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A new CFD modeling method for flow blockage accident investigations
Nuclear Engineering and Design 303 (2016) 31–41
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Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
A new CFD modeling method for flow blockage accident investigations Wenyuan Fan, Changhong Peng, Yangli Chen, Yun Guo ∗ School of Nuclear Science and Technology, University of Science and Technology of China, Hefei 230026, China
h i g h l i g h t s • • • • •
Porous-jump treatment is applied to CFD simulation on flow blockages. Porous-jump treatment predicts consistent results with direct CFD treatment. Relap5 predicts abnormal flow rate profiles in MTR SFA blockage scenario. Relap5 fails to simulate annular heat flux in blockage case of annular assembly. Porous-jump treatment provides reasonable and generalized CFD results.
a r t i c l e
i n f o
Article history: Received 31 October 2015 Received in revised form 28 March 2016 Accepted 6 April 2016
a b s t r a c t Inlet flow blockages in both flat and annular plate-type fuel assemblies are simulated by (Computational Fluid Dynamics) CFD and system analysis methods, with blockage ratio ranging from 60 to 90%. For all the blockage scenarios, mass flow rate of the blocked channel drops dramatically as blockage ratio increases, while mass flow rates of non-blocked channels are almost steady. As a result of over-simplifications, the system code fails to capture details of mass flow rate profiles of non-blocked channels and power redistribution of fuel plates. In order to acquire generalized CFD results, a new blockage modeling method is developed by using the porous-jump condition. For comparisons, direct CFD simulations are conducted toward postulated blockages. For the porous-jump treatment, conservative flow and heat transfer conditions are predicted for the blocked channel, while consistent predictions are obtained for non-blocked channels. Besides, flow fields in the blocked channel, asymmetric power redistributions of fuel plates, and complex heat transfer phenomena in annular fuel assembly are obtained and discussed. The present study indicates that the porous-jump condition is a reasonable blockage modeling method, which predicts generalized CFD results for flow blockages. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Flow blockages of coolant channels are severe accidents in nuclear reactors. Since the detection of local effects of the accident is too difficult to activate the protecting system, flow blockage may cause serious consequences. Although several experiments were conducted toward flow blockages, they failed to capture details of flow and temperature fields (Ohtsubo and Uruwashi, 1972; Kikuchi et al., 1977; Sudo and Osakabe, 1983). Compact experiment layouts and difficulties in measurement might be the main challenges for such experiments. As a result, numerical methods are always employed to investigate flow blockages.
∗ Corresponding author. E-mail addresses: [email protected] (W. Fan), [email protected] (C. Peng), [email protected] (Y. Chen), [email protected] (Y. Guo). http://dx.doi.org/10.1016/j.nucengdes.2016.04.006 0029-5493/© 2016 Elsevier B.V. All rights reserved.
One-dimensional system analysis codes were firstly applied to flow blockage analyses (Adorni et al., 2005; Lu et al., 2009a, Lu et al., 2009b; Son et al., 2015), because only limited computing resources are required. In these one-dimensional simulations, all the investigated fuel assemblies are rectangular standard fuel assemblies (SFAs) in a material test reactor (MTR), which was defined by IAEA (IAEA, 1992). The most significant reason for this selection is that flow and heat transfer phenomena inside MTR SFA could be simplified two-dimensionally. When considering the two-side heat transfer modeling ability of one-dimensional codes, it seems reasonable and adequate to simulate flow blockages inside MTR SFA with such system analysis codes. Developments in computing hardware and algorithms make larger scale CFD simulations practicable, including CFD simulations on flow blockage analyses which could provide higher dimensional results. Though there are researches about flow blockages in bundles (Piazza et al., 2014; Rasu et al., 2014), most investigations are about plate-type assemblies. For instance, Salama
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and El-Morshedy (2012) conducted two-dimensional simulations toward blockages caused by buckling of fuel plates; Salama et al. (2015) and Davari et al. (2015) simulated such blockage scenarios three-dimensionally; Fan et al. (2015) investigated blockage caused by a plan transiently, using the dynamic mesh technique. Although there are so many simulations toward flow blockages in plate-type assemblies, all investigated assemblies consist of flat fuel plates. There are annular assemblies which consist of annular fuel plates, such as assemblies in Jules Horowitz Reactor (Pegonen et al., 2016) and those in HFETR of China (Chen and Jiang, 1982). Therefore, further investigations should be conducted. On the one hand, since assembly structures are more complicated, the availability of one-dimensional codes applied in previous studies should be tested. On the other hand, by analyzing simulation results of blockage conditions, a better understanding of flow and heat transfer phenomena inside annular assemblies could be acquired. In the present paper, both FLUENT and Relap5 codes are applied to investigate flow blockages in both rectangular and annular assemblies. Firstly, based on the MTR SFA, a new blockage modeling method called porous-jump treatment is developed for CFD simulations, which is relatively independent of blockage forms. Subsequently, simulations on an annular plate-type fuel assembly are conducted, and results of different methods are compared and analyzed. 2. Simulated domain 2.1. Assembly configuration Two kinds of plate-type assemblies are taken into consideration in this study: one is an MTR SFA, which consists of flat fuel plates, as depicted in Fig. 1a; the other is newly designed by Nuclear Power
Fig. 1. Cross-sectional view of simulated assemblies (dimensions in mm).
Institute of China, which consists of annular type plates, as illustrated in Fig. 1b. Detailed parameters of both assemblies are shown in Table 1, specific heats of MTR fuel and cladding do not change with temperature, and they are 728 J/(kg K)and 892 J/(kg K) respectively. However, these values of the annular assembly vary with temperature, as shown in Table 2. For the annular assembly, there are eight coolant channels in total, in which the inner diameter of the innermost channel is 14 mm and the outer diameter of the outermost channel is 67 mm. In the present study, it is assumed that both reactors are working under normal conditions, and all the coolant channels in both investigated assemblies are hot channels. For the MTR SFA, the heat source strength is same to that given in Salama and El-Morshedy (2012). For the annular assembly, the heat source strength of the active zone in the fuel plate is shown in Fig. 2. 2.2. Investigated domain It is undeniable that flow blockages significantly change local flow and temperature fields; it is also true that flow rate distribution and heat transfer condition of the entire core could be affected. However, for the current computing ability, CFD method is too computationally expensive to be applied to investigating the whole reactor system. Therefore, proper assumptions and simplifications should be made to make CFD simulations reasonable and computationally acceptable. Though a full assembly scale modeling is affordable, according to the work of Lu et al. (2009a), Lu et al. (2009b) and Salama and El-Morshedy (2012), parameters in the blocked channel and its adjacent channel are affected mostly, while those in the third channel are slightly influenced. Therefore, only limited coolant channels in assemblies are modeled and investigated. Since coolant channels in the SFA of MTR are of high aspect ratio, and active zone occupies most of the fuel plate in the width direction, it is reasonable to construct a two-dimensional model for current study, which aims at developing a new blockage modeling method. After careful selection, seven channels including one blocked channel and six non-blocked channels are modeled, as shown in Fig. 3. For the annular type fuel assembly, due to its complicated structure, three-dimensional modeling is necessary for CFD approach. Fifteen channels in five layers are selected, among which one channel in the middle layer is blocked and other channels are non-blocked, as depicted in Fig. 4. In order to accurately locate the simulated domain, two more parameters are needed:
Fig. 2. Heat source strength of the active zone in annular assembly.
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Table 1 Specifications investigated assemblies.
coolant coolant flow direction inlet coolant temperature(K) system pressure (MPa) average velocity in coolant channels(m/s) fuel thermal conductivity(W/(m. K)) cladding thermal conductivity(W/(m. K)) fuel density (kg/m3) cladding density (kg/m3) fuel elements in an assembly dimensions(mm)
fuel thickness cladding thickness coolant channel thickness Height
Table 2 Fuel and cladding-specific heat of annular assembly. temperature(K)
273.15
373.15
473.15
573.15
fuel-specific heat (J/(kg K)) cladding-specific heat (J/(kg K))
346.13 703.53
359.32 722.26
373.27 743.39
387.12 764.52
inner diameter of the innermost channel and outer diameter of the outermost one. They are 21 and 53 mm, respectively. In addition, upper plenums and lower plenums are added to both models; therefore, mass flow rate redistribution of the blocked and nonblocked channels could be obtained. 2.3. Boundary condition Besides the selection of the simulated domain, the choice of the inlet and outlet boundary conditions is significant as well, because it is the latter that separates the simulated domain from the closed loop of the whole reactor and determines the simulation accuracy. On the basic assumption that, compared with the total pressure drop of the core, local pressure drop caused by the blockage is so small that the mass flow rate of the total reactor does not change in blocked scenarios. Then the velocity-inlet condition might be a proper choice, and it is often used for its easy setup and quick
Fig. 3. Simulated domain of the SFA. (not to scale).
MTR light water downward 311.15 0.17 3.4 158 180 680 2700 23 0.51 0.38 2.23 600
annular light water downward 318.15 2 12 50 130 5900 2700 7 0.6 0.45 2 50/1000/60 (in-inactive/active/out-inactive)
convergence. For instance, velocity-inlet is used in Lu et al. (2009a), Lu et al. (2009b). However, the previous assumption becomes less valid, especially when few channels are modeled and calculated, the rise in flow resistance of the total domain, caused by the blockage, is too large to ignore. For instance, if just the blocked channel is modeled and calculated using velocity-inlet boundary condition, no drop in the mass flow rate is predicted. Therefore, boundary conditions which suit for limited channels should be employed. Since all coolant channels are parallelized in the core, then the pressure drop is same for each single channel. Still ignoring the local blockage effect on the pressure drop of the whole core, pressures of the core inlet and outlet are same to those in the non-blocked case. Then keeping pressures of the upper plenum inlet and the lower plenum outlet unchanged in both non-blocked and blocked scenarios is a reasonable selection of boundary conditions. 3. Blockage modeling methodology In real operating conditions, flow blockages may occur in buckled and non-buckled channels. Therefore, detailed blockage forms are difficult to predict. In this paper, it is assumed that the blockage is caused by the presence of blockage materials only. When investigating flow blockages caused by both debris and buckling, researchers can combine methods provided in this paper and those
Fig. 4. Simulated domain of the annular assembly (cross-sectional view).
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suggested by Salama and El-Morshedy (2012), Salama et al. (2015) and Davari et al. (2015). For a non-buckled channel, the blockage can only occur at the inlet of the coolant channel. 3.1. System codes treatment Since system codes are firstly used for flow blockage analyses, in the present study, besides CFD simulations, Relap5 simulations are also done for comparisons. Due to the limitation in modeling the geometry details of the blockage, one-dimensional simulations are always done based on a parameter called blockage ratio, which is defined as follows: blockage area blockage ratio = the total area of the flow channel
(1)
Motor valve component is useful when considering the transient effect during the formation of the blockage (Lu et al., 2009a, Lu et al., 2009b). Assuming only steady blockage result is needed, the blockage can be simulated by changing the flow area of the single junction which is used to connect the inlet plenum and the blocked channel. Therefore, this method is applied in the present study. Using the steam generator model in Relap5, heat transfer between fuel plate and coolants on its both sides could be calculated. For the SFA case, the Relap5 model is easy to set up according to Fig. 3. However, for the annular assembly, the simulated domain must be separated into three independent parts. As shown in Fig. 5, for coolant channels, the first number identifies which layer the channel belongs to, for instance, 2 represents the innermost layer, and 6 stands for the outermost layer; for each layer, channels are numbered 01, 02 and 03, and channel 401 is selected as the blocked channel. In this treatment, each fuel plate is divided into three subplates, and power of every sub-plate is set to 1/3 of that of the corresponding full plate. 3.2. CFD treatment Blockages may be caused by different debris; unfortunately the exact shape and size of the debris are unpredictable before the formation of the blockage. CFD method can simulate flow blockage caused by any complex debris, and this directly modeling method is called direct CFD treatment in this paper. However, flow and heat transfer conditions may change with blockage forms. As a result, a generalized result cannot be acquired from a direct CFD simulation toward certain debris. Therefore, a new blockage modeling method, which is less dependent on the detailed size of the blockage, should be developed for CFD simulations.
Fig. 5. Relap5 model for annular assembly case.
3.2.1. Porous-jump treatment Inspired by the system codes modeling method, blockage ratio can also be used in CFD method. Then for different blockages, if they are of the same blocked area, they have the same blockage ratio. Compared with the exact form of the blockage, blockage ratio is a more generalized parameter. Porous media is a cell zone condition in CFD calculations. Porous-jump is the one-dimensional simplification of porous media model (ANSYS, 2009). When ignoring the permeability of the medium, the thin porous medium has a finite thickness over which the pressure change is defined as: 1 p = −Cm v2 2
(2)
where C is the pressure-jump coefficient, v is the velocity normal to the porous face, and m is the thickness of the medium. This form is quite similar to the common expression of local resistance factor, but v is the velocity of the whole porous-jump area, not the real velocity w, which is the velocity of the area open to flow, then the former formula can be expressed as follows: p = −Cm(
Af 2 1 1 ) w2 = − w2 Ap 2 2
(3)
where Af is the area open to flow, Ap is the total porous-jump area, is the common local resistance factor. Therefore, is the key input parameter for each blockage scenario, and the selection of determines the accuracy of the simulation. Considering coolants from upper plenum flow through the gap in the inlet of the blocked channel, then flow into the blocked channel, this phenomenon is similar to that illustrated in Fig. 6, of which the pressure drop coefficient can be expressed by an empirical formula (Hua and Yang, 1985): w0 2 = p/ = 2
1 + 0.707
F0 F0 1− − F1 F2
2 (4)
Obviously, since coolants in the upper plenum flow into different channels, term F1 is hard to determine. On the basis that F1 > F2 > F0 , to get a conservative prediction, it is assumed that F1 > >F0 , then the empirical formula can be written as follow: = p/
w0 2 = 2
1.707 −
F0 F2
2
(5)
3.2.2. Direct CFD treatment Besides comparisons with Relap5 code, porous-jump results are also compared with those calculated by direct CFD method. For channels in the SFA of MTR, direct CFD simulations are done toward four postulated blockages for each blockage ratio, as illustrated
Fig. 6. Flows from one plenum to another plenum through a hole.
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Fig. 7. Postulated blockages (b stands for blockage ratio).
in Fig. 7. Since it is difficult to choose a reasonable thickness for the blockage, the blockage is set to zero-thickness. Since three-dimensionally simulation on annular flow channels is computational expensive, only blockage in the middle of the inlet of the blocked channel are investigated, is the red line surrounding zone in Fig. 4. 3.2.3. Discretization Though structures of plate-type assemblies are quite compact, they are regular for meshing process. Therefore, structured mesh is employed for both assemblies to decrease the mesh size. The realizable k-ε model is quite popular in industrial flows and heat transfers. Besides, according to Salama et al. (2015), when comparing temperatures of the coolant, cladding and fuel calculated by the realizable k-ε model and one-dimensional model, very good agreement is obtained. Therefore, the realizable k-ε model is used in the present paper. Since the realizable k-ε model is designed for fully developed turbulent flows, proper near-wall treatment should be added to solve the viscosity-affected regions. For the SFA case, since more postulated blockages are investigated, the enhanced wall treatment is applied to resolve the near-wall region precisely. Therefore, meshes are generated according to the basic requirement on the near-wall mesh, that is y+ ≈ 1, in which y+ is a non-dimensional distance defined by: y+ =
u yP
(6)
where P is the fluid node which is closest to the wall, u is the friction velocity at point P, yP is the distance from point P to the wall, and is the fluid viscosity at point P. While for the annular assembly case, much more nodes are needed to discretize the three-dimensional domain, therefore scalable wall functions are employed to reduce the requirement on computing resources. In ANSYS FLUENT, these functions are based on another non-dimensional parameter y˜ ∗ = max(y∗, 11.225), in which y* is defined as follows:
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The limitator used in scalable wall functions significantly extends the application of wall functions to complex flow fields, such as inlet and outlet regions of channels, and diverse stagnant regions behind blockages in direct CFD treatment as well. Simulations are conducted by ANSYS FLUENT, and SIMPLE method is employed for pressure−velocity coupling. The gradient term and the pressure term are calculated by interpolation using the least squares cell based scheme and the PRESTO! scheme, respectively. The second-order upwind scheme is used for all the variables. Mesh sensitivity analyses are done to make the result independent of the mesh size. The maximum temperature difference, which is defined as the difference between the highest domain and the corresponding inlet temperature, is selected in the sensitivity check process. Comparisons of maximum temperature differences in nonblocked cases are shown in Table 3, for SFA and annular assembly, there are 1084432 and 36505323 nodes in the final chosen meshes, respectively. 3.3. Validation consideration Usually, CFD codes should be validated against experiment data before applications to real case studies. However, the compact structure and extremely high heat flux in the plate-type fuel assemblies make it difficult for measurements. Considering the present study aims at developing a new blockage modeling method, in order to evaluate the new method, results obtained by the new method are compared with those calculated by direct CFD methods. In addition, as will be seen in the following, the newly developed method will simplify the experiment and validation process. 4. Results and discussions Simulations are done toward four given blockage ratios: 60, 70, 80 and 90%. For each blockage scenario, besides the porousjump and Relap5 calculations, direct CFD simulations toward given blockages (illustrated in Figs. 4 and 7) are also done for comparisons. 4.1. Blockages in SFA In order to evaluate different blockage modeling methods, simulations are firstly conducted toward the SFA of MTR. On the one hand, it is widely investigated for severe accidents analyses (ElMessiry, 2000; Bousbia-salah and Hamidouche, 2005; Varvayanni et al., 2005; Hainouna and Bousbia-salah, 2010; Hamidouche and Bousbia-salah, (2010); El-Morshedy, 2011; Chatzidakisa et al., 2013). On the other hand, many flow blockage analyses have been done on it (Adorni et al., 2005; Lu et al., 2009a; Lu et al., 2009b; Son et al., 2015; Salama and El-Morshedy, 2012; Salama et al., 2015; Davari et al., 2015; Fan et al., 2015), at the same time, the requirement on computing resources is relatively small.
1/4 1/2
y∗ =
C kP yP
(7)
where C is a constant for standard and RNG k-ε models, but is a variable in realizable k-ε model; kP is turbulence kinetic energy at P.
4.1.1. Flow fields obtained by direct CFD An advantage of the direct CFD approach is that flow details caused by the blockage are fully captured, and the local effect of the blockage can be investigated. Though the blockage ratio varies
Table 3 Mesh sensitivity analysis. Plate type Mesh Nodes Cells Max temperature difference/(K)
fuel cladding coolant
SFA of MTR 1 572832 544613 45.55 45.04 39.23
2 819422 781990 45.47 44.96 39.15
3 1084432 1037763 45.48 44.99 39.15
Annular assembly 1 13096108 10983258 131.09 108.41 85.45
2 26399048 22642620 123.5 110.62 86.06
3 36505323 32439888 122.77 111.46 85.65
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Fig. 8. Flow fields around channel inlets (80% blockage, direct CFD).
from 60 to 90%, the flow fields for each postulated blockage case are quite similar. Therefore, only the direct CFD results of 80% blockage scenario are analyzed in this paper. As depicted in Fig. 8, as a sequence of the asymmetric blockage (as illustrated in Fig. 7), flow fields for case 1 and case 2 are asymmetric. However, quite different results are acquired for cases 3 and 4 (the detailed blockage forms are depicted in Fig. 7), in which investigated domains are symmetric. For case 4, the vortex sizes are a little different, but the flow field can still be regarded as a symmetric field. While obvious asymmetric effect is predicted for case 3. Actually for a symmetric channel with a sudden expansion, when the Re number exceed the critical value Rec , such phenomena would happen. Though, these phenomena have been studied experimentally, numerically and theoretically, the detailed mechanism is still unclear (Fearn et al., 1990; Hawa and Rusak, 2001; Neofytou, 2006). Therefore, symmetric flow and heat transfer results may not happen in symmetric geometries. Direct CFD results demonstrate that even though the investigated domain is symmetric, modeling of the total domain is required for each specific shape blockage. This requires more computing facilities to simulate detailed blockages.
4.1.2. Mass flow rates comparisons Mass flow rates of channel-1 are compared firstly, as shown in Fig. 9. For porous-jump treatment and Relap5 calculations, quite close mass flow rates are obtained, and the largest difference is still less than 5%. For each blockage ratio of direct CFD treatment, consistent mass flow rates are predicted for all the four postulated blockages. In 60, 70, 80 and 90% blockage scenarios, the differences between the maximum values and the minimum values are 2.0, 2.4, 3.3 and 6.9%, respectively. The little range indicates that it is proper to conduct simulations independently of the blockage shapes. However, for porous-jump treatment, detailed blockage form is ignored, then there is only one output for a given blockage ratio. As a result, when comparing a single value with several different values, there must be differences. As shown in Fig. 9, for direct CFD approach, most mass flow rates of channel-1 are higher than those predicted by porous-jump treatment, except case 4 in the 90% blockage scenario, in which the difference is about 1%. When comparing with results obtained by Relap5 and direct CFD, all mass flow rates of channel-1 are larger. Therefore, for the empirical formula used in the present study, relatively conservative mass flow rates are predicted for channel-1.
Fig. 9. Comparisons of channel-1 mass flow rate.
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Fig. 10. Mass flow rate profiles (80% blockage, direct CFD and porous-jump treatment).
Subsequently, mass flow rate profiles of both blocked and nonblocked channels are compared; again, the 80% blockage scenario is selected for comparison, as shown in Fig. 10. Close non-blocked channel mass flow rates are predicted, in which the maximum relative dissimilarity between porous-jump results and average direct CFD result is 5.6 × 10−4 . Compared with direct CFD approach, though conservative blocked channel mass flow rates are predicted by porous-jump treatment, consistent mass flow rates are predicted for non-blocked channels. For all four postulated blockages and the porous-jump treatment, V-type profiles are obtained, in which mass flow rates in channel-1 are the lowest; on each side of channel-1, the larger the channel number is, the more coolant flowing through the channel there is. This is because channels with larger numbers are further from the blockage, therefore are less affected by the blockage. However, there are some different details in these V-type profiles. For cases 1 and 2, mass flow rates of left side channels are slightly higher than those of the right side channel. For instance, mass flow rates of channel-2 on the right are 0.4 and 0.2% lower than those of channel-1 on the left in cases 1 and 2, respectively. This dissimilarity also results from relative geometric position
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between channels and the blockage, since channels on the right are closer to the blockage, and then they are more affected by the blockage. While for case 3, the investigated domain is symmetric, but flow field in channel-1 is asymmetric. However, flow fields of non-blocked channels are almost symmetric, for instance, relative difference in mass flow rates for channel-2 on both sides is 1.7 × 10−5 . For case 4, flow fields of non-blocked channels are more symmetric than case 3, relative dissimilarity in mass flow rates for channel-2 on both sides is 1.2 × 10−7 . It can be concluded that, channels that are closer to the blockage are more affected by the blockage, and relatively less coolant will flow through; for symmetric investigated domains, flow fields of non-blocked channels are almost symmetric. Since non-blocked channel mass flow rate profiles calculated by both CFD methods are quite close, and it will make the figure too crowded to present direct CFD results, therefore, Relap5 results are only compared with porous-jump results, as illustrated in Fig. 11. Though maximum dissimilarity between two methods is less than 2%, an abnormal trend is predicted in the Relap5 result. Unlike Vtype profiles obtained by both CFD methods, more coolants flow through channel-2 than channel-3, and mass flow rates of channel3 are still slightly higher than those of channel-4. In addition, this different profile is obtained by Lu et al. (2009a), Lu et al. (2009b) as well. These two opposite trends result from different mass flow rate redistribution calculation methods. In CFD approach, the redistribution is calculated by solving governing equations of the domain. Therefore, channels adjacent to channel-1 are more affected by the blockage, and are of lower mass flow rates. While one-dimensional simulations use empirical formulas which are based on area changes to calculate local pressure-drop coefficient between the plenum and the coolant channel. For non-blocked channels, flow areas stay the same. No matter how large the blockage ratio is, their inlet local pressure-drop coefficients do not change. Therefore, blockage effects outside the blocked channels could not be obtained, leading to abnormal flow distribution patterns. In addition, the higher channel-2 mass flow rate over-estimates not only the heat transfer condition of channel-2, but also that of channel-1. Because for channel-2, a larger mass flow rate obviously removes more power from the fuel plates, then less power are transferred to channel-1. 4.1.3. Heat transfer redistributions As a consequence of changes in mass flow rate profiles, heat transfer conditions of the fuel plates change, leading to heat
Fig. 11. Mass flow rates profiles of non-blocked channels (Relap5 and porous-jump).
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Fig. 12. Power proportions that transferred to channel-1.
transfer redistributions of fuel plates, especially those adjacent to channel-1. For channel-1 and channel-2, quite different mass flow rates are predicted, and then asymmetric power proportions occur in the fuel plates which are between the blocked and non-blocked channels. As shown in Fig. 12, proportions of power transferred to channel-1 are calculated for all the simulations. For two CFD approaches, close non-blocked channel mass flow rates are predicted, while direct predicted larger mass flow rates for channel-1. Therefore, for channel-1, better heat transfer capacity is calculated by direct CFD method, and the proportions are higher than those predicted by porous-jump treatment. Exceptionally, for 90% blockage scenario, mass flow rate calculated by direct CFD is smaller than that of porous-jump treatment. Therefore, the power proportion of the former is smaller than that of the latter. Though abnormal mass flow rate profiles are predicted by Relap5, the proportions are close to those simulated by porous-jump treatment. In order to illustrate the asymmetric power distribution of fuel plates clearly, power proportions and temperature fields of fuel plates (70% blockage, porous-jump treatment) are depicted in Fig. 13. Besides the plate between channel-1 and channel-2, there are also asymmetric power distributions in other plates. However, the asymmetry degree depends on mass flow rate differences on the two sides of the plate, for the plate between channel-2 and channel-3, a 2% difference is predicted; while for the plate between channel-3 and channel-4, the difference is 0.1%, and then it can be regarded as a symmetric distribution. Therefore, it can be concluded that only four plates and five channels are mostly affected by the blockage. On the other hand, the consequence of these asymmetric distributions should be discussed. The asymmetric power distribution does avoid coolants in channel-1 being over heated; however, the bad flow conditions in channel-1 and channel-2 make the temperature of the plate between them the highest. Therefore, asymmetric power distribution of the plate is only a mitigation measure for the flow blockage accident. It cannot cover the fact that a local LOFA inside the blocked channel occurs due to the blockage, and the integrity of plate might be threatened. 4.2. Blockages in annular assembly According to above simulations on the SFA of MTR, porous-jump treatment results agree well with those calculated by direct CFD, while Relap5 fails in capturing mass flow rate distribution patterns.
Fig. 13. Temperature fields of fuel plates and power proportions (70% blockage, porous-jump treatment).
These methods are subsequently applied to investigation on flow blockages in annular assembly. 4.2.1. Mass flow rate comparisons Corresponding mass flow rates are depicted in Fig. 14. For mass flow rate of the blocked channel, like predictions of the SFA, close results are obtained, and mass flow rates calculated by both porousjump treatment and Relap5 are a little lower than that calculated by direct CFD method. Also, the presence of the blockage leads to drop in the total mass flow rate. The trends of total mass flow rate profiles are quite similar to those of the blocked channel, since they are almost parallel to each other. When checking mass flow rates of all the non-blocked channels, all the profiles almost stay unchanged in different blockage scenarios. Actually, when considering the mass flow rate in each single non-blocked channel, the profile is still stable. For instance, the average mass flow rate of channel 1 and channel 2 (which are in the same layer as the blocked channel, as depicted in Fig. 4) varies little with the blockage ratio in all three methods, in which the difference is no more than 0.7%. After checking previous simulations results of the SFA, it is found that for each non-blocked channel, there are 24 mass flow rate predictions for different blockage ratios and different values, the largest dissimilarity of these values is less than 1.4%. Therefore, it can be concluded that only the blocked channel is mostly affected when considering the mass flow rate redistribution effects of the blockage. 4.2.2. Heat transfer comparisons For heat transfer redistribution, the average outlet coolant temperature of the blocked channel and the lower plenum are compared respectively. As shown in Fig. 15, the outlet temperatures of the lower plenum are in accord with each other, while those of the blocked channel are not. The difference between values that calculated by two CFD method results from the dissimilarity in mass flow rate prediction. However, a nearly 20 K difference between values calculated by Relap5 code and porous-jump treatment in 90% blockage scenario cannot be explained by mass flow rate difference only, because of the quite similar prediction in mass flow rate of these approaches. A modification is done toward Relap5 results based on following discussions.
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Fig. 14. Mass flow rate comparisons (annular assembly).
This dissimilarity is caused by different heat transfer modeling method in each approach. As mentioned above, for Relap5 simulation, only radical heat transfer is considered. While in both CFD approaches, heat transfer is calculated three-dimensionally correspondingly to the mass flow rate redistribution. Take the porous-jump treatment results of 90% blockage for instance, as illustrated in Fig. 16, in which velocity vector is colored by temperature. For the blocked channel, coolants are of low speed and high temperature, worsening heat transfer condition of fuel plates that adjacent to the blocked channel. However, other parts of these fuel plates are well-cooled because of the better heat transfer condition. Dividing fuel plates adjacent to the blocked channels into three parts: blocked, side-1 and side-2, just like the Relap5 modeling process does. However, this is a virtual separation for the sake of easy demonstration, these parts are connected to each other
Fig. 15. Outlet temperature comparisons.
in the modeling and calculating process. As depicted in Fig. 17, the larger the blockage ratio is, the higher average temperature is predicted for fuels around the blocked channel. In 90% blockage scenario, average temperature of blocked part is 44 K higher than that of side parts. This will lead to annular heat transfer, driven by annular temperature difference, from the fuel adjacent to the blocked channel to the side fuels, as illustrated in Fig. 18. Since the annular temperature difference increases dramatically with the blockage percentage, more power will transfer annularly.
Fig. 16. Flow and temperature fields (90% blockage, porous-jump treatment).
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non-blocked case. The extra temperature rise, therefore, becomes much larger in high blockage ratios, due to the relatively high extra energy and quite low mass flow rate. All the extra temperatures are calculated and subtracted from the original outlet temperature of the blocked channel, as shown in Fig. 15 (blocked channel-Relap5modified). The modified values are much closer to those calculated by CFD methods.
5. Conclusions and outlook
Fig. 17. Average temperature of the fuel around the blocked channel (porous-jump treatment).
While in Relap5 simulation, the power of the blocked part fuel is fixed to a third of the total power of the layer, therefore, an extra energy is added to the fuel adjacent to the blocked channel. However, it is difficult to calculate the extra energy in such a complex geometry. Then, for the sake of easy illustration, ignoring heat transfer in fins, only power transferred annularly in the fuel plates is considered, as shown in Fig. 18. Obviously, an extra temperature rise of the coolant is predicted. The larger the blockage percentage is, the hotter coolant in the blocked channel is. Also, as shown in Fig. 14, mass flow rate of the blocked channel drops sharply with the blockage ratio. In 90% blockage scenario, the corresponding blocked channel mass flow rate is only 15% of that in
Inlet flow blockages are investigated by Relap5, direct CFD and porous-jump treatments in this study. The results indicate that Relap5 is a very powerful system analysis code to investigate flow blockage accidents, which can simulate both flow and power redistributions. However, due to the limitation of one-dimensional modeling, abnormal mass flow rate profiles are predicted. Moreover, when applying this code to the annular fuel assembly, it fails to simulate the complex heat transfer effects caused by the blockage. Therefore, it is not proper to use system codes to investigate flow blockages at assembly scales, especially those occur in assemblies which are of complicated geometries. The direct CFD simulations confirm that blockage form affects flow fields significantly. Nevertheless, quite consistent results are acquired for four postulated blockages, indicating that blockage ratio is a reasonable input for flow blockage analyses. Based on this conclusion and innovated by Relap5, the porous-jump treatment is employed to flow blockage investigations, and good agreements are acquired when comparing mass flow rate and heat transfer redistributions with direct CFD results. This indicates that porous-jump treatment could provide generalized and reasonable predictions for flow blockage accidents. The current study shows the significance of applying CFD methods to flow blockage investigations and the advantages of porous-jump treatment. However, experiments are needed to validate and modify these methods. Though direct thermal-hydraulics experiments are hard to conduct, experiments on local resistances are more practical and will provide more accurate and reasonable input for further simulations.
Fig. 18. Heat fluxes in fuel plates (90% blockage, porous-jump treatment).
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Acknowledgements This work was supported by the Science and Technology on Reactor System Design Technology Laboratory of Nuclear Power Institute of China [grant number HT-CENT-02-2014001]; and the National Natural Science Foundation of China [grant number 11305169]. References Adorni, M., Bousbia-Salah, A., Hamidouche, T., et al., 2005. Analysis of partial and total blockage of a single fuel assembly of an MTR research reactor core. Ann. Nucl. Energ. 32, 1679–1692. ANSYS, Inc., 2009. ANASYS FLUENT 12.0 Theory Guide. Canonsburg, PA, USA. Bousbia-salah, A., Hamidouche, T., 2005. Analysis of the IAEA research reactor benchmark problem by the RETRAC-PC code. Nucl. Eng. Des. 235, 661–674. Chatzidakisa, S., Ikonomopoulosa, A., Ridikasb, D., 2013. Evaluation of RELAP5/MOD3 behavior against loss of flow experimental results from two research reactor facilities. Nucl. Eng. Des. 255, 321–329. Chen, D., Jiang, P., 1982. The measurements of the dynamic state thermal parameters of HFETR fuel element: the loss-of-power accident, the shutdown cooling and the decay heat experiment. Nucl. Power Eng. 3, 6–12. 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. Energ. 85, 605–612. El-Messiry, A.M., 2000. Cobalt irradiation box ejection accident of ETRR-2. Nucl. Eng. Des. 198, 287–293. El-Morshedy, S.E., 2011. Prediction, analysis and solution of the flow inversion phenomenon in a typical MTR-reactor with upward core cooling. Nucl. Eng. Des. 241, 226–235. Fan, W., Peng, C., Guo, Y., 2015. CFD study on inlet flow blockage accidents in rectangular fuel assembly. Nucl. Eng. Des. 292, 177–186. Fearn, R.M., Mullin, T., Cliffe, K.A., 1990. Nonlinear flow phenomena in a symmetric sudden expansion. J. Fluid Mech. 211, 595–608. 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. Energ. 70, 64–81.
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Hawa, T., Rusak, Z., 2001. The dynamics of a laminar flow in a symmetric channel with a sudden expansion. J. Fluid Mech. 436, 283–320. Hua, S., Yang, X., 1985. Practical Manual of Flow Resistance. National Defence Industry Press, Beijing, pp. 146. IAEA-TECDOC-643, 1992. Research reactor core conversion guidebook, 3. Analytical verification (Appendices G and H). Kikuchi, Y., Daigo, Y., Ohtsubo, A., 1977. Local sodium boiling behind local flow blockage in simulated LMFBR fuel subassembly. J. Nucl. Sci. Technol. 14, 774–790. Lu, Q., Qiu, S., Su, G.H., 2009a. Flow blockage analysis of a channel in a typical material test reactor core. Nucl. Eng. Des. 239, 45–50. Lu, Q., Qiu, S., Su, G.H., 2009b. Development of a thermal–hydraulic analysis code for research reactors with plate fuels. Ann. Nucl. Energ. 36, 433–447. Neofytou, P., 2006. Transition to asymmetry of generalised Newtown fluid flows through a symmetric sudden expansion. J. Non-Newton. Fluid Mech. 133, 132–140. Ohtsubo, A., Uruwashi, S., 1972. Stagnant fluid due to local flow blockage. J. Nucl. Sci. Technol. 9, 433–434. Pegonen, R., Bourdon, S., Gonnier, C., et al., 2016. Hot fuel element thermalhydraulics in the Jules Horowitz Reactor. Nucl. Eng. Des. 300, 149–160. Piazza, I.D., 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. 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 Trans. Eng. 36, 152–165. Salama, A., El-Morshedy, S.E., 2012. CFD simulation of flow blockage through a coolant channel of a typical material testing reactor core. Ann. Nucl. Energ. 41, 26–39. Son, H.M., Yang, S.H., Park, C., et al., 2015. Transient thermal-hydraulic analysis of complete single channel blockage accident of generic 10MW research reactor. Ann. Nucl. Energ. 75, 44–53. Sudo, Y., Osakabe, M., 1983. Effects of partial flow blockage on core heat transfer in forced-feed reflood tests. J. Nucl. Sci. Technol. 20, 322–332. Varvayanni, M., Stakakis, E., Catsaros, N., Antonopoulos-Domis, M., 2005. Void induced reactivity in a mixed MTR core. Nucl. Eng. Des. 235, 855–865. Hainouna, A., Ghazia, N., Mansour Abdul-Moaizb, B., 2010. Safety analysis of the IAEA reference research reactor during loss of flow accident using the code MERSAT. Nucl. Eng. Des. 240, 1132–1138. Hamidouche, T., Bousbia-salah, A., 2010. Assessment of RELAP5 point kinetic model against reactivity insertion transient in the IAEA 10MW MTR research reactor. Nucl. Eng. Des. 240, 672–677.
Contents lists available at ScienceDirect
Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
A new CFD modeling method for flow blockage accident investigations Wenyuan Fan, Changhong Peng, Yangli Chen, Yun Guo ∗ School of Nuclear Science and Technology, University of Science and Technology of China, Hefei 230026, China
h i g h l i g h t s • • • • •
Porous-jump treatment is applied to CFD simulation on flow blockages. Porous-jump treatment predicts consistent results with direct CFD treatment. Relap5 predicts abnormal flow rate profiles in MTR SFA blockage scenario. Relap5 fails to simulate annular heat flux in blockage case of annular assembly. Porous-jump treatment provides reasonable and generalized CFD results.
a r t i c l e
i n f o
Article history: Received 31 October 2015 Received in revised form 28 March 2016 Accepted 6 April 2016
a b s t r a c t Inlet flow blockages in both flat and annular plate-type fuel assemblies are simulated by (Computational Fluid Dynamics) CFD and system analysis methods, with blockage ratio ranging from 60 to 90%. For all the blockage scenarios, mass flow rate of the blocked channel drops dramatically as blockage ratio increases, while mass flow rates of non-blocked channels are almost steady. As a result of over-simplifications, the system code fails to capture details of mass flow rate profiles of non-blocked channels and power redistribution of fuel plates. In order to acquire generalized CFD results, a new blockage modeling method is developed by using the porous-jump condition. For comparisons, direct CFD simulations are conducted toward postulated blockages. For the porous-jump treatment, conservative flow and heat transfer conditions are predicted for the blocked channel, while consistent predictions are obtained for non-blocked channels. Besides, flow fields in the blocked channel, asymmetric power redistributions of fuel plates, and complex heat transfer phenomena in annular fuel assembly are obtained and discussed. The present study indicates that the porous-jump condition is a reasonable blockage modeling method, which predicts generalized CFD results for flow blockages. © 2016 Elsevier B.V. All rights reserved.
1. Introduction Flow blockages of coolant channels are severe accidents in nuclear reactors. Since the detection of local effects of the accident is too difficult to activate the protecting system, flow blockage may cause serious consequences. Although several experiments were conducted toward flow blockages, they failed to capture details of flow and temperature fields (Ohtsubo and Uruwashi, 1972; Kikuchi et al., 1977; Sudo and Osakabe, 1983). Compact experiment layouts and difficulties in measurement might be the main challenges for such experiments. As a result, numerical methods are always employed to investigate flow blockages.
∗ Corresponding author. E-mail addresses: [email protected] (W. Fan), [email protected] (C. Peng), [email protected] (Y. Chen), [email protected] (Y. Guo). http://dx.doi.org/10.1016/j.nucengdes.2016.04.006 0029-5493/© 2016 Elsevier B.V. All rights reserved.
One-dimensional system analysis codes were firstly applied to flow blockage analyses (Adorni et al., 2005; Lu et al., 2009a, Lu et al., 2009b; Son et al., 2015), because only limited computing resources are required. In these one-dimensional simulations, all the investigated fuel assemblies are rectangular standard fuel assemblies (SFAs) in a material test reactor (MTR), which was defined by IAEA (IAEA, 1992). The most significant reason for this selection is that flow and heat transfer phenomena inside MTR SFA could be simplified two-dimensionally. When considering the two-side heat transfer modeling ability of one-dimensional codes, it seems reasonable and adequate to simulate flow blockages inside MTR SFA with such system analysis codes. Developments in computing hardware and algorithms make larger scale CFD simulations practicable, including CFD simulations on flow blockage analyses which could provide higher dimensional results. Though there are researches about flow blockages in bundles (Piazza et al., 2014; Rasu et al., 2014), most investigations are about plate-type assemblies. For instance, Salama
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and El-Morshedy (2012) conducted two-dimensional simulations toward blockages caused by buckling of fuel plates; Salama et al. (2015) and Davari et al. (2015) simulated such blockage scenarios three-dimensionally; Fan et al. (2015) investigated blockage caused by a plan transiently, using the dynamic mesh technique. Although there are so many simulations toward flow blockages in plate-type assemblies, all investigated assemblies consist of flat fuel plates. There are annular assemblies which consist of annular fuel plates, such as assemblies in Jules Horowitz Reactor (Pegonen et al., 2016) and those in HFETR of China (Chen and Jiang, 1982). Therefore, further investigations should be conducted. On the one hand, since assembly structures are more complicated, the availability of one-dimensional codes applied in previous studies should be tested. On the other hand, by analyzing simulation results of blockage conditions, a better understanding of flow and heat transfer phenomena inside annular assemblies could be acquired. In the present paper, both FLUENT and Relap5 codes are applied to investigate flow blockages in both rectangular and annular assemblies. Firstly, based on the MTR SFA, a new blockage modeling method called porous-jump treatment is developed for CFD simulations, which is relatively independent of blockage forms. Subsequently, simulations on an annular plate-type fuel assembly are conducted, and results of different methods are compared and analyzed. 2. Simulated domain 2.1. Assembly configuration Two kinds of plate-type assemblies are taken into consideration in this study: one is an MTR SFA, which consists of flat fuel plates, as depicted in Fig. 1a; the other is newly designed by Nuclear Power
Fig. 1. Cross-sectional view of simulated assemblies (dimensions in mm).
Institute of China, which consists of annular type plates, as illustrated in Fig. 1b. Detailed parameters of both assemblies are shown in Table 1, specific heats of MTR fuel and cladding do not change with temperature, and they are 728 J/(kg K)and 892 J/(kg K) respectively. However, these values of the annular assembly vary with temperature, as shown in Table 2. For the annular assembly, there are eight coolant channels in total, in which the inner diameter of the innermost channel is 14 mm and the outer diameter of the outermost channel is 67 mm. In the present study, it is assumed that both reactors are working under normal conditions, and all the coolant channels in both investigated assemblies are hot channels. For the MTR SFA, the heat source strength is same to that given in Salama and El-Morshedy (2012). For the annular assembly, the heat source strength of the active zone in the fuel plate is shown in Fig. 2. 2.2. Investigated domain It is undeniable that flow blockages significantly change local flow and temperature fields; it is also true that flow rate distribution and heat transfer condition of the entire core could be affected. However, for the current computing ability, CFD method is too computationally expensive to be applied to investigating the whole reactor system. Therefore, proper assumptions and simplifications should be made to make CFD simulations reasonable and computationally acceptable. Though a full assembly scale modeling is affordable, according to the work of Lu et al. (2009a), Lu et al. (2009b) and Salama and El-Morshedy (2012), parameters in the blocked channel and its adjacent channel are affected mostly, while those in the third channel are slightly influenced. Therefore, only limited coolant channels in assemblies are modeled and investigated. Since coolant channels in the SFA of MTR are of high aspect ratio, and active zone occupies most of the fuel plate in the width direction, it is reasonable to construct a two-dimensional model for current study, which aims at developing a new blockage modeling method. After careful selection, seven channels including one blocked channel and six non-blocked channels are modeled, as shown in Fig. 3. For the annular type fuel assembly, due to its complicated structure, three-dimensional modeling is necessary for CFD approach. Fifteen channels in five layers are selected, among which one channel in the middle layer is blocked and other channels are non-blocked, as depicted in Fig. 4. In order to accurately locate the simulated domain, two more parameters are needed:
Fig. 2. Heat source strength of the active zone in annular assembly.
W. Fan et al. / Nuclear Engineering and Design 303 (2016) 31–41
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Table 1 Specifications investigated assemblies.
coolant coolant flow direction inlet coolant temperature(K) system pressure (MPa) average velocity in coolant channels(m/s) fuel thermal conductivity(W/(m. K)) cladding thermal conductivity(W/(m. K)) fuel density (kg/m3) cladding density (kg/m3) fuel elements in an assembly dimensions(mm)
fuel thickness cladding thickness coolant channel thickness Height
Table 2 Fuel and cladding-specific heat of annular assembly. temperature(K)
273.15
373.15
473.15
573.15
fuel-specific heat (J/(kg K)) cladding-specific heat (J/(kg K))
346.13 703.53
359.32 722.26
373.27 743.39
387.12 764.52
inner diameter of the innermost channel and outer diameter of the outermost one. They are 21 and 53 mm, respectively. In addition, upper plenums and lower plenums are added to both models; therefore, mass flow rate redistribution of the blocked and nonblocked channels could be obtained. 2.3. Boundary condition Besides the selection of the simulated domain, the choice of the inlet and outlet boundary conditions is significant as well, because it is the latter that separates the simulated domain from the closed loop of the whole reactor and determines the simulation accuracy. On the basic assumption that, compared with the total pressure drop of the core, local pressure drop caused by the blockage is so small that the mass flow rate of the total reactor does not change in blocked scenarios. Then the velocity-inlet condition might be a proper choice, and it is often used for its easy setup and quick
Fig. 3. Simulated domain of the SFA. (not to scale).
MTR light water downward 311.15 0.17 3.4 158 180 680 2700 23 0.51 0.38 2.23 600
annular light water downward 318.15 2 12 50 130 5900 2700 7 0.6 0.45 2 50/1000/60 (in-inactive/active/out-inactive)
convergence. For instance, velocity-inlet is used in Lu et al. (2009a), Lu et al. (2009b). However, the previous assumption becomes less valid, especially when few channels are modeled and calculated, the rise in flow resistance of the total domain, caused by the blockage, is too large to ignore. For instance, if just the blocked channel is modeled and calculated using velocity-inlet boundary condition, no drop in the mass flow rate is predicted. Therefore, boundary conditions which suit for limited channels should be employed. Since all coolant channels are parallelized in the core, then the pressure drop is same for each single channel. Still ignoring the local blockage effect on the pressure drop of the whole core, pressures of the core inlet and outlet are same to those in the non-blocked case. Then keeping pressures of the upper plenum inlet and the lower plenum outlet unchanged in both non-blocked and blocked scenarios is a reasonable selection of boundary conditions. 3. Blockage modeling methodology In real operating conditions, flow blockages may occur in buckled and non-buckled channels. Therefore, detailed blockage forms are difficult to predict. In this paper, it is assumed that the blockage is caused by the presence of blockage materials only. When investigating flow blockages caused by both debris and buckling, researchers can combine methods provided in this paper and those
Fig. 4. Simulated domain of the annular assembly (cross-sectional view).
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suggested by Salama and El-Morshedy (2012), Salama et al. (2015) and Davari et al. (2015). For a non-buckled channel, the blockage can only occur at the inlet of the coolant channel. 3.1. System codes treatment Since system codes are firstly used for flow blockage analyses, in the present study, besides CFD simulations, Relap5 simulations are also done for comparisons. Due to the limitation in modeling the geometry details of the blockage, one-dimensional simulations are always done based on a parameter called blockage ratio, which is defined as follows: blockage area blockage ratio = the total area of the flow channel
(1)
Motor valve component is useful when considering the transient effect during the formation of the blockage (Lu et al., 2009a, Lu et al., 2009b). Assuming only steady blockage result is needed, the blockage can be simulated by changing the flow area of the single junction which is used to connect the inlet plenum and the blocked channel. Therefore, this method is applied in the present study. Using the steam generator model in Relap5, heat transfer between fuel plate and coolants on its both sides could be calculated. For the SFA case, the Relap5 model is easy to set up according to Fig. 3. However, for the annular assembly, the simulated domain must be separated into three independent parts. As shown in Fig. 5, for coolant channels, the first number identifies which layer the channel belongs to, for instance, 2 represents the innermost layer, and 6 stands for the outermost layer; for each layer, channels are numbered 01, 02 and 03, and channel 401 is selected as the blocked channel. In this treatment, each fuel plate is divided into three subplates, and power of every sub-plate is set to 1/3 of that of the corresponding full plate. 3.2. CFD treatment Blockages may be caused by different debris; unfortunately the exact shape and size of the debris are unpredictable before the formation of the blockage. CFD method can simulate flow blockage caused by any complex debris, and this directly modeling method is called direct CFD treatment in this paper. However, flow and heat transfer conditions may change with blockage forms. As a result, a generalized result cannot be acquired from a direct CFD simulation toward certain debris. Therefore, a new blockage modeling method, which is less dependent on the detailed size of the blockage, should be developed for CFD simulations.
Fig. 5. Relap5 model for annular assembly case.
3.2.1. Porous-jump treatment Inspired by the system codes modeling method, blockage ratio can also be used in CFD method. Then for different blockages, if they are of the same blocked area, they have the same blockage ratio. Compared with the exact form of the blockage, blockage ratio is a more generalized parameter. Porous media is a cell zone condition in CFD calculations. Porous-jump is the one-dimensional simplification of porous media model (ANSYS, 2009). When ignoring the permeability of the medium, the thin porous medium has a finite thickness over which the pressure change is defined as: 1 p = −Cm v2 2
(2)
where C is the pressure-jump coefficient, v is the velocity normal to the porous face, and m is the thickness of the medium. This form is quite similar to the common expression of local resistance factor, but v is the velocity of the whole porous-jump area, not the real velocity w, which is the velocity of the area open to flow, then the former formula can be expressed as follows: p = −Cm(
Af 2 1 1 ) w2 = − w2 Ap 2 2
(3)
where Af is the area open to flow, Ap is the total porous-jump area, is the common local resistance factor. Therefore, is the key input parameter for each blockage scenario, and the selection of determines the accuracy of the simulation. Considering coolants from upper plenum flow through the gap in the inlet of the blocked channel, then flow into the blocked channel, this phenomenon is similar to that illustrated in Fig. 6, of which the pressure drop coefficient can be expressed by an empirical formula (Hua and Yang, 1985): w0 2 = p/ = 2
1 + 0.707
F0 F0 1− − F1 F2
2 (4)
Obviously, since coolants in the upper plenum flow into different channels, term F1 is hard to determine. On the basis that F1 > F2 > F0 , to get a conservative prediction, it is assumed that F1 > >F0 , then the empirical formula can be written as follow: = p/
w0 2 = 2
1.707 −
F0 F2
2
(5)
3.2.2. Direct CFD treatment Besides comparisons with Relap5 code, porous-jump results are also compared with those calculated by direct CFD method. For channels in the SFA of MTR, direct CFD simulations are done toward four postulated blockages for each blockage ratio, as illustrated
Fig. 6. Flows from one plenum to another plenum through a hole.
W. Fan et al. / Nuclear Engineering and Design 303 (2016) 31–41
Fig. 7. Postulated blockages (b stands for blockage ratio).
in Fig. 7. Since it is difficult to choose a reasonable thickness for the blockage, the blockage is set to zero-thickness. Since three-dimensionally simulation on annular flow channels is computational expensive, only blockage in the middle of the inlet of the blocked channel are investigated, is the red line surrounding zone in Fig. 4. 3.2.3. Discretization Though structures of plate-type assemblies are quite compact, they are regular for meshing process. Therefore, structured mesh is employed for both assemblies to decrease the mesh size. The realizable k-ε model is quite popular in industrial flows and heat transfers. Besides, according to Salama et al. (2015), when comparing temperatures of the coolant, cladding and fuel calculated by the realizable k-ε model and one-dimensional model, very good agreement is obtained. Therefore, the realizable k-ε model is used in the present paper. Since the realizable k-ε model is designed for fully developed turbulent flows, proper near-wall treatment should be added to solve the viscosity-affected regions. For the SFA case, since more postulated blockages are investigated, the enhanced wall treatment is applied to resolve the near-wall region precisely. Therefore, meshes are generated according to the basic requirement on the near-wall mesh, that is y+ ≈ 1, in which y+ is a non-dimensional distance defined by: y+ =
u yP
(6)
where P is the fluid node which is closest to the wall, u is the friction velocity at point P, yP is the distance from point P to the wall, and is the fluid viscosity at point P. While for the annular assembly case, much more nodes are needed to discretize the three-dimensional domain, therefore scalable wall functions are employed to reduce the requirement on computing resources. In ANSYS FLUENT, these functions are based on another non-dimensional parameter y˜ ∗ = max(y∗, 11.225), in which y* is defined as follows:
35
The limitator used in scalable wall functions significantly extends the application of wall functions to complex flow fields, such as inlet and outlet regions of channels, and diverse stagnant regions behind blockages in direct CFD treatment as well. Simulations are conducted by ANSYS FLUENT, and SIMPLE method is employed for pressure−velocity coupling. The gradient term and the pressure term are calculated by interpolation using the least squares cell based scheme and the PRESTO! scheme, respectively. The second-order upwind scheme is used for all the variables. Mesh sensitivity analyses are done to make the result independent of the mesh size. The maximum temperature difference, which is defined as the difference between the highest domain and the corresponding inlet temperature, is selected in the sensitivity check process. Comparisons of maximum temperature differences in nonblocked cases are shown in Table 3, for SFA and annular assembly, there are 1084432 and 36505323 nodes in the final chosen meshes, respectively. 3.3. Validation consideration Usually, CFD codes should be validated against experiment data before applications to real case studies. However, the compact structure and extremely high heat flux in the plate-type fuel assemblies make it difficult for measurements. Considering the present study aims at developing a new blockage modeling method, in order to evaluate the new method, results obtained by the new method are compared with those calculated by direct CFD methods. In addition, as will be seen in the following, the newly developed method will simplify the experiment and validation process. 4. Results and discussions Simulations are done toward four given blockage ratios: 60, 70, 80 and 90%. For each blockage scenario, besides the porousjump and Relap5 calculations, direct CFD simulations toward given blockages (illustrated in Figs. 4 and 7) are also done for comparisons. 4.1. Blockages in SFA In order to evaluate different blockage modeling methods, simulations are firstly conducted toward the SFA of MTR. On the one hand, it is widely investigated for severe accidents analyses (ElMessiry, 2000; Bousbia-salah and Hamidouche, 2005; Varvayanni et al., 2005; Hainouna and Bousbia-salah, 2010; Hamidouche and Bousbia-salah, (2010); El-Morshedy, 2011; Chatzidakisa et al., 2013). On the other hand, many flow blockage analyses have been done on it (Adorni et al., 2005; Lu et al., 2009a; Lu et al., 2009b; Son et al., 2015; Salama and El-Morshedy, 2012; Salama et al., 2015; Davari et al., 2015; Fan et al., 2015), at the same time, the requirement on computing resources is relatively small.
1/4 1/2
y∗ =
C kP yP
(7)
where C is a constant for standard and RNG k-ε models, but is a variable in realizable k-ε model; kP is turbulence kinetic energy at P.
4.1.1. Flow fields obtained by direct CFD An advantage of the direct CFD approach is that flow details caused by the blockage are fully captured, and the local effect of the blockage can be investigated. Though the blockage ratio varies
Table 3 Mesh sensitivity analysis. Plate type Mesh Nodes Cells Max temperature difference/(K)
fuel cladding coolant
SFA of MTR 1 572832 544613 45.55 45.04 39.23
2 819422 781990 45.47 44.96 39.15
3 1084432 1037763 45.48 44.99 39.15
Annular assembly 1 13096108 10983258 131.09 108.41 85.45
2 26399048 22642620 123.5 110.62 86.06
3 36505323 32439888 122.77 111.46 85.65
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Fig. 8. Flow fields around channel inlets (80% blockage, direct CFD).
from 60 to 90%, the flow fields for each postulated blockage case are quite similar. Therefore, only the direct CFD results of 80% blockage scenario are analyzed in this paper. As depicted in Fig. 8, as a sequence of the asymmetric blockage (as illustrated in Fig. 7), flow fields for case 1 and case 2 are asymmetric. However, quite different results are acquired for cases 3 and 4 (the detailed blockage forms are depicted in Fig. 7), in which investigated domains are symmetric. For case 4, the vortex sizes are a little different, but the flow field can still be regarded as a symmetric field. While obvious asymmetric effect is predicted for case 3. Actually for a symmetric channel with a sudden expansion, when the Re number exceed the critical value Rec , such phenomena would happen. Though, these phenomena have been studied experimentally, numerically and theoretically, the detailed mechanism is still unclear (Fearn et al., 1990; Hawa and Rusak, 2001; Neofytou, 2006). Therefore, symmetric flow and heat transfer results may not happen in symmetric geometries. Direct CFD results demonstrate that even though the investigated domain is symmetric, modeling of the total domain is required for each specific shape blockage. This requires more computing facilities to simulate detailed blockages.
4.1.2. Mass flow rates comparisons Mass flow rates of channel-1 are compared firstly, as shown in Fig. 9. For porous-jump treatment and Relap5 calculations, quite close mass flow rates are obtained, and the largest difference is still less than 5%. For each blockage ratio of direct CFD treatment, consistent mass flow rates are predicted for all the four postulated blockages. In 60, 70, 80 and 90% blockage scenarios, the differences between the maximum values and the minimum values are 2.0, 2.4, 3.3 and 6.9%, respectively. The little range indicates that it is proper to conduct simulations independently of the blockage shapes. However, for porous-jump treatment, detailed blockage form is ignored, then there is only one output for a given blockage ratio. As a result, when comparing a single value with several different values, there must be differences. As shown in Fig. 9, for direct CFD approach, most mass flow rates of channel-1 are higher than those predicted by porous-jump treatment, except case 4 in the 90% blockage scenario, in which the difference is about 1%. When comparing with results obtained by Relap5 and direct CFD, all mass flow rates of channel-1 are larger. Therefore, for the empirical formula used in the present study, relatively conservative mass flow rates are predicted for channel-1.
Fig. 9. Comparisons of channel-1 mass flow rate.
W. Fan et al. / Nuclear Engineering and Design 303 (2016) 31–41
Fig. 10. Mass flow rate profiles (80% blockage, direct CFD and porous-jump treatment).
Subsequently, mass flow rate profiles of both blocked and nonblocked channels are compared; again, the 80% blockage scenario is selected for comparison, as shown in Fig. 10. Close non-blocked channel mass flow rates are predicted, in which the maximum relative dissimilarity between porous-jump results and average direct CFD result is 5.6 × 10−4 . Compared with direct CFD approach, though conservative blocked channel mass flow rates are predicted by porous-jump treatment, consistent mass flow rates are predicted for non-blocked channels. For all four postulated blockages and the porous-jump treatment, V-type profiles are obtained, in which mass flow rates in channel-1 are the lowest; on each side of channel-1, the larger the channel number is, the more coolant flowing through the channel there is. This is because channels with larger numbers are further from the blockage, therefore are less affected by the blockage. However, there are some different details in these V-type profiles. For cases 1 and 2, mass flow rates of left side channels are slightly higher than those of the right side channel. For instance, mass flow rates of channel-2 on the right are 0.4 and 0.2% lower than those of channel-1 on the left in cases 1 and 2, respectively. This dissimilarity also results from relative geometric position
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between channels and the blockage, since channels on the right are closer to the blockage, and then they are more affected by the blockage. While for case 3, the investigated domain is symmetric, but flow field in channel-1 is asymmetric. However, flow fields of non-blocked channels are almost symmetric, for instance, relative difference in mass flow rates for channel-2 on both sides is 1.7 × 10−5 . For case 4, flow fields of non-blocked channels are more symmetric than case 3, relative dissimilarity in mass flow rates for channel-2 on both sides is 1.2 × 10−7 . It can be concluded that, channels that are closer to the blockage are more affected by the blockage, and relatively less coolant will flow through; for symmetric investigated domains, flow fields of non-blocked channels are almost symmetric. Since non-blocked channel mass flow rate profiles calculated by both CFD methods are quite close, and it will make the figure too crowded to present direct CFD results, therefore, Relap5 results are only compared with porous-jump results, as illustrated in Fig. 11. Though maximum dissimilarity between two methods is less than 2%, an abnormal trend is predicted in the Relap5 result. Unlike Vtype profiles obtained by both CFD methods, more coolants flow through channel-2 than channel-3, and mass flow rates of channel3 are still slightly higher than those of channel-4. In addition, this different profile is obtained by Lu et al. (2009a), Lu et al. (2009b) as well. These two opposite trends result from different mass flow rate redistribution calculation methods. In CFD approach, the redistribution is calculated by solving governing equations of the domain. Therefore, channels adjacent to channel-1 are more affected by the blockage, and are of lower mass flow rates. While one-dimensional simulations use empirical formulas which are based on area changes to calculate local pressure-drop coefficient between the plenum and the coolant channel. For non-blocked channels, flow areas stay the same. No matter how large the blockage ratio is, their inlet local pressure-drop coefficients do not change. Therefore, blockage effects outside the blocked channels could not be obtained, leading to abnormal flow distribution patterns. In addition, the higher channel-2 mass flow rate over-estimates not only the heat transfer condition of channel-2, but also that of channel-1. Because for channel-2, a larger mass flow rate obviously removes more power from the fuel plates, then less power are transferred to channel-1. 4.1.3. Heat transfer redistributions As a consequence of changes in mass flow rate profiles, heat transfer conditions of the fuel plates change, leading to heat
Fig. 11. Mass flow rates profiles of non-blocked channels (Relap5 and porous-jump).
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Fig. 12. Power proportions that transferred to channel-1.
transfer redistributions of fuel plates, especially those adjacent to channel-1. For channel-1 and channel-2, quite different mass flow rates are predicted, and then asymmetric power proportions occur in the fuel plates which are between the blocked and non-blocked channels. As shown in Fig. 12, proportions of power transferred to channel-1 are calculated for all the simulations. For two CFD approaches, close non-blocked channel mass flow rates are predicted, while direct predicted larger mass flow rates for channel-1. Therefore, for channel-1, better heat transfer capacity is calculated by direct CFD method, and the proportions are higher than those predicted by porous-jump treatment. Exceptionally, for 90% blockage scenario, mass flow rate calculated by direct CFD is smaller than that of porous-jump treatment. Therefore, the power proportion of the former is smaller than that of the latter. Though abnormal mass flow rate profiles are predicted by Relap5, the proportions are close to those simulated by porous-jump treatment. In order to illustrate the asymmetric power distribution of fuel plates clearly, power proportions and temperature fields of fuel plates (70% blockage, porous-jump treatment) are depicted in Fig. 13. Besides the plate between channel-1 and channel-2, there are also asymmetric power distributions in other plates. However, the asymmetry degree depends on mass flow rate differences on the two sides of the plate, for the plate between channel-2 and channel-3, a 2% difference is predicted; while for the plate between channel-3 and channel-4, the difference is 0.1%, and then it can be regarded as a symmetric distribution. Therefore, it can be concluded that only four plates and five channels are mostly affected by the blockage. On the other hand, the consequence of these asymmetric distributions should be discussed. The asymmetric power distribution does avoid coolants in channel-1 being over heated; however, the bad flow conditions in channel-1 and channel-2 make the temperature of the plate between them the highest. Therefore, asymmetric power distribution of the plate is only a mitigation measure for the flow blockage accident. It cannot cover the fact that a local LOFA inside the blocked channel occurs due to the blockage, and the integrity of plate might be threatened. 4.2. Blockages in annular assembly According to above simulations on the SFA of MTR, porous-jump treatment results agree well with those calculated by direct CFD, while Relap5 fails in capturing mass flow rate distribution patterns.
Fig. 13. Temperature fields of fuel plates and power proportions (70% blockage, porous-jump treatment).
These methods are subsequently applied to investigation on flow blockages in annular assembly. 4.2.1. Mass flow rate comparisons Corresponding mass flow rates are depicted in Fig. 14. For mass flow rate of the blocked channel, like predictions of the SFA, close results are obtained, and mass flow rates calculated by both porousjump treatment and Relap5 are a little lower than that calculated by direct CFD method. Also, the presence of the blockage leads to drop in the total mass flow rate. The trends of total mass flow rate profiles are quite similar to those of the blocked channel, since they are almost parallel to each other. When checking mass flow rates of all the non-blocked channels, all the profiles almost stay unchanged in different blockage scenarios. Actually, when considering the mass flow rate in each single non-blocked channel, the profile is still stable. For instance, the average mass flow rate of channel 1 and channel 2 (which are in the same layer as the blocked channel, as depicted in Fig. 4) varies little with the blockage ratio in all three methods, in which the difference is no more than 0.7%. After checking previous simulations results of the SFA, it is found that for each non-blocked channel, there are 24 mass flow rate predictions for different blockage ratios and different values, the largest dissimilarity of these values is less than 1.4%. Therefore, it can be concluded that only the blocked channel is mostly affected when considering the mass flow rate redistribution effects of the blockage. 4.2.2. Heat transfer comparisons For heat transfer redistribution, the average outlet coolant temperature of the blocked channel and the lower plenum are compared respectively. As shown in Fig. 15, the outlet temperatures of the lower plenum are in accord with each other, while those of the blocked channel are not. The difference between values that calculated by two CFD method results from the dissimilarity in mass flow rate prediction. However, a nearly 20 K difference between values calculated by Relap5 code and porous-jump treatment in 90% blockage scenario cannot be explained by mass flow rate difference only, because of the quite similar prediction in mass flow rate of these approaches. A modification is done toward Relap5 results based on following discussions.
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Fig. 14. Mass flow rate comparisons (annular assembly).
This dissimilarity is caused by different heat transfer modeling method in each approach. As mentioned above, for Relap5 simulation, only radical heat transfer is considered. While in both CFD approaches, heat transfer is calculated three-dimensionally correspondingly to the mass flow rate redistribution. Take the porous-jump treatment results of 90% blockage for instance, as illustrated in Fig. 16, in which velocity vector is colored by temperature. For the blocked channel, coolants are of low speed and high temperature, worsening heat transfer condition of fuel plates that adjacent to the blocked channel. However, other parts of these fuel plates are well-cooled because of the better heat transfer condition. Dividing fuel plates adjacent to the blocked channels into three parts: blocked, side-1 and side-2, just like the Relap5 modeling process does. However, this is a virtual separation for the sake of easy demonstration, these parts are connected to each other
Fig. 15. Outlet temperature comparisons.
in the modeling and calculating process. As depicted in Fig. 17, the larger the blockage ratio is, the higher average temperature is predicted for fuels around the blocked channel. In 90% blockage scenario, average temperature of blocked part is 44 K higher than that of side parts. This will lead to annular heat transfer, driven by annular temperature difference, from the fuel adjacent to the blocked channel to the side fuels, as illustrated in Fig. 18. Since the annular temperature difference increases dramatically with the blockage percentage, more power will transfer annularly.
Fig. 16. Flow and temperature fields (90% blockage, porous-jump treatment).
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non-blocked case. The extra temperature rise, therefore, becomes much larger in high blockage ratios, due to the relatively high extra energy and quite low mass flow rate. All the extra temperatures are calculated and subtracted from the original outlet temperature of the blocked channel, as shown in Fig. 15 (blocked channel-Relap5modified). The modified values are much closer to those calculated by CFD methods.
5. Conclusions and outlook
Fig. 17. Average temperature of the fuel around the blocked channel (porous-jump treatment).
While in Relap5 simulation, the power of the blocked part fuel is fixed to a third of the total power of the layer, therefore, an extra energy is added to the fuel adjacent to the blocked channel. However, it is difficult to calculate the extra energy in such a complex geometry. Then, for the sake of easy illustration, ignoring heat transfer in fins, only power transferred annularly in the fuel plates is considered, as shown in Fig. 18. Obviously, an extra temperature rise of the coolant is predicted. The larger the blockage percentage is, the hotter coolant in the blocked channel is. Also, as shown in Fig. 14, mass flow rate of the blocked channel drops sharply with the blockage ratio. In 90% blockage scenario, the corresponding blocked channel mass flow rate is only 15% of that in
Inlet flow blockages are investigated by Relap5, direct CFD and porous-jump treatments in this study. The results indicate that Relap5 is a very powerful system analysis code to investigate flow blockage accidents, which can simulate both flow and power redistributions. However, due to the limitation of one-dimensional modeling, abnormal mass flow rate profiles are predicted. Moreover, when applying this code to the annular fuel assembly, it fails to simulate the complex heat transfer effects caused by the blockage. Therefore, it is not proper to use system codes to investigate flow blockages at assembly scales, especially those occur in assemblies which are of complicated geometries. The direct CFD simulations confirm that blockage form affects flow fields significantly. Nevertheless, quite consistent results are acquired for four postulated blockages, indicating that blockage ratio is a reasonable input for flow blockage analyses. Based on this conclusion and innovated by Relap5, the porous-jump treatment is employed to flow blockage investigations, and good agreements are acquired when comparing mass flow rate and heat transfer redistributions with direct CFD results. This indicates that porous-jump treatment could provide generalized and reasonable predictions for flow blockage accidents. The current study shows the significance of applying CFD methods to flow blockage investigations and the advantages of porous-jump treatment. However, experiments are needed to validate and modify these methods. Though direct thermal-hydraulics experiments are hard to conduct, experiments on local resistances are more practical and will provide more accurate and reasonable input for further simulations.
Fig. 18. Heat fluxes in fuel plates (90% blockage, porous-jump treatment).
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