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Design and analysis of 19 pin annular fuel rod cluster for pressure tube type boiling water reactor
Nuclear Engineering and Design 276 (2014) 64–73
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Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
Design and analysis of 19 pin annular fuel rod cluster for pressure tube type boiling water reactor A.P. Deokule a,∗ , A.K. Vishnoi b , A. Dasgupta b , K. Umasankari b , D.K. Chandraker b , P.K. Vijayan b a b
Homi Bhabha National Institute, Trombay 400 085, Mumbai, India Bhabha Atomic Research Centre, Trombay 400 085, Mumbai, India
h i g h l i g h t s • Development of 19 pin annular fuel rod cluster. • Reactor physics study of designed annular fuel rod cluster. • Thermal hydraulic study of annular fuel rod cluster.
a r t i c l e
i n f o
Article history: Received 31 August 2013 Received in revised form 6 May 2014 Accepted 12 May 2014
a b s t r a c t An assessment of 33 pin annular fuel rod cluster has been carried out previously for possible use in a pressure tube type boiling water reactor. Despite the benefits such as negative coolant void reactivity and larger heat transfer area, the 33 pin annular fuel rod cluster is having lower discharge burn up as compared to solid fuel rod cluster when all other parameters are kept the same. The power rating of this design cannot be increased beyond 20% of the corresponding solid fuel rod cluster. The limitation on the power is not due to physics parameters rather it comes from the thermal hydraulics side. In order to increase power rating of the annular fuel cluster, keeping same pressure tube diameter, the pin diameter was increased, achieving larger inside flow area. However, this reduces the number of annular fuel rods. In spite of this, the power of the annular fuel cluster can be increased by 30% compared to the solid fuel rod cluster. This makes the nineteen pin annular fuel rod cluster a suitable option to extract more power without any major changes in the existing design of the fuel. In the present study reactor physics and thermal hydraulic analysis carried out with different annular fuel rod cluster geometry is reported in detail. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Annular fuel rod for AHWR has distinct advantages over the existing solid fuel rod such as low operating peak temperature and energy per unit temperature rise in fuel. Besides it leads to rise of MCHFR/CPR margin due to the reduction of surface heat flux. This allows substantial power density increase of up to 50% in the fuel. In addition, the amount of fission gas released and reduction of pellet cracking are reduced due to low temperature gradient in the fuel pin. Previously a thirty three pin annular fuel rod bundle has been studied for a pressure tube type BWR and
∗ Corresponding author. Tel.: +91 02225560200. E-mail address: [email protected] (A.P. Deokule). http://dx.doi.org/10.1016/j.nucengdes.2014.05.017 0029-5493/© 2014 Elsevier B.V. All rights reserved.
is reported in Deokule et al. (2013). Despite the benefits there is no intension of replacement of existing solid fuel rod cluster by annular fuel rod cluster in the present design of solid fuel rod. A distinct flaw of the 33 pin annular fuel rod cluster design (which became evident in the process of thermal hydraulic subchannel analysis) is its lower thermal margin. The thirty three pin annular fuel cluster design has smaller inner diameter which reduces the flow through the annular pin resulting in reduced thermal margin of the designed annular fuel rod bundle. It was found in the analysis that the power cannot be increased beyond 20% due to Minimum Critical Heat Flux Ratio (MCHFR) limitations. To overcome these defects a new 19 pin annular fuel rod cluster has been designed and analyzed for reactor physics and thermal hydraulics parameters. The MCHFR limitation was due to the smaller inside flow passage of the annular fuel pin. Development of annular fuel rod bundle so that power can be increased beyond 30% was
A.P. Deokule et al. / Nuclear Engineering and Design 276 (2014) 64–73
considered essential. While achieving higher power it is needed to control safety related parameters such as coolant void reactivity, moderator temperature reactivity, power coefficient etc. In order to achieve this, design with bigger pin has been selected in the form of 19 pin annular fuel rod cluster. The objectives of the work reported here are to determine the neutronically-achievable high power potential and viable high burnup bundle designs taking into consideration the operational neutronic parameters (such as reactivity control and feedback), engineering constraints (such as thermal hydraulics and fuel performance) and other important aspects (such as spent fuel characteristics, proliferation resistance, nuclear fuel cycle economics, etc.). The most effective way is to increase the average reload enrichment (higher initial reactivity), which needs detailed analysis/verification in order to satisfy safety margins. However, when taking a broader view, one should optimize the bundle design to achieve high burnup and high power. In addition, various new fuel options, including annular fuel with or without internal cooling, and new fuel material compositions need to be considered. The overall strategies for design and deployment of high burnup cores need to be addressed and analyzed. The impact of high burnup fuels on the current fuel cycle in a sustainable environment also needs to be assessed. 1.1. Literature review Since the introduction of numerical subchannel analysis methods 1960s a great number of computer tools have been developed for utilizing this approach. The homogeneous equilibrium set of conservation equations of COBRA-IV will be used which were presented by Stewart (1977). In Addition to the conservation equations, it is necessary to specify fluid properties and constitutive equations to form a closed set of equations to form for solution. The fluid properties are obtained from an equation of state. The parameters for which constitutive relations are needed can be identified by inspecting the subchannel conservation equations. This approach was introduced by Meyer (1961) as momentum integral model and is judged for a wide class of intermediate speed reactor coolant channel transients. Different parameters required for the analysis are surface heat transfer coefficients and axial friction drag, enthalpy and axial velocity transported by pressure driven drag cross flow. Rouhani (1978) reviewed the historical development of formulation for this transverse flow and fixed its value to 0.5. For the two phase flow modeling various methods have been proposed such as Tong and Weisman (1979) consider the homogeneous flow model with vapour and liquid having the same velocity in thermal equilibrium. Kroger (1976) included thermal non equilibrium in his drift flux formulation of conservation equations. He did assume vapour to be at saturation conditions and liquid to have constant density. Espinosa Paredes et al. (2008) have carried out some simulations, specifically loss of coolant accidents (LOCA) scenario in boiling water reactor (BWR) with the MARK-II containment design. The simulations results show that the Fuzzy Cognitive Mapping predicts properly the phenomenon in the reactor vessel and primary containment. 1.2. Description of the optimized annular fuel cluster In order to get improvement in the design, a completely new cluster is designed in which fuel pins are arranged in the two rings in the cluster. During the process of evolution of 19 pin annular fuel rod cluster the pin diameter is gradually increased. The intermediate step of evolution of 19 pin rod from 33 pin annular fuel cluster was 25 pin annular fuel rod clusters. This improvement resulted in increased inner flow diameter on the inside of the annular fuel rod. The diameter of inner flow passage has increased from 8 mm to 10 mm in case of 25 pin annular fuel rod cluster and 11.8 mm
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in case of 19 pin annular fuel rod cluster so that more flow will be diverted to inner side. This strategy results in an advantage of having critical heat flux on outer side of the tube. For ready reference the two designs have been shown in Fig. 1. In the advanced 19 pin design the pin diameter is increased and the tie rod diameter is decreased and the number of tie rods is increased from 4 to 6 to strengthen the cluster. All the other parameters of the two designs are compared in Table 1. In order to qualify the annual fuel, detailed physics simulations were done to estimate the safety margins and various reactivity coefficients of the design. 2. Reactor physics analysis of the annular fuel rod bundle Reactor physics studies of the 19 pin cluster have been carried out by using lattice code. The new 19 rod cluster has been simulated as a reactor lattice cell with the lattice code WIMSD (Askew et al., 1966). The circular arrayed fuel assembly has been modeled as a super cell and the calculation proceeds from heterogeneous infinite lattice calculation in hyperfine energy group structure to a homogeneous leakage correction. The burn up simulations has been performed using a critical flux spectrum and operating temperature condition. The flux distribution across the cluster has been expanded using discrete ordinates method with Sn-16 approximation which means that the angular domain has been discretized in 16 directions. The nuclear data set used in the multigroup cross section set condensed in 69 discrete energy groups from the evaluated nuclear data file ENDF/B-VI.8 dataset (WLUP, 2003). In the current design of 19 pin annular fuel rod cluster, Thorium–Low Enriched Uranium (Th, LEU) metal oxide (MOX) fuel is used. The LEU composition consists of a mixture of 19.75% 235 U and 80.25% 238 U. The fuel cluster uses 20% Low Enriched Uranium (LEU) mixed with 80% Thorium in oxide form. 2.1. Results and discussion of reactor physics analysis of 19 pin annular fuel rod cluster In a boiling light water cooled system the coolant void reactivity (CVR) is an important safety parameter. AHWR is a pressure tube type reactor and uses boiling light water as coolant. The low temperature moderator is heavy water and is outside the pressure boundary. Voiding of coolant implies that only the light water coolant inside the pressure tube voids. CVR is a measure of the reactivity changes with void (typically due to steam bubbles) fraction in the reactor coolant. This is also a major parameter, which governs the cluster design. Similarly other reactivity coefficients governing the design are Doppler reactivity and moderator temperature reactivity (MTR). Effect of Doppler broadened cross sections on reactivity due to temperature rise in fuel is taken into account by fuel temperature reactivity (FTR). The moderator temperature reactivity is defined as the change in reactivity per unit change in the moderator temperature. WIMS code is used for the analysis of the annular fuel rod cluster. The variation of coolant void reactivity as a function of change in coolant density (or voids) is presented in Fig. 2 for different average in-core burnups. It is seen that the void coefficient is negative over the operational regimes of burnups and void fractions. The core averaged coolant void reactivity has been presented as CVR-1 and CVR-2. Coolant Void Reactivity (CVR-1) is the reactivity change for 0.74–0.45 gm/cc density of coolant and CVR2 is for accidental condition (density of coolant 0.45–0.03 gm/cc) which is the reactivity introduced for voiding from normal operating condition. Various other reactivity parameters calculated are moderator temperature reactivity coefficient (MTR), channel temperature reactivity (CTR), fuel temperature reactivity (FTR), and power coefficient (PC). The results have been tabulated in Table 2.
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Fig. 1. (a) Thirty-three pin annular fuel cluster. (b) Nineteen pin annular fuel rod cluster.
During the process of evolution of final 19 pin annular fuel rod cluster from 33 pin fuel rod cluster a 25 pin design is also tested. The details of the various fuel rod clusters are tabulated in Table 3. Two options of the 19 pin annular fuel rod cluster are considered which are designated as Option R-5 and Option R-6 for convenience. The geometry R-5 and R-6 are evolved from the same 19 pin geometry; the only differences in the two geometries being the number of tie rods used. In Option R-6, the number of rods has been increased to 18 from 6 in R-5 option. The reason behind this change is important from thermal hydraulics of the channel and explained in Section 3.5 of the article. It is clear from Table 3 that the 25 pin annular fuel rod cluster is discarded due to higher value of positive coolant void reactivity. The CVR as a function of burn up for 33 pin and 19 pin annular fuel rod clusters is shown in Fig. 3. The 19 pin annular fuel
rod cluster is having more negative coolant void reactivity than the 33 pin annular fuel rod and it changes more slowly with the burn up. Even at 30,000 MWd/t burn up, the 19 pin fuel cluster shows significant negative void reactivity making it more attractive than 33 pin. 3. Thermal hydraulic analysis of the annular fuel rod cluster Thermal hydraulic analysis of the annular fuel rod bundle has been carried out by using two methods. 1. Bundle average method 2. Subchannel method
Table 1 Comparison between thirty three pin design and nineteen pin design. Description
33 pin design
19 pin design
Fuel No. of fuel pins Fuel pin ID/OD (mm) Fuel pellet ID/OD (mm) Coolant annulus mm Inner clad material ID/OD (mm) Outer clad material/ID/OD (mm) Clad Material/Density (g/cc) Clad thickness (mm) Fuel density (g/cc) No. of fuel rings No of fuel pins in each ring Pitch circle diameters of the fuel rings (mm)
33 8/17.1 9.5/15.3 8 8/9.3 15.6/17.1 Zircaloy-2/6.55 0.65 9.3 3 6/9/18 51.4/77.4/103.7
19 11.8/22.3 13.1/21.2 11.8 11.8/13.1 20/22.3 Zircaloy-2/6.55 0.65 9.3 2 1/6/12 0/47.4/93.3
Fuel types/enrichment (%) Ring 1 Ring 2 Ring 3
(Th,233 U)MOX/3.0% (Th,233 U)MOX/3.75% (Th,Pu)MOX/3.25% (average)
(Th,LEU)MOX/20% (Th,LEU)MOX/20% (Th,LEU)MOX/20% (average)
Arrangement of tie rods Pitch Circle Diameter (PCD) of central rod (mm) Pitch Circle Diameter (PCD) of other tie rods (mm) Material/Density (g/cc)/OD (mm)
0.0 No central tie rod 77.4 Zr-2/6.55/17.1
65.7 Zr-2/6.55/12
Pressure tube ID/OD (mm) Material/density (g/cc)
120/128 Zr-2.5%Nb/6.55
120/128 Zr-2.5%Nb/6.55
Calandria tube ID/OD Material/Density (g/cc)
163.8/168 Zircaloy-2/6.55
163.8/168 Zircaloy-2/6.55
Coolant Material Average coolant temperature and pressure, ◦ C and bar/average coolant density (g/cc) Heavy metal per bundle (kg) Specific power (kW/kg)
Light water 285/70/0.45 116.5 18.6
Light water 285/70/0.45 87.88 30.5
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Table 2 Comparison of various reactivity parameters of the designed bundle. No.
Pins
Description Fuel used
Average Enrichment in cluster
Achievable discharge burnup MWd/t
MTR (mk)
1
54 (Ref)
(Th,U233) MOX (Th,Pu)MOX
3.45% 233 U
42,000
2.38
2
33
(Th,U233) MOX (Th,Pu)MOX
3.25% Pu 3.45% 233 U
29,500
3
25
(Th,U233) MOX (Th,Pu)MOX
3.25% Pu 3.75% 233 U
4 5
19 (R-5) 19 (R-6)
(Th,LEU)MOX (Th,LEU)MOX
3.25% Pu 3.95% 235 U 3.95% 235 U
CTR (mk)
FTC (mk)
CVR-1 (0.74 to 0.45 g/cc) (mk)
6.056
−4.21
−0.459
2.08
4.638
−3.936
−4.3887
29,500
0.46
−2.356
−3.123
9.12
5.356
58,000 58,000
0.96 −0.76
−5.702 −4.508
−4.635 −4.531
−3.671 −2.492
−8.3061 −7.0241
Power Coefficient (mk) 4.674
−8.325
CVR-2 under LOCA (0.45–0.03 g/cc) (mk) −3.56
−8.927
9.20
−6.82 −5.52
4.0
Coolant void reactivity mk
2.0 0.0 (Xe sat) MWD/T 10000 MWD/T 20000 MWD/T 26000 MWD/T
0.0 -2.0 -4.0 -6.0 -8.0 -10.0 -12.0 0.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
80.0
90.0 100.0
Change in coolant density % Fig. 2. Variation of coolant void reactivity with change in coolant density at different average in core burn ups (data obtained by WIMS calculations).
Fig. 3. Comparison of coolant void reactivity of 33 pin and 19 pin annular fuel rod cluster for AHWR (data obtained by WIMS calculations).
3.1. Bundle average method analysis The first method is widely used where whole bundle is supposed to be a single pin and total fuel mass inside the bundle is concentrated in the inner and outer rings of the clad. Similarly whole zirconium cladding is replaced with two layers of the zirconium an inner and an outer layer. This method is called as the bundle average method as everything in the bundle is averaged out at the center. However in the design simulation by bundle average method whole bundle is assumed to be as single pin in case of solid fuel pin. In case of annular fuel pin working in this way does not suffice the purpose as it changes inside and outside heat flux distribution of
every pin which is different in every case. Therefore in case of annular fuel pin equivalent hydraulic diameter per pin is calculated and analysis is carried out for the pin where radial and axial peaking factors are maximum. Minimum Critical Heat Flux Ratio (MCHFR) value estimated using Jensen–Levy is very high at nominal power, so that the bundle power can be increased. The comparison of the values of MCHFR is made with the standard solid fuel rod cluster (Sinha and Kakodkar, 2006; Rouhani, 1978) and subsequently detailed subchannel analysis of these geometries has been carried out at a higher power. For the ready reference the geometries are shown in Fig. 4.
Table 3 Comparison of annular fuel rod cluster performance with solid fuel rod cluster by bundle average method.
Annular fuel (R5) Cluster Annular fuel (R6) Cluster Solid Fuel cluster
Power (MW)
No. of Fuel Pins
2.6
19
2.6 2.6
Fuel Pin Max Temp (K)
MCHFR (by Jensen-Levy)
Quality inside
919
3.66
0.226
19
782
2.08
0.176
54
1070
1.90
0.260
Mass Flux Inside G inside (kg/m2 s)
Mass Flux Outside G outside (kg/m2 s)
Heat Flow Inside (%)
Heat Flow Outside (%)
0.298
1266
663
47.90
52.10
0.395
1490
586
48.00
52.00
Quality outside
998
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Fig. 4. (a) 19 pin annular fuel rod cluster (option R5) (b) 19 Pin advanced annular fuel rod cluster (option R6).
3.2. Subchannel analysis There are two approaches to the definition of subchannel analysis. The traditional approach for subchannel analysis is coolant centered and is discussed in the present study. Subchannel properties like axial velocity and density are represented by single averaged values. Constitutive equations are required for input parameters like friction factors and lateral momentum equation and energy exchange rates between adjacent subchannels. In the subchannel approach a major simplification is made in the treatment of the lateral exchange between adjacent subchannels. A fully three dimensional physical situation can be represented simply by connecting the channels in a three dimensional array. This leads to simplifications in the lateral convective terms of the linear momentum balance equation. A computer code – SAAP (Subchannel Analysis of Annular Pin bundle) has been developed for subchannel analysis of annular fuel cluster. In this code subchannel analysis has been performed using the model of COBRA-IV-I. For fuel heat transfer calculations a separate heat transfer module HeAP (Heat Transfer in Annular fuel Pins) has been developed, that computes the heat flux partitioning between the inner and outer faces of the annular pin. HeAP and COBRA-IV-I are coupled externally and subchannel analysis of the annular fuel rod cluster is carried out. The development of subchannel analysis code for annular fuel rod cluster is reported by Vishnoi et al. (2013) in detail. Still for the ready reference, the procedure of subchannel analysis of annular fuel rod bundle by computer code SAAP is given in the Appendix-I. 3.3. Thermal hydraulic analysis of 19 pin annular fuel rod cluster For the thermal hydraulic analysis of the annular fuel rod bundle COBRA-IV-I code has been used. COBRA-IV-I (Wheeler et al., 1976; Jensen and Levy, 1962) is a transient subchannel analysis code. The calculation methodology involves dividing the bundle into computational cells and conservation laws of mass, momentum and energy for the fluid are then solved. The fuel rods and other solid materials in the computational domain act as heat sources or sinks. The code also has a conduction model to carry out heat transfer within cylindrical or plate type fuels. No such model exists for annular fuel pins. Thus, the heat transfer model (HeAP) has been coupled for calculations involving annular fuel pins. Critical Heat Flux (CHF) calculations can also be performed using appropriate correlations. While B&W-2 and W-3 Tong (1967) CHF correlations are built into COBRA computer code, Jensen–Levy (Jensen and Levy, 1962; Wheeler et al., 1976) correlation were programmed into
Fig. 5. 19 Pin annular fuel bundle geometry (R5).
COBRA-IV-I for inclusion in SAAP. In conventional sub-channel analysis, since sub-channels are ventilated, cross-flow between the adjacent sub-channels ensures the equalization of pressures at an axial level. For annular pins, however, the inner sub-channel is not connected to any other sub-channel thus; the mass flow rate must be adjusted among the sub-channels in such a way that the total pressure drop across the bundle length is same for all inner and outer sub-channels. For this purpose, the pressure drop boundary condition available in COBRA-IV-I is used. This ensures that the flow in each sub-channel is adjusted such that the total pressure drop equals a specified value. 3.4. Subchannel analysis of 19 pin annular fuel rod bundle Geometric arrangement of the fuel pins of the 19 pin annular fuel rod cluster is shown in Fig. 5. For the computational simplicity and from symmetry of the bundle, one sixth (1/6) geometric section is taken for the sub-channel analysis of the cluster. This symmetric section is shown in Fig. 6. The maximum bundle is 3.4 MW which is obtained by reactor physics analysis. Therefore subchannel analysis has been carried out at bundle power of 3.4 MW. Complete calculations are carried out for the section and enthalpy variation and exit quality of every subchannel is calculated. For the convenience the enthalpy variation of subchannels 1, 3, 4 and 6 along the axial length is shown in Fig. 7 along with a saturation liquid enthalpy line. It can be observed from the results that exit quality in subchannel
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Table 4 Mass flux and exit quality at each sub-channel. Subchannel
Enthalpy (kJ/kg)
Mass flow rate (kg/s)
1 2 3 4 5 6 7 8 9 10 11 12
2340.6 2330.2 1849.8 1777.5 1840.8 1452.3 1483.9 1452.3 1590.8 1687.2 1997.4 1997.4
0.013 0.013 0.051 0.064 0.051 0.100 0.191 0.100 0.023 0.129 0.104 0.104
Mass flux (G) (kg/m2 s)
Exit quality (x)
480 480 692 852 692 1308 1246 1308 1286 1176 950 950
0.713 0.712 0.387 0.339 0.386 0.123 0.144 0.123 0.215 0.279 0.485 0.485
5.0 4.5 4.0
MCHFR
3.5 3.0 2.5 2.0 1.5 1.0 0
5
10
15
20
25
axial node Fig. 6. Sub-channel geometry.
6 is very low as compared to the other subchannels due to the flow area to heated perimeter ratio. In these subchannels the flow area to heated perimeter ratio is much higher compared to other subchannels. Exit quality and mass flux of different subchannels are listed in Table 4. It is clear from Fig. 7, that the enthalpy in the subchannel 1 is higher than the enthalpy in the subchannel 6. It is clear from Table 4, that exit quality of the subchannel 1 is higher than the exit quality of the subchannel 6. Due to different void fraction in the adjacent
Fig. 8. Critical heat flux ratio of annular fuel cluster (option R5) (data obtained by bundle average method).
subchannels there is cross flow causing turbulent mass interchange. To avoid the differential flow regimes as well as to obtain a balanced exit enthalpy of all subchannels further improvement in the cluster has been made and analyzed subsequently. In the improved design the flow passage of the subchannel 6 can be reduced by providing a cylindrical rod. This reduces the flow through the subchannel 6 and which improves its exit quality. The MCHFR by bundle average method is an important aspect which must be considered along with the subchannel analysis. The designer has to keep MCHFR value above unity for safe operating conditions. The method of finding Critical Heat Flux Ratio (CHFR) of the annular fuel bundle is explained in detail by Deokule et al. (2013). The CHFR curve along the axial length of the fuel cluster by bundle average method is shown in Fig. 8. MCHFR value at 7 MPa pressure and 285 ◦ C is estimated as 1.22 for R-5 annular fuel cluster. 3.5. Improvements in the 19 pin geometry
Fig. 7. Axial enthalpy variation of different sub-channels (data obtained by subchannel analysis).
Subchannel analysis of the 19 pin annular fuel rod cluster has led to an important conclusion that the exit enthalpy of the various channels is different. It becomes necessary to put extra tie rods to block the flow at the subchannel where the mass flow rate is higher. The improvements in the design of the annular fuel rod cluster have led to the geometry R6 which is shown in Fig. 9. It consists of 19 annular fuel pins, 6 numbers of 10 mm tie rods in middle ring and 12 numbers 6 mm tie rods in the outer ring. The reactor physics parameters of this cluster have not changed as the absorption cross section of the additional zirconium tie rods is very
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Fig. 12. Subchannel geometry of the section R-6. Fig. 9. Improved 19 pin geometry – R6.
Fig. 13. Axial enthalpy variation of inner subchannel. Fig. 10. Symmetric subchannel section in option R-6.
4.5 4.0
MCHFR
3.5 3.0 2.5 2.0 1.5 1.0 0
3
6
9
12
15
18
21
24
axial node Fig. 14. Critical heat flux ratio of annular fuel cluster (option R6-data obtained by bundle average method). Fig. 11. Axial enthalpy variation of different subchannel in geometry R-6 (data obtained by subchannel analysis).
small. The tie rods in the outer ring do not provide any structural support to the cluster. They are provided to reduce the flow passage on the outer side of the bundle. For the subchannel analysis one sixth (1/6th) geometric section is taken which is shown in Fig. 10.
Subchannel analysis of this annular fuel bundle has been carried out at bundle power of 3.82 MW. The symmetric cross section enthalpy variation of outer sub-channels is shown in Fig. 11. It can be seen that all the outer subchannels have almost same enthalpy variation, only subchannel 6 shows slightly lower enthalpy because of higher flow to heat ratio.
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Table 5 Mass flux and exit quality at each sub-channel. Subchannel
Enthalpy (kJ/kg)
Mass flow rate (kg/s)
Mass flux (G) (kg/m2 s)
Exit quality (x)
1 2 3 4 5 6 7 8 9 10 11 12
1803 1803 1804 1807 1804 1734 1747 1734 1513 1615 1929 1929
0.039 0.039 0.069 0.080 0.069 0.048 0.095 0.048 0.031 0.162 0.125 0.125
983 983 913 1038 913 854 843 854 1676 1484 1146 1146
0.352 0.352 0.353 0.355 0.353 0.307 0.315 0.307 0.159 0.227 0.436 0.436
Table 6 Comparisons between 19 pin improved annular fuel rod cluster and solid fuel rod cluster. Type of fuel
No. of pins
Bundle power
MCHFR (at 120% power)
Max. fuel temp. (K)
Solid fuel Annular fuel bundle (R6)
54 19
2.6 MW 3.2 MW
1.16 1.10
1293 933
The inner subchannels typically subchannel nos. 9–11 are shown in Fig. 12 and enthalpy variations are shown in Fig. 13 subsequently. It can be seen that in the subchannel 11, coolant has the highest enthalpy while in the subchannel 9 has the lowest exit enthalpy. This variation in the enthalpy is due to local peaking factors 0.79, 0.87, 1.08 in the respective subchannels. The exit quality, mass flux and mass flow rate of each subchannel are listed in Table 5. It can be observed that exit quality of each subchannel is in the same range (0.039–0.127) and there is large variation in the inner subchannel due to the local peaking. The CHFR curve along the axial length of the fuel by bundle average method is shown in Fig. 14. MCHFR value at 7 MPa pressure and 285 ◦ C is estimated as 1.10. MCHFR and maximum fuel temperature of R6 geometry with 54 rods AHWR bundle geometry are compared in Table 6. It can be observed that with this geometry the cluster power can be enhanced to 3.2 MW with same thermal margin as of current solid AHWR fuel cluster.
fuel Pins) has been developed, that computes the heat partitioning between the inner and outer faces of the annular pin.
4. Conclusions
−k
It can be concluded that a suitable cluster with annular fuel for pressure tube type boiling water reactor can be designed without any major revision of design parameters of the solid fuel rods. The designed annular fuel rod cluster is having better performance parameters from physics as well as thermal hydraulic point of view such as negative void coolant reactivity and MCHFR. These distinct advantages make the 19 pin annular fuel rod cluster more suitable than the existing solid fuel rod cluster. Subchannel analysis of the annular fuel rod cluster shows that reducing the subchannel flow area on the outside, diverts the flow through the hottest channel improving the MCHFR margin in the hottest channel. From the analysis it is clear that final design with 19 pin annular fuel rod cluster is suitable for generation of higher power.
Appendix-I. Development of Computer Code SAAP (Subchannel Analysis for Annular Pin) A computer code – SAAP (Sub-channel Analysis of Annular Pin bundle) has been developed for sub-channel analysis of annular fuel cluster. In this code sub-channel analysis has been performed using the model of COBRA-IV-I. For fuel heat transfer calculations a separate heat transfer module HeAP (Heat Transfer in Annular
A.1. Mathematical formulation of HeAP A heat transfer analysis module, HeAP (Heat Transfer in Annular fuel Pins), capable of modeling both internally and externally cooled annular fuel pins is developed. It calculates the heat flux distribution in the inner and outer surfaces of the annular fuel assembly. It also calculates the temperature distribution of the fuel. In HeAP radial conduction equation is solved by finite difference method. For radial heat transfer inside the fuel pin, 1-D radial conduction Eq. (1a) is solved by finite difference method. ∂2 T 1 ∂T 1 ∂T + q= + ˛ ∂t k r∂r ∂r 2
for
r= / 0
(1a)
Boundary conditions at the center of the fuel and at wall coolant interface are given in Eqs. 1(b) and 1(c).
k
∂T + hin T0 = hin Tlin ∂r
∂T + hout Tm = hout Tlout ∂r
for i = 0 for i = m
(1b) (1c)
Explicit method is applied to discretize the radial conduction equation with source term in cylinder geometry. On discretization of the Eqs. 1(a) and 1(c), we get equations required numerical equations which are solved using computer program. A.2. Description of COBRA-IV-I COBRA-IV-I (Wheeler et al., 1976) is a transient sub-channel analysis code. The calculation methodology involves dividing the bundle into computational cells. Conservation laws of mass, momentum and energy for the fluid are solved. The fuel rods and other solid materials in the computational domain act as heat sources or sinks. The code also has a conduction model to solve for heat transfer within cylindrical or plate type fuels. No such model exists for annular fuel pins. Thus, the heat transfer model of HeAP has been coupled for calculations involving annular fuel pins. CHF calculations can also be performed using appropriate correlations. While B&W-2 and W-3 (Tong, 1967) correlations are built into COBRA, the 1995 LUT and Jensen–Levy (Jensen and Levy, 1962) correlation were programmed into COBRA-IV-I for inclusion in SAAP.
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Fig. A1. (A) Flow chart of SAAP computer program.
A.3. Calculation procedure of SAAP HeAP and COBRA-IV-I have been coupled for sub-channel analysis of annular fuel cluster. To begin with, additional isolated inner sub-channels of the annular fuel pins are defined in the input data of the COBRA IV. Then COBRA is executed as per the regular procedure. When COBRA calculations are converged, coolant temperature, mass flux and quality of each sub-channel are collected.
From the collected data, heat transfer coefficients of coolant and temperatures of the inner and outer surfaces of the seed pins are calculated by executing HeAP. Finally heat directed to the inner and outer sub-channels are calculated. The next step is to check if the previously assumed heat transfer fractions are within the allowable margin of error. If they are within the limits the calculation stops. This loop is repeated until the heat transfer fraction is within the error tolerance. The flow chart is shown in Fig. I(A). Fuel
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cluster is simulated by bundle average method. Different inputs which are required for the computer code are power, geometry, inlet sub-cooling of the feed water, system pressure, total pressure drop across bundle, axial flux distribution and local peaking. References Askew, J.R., Fayers, F.J., Kemshell, P.B., October 1966. A general description of the lattice code WIMS. Brit. Nucl. Energy Soc., 564. Deokule, A.P., Vishnoi, A.K., Umasankeri, K., Chandraker, D.K., Vijayan, P.K., Ganesan, S., 2013. Design of 33 pin annular fuel rod cluster for advanced heavy water reactor. Nucl. Eng. Des., 94–101. Espinosa Paredes, G., Nunez Carrera, A., Laureano Cruces, A.L., Vazquez Rodriguez, A., Espinoza-Martinez, E., 2008. Emergency management for nuclear power plant using fuzzy cognitive maps. Ann. Nucl. Energy 35, 2387–2396. Jensen, E., Levy, S., 1962. Burnout Limit Curves for Water Reactors, General Electric Report No. APED-3892. Kroger, P.G., 1976. Application of Nonequilibrium Drift Flux Model to Two Phase Blow Down Experiments, BNL-NUREG-21506-R. BROOK, Upton, MA.
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Meyer, J., 1961. Hydrodynamic models for the treatment of reactor thermal transients. Nucl. Eng. Des. 10, 269–277. Rouhani, A., 1978. In: Ginoux, J. (Ed.), Steady State Subchannel Analysis in Two Phase Flows and Application to Nuclear Reactor Design Problems. Hemisphere/Mcgraw Hill, New York, pp. 301–327. Sinha, R.K., Kakodkar, A., 2006. Design and development of AHWR-the Indian Thorium fueled innovative reactor. Nucl. Eng. Des. 236 (7–8), 683–700. Stewart, C.W., July 1977. COBRA-IV: The model and the Method: BNWL 2214 NRC-4. Tong, L.S., 1967. Heat transfer in water cooled nuclear reactors. Nucl. Eng. Des. 6, 301–304. Tong, L.S., Weisman, J., 1979. Thermal Analysis of Pressurized Water Reactors, 2nd edition. American Nuclear Society, Hindsdale, IL. Vishnoi, A.K., Dasgupta, A., Chanrakar, D.K., Vijayan, P.K., 2013. Thermal hydraulics analysis of annular fuel assembly. In: The 15th International Topical Meeting on Nuclear Reactor Thermal – Hydraulics, NURETH-15, Pisa, Italy, May 12–17. Wheeler, C.L., et al., 1976. COBRA-IV-I: An Interim Version of COBRA for Thermal Hydraulic Analysis of Rod Bundle Nuclear Fuel Elements and Cores BNWL-1962, UC-32. WLUP, 2003. See: http://www-nds.indcentre.iaea.org.in/∼wlup/WIMS Library Update Project.
Contents lists available at ScienceDirect
Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
Design and analysis of 19 pin annular fuel rod cluster for pressure tube type boiling water reactor A.P. Deokule a,∗ , A.K. Vishnoi b , A. Dasgupta b , K. Umasankari b , D.K. Chandraker b , P.K. Vijayan b a b
Homi Bhabha National Institute, Trombay 400 085, Mumbai, India Bhabha Atomic Research Centre, Trombay 400 085, Mumbai, India
h i g h l i g h t s • Development of 19 pin annular fuel rod cluster. • Reactor physics study of designed annular fuel rod cluster. • Thermal hydraulic study of annular fuel rod cluster.
a r t i c l e
i n f o
Article history: Received 31 August 2013 Received in revised form 6 May 2014 Accepted 12 May 2014
a b s t r a c t An assessment of 33 pin annular fuel rod cluster has been carried out previously for possible use in a pressure tube type boiling water reactor. Despite the benefits such as negative coolant void reactivity and larger heat transfer area, the 33 pin annular fuel rod cluster is having lower discharge burn up as compared to solid fuel rod cluster when all other parameters are kept the same. The power rating of this design cannot be increased beyond 20% of the corresponding solid fuel rod cluster. The limitation on the power is not due to physics parameters rather it comes from the thermal hydraulics side. In order to increase power rating of the annular fuel cluster, keeping same pressure tube diameter, the pin diameter was increased, achieving larger inside flow area. However, this reduces the number of annular fuel rods. In spite of this, the power of the annular fuel cluster can be increased by 30% compared to the solid fuel rod cluster. This makes the nineteen pin annular fuel rod cluster a suitable option to extract more power without any major changes in the existing design of the fuel. In the present study reactor physics and thermal hydraulic analysis carried out with different annular fuel rod cluster geometry is reported in detail. © 2014 Elsevier B.V. All rights reserved.
1. Introduction Annular fuel rod for AHWR has distinct advantages over the existing solid fuel rod such as low operating peak temperature and energy per unit temperature rise in fuel. Besides it leads to rise of MCHFR/CPR margin due to the reduction of surface heat flux. This allows substantial power density increase of up to 50% in the fuel. In addition, the amount of fission gas released and reduction of pellet cracking are reduced due to low temperature gradient in the fuel pin. Previously a thirty three pin annular fuel rod bundle has been studied for a pressure tube type BWR and
∗ Corresponding author. Tel.: +91 02225560200. E-mail address: [email protected] (A.P. Deokule). http://dx.doi.org/10.1016/j.nucengdes.2014.05.017 0029-5493/© 2014 Elsevier B.V. All rights reserved.
is reported in Deokule et al. (2013). Despite the benefits there is no intension of replacement of existing solid fuel rod cluster by annular fuel rod cluster in the present design of solid fuel rod. A distinct flaw of the 33 pin annular fuel rod cluster design (which became evident in the process of thermal hydraulic subchannel analysis) is its lower thermal margin. The thirty three pin annular fuel cluster design has smaller inner diameter which reduces the flow through the annular pin resulting in reduced thermal margin of the designed annular fuel rod bundle. It was found in the analysis that the power cannot be increased beyond 20% due to Minimum Critical Heat Flux Ratio (MCHFR) limitations. To overcome these defects a new 19 pin annular fuel rod cluster has been designed and analyzed for reactor physics and thermal hydraulics parameters. The MCHFR limitation was due to the smaller inside flow passage of the annular fuel pin. Development of annular fuel rod bundle so that power can be increased beyond 30% was
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considered essential. While achieving higher power it is needed to control safety related parameters such as coolant void reactivity, moderator temperature reactivity, power coefficient etc. In order to achieve this, design with bigger pin has been selected in the form of 19 pin annular fuel rod cluster. The objectives of the work reported here are to determine the neutronically-achievable high power potential and viable high burnup bundle designs taking into consideration the operational neutronic parameters (such as reactivity control and feedback), engineering constraints (such as thermal hydraulics and fuel performance) and other important aspects (such as spent fuel characteristics, proliferation resistance, nuclear fuel cycle economics, etc.). The most effective way is to increase the average reload enrichment (higher initial reactivity), which needs detailed analysis/verification in order to satisfy safety margins. However, when taking a broader view, one should optimize the bundle design to achieve high burnup and high power. In addition, various new fuel options, including annular fuel with or without internal cooling, and new fuel material compositions need to be considered. The overall strategies for design and deployment of high burnup cores need to be addressed and analyzed. The impact of high burnup fuels on the current fuel cycle in a sustainable environment also needs to be assessed. 1.1. Literature review Since the introduction of numerical subchannel analysis methods 1960s a great number of computer tools have been developed for utilizing this approach. The homogeneous equilibrium set of conservation equations of COBRA-IV will be used which were presented by Stewart (1977). In Addition to the conservation equations, it is necessary to specify fluid properties and constitutive equations to form a closed set of equations to form for solution. The fluid properties are obtained from an equation of state. The parameters for which constitutive relations are needed can be identified by inspecting the subchannel conservation equations. This approach was introduced by Meyer (1961) as momentum integral model and is judged for a wide class of intermediate speed reactor coolant channel transients. Different parameters required for the analysis are surface heat transfer coefficients and axial friction drag, enthalpy and axial velocity transported by pressure driven drag cross flow. Rouhani (1978) reviewed the historical development of formulation for this transverse flow and fixed its value to 0.5. For the two phase flow modeling various methods have been proposed such as Tong and Weisman (1979) consider the homogeneous flow model with vapour and liquid having the same velocity in thermal equilibrium. Kroger (1976) included thermal non equilibrium in his drift flux formulation of conservation equations. He did assume vapour to be at saturation conditions and liquid to have constant density. Espinosa Paredes et al. (2008) have carried out some simulations, specifically loss of coolant accidents (LOCA) scenario in boiling water reactor (BWR) with the MARK-II containment design. The simulations results show that the Fuzzy Cognitive Mapping predicts properly the phenomenon in the reactor vessel and primary containment. 1.2. Description of the optimized annular fuel cluster In order to get improvement in the design, a completely new cluster is designed in which fuel pins are arranged in the two rings in the cluster. During the process of evolution of 19 pin annular fuel rod cluster the pin diameter is gradually increased. The intermediate step of evolution of 19 pin rod from 33 pin annular fuel cluster was 25 pin annular fuel rod clusters. This improvement resulted in increased inner flow diameter on the inside of the annular fuel rod. The diameter of inner flow passage has increased from 8 mm to 10 mm in case of 25 pin annular fuel rod cluster and 11.8 mm
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in case of 19 pin annular fuel rod cluster so that more flow will be diverted to inner side. This strategy results in an advantage of having critical heat flux on outer side of the tube. For ready reference the two designs have been shown in Fig. 1. In the advanced 19 pin design the pin diameter is increased and the tie rod diameter is decreased and the number of tie rods is increased from 4 to 6 to strengthen the cluster. All the other parameters of the two designs are compared in Table 1. In order to qualify the annual fuel, detailed physics simulations were done to estimate the safety margins and various reactivity coefficients of the design. 2. Reactor physics analysis of the annular fuel rod bundle Reactor physics studies of the 19 pin cluster have been carried out by using lattice code. The new 19 rod cluster has been simulated as a reactor lattice cell with the lattice code WIMSD (Askew et al., 1966). The circular arrayed fuel assembly has been modeled as a super cell and the calculation proceeds from heterogeneous infinite lattice calculation in hyperfine energy group structure to a homogeneous leakage correction. The burn up simulations has been performed using a critical flux spectrum and operating temperature condition. The flux distribution across the cluster has been expanded using discrete ordinates method with Sn-16 approximation which means that the angular domain has been discretized in 16 directions. The nuclear data set used in the multigroup cross section set condensed in 69 discrete energy groups from the evaluated nuclear data file ENDF/B-VI.8 dataset (WLUP, 2003). In the current design of 19 pin annular fuel rod cluster, Thorium–Low Enriched Uranium (Th, LEU) metal oxide (MOX) fuel is used. The LEU composition consists of a mixture of 19.75% 235 U and 80.25% 238 U. The fuel cluster uses 20% Low Enriched Uranium (LEU) mixed with 80% Thorium in oxide form. 2.1. Results and discussion of reactor physics analysis of 19 pin annular fuel rod cluster In a boiling light water cooled system the coolant void reactivity (CVR) is an important safety parameter. AHWR is a pressure tube type reactor and uses boiling light water as coolant. The low temperature moderator is heavy water and is outside the pressure boundary. Voiding of coolant implies that only the light water coolant inside the pressure tube voids. CVR is a measure of the reactivity changes with void (typically due to steam bubbles) fraction in the reactor coolant. This is also a major parameter, which governs the cluster design. Similarly other reactivity coefficients governing the design are Doppler reactivity and moderator temperature reactivity (MTR). Effect of Doppler broadened cross sections on reactivity due to temperature rise in fuel is taken into account by fuel temperature reactivity (FTR). The moderator temperature reactivity is defined as the change in reactivity per unit change in the moderator temperature. WIMS code is used for the analysis of the annular fuel rod cluster. The variation of coolant void reactivity as a function of change in coolant density (or voids) is presented in Fig. 2 for different average in-core burnups. It is seen that the void coefficient is negative over the operational regimes of burnups and void fractions. The core averaged coolant void reactivity has been presented as CVR-1 and CVR-2. Coolant Void Reactivity (CVR-1) is the reactivity change for 0.74–0.45 gm/cc density of coolant and CVR2 is for accidental condition (density of coolant 0.45–0.03 gm/cc) which is the reactivity introduced for voiding from normal operating condition. Various other reactivity parameters calculated are moderator temperature reactivity coefficient (MTR), channel temperature reactivity (CTR), fuel temperature reactivity (FTR), and power coefficient (PC). The results have been tabulated in Table 2.
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Fig. 1. (a) Thirty-three pin annular fuel cluster. (b) Nineteen pin annular fuel rod cluster.
During the process of evolution of final 19 pin annular fuel rod cluster from 33 pin fuel rod cluster a 25 pin design is also tested. The details of the various fuel rod clusters are tabulated in Table 3. Two options of the 19 pin annular fuel rod cluster are considered which are designated as Option R-5 and Option R-6 for convenience. The geometry R-5 and R-6 are evolved from the same 19 pin geometry; the only differences in the two geometries being the number of tie rods used. In Option R-6, the number of rods has been increased to 18 from 6 in R-5 option. The reason behind this change is important from thermal hydraulics of the channel and explained in Section 3.5 of the article. It is clear from Table 3 that the 25 pin annular fuel rod cluster is discarded due to higher value of positive coolant void reactivity. The CVR as a function of burn up for 33 pin and 19 pin annular fuel rod clusters is shown in Fig. 3. The 19 pin annular fuel
rod cluster is having more negative coolant void reactivity than the 33 pin annular fuel rod and it changes more slowly with the burn up. Even at 30,000 MWd/t burn up, the 19 pin fuel cluster shows significant negative void reactivity making it more attractive than 33 pin. 3. Thermal hydraulic analysis of the annular fuel rod cluster Thermal hydraulic analysis of the annular fuel rod bundle has been carried out by using two methods. 1. Bundle average method 2. Subchannel method
Table 1 Comparison between thirty three pin design and nineteen pin design. Description
33 pin design
19 pin design
Fuel No. of fuel pins Fuel pin ID/OD (mm) Fuel pellet ID/OD (mm) Coolant annulus mm Inner clad material ID/OD (mm) Outer clad material/ID/OD (mm) Clad Material/Density (g/cc) Clad thickness (mm) Fuel density (g/cc) No. of fuel rings No of fuel pins in each ring Pitch circle diameters of the fuel rings (mm)
33 8/17.1 9.5/15.3 8 8/9.3 15.6/17.1 Zircaloy-2/6.55 0.65 9.3 3 6/9/18 51.4/77.4/103.7
19 11.8/22.3 13.1/21.2 11.8 11.8/13.1 20/22.3 Zircaloy-2/6.55 0.65 9.3 2 1/6/12 0/47.4/93.3
Fuel types/enrichment (%) Ring 1 Ring 2 Ring 3
(Th,233 U)MOX/3.0% (Th,233 U)MOX/3.75% (Th,Pu)MOX/3.25% (average)
(Th,LEU)MOX/20% (Th,LEU)MOX/20% (Th,LEU)MOX/20% (average)
Arrangement of tie rods Pitch Circle Diameter (PCD) of central rod (mm) Pitch Circle Diameter (PCD) of other tie rods (mm) Material/Density (g/cc)/OD (mm)
0.0 No central tie rod 77.4 Zr-2/6.55/17.1
65.7 Zr-2/6.55/12
Pressure tube ID/OD (mm) Material/density (g/cc)
120/128 Zr-2.5%Nb/6.55
120/128 Zr-2.5%Nb/6.55
Calandria tube ID/OD Material/Density (g/cc)
163.8/168 Zircaloy-2/6.55
163.8/168 Zircaloy-2/6.55
Coolant Material Average coolant temperature and pressure, ◦ C and bar/average coolant density (g/cc) Heavy metal per bundle (kg) Specific power (kW/kg)
Light water 285/70/0.45 116.5 18.6
Light water 285/70/0.45 87.88 30.5
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Table 2 Comparison of various reactivity parameters of the designed bundle. No.
Pins
Description Fuel used
Average Enrichment in cluster
Achievable discharge burnup MWd/t
MTR (mk)
1
54 (Ref)
(Th,U233) MOX (Th,Pu)MOX
3.45% 233 U
42,000
2.38
2
33
(Th,U233) MOX (Th,Pu)MOX
3.25% Pu 3.45% 233 U
29,500
3
25
(Th,U233) MOX (Th,Pu)MOX
3.25% Pu 3.75% 233 U
4 5
19 (R-5) 19 (R-6)
(Th,LEU)MOX (Th,LEU)MOX
3.25% Pu 3.95% 235 U 3.95% 235 U
CTR (mk)
FTC (mk)
CVR-1 (0.74 to 0.45 g/cc) (mk)
6.056
−4.21
−0.459
2.08
4.638
−3.936
−4.3887
29,500
0.46
−2.356
−3.123
9.12
5.356
58,000 58,000
0.96 −0.76
−5.702 −4.508
−4.635 −4.531
−3.671 −2.492
−8.3061 −7.0241
Power Coefficient (mk) 4.674
−8.325
CVR-2 under LOCA (0.45–0.03 g/cc) (mk) −3.56
−8.927
9.20
−6.82 −5.52
4.0
Coolant void reactivity mk
2.0 0.0 (Xe sat) MWD/T 10000 MWD/T 20000 MWD/T 26000 MWD/T
0.0 -2.0 -4.0 -6.0 -8.0 -10.0 -12.0 0.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
80.0
90.0 100.0
Change in coolant density % Fig. 2. Variation of coolant void reactivity with change in coolant density at different average in core burn ups (data obtained by WIMS calculations).
Fig. 3. Comparison of coolant void reactivity of 33 pin and 19 pin annular fuel rod cluster for AHWR (data obtained by WIMS calculations).
3.1. Bundle average method analysis The first method is widely used where whole bundle is supposed to be a single pin and total fuel mass inside the bundle is concentrated in the inner and outer rings of the clad. Similarly whole zirconium cladding is replaced with two layers of the zirconium an inner and an outer layer. This method is called as the bundle average method as everything in the bundle is averaged out at the center. However in the design simulation by bundle average method whole bundle is assumed to be as single pin in case of solid fuel pin. In case of annular fuel pin working in this way does not suffice the purpose as it changes inside and outside heat flux distribution of
every pin which is different in every case. Therefore in case of annular fuel pin equivalent hydraulic diameter per pin is calculated and analysis is carried out for the pin where radial and axial peaking factors are maximum. Minimum Critical Heat Flux Ratio (MCHFR) value estimated using Jensen–Levy is very high at nominal power, so that the bundle power can be increased. The comparison of the values of MCHFR is made with the standard solid fuel rod cluster (Sinha and Kakodkar, 2006; Rouhani, 1978) and subsequently detailed subchannel analysis of these geometries has been carried out at a higher power. For the ready reference the geometries are shown in Fig. 4.
Table 3 Comparison of annular fuel rod cluster performance with solid fuel rod cluster by bundle average method.
Annular fuel (R5) Cluster Annular fuel (R6) Cluster Solid Fuel cluster
Power (MW)
No. of Fuel Pins
2.6
19
2.6 2.6
Fuel Pin Max Temp (K)
MCHFR (by Jensen-Levy)
Quality inside
919
3.66
0.226
19
782
2.08
0.176
54
1070
1.90
0.260
Mass Flux Inside G inside (kg/m2 s)
Mass Flux Outside G outside (kg/m2 s)
Heat Flow Inside (%)
Heat Flow Outside (%)
0.298
1266
663
47.90
52.10
0.395
1490
586
48.00
52.00
Quality outside
998
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Fig. 4. (a) 19 pin annular fuel rod cluster (option R5) (b) 19 Pin advanced annular fuel rod cluster (option R6).
3.2. Subchannel analysis There are two approaches to the definition of subchannel analysis. The traditional approach for subchannel analysis is coolant centered and is discussed in the present study. Subchannel properties like axial velocity and density are represented by single averaged values. Constitutive equations are required for input parameters like friction factors and lateral momentum equation and energy exchange rates between adjacent subchannels. In the subchannel approach a major simplification is made in the treatment of the lateral exchange between adjacent subchannels. A fully three dimensional physical situation can be represented simply by connecting the channels in a three dimensional array. This leads to simplifications in the lateral convective terms of the linear momentum balance equation. A computer code – SAAP (Subchannel Analysis of Annular Pin bundle) has been developed for subchannel analysis of annular fuel cluster. In this code subchannel analysis has been performed using the model of COBRA-IV-I. For fuel heat transfer calculations a separate heat transfer module HeAP (Heat Transfer in Annular fuel Pins) has been developed, that computes the heat flux partitioning between the inner and outer faces of the annular pin. HeAP and COBRA-IV-I are coupled externally and subchannel analysis of the annular fuel rod cluster is carried out. The development of subchannel analysis code for annular fuel rod cluster is reported by Vishnoi et al. (2013) in detail. Still for the ready reference, the procedure of subchannel analysis of annular fuel rod bundle by computer code SAAP is given in the Appendix-I. 3.3. Thermal hydraulic analysis of 19 pin annular fuel rod cluster For the thermal hydraulic analysis of the annular fuel rod bundle COBRA-IV-I code has been used. COBRA-IV-I (Wheeler et al., 1976; Jensen and Levy, 1962) is a transient subchannel analysis code. The calculation methodology involves dividing the bundle into computational cells and conservation laws of mass, momentum and energy for the fluid are then solved. The fuel rods and other solid materials in the computational domain act as heat sources or sinks. The code also has a conduction model to carry out heat transfer within cylindrical or plate type fuels. No such model exists for annular fuel pins. Thus, the heat transfer model (HeAP) has been coupled for calculations involving annular fuel pins. Critical Heat Flux (CHF) calculations can also be performed using appropriate correlations. While B&W-2 and W-3 Tong (1967) CHF correlations are built into COBRA computer code, Jensen–Levy (Jensen and Levy, 1962; Wheeler et al., 1976) correlation were programmed into
Fig. 5. 19 Pin annular fuel bundle geometry (R5).
COBRA-IV-I for inclusion in SAAP. In conventional sub-channel analysis, since sub-channels are ventilated, cross-flow between the adjacent sub-channels ensures the equalization of pressures at an axial level. For annular pins, however, the inner sub-channel is not connected to any other sub-channel thus; the mass flow rate must be adjusted among the sub-channels in such a way that the total pressure drop across the bundle length is same for all inner and outer sub-channels. For this purpose, the pressure drop boundary condition available in COBRA-IV-I is used. This ensures that the flow in each sub-channel is adjusted such that the total pressure drop equals a specified value. 3.4. Subchannel analysis of 19 pin annular fuel rod bundle Geometric arrangement of the fuel pins of the 19 pin annular fuel rod cluster is shown in Fig. 5. For the computational simplicity and from symmetry of the bundle, one sixth (1/6) geometric section is taken for the sub-channel analysis of the cluster. This symmetric section is shown in Fig. 6. The maximum bundle is 3.4 MW which is obtained by reactor physics analysis. Therefore subchannel analysis has been carried out at bundle power of 3.4 MW. Complete calculations are carried out for the section and enthalpy variation and exit quality of every subchannel is calculated. For the convenience the enthalpy variation of subchannels 1, 3, 4 and 6 along the axial length is shown in Fig. 7 along with a saturation liquid enthalpy line. It can be observed from the results that exit quality in subchannel
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Table 4 Mass flux and exit quality at each sub-channel. Subchannel
Enthalpy (kJ/kg)
Mass flow rate (kg/s)
1 2 3 4 5 6 7 8 9 10 11 12
2340.6 2330.2 1849.8 1777.5 1840.8 1452.3 1483.9 1452.3 1590.8 1687.2 1997.4 1997.4
0.013 0.013 0.051 0.064 0.051 0.100 0.191 0.100 0.023 0.129 0.104 0.104
Mass flux (G) (kg/m2 s)
Exit quality (x)
480 480 692 852 692 1308 1246 1308 1286 1176 950 950
0.713 0.712 0.387 0.339 0.386 0.123 0.144 0.123 0.215 0.279 0.485 0.485
5.0 4.5 4.0
MCHFR
3.5 3.0 2.5 2.0 1.5 1.0 0
5
10
15
20
25
axial node Fig. 6. Sub-channel geometry.
6 is very low as compared to the other subchannels due to the flow area to heated perimeter ratio. In these subchannels the flow area to heated perimeter ratio is much higher compared to other subchannels. Exit quality and mass flux of different subchannels are listed in Table 4. It is clear from Fig. 7, that the enthalpy in the subchannel 1 is higher than the enthalpy in the subchannel 6. It is clear from Table 4, that exit quality of the subchannel 1 is higher than the exit quality of the subchannel 6. Due to different void fraction in the adjacent
Fig. 8. Critical heat flux ratio of annular fuel cluster (option R5) (data obtained by bundle average method).
subchannels there is cross flow causing turbulent mass interchange. To avoid the differential flow regimes as well as to obtain a balanced exit enthalpy of all subchannels further improvement in the cluster has been made and analyzed subsequently. In the improved design the flow passage of the subchannel 6 can be reduced by providing a cylindrical rod. This reduces the flow through the subchannel 6 and which improves its exit quality. The MCHFR by bundle average method is an important aspect which must be considered along with the subchannel analysis. The designer has to keep MCHFR value above unity for safe operating conditions. The method of finding Critical Heat Flux Ratio (CHFR) of the annular fuel bundle is explained in detail by Deokule et al. (2013). The CHFR curve along the axial length of the fuel cluster by bundle average method is shown in Fig. 8. MCHFR value at 7 MPa pressure and 285 ◦ C is estimated as 1.22 for R-5 annular fuel cluster. 3.5. Improvements in the 19 pin geometry
Fig. 7. Axial enthalpy variation of different sub-channels (data obtained by subchannel analysis).
Subchannel analysis of the 19 pin annular fuel rod cluster has led to an important conclusion that the exit enthalpy of the various channels is different. It becomes necessary to put extra tie rods to block the flow at the subchannel where the mass flow rate is higher. The improvements in the design of the annular fuel rod cluster have led to the geometry R6 which is shown in Fig. 9. It consists of 19 annular fuel pins, 6 numbers of 10 mm tie rods in middle ring and 12 numbers 6 mm tie rods in the outer ring. The reactor physics parameters of this cluster have not changed as the absorption cross section of the additional zirconium tie rods is very
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Fig. 12. Subchannel geometry of the section R-6. Fig. 9. Improved 19 pin geometry – R6.
Fig. 13. Axial enthalpy variation of inner subchannel. Fig. 10. Symmetric subchannel section in option R-6.
4.5 4.0
MCHFR
3.5 3.0 2.5 2.0 1.5 1.0 0
3
6
9
12
15
18
21
24
axial node Fig. 14. Critical heat flux ratio of annular fuel cluster (option R6-data obtained by bundle average method). Fig. 11. Axial enthalpy variation of different subchannel in geometry R-6 (data obtained by subchannel analysis).
small. The tie rods in the outer ring do not provide any structural support to the cluster. They are provided to reduce the flow passage on the outer side of the bundle. For the subchannel analysis one sixth (1/6th) geometric section is taken which is shown in Fig. 10.
Subchannel analysis of this annular fuel bundle has been carried out at bundle power of 3.82 MW. The symmetric cross section enthalpy variation of outer sub-channels is shown in Fig. 11. It can be seen that all the outer subchannels have almost same enthalpy variation, only subchannel 6 shows slightly lower enthalpy because of higher flow to heat ratio.
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Table 5 Mass flux and exit quality at each sub-channel. Subchannel
Enthalpy (kJ/kg)
Mass flow rate (kg/s)
Mass flux (G) (kg/m2 s)
Exit quality (x)
1 2 3 4 5 6 7 8 9 10 11 12
1803 1803 1804 1807 1804 1734 1747 1734 1513 1615 1929 1929
0.039 0.039 0.069 0.080 0.069 0.048 0.095 0.048 0.031 0.162 0.125 0.125
983 983 913 1038 913 854 843 854 1676 1484 1146 1146
0.352 0.352 0.353 0.355 0.353 0.307 0.315 0.307 0.159 0.227 0.436 0.436
Table 6 Comparisons between 19 pin improved annular fuel rod cluster and solid fuel rod cluster. Type of fuel
No. of pins
Bundle power
MCHFR (at 120% power)
Max. fuel temp. (K)
Solid fuel Annular fuel bundle (R6)
54 19
2.6 MW 3.2 MW
1.16 1.10
1293 933
The inner subchannels typically subchannel nos. 9–11 are shown in Fig. 12 and enthalpy variations are shown in Fig. 13 subsequently. It can be seen that in the subchannel 11, coolant has the highest enthalpy while in the subchannel 9 has the lowest exit enthalpy. This variation in the enthalpy is due to local peaking factors 0.79, 0.87, 1.08 in the respective subchannels. The exit quality, mass flux and mass flow rate of each subchannel are listed in Table 5. It can be observed that exit quality of each subchannel is in the same range (0.039–0.127) and there is large variation in the inner subchannel due to the local peaking. The CHFR curve along the axial length of the fuel by bundle average method is shown in Fig. 14. MCHFR value at 7 MPa pressure and 285 ◦ C is estimated as 1.10. MCHFR and maximum fuel temperature of R6 geometry with 54 rods AHWR bundle geometry are compared in Table 6. It can be observed that with this geometry the cluster power can be enhanced to 3.2 MW with same thermal margin as of current solid AHWR fuel cluster.
fuel Pins) has been developed, that computes the heat partitioning between the inner and outer faces of the annular pin.
4. Conclusions
−k
It can be concluded that a suitable cluster with annular fuel for pressure tube type boiling water reactor can be designed without any major revision of design parameters of the solid fuel rods. The designed annular fuel rod cluster is having better performance parameters from physics as well as thermal hydraulic point of view such as negative void coolant reactivity and MCHFR. These distinct advantages make the 19 pin annular fuel rod cluster more suitable than the existing solid fuel rod cluster. Subchannel analysis of the annular fuel rod cluster shows that reducing the subchannel flow area on the outside, diverts the flow through the hottest channel improving the MCHFR margin in the hottest channel. From the analysis it is clear that final design with 19 pin annular fuel rod cluster is suitable for generation of higher power.
Appendix-I. Development of Computer Code SAAP (Subchannel Analysis for Annular Pin) A computer code – SAAP (Sub-channel Analysis of Annular Pin bundle) has been developed for sub-channel analysis of annular fuel cluster. In this code sub-channel analysis has been performed using the model of COBRA-IV-I. For fuel heat transfer calculations a separate heat transfer module HeAP (Heat Transfer in Annular
A.1. Mathematical formulation of HeAP A heat transfer analysis module, HeAP (Heat Transfer in Annular fuel Pins), capable of modeling both internally and externally cooled annular fuel pins is developed. It calculates the heat flux distribution in the inner and outer surfaces of the annular fuel assembly. It also calculates the temperature distribution of the fuel. In HeAP radial conduction equation is solved by finite difference method. For radial heat transfer inside the fuel pin, 1-D radial conduction Eq. (1a) is solved by finite difference method. ∂2 T 1 ∂T 1 ∂T + q= + ˛ ∂t k r∂r ∂r 2
for
r= / 0
(1a)
Boundary conditions at the center of the fuel and at wall coolant interface are given in Eqs. 1(b) and 1(c).
k
∂T + hin T0 = hin Tlin ∂r
∂T + hout Tm = hout Tlout ∂r
for i = 0 for i = m
(1b) (1c)
Explicit method is applied to discretize the radial conduction equation with source term in cylinder geometry. On discretization of the Eqs. 1(a) and 1(c), we get equations required numerical equations which are solved using computer program. A.2. Description of COBRA-IV-I COBRA-IV-I (Wheeler et al., 1976) is a transient sub-channel analysis code. The calculation methodology involves dividing the bundle into computational cells. Conservation laws of mass, momentum and energy for the fluid are solved. The fuel rods and other solid materials in the computational domain act as heat sources or sinks. The code also has a conduction model to solve for heat transfer within cylindrical or plate type fuels. No such model exists for annular fuel pins. Thus, the heat transfer model of HeAP has been coupled for calculations involving annular fuel pins. CHF calculations can also be performed using appropriate correlations. While B&W-2 and W-3 (Tong, 1967) correlations are built into COBRA, the 1995 LUT and Jensen–Levy (Jensen and Levy, 1962) correlation were programmed into COBRA-IV-I for inclusion in SAAP.
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Fig. A1. (A) Flow chart of SAAP computer program.
A.3. Calculation procedure of SAAP HeAP and COBRA-IV-I have been coupled for sub-channel analysis of annular fuel cluster. To begin with, additional isolated inner sub-channels of the annular fuel pins are defined in the input data of the COBRA IV. Then COBRA is executed as per the regular procedure. When COBRA calculations are converged, coolant temperature, mass flux and quality of each sub-channel are collected.
From the collected data, heat transfer coefficients of coolant and temperatures of the inner and outer surfaces of the seed pins are calculated by executing HeAP. Finally heat directed to the inner and outer sub-channels are calculated. The next step is to check if the previously assumed heat transfer fractions are within the allowable margin of error. If they are within the limits the calculation stops. This loop is repeated until the heat transfer fraction is within the error tolerance. The flow chart is shown in Fig. I(A). Fuel
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cluster is simulated by bundle average method. Different inputs which are required for the computer code are power, geometry, inlet sub-cooling of the feed water, system pressure, total pressure drop across bundle, axial flux distribution and local peaking. References Askew, J.R., Fayers, F.J., Kemshell, P.B., October 1966. A general description of the lattice code WIMS. Brit. Nucl. Energy Soc., 564. Deokule, A.P., Vishnoi, A.K., Umasankeri, K., Chandraker, D.K., Vijayan, P.K., Ganesan, S., 2013. Design of 33 pin annular fuel rod cluster for advanced heavy water reactor. Nucl. Eng. Des., 94–101. Espinosa Paredes, G., Nunez Carrera, A., Laureano Cruces, A.L., Vazquez Rodriguez, A., Espinoza-Martinez, E., 2008. Emergency management for nuclear power plant using fuzzy cognitive maps. Ann. Nucl. Energy 35, 2387–2396. Jensen, E., Levy, S., 1962. Burnout Limit Curves for Water Reactors, General Electric Report No. APED-3892. Kroger, P.G., 1976. Application of Nonequilibrium Drift Flux Model to Two Phase Blow Down Experiments, BNL-NUREG-21506-R. BROOK, Upton, MA.
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Meyer, J., 1961. Hydrodynamic models for the treatment of reactor thermal transients. Nucl. Eng. Des. 10, 269–277. Rouhani, A., 1978. In: Ginoux, J. (Ed.), Steady State Subchannel Analysis in Two Phase Flows and Application to Nuclear Reactor Design Problems. Hemisphere/Mcgraw Hill, New York, pp. 301–327. Sinha, R.K., Kakodkar, A., 2006. Design and development of AHWR-the Indian Thorium fueled innovative reactor. Nucl. Eng. Des. 236 (7–8), 683–700. Stewart, C.W., July 1977. COBRA-IV: The model and the Method: BNWL 2214 NRC-4. Tong, L.S., 1967. Heat transfer in water cooled nuclear reactors. Nucl. Eng. Des. 6, 301–304. Tong, L.S., Weisman, J., 1979. Thermal Analysis of Pressurized Water Reactors, 2nd edition. American Nuclear Society, Hindsdale, IL. Vishnoi, A.K., Dasgupta, A., Chanrakar, D.K., Vijayan, P.K., 2013. Thermal hydraulics analysis of annular fuel assembly. In: The 15th International Topical Meeting on Nuclear Reactor Thermal – Hydraulics, NURETH-15, Pisa, Italy, May 12–17. Wheeler, C.L., et al., 1976. COBRA-IV-I: An Interim Version of COBRA for Thermal Hydraulic Analysis of Rod Bundle Nuclear Fuel Elements and Cores BNWL-1962, UC-32. WLUP, 2003. See: http://www-nds.indcentre.iaea.org.in/∼wlup/WIMS Library Update Project.