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Energetics of core disruptive accident for different fuels for a medium sized fast reactor
Annals of Nuclear Energy 29 (2002) 673–683 www.elsevier.com/locate/anucene
Energetics of core disruptive accident for different fuels for a medium sized fast reactor Om Pal Singh, R. Harish* Reactor Physics Division, Indira Gandhi Centre for Atomic Research, Kalpakkam 603 102, Tamil Nadu, India Received 23 April 2001; accepted 30 May 2001
Abstract A comparative study has been made on the mechanical energy released in a core disruptive accident resulting from an unprotected loss of flow accident (LOFA) in a medium sized liquid metal fast breeder reactor with oxide, carbide and metal fuels. The study is conducted by ignoring the passive safety features incorporated in the design so that the accident scenario culminates in an energetic disassembly of the core with large energy release. The paper further provides the salient features of the analysis and presents the results with suitable physical explanations. # 2002 Elsevier Science Ltd. All rights reserved.
1. Introduction The choice of fuel material for any nuclear reactor is necessarily a process of optimization based on considerations of fuel cycle cost, growth potential and reactor safety. Reactor safety itself is not uniquely defined. A nuclear reactor with a fuel like (U–Pu–Zr) (Wade and Chang, 1988) ternary alloy may have the largest safety margin in the case of an unprotected loss of flow accident, as long as the required flow coast down is assured with the assistance of adequate stored energy in the form of flywheels directly mounted on the shaft of primary sodium pumps or when some equivalent provision is made to provide the energy required to drive the pump when it is coasting down. However, the same reactor may yield higher energy release compared to a mixed oxide core in a core disruptive accident. Therefore, a study has been carried out to study the mechanical energy released in a core disruptive * Corresponding author. E-mail address: [email protected] (R. Harish). 0306-4549/02/$ - see front matter # 2002 Elsevier Science Ltd. All rights reserved. PII: S0306-4549(01)00070-6
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accident (CDA) in a medium sized fast reactor with power of 500 MWe (1200 MWth) and fueled with oxide, carbide or metal fuels. The study specifically pertains to the loss of flow accident (LOFA). A fast flow coast down with a flow halving time of 2 s is taken and it is pessimistically assumed that the considered accident scenario leads to the disassembly of the core. In Section 2 below the relevant parameters of the three systems having a bearing on the results, are presented. Section 3 provides the results of operations and analysis and in Section 4 the conclusions are summarized.
2. Thermophysical and design parameters A medium sized (500 MWe) fast reactor cooled by liquid sodium is considered. The reactor is made up of 180 fuel subassemblies and 12 control subassemblies. The core is further subdivided into two zones, the outer zone with a higher Pu enrichment for a flatter power profile across the core. The core is divided into seven radial flow channels with four in the lower enrichment zone and three in the outer higher enrichment zone, with ten axial meshes for each channel. The CDA is analyzed with a choice of three different fuels, viz., mixed oxide, mixed carbide and metal. The cores for the three fuels are designed to have the same power. Important design and thermo-physical parameters of the reactor are given in Tables 1 and 2 respectively. The reactivity coefficients are given in Table 3. From these data, we may note the following: (i) (ii)
Reactor power being the same, linear power for the carbide system is more than that for the oxide and metal systems. Average fuel operating temperatures for oxide, carbide and metal fuels are about 1300, 1000 and 600 C, respectively. These temperatures influence the power reactivity feedback coming from the Doppler effect.
Table 1 Important design parameters of the reactor with oxide, carbide and metal fuels Parameter Reactor Power (MWe) Fuel pin diameter (mm) No. of pins/subassembly Maximum linear power (W/cm) Reactor inlet temperature ( C) Coolant temperature rise across the core ( C) Number of subassemblies in the core Peak fuel temperature ( C) Fuel average temperature ( C) Clad average temperature ( C)
Oxide 500 6.5 217 450 380 164 180 2348 1289 511
Carbide
Metal
500 8.83 127 750 380 164 180 1490 1007 518
500 6.5 217 450 380 164 180 764 590 502
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(iii) Fuel density is highest for metal fuel, followed by carbide and oxide fuels. Hence, the fuel reactivity worth per cm of the core is correspondingly maximum for metal and minimum for oxide cores. (iv) Thermal conductivity is maximum for metal fuel and minimum for oxide fuel. It results in lower fuel operating temperatures for metal fuel and also influences the course of fuel coolant interaction (FCI). (v) Specific heat for oxide fuel is large while for carbide and metal fuels it is comparable. This has important consequences. For a given amount of energy release, temperature rise is lower for the oxide core as compared to carbide and metal fuels. Thus in a power transient, reactivity feedback per unit power rise is lower for oxide fuel as compared to carbide and metal fuels.
Table 2 Thermophysical data for oxide, carbide and metal fuels Parameter
Oxide
Carbide
Metal
Fuel density (g/cm3) Smeared density (g/cm3) Linear expansion coefficient ( C1) Thermal conductivity (W/cm/ C) Specific heat (J/g/ C) Melting point ( C) Gap conductance (W/cm2/ C) Boiling point ( C) Latent heat of fusion (J/g) Latent heat of vaporization (J/g)
11.08 9.42 11.2106 0.02 0.325 2750 0.65 3387 270 2000
13.60 10.88 11.2106 0.15 0.250 2370 0.65 3900 186 1759
15.80 11.85 20.0106 0.18 0.200 1160 27.02 3932 38 1641
Table 3 Static temperature coefficient, KT (pcm/ C) and power coefficient, KP (pcm/MWt) of reactivity Parameter
Oxide
Carbide
Metal
Doppler
KT KP
0.293 0.242
0.494 0.268
0.537 0.095
Fuel axial expansion
KT KP
0.265 0.198
0.279 0.154
0.431 0.079
Steel axial expansion
KT KP
0.079 0.008
0.074 0.009
0.086 0.009
Sodium expansion
KT KP
0.367 0.026
0.326 0.026
0.645 0.049
Grid plate expansion
KT KP
0.929 0.063
1.110 0.085
1.210 0.039
Total
KT KP
1.041 0.469
1.483 0.472
1.447 0.155
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(vi) There is a large difference between melting and boiling points of metal fuel. For oxide, the difference is the least and for carbide it is in between. This shows that a larger part of the core would melt for metal fuel before the core disassembles due to fuel vapor expansion. (vii) It may be seen that though T dk/dT due to Doppler feedback is smallest for metal fuel, Doppler coefficient in units of pcm/oC near operating temperatures is lowest for oxide fuel and maximum for metal fuel. Static power coefficient of reactivity is very small for metal fuel but comparable for oxide and carbide fuels. Axial fuel expansion and sodium expansion reactivity coefficients are, maximum for metal fuel. This will have effect on transient behaviour of the system. (viii) Equation of state used for the three fuels is depicted in Fig. 1. Vapour pressure being higher for oxide fuel, it would tend to terminate the disassembly faster as compared to carbide and metal fuels. (ix) The delayed neutron parameters () and prompt neutron life time () for the three systems are comparable ( ¼ 340, 371 and 382 pcm respectively for oxide, carbide and metal cores and corresponding values of are 0.44, 0.36 and 0.30 ms). Hence, the delayed critical reactor kinetics in the absence of reactivity feedback would be similar in the three cases.
3. Results of calculations and analysis Calculations have been performed using the codes PREDIS (Singh et al., 1985) and VENUS (Jackson and Nicholson, 1972) in the pre-disassembly and disassembly phases respectively. The flow halving time for LOFA is taken as 2 s.
Fig. 1. Pressure as a function of temperature for oxide, carbide and metal fuels.
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3.1. Pre-disassembly phase Pre-disassembly phase of the analysis starts at the initiation of LOFA and ends when the peak fuel temperature in the highest rated subassembly reaches boiling point. Core geometry remains intact unless the fuel starts melting. The dominant reactivity feedback mechanisms governing the course of the accident in the pre-disassembly phase are Doppler, coolant expansion, coolant voiding and fuel slumping. Fuel axial and radial expansion feedbacks are neglected for oxide and carbide fuels but are considered for metal fuel. The axial expansion feedback gets ignored once the fuel melts. The significant results from this phase are the times of initiation of coolant boiling and fuel slumping (see Table 4), reactor power, net reactivity of the system, fraction of the voided coolant, fraction of molten fuel, reactivity addition rates due to sodium voiding, fuel slumping and FCI initiated voiding, net thermal energy above the saturation point of sodium and the phase duration (see Table 5). One can make the following remarks on these results. Coolant boiling in the three cases starts in the central channel and in the upper part of the core. For a LOFA incident, boiling starts early in oxide core and is followed by carbide and metal cases. It is because a smaller reactivity feedback from oxide fuel results in slower power reduction and hence rapid sodium heating. For the same reasons, spread of boiling in other channels is also rapid for oxide core. At the end of the pre-disassembly phase, the metal core is voided to an extent of 39%, while the carbide and oxide cores are voided to 34 and 32%, respectively. Fuel Table 4a Coolant boiling initiation times (s) Channel No.
Oxide
Carbide
Metal
1 2 3 4 5 6 7
5.062 5.087 5.177 5.297 5.337 5.492 5.907
5.367 5.422 5.447 5.602 5.897 5.014 6.634
8.255 8.455 8.695 8.765 8.895 9.445 10.545
Channel No.
Oxide
Carbide
Metal
1 2 5 3 4 6 7
7.557 7.560 7.562 7.567 – – –
8.370 8.372 8.373 8.375 8.380 8.385 –
21.145 21.335 21.379 21.401 21.405 21.419 21.422
Table 4b Fuel slumping initiation times (s)
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Table 5 Results of the pre-disassembly phase Parameter Thermal power (W) Reactivity ($) Coolant void fraction Molten fuel fraction Coolant voiding reactivity rate ($/s) Fuel slumping reactivity addition rate ($/s) Reactivity addition rate due to FCI ($/s) Phase duration (s)
Oxide
Carbide 10
6.910 0.96 0.32 0.53 <1 8 35 7.574
11
1.310 0.97 0.34 0.79 <1 16 70 8.400
Metal 2.81012 1.02 0.39 1.00 <1 28 4 21.428
melting and fuel slumping starts in the first channel and is followed by the second, fifth, third, fourth etc., in that order. The fifth channel represents the first ring of the fuel subassemblies of the higher enrichment zone where power densities are high and hence early fuel melting and fuel slumping. The time elapsed between initiation of fuel slumping and initiation of disassembly is 17 ms for oxide and 30 and 283 ms for carbide and metal cores, respectively. This means that more quantity of fuel will be molten before disassembly for the metal case, followed by carbide and oxide in decreasing order. Hence, correspondingly the rates of reactivity addition due to fuel slumping would be maximum for metal case and minimum for oxide case. Metal core is in 100% molten state at the end of pre-disassembly phase while carbide and oxide cores are respectively 79 and 53% in molten state. It is closely related to the difference in the boiling and melting points of the three fuels which are maximum for metal fuel and minimum for the oxide fuel. The reactivity at the end of the pre-disassembly phase corresponding to the three cases is 0.96, 0.97, and 1.02 $. Power and reactivity at the end of the pre-disassembly phase depend very much on the state of power transient at the time fuel starts vapourizing, particularly on the balance of positive reactivity coming from coolant voiding and fuel slumping and the negative reactivity from Doppler and core expansion. Reactivity addition rates due to fuel slumping for oxide, carbide and metal cases are 8, 16 and 28 $/s. Boiling initiated reactivity addition rates are less than 1 $/s in the three cases. Fuel Coolant Interaction (FCI) is basically benign for metal fuel and so FCI initiated voiding rates are small for metal case and are 10–15 m/s for oxide fuel (Singh et al., 1985). For carbide, FCI initiated voiding rates are found to be around two times the rates for oxide case. But, in the present case, FCI initiated voiding is not expected to occur in either of the cases, because, clad failure occurs in the upper part of the core where only sodium void exists and hence no violent FCI would be possible. If FCI occurs in a subassembly full of sodium, then it would result in about 35 $/s reactivity addition rates for oxide and 70 $/s for carbide case. For metal it is about 4 $/s (Singh et al., 1985; Bhaskar Rao and Singh, 1989). The net thermal energy above the saturation of temperature of sodium, at the end of predisassembly phase in the three (oxide, carbide and metal) cases are 6049, 6815 and 3913 MJ respectively. The value basically depends on the specific heat of fusion. For
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metal case, all the three parameters are small compared to carbide and oxide cases and hence the net thermal energy is small. In the carbide case, the energy is high compared to oxide case because the temperature of fuel at the end of pre-disassembly phase is more than that of the oxide case. The pre-disassembly phase lasts 7.6 s for the oxide case, 8.4 s for the carbide case and 21.4 s for the metal case. The phase lasts longer for the metal case, because in this case the reactivity feedbacks are more effective due to large margin in the operating temperatures of the fuel and the boiling point of the fuel. 3.2. Disassembly phase In this phase, it is assumed that the core has lost its integrity and the whole core is assumed as a fluid. Reactivity feedback arising from Doppler effect and displacement of the fuel alone are assumed to be effective. Fuel displacement ultimately terminates the neutronic power excursion. Work potential of the thermal energy released in the excursion is calculated by assuming isentropic expansion of the fuel. The results of the disassembly phase calculations in terms of thermal and mechanical energy release, maximum temperature and pressure reached, fuel void fraction etc., are given in Table 6. Keeping in view the reactivity addition rates resulting from FCI initiated voiding and fuel melting and slumping at the beginning of the dis-assembly phase mentioned above, conservatively 50, 75 and 50 $/s reactivity addition rates have been assumed during the disassembly phase. It can be seen that metal fuel gives maximum amount of mechanical energy released and then followed by carbide and oxide fuels in the decreasing order. The main reason for the large energy released for the metal case is its relatively lower value of Doppler coefficient. The whole core being in molten stage at the end of pre-disassembly phase (see Table 5), a large part of the core participates in disassembly for this fuel as compared to oxide and carbide cases. This is also reflected by the fuel vapour fraction that exists at the end of disassembly phase (see Table 6) and which is maximum for the metal fuel. Before drawing general conclusions, we present below the results of some parametric studies.
Table 6 Results of the disassembly phase calculations Parameter
Oxide
Carbide
Metal
Reactivity ramp rate ($/s) Thermal energy release (MJ) Mechanical work-potential (MJ) Maximum fuel temperature (K) Maximum fuel vapour pressure (atm) Fuel vapour fraction Molten fuel fraction Phase duration (ms)
50 2130 23 4274 10 0.21 0.85 13.3
75 3074 87 5342 15 0.25 – 9.6
50 2748 140 5854 48 0.40 1.00 3.6
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3.2.1. Reactivity addition rates The results of mechanical energy release for the three cases and for different reactivity addition rates during the disassembly phase are given in Fig. 2. The initial conditions before the disassembly phase for the three cases are the same as described above and given in Table 5. It can be seen that for oxide core, energy release is quite sensitive to the reactivity addition rates. It is not so sensitive for the metal case. For the carbide case, the sensitivity is in between. The trend appears to be related to the fraction of core that exists in the molten stage at the end of the pre-disassembly phase. The smaller the fraction of the core in the molten stage before the disassembly, the greater is the sensitivity of the energy release with the reactivity addition rates. It is, because, for lower reactivity addition rates and for a small fraction of the core being in molten stage before the disassembly phase, a relatively smaller part of the core participates in disassembly. However, a relatively large portion of the core would participate in the disassembly for large reactivity addition rates and hence, would result in larger energy release. Once the whole core starts participating in the disassembly, the sensitivity of energy release to the reactivity addition rates reduces. It is clear from these results that as long as rates of reactivity addition are of the order of 50 $/s or less, the oxide and carbide cores result in relatively small energy release and metal core releases the maximum energy. For 100 $/s or more, oxide core gives maximum energy release, followed by the carbide and metal cores in decreasing order. Around 75 $/s the oxide core again gives maximum energy release followed by metal and then carbide in decreasing order. The metal core is found to give lower energy release as compared to the oxide and carbide cores for large reactivity addition rates ( 100 $/s), when the whole core participates in the disassembly. It is in spite of the fact that the Doppler coefficient (Tdk/dT) for the metal fuel is the smallest which creates apprehensions that metal core disassembly will be more energetic than the oxide and carbide cores. The results
Fig. 2. Energy release for different reactivity addition rates for oxide, carbide and metal fuels.
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are contrary to the apprehensions, because, for the metal fuel, the specific heat being smallest, temperature rise per unit energy release is high and hence, the effective Doppler reactivity feedback is greater resulting in quenching the power excursion and so a lower value of the energy release. The variation of the Doppler reactivity feedback with time in the disassembly phase and for 100 $/s reactivity addition rates is shown in Fig. 3. 3.2.2. Doppler effect The sensitivity of the mechanical energy release with Doppler effect for different reactivity addition rates is brought out by the results presented in Fig. 4. For 50 $/s case, because of the reasons given above, metal core gives greater energy release than the carbide and oxide cores for all values of Doppler reactivity coefficient. Between the carbide and oxide cores, the carbide core gives higher energy release than the oxide core for lower values of the Doppler coefficient. It appears to be due to the lower vapour pressures for carbide core and hence delayed disassembly. However, for larger values of the Doppler coefficient, the oxide core gives more energy release than the carbide core. This is, because, due to the lower specific heat of carbide fuel, temperature rise is faster and it provides more Doppler reactivity feedback effect. For reactivity addition rate of 100 $/s, the energy release is high for all the cases. The trend of energy release for the oxide and carbide cases remains the same as for the 50 $/s case. However, for metal case energy release is lower than that of the oxide and carbide cores. This is consistent with results given in Fig. 2. 3.2.3. Temperature gradient in the core The energy release in the disassembly phase is also sensitive to the temperature gradient existing in the core at the beginning of this phase. For reactivity addition
Fig. 3. Time variation of Doppler reactivity feedback in the disassembly phase for reactivity addition rate of 100 $/s for oxide, carbide and metal fuels.
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Fig. 4. Mechanical work-potential for different Doppler reactivity coefficients for oxide, carbide and metal fuels.
rate of 50 $/s, the energy release for the oxide, carbide and metal cases are 23, 17 and 140 MJ for the case of a finite temperature distribution obtained at the end of the pre-disassembly phase. The corresponding energy releases for a flat temperature distribution for the three cases are 269, 88 and 230 MJ. Thus a constant temperature distribution case gives higher energy release than the realistic case of a finite temperature gradient. In the realistic cases, the finite temperature gradient gives rise to a corresponding pressure gradient leading to a quicker disassembly of the core.
4. Conclusions One can draw the following conclusions from this study. 1. The sodium voiding is initiated in the upper part of the core in the central subassembly for all the three cases and then propagates axially and radially in other subassemblies in various rings. Following LOFA, sodium voiding starts early in oxide core as compared to carbide and metal-fueled cores. Voiding propagation is fastest for oxide core and slowest for the metal core. Thus, more time is available for corrective action for the metal-fueled reactor. Similarly it is also found that initiation of fuel melting in metal fuel takes longer time following LOF as compared to carbide and oxide fuels. Fuel melting propagation is also slower for metal fuel. So, though the sodium void reactivity coefficient for metal fuel is highest among the three fuels the initiating (pre-disassembly) phase lasts longest for metal fuel. 2. For the metal fuel, operating temperature and the melting points are low. This would result in a benign FCI.
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3. The difference between melting point and boiling point of metal fuel being large, the metal-fueled core will take a large time for fuel vapourization. The potential for large reactivity addition rates due to fuel slumping is also high for this case. 4. A benign core disassembly occurs in oxide and carbide cores for smaller reactivity addition rates because only a small portion of the core takes part in the vaporisation and disassembly. For reactivity addition rates of 100 $/s, metal core is not potentially more dangerous than other fuels though it has a large positive sodium void coefficient and small negative Doppler reactivity coefficient. 5. A flat temperature distribution across the core leads to a large energy release as compared to a temperature distribution with a finite gradient.
References Bhaskar Rao P., Singh, O.P, 1989, Coolant Expulsion Rates in Oxide, Carbide and Metal Fueled LMFBRs due to Fuel Coolant Interaction, Internal Note RPD/01117/SNAS-23. Jackson J.F., Nicholson, R.B., 1972. VENUS-II A LMFBR Disassembly Programme, ANL-7951. Singh, O.P., Bhaskar Rao, P., Ponpandi, S., Shankar Singh, R., 1985. Design basis accident analysis work at RRC. In: Proc. Indo-German Workshop on Transient Analysis and Emergency Core Cooling Systems, BARC, Trombay, Bombay. Wade, D.C., Chang, Y.I., 1988. The integral fast reactor concept: physics of operation and safety. Nuclear Science and Engineering 100, 507–525.
Energetics of core disruptive accident for different fuels for a medium sized fast reactor Om Pal Singh, R. Harish* Reactor Physics Division, Indira Gandhi Centre for Atomic Research, Kalpakkam 603 102, Tamil Nadu, India Received 23 April 2001; accepted 30 May 2001
Abstract A comparative study has been made on the mechanical energy released in a core disruptive accident resulting from an unprotected loss of flow accident (LOFA) in a medium sized liquid metal fast breeder reactor with oxide, carbide and metal fuels. The study is conducted by ignoring the passive safety features incorporated in the design so that the accident scenario culminates in an energetic disassembly of the core with large energy release. The paper further provides the salient features of the analysis and presents the results with suitable physical explanations. # 2002 Elsevier Science Ltd. All rights reserved.
1. Introduction The choice of fuel material for any nuclear reactor is necessarily a process of optimization based on considerations of fuel cycle cost, growth potential and reactor safety. Reactor safety itself is not uniquely defined. A nuclear reactor with a fuel like (U–Pu–Zr) (Wade and Chang, 1988) ternary alloy may have the largest safety margin in the case of an unprotected loss of flow accident, as long as the required flow coast down is assured with the assistance of adequate stored energy in the form of flywheels directly mounted on the shaft of primary sodium pumps or when some equivalent provision is made to provide the energy required to drive the pump when it is coasting down. However, the same reactor may yield higher energy release compared to a mixed oxide core in a core disruptive accident. Therefore, a study has been carried out to study the mechanical energy released in a core disruptive * Corresponding author. E-mail address: [email protected] (R. Harish). 0306-4549/02/$ - see front matter # 2002 Elsevier Science Ltd. All rights reserved. PII: S0306-4549(01)00070-6
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accident (CDA) in a medium sized fast reactor with power of 500 MWe (1200 MWth) and fueled with oxide, carbide or metal fuels. The study specifically pertains to the loss of flow accident (LOFA). A fast flow coast down with a flow halving time of 2 s is taken and it is pessimistically assumed that the considered accident scenario leads to the disassembly of the core. In Section 2 below the relevant parameters of the three systems having a bearing on the results, are presented. Section 3 provides the results of operations and analysis and in Section 4 the conclusions are summarized.
2. Thermophysical and design parameters A medium sized (500 MWe) fast reactor cooled by liquid sodium is considered. The reactor is made up of 180 fuel subassemblies and 12 control subassemblies. The core is further subdivided into two zones, the outer zone with a higher Pu enrichment for a flatter power profile across the core. The core is divided into seven radial flow channels with four in the lower enrichment zone and three in the outer higher enrichment zone, with ten axial meshes for each channel. The CDA is analyzed with a choice of three different fuels, viz., mixed oxide, mixed carbide and metal. The cores for the three fuels are designed to have the same power. Important design and thermo-physical parameters of the reactor are given in Tables 1 and 2 respectively. The reactivity coefficients are given in Table 3. From these data, we may note the following: (i) (ii)
Reactor power being the same, linear power for the carbide system is more than that for the oxide and metal systems. Average fuel operating temperatures for oxide, carbide and metal fuels are about 1300, 1000 and 600 C, respectively. These temperatures influence the power reactivity feedback coming from the Doppler effect.
Table 1 Important design parameters of the reactor with oxide, carbide and metal fuels Parameter Reactor Power (MWe) Fuel pin diameter (mm) No. of pins/subassembly Maximum linear power (W/cm) Reactor inlet temperature ( C) Coolant temperature rise across the core ( C) Number of subassemblies in the core Peak fuel temperature ( C) Fuel average temperature ( C) Clad average temperature ( C)
Oxide 500 6.5 217 450 380 164 180 2348 1289 511
Carbide
Metal
500 8.83 127 750 380 164 180 1490 1007 518
500 6.5 217 450 380 164 180 764 590 502
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(iii) Fuel density is highest for metal fuel, followed by carbide and oxide fuels. Hence, the fuel reactivity worth per cm of the core is correspondingly maximum for metal and minimum for oxide cores. (iv) Thermal conductivity is maximum for metal fuel and minimum for oxide fuel. It results in lower fuel operating temperatures for metal fuel and also influences the course of fuel coolant interaction (FCI). (v) Specific heat for oxide fuel is large while for carbide and metal fuels it is comparable. This has important consequences. For a given amount of energy release, temperature rise is lower for the oxide core as compared to carbide and metal fuels. Thus in a power transient, reactivity feedback per unit power rise is lower for oxide fuel as compared to carbide and metal fuels.
Table 2 Thermophysical data for oxide, carbide and metal fuels Parameter
Oxide
Carbide
Metal
Fuel density (g/cm3) Smeared density (g/cm3) Linear expansion coefficient ( C1) Thermal conductivity (W/cm/ C) Specific heat (J/g/ C) Melting point ( C) Gap conductance (W/cm2/ C) Boiling point ( C) Latent heat of fusion (J/g) Latent heat of vaporization (J/g)
11.08 9.42 11.2106 0.02 0.325 2750 0.65 3387 270 2000
13.60 10.88 11.2106 0.15 0.250 2370 0.65 3900 186 1759
15.80 11.85 20.0106 0.18 0.200 1160 27.02 3932 38 1641
Table 3 Static temperature coefficient, KT (pcm/ C) and power coefficient, KP (pcm/MWt) of reactivity Parameter
Oxide
Carbide
Metal
Doppler
KT KP
0.293 0.242
0.494 0.268
0.537 0.095
Fuel axial expansion
KT KP
0.265 0.198
0.279 0.154
0.431 0.079
Steel axial expansion
KT KP
0.079 0.008
0.074 0.009
0.086 0.009
Sodium expansion
KT KP
0.367 0.026
0.326 0.026
0.645 0.049
Grid plate expansion
KT KP
0.929 0.063
1.110 0.085
1.210 0.039
Total
KT KP
1.041 0.469
1.483 0.472
1.447 0.155
676
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(vi) There is a large difference between melting and boiling points of metal fuel. For oxide, the difference is the least and for carbide it is in between. This shows that a larger part of the core would melt for metal fuel before the core disassembles due to fuel vapor expansion. (vii) It may be seen that though T dk/dT due to Doppler feedback is smallest for metal fuel, Doppler coefficient in units of pcm/oC near operating temperatures is lowest for oxide fuel and maximum for metal fuel. Static power coefficient of reactivity is very small for metal fuel but comparable for oxide and carbide fuels. Axial fuel expansion and sodium expansion reactivity coefficients are, maximum for metal fuel. This will have effect on transient behaviour of the system. (viii) Equation of state used for the three fuels is depicted in Fig. 1. Vapour pressure being higher for oxide fuel, it would tend to terminate the disassembly faster as compared to carbide and metal fuels. (ix) The delayed neutron parameters () and prompt neutron life time () for the three systems are comparable ( ¼ 340, 371 and 382 pcm respectively for oxide, carbide and metal cores and corresponding values of are 0.44, 0.36 and 0.30 ms). Hence, the delayed critical reactor kinetics in the absence of reactivity feedback would be similar in the three cases.
3. Results of calculations and analysis Calculations have been performed using the codes PREDIS (Singh et al., 1985) and VENUS (Jackson and Nicholson, 1972) in the pre-disassembly and disassembly phases respectively. The flow halving time for LOFA is taken as 2 s.
Fig. 1. Pressure as a function of temperature for oxide, carbide and metal fuels.
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3.1. Pre-disassembly phase Pre-disassembly phase of the analysis starts at the initiation of LOFA and ends when the peak fuel temperature in the highest rated subassembly reaches boiling point. Core geometry remains intact unless the fuel starts melting. The dominant reactivity feedback mechanisms governing the course of the accident in the pre-disassembly phase are Doppler, coolant expansion, coolant voiding and fuel slumping. Fuel axial and radial expansion feedbacks are neglected for oxide and carbide fuels but are considered for metal fuel. The axial expansion feedback gets ignored once the fuel melts. The significant results from this phase are the times of initiation of coolant boiling and fuel slumping (see Table 4), reactor power, net reactivity of the system, fraction of the voided coolant, fraction of molten fuel, reactivity addition rates due to sodium voiding, fuel slumping and FCI initiated voiding, net thermal energy above the saturation point of sodium and the phase duration (see Table 5). One can make the following remarks on these results. Coolant boiling in the three cases starts in the central channel and in the upper part of the core. For a LOFA incident, boiling starts early in oxide core and is followed by carbide and metal cases. It is because a smaller reactivity feedback from oxide fuel results in slower power reduction and hence rapid sodium heating. For the same reasons, spread of boiling in other channels is also rapid for oxide core. At the end of the pre-disassembly phase, the metal core is voided to an extent of 39%, while the carbide and oxide cores are voided to 34 and 32%, respectively. Fuel Table 4a Coolant boiling initiation times (s) Channel No.
Oxide
Carbide
Metal
1 2 3 4 5 6 7
5.062 5.087 5.177 5.297 5.337 5.492 5.907
5.367 5.422 5.447 5.602 5.897 5.014 6.634
8.255 8.455 8.695 8.765 8.895 9.445 10.545
Channel No.
Oxide
Carbide
Metal
1 2 5 3 4 6 7
7.557 7.560 7.562 7.567 – – –
8.370 8.372 8.373 8.375 8.380 8.385 –
21.145 21.335 21.379 21.401 21.405 21.419 21.422
Table 4b Fuel slumping initiation times (s)
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Table 5 Results of the pre-disassembly phase Parameter Thermal power (W) Reactivity ($) Coolant void fraction Molten fuel fraction Coolant voiding reactivity rate ($/s) Fuel slumping reactivity addition rate ($/s) Reactivity addition rate due to FCI ($/s) Phase duration (s)
Oxide
Carbide 10
6.910 0.96 0.32 0.53 <1 8 35 7.574
11
1.310 0.97 0.34 0.79 <1 16 70 8.400
Metal 2.81012 1.02 0.39 1.00 <1 28 4 21.428
melting and fuel slumping starts in the first channel and is followed by the second, fifth, third, fourth etc., in that order. The fifth channel represents the first ring of the fuel subassemblies of the higher enrichment zone where power densities are high and hence early fuel melting and fuel slumping. The time elapsed between initiation of fuel slumping and initiation of disassembly is 17 ms for oxide and 30 and 283 ms for carbide and metal cores, respectively. This means that more quantity of fuel will be molten before disassembly for the metal case, followed by carbide and oxide in decreasing order. Hence, correspondingly the rates of reactivity addition due to fuel slumping would be maximum for metal case and minimum for oxide case. Metal core is in 100% molten state at the end of pre-disassembly phase while carbide and oxide cores are respectively 79 and 53% in molten state. It is closely related to the difference in the boiling and melting points of the three fuels which are maximum for metal fuel and minimum for the oxide fuel. The reactivity at the end of the pre-disassembly phase corresponding to the three cases is 0.96, 0.97, and 1.02 $. Power and reactivity at the end of the pre-disassembly phase depend very much on the state of power transient at the time fuel starts vapourizing, particularly on the balance of positive reactivity coming from coolant voiding and fuel slumping and the negative reactivity from Doppler and core expansion. Reactivity addition rates due to fuel slumping for oxide, carbide and metal cases are 8, 16 and 28 $/s. Boiling initiated reactivity addition rates are less than 1 $/s in the three cases. Fuel Coolant Interaction (FCI) is basically benign for metal fuel and so FCI initiated voiding rates are small for metal case and are 10–15 m/s for oxide fuel (Singh et al., 1985). For carbide, FCI initiated voiding rates are found to be around two times the rates for oxide case. But, in the present case, FCI initiated voiding is not expected to occur in either of the cases, because, clad failure occurs in the upper part of the core where only sodium void exists and hence no violent FCI would be possible. If FCI occurs in a subassembly full of sodium, then it would result in about 35 $/s reactivity addition rates for oxide and 70 $/s for carbide case. For metal it is about 4 $/s (Singh et al., 1985; Bhaskar Rao and Singh, 1989). The net thermal energy above the saturation of temperature of sodium, at the end of predisassembly phase in the three (oxide, carbide and metal) cases are 6049, 6815 and 3913 MJ respectively. The value basically depends on the specific heat of fusion. For
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metal case, all the three parameters are small compared to carbide and oxide cases and hence the net thermal energy is small. In the carbide case, the energy is high compared to oxide case because the temperature of fuel at the end of pre-disassembly phase is more than that of the oxide case. The pre-disassembly phase lasts 7.6 s for the oxide case, 8.4 s for the carbide case and 21.4 s for the metal case. The phase lasts longer for the metal case, because in this case the reactivity feedbacks are more effective due to large margin in the operating temperatures of the fuel and the boiling point of the fuel. 3.2. Disassembly phase In this phase, it is assumed that the core has lost its integrity and the whole core is assumed as a fluid. Reactivity feedback arising from Doppler effect and displacement of the fuel alone are assumed to be effective. Fuel displacement ultimately terminates the neutronic power excursion. Work potential of the thermal energy released in the excursion is calculated by assuming isentropic expansion of the fuel. The results of the disassembly phase calculations in terms of thermal and mechanical energy release, maximum temperature and pressure reached, fuel void fraction etc., are given in Table 6. Keeping in view the reactivity addition rates resulting from FCI initiated voiding and fuel melting and slumping at the beginning of the dis-assembly phase mentioned above, conservatively 50, 75 and 50 $/s reactivity addition rates have been assumed during the disassembly phase. It can be seen that metal fuel gives maximum amount of mechanical energy released and then followed by carbide and oxide fuels in the decreasing order. The main reason for the large energy released for the metal case is its relatively lower value of Doppler coefficient. The whole core being in molten stage at the end of pre-disassembly phase (see Table 5), a large part of the core participates in disassembly for this fuel as compared to oxide and carbide cases. This is also reflected by the fuel vapour fraction that exists at the end of disassembly phase (see Table 6) and which is maximum for the metal fuel. Before drawing general conclusions, we present below the results of some parametric studies.
Table 6 Results of the disassembly phase calculations Parameter
Oxide
Carbide
Metal
Reactivity ramp rate ($/s) Thermal energy release (MJ) Mechanical work-potential (MJ) Maximum fuel temperature (K) Maximum fuel vapour pressure (atm) Fuel vapour fraction Molten fuel fraction Phase duration (ms)
50 2130 23 4274 10 0.21 0.85 13.3
75 3074 87 5342 15 0.25 – 9.6
50 2748 140 5854 48 0.40 1.00 3.6
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3.2.1. Reactivity addition rates The results of mechanical energy release for the three cases and for different reactivity addition rates during the disassembly phase are given in Fig. 2. The initial conditions before the disassembly phase for the three cases are the same as described above and given in Table 5. It can be seen that for oxide core, energy release is quite sensitive to the reactivity addition rates. It is not so sensitive for the metal case. For the carbide case, the sensitivity is in between. The trend appears to be related to the fraction of core that exists in the molten stage at the end of the pre-disassembly phase. The smaller the fraction of the core in the molten stage before the disassembly, the greater is the sensitivity of the energy release with the reactivity addition rates. It is, because, for lower reactivity addition rates and for a small fraction of the core being in molten stage before the disassembly phase, a relatively smaller part of the core participates in disassembly. However, a relatively large portion of the core would participate in the disassembly for large reactivity addition rates and hence, would result in larger energy release. Once the whole core starts participating in the disassembly, the sensitivity of energy release to the reactivity addition rates reduces. It is clear from these results that as long as rates of reactivity addition are of the order of 50 $/s or less, the oxide and carbide cores result in relatively small energy release and metal core releases the maximum energy. For 100 $/s or more, oxide core gives maximum energy release, followed by the carbide and metal cores in decreasing order. Around 75 $/s the oxide core again gives maximum energy release followed by metal and then carbide in decreasing order. The metal core is found to give lower energy release as compared to the oxide and carbide cores for large reactivity addition rates ( 100 $/s), when the whole core participates in the disassembly. It is in spite of the fact that the Doppler coefficient (Tdk/dT) for the metal fuel is the smallest which creates apprehensions that metal core disassembly will be more energetic than the oxide and carbide cores. The results
Fig. 2. Energy release for different reactivity addition rates for oxide, carbide and metal fuels.
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are contrary to the apprehensions, because, for the metal fuel, the specific heat being smallest, temperature rise per unit energy release is high and hence, the effective Doppler reactivity feedback is greater resulting in quenching the power excursion and so a lower value of the energy release. The variation of the Doppler reactivity feedback with time in the disassembly phase and for 100 $/s reactivity addition rates is shown in Fig. 3. 3.2.2. Doppler effect The sensitivity of the mechanical energy release with Doppler effect for different reactivity addition rates is brought out by the results presented in Fig. 4. For 50 $/s case, because of the reasons given above, metal core gives greater energy release than the carbide and oxide cores for all values of Doppler reactivity coefficient. Between the carbide and oxide cores, the carbide core gives higher energy release than the oxide core for lower values of the Doppler coefficient. It appears to be due to the lower vapour pressures for carbide core and hence delayed disassembly. However, for larger values of the Doppler coefficient, the oxide core gives more energy release than the carbide core. This is, because, due to the lower specific heat of carbide fuel, temperature rise is faster and it provides more Doppler reactivity feedback effect. For reactivity addition rate of 100 $/s, the energy release is high for all the cases. The trend of energy release for the oxide and carbide cases remains the same as for the 50 $/s case. However, for metal case energy release is lower than that of the oxide and carbide cores. This is consistent with results given in Fig. 2. 3.2.3. Temperature gradient in the core The energy release in the disassembly phase is also sensitive to the temperature gradient existing in the core at the beginning of this phase. For reactivity addition
Fig. 3. Time variation of Doppler reactivity feedback in the disassembly phase for reactivity addition rate of 100 $/s for oxide, carbide and metal fuels.
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Fig. 4. Mechanical work-potential for different Doppler reactivity coefficients for oxide, carbide and metal fuels.
rate of 50 $/s, the energy release for the oxide, carbide and metal cases are 23, 17 and 140 MJ for the case of a finite temperature distribution obtained at the end of the pre-disassembly phase. The corresponding energy releases for a flat temperature distribution for the three cases are 269, 88 and 230 MJ. Thus a constant temperature distribution case gives higher energy release than the realistic case of a finite temperature gradient. In the realistic cases, the finite temperature gradient gives rise to a corresponding pressure gradient leading to a quicker disassembly of the core.
4. Conclusions One can draw the following conclusions from this study. 1. The sodium voiding is initiated in the upper part of the core in the central subassembly for all the three cases and then propagates axially and radially in other subassemblies in various rings. Following LOFA, sodium voiding starts early in oxide core as compared to carbide and metal-fueled cores. Voiding propagation is fastest for oxide core and slowest for the metal core. Thus, more time is available for corrective action for the metal-fueled reactor. Similarly it is also found that initiation of fuel melting in metal fuel takes longer time following LOF as compared to carbide and oxide fuels. Fuel melting propagation is also slower for metal fuel. So, though the sodium void reactivity coefficient for metal fuel is highest among the three fuels the initiating (pre-disassembly) phase lasts longest for metal fuel. 2. For the metal fuel, operating temperature and the melting points are low. This would result in a benign FCI.
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3. The difference between melting point and boiling point of metal fuel being large, the metal-fueled core will take a large time for fuel vapourization. The potential for large reactivity addition rates due to fuel slumping is also high for this case. 4. A benign core disassembly occurs in oxide and carbide cores for smaller reactivity addition rates because only a small portion of the core takes part in the vaporisation and disassembly. For reactivity addition rates of 100 $/s, metal core is not potentially more dangerous than other fuels though it has a large positive sodium void coefficient and small negative Doppler reactivity coefficient. 5. A flat temperature distribution across the core leads to a large energy release as compared to a temperature distribution with a finite gradient.
References Bhaskar Rao P., Singh, O.P, 1989, Coolant Expulsion Rates in Oxide, Carbide and Metal Fueled LMFBRs due to Fuel Coolant Interaction, Internal Note RPD/01117/SNAS-23. Jackson J.F., Nicholson, R.B., 1972. VENUS-II A LMFBR Disassembly Programme, ANL-7951. Singh, O.P., Bhaskar Rao, P., Ponpandi, S., Shankar Singh, R., 1985. Design basis accident analysis work at RRC. In: Proc. Indo-German Workshop on Transient Analysis and Emergency Core Cooling Systems, BARC, Trombay, Bombay. Wade, D.C., Chang, Y.I., 1988. The integral fast reactor concept: physics of operation and safety. Nuclear Science and Engineering 100, 507–525.