 7
Fig. 7. Temperature profiles in both solid and coolant regions upstream and downstream the blockage.
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a)
c)
Case 0
b)
Case 3
d)
e)
Case 1
Case 5
Case 7
Fig. 8. Coolant axial velocity profiles upstream and downstream the blockage in different cases.
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a)
Case 0
b)
Case 1
c)
Case 5
d)
Case 7
Fig. 9. Rod surface temperature vs. axial position for different rods in selected cases.
a)
Rod 1
b)
Rod 12
Fig. 10. Rod surface temperature vs. axial position for selected rods.
occupied by the blockage is excluded in these figures and hence a gap region exists for blocked cases. From these figures, it is clearly indicated that the influence from a small blockage on the rod surface temperature is not obvious as shown in Case 1. As blockage area increases, a high peak of rod surface temperature can be found in Case 5. Moreover, the central blockage has little influence on Rod12 and Rod13 which are next to the outer wall of the hexagonal channel. Analogously, a local effect can be also observed when the blockage is in the side subchannel. In order to systematically investigate the influence from blockage area, the rod surface temperature in the selected cases are circumferentially averaged and plotted against its axial position. The simulation results of blockages in both central and side sub-channels are included
as shown in Fig. 7. Moreover, the recirculation region formed by the blockage in the side sub-channels is much larger as shown in Fig. 8e. This explains that why the coolant temperature far downstream of the blockage is still much larger than that in its neighboring sub-channels. As discussed before, blockage geometry and its location may affect the recirculation region downstream the blockage and a local temperature peak can be found in this region. In Fig. 9, the rod surface temperature is circumferentially averaged and plotted against its axial position. With consideration of the rod bundle geometry, four typical rods such as Rod1, Rod4, Rod12 and Rod13 are chosen to compare the rod surface temperature in different cases. As shown in Fig. 7, the blockage temperature is much higher than coolant due to a higher thermal conductivity of LBE. For the sake of clearness, the region 117
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secondary peak. This phenomenon can be attributed to the cross flow between sub-channels. It is confirmed that the influence from the recirculation region and the cross flow caused by the wire-wrapped spacer has to be considered together to account for the variance of rod surface temperature downstream the blockage. In Fig. 10b, the temperature profile downstream of the blockage is modified as well as its magnitude. This phenomenon can be related to the mechanisms which govern the cross flow between sub-channels. Cross flows in the central sub-channels are mainly determined by the wire-wrapper spacer while the outer wall of the hexagonal channel also has an important influence on the cross flow between side and corner sub-channels. Hence, a more complex phenomenon can be observed for blockages in the side and corner sub-channels. The peak temperature downstream the blockage is higher for Case 7 than Case 8. This phenomenon may be related to the larger blockage area in Case 8 which drives the coolant flows into the sub-channels which are adjacent to Rod 12 as shown in Fig. 5. The obtained simulation results clearly indicate that the influence from blockage area on rod surface temperature, so that it is necessary to evaluate the relationship between them. The maximum temperature difference between blocked and unblocked cases ΔTmax is calculated based on the simulation results and plotted against the blockage area in Fig. 11. In this figure, a good linear relationship crosses the origin point between the blockage area and the maximum temperature difference is obtained except for Case7 and Case8 in which side sub-channels are occupied by the blockage. It proves that the influence from the blockages in the side sub-channels is relatively small while central blockages may result in a more significant influence. This reflects the simple fact that the mass flow rate in side sub-channels is much higher than that in the central sub-channels due to a lower flow resistance. When flow blockage occurs in the side sub-channels, the coolant which flows inside these blocked sub-channels are forced to neighboring subchannels which yields a better cooling ability in the region downstream the blockage. The pressure difference is also shown in Fig. 12. From this figure, it is clearly indicated that the present of blockage increases the pressure difference between inlet and outlet. Generally, the pressure loss increases as blockage area increases while the blockages in the side and corner sub-channels results in a higher pressure loss. In the design and safety assessment of flow blockage accident, whether the local effect from the blockages can be detected is very important to trigger the protection system to shut down the reactor. Due to the limitation of measurement in the reactor, thermocouples are usually placed in the plenum region of the FA and their locations may be quite far away from blockages. Hence, it is necessary to assure whether the influence from the blockage can be detected in the region which is far away from the blockage. The averaged rod surface temperature near the outlet is obtained in both blocked and unblocked cases and shown in Fig. 13. The distance from the measurement
Fig. 11. Maximum temperature difference between blocked and unblocked cases vs. blockage area.
Fig. 12. Pressure difference between inlet and outlet vs. blockage area.
in Fig. 10, respectively. With consideration of the geometry of rod bundle, Rod1 is chosen to post process surface temperature in central blockage cases while Rod12 is chosen for other cases. Fig. 10 clearly indicates the influence from the blockage area on the rod surface temperature, especially in the region downstream the blockage. The rod surface temperature increases as the blockage area increases. However, the influence from the blockage is only limited to a quite small region near the blockage. As shown in Fig. 10a, as flow develops in the flow direction, rod surface temperature tends to approach the results of nonblocked case quickly. For Case4 and Case5 in which more sub-channels are occupied by the blockage, their rod surface temperatures show a
a)
Relative difference
b)
Absolute difference
Fig. 13. Comparison of rod surface temperature between blocked and unblocked cases near the outlet. 118
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a)
Gap3
b)
c)
Gap7
Gap10
Fig. 14. Cross flow between sub-channels vs. axial position in the region downstream the blockage.
more flattened temperature profile can be expected in the region downstream the blockages. The impairment of heat transfer which occurs in the region downstream the blockage is governed by two different mechanisms: the recirculation region caused by the blockage and the inter-channel mixing enhanced by the wire-wrapped spacer. The recirculation region downstream the blockage leads to a local minimum of the heat transfer and a cladding temperature peak while the cross flow enhanced by the rotating wire may flatten the temperature profile. In the current study, cross flow is carefully investigated by averaging the transverse velocity from sub-channel i to sub-channel j over gap k ωik, j . The direction of the transverse velocity is always normal to the interface between relevant sub-channels. The obtained results are plotted against its axial position and shown in Fig. 14. For the sake of clearness, only the region downstream the blockage is shown and the area occupied by the blockage is indicated as a shadow region. From the inner region to the outer region of rod bundle, several typical gaps like Gap3, Gap7 and Gap10 are chosen in the following analysis. The locations of these three gaps can be found in Fig. 1. As shown in these figures, a similar tendency can be found in Gap3 and Gap7 in which cross flows through these gaps are greatly enhanced in the region close to the blockage. Moreover, the maximum value of cross flow is also amplified as blockage area increases. However, the influence is limited to a small region downstream the blockage. For Gap10 which is close to the outer wall of the hexagonal channel and far away from the blockage, the variance of blockage area has negligible influence on the cross flow. As shown in Fig. 14, the maximum value of cross flows through Gap3 and Gap7 is dependent on the blockage area. Based on the simulation results in which blockage area varies in a wide range as shown in Table 1, the dependence of the maximum value of cross flow on the blockage area is plotted in Fig. 15. As indicated in this figure, a good
Fig. 15. Dependency of maximum cross flow on the blockage area.
location to the outlet is equal to 5% height of fuel assembly to ensure that there is no influence from the boundary condition of outlet. In the selected cases, the distance from the upper surface of blockage to the measurement location is equal to 0.325 m. Both relative and absolute differences between blocked and unblocked cases are included in Fig. 13. It is illustrated that the relative difference is smaller than 2%. The dependency of the absolute difference on the blockage area is also shown in Fig. 13b. It is clearly indicated that the variation of blockage area has negligible influence on the rod surface temperature which is far away from the blockage. Based on these simulation results, it can be concluded that it is difficult to detect the influence from blockage with thermocouples when the location of blockage is not close enough to the thermocouples, even if the blockage area varies in a wide range. This phenomenon may be related to the cross flow between sub-channels. In the LFR fuel assembly, the wire-wrapped spacer is employed to avoid pin-to-pin contact and enhances the inter-channel mixing. Hence, a 119
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a)
Case 0
b)
Case 5
Fig. 16. Transverse velocity contours 1 mm downstream the blockage in different cases.
a)
Nblock=1
b)
Nblock=6
Fig. 17. Influence from the axial length of blockage on the surface temperature of Rod1.
describes the cross flow caused by the wire-wrapped spacer and the blockage could be proposed in a more general way. Transverse velocity contours downstream the blockage is also shown in Fig. 16. In these figures, it is confirmed the fact that the existence of blockage enhances the inter-channel mixing through Gap 3 from Sub-channel 2 to 11. However, due to the existence of wirewrapped spacer, the profile of inter-channel mixing is quite complex and further studies need to be carried out to propose a more general model which could be used to evaluate the inter-channel mixing downstream the blockage in the sub-channel code. In order to investigate the influence from the axial size of blockage, the temperature profile of Rod1 are plotted against its axial position in Fig. 17 in which blockages which occupy one and six sub-channels are included, respectively. The regions which are occupied by the blockage are also excluded in these figures. It is clearly indicated that the rod surface temperature is obviously increased as the axial length of blockage increases. However, discrepancies can be still observed which are supposed to be caused by the blockage area. When single subchannel is blocked, the rod surface temperature is greatly increased in the region which is far away from the blockage. A different tendency can be found when six sub-channels are occupied. It is not surprising since as discussed before the contribution from the recirculation region is modified as blockage area varies. This phenomenon suggests that fluid-solid conjugate heat transfer has to be considered to account for the influence from blockages. The maximum temperature increase of rod surface is also important when cladding-failure has to be considered in the flow blockage accident. Its value is shown in Fig. 18 which includes the influence from
Fig. 18. Maximum temperature difference when blockage area and its axial length vary.
linear relationship crossing the origin point between maximum cross flow and blockage area is obtained. For Gap3, the value of the obtained linear function for maximum cross flow is larger than that of Gap7. The slopes of both linear functions are around 0.012 while the R2 value for Gap3 and Gap7 are 0.96 and 0.965, respectively. Moreover, it confirms the fact that cross flows between sub-channels which are close to the blockage are much stronger than those which are far away from the blockage. This phenomenon suggests that a constitutive relation which 120
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blockage area and its axial length. As the blockage area increases, a much larger surface temperature can be expected. However, the influence from the axial length of blockage is quite complicated. As shown in this figure, the variance of the axial length may impair the heat transfer properties when the blockage is small. As the axial length of blockage increases, the temperature differences tend to approach a constant value.
Hamman, K.D., Berry, R., 2010. A, A CFD simulation process for fast reactor fuel assemblies. Nucl. Eng. Des. 240, 2304–2312. Han, J.T., 1977. Blockages in LMFBR Fuel Assemblies: A Review of Experimental and Theoretical Studies. Oak Ridge National Lab, TN (USA). Jeong, H.Y., Ha, K.S., Chang, W.P., et al., 2005. Modeling of flow blockage in a liquid metal-cooled reactor subassembly with a subchannel analysis code. Nucl. Technol. 149 (1), 71–87. Kikuchi, Y., Daigo, Y., Ohtsubo, A., 1977. Local sodium boiling behind local flow blockage in simulated LMFBR fuel subassembly. J. Nucl. Sci. Technol. 14 (11), 774–790. Kirsch, D., 1974. Investigations on the flow and temperature distribution downstream of local coolant blockages in rod bundle subassemblies. Nucl. Eng. Des. 31 (2), 266–279. Kramer, W., Schleisiek, K., Schmidt, L., et al., 1979. In-pile experiments''Mol 7C''related to pin to pin failure propagation. In: Proceedings of the international meeting on fast reactor safety technology, 1979. Lu, Q., Qiu, S., Su, G.H., 2009. Flow blockage analysis of a channel in a typical material test reactor core. Nucl. Eng. Des. 239 (1), 45–50. Martelli, D., Marinari, R., Barone, G., et al., 2017. CFD thermo-hydraulic analysis of the CIRCE fuel bundle. Ann. Nucl. Energy 103, 294–305. Merzari, E., Pointer, W.D., Smith, J., 2012. G, Tentner A, Fischer P, Numerical simulation of the flow in wire-wrapped pin bundles: effect of pin-wire contact modeling. Nucl. Eng. Des. 253, 374–386. Nguyen, T., Goth, N., Jones, P., et al., 2017. PIV measurements of turbulent flows in a 61pin wire-wrapped hexagonal fuel bundle. Int. J. Heat Fluid Flow 65, 47–59. Nguyen, T., Goth, N., Jones, P., et al., 2018. Stereoscopic PIV measurements of near-wall flow in a tightly packed rod bundle with wire spacers. Exp. Therm. Fluid Sci. 92, 420–435. Ohtsubo, A., Uruwashi, S., 1972. Stagnant fluid due to local flow blockage. J. Nucl. Sci. Technol. 9 (7), 433–434. Pacio, J., Daubner, M., Fellmoser, F., Litfin, K., Marocco, L., Stieglitz, R., Wetzel, T., 2014. Heavy-liquid metal heat transfer experiment in a 19-rod bundle with grid spacers. Nucl. Eng. Des. 273, 33–46. Pacio, J., Litfin, K., Batta, A., Viellieber, M., Class, A., Doolaard, H., 2015. B, ttcher M, Heat transfer to liquid metals in a hexagonal rod bundle with grid spacers: experimental and simulation results. Nucl. Eng. Des. 290, 27–39. Pacio, J., Daubner, M., Fellmoser, F., Litfin, K., Wetzel, T., 2016. Experimental study of heavy-liquid metal (LBE) flow and heat transfer along a hexagonal 19-rod bundle with wire spacers. Nucl. Eng. Des. 301, 111–127. Pacio, J., Wetzel, T., Doolaard, H., Roelofs, F., Van Tichelen, K., 2017. Thermal-hydraulic study of the LBE-cooled fuel assembly in the MYRRHA reactor: experiments and simulations. Nucl. Eng. Des. 312, 327–337. Raj, M.N., Velusamy, K., 2016. Characterization of velocity and temperature fields in a 217 pin wire wrapped fuel bundle of sodium cooled fast reactor. Ann. Nucl. Energy 87, 331–349. Ranjan, R., Pantano, C., Fischer, P., 2010. Direct simulation of turbulent swept flow over a wire in a channel. J. Fluid Mech. 651, 165–209. Rasu, N.G., Velusamy, K., Sundararajan, T., et al., 2014. Thermal hydraulic effect of porous blockage in fuel subassembly of sodium cooled fast reactor. Ann. Nucl. Energy 70, 64–81. Rasu, N.G., Velusamy, K., Sundararajan, T., et al., 2014. Simultaneous development of flow and temperature fields in wire-wrapped fuel pin bundles of sodium cooled fast reactor. Nucl. Eng. Des. 267, 44–60. Rehme, K., 1992. The structure of turbulence in rod bundles and the implications on natural mixing between the subchannels. Int. J. Heat Mass Transf. 35 (2), 567–581. Salama, A., 2012. CFD analysis of fast loss of flow accident in typical MTR reactor undergoing partial and full blockage: the average channel scenario. Prog. Nucl. Energy 60, 1–13. Salama, A., El-Amin, M.F., Sun, S., 2015. Three-dimensional, numerical investigation of flow and heat transfer in rectangular channels subject to partial blockage. Heat Transfer Eng. 36 (2), 152–165. Sudo, Y., Osakabe, M., 1983. Effects of partial flow blockage on core heat transfer in forced-feed reflood tests. J. Nucl. Sci. Technol. 20 (4), 322–332. Vaghetto, R., Jones, P., Goth, N., et al., 2018. Pressure measurements in a wire-wrapped 61-pin hexagonal fuel bundle. J. Fluids Eng. 140 (3), 031104. Zhukov, A.V., Kirillov, P.L., Sorokin, A.P., et al., 1994. Transverse turbulent momentum and energy exchange in the channels of complicated form. Institution of Chemical Engineers Symposium Series. Hemsphere Publishing Corporation, pp. 327.
5. Conclusion In this paper, numerical method is used to simulate the flow and heat transfer properties when flow blockage accident occurs in LBEcooled 19-pin wire-wrapped rod bundle. Based on RANS method, the influence from the blockage geometry and its axial length on rod surface temperature and cross flow between sub-channels were investigated. In order to quantitatively investigate the simulation results, several typical rods and gaps are chosen to show the influence from blockages. Based on a systematic CFD analysis covering a wide range of blockage geometry and its axial length, a close examination of surface temperature reveals that for the blockages in the inner region of the bundle, a linear dependency of blockage area on the maximum temperature difference can be found while the influence from the blockages in the side sub-channels show a relatively smaller influence. The cross flow between sub-channels downstream the blockage is also carefully investigated which reveals that blockage area attributes to the enhancement of inter-channel mixing and a linear dependency can be found between the blockage area and the maximum cross flow. Moreover, if considering the influence from the axial length of blockage, two important features can be confirmed: the extension of blockage in the flow direction may impair the heat transfer in the region downstream the blockage and the maximum rod surface temperature tends to approach a constant value as blockage axial length increases. Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.nucengdes.2019.01.019. References Bertini, H.W., 1980. Descriptions of Selected Accidents that have Occurred at Nuclear Reactor Facilities. Oak Ridge National Lab, TN (USA). CD-ADAPCO, 2012. STAR-CCM+ version 7.06 user guide. Cheng, X., Tak, N.I., 2006. CFD analysis of thermal–hydraulic behavior of heavy liquid metals in sub-channels. Nucl. Eng. Des. 236, 1874–1885. Davari, A., Mirvakili, S.M., Abedi, E., 2015. Three-dimensional analysis of flow blockage accident in Tehran MTR research reactor core using CFD. Prog. Nucl. Energy 85, 605–612. Di Piazza, I., Magugliani, F., Tarantino, M., et al., 2014. A CFD analysis of flow blockage phenomena in ALFRED LFR demo fuel assembly. Nucl. Eng. Des. 276, 202–215. Fan, W., Peng, C., Guo, Y., 2015. CFD study on inlet flow blockage accidents in rectangular fuel assembly. Nucl. Eng. Des. 292, 177–186. Goth, N., Jones, P., Nguyen, T.D., et al., 2018. PTV/PIV measurements of turbulent flows in interior subchannels of a 61-pin wire-wrapped hexagonal fuel bundle. Int. J. Heat Fluid Flow 71, 295–304.
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CFD analysis of flow blockage phenomena in a LBE-cooled 19-pin wirewrapped rod bundle
T
⁎
Xiang Chai , Xiaojing Liu, Jinbiao Xiong, Xu Cheng School of Nuclear Science and Engineering, Shanghai Jiao Tong University, China
A R T I C LE I N FO
A B S T R A C T
Keywords: CFD Lead-bismuth eutectic Flow blockage accident Rod bundle Inter-channel mixing
Flow blockage accident is a severe accident. When fuel assembly is partially or totally blocked, the heat transfer between coolant and cladding is significant impaired due to a rapid decrease of coolant flow, which leads to a local increase of cladding and coolant temperature and possibly results in a release of fission products. A recirculation region is formed downstream the blockage and a temperature peak can be found in this region. In this paper, CFD modelling and simulation for a LBE-cooled 19-pin wire-wrapped bundle were carried out to consider the influence from the flow blockage on the rod surface temperature and cross flow. Three-dimensional flow and temperature distributions of LBE were obtained using commercial CFD software. The influence from the blockage area and its location was investigated as well as the axial length of blockages. It was found that flow blockages in the center of bundle result in a higher surface temperature while comparing with blockages in the side sub-channels. The cross flow between sub-channels through gaps has been evaluated and their dependency on the blockage area is also evaluated based on CFD simulation results.
1. Introduction Lead-cooled fast reactor (LFR), which is considered to be part of new generation of nuclear power plant designs has drawn a lot of attentions due to its good thermodynamic properties (Martelli et al., 2017), safety and closed fuel cycle. Due to the high heat removal capability, the pitch to diameter ratio (P/D) of the pin bundle is kept around 1.28 in the design of LFR which is smaller compared to PWR and BWR (1.30–1.33). Moreover, P/D of sodium fast reactor (1.16–1.23) is usually smaller than LFR in order to reduce pressure drop in LFR. Wire-wrapped spacers are provided over each fuel pin to avoid pin-to-pin contact and to guard the pin bundle against flow-induced vibration (Rasu et al., 2014). Flow blockage of coolant channels, which is a severe accident, may occur in fuel assembly. A partial blockage at the fuel assembly foot may be caused by foreign materials left during construction. Furthermore, the corrosion of the structural material is accelerated due to the high operating temperature of LFR and corrosion products as well as debris from failed fuel pins or broken wire may accumulate in the flow channels and results in an internal blockage, which can be even more dangerous (Bertini, 1980). In addition, deformation of cladding caused by radiation may also lead to a reduction of coolant flow area. When fuel assembly is partially or totally blocked, the heat transfer between coolant and cladding is significant impaired
⁎
due to a rapid decrease of coolant flow, which leads to a local increase of cladding and coolant temperature and possibly results in a release of fission products. However, flow blockage of coolant channels has negligible effect on the total mass flow rate and it is difficult for the protect system to detect the local effect caused by flow blockages. Hence, flow blockage accident is considered to be one of the important issues to be addressed for LFR fuel assembly and it is necessarily important to investigate the progression and underlying phenomenon caused by the flow blockage. However, it remains a great challenge to accurately assess the consequence of flow blockage accident due to the complex mechanism involved. In the past decades, a lot of researches have been carried out to investigate the flow and heat transfer process in a bare or wire-wrapped rod bundle. Experimental studies have been also carried out to investigate the flow properties in a 61-pin wire-wrapped fuel bundle based on MIR method in which water is chosen as the working medium (Nguyen et al., 2017; Goth et al., 2018). The pin and wire diameter are 15.9 mm and 3 mm, respectively. A large amount of experimental data is provided which includes ensemble-averaged velocity, root-meansquare fluctuating velocity, Reynolds stress, and integral length scales. Based on MIR method, it is also capable to visualize 3D vorticity isosurfaces and show the movement of vortical structures in the streamwise direction which were generated from shear layers of neighboring
Corresponding author. E-mail address: [email protected] (X. Chai).
https://doi.org/10.1016/j.nucengdes.2019.01.019 Received 10 August 2018; Received in revised form 15 January 2019; Accepted 17 January 2019 0029-5493/ © 2019 Elsevier B.V. All rights reserved.
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results indicated that the influence from porous blockage is found to be limited to the porous zone and a non-linear relationship between peak cladding temperature and the blockage porous was clearly indicated. A CFD study was carried out by Di Piazza et al. (2014) to analyze flow blockage phenomena in the lead-cooled fuel pin bundle of the ALFRED LFR DEMO without wire-wrapped spacer. In the simulation, the blockage area was placed at the beginning of the active region so that both local and global effects were considered. It was found that for large blockage, a temperature peak behind the blockage can be found in the recirculation region downstream the blockage while the lower mass flow rate in the blocked sub-channels leads to a temperature peak at the end of the active region for small blockage. This simulation also indicated that blockages greater than 15% could be detected by putting some thermocouples in the plenum region of the FA. Although lots of researches were carried out to investigate flow blockage in bundles, more investigations focus on simulating such blockage scenarios in plate-type assemblies with two-dimensional or three-dimensional method (Salama, 2012; Salama et al. (2015); Fan et al. (2015); Davari et al., 2015). Based on previous experimental and numerical studies, it was found that flow blockage accident may lead to a temperature peak behind the blockage or at the outlet which is dependent on the blockage area. Nevertheless most of work were carried out based on system codes like RELAP (Lu et al., 2009). Although some CFD studies have been carried out to show the influence from the blockage geometry, location and so on, the information about the inter-channel mixing downstream the blockage is still quite limited, especially for a rod bundle with wirewrapped spacer in which cross flows are greatly enhanced due to the rotation of wire. In this paper, RANS model is employed to predict the flow and heat transfer properties affected by flow blockage in a LBEcooled 19-pin wire-wrapped rod bundle. Based on this numerical configuration, blockage geometry and its location were systematically varied in a parametric study to consider their influence on the threedimensional flow and temperature distributions. The rod surface temperature is quantitatively investigated as well as the cross flow between sub-channels. The dependency of maximum temperature difference between blocked and unblocked cases was evaluated as well as the inter-channel mixing based on simulation results in which blockage geometry varies in a wide range.
rods (Nguyen et al., 2018; Vaghetto et al., 2018). Pacio et al. (2014, 2015, 2016, 2017) investigated the heat transfer characteristics in a 19pin rod bundle with grid spacer or wire-wrapped spacer. The obtained results can be also employed to prove the correctness of the numerical configuration. Due to the limitation of measurement, CFD method is a quite popular way which can provide a detailed profile of velocity and temperature inside the rod bundle. Based on these numerical methods, the influence from the secondary flow in the sub-channel was identified in which the influence from the turbulent Prandtl number is clearly clarified (Cheng and Tak, 2006). Although difficulties arise at the contacting point between wire-wrapped spacer which impairs the mesh quality, different methods have been proposed to mesh the geometry of rod bundle based on a general validation methodology which includes a detailed analysis of velocity, temperature and pressure loss (Merzari et al., 2012). Based on these efforts, the influence from the wirewrapped spacer on the flow and heat transfer properties is carefully investigated. And it has been found that the inter-channel mixing between neighboring sub-channels has been greatly enhanced and several correlations have been proposed to evaluate the transvers flow caused by the wire-wrapped spacer (Raj and Velusamy, 2016). For the design and safety assessment of flow blockage accident, a vast of studies which include both experimental and numerical studies have been carried out to investigate the flow blockage in a bare or wirewrapped rod bundle. In 1970s, experiments were carried out in Karlsruhe to investigate the influence from flow blockages on heat transfer process in the coolant channels (Kramer et al., 1979), especially the integrity of the fuel assembly (FA). It was concluded that the crosssection area occupied by channel blockage cannot be too high. A possible explanation for this phenomenon can be given based on the accumulation of corrosive products or foreign materials which is quite a slow process. A rapid decrease of coolant flow caused by channel blockage may not affect its neighboring fuel rods and the blockage can be detected by delayed neutron detection signal which will trigger the protection system to shut down the reactor. Due to the limitation of measurement, the information about the flow and heat transfer properties cannot be provided. In addition, the influence from the blockage is three-dimensional, which again makes the measurement and interpretation problematic, such as Ohtsubo and Uruwashi (1972), Kikuchi et al. (1977), Sudo and Osakabe (1983). With increasing computer power, the employment of the numerical approach has gained considerable attentions to investigate flow blockage accident. In 70s, Kirsch (Kirsch, 1974) theoretically evaluated the flow and heat transfer properties of sodium downstream the blockage with an assumption that the heat transfer is dominated by turbulent diffusion and molecular heat transfer can be neglected. It was found that the dimensionless temperature distribution in the recirculation region is independent of Reynolds and Prandtl number if Reynolds number is larger than 105. Han and Fontana (Han, 1977) summarized a comprehensive review on the experimental and analytical investigations of flow blockage accident in fuel assemblies of sodium cooled fast reactors performed in United States and Germany. An analytical approach was proposed to estimate the flow blockage effect. Jeong et al. (2005) investigated flow blockage accident in a subassembly of a liquid metal cooled reactor (LMR). In their analysis, in order to guarantee the design safety, turbulent mixing model was evaluated based on the experimental data of the Oak Ridge National Laboratory 19- pin bundle in which blockages with both high-flow and low-flow conditions are included. The turbulent mixing models suggested by Rehme (1992) and by Zhukov et al. (1994) were found to be appropriate for the description of the flow blockage in an LMR subassembly with which user selective constants are not needed anymore. Rasu et al. (2014) investigated three-dimensional flow and temperature fields within a 19-pin wire-wrapped fuel bundle of fast reactor with internal blockage. A porous blockage is considered in the simulation. Blockage geometry, its location and porosity were systematically varied in a parametric study to consider their influence on the coolant and cladding temperature. The simulation
2. Mathematical formulation
Axial Pitch
In the current study, RANS model is used to predict flow and heat transfer properties downstream the blockage in a LBE-cooled 19-pin wire-wrapped rod bundle. The main geometrical parameters of simulation domain is the same as the experimental work of Pacio et al. (2016, 2017). A schematic sketch of the cross-section of the simulation domain at the inlet is shown in Fig. 1. The geometry size of the simulation domain such as pitch P, diameter D, height H, apothem A are 10.49 mm, 8.2 mm, 870 mm and 24.65 mm, respectively. In order to consider the influence from the flow blockage on the three-dimensional
Fig. 1. Schematic diagram of a hexagonal 19-pin fuel assembly. 108
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temperature distribution in the solid region, the cladding is also included in the simulation. The inner diameter of cladding is set to 6.56 mm which is consistent with the experimental work (Pacio et al., 2017). The diameter of wire is 2.2 mm and its axial pitch is 328 mm. In the flow direction (upward), the wires follow a counter-clockwise spiral. The simulation domain has been discretized by unstructured meshes based on a sensitive analysis of grid resolution. In order to accurately capture the turbulent and heat transfer properties in the nearwall region, the value of y + is kept around 1 based on the prism layer mesher which creates the boundary layer elements necessary to resolve the momentum boundary layer. The mass flow rate and inlet temperature used in the simulation are 19.18 kg/s and 473.15 K, respectively. LBE flows upward in the rod bundle. More detailed descriptions of the experimental facility can be found in Pacio et al. (2016, 2017). Different blockage geometries are considered in the simulation. Both steel cladding wall and fluid region were included in the simulation region. A temperature-dependent thermo-physical property for LBE was adopted in the simulation. In the experimental study of Pacio et al. (2017), wire-wrapped spacer is employed to fix the position of the heated rod and this configuration introduces difficulties to generate the mesh. The contact point between the wire and rod introduces great difficulties to generate the mesh. In order to circumvent this problem, each helical wire is pushed toward its adjacent fuel rod around 0.1 mm without employing a circular fillet between cladding and wire. Hence, the wire and wall are considered in contact and merged with an angle of 11° as shown in Fig. 2, as suggested by Ranjan et al. (2010). This configuration leads to a small gap between each helical wire spacer and adjacent pin. This numerical configuration is obtained based on a sensitive analysis which provides a best compromise between the requirement of prediction accuracy and the wire contact angle. As discussed in the numerical work proposed by Merzari et al. (2012), RANS-based techniques are sufficient to provide an accurate simulation result of a wire-wrapped pin bundle. Due to its numerically economic, SST k-ω model is employed to investigate the flow and heat transfer properties downstream the blockage. If employing a temperature-dependent physical property, the system of averaged governing equations for the mass, momentum and energy is given in the steadystate form by:
∂ρUj ∂x j
∂x j
Fig. 4. Influence from the inlet velocity profile on rod surface temperature.
∂ (ρUj T )
=0
∂ (ρUi Uj )
Fig. 3. Typical mesh near the helical wire space.
∂x j
(1)
=−
∂P ∂ ⎛ ∂Ui ⎞ + ⎜μ ⎟ − ρgi ∂x i ∂x j ⎝ eff ∂x j ⎠
=
μ ∂T ⎞ ∂ ⎛⎛ μ + t⎞ ⎜ ⎟ ∂x j ⎝ ⎝ Pr Prt ⎠ ∂x j ⎠ ⎜
⎟
(3)
where U, T and P are velocity, temperature and pressure, respectively. Pr and Prt are Prandtl and turbulent Prandtl number, respectively. In order to close the modeling, the effective viscosity which is composed by laminar viscosity and turbulence viscosity is calculated as follows:
(2)
μeff = μ + μt
(4)
In the previous numerical studies of the forced convection flow in the rod bundle, different turbulence models are employed to evaluate the value of turbulent viscosity, such as k-ε model, shear stress transport model and so on. STAR-CCM + provides several two-equation models with corresponding wall function to predict the turbulent properties. In the current study, SST (Mentor) k-ω turbulence model with low y + wall treatment are adopted due to their robust, accuracy and computational efficiency as suggested by Hamman and Berry (Hamman and Berry, 2010). More details about the turbulence models and the corresponding wall treatment can be found in the user guide of STARCCM (CD-ADAPCO, 2012). The initial turbulent intensity is I set to 5% which is a default value of STAR-CCM. Based on turbulent intensity, turbulent kinetic energy is − − 3 evaluated by k = 2 (IU )2 in which U is the averaged coolant velocity. The hydraulic diameter of rod bundle is chosen as the characteristic length in the current study. The mass flow inlet is chosen as the boundary condition of inlet and the mass flow rate and inlet
Fig. 2. Top view of simulation domain including solid and fluid regions. 109
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Table 1 Test matrix adopted for the flow blockage computations. Case number
Block Type
Nblock
Axial Length [mm]
A [mm2]
Cross section
Case 0 Case 1
None Central
0 1
0 10
0 19.3705
See Fig. 1
Case 2
Central
2
10
38.7411
Case 3
Central
3
10
58.1116
Case 4
Central
4
10
77.4821
(continued on next page)
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Table 1 (continued) Case number
Block Type
Nblock
Axial Length [mm]
A [mm2]
Case 5
Central
6
10
116.2232
Case 6
Side
1
10
37.8287
Case 7
Side
2
10
75.6575
Case 8
Side
4
10
102.1293
Cross section
(continued on next page)
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Table 1 (continued) Case number
Block Type
Nblock
Axial Length [mm]
A [mm2]
Case 9
Corner
1
10
15.109
Case Case Case Case Case Case Case Case Case
Central Central Central Central Central Central Central Central Central
1 1 1 3 3 3 6 6 6
20 40 80 20 40 80 20 40 80
19.3705 19.3705 19.3705 58.1116 58.1116 58.1116 116.2232 116.2232 116.2232
10 11 12 13 14 15 16 17 18
Cross section
See See See See See See See See See
Case Case Case Case Case Case Case Case Case
1 1 1 3 3 3 5 5 5
temperature are set to 19.18 kg/s and 473.15 K, respectively. The boundary condition named “pressure outlet” is used for outlet. For other boundaries, the “wall” boundary is used. As discussed before, the steel cladding wall is considered in the simulation and hence, a uniform heat flux is applied to the inner surface of cladding with which the total heat power is nearly identical to the experimental value 197 kW. The default coefficients are employed in the numerical configuration and their values can be found in the manual of STAR-CCM (CD-ADAPCO, 2012). The total number of the meshes of coolant and cladding is around 42 million and 11 million, respectively. A typical mesh near the helical wire spacer can be found in Fig. 3. The simulation domain employed in the current study is consistent with the experimental facility proposed by Pacio et al. (2017). In order to prove the correctness of the numerical configuration employed in the current study, the experimental data which includes both rod surface temperature and coolant temperature are compared against the simulation results obtained in unblocked case. The different measurement levels are provided in the literature which include both inlet and fullydeveloped regions. Sensitive analysis of mesh is firstly carried out which includes three different mesh resolutions. The mesh number of fluid region is varied from 21 million to 42 million. The finest mesh is proved to be the best compromise between the requirement of prediction accuracy and computational efforts. Moreover, three different turbulence models are chosen in the sensitive analysis of turbulence model which includes k-ε model, realizable k-ε model and SST k-ω model. The root-mean-square errors of the predicted rod surface temperature and coolant temperature obtained by these three models are 1.65%, 1.46% and 1.38%, respectively. Hence, SST k-ω model is used in the current study. The influence from the boundary condition of inlet velocity is also investigated. The surface temperature of Rod 1 is circumferentially averaged and plotted against its axial position. As shown in Fig. 4, it is confirmed that the simulation results of rod surface temperature produced by a uniformed profile and a fully-developed profile are almost the same in an unblocked case.
profile at the inlet based on the mass flow rate. As the flow develops, a recirculation region is formed downstream the blockage which results in a temperature peak in both cladding and fluid regions. The Reynolds number Re and Prandtl number Pr at the inlet of simulation domain are 35,830 and 0.039, respectively. The hydraulic diameter dh of rod bundle is equal to 4.7362 mm. As discussed above, blockage geometry and its location have a great influence on the flow and heat transfer properties inside the fuel assembly. However, the knowledge of how to model blockage is still quite limited. A partial blockage at the inlet of fuel assembly may be most dangerous for the integrity of fuel assembly. With the progress of fast reactor, a filter is usually placed at the inlet of core in order to prevent solid particles from entering the fuel assembly. In this case, broken wires show a possible way to block sub-channels and cause an internal blockage. Hence, blockages formed of wire and located at the center of fuel assembly are considered in the current study. The material of blockage is set to stainless steel and its heat conductivity is set to λ = 9.248 + 0.01571T . In the current study, the fluid motion inside the blockage is not considered in the current study. In Table 1, the computational test matrix is reported with the following fields: case number, block type, number of blocked sub-channels (Nblock). The distance from the bottom surface of blockage to the inlet is set to 492 mm which is as 1.5 times as wire axial pitch. The blockage and cladding are combined together and named “solid region” in which the same material is employed. The vertical distance from the upper surface of blockage to its bottom surface is defined as its axial length. As discussed before, blockages may result in a lower mass flow rate in the blocked fuel assembly and leads to an increase of the bulk flow temperature. It has to be noted that the reduction of mass flow is not linear with the blockage area. In the current study, the reduction of mass flow rate due to the higher hydraulic resistance is not considered for the reason that the present work only focuses on the influence from the blockage on the coolant and cladding temperature. The influence from the mass flow rate can be estimated based on the system code (Davari et al., 2015) and it is beyond the scope of the current study.
3. Modeling of the blockage
4. Simulation and analysis of the thermal hydraulics in the rod bundle
The purpose of the current study is to compare the numerical results obtained in both blocked and unblocked cases which include both solid and fluid regions. The simulation is initialized with a constant velocity
In Fig. 5, a transverse plane perpendicular to the axial flow direction chosen to present the temperature distribution in both solid and fluid 112
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e)
a)
Case 0
b)
Case 1
c)
Case 3
d)
Case 5
Case 7
f)
Case 9
Fig. 5. Cross-sectional profiles of temperature in fluid and solid regions.
channels which are close to the blockage is obviously reduced due to a lower coolant temperature in side sub-channels. The existence of blockage drives coolant from the side channels to their neighboring channels and leads to a reduced temperature in these sub-channels. Fig. 6 shows velocity magnitude profiles in different cases. The chosen plane is the same as those in Fig. 5. The solid part is also included in these figures to show the locations of cladding and blockage. From these figures, it is indicated that generally the coolant velocity in the side sub-channels is much larger than that in the central subchannels due to a lower flow resistance and this phenomenon is consistent with the unperturbed case. Moreover, the existence of blockage shows an evidently influence on the coolant velocity. The coolant near the blockage flows backward due a sudden reduction of flow area,
regions. The distances from the selected plane to the bottom of blockage is set to 5 mm and this value corresponds to half of the axial length of blockage. The areas occupied by cladding and blockage are indicated as the dashed lines. From these figures, it is clearly shown that coolant temperature in sub-channels which are close to the blockages shows an obvious increase while the variance of coolant temperature in other sub-channels can be neglected if comparing with the unblocked case. Furthermore, the maximum temperature difference between blocked and unblocked cases can be found in the solid region for the reason that the cooling ability of LBE is much better than steel. When blockage area varies from 19.37 to 116.22 mm2, the maximum temperature increases almost 100 K. In contrast to central blockages, when side sub-channels are occupied as shown in Case 7, the coolant temperature in the sub113
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a)
Case 0
b)
Case 1
c)
Case 3
d)
Case 5
e)
Case 7
f)
Case 9
Fig. 6. Cross-sectional profiles of coolant axial velocity.
coolant regions. The maximum coolant temperature can be found in the region close the blockage. Furthermore, the influence from central blockages on the coolant temperature tends to vanish when the distance to the upper surface of blockage is larger than 10 times of hydraulic diameters. Coolant temperature in the neighboring sub-channels shows a similar profile comparing with the unblocked case. However, for the blockage in the side-channels, the influence from the blockage is still obvious even if it is far downstream of the blockage. The axial velocity profiles near the blockage are shown in Fig. 8. The chosen planes are the same as those in Fig. 7. A similar tendency can be observed in these figures. A typical recirculation region attached to the top surface of blockages can be found in all cases and these recirculation regions directly correspond to the high temperature regions
suggesting that a local hot peak of coolant can be found in this region due a slow movement of coolant. As shown above, the existence of blockage leads to a sudden reduction of flow area and recirculation regions can be found beside and downstream the blockage. Hence, several planes are chosen to present the axial velocity and temperature profiles affected by blockages. The selected planes are parallel to the flow direction and their locations can be found in Fig. 5. Both solid and coolant regions are included in the following figures. The areas occupied by blockages are also indicated as the dashed lines. A sudden reduction of flow area leads to a higher temperature value in both solid and coolant. The peak temperature in the solid region is much larger than that in the fluid region. As blockage area increases, a higher temperature can be expected in both solid and 114
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a)
Case 0
b)
Case 1
c)
Case 3
d)
Case 5
e)
Case 7
Fig. 7. Temperature profiles in both solid and coolant regions upstream and downstream the blockage.
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a)
c)
Case 0
b)
Case 3
d)
e)
Case 1
Case 5
Case 7
Fig. 8. Coolant axial velocity profiles upstream and downstream the blockage in different cases.
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a)
Case 0
b)
Case 1
c)
Case 5
d)
Case 7
Fig. 9. Rod surface temperature vs. axial position for different rods in selected cases.
a)
Rod 1
b)
Rod 12
Fig. 10. Rod surface temperature vs. axial position for selected rods.
occupied by the blockage is excluded in these figures and hence a gap region exists for blocked cases. From these figures, it is clearly indicated that the influence from a small blockage on the rod surface temperature is not obvious as shown in Case 1. As blockage area increases, a high peak of rod surface temperature can be found in Case 5. Moreover, the central blockage has little influence on Rod12 and Rod13 which are next to the outer wall of the hexagonal channel. Analogously, a local effect can be also observed when the blockage is in the side subchannel. In order to systematically investigate the influence from blockage area, the rod surface temperature in the selected cases are circumferentially averaged and plotted against its axial position. The simulation results of blockages in both central and side sub-channels are included
as shown in Fig. 7. Moreover, the recirculation region formed by the blockage in the side sub-channels is much larger as shown in Fig. 8e. This explains that why the coolant temperature far downstream of the blockage is still much larger than that in its neighboring sub-channels. As discussed before, blockage geometry and its location may affect the recirculation region downstream the blockage and a local temperature peak can be found in this region. In Fig. 9, the rod surface temperature is circumferentially averaged and plotted against its axial position. With consideration of the rod bundle geometry, four typical rods such as Rod1, Rod4, Rod12 and Rod13 are chosen to compare the rod surface temperature in different cases. As shown in Fig. 7, the blockage temperature is much higher than coolant due to a higher thermal conductivity of LBE. For the sake of clearness, the region 117
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secondary peak. This phenomenon can be attributed to the cross flow between sub-channels. It is confirmed that the influence from the recirculation region and the cross flow caused by the wire-wrapped spacer has to be considered together to account for the variance of rod surface temperature downstream the blockage. In Fig. 10b, the temperature profile downstream of the blockage is modified as well as its magnitude. This phenomenon can be related to the mechanisms which govern the cross flow between sub-channels. Cross flows in the central sub-channels are mainly determined by the wire-wrapper spacer while the outer wall of the hexagonal channel also has an important influence on the cross flow between side and corner sub-channels. Hence, a more complex phenomenon can be observed for blockages in the side and corner sub-channels. The peak temperature downstream the blockage is higher for Case 7 than Case 8. This phenomenon may be related to the larger blockage area in Case 8 which drives the coolant flows into the sub-channels which are adjacent to Rod 12 as shown in Fig. 5. The obtained simulation results clearly indicate that the influence from blockage area on rod surface temperature, so that it is necessary to evaluate the relationship between them. The maximum temperature difference between blocked and unblocked cases ΔTmax is calculated based on the simulation results and plotted against the blockage area in Fig. 11. In this figure, a good linear relationship crosses the origin point between the blockage area and the maximum temperature difference is obtained except for Case7 and Case8 in which side sub-channels are occupied by the blockage. It proves that the influence from the blockages in the side sub-channels is relatively small while central blockages may result in a more significant influence. This reflects the simple fact that the mass flow rate in side sub-channels is much higher than that in the central sub-channels due to a lower flow resistance. When flow blockage occurs in the side sub-channels, the coolant which flows inside these blocked sub-channels are forced to neighboring subchannels which yields a better cooling ability in the region downstream the blockage. The pressure difference is also shown in Fig. 12. From this figure, it is clearly indicated that the present of blockage increases the pressure difference between inlet and outlet. Generally, the pressure loss increases as blockage area increases while the blockages in the side and corner sub-channels results in a higher pressure loss. In the design and safety assessment of flow blockage accident, whether the local effect from the blockages can be detected is very important to trigger the protection system to shut down the reactor. Due to the limitation of measurement in the reactor, thermocouples are usually placed in the plenum region of the FA and their locations may be quite far away from blockages. Hence, it is necessary to assure whether the influence from the blockage can be detected in the region which is far away from the blockage. The averaged rod surface temperature near the outlet is obtained in both blocked and unblocked cases and shown in Fig. 13. The distance from the measurement
Fig. 11. Maximum temperature difference between blocked and unblocked cases vs. blockage area.
Fig. 12. Pressure difference between inlet and outlet vs. blockage area.
in Fig. 10, respectively. With consideration of the geometry of rod bundle, Rod1 is chosen to post process surface temperature in central blockage cases while Rod12 is chosen for other cases. Fig. 10 clearly indicates the influence from the blockage area on the rod surface temperature, especially in the region downstream the blockage. The rod surface temperature increases as the blockage area increases. However, the influence from the blockage is only limited to a quite small region near the blockage. As shown in Fig. 10a, as flow develops in the flow direction, rod surface temperature tends to approach the results of nonblocked case quickly. For Case4 and Case5 in which more sub-channels are occupied by the blockage, their rod surface temperatures show a
a)
Relative difference
b)
Absolute difference
Fig. 13. Comparison of rod surface temperature between blocked and unblocked cases near the outlet. 118
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a)
Gap3
b)
c)
Gap7
Gap10
Fig. 14. Cross flow between sub-channels vs. axial position in the region downstream the blockage.
more flattened temperature profile can be expected in the region downstream the blockages. The impairment of heat transfer which occurs in the region downstream the blockage is governed by two different mechanisms: the recirculation region caused by the blockage and the inter-channel mixing enhanced by the wire-wrapped spacer. The recirculation region downstream the blockage leads to a local minimum of the heat transfer and a cladding temperature peak while the cross flow enhanced by the rotating wire may flatten the temperature profile. In the current study, cross flow is carefully investigated by averaging the transverse velocity from sub-channel i to sub-channel j over gap k ωik, j . The direction of the transverse velocity is always normal to the interface between relevant sub-channels. The obtained results are plotted against its axial position and shown in Fig. 14. For the sake of clearness, only the region downstream the blockage is shown and the area occupied by the blockage is indicated as a shadow region. From the inner region to the outer region of rod bundle, several typical gaps like Gap3, Gap7 and Gap10 are chosen in the following analysis. The locations of these three gaps can be found in Fig. 1. As shown in these figures, a similar tendency can be found in Gap3 and Gap7 in which cross flows through these gaps are greatly enhanced in the region close to the blockage. Moreover, the maximum value of cross flow is also amplified as blockage area increases. However, the influence is limited to a small region downstream the blockage. For Gap10 which is close to the outer wall of the hexagonal channel and far away from the blockage, the variance of blockage area has negligible influence on the cross flow. As shown in Fig. 14, the maximum value of cross flows through Gap3 and Gap7 is dependent on the blockage area. Based on the simulation results in which blockage area varies in a wide range as shown in Table 1, the dependence of the maximum value of cross flow on the blockage area is plotted in Fig. 15. As indicated in this figure, a good
Fig. 15. Dependency of maximum cross flow on the blockage area.
location to the outlet is equal to 5% height of fuel assembly to ensure that there is no influence from the boundary condition of outlet. In the selected cases, the distance from the upper surface of blockage to the measurement location is equal to 0.325 m. Both relative and absolute differences between blocked and unblocked cases are included in Fig. 13. It is illustrated that the relative difference is smaller than 2%. The dependency of the absolute difference on the blockage area is also shown in Fig. 13b. It is clearly indicated that the variation of blockage area has negligible influence on the rod surface temperature which is far away from the blockage. Based on these simulation results, it can be concluded that it is difficult to detect the influence from blockage with thermocouples when the location of blockage is not close enough to the thermocouples, even if the blockage area varies in a wide range. This phenomenon may be related to the cross flow between sub-channels. In the LFR fuel assembly, the wire-wrapped spacer is employed to avoid pin-to-pin contact and enhances the inter-channel mixing. Hence, a 119
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a)
Case 0
b)
Case 5
Fig. 16. Transverse velocity contours 1 mm downstream the blockage in different cases.
a)
Nblock=1
b)
Nblock=6
Fig. 17. Influence from the axial length of blockage on the surface temperature of Rod1.
describes the cross flow caused by the wire-wrapped spacer and the blockage could be proposed in a more general way. Transverse velocity contours downstream the blockage is also shown in Fig. 16. In these figures, it is confirmed the fact that the existence of blockage enhances the inter-channel mixing through Gap 3 from Sub-channel 2 to 11. However, due to the existence of wirewrapped spacer, the profile of inter-channel mixing is quite complex and further studies need to be carried out to propose a more general model which could be used to evaluate the inter-channel mixing downstream the blockage in the sub-channel code. In order to investigate the influence from the axial size of blockage, the temperature profile of Rod1 are plotted against its axial position in Fig. 17 in which blockages which occupy one and six sub-channels are included, respectively. The regions which are occupied by the blockage are also excluded in these figures. It is clearly indicated that the rod surface temperature is obviously increased as the axial length of blockage increases. However, discrepancies can be still observed which are supposed to be caused by the blockage area. When single subchannel is blocked, the rod surface temperature is greatly increased in the region which is far away from the blockage. A different tendency can be found when six sub-channels are occupied. It is not surprising since as discussed before the contribution from the recirculation region is modified as blockage area varies. This phenomenon suggests that fluid-solid conjugate heat transfer has to be considered to account for the influence from blockages. The maximum temperature increase of rod surface is also important when cladding-failure has to be considered in the flow blockage accident. Its value is shown in Fig. 18 which includes the influence from
Fig. 18. Maximum temperature difference when blockage area and its axial length vary.
linear relationship crossing the origin point between maximum cross flow and blockage area is obtained. For Gap3, the value of the obtained linear function for maximum cross flow is larger than that of Gap7. The slopes of both linear functions are around 0.012 while the R2 value for Gap3 and Gap7 are 0.96 and 0.965, respectively. Moreover, it confirms the fact that cross flows between sub-channels which are close to the blockage are much stronger than those which are far away from the blockage. This phenomenon suggests that a constitutive relation which 120
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blockage area and its axial length. As the blockage area increases, a much larger surface temperature can be expected. However, the influence from the axial length of blockage is quite complicated. As shown in this figure, the variance of the axial length may impair the heat transfer properties when the blockage is small. As the axial length of blockage increases, the temperature differences tend to approach a constant value.
Hamman, K.D., Berry, R., 2010. A, A CFD simulation process for fast reactor fuel assemblies. Nucl. Eng. Des. 240, 2304–2312. Han, J.T., 1977. Blockages in LMFBR Fuel Assemblies: A Review of Experimental and Theoretical Studies. Oak Ridge National Lab, TN (USA). Jeong, H.Y., Ha, K.S., Chang, W.P., et al., 2005. Modeling of flow blockage in a liquid metal-cooled reactor subassembly with a subchannel analysis code. Nucl. Technol. 149 (1), 71–87. Kikuchi, Y., Daigo, Y., Ohtsubo, A., 1977. Local sodium boiling behind local flow blockage in simulated LMFBR fuel subassembly. J. Nucl. Sci. Technol. 14 (11), 774–790. Kirsch, D., 1974. Investigations on the flow and temperature distribution downstream of local coolant blockages in rod bundle subassemblies. Nucl. Eng. Des. 31 (2), 266–279. Kramer, W., Schleisiek, K., Schmidt, L., et al., 1979. In-pile experiments''Mol 7C''related to pin to pin failure propagation. In: Proceedings of the international meeting on fast reactor safety technology, 1979. Lu, Q., Qiu, S., Su, G.H., 2009. Flow blockage analysis of a channel in a typical material test reactor core. Nucl. Eng. Des. 239 (1), 45–50. Martelli, D., Marinari, R., Barone, G., et al., 2017. CFD thermo-hydraulic analysis of the CIRCE fuel bundle. Ann. Nucl. Energy 103, 294–305. Merzari, E., Pointer, W.D., Smith, J., 2012. G, Tentner A, Fischer P, Numerical simulation of the flow in wire-wrapped pin bundles: effect of pin-wire contact modeling. Nucl. Eng. Des. 253, 374–386. Nguyen, T., Goth, N., Jones, P., et al., 2017. PIV measurements of turbulent flows in a 61pin wire-wrapped hexagonal fuel bundle. Int. J. Heat Fluid Flow 65, 47–59. Nguyen, T., Goth, N., Jones, P., et al., 2018. Stereoscopic PIV measurements of near-wall flow in a tightly packed rod bundle with wire spacers. Exp. Therm. Fluid Sci. 92, 420–435. Ohtsubo, A., Uruwashi, S., 1972. Stagnant fluid due to local flow blockage. J. Nucl. Sci. Technol. 9 (7), 433–434. Pacio, J., Daubner, M., Fellmoser, F., Litfin, K., Marocco, L., Stieglitz, R., Wetzel, T., 2014. Heavy-liquid metal heat transfer experiment in a 19-rod bundle with grid spacers. Nucl. Eng. Des. 273, 33–46. Pacio, J., Litfin, K., Batta, A., Viellieber, M., Class, A., Doolaard, H., 2015. B, ttcher M, Heat transfer to liquid metals in a hexagonal rod bundle with grid spacers: experimental and simulation results. Nucl. Eng. Des. 290, 27–39. Pacio, J., Daubner, M., Fellmoser, F., Litfin, K., Wetzel, T., 2016. Experimental study of heavy-liquid metal (LBE) flow and heat transfer along a hexagonal 19-rod bundle with wire spacers. Nucl. Eng. Des. 301, 111–127. Pacio, J., Wetzel, T., Doolaard, H., Roelofs, F., Van Tichelen, K., 2017. Thermal-hydraulic study of the LBE-cooled fuel assembly in the MYRRHA reactor: experiments and simulations. Nucl. Eng. Des. 312, 327–337. Raj, M.N., Velusamy, K., 2016. Characterization of velocity and temperature fields in a 217 pin wire wrapped fuel bundle of sodium cooled fast reactor. Ann. Nucl. Energy 87, 331–349. Ranjan, R., Pantano, C., Fischer, P., 2010. Direct simulation of turbulent swept flow over a wire in a channel. J. Fluid Mech. 651, 165–209. Rasu, N.G., Velusamy, K., Sundararajan, T., et al., 2014. Thermal hydraulic effect of porous blockage in fuel subassembly of sodium cooled fast reactor. Ann. Nucl. Energy 70, 64–81. Rasu, N.G., Velusamy, K., Sundararajan, T., et al., 2014. Simultaneous development of flow and temperature fields in wire-wrapped fuel pin bundles of sodium cooled fast reactor. Nucl. Eng. Des. 267, 44–60. Rehme, K., 1992. The structure of turbulence in rod bundles and the implications on natural mixing between the subchannels. Int. J. Heat Mass Transf. 35 (2), 567–581. Salama, A., 2012. CFD analysis of fast loss of flow accident in typical MTR reactor undergoing partial and full blockage: the average channel scenario. Prog. Nucl. Energy 60, 1–13. Salama, A., El-Amin, M.F., Sun, S., 2015. Three-dimensional, numerical investigation of flow and heat transfer in rectangular channels subject to partial blockage. Heat Transfer Eng. 36 (2), 152–165. Sudo, Y., Osakabe, M., 1983. Effects of partial flow blockage on core heat transfer in forced-feed reflood tests. J. Nucl. Sci. Technol. 20 (4), 322–332. Vaghetto, R., Jones, P., Goth, N., et al., 2018. Pressure measurements in a wire-wrapped 61-pin hexagonal fuel bundle. J. Fluids Eng. 140 (3), 031104. Zhukov, A.V., Kirillov, P.L., Sorokin, A.P., et al., 1994. Transverse turbulent momentum and energy exchange in the channels of complicated form. Institution of Chemical Engineers Symposium Series. Hemsphere Publishing Corporation, pp. 327.
5. Conclusion In this paper, numerical method is used to simulate the flow and heat transfer properties when flow blockage accident occurs in LBEcooled 19-pin wire-wrapped rod bundle. Based on RANS method, the influence from the blockage geometry and its axial length on rod surface temperature and cross flow between sub-channels were investigated. In order to quantitatively investigate the simulation results, several typical rods and gaps are chosen to show the influence from blockages. Based on a systematic CFD analysis covering a wide range of blockage geometry and its axial length, a close examination of surface temperature reveals that for the blockages in the inner region of the bundle, a linear dependency of blockage area on the maximum temperature difference can be found while the influence from the blockages in the side sub-channels show a relatively smaller influence. The cross flow between sub-channels downstream the blockage is also carefully investigated which reveals that blockage area attributes to the enhancement of inter-channel mixing and a linear dependency can be found between the blockage area and the maximum cross flow. Moreover, if considering the influence from the axial length of blockage, two important features can be confirmed: the extension of blockage in the flow direction may impair the heat transfer in the region downstream the blockage and the maximum rod surface temperature tends to approach a constant value as blockage axial length increases. Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.nucengdes.2019.01.019. References Bertini, H.W., 1980. Descriptions of Selected Accidents that have Occurred at Nuclear Reactor Facilities. Oak Ridge National Lab, TN (USA). CD-ADAPCO, 2012. STAR-CCM+ version 7.06 user guide. Cheng, X., Tak, N.I., 2006. CFD analysis of thermal–hydraulic behavior of heavy liquid metals in sub-channels. Nucl. Eng. Des. 236, 1874–1885. Davari, A., Mirvakili, S.M., Abedi, E., 2015. Three-dimensional analysis of flow blockage accident in Tehran MTR research reactor core using CFD. Prog. Nucl. Energy 85, 605–612. Di Piazza, I., Magugliani, F., Tarantino, M., et al., 2014. A CFD analysis of flow blockage phenomena in ALFRED LFR demo fuel assembly. Nucl. Eng. Des. 276, 202–215. Fan, W., Peng, C., Guo, Y., 2015. CFD study on inlet flow blockage accidents in rectangular fuel assembly. Nucl. Eng. Des. 292, 177–186. Goth, N., Jones, P., Nguyen, T.D., et al., 2018. PTV/PIV measurements of turbulent flows in interior subchannels of a 61-pin wire-wrapped hexagonal fuel bundle. Int. J. Heat Fluid Flow 71, 295–304.
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