Nuclear Technology ISSN: 0029-5450 (Print) 1943-7471 (Online) Journal homepage: http://www.tandfonline.com/loi/unct20 On the Use of Reduced-Moderation LWRs for Transuranic Isotope Burning in Thorium Fuel—II: Core Analysis Benjamin A. Lindley, N. Zara Zainuddin, Paolo Ferroni, Andrew Hall, Fausto Franceschini & Geoffrey T. Parks To cite this article: Benjamin A. Lindley, N. Zara Zainuddin, Paolo Ferroni, Andrew Hall, Fausto Franceschini & Geoffrey T. Parks (2014) On the Use of Reduced-Moderation LWRs for Transuranic Isotope Burning in Thorium Fuel—II: Core Analysis, Nuclear Technology, 185:2, 147-173, DOI: 10.13182/NT13-54 To link to this article: https://doi.org/10.13182/NT13-54 Published online: 20 Mar 2017. Submit your article to this journal Article views: 3 View related articles View Crossmark data Full Terms & Conditions of access and use can be found at http://www.tandfonline.com/action/journalInformation?journalCode=unct20 ON THE USE OF REDUCEDMODERATION LWRS FOR TRANSURANIC ISOTOPE BURNING IN THORIUM FUEL—II: CORE ANALYSIS FUEL CYCLE AND MANAGEMENT KEYWORDS: thorium, transuranics, reduced-moderation LWR BENJAMIN A. LINDLEY,a* N. ZARA ZAINUDDIN,a PAOLO FERRONI,b ANDREW HALL,c FAUSTO FRANCESCHINI,b and GEOFFREY T. PARKSa a University of Cambridge, Department of Engineering, Trumpington Street Cambridge CB2 1PZ, United Kingdom b Westinghouse Electric Company LLC, Cranberry Township, Pennsylvania c University of Michigan, Nuclear Engineering and Radiological Sciences, Ann Arbor, Michigan Received March 28, 2013 Accepted for Publication July 17, 2013 http://dx.doi.org/10.13182/NT13-54 Multiple recycle of transuranic (TRU) isotopes in thermal reactors results in a degradation of the plutonium (Pu) fissile quality with buildup of higher actinides (e.g., Am, Cm, Cf), some of which are thermal absorbers. These phenomena lead to increasing amounts of Pu feed being required to sustain criticality and accordingly larger TRU content in the multirecycled fuel inventory, ultimately resulting in a positive moderator temperature coefficient (MTC) and void reactivity coefficient (VC). Because of the favorable impact fostered by use of thorium (Th) on these coefficients, the feasibility of Th-TRU multiple recycle in reduced-moderation (RM) pressurized water reactors (PWRs) and RM boiling water reactors (called RMPWRs and RBWRs, respectively) has been investigated. In this paper, Part II of two companion papers, the results of the single-assembly analyses of Part I are developed to investigate full-core feasibility. A large reduction in moderation is necessary to allow full actinide recycle. This increases the core pressure drop, which poses some thermal-hydraulic challenges, which are more pronounced if the design implementation is through retrofitting an existing PWR. For a given reactor cooling pump, the core flow rate is reduced. Despite this, it is possible to achieve feasible inlet and outlet temperatures and minimum departure from nucleate boiling ratio, for the reduction in moderation considered here. Reflood after loss-of-coolant accident is expected to be slower, which may lead to unacceptable peak clad temperatures and/or clad oxidation. Equilibrium cycles are presented for the RMPWR and RBWR, with a negative MTC and VC. However, the RMPWR may have positive reactivity when fully voided, and the hard spectrum makes it difficult to achieve an adequate shutdown margin, such that for the considered fuel designs, additional rod banks would be required. I. INTRODUCTION each recycle. Thorium-232 is a suitable fertile isotope due to its beneficial effect on the moderator temperature coefficient (MTC) and/or void reactivity coefficient (VC), which tend to be limiting for TRU incineration in LWRs. In the Part I companion paper,1 assembly calculations for TRU recycle in reduced-moderation (RM) pressurized water reactors (PWRs) and RM boiling water reactors (BWRs) (called RMPWRs and RBWRs, respectively) are Transuranic (TRU) incineration can be performed in light water reactors (LWRs) by mixing an external TRU feed with a fertile isotope and recycling all actinides after *E-mail: bal29@cam.ac.uk NUCLEAR TECHNOLOGY VOL. 185 FEB. 2014 Note: Some figures in this paper may be in color only in the electronic version. 147 Lindley et al. REDUCED-MODERATION LWRs FOR TRU BURNING IN Th FUEL—II presented. The external TRU feed was typical for PWR UO2 used fuel, i.e., 4.4 wt% low-enriched uranium PWR discharge, burned to 52 GWd/tiHM (tonnes initial heavy metal) and cooled for 10 years (Table I). Lattice calculations were performed using a development version of WIMS 10 (Ref. 2). It is possible to achieve a harder neutron spectrum in RBWRs than RMPWRs. With axially homogeneous fuel, which is preferred to reduce the difficulty of remote fuel fabrication, the fissile inventory ratioa of the RBWR is therefore intrinsically higher, which reduces the incineration rate. However, reducing moderation improves the overall trade-off between discharge burnup and MTC/VC. There are therefore neutronic advantages and disadvantages to each design. However, thermal-hydraulic and full-core analyses are necessary to investigate the feasibility of these designs in more detail. For RMPWRs, it is highly desirable to implement the design by retrofitting an existing plant, if this is possible. This is anticipated to reduce the time to feasible implementation and to mitigate the costs associated with licensing and constructing RM plants, especially as a large incinerator fleet is needed to produce a meaningful reduction in TRU waste. The RBWR is a larger departure from existing designs, and so it is unlikely to be possible to retrofit an existing core. Retrofit imposes thermalhydraulic feasibility constraints. It is necessary to check if TABLE I Reload Isotope Vector Isotope 241 Am Am 243 Am 242 Cm 243 Cm 244 Cm 245 Cm 246 Cm 247 Cm 248 Cm 237 Np 238 Pu 239 Pu 240 Pu 241 Pu 243 Pu 242m a Atomic Percent 5.77 7.15E{03a 1.60 2.99E{07 5.73E{03 0.50 0.06 6.46E{03 9.34E{05 7.04E{06 4.94 2.74 48.45 21.03 8.45 6.46 Read as 7.15|10{3. a Defined as the ratio of 233Uz235Uz239Puz241Pu at unloading compared to that at loading. 148 the reduction in moderation identified in the Part I companion paper,1 as required for neutronic reasons, can meet these thermal-hydraulic constraints. While the MTC of the assembly designs in Part I is negative, it is possible for the fully voided core to have positive reactivity, and this requires full-core models to calculate, as it is highly leakage dependent. Finally, a preliminary assessment of whether it is possible for the reactor to achieve an adequate shutdown margin (SDM) is made. There is strong feedback between power and void distribution in an RBWR, and a coupled full-core model is necessary to evaluate it. This affects the equilibrium cycle length and the VC. In particular, a VC calculation based on a core-average void fraction (VF) calculation is insufficient, and full-core VC calculations for the assembly designs from the Part I companion paper1 are presented here. The equilibrium isotope vectors considered in the full-core analyses are given in Table II. II. THERMAL-HYDRAULIC STUDY OF RMPWRs A simplified thermal-hydraulic study has been performed to investigate the feasibility of the RMPWR concept and to identify the main thermal-hydraulic challenges characterizing this design. The trade-off between burnup and MTC, and therefore the neutronic performance, tends to improve as the assembly lattice becomes tighter. Therefore, the interest is focused on the tightest geometry likely to be achievable when accounting for constraints on rod-to-rod spacing and on the design implementation strategy adopted in this study, i.e., use of 17|17 assemblies with the same footprint as the reference design. The rod-to-rod spacing is a hard constraint imposing a lower limit on the minimum distance between adjacent fuel rods. The numerical value of this constraint depends on the rod support technique adopted: If grid spacers are used, it is reasonable to require the space needed for the grid strap and dimples to be at least 2 mm, which, for a 12.6-mm fuel rod pitch, would limit the maximum fuel rod diameter to *10.6 mm. On the other hand, if tighter lattices are required, wire-wraps can be used in place of spacer grids, since they allow a reduction in the minimum rod-to-rod spacing to *1.1 mm. [The choice for this limit was not based on calculations or manufacturing tests but on past experience with wire-wraps in fast reactors. According to data found in Refs. 3, 4, and 5, wire-wrap diameters for experimental fast reactors ranged between 0.7 mm (BOR-60) and 2.1 mm (JOYO), with more frequent values in the 1.1- to 1.5-mm range.] This corresponds to a maximum pin diameter of 11.5 mm in an unmodified pitch lattice. The design implementation strategy is instead a soft constraint approach related to the possible implementation of an RM core in an existing reactor (backfit approach), in NUCLEAR TECHNOLOGY VOL. 185 FEB. 2014 Lindley et al. REDUCED-MODERATION LWRs FOR TRU BURNING IN Th FUEL—II TABLE II SOC Equilibrium Isotope Vectors (atom/b?cm) for Selected Cases Isotope 241 Am Am 243 Am 242 Cm 243 Cm 244 Cm 245 Cm 246 Cm 247 Cm 248 Cm 237 Np 238 Pu 239 Pu 240 Pu 241 Pu 242 Pu 232 Th 233 U 234 U 235 U 236 U O 242m a RBWR Homogeneous 26% TRU Reload RBWR Homogeneous 30% TRU Reload RMPWR 11-mm Pin o.d. Heterogeneous 50% TRU Reload 132 Th-TRU Pins 1.391E{04a 5.374E{06 7.251E{05 3.548E{09 4.353E{07 4.029E{05 2.237E{05 1.667E{05 3.824E{06 1.492E{06 7.273E{05 2.210E{04 3.567E{04 4.588E{04 1.018E{04 1.918E{04 1.639E{02 1.109E{03 3.935E{04 1.433E{04 1.067E{04 3.970E{02 1.540E{04 5.978E{06 8.608E{05 5.479E{09 7.019E{07 5.428E{05 2.808E{05 2.023E{05 4.633E{06 1.729E{06 7.705E{05 2.460E{04 4.294E{04 5.753E{04 1.289E{04 2.435E{04 1.606E{02 1.123E{03 3.769E{04 1.379E{04 1.008E{04 3.970E{02 3.158E{04 8.525E{06 1.708E{04 1.467E{08 1.108E{06 1.143E{04 4.847E{05 4.586E{05 1.068E{05 5.010E{06 1.293E{04 5.345E{04 7.810E{04 1.204E{03 2.380E{04 6.370E{04 1.660E{02 5.667E{04 4.906E{04 1.421E{04 1.460E{04 4.437E{02 RMPWR 11-mm Pin o.d. Heterogeneous 52.5% TRU Reload 152 Th-TRU Pins RMPWR 11.5-mm Pin o.d. Heterogeneous 40% TRU Reload 132 Th-TRU Pins 3.226E{04 8.573E{06 1.838E{04 1.468E{08 1.194E{06 1.317E{04 5.630E{05 5.031E{05 1.137E{05 5.327E{06 1.290E{04 5.567E{04 8.412E{04 1.247E{03 2.707E{04 6.713E{04 1.627E{02 6.331E{04 5.099E{04 1.467E{04 1.426E{04 4.437E{02 2.643E{04 7.780E{06 1.488E{04 1.190E{08 9.815E{07 1.012E{04 4.482E{05 4.171E{05 1.014E{05 4.633E{06 1.081E{04 4.569E{04 6.180E{04 1.039E{03 2.011E{04 5.460E{04 1.712E{02 6.697E{04 5.094E{04 1.514E{04 1.453E{04 4.437E{02 Read as 1.391|10{4. which case, it would be preferable to preserve the location of the control guide thimbles. To facilitate this, the assembly lattice (square) and the fuel rod pitch (12.6 mm) are maintained unchanged with respect to the reference plant. An actual optimization of the RMPWR lattice geometry would require relaxation of the soft constraint on the lattice type and fuel rod pitch and would likely yield a very different lattice compared to that of typical PWRs. This design approach, incompatible with a backfit approach but with clear advantages from a reactor performance viewpoint, will be the subject of future studies. II.A. Thermal-Hydraulic Constraints In this study, RM is obtained by maintaining the fuel rod pitch at the reference value while increasing the fuel rod diameter. This modification has several interdependent consequences on the reactor thermal hydraulics, which need to be assessed to guarantee that reactor operation is possible, while satisfying safety limits. For example, the transition to the new lattice geometry results in a larger heat transfer area and, therefore, if the core power is kept constant, a lower heat flux to the coolant, which is known to have a beneficial effect on the minimum departure from NUCLEAR TECHNOLOGY VOL. 185 FEB. 2014 nucleate boiling ratio (MDNBR). However, lattice tightening also results in a smaller flow area and hydraulic diameter, which, mainly because of pressure drop considerations, require the coolant flow rate to be reduced. Depending on core power and core inlet temperature (Tin ), this reduced flow may result in a higher coolant enthalpy throughout the core, which is detrimental to the MDNBR. Therefore, whether or not the RMPWR performs better than the reference PWR, from the MDNBR viewpoint, depends on how heat flux, coolant velocity, and enthalpy compare to those in the reference PWR. In addition, it also depends on the effect that the lattice tightening has, per se, on departure from nucleate boiling (DNB), as discussed in Sec. II.A.1. Sections II.A.1 through II.A.5 discuss the thermalhydraulic constraints that have been accounted for to reasonably guarantee operability and safety of the proposed RMPWR designs. Table III summarizes the limit values selected for each constraint. II.A.1. Minimum Departure from Nucleate Boiling Ratio The design of an RMPWR that can satisfy safety requirements was performed by imposing a minimum 149 Lindley et al. REDUCED-MODERATION LWRs FOR TRU BURNING IN Th FUEL—II TABLE III Thermal-Hydraulic Constraints Design Constraint Value MDNBR 1.31 RCP performance Constrained by the RCP characteristic curve 600 K (feasible case); 603 K (stretch case) Core outlet temperature, Tout Core inlet temperature, Tin Assembly liftoff force 560.3 K n/a Rationale MDNBR for the reference core, computed with the Dalle Donne– Hame correlation; see Sec. II.A.1 See Sec. II.A.2 Two values, the lower of which is that of the reference plant; see Sec. II.A.3 5 K less than the reference case; see Sec. II.A.4 Calculated, but not used to constrain the design; see Sec. II.A.5 allowed DNB ratio when the reactor is assumed to operate at 112% of its nominal power, 95% of nominal flow, and with a Tin 2 K higher than the nominal. This minimum value is selected to be equal to the MDNBR of the reference PWR when analyzed in the same conditions, and with the same critical heat flux (CHF) correlation. This approach, although not rigorous, is often used in simplified analyses since it affords reasonable protection against DNB without the need to analyze both nominal conditions and transient-specific power levels. The rationale behind the method is that, from the DNB perspective, condition I and II transients are bounded by the operating conditions mentioned above. The CHF correlation used to compute the MDNBR is that developed by Dalle Donne and Hame,6 which, unlike the most well-known correlations typically used for open lattices, e.g., the W-3 correlation, was developed specifically for tight lattices and demonstrated to be accurate for both. It must be mentioned, however, that this correlation was originally formulated for triangular lattices, whereas the present investigation focuses on square lattices. Even though no systematic study has been found on the effect of the lattice type on the CHF, it is reasonable to assume that the correlation will give good results despite this approximation, but further analysis may be required to support this. To highlight the nonconservative results that would be obtained if a CHF correlation developed for open lattices was used for tight 150 lattices, results obtained with the W-3 correlation are also presented.7 The W-3 result is taken directly from a singleassembly analysis performed with the COBRA code (see Sec. II.B) and assuming eight grid spacers in all cases, while a separate calculation, for a single hot channel, was used to compute the Dalle Donne–Hame MDNBR. An important parameter in the Dalle Donne–Hame correlation is the pitch of the wire-wrap (H ). The correlation is valid for the range 13:6ƒH=Dƒ50, and values of 14 and 50 are used as bounding cases on the design, where D is the pin diameter. II.A.2. Reactor Cooling Pump Performance The flow rate through the reactor cooling system (RCS) is constrained by the performance of the reactor cooling pumps (RCPs) and, specifically, by their head versus flow characteristic curve. In existing PWRs, the RCPs operate at constant speed, which means that the relationship between RCS pressure drop and delivered flow is a fixed curve. Therefore, if one of these plants is retrofitted with an RM core, the flow resistance increase resulting from this transition will prevent the RCPs from delivering the same flow as in the original design, and a flow reduction will occur. The new operating point, and therefore the new flow, can be established by finding the intersection of the RCP characteristic curve, which is known, with the RCS curve, which, for the RMPWR, needs to be determined. The pump characteristic curve selected in this study is that of the RCPs of the four-loop Watts Bar plant, available from Ref. 8 and shown in Fig. 1. The RCS curve of the RMPWR can be estimated as a function of the fuel rod diameter, by means of a simplified but reasonable method relying on four main assumptions, listed in the order they are used in the calculation method: Assumption 1: In the highly turbulent regime (Re&105 ), the form loss coefficient for spacer grids is assumed to be proportional to (mass flow rate){0.2. This Fig. 1. Four-loop PWR RCS operating point for different pin diameters. RCP curve based on data from Ref. 8. NUCLEAR TECHNOLOGY VOL. 185 FEB. 2014 Lindley et al. REDUCED-MODERATION LWRs FOR TRU BURNING IN Th FUEL—II has been inferred from trends found in Ref. 9 referring to grids provided with nonsplit mixing vanes. Assumption 2: The form loss coefficient associated with the total pressure drop loss at the entrance (lower core plate and assembly bottom nozzle) and exit (assembly upper nozzle and core upper plate) of the RM core is assumed to be the same as that of the reference core. Assumption 3: The fraction of RCS flow that is not effective for removing core heat, i.e., the bypass flow fraction, is the same in the RMPWR and in the reference plant. Assumption 4: In a typical PWR, the core contributes *30% of the overall RCS pressure drop. The friction pressure drop for a bare-rod bundle core, i.e., without either grids or wire-wraps, can be expressed as     L G2 0:184 L G2 GDeq {0:2 L G2 G1:8 Lm0:2 ~ ~0:184 ~0:092 Dpcore, bare ~f Deq 2r Re0:2 Deq 2r Deq 2r m D1:2 eq r  1:8   1:8 0:2 1:2 0:2 m_ core Lm p 1:2 LD m_ core m , ~0:092  1:2 ~0:092 NAflow 4 N 1:8 A3flow r Aflow r 4 Pwetted ð1Þ where Hence, for the reference, grid spacer–provided core, the friction and form pressure drops can be expressed by combining Eq. (1) with Eq. (2): L 5 fuel rod length D 5 fuel rod outside diameter (o.d.) m_ core 5 coolant flow rate through the core Dpcore, ref ~Dpcore, bare zDpcore, form " p1:2 LD1:2 m0:2 m_ 1:8 0:184 ~ 1:8core1:8 4 A1:2 2N Aflow r flow #   m_ core, nom 0:2 Kcore, nom : z NAflow N 5 number of subchannels in the core f 5 friction factor r 5 coolant density G 5 coolant mass velocity m 5 dynamic viscosity Pwetted 5 wetted perimeter Aflow 5 subchannel flow area. Using assumption 1, the form pressure drop, due to grid spacers as well as losses at the assembly entrance and exit, can be expressed as   G2 G{0:2 G2 Dpcore, form ~Kcore ~ Kcore, nom {0:2 2r Gnom 2r     m_ core 1:8 m_ core, nom 0:2 1 , ~Kcore, nom 2r NAflow NAflow ð2Þ where Kcore 5 sum of all the core form loss coefficients (core inlet, grids, and core outlet), which is flow rate dependent Kcore, nom 5 value of Kcore at the nominal flow rate conditions. NUCLEAR TECHNOLOGY VOL. 185 FEB. 2014 ð3Þ For an RM core provided with wire-wraps, form losses are located at the assembly entrance and exit only, whereas throughout the heated length, the pressure drop can be expressed using a Darcy friction factor specifically formulated for wire-wrap–provided rods using the correlation developed by Ref. 10 for the turbulent regime (although this correlation is for hexagonal bundles), i.e., f~ Cf T , Re0:18 ð4Þ which is valid for RewReT ~10ð3:3z0:7P=DÞ , with the coefficient Cf T given by    H CfT ~ 0:8063{0:9022 log10 D )    9:7  1:78{2ðP=DÞ H 2 P H z0:3526 log10 , D D D ð5Þ 151 Lindley et al. REDUCED-MODERATION LWRs FOR TRU BURNING IN Th FUEL—II where P 5 rod pitch H 5 wire pitch D 5 fuel rod o.d. The pressure drop through the core for the wire-wrap design is therefore equal to     L G2 G2 Cf T L G2 G{0:2 G2 zKinzout ~ z Kinzout, nom {0:2 Dpcore, RM ~f Deq 2r 2r Gnom 2r Re0:18 Deq 2r  {0:18     m_ 2core m_ core 1:8 m_ core, nom 0:2 1 GDeq L ~Cf T zKinzout, nom m NAflow NAflow Deq 2rN 2 A2flow 2r      {0:18 m_ 2core m_ core 1:8 m_ core, nom 0:2 1 4m_ core LPwetted zKinzout, nom ~Cf T 2r NAflow NAflow NmPwetted 4Aflow 2rN 2 A2flow     m_ 1:82 m_ core 1:8 m_ core, nom 0:2 1 LP1:18 m0:18 core , zK ~Cf T wetted0:18 inzout, nom 2r NAflow NAflow 8|4 rN 1:82 A3flow ð6Þ where Kinzout is a form loss coefficient associated with the total pressure drop loss experienced by the coolant at the core inlet (lower core plate and assembly bottom nozzle) and outlet (assembly upper nozzle and core upper plate). Equation (6) can be rewritten as   ! 0:18 m_ 1:8 m_ 0:02 m_ core, nom 0:2 LP1:18 core core wetted m Cf T : Dpcore: RM ~ 1:8 1:8 zKinzout, nom 0:02 NAflow 4|40:18 A1:2 2N Aflow r flow N ð7Þ Thus, given an existing PWR retrofitted with an RM core, the core pressure drop ratio can be expressed as ðDpcore ÞRM ~ ðDpcore Þref m_ 1:8 core A1:8 flow ! m_ 1:8 core A1:8 flow !RM ref " #  0:02  0:2 0:18 _ _ m LP1:18 m m core core, nom wetted Cf T z Kinzout, nom N NAflow 4|40:18 A1:2 flow RM " # :X : 0:2 p1:2 LD1:2 m0:2 m_ core, nom 0:184 Kcore, nom z 4 NAflow A1:2 flow ð8Þ ref The only unknowns in the ratio above are ðm_ core ÞRM and (D)RM since the reference core parameters are known, the values for L, m, and fuel rod pitch (the latter is needed to compute Aflow ) are the same for the two cores, and the loss coefficient representing the pressure drop losses at the entrance and exit of the RM core is assumed to be the same as that of the reference core, as per assumption 2.b The overall pressure drop through the RCS (DpRCS ) can be calculated as the sum of two contributions: the pressure drop through the core and that through the remaining RCS components. The latter, referred to as Dprest , depends on the coolant flow rate and on the geometry of the RCS components upstream and downstream of the core, which, because of the retrofit approach, is the same for the RMPWR and the reference plant. Thus, " #1:8 ðm_ RCS ÞRM ðDpRCS ÞRM ~ðDpcore ÞRM zðDprest ÞRM ~X ðDpcore Þref z ðDprest Þref , ðm_ RCS Þref ð9Þ b For the reference core, the coefficient Kinzout,nom is calculated as Kcore,nom {8Kgrid , where the loss coefficient for the eight grids is assumed to be *1 and Kcore,nom is obtained from Eq. (3), in which Dpcore,ref is obtained from DpRCS,ref (known from Ref. 8) as DpRCS,ref 0:3, as per assumption 4. This gives Kcore,nom ~14:5 and Kinzout,nom ~6:5. 152 NUCLEAR TECHNOLOGY VOL. 185 FEB. 2014 Lindley et al. REDUCED-MODERATION LWRs FOR TRU BURNING IN Th FUEL—II which, using assumption 3 concerning the core bypass flow, can be rewritten as " #1:8 ðm_ core ÞRM ðDprest Þref : ðDpRCS ÞRM ~X ðDpcore Þref z ðm_ core Þref ð10Þ For the reference plant, the pressure drop through the noncore RCS components can be expressed as a function of the core pressure drop using assumption 4: ðDprest Þref ~ðDpRCS Þref {ðDpcore Þref ~ ðDpcore Þref 0:7 ðDpcore Þref : {ðDpcore Þref ~ 0:3 0:3 ð11Þ By introducing Eq. (11) into Eq. (10), the RCS pressure drop for the RMPWR can be expressed as 8 " #1:8 9 < 0:7 ðm_ core ÞRM = ðDpRCS ÞRM ~ Xz ðDpcore Þref : : ; 0:3 ðm_ core Þref TABLE IV RCS Flow Rates for RM Designs Relative to Reference Case Pin Diameter (mm) H=D RCS Flow Rate (%) 11 11.5 11 11.5 14 14 50 50 91.6 86.5 95.7 89.8 VOL. 185 FEB. 2014 II.A.3. Core Exit Temperature The flow rate reduction imposed by the constraint on RCS pressure drop has implications on the coolant enthalpy content at the exit of the core. Specifically, since Tin cannot be significantly reduced with respect to the reference value (see Sec. II.A.4), constancy of core power with respect to the reference plant results in a higher temperature for the coolant at the exit of the core and, consequently, for the steam generator (SG) tubes. In existing plants, the material these tubes are made of, i.e., INCONELH alloy 600,c experiences a degradation of mechanical properties above 600 K (Ref. 11). The SG tube material used in new plants, i.e., INCONEL alloy 690, has been operated in the range 600 to 603 K (Refs. 12 and 13) and can theoretically go higher, but this has not been experimentally tested yet. Hence, in this analysis, 600 and 603 K are used as core exit temperature limits for a feasible design and a stretch design, respectively. ð12Þ Equation (12), with X expressed by means of Eq. (8), can be used to obtain the RCS pressure drop versus flow curve for an existing PWR retrofitted with an RM core, once a certain rod diameter and wire-wrap pitch have been chosen. Four of these curves, for rod diameters of 11 and 11.5 mm and wire-wrap H=D values of 14 and 50, are shown in Fig. 1 together with the RCS curve of the reference plant, as well as the RCP characteristic curve. The intersection between these curves identifies the operating points associated with each case. The RCS flow rates obtained in this way for the RM cases are summarized in Table IV. It must be emphasized that if the design implementation strategy adopted for this study allowed replacement of the RCPs, the range of achievable flow rates would no NUCLEAR TECHNOLOGY longer be constrained to a single value but would be wider and dependent on the performance of the RCPs available on the market. It must be noted, however, that a nonretrofit plant would likely have completely different geometry, such as a shorter core, which would make the constraint on flow rate less limiting. II.A.4. Core Inlet Temperature Reducing Tin has a beneficial effect on both DNB (by lowering the coolant enthalpy) and pressure drop (by allowing a reduced flow to remove the same power without increasing Tout ). However, such a reduction must be constrained in order to limit the negative effect on the plant thermodynamic efficiency and, if a backfit approach is followed, to avoid challenging the plant limits related to overcooling events. This is because not only will the reactor operate at a lower average temperature, but it will also reach lower temperatures upon overcooling accidents, e.g., a steam line break. Components such as the reactor pressure vessel are licensed to operate within preestablished pressure-temperature ranges, and since the lower the temperature, the lower the maximum pressure has to be, reduction in the minimum temperature expected during the vessel operating life would restrict the pressure operation range for the component. If not constrained, this reduction in Tin may require the plant, for example, to operate at a lower nominal pressure or to be provided with more efficient depressurization systems, both of which are requirements clearly incompatible with a backfit approach. The maximum allowed reduction in Tin mentioned above, i.e., 5 K, was not calculated but was arbitrarily chosen to limit the deviation from the reference plant operating conditions, while allowing for some flexibility. Some c INCONEL is a registered trademark of the Special Metals Corporation group of companies. 153 Lindley et al. REDUCED-MODERATION LWRs FOR TRU BURNING IN Th FUEL—II plants have been permitted to operate with a reduced Tin to limit Tout , with temperatures as low as 550uF (560.9 K) being permitted at operating power in some cases.14,15 Fratio ~ II.A.5. Fuel Assembly Lift-Off Fuel assemblies are subjected to a lift-off force due to the interaction with coolant flow. The net force resulting from the balance among this force, buoyancy, and gravity is used to design the fuel assembly hold-down springs so that the fuel assemblies are guaranteed to remain in contact with the lower core plate during normal operation, as well as during most of the condition I and II events. The changes in assembly geometry and core flow investigated in this study cause the lift-off force to change, thereby necessitating verification of the adequacy of the reference hold-down spring design to the new conditions. It must be stressed, however, that in contrast to replacing other plant components such as the RCPs, redesigning the hold-down springs can be considered a design modification within the boundary of the retrofit implementation strategy examined in this study. For this reason, assembly lift-off is not used as a hard constraint for the RMPWR design, and the analysis performed here only assesses whether the implementation of an RM core requires the hold-down springs to be redesigned. There are three forces acting on the assembly: 1. Drag force (Fdrag ): The friction force between the coolant and the fuel assembly. By Newton’s third law, this is equal to the force acting on the coolant, which can be calculated from the friction plus form pressure dropd experienced by the coolant while flowing through the core, as Fdrag ~Dpcore P2FA , ð13Þ where PFA is the assembly pitch.e 2. Buoyancy force (Fbuoy ): Equal to the weight of the water displaced by the assembly. 3. Weight force (Fweight ): The force due to gravity acting on the fuel assembly, which acts against the other two forces. This includes nozzle weight (16 kg, taken from Ref. 16); grid spacer weight (0.9 kg, taken from Ref. 17); and treatment of the fuel, cladding, and guide tubes using appropriate volumes and densities. The effect of the design changes on the net axial force acting on the assembly can be estimated by calculating the d In the calculation performed in this study, acceleration pressure drop is neglected. This is reasonable since in typical PWR operating conditions, the acceleration term is very small. e The area of the assembly envelope is used, in place of the assembly flow area, since Dpcore is measured from just below the lower core plate to just above the core upper plate. 154 ratio between the net force on the RM assembly and that on the reference assembly, i.e., Fdrag RM Fdrag z Fbuoy ref X Fdrag ~ z Fbuoy Fdrag ref RM { Fweight { Fweight ref zY Fbuoy z Fbuoy ref ref RM ref {Z Fweight { Fweight ref ref ref , ð14Þ where X 5 core pressure drop ratio defined by Eq. (8) Y 5 ratio of the total volumes displaced by the two assemblies (including grid spacer and nozzle volumes, which are approximately constant) Z 5 ratio of the total weights of the two assemblies, assuming that the grid and nozzle weights are constant and calculating the new cladding and fuel weights based upon their changed areas. Therefore, given an RM core with a certain geometry and coolant flow, Eq. (14) combined with Eqs. (8) and (13) can be used to estimate the lift-off force ratio. If this ratio is found to be larger than 1, the retrofit strategy aimed at implementing an RM core should also include a redesign of the assembly hold-down mechanism. II.B. Single-Assembly Thermal-Hydraulic Analysis II.B.1. Model Characteristics Single-assembly analyses, with the subchannel code COBRA-EN (Ref. 18), were performed to evaluate the thermal-hydraulic performance of the 11- and 11.5-mm rod diameter cases, as well as the 9.5-mm case used as reference. Because of the incapability of the code to model the wire-wrap assumed for the large rod cases, for these designs, the pressure drop and the MDNBR were calculated separately, since these parameters are significantly affected by the presence of the wires. Parameters not characterized by such dependency, such as the coolant enthalpy axial profile, are instead predicted with the COBRA code. Consistent with the retrofit approach requiring RCPs not to be replaced, the coolant flow rate resulted from application of the RCP performance constraint discussed in Sec. II.A.2 and, specifically, from Fig. 1. Assembly operating conditions, shown in Table V, were selected to be representative of the hot assembly of an RMPWR core, and since no core-wide thermalhydraulic–neutronics coupled analysis has been performed, some assumptions were needed concerning the power peaking factors. Specifically, the values used for these parameters are typical design values used for NUCLEAR TECHNOLOGY VOL. 185 FEB. 2014 Lindley et al. REDUCED-MODERATION LWRs FOR TRU BURNING IN Th FUEL—II TABLE V Parameters Used for Thermal-Hydraulic Analysis Fixed Parameters Assembly lattice type Assembly length Assembly heated length Number of fuel rods per assembly Assembly pitch Fuel rod pitch Control rod guide tube and instrumentation tube o.d. Assembly power and percentage with respect to nominal Axial power profile Assembly radial power peaking factor Hot pin power peaking factor Enthalpy rise hot channel factor Power fraction in coolant Lower and upper plate and nozzle total loss coefficient (Kinzout, nom ) II.B.2. Results 17|17, square 4.063 m 3.66 m 264 0.215 m 12.6 mm 12.24 mm 31.4 MW(thermal), 112% Chopped cosine, 1.55 peak 1.587 1.06 1.682 (5 1.587|1.06) 2.6% 6.5 Variable Parameters Fuel rod o.d. Tin Coolant inlet mass flux Wall friction factor Rod support type Number of grid spacers per assembly Grid spacer loss coefficient 9.5 (reference), 11, and 11.5 mm Variable (565.3 K is the nominal value for the reference design, increased by 2 K for MDNBR calculation) Constant with nominal value 3728 kg/(m2?s), then reduced by 5% for MDNBR calculations (413 200 gal/min (26 073 m3/s) flow rate, 9.6% bypass flow 5 nominal value for the reference design)8 Smooth tube friction factor for grid-supported rods; Eq. (4) for wire-wrap designs Grids (reference); otherwise wire-wrap Eight (reference assembly design only) 1.0 UO2-fueled PWRs and are therefore assumed to be reasonably conservative for RMPWRs as well. It was also assumed that an RM assembly could be designed with a NUCLEAR TECHNOLOGY VOL. 185 pin peaking factor as low as that in the UO2 reference case (1.06) by careful distribution of pins with varying fissile contents. FEB. 2014 The performance of 11- and 11.5-mm pin diameters relative to the reference case (case 0) is presented in Table VI. First, Tin is held constant and equal to the nominal value (case 1), and then it is dropped by 5 K (case 2). The RCS flow rate is determined from Table IV. Finally, the mass flow rate is reduced by 10% to examine the sensitivity of the calculations to the pressure drop calculations (case 3). Wire-wrap H=D of 14 and 50 were considered. For cases 1, 2, and 3, a highlighting scheme is adopted to more easily distinguish between acceptable and unacceptable cases based on how the MDNBR and the coolant exit temperature compare with the corresponding limits. Specifically, bold indicates an acceptable value, bold-italics indicates a value exceeding the feasible case limit but still below the ‘‘stretch case’’ limit, whereas italics indicates an unacceptable value.f From Table VI, the following can be seen: 1. For the 11-mm pin diameter design, the thermalhydraulic design constraints are met in case 1a (nominal Tin and H=D~14) and cases 2a and 2c (reduced Tin with H=D~14 and 50, respectively). Hence, with this pin size, the MDNBR constraint can be satisfied without lowering Tin (case 1a). However, Tout is slightly too high for the feasible case but still within the stretch case limit. This can be readily rectified by dropping Tin very slightly, as can be inferred from the increase in MDNBR achieved when Tin is reduced to the lowest acceptable value (case 2a). As for the transition to the H=D~50 wire design, unless Tin is reduced (case 2c), the transition to this looser wire configuration results in an unacceptable MDNBR (case 1c). This is because the beneficial effect on MDNBR of the increase in mass flux [4612 to 4818 kg/(m2?s)] allowed by the lower pressure drop is offset by the less efficient coolant mixing resulting from the higher H=D, which yields an overall reduction in MDNBR. 2. For the 11.5-mm pin diameter design, the thermalhydraulic constraints are met in case 2b only (reduced Tin and H=D~14). Hence, for this rod size design, a drop in Tin is required to satisfy the MDNBR constraint. 3. If the actual core mass flow is 10% lower than that predicted using the methodology of Sec. II.A.2, the RM cases are not feasible, even if Tin is dropped by 5 K. f As shown in Table III, while a single limit is used for the MDNBR, for the coolant exit temperature, a feasible case limit and a stretch case limit are used. 155 Lindley et al. REDUCED-MODERATION LWRs FOR TRU BURNING IN Th FUEL—II TABLE VI Results of Thermal-Hydraulic Analysis (Infeasible/Stretch/Feasible) Case Pin o.d. (mm) 0 9.5 1a 1b 1c 1d 2a 2b 2c 2d 3a 3b 11 11.5 11 11.5 11 11.5 11 11.5 11 11.5 Wire H=D n/a (grid spacers) 14 14 50 50 14 14 50 50 14 14 Core Flow Rate Relative to Reference (%) Hot Assembly Mass Flux [kg/(m2?s)] Tin (K) Tout (K) Dalle Donne– Hame W-3a 100.0 3728 565.3 598.4 1.31 1.72 91.6 86.5 95.7 89.8 91.6 86.5 95.7 89.8 82.4 77.9 4612 4995 4818 5186 4612 4995 4818 5186 4150 4496 565.3 565.3 565.3 565.3 560.3 560.3 560.3 560.3 560.3 560.3 601.1 603.0 599.7 601.8 597.0 599.0 595.6 597.7 600.6 602.8 1.33 1.27 1.27 1.20 1.39 1.32 1.33 1.25 1.29 1.23 2.25 2.17 2.52 2.46 2.69 2.69 2.98 3.01 2.01 1.85 MDNBR a Although not used for determining design acceptability, the MDNBR calculated with the W-3 correlation is also shown to highlight the nonconservative results that would be obtained if this correlation was used for tight lattices. This value was calculated without mixing due to wire-wraps for the RM cases. The W-3 correlation gives an inaccurate prediction of the relative performance of (a) the tight-lattice geometries with respect to the reference, open-lattice, geometry and (b) the H=D~14 design with respect to the H=D~50 design. As for the former inaccuracy, the W-3 correlation predicts that all the RM cases (cases 1a through 3b) have much better DNB performance than the reference case (case 0). This is clearly a consequence of neglecting the inherent differences between large and narrow channel behavior with respect to DNB, which results in the comparison between tight and regular lattices being mainly driven by mass flux differences. The W-3 correlation is also incapable of capturing the wire pitch effect on MDNBR. Unlike the Dalle Donne–Hame correlation, which predicts a higher MDNBR for the H=D~14 cases compared to the H=D~50 cases (see, for example, cases 1a and 1c), the W-3 correlation shows the opposite trend (MDNBR1a vMDNBR1c ). This is because it does not capture any wire-induced mixing effects, so the difference in DNB performance is driven by the difference in mass flux only. Assembly lift-off results are presented in Table VII. As mentioned in Sec. II.A.5, assembly lift-off is not a hard constraint, and design retrofittability should not be based on whether the lift-off forces are higher or lower than the reference design. It can be seen that for the preferred H=D~14, the lift-off force is 1.9 and 2.7 times higher than for the reference assembly, for 11- and 11.5-mm pin diameters, respectively. This increase is mainly driven by the higher drag, which, in turn, is due to the higher pressure drop experienced by the coolant while flowing 156 through a wire-wrap–provided tight lattice. From Table VII, it can also be seen that the effect of the higher drag on the net lift-off force is partly reduced by the larger weight of the tight-lattice assemblies, which feature larger, and therefore heavier, fuel rods. Based on the thermal-hydraulic performance summarized in Tables VI and VII, the use of a tightly coiled wire-wrap, i.e., with small H=D, is recommended since it clearly helps to satisfy the DNB safety requirement, especially when Tin cannot be reduced below the reference value. Adoption of this wire design would also benefit rod performance from the vibration standpoint, since a lower H=D implies more rod support points per unit of length. The higher pressure drop resulting from the use of a tightly coiled wire is not considered to be a showstopper since the reduction in core flow due to the TABLE VII Estimated Lift-Off Force per Fuel Assembly Pin Diameter (mm) 9.5 11 11.5 11 11.5 H=D Fdrag (kN) Fbuoy (kN) Fweight (kN) Net Force (kN) 14 14 50 50 8.7 13.4 16.5 11.1 14.5 0.5 0.7 0.8 0.7 0.8 6.2 8.4 9.1 8.4 9.1 3.0 5.8 8.1 3.5 6.1 NUCLEAR TECHNOLOGY VOL. 185 FEB. 2014 Lindley et al. REDUCED-MODERATION LWRs FOR TRU BURNING IN Th FUEL—II constrained RCP performance is accounted for in the DNB analysis and the higher lift-off forces can be accommodated by eventually redesigning the assembly hold-down mechanism. Alternatively, because of the beneficial effect that a reduction in Tin has on DNB, combining a small H=D with a slight reduction in Tin would also yield acceptable performance. This design choice, as opposed to having a small H=D while still keeping Tin at the reference value, is particularly useful for the 11.5-mm rod size design, which was demonstrated to satisfy the DNB constraint only if Tin is reduced. II.C. Reduced-Moderation Pressurized Water Reactor Post–Loss-of-Coolant-Accident Reflood The effect of tightening the fuel rod lattice on the reflood phase of a large-break loss-of-coolant accident (LBLOCA) needs to be investigated to assess whether safety criteria on peak clad temperature (PCT) and clad oxidation are satisfied. Studies performed in the past on the reflooding of tight lattices, such as Refs. 19, 20, and 21, provided experimental evidence that as expected, tight lattices are more challenging to reflood than open lattices. In particular, according to Ref. 19, the quench time and PCT will both be worse for a tight-lattice design due to the increased pressure drop across the core and lower coolant inventory. In the present study, the reflood of the RM designs has not been investigated either experimentally or computationally. Only some simplified analytical considerations are presented, with the purpose of estimating the difference in coolant upflow velocity between tight and open lattices under the assumptions of the same gravity head and single-phase coolant, i.e., no vaporization. The first assumption is motivated by the fact that, in a post-LOCA scenario, reflooding is driven by the gravity head of the liquid downcomer, which has to overcome the pressure drop through the core. Since a tight-lattice core has a higher friction pressure drop than an open one, and since the downcomer gravity head is independent of the lattice, a tight lattice will have a lower reflood velocity. Experimental data collected in the past, for example, Refs. 19, 20, and 21, compared open and tight lattice reflooding capabilities by imposing the same reflooding velocity at the bundle inlet: a boundary condition that is clearly not representative of a gravity-driven phenomenon, in which the inlet velocity depends instead on a momentum balance between the downcomer gravity head and the core pressure drop. The importance of an experimental comparison between tight and open lattices in conditions representative of a gravity-driven reflooding is recognized in Ref. 22, but no data of this type have been found in the literature. As for the second assumption, i.e., no vaporization, although not representative of postLOCA scenarios, it simplifies the calculation and allows NUCLEAR TECHNOLOGY VOL. 185 FEB. 2014 an upper bound for the tight-to-open lattice reflooding velocity ratio to be obtained. In fact, as experimentally verified in Ref. 22, for the same linear power conditions, steam generation will occur earlier in the reflood of the tight lattice due to the lower coolant flow rate, which increases the pressure drop and thus reduces the tight-toopen lattice reflooding velocity ratio below that obtained by neglecting vaporization. The analysis is performed for both the simplified case in which the effect of rod-supporting devices, i.e., grid spacers and wire-wraps, is neglected (bare rods; see Sec. II.C.1) and for the more realistic case in which it is accounted for (Sec. II.C.2). Also, for completeness, both laminar and turbulent regimes are considered, and the operating conditions are arbitrarily assumed to be 0.2 MPa and 100uC. II.C.1. Reflooding Velocity Comparison for Bare-Rod Bundles According to Ref. 23, the laminar friction factor for interior subchannels of square-lattice bundles can be calculated as  0:435 40:70 P {1 , ð15Þ f~ Re D where P 5 fuel rod pitch D 5 fuel rod o.d. Therefore, the friction pressure drop is  0:435 L rv2 40:70m P L rv2 {1 ~ , ð16Þ Dpfric ~f Deq 2 rvDeq D Deq 2 where v 5 reflood velocity Deq 5 equivalent diameter. Therefore, for the simplified case of bare rods, the pressure drop due to friction:  0:435 P v {1 ð17Þ Dpfric ! D D2eq in the laminar regime, and v1:8 Dpfric ! 1:2 Deq ð18Þ in the turbulent regime [as shown in Eq. (1)]. Therefore, for the same downcomer gravity head, the relation between the inlet velocity of a tight and an open lattice can be estimated by equating the friction pressure drop for the two bare-rod lattices, which leads to the following expression: 157 Lindley et al. REDUCED-MODERATION LWRs FOR TRU BURNING IN Th FUEL—II  30:435 P " #2 {1 7 Deq tight vtight 6 6D open 7  7 *6 5 vopen 4 P Deq open {1 D tight 32  30:435 2  2 2 P P p { 7 6  6 D {1 7 6 Dtight D tight 4 7 6 open 7 7 6  7 ~6 7 6 Dopen  P 2 4 P 5 p 5 4 {1 { D D open 4 tight " #  0:435 40:70m P L rv2 Dpref ~ {1 zKcore rvDeq D Deq 2   2 C1 rv zKcore : ~ v 2 2 ð21Þ For wire-supported rods, the friction factor in the laminar regime can be expressed as10 ð19Þ f~ Cf L , where Re (  2 ) 0:06{0:085(P=D) P P H : Cf L ~ {974:6z1612 {598:5 D D D in the laminar regime, and ð22Þ vtight * vopen " Deq Deq 30:667  2 P p #1:2 6 { 7  1:8 6 D tight 4 7 Dtight tight 6 7 ~6  2 7 D open P p 4 5 open { D open 4 2 ð20Þ in the turbulent regime. Using Eqs. (19) and (20), it can be seen that 1. for the 11.5-mm pin diameter case,  0:45 in the laminar regime , vtight ~ vopen 0:64 in the turbulent regime ; 2. for the 11-mm pin diameter case,  0:56 in the laminar regime , vtight ~ vopen 0:73 in the turbulent regime : II.C.2. Reflooding Velocity Comparison for Grid/WireSupported Rod Bundles For grid-supported rod bundles, the friction pressure drop in the laminar regime can be expressed as " " 158 Cf T Hence, the following relation can be obtained for the pressure drop for the RM design:   2 Cf L L rv zKinzout DpRM ~ 2 Re Deq   2 Cf L m L rv zKinzout ~ rvDeq Deq 2   2 C2 rv ~ : zKinzout 2 v ð23Þ Equating the pressure drops for the two assembly designs, i.e., Eqs. (21) and (23), gives C1 vzKcore v2 open ~ C2 vzKinzout v2 tight , ð24Þ where Kinzout, nom ~6:5 and Kcore, nom ~14:5 (from Table V); C1 is *0.3, and C2 ranges between 2.2 and 3 depending on the tight lattice considered. It must be stressed that Eq. (24) is only valid for Reynolds numbers below ReL ~10ð0:78z1:7P=DÞ , which represents the validity range for Eq. (22) (Ref. 10). This value is approximately 500 for both tight-lattice geometries considered in this study, which corresponds to a coolant velocity vtight of *2 cm/s for the operating conditions mentioned earlier. Using a typical laminar regime boundary of Re~2100 for the reference bundle, the maximum vopen for which Eq. (21) is valid is *5 cm/s. For the turbulent case, rearranging Eq. (8) with the pressure drop ratio across the core set equal to unity gives # 0:2 p1:2 LD1:2 m0:2 m_ core, nom K core, nom 0:184 z 4 NAflow A1:2 flow   vtight 1:8 : ~ vopen open #     0:18 LP1:18 m_ core 0:02 m_ core, nom 0:2 wetted m z K inzout, nom N NAflow, nom 4|40:18 A1:2 flow ð25Þ tight NUCLEAR TECHNOLOGY VOL. 185 FEB. 2014 Lindley et al. REDUCED-MODERATION LWRs FOR TRU BURNING IN Th FUEL—II Using the same values for the water properties and loss coefficients as those adopted for the laminar regime case, Eq. (25) can be rewritten as " # D1:2 open 0:109 1:2 z74:3v0:2 open Aflow, open " # 0:02 0:02 Lp1:18 m0:18 D1:18 tight vtight r 0:2 z44:6 vtight Cf T 41:18 A1:18 flow, tight   vtight 1:8 : ð26Þ ~ vopen By entering the geometric parameters of the reference open lattice, Eq. (26) becomes h i   30:1z74:3 v0:2 open vtight 1:8 : ð27Þ " # ~ vopen 0:02 v D1:18 tight tight 0:800 Cf T 1:18 z44:6 v0:2 tight Aflow, tight Equation (27) simplifies to 2 1:82 2 30:1v1:8 open z74:3vopen ~Cvtight z44:6vtight , ð28Þ where the coefficient C, expressed as C~0:800CfT 1:18 Dtight Aflow, tight , is *80 and *51 for the 11-mm rod o.d. case (for H=D~14 and 50, respectively) and *85 and *62 for the 11.5-mm rod o.d. case (for H=D~14 and 50, respectively). Equation (28) can readily be solved by the Newton-Raphson method for given vopen . Also, by taking the exponents 1.8, 1.82, and 2 to be 1.9, which gives indicative results for reflood velocities *1 m/s, this simplifies to   vtight 104:4 1=1:9 & , 44:6zC vopen ð29Þ i.e., vtight vopen is approximately constant, and 1. for the 11.5-mm pin diameter case,  0:89 for H=D~14 , vtight ~ vopen 0:99 for H=D~50 ; 2. for the 11-mm pin diameter case,  0:91 for H=D~14 , vtight ~ vopen 1:05 for H=D~50 : It must be stressed that Eq. (28) is only applicable to the turbulent regime, which, for tight lattices, was identified by Ref. 10 as RewReT ~10ð3:3z0:7P=DÞ [see Eq. (4)]. This value is approximately 12 000 for both tight-lattice geometries considered in this study, which corresponds to a coolant velocity vtight of *50 cm/s. Using a turbulent regime boundary of Re w10 000 for the reference bundle, the minimum vopen for which the numerator of Eq. (25), and therefore Eq. (28), is valid is *25 cm/s. From Eqs. (24) and (28), it can be seen that unlike for the bare-rod case examined in Sec. II.C.1, when accounting for the rod supports, vtight vopen is dependent on the reflood velocity. This is shown in Fig. 2 (laminar regime) and Fig. 3 (turbulent regime). In both figures, the following can be seen: 1. The maximum and minimum ratios correspond to the 11-mm rod o.d. with H=D~50 and the 11.5-mm rod o.d. with H=D~14, respectively. This is expected since these RM geometries are those that provide the minimum and maximum resistance to flow, respectively. 2. The velocity ratio increases as vopen increases. This is because, as the velocity increases, the increased friction drag in the RM case becomes less significant Fig. 2. Estimated coolant velocity ratio for different tight-lattice geometries, in the laminar regime (constant gravity head, no vaporization). NUCLEAR TECHNOLOGY VOL. 185 FEB. 2014 159 Lindley et al. REDUCED-MODERATION LWRs FOR TRU BURNING IN Th FUEL—II Fig. 3. Estimated coolant velocity ratio for different tight-lattice geometries, in the turbulent regime (constant gravity head, no vaporization). relative to the form drag of the grid spacers. This is particularly true in the laminar case, where at very low velocities, the friction drag dominates [constant terms in Eq. (24)]. In the turbulent case, the reflood velocities are similar, as the form drag is much larger, including Kinzout , which is the same for both open and tight lattices. 3. For the specific case of the laminar regime, accounting for the velocity validity range for Eq. (24), velocity ratios are between *0.1 and *0.5. For a hypothetical reflooding velocity of 2 cm/s, the ratio is *0.2 to *0.3, depending on the tight-lattice geometry considered. Note that the calculation assuming bare rods (Sec. II.C.1) provided velocity ratios of 0.45 and 0.56 for the 11.5- and 11-mm rod o.d. cases, respectively. The wire-wraps cause a pressure drop due to friction, which is larger at low reflood velocities than a grid spacer form loss, which makes the situation worse. 4. In the turbulent case, the higher velocity makes the grid spacer loss coefficient of the reference case much larger than the wire-wrap friction. This offsets the higher rod friction of the RM lattice, leading to similar reflood velocities. Note that the calculation assuming bare rods (Sec. II.C.1) provided velocity ratios in the turbulent regime of 0.64 and 0.73 for the 11.5- and 11-mm rod o.d. cases, respectively, which, in contrast to the laminar case, is lower than when accounting for form losses and wire-wraps. It must be emphasized that because of the simplifying assumptions made (mainly the no-vaporization assumption), Figs. 2 and 3 are not intended to show the actual tight-to-open lattice reflooding velocity ratio, but an upflow velocity ratio under the assumptions of gravity-driven flooding and no vaporization. Because of the considerations presented at the beginning of Sec. II.C.2, these ratios are expected to represent the upper bound of the actual reflooding velocity ratio. 160 II.C.3. Impact of Slower Reflooding on PCT and Cladding Oxidation As mentioned earlier, experimental results on the reflooding characteristics of tight versus open lattices under gravity-driven conditions have not been found in the open literature, and only data collected imposing the same reflooding velocity for both lattice types are available. References 19, 20, and 21 performed experimental analyses of reflood for tight lattices and compared it with open lattices. In all cases, experiments were performed by fixing the inlet velocity. Experimental results for quenching times are available for reductions in hydraulic diameter from the reference (11.8 mm) to values ranging from 4 to 7.9 mm. This compares to 7.4 and 6.1 mm for the 11- and 11.5-mm pin diameters considered in this study, respectively. The quenching time generally increased by a factor of 1.5 to 3, which if translated into a tight-to-open reflooding velocity ratio, would be equivalent to the 0.3 to 0.7 range. This is shown in Table VIII and Fig. 4. Since the higher PCT resulting from the delay in quenching may violate the cladding temperature limit typically imposed for LOCA scenarios, the effect of tightening the lattice on the reflooding characteristics should be captured in the LOCA analysis model. References 19 and 20 report increases in the PCT of up to 190 K relative to the reference case, although Ref. 21 measures a much lower (*20 K) increase in PCT. According to the U.S. Nuclear Regulatory Commission (NRC) regulations, the limit on PCT is 1478 K (Ref. 24). Reference 25 modeled an LBLOCA in an AP1000Hg and found a PCT of 1309 K. The increase in PCT for the tight lattice may violate this limit, necessitating a core derating or a reduction in the core height (i.e., a nonretrofit core). g AP1000 is a trademark or registered trademark of Westinghouse Electric Company LLC. NUCLEAR TECHNOLOGY VOL. 185 FEB. 2014 Lindley et al. REDUCED-MODERATION LWRs FOR TRU BURNING IN Th FUEL—II TABLE VIII Comparison Between Quenching Time and PCT of an Open and a Tight Lattice for Different Initial Wall Temperature (Twi ) and Linear Power (q’ave )* Triangular Lattice (Tight) (Drod ~9:5 mm, Prod ~12:23 mm, Dhyd ~7:86 mm) Wall Temperature, Linear Power Case 1 (Twi ~600uC, q’ave ~1 kW=m) Case 2 (Twi ~600uC, q’ave ~0:87 kW=m) Case 3 (Twi ~385uC, q’ave ~0:68 kW=m) Square Lattice (Open) (Drod ~9:5 mm, Prod ~12:6 mm, Dhyd ~11:8 mm) Tight Versus Open Lattice Comparison Quenching Time (s) PCT (uC) Quenching Time (s) PCT (uC) Quenching Time Ratio PCT Difference (uC) 550 930 350 810 1.6 120 525 875 280 710 1.9 165 330 650 120 530 2.8 120 *Inlet flooding velocity *3.7 cm/s, Tflood, in ~73:5uC, p~0:3 MPa, and axial peaking 5 1.6 (from Ref. 20). Fig. 4. Reflood of reference and tight triangular lattices (Ref. 21). In addition to challenging the limit on cladding temperature, having a longer quenching time and a higher PCT results in more significant cladding oxidation, which could exceed the 17% oxide thickness limit imposed by NUCLEAR TECHNOLOGY VOL. 185 FEB. 2014 the NRC (Ref. 24). The oxidation progression can be predicted using the reaction constant KR found by means of the Baker-Just correlation.26 The time variation of the oxide thickness (in meters) can be expressed as 161 Lindley et al. REDUCED-MODERATION LWRs FOR TRU BURNING IN Th FUEL—II sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi KR dt ~ d2t{Dt zDt 2 rc sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3330 exp({22896=T) ~ d2t{Dt zDt , r2c ð30Þ where T 5 cladding temperature (K) rc 5 nonoxidized cladding density (kg/m3). A higher quenching time and PCT can therefore significantly increase cladding oxidation. Equation (30) allows a very rough estimate of the relative increase in oxidation resulting from a longer quenching time and/or a higher cladding temperature. Figure 5 shows the percentage of cladding thickness converted to oxide as a function of time and cladding temperature, for the reference lattice, obtained using Eq. (30) and assuming constant temperature with time. It can be seen that, with respect to an assumed temperature of 1100 K, an increase in temperature that can be reasonably expected for a tight-lattice design, i.e., 200 K, would result in an oxidation percentage: 1. four to five times higher if the quenching time is assumed to be the same for the two lattices 2. more than five times higher if, in addition to the higher temperature, a longer quenching time is also assumed. Clearly, this increase would not be acceptable if the margin from the 17% limit of the reference case was small, like in the case shown by Ref. 25 where the maximum local clad oxidation was v12.9% with 95% confidence (compared to a maximum of 17%), and the maximum core-wide clad oxidation was 0.73% (compared to a maximum of 1%). Fig. 5. Effect of quench time and cladding temperature on clad oxidation. 162 In conclusion, experimental evidence and analytical calculations seem to indicate that a retrofit RMPWR core will have reduced margin, or even no margin, from LOCA licensing limits if compared to the reference core design. This needs to be confirmed through computational analysis and, ultimately, experimental tests. If proven to be the case, retrofitting a typical PWR core with an RM core would be feasible only after either derating the plant or switching to a cladding material with better LOCA performance than Zr-based alloys. Another solution, preferable for optimizing the overall reactor performance, but incompatible with the retrofit approach investigated in this study, would be to design a shorter but wider core, so that the total core power could be preserved while lowering the axial hot spot and, eventually, reducing the linear power. An LBLOCA computational analysis will be performed to reach a more definitive conclusion. III. REDUCED-MODERATION PRESSURIZED WATER REACTOR FULL-CORE ANALYSIS In the Part I companion paper,1 single-assembly analyses were used to derive equilibrium fuel designs and isotope vectors for the RMPWR. The fuel pin diameter of a standard 17|17 Westinghouse assembly was increased from 9.5 to 11.5 mm in order to permit full TRU recycle with adequate discharge burnup (*40 GWd/tiHM) with a negative MTC. To achieve this, spatial separation of ThTRU and Th-U3 was necessary. The heterogeneous loading implemented here consists of placing Th-TRU pins in the center of the assembly and Th-U3 pins in the periphery (TCUP) (Fig. 6). Fig. 6. 144 Th-TRU pin (blue) 120 Th-U3 pin (green) TCUP assembly design (WIMS model), one octant (color online). NUCLEAR TECHNOLOGY VOL. 185 FEB. 2014 Lindley et al. REDUCED-MODERATION LWRs FOR TRU BURNING IN Th FUEL—II A full-core model based on a 193-assembly four-loop Westinghouse PWR was used to evaluate the main indicators of the core performance. The analysis was performed using PANTHER (Ref. 27). Cross sections for PANTHER were generated using WIMS with the same equilibrium isotope vector used in the assembly analysis. This is valid as the discharge burnup is very similar to the estimated burnup used in the isotopic convergence in all cases. The fuel conductivity for Th-TRU is estimated using the model for Th-Pu in Ref. 28, with the TRU proportion taken as the Pu proportion. This significant assumption is made due to limited data availability. The conductivity for Th-U3 is taken from Ref. 29. For TCUP assemblies, the conductivity was taken as an average of the Th-TRU and Th-U3 conductivities, weighted by the number of pins of each. This simplification was necessary as PANTHER cannot treat different fuel conductivities within the same assembly. This approach is sufficient to treat neutronic– thermal-hydraulic feedback effects to a reasonable degree of accuracy, as the Doppler coefficients (DCs) of the two fuel types are very similar (approximately {3.5 pcm/K). However, it is not ideal. Achieving a high rod worth is difficult in a hard neutron spectrum. The control rods adopted contained solid pellets of B4C with 95% 10B enriched boron and a radius of 0.433 cm. Even so, it is difficult to achieve an adequate SDM, partly due to the use of a portion of the rods to provide mechanical shim. Three full-core cases were analyzed based on the TCUP assembly design. The specifications are given in Table IX. The three-batch loading pattern (LP) for the equilibrium cycle is shown in Fig. 7. There were 53 rod banks, in the typical locations for a 193-assembly core.27,30 These are shown in Fig. 8. Gadolinium burnable poisons (BPs) were employed for power shaping and reactivity hold-down at the concentrations shown in Table IX. Soluble boron was not employed as control rods are foreseen for reactivity control. Note, however, that the results reported refer to all-rods-out conditions; a suitable control rod program (CRP) needs to be devised with results to be reported in the future. The start-of-cycle (SOC) normalized hot pin Fig. 8. RMPWR rod bank positions. rises in enthalpy (FDH) at these conditions (for the entire assembly, not for the hot pin) are given in Fig. 9. FDH is quite high, especially in case 2, and further LP optimization is necessary to decrease it. This will be performed in future work but is not necessary now as this feasibility study focuses on reactivity coefficients, discharge burnup, and SDM. The maximum hot pin FDH will be higher, and the assembly design must be optimized to minimize this (see the Part I companion paper1). Case 1 was identified in the assembly analysis in Part I as having a negative MTC and a good discharge burnup. However, as will be shown, the fully voided reactivity is positive. The fully voided reactivity can be reduced by reducing the TRU reload fraction (case 2) and made negative by increasing the pin diameter (case 3). Increasing the pin diameter allows the TRU reload fraction to be substantially reduced, which reduces the fully voided reactivity. The hot assembly is a fresh assembly for cases 1 and 3, but in case 2, the hot assembly is in the second batch, which is not surprising, given the relatively flat reactivity profile of RMPWR fuel with irradiation. This complicates the balancing of pin powers using variable fissile content, as it is not sufficient to balance the assembly form factors only for the first irradiation cycle; these must also be balanced for the subsequent cycles. TABLE IX Specifications of RMPWR Full-Core Cases Case Fig. 7. RMPWR analyzed cycle loading schemes (quarter-core). NUCLEAR TECHNOLOGY VOL. 185 FEB. 2014 Pin diameter (mm) TRU reload fraction (at. %) Number of Th-TRU pins per assembly Gadolinium in Th-U3 pins (wt%) 1 11 52.5 152 0.2 2 11 50 132 0.2 3 11.5 40 132 0.1 163 Lindley et al. REDUCED-MODERATION LWRs FOR TRU BURNING IN Th FUEL—II The equilibrium cycle burnup matches well with estimated values from the linear reactivity model and also with the discharge burnup assumed in the isotopic convergence (in case 1, it is slightly higher, which makes the results slightly pessimistic). The burnup of case 1 is competitive compared to current PWR discharge burnup; the burnup of cases 2 and 3 is reduced but still acceptable (Table X). The cycle length for case 3 is longer than for case 2 at similar discharge burnup due to the larger pin diameter and, therefore, reduced fuel rating. The cycle lengths do not directly correspond to 12-/18-month cycles. At this stage, the principal aim is to assess the feasibility and relative merits of different cases. The feasibility of altering the refueling strategy (e.g., finetuning the TRU reload fraction on a cycle-by-cycle basis) and/or LP to allow 12-/18-month cycles will be examined in future work. The 10B in the control rods exposed at the high core neutron flux will deplete. This will require dedicated management of the control rods, including shuffling or replacement when the worth has decreased to unacceptable levels or the rod mechanical performance has degraded. The control rods lose *5% of their worth when burned to 20 GWd/tiHM. For cycle-average control using 12% of the available worth (typical), this equates to *5% loss of rod worth over 16 years of operation. The rods will need to be shuffled and replaced regularly, and the reduction in worth needs to be taken into account, but this should not represent a fundamental barrier to feasibility. These effects will be considered in more detail in future work. TABLE X RMPWR Core Performance Fig. 9. SOC power peaking (FDH). 164 Case 1 2 3 Core-average burnup (GWd/tiHM) Cycle length (days) SDM (pcm) Maximum assembly radial power peaking (FDH) over cycle HFP reactivity swing over cycle (pcm, Xe, no rods) SOC reactivity at 100% VF (pcm, no rods) SOC DC (pcm/K) EOC DC (pcm/K) SOC HFP rod worth (pcm) 52.0 40.1 41.3 592 {547 1.43 456 –1077 1.53 520 –843 1.44 2533 1572 2204 3934 1257 –765 –3.6 –3.9 –6141 –3.5 –3.9 –7474 –4.1 –4.3 –6537 NUCLEAR TECHNOLOGY VOL. 185 FEB. 2014 Lindley et al. REDUCED-MODERATION LWRs FOR TRU BURNING IN Th FUEL—II The SDM was calculated for a reactor trip from hot full power (HFP) to hot zero power, with no change in Xe population, with the highest worth rod remaining out of the core. A 10% reduction is made for modeling uncertainties, and a 10% reduction is also made to account for control rod depletion (i.e., an overall reduction of 20%). In each case, the worst SDM is at SOC, with the SDM becoming more negative over the cycle to approximately {3000 pcm at end of cycle (EOC). In each case, the rods in position F10 and symmetry positions are the highest worth rods, and one of these is considered stuck. The available SDM is substantially less than the minimum required (1300 to 1600 pcm) (Ref. 31). An improvement of approximately {300 pcm is possible by inverting the TCUP assembly design to place the rodded positions nearer to the more thermal Th-U3 pins, but this still results in an insufficient SDM for cases 1 and 3 and a barely sufficient SDM for case 2. The RMPWR therefore requires additional rod control cluster assemblies (RCCAs) or a modified fuel design (e.g., additional BPs, although this makes the MTC worse). It is possible that the SDM is sufficiently LP dependent that the LP could be optimized to improve the SDM. It is also worth considering separating Th-U3 and Th-TRU into separate assemblies and placing the more thermal Th-U3 assemblies in the rodded positions to further increase the control rod worth. This will be considered in future work. A large proportion of the available rod worth is necessary to control the core at SOC (Table X), and mechanical shim may therefore require a large proportion of the control rods, such that there are few or even no dedicated shutdown banks. The DC varies little over the cycle (Table X). The MTC is shown in Fig. 10. It is slightly more negative than Fig. 10. MTC over the equilibrium cycle. that expected by linearly averaging the results of the single-assembly analysis of multiple batches as a result of neutron leakage. Despite the BP causing a positive MTC in the first batch, the overall core MTC is still negative as a result of the other batches. From Fig. 10, it would appear that the TRU reload fraction or BP proportion could be increased. However, the VC at 100% VF is positive for cases 1 and 2 (Table X), although there is a large amount of uncertainty in its value due to the limitations of WIMS for a fully voided core and data library uncertainties (see the Part I companion paper1). The fully voided core scenario is relevant if there is an LBLOCA without scram. In this extremely unlikely event, the reactivity of the core is positive, and very large negative reactivity feedback from an increase in the fuel temperature would be necessary to counterbalance this (Table XI). A sufficiently high temperature increase TABLE XI Analysis of 100% VF Condition Case SOC keff (no rods) SOC 100% VF keff (no rods) SOC keff (all rods in) SOC 100% VF keff (all rods in) SOC 0% VF HFP rod worth (pcm) SOC 100% VF rod worth without thermalhydraulic feedback (pcm) Proportion rod worth deployed for keff ~1a Proportion rod worth deployed for negative 100% VCa SOC DC (as Table X) (pcm/K) Fuel temperature rise (K) for zero negative reactivity (no rods) a 1 2 3 1.027 1.070 0.966 0.941 –6141 –12821 1.016 1.030 0.944 0.914 –7474 –12278 1.023 1.015 0.959 0.911 –6537 –11313 0.412 0.589 0.211 0.262 0.337 0 –3.6 1096 –3.5 359 –4.1 0 This is the required rod worth/total rod worth, not the proportion of inserted rods. NUCLEAR TECHNOLOGY VOL. 185 FEB. 2014 165 Lindley et al. REDUCED-MODERATION LWRs FOR TRU BURNING IN Th FUEL—II results in zero overall reactivity through the DC, but this may result in a full or partial meltdown. Case 3, which has a larger pin diameter, lower TRU loading, and lower BP loading, has negative reactivity when fully voided. The rod worth at 100% VF is larger than at nominal conditions (Table XI). This means that the reactor is very subcritical when fully voided if the control rod insertion can be credited. This calculation is performed without thermal-hydraulic feedback so the fuel does not cool down, which partially contributes to the large subcriticality margin. In addition, when a large proportion of the available rod worth is engaged performing mechanical shim, the insertion of these shim rods ensures that the core has negative reactivity at 100% VF without crediting the shutdown rods to be inserted. Increasing the proportion of excess reactivity that is controlled with rods (which implies reducing the BP content of the fuel) greatly reduces reactivity at 100% VF, first, because the BPs are effectively transparent at 100% VF, and second, through an increase in deployed rod worth, which itself benefits the VC. From Fig. 11, it is apparent that 0.2 wt% Gd in the Th-U3 pins adds over 0.01 to keff at 100% VF (when averaging over three batches) for case 2 at SOC. It is desirable to limit the pin diameter to 11 mm (cases 1 and 2), compared to 11.5 mm (case 3) for thermal-hydraulic reasons (Sec. II). Based on the results of this section, it may be possible to adapt case 2 to provide negative fully voided reactivity by using additional control rods instead of BPs or by reducing the SDM within acceptable limits. Further optimization of the fuel configuration is also being investigated. From Table XI, 20.6% of the available control rod worth is required to bring the reactor to criticality at SOC. If this is increased to 30.4%, the fully voided reactivity will be *0, but this will correspondingly erode the SDM. The SDM can be improved by adding soluble boron, but this will make the fully voided reactivity more positive. It must be noted that for a given total control rod worth, adding BP to the core does not increase the fully voided reactivity when the core is tripped. Substituting the BPs for mechanical shim increases the fully voided reactivity without trip, but the required control rod insertion to shut down the reactor is at most the same as without the BPs. In the extremely unlikely case of an LBLOCA combined with ejection of all the control rods, the core will undergo a severe accident, even if the VC at 100% VF is kept negative by using rods. Any reactor that relies on mechanical shim (e.g., any BWR) will experience a more severe accident if an LBLOCA is combined with simultaneous full rod withdrawal from the core. LBLOCA without trip is presumably a more likely event (in particular, common-mode failures must be rigorously investigated), but a full understanding of the licensing requirement is necessary to properly optimize the design. In summary, without considering LBLOCA without trip, case 1 appears preferable because of better fuel utilization than cases 2 and 3, higher TRU incineration rate, and thermal-hydraulic characteristics (smaller pin diameter than case 3). However, with consideration of this accident, only case 3 (11.5-mm rod diameter) is fully acceptable, although case 2 (11-mm rod diameter) may be acceptable with additional use of mechanical shim control rods, which would make retrofitting a current plant impractical. Finally, it must be noted from the Part I companion paper1 that the fully voided reactivity is overestimated due to the unsuitability of the 172-group cross-section library preparation for the RMPWR spectrum, and the JEF-2.2 library, employed for these calculations, tends to predict a higher fully voided reactivity than ENDF/B7.0. The former effect increases the excess reactivity by *500 pcm. While JEF-2.2 may or may not be more accurate than ENDF/B7.0 in this case, it certainly gives the more pessimistic case, potentially by more than 1000 pcm. If the 100% VC was overestimated by 1500 pcm, the fully voided reactivity of case 2 would be slightly negative. However, the fully voided reactivity for case 1 would still be positive. IV. REDUCED-MODERATION BOILING WATER REACTOR FULL-CORE ANALYSIS Fig. 11. Assembly-level calculation of the reactivity excess at 100% VC for case 2 (Gd at 0.2% in Th-U3 pins, no control rods, no soluble boron, no leakage). 166 In the Part I companion paper,1 a single-assembly analysis was performed of a 217-pin RBWR assembly based on the Japan Atomic Energy Agency design from Ref. 32 (Fig. 12). A homogeneous fuel composition was found to give acceptable neutronic performance, although further work will consider the TCUP assembly configuration to improve neutronic performance. NUCLEAR TECHNOLOGY VOL. 185 FEB. 2014 Lindley et al. REDUCED-MODERATION LWRs FOR TRU BURNING IN Th FUEL—II Fig. 12. Fuel assembly design considered for the RBWR case. A coupled neutronic–thermal-hydraulic model is required to accurately analyze an RBWR core, due to strong feedback between neutronics and thermal-hydraulics. Axial leakage is often an important mechanism in ensuring a negative VC, and this is sensitive to treatment of the axial reflectors and blankets. Many RBWR designs proposed are highly heterogeneous in the axial direction, necessitating three-dimensional neutronic models with accurate coolant density distributions, which are themselves dependent on the power and therefore flux solutions. The Th-fueled RBWR was modeled by coupling the nodal code PARCS (Ref. 33) with the thermal-hydraulic code RELAP5 (Ref. 34). The PARCS model was based on an RBWR model developed at the University of Michigan, rated at 3926 MW(thermal) with 720 assemblies with one-third rotational symmetry.35 The LP consists of four complete batches and one partial batch (Fig. 13). The RELAP5 model was also based on the University of Michigan model, with 121 parallel pipe components, each modeling the flow through one or two assemblies (Fig. 14). As described in Ref. 12, PARCS and RELAP5 are coupled using a general interface (GI). PARCS, RELAP5, and the GI are separate processes that communicate using message passing protocols in the parallel virtual machine. As discussed in Sec. II, 125- and 200-cm cores were modeled to investigate the relative merits of high and low leakage. The core power is the same in both cases, and the 200-cm core contains more fuel and so has a lower fuel rating. The shim rods contain 95% enriched 10B4C in 20 vertical solid pellets of 0.471-cm diameter in each blade. Lower and upper water reflector regions of 7 and 30 cm, respectively, were modeled in PARCS. It is possible to borate either or both reflectors to increase neutron leakage,35 but this was not considered here. There are 43 shim rods in NUCLEAR TECHNOLOGY VOL. 185 FEB. 2014 Fig. 13. RBWR core fuel LP in one-third rotational symmetry . Fig. 14. RELAP5 model. the core, distributed approximately evenly within the central region (batches 3 and 4) of the core. RELAP5 was first run in stand-alone mode to generate an initial guess at the thermal-hydraulic solution, which was used in the coupled analysis. The equilibrium cycle was determined by depleting over a cycle, shuffling, and refueling until the equilibrium cycle had converged. The equilibrium cycle is influenced by the CRP, but determination of an appropriate CRP is beyond the scope of an initial analysis, so the depletion was performed with rods out. This will change how the core depletes but should not greatly affect the equilibrium cycle burnup. The VC and DC of the equilibrium cycle were evaluated at SOC and EOC by alternately perturbing the core power and flow rate and solving Eq. (31) (Ref. 35),  DVoid1 DTemp1 DVoid2 DTemp2     r1 : ~ r2 DC VC ð31Þ 167 Lindley et al. REDUCED-MODERATION LWRs FOR TRU BURNING IN Th FUEL—II TABLE XII Calculation of VC and DC for RBWR Perturbations Fuel temperature only from 110% overpower; 75% flow 110% overpower; 75% flow 110% overpower; fuel temperature only from 110% overpower SOC DC (pcm/K) SOC VC (pcm/%Void) EOC DC (pcm/K) EOC VC (pcm/%Void) {4.6 pcm {30.7 {4.3 {12.0 {5.9 pcm {4.2 pcm {30.7 –57.1 –5.2 –4.3 –12.0 –26.8 Because of the coupled code system, perturbing the power and flow rate affects both the void and temperatures, so a linear system is required in order to solve for the reactivity coefficients. The perturbed conditions were 110% overpower and 90% flow rate. A 75% flow rate condition was also considered in some cases. A few depletion cycles are necessary for RELAP5 to converge on the correct flow distribution, so the RELAP5 restart file used for the 90% flow calculation was produced by depleting the reactor for a few cycles at 90% flow rate. Evaluating with the perturbed conditions at a single state point generally did not significantly change the flow conditions from their converged values. It is problematic to accurately converge RELAP5 for the perturbation cases. This makes the VC and DC sensitive to how they are evaluated and therefore leads to uncertainty in the calculated values. More consistent values for the DC and VC were achieved by performing the 110% power calculation with the same flow solution as the 100% power case, i.e., without depleting the reactor with the reduced flow case (Table XII). In the test case shown in Table XII, three perturbations were performed: overpower, flow reduction, and overpower without updating the flow solution. Combining the reactivity results from any two of these perturbations enables the DC and VC to be found using Eq. (31). The selected combination of perturbations gives a VC in agreement with one of the other cases and a DC in agreement with the third case. There was some variation in the VC calculation. The VC is sensitive to the radial power distribution, which requires good convergence of RELAP5 to accurately calculate. This is often difficult to achieve. The calculation methodology therefore needs improving, or a large margin needs to be placed on the design to account for uncertainty. In particular, an improved thermal-hydraulic solution (perhaps using a steady-state solution rather than a time-marching approach) would be preferable to reduce uncertainty. For the axially homogeneous fuel proposed in the Thbased RBWR design investigated, two-dimensional (2-D) lattice calculations are appropriate for lattice data 168 generation for the core simulator. Therefore, 12-group cross sections were generated using WIMS and converted to the PMAXS format required in PARCS (Ref. 36). The branch and history cases were again based on the University of Michigan’s models. Six histories (three coolant densities with rods in and out) were modeled, and 22 branches were evaluated per burnup step, including the reference case. This encompassed five coolant densities, three fuel temperatures, and the control rods. Two short burnup steps of 60 and 440 MWd/tiHM were used to model Xe and Sm buildup, followed by ten 2500 MWd/tiHM steps and subsequently 5000 MWd/ tiHM steps. In comparison, 2000 MWd/tiHM steps were used in the assembly analysis. Larger steps were used for the full-core analysis to limit the number of state points required and therefore the computational cost. A TRU reload fraction of 26% was selected for the 200-cm-high core based on the analysis. The leakage fraction from the fuel region was calculated at *4.5%, *1%, and 3.5% radially and axially, respectively. To find the achievable discharge burnup, the cycle length in the full-core analysis was increased until the EOC keff was v1. The equilibrium cycle burnup was *94 GWd/tiHM, so it is apparent that a large burnup is neutronically achievable in the RBWR core design considered (Table XIII). The cycle length is very long, therefore, the assembly core residence time is 18.5 years (for the five-batch assemblies), which may exceed cladding limits. The VC was negative, but there was a large uncertainty in its value depending on how it was calculated, so it may be appropriate to introduce a substantial uncertainty margin on the maximum allowable VC and/or improve the calculation methodology. As the burnup was increased, the radial power profile (Fig. 15) flattened, with a peak toward the core peripheral assemblies appearing at high burnups. This is a consequence of the RBWR LP, where fuel is moved inward over the first four batches (Fig. 13), with an incomplete fifth batch at the core periphery. The axial power distribution was approximately cosinusoidal as the fuel of the Th-fueled RBWR is axially homogeneous. There is a slight axial positive skew at the all-rods-out NUCLEAR TECHNOLOGY VOL. 185 FEB. 2014 Lindley et al. REDUCED-MODERATION LWRs FOR TRU BURNING IN Th FUEL—II TABLE XIII RBWR 200-cm Core Performance Discharge Burnup (GWd/tiHM) *47 75.5 90.5 94.3 94.3 (different RELAP restart file) 104.9 EOC keff 1.032 1.010 1.009 1.005 SOC DC (pcm/K) SOC VC (pcm/%Void) EOC DC (pcm/K) EOC VC (pcm/%Void) Cycle Length (years) –2.6 –4.6 –3.4 –3.5 –3.8 –50.4 –30.7 –19.7 –10.3 –18.0 (–39.4 with all shim rods in) –4.3 –4.3 –4.8 –3.9 –4.4 –30.8 –12.0 –10.6 –9.8 –8.2 1.9 3.2 3.5 3.7 3.7 4.1 v1 Fig. 15. Radial power distribution in the 200-cm RBWR core for different discharge burnups. condition due to the slightly negative VC and a significant reflector effect (Fig. 16). The VC shown in Table XIII deteriorates at higher burnup, which may impose a lower TRU reload fraction to comply with the VC requirement. This is consistent with the results of the assembly calculations in the Part I companion paper.1 In particular, the assembly-level VC in the high-VF history increases rapidly over the cycle. Better quantification of the uncertainties in the VC calculation is required and will be performed in future work. The spectrum is too hard to use BPs, so mechanical shim is necessary to control the reactor. The shim rod configuration is the same as in Ref. 35. With all the shim rods in, keff was reduced from 1.021 to 0.997. The shim rods therefore just provide sufficient worth to control the reactor over the cycle, although this may result in unacceptable form factors due to the need for nearly full shim rod insertion at SOC. The CRP used in Ref. 35 has NUCLEAR TECHNOLOGY VOL. 185 FEB. 2014 partial insertion of all the shim rods at SOC, so the number of shim rods being operated simultaneously is the same. The cold SDM may be worse than the U-Pu RBWR due to the more negative VC, and this requires further investigation. It may be necessary to increase the number of control rods in the reactor, which can be accomplished by placing rods on all sides of the assembly. This increases moderation slightly, but, as the achievable burnup is high, this should not greatly affect performance. Similar to the RMPWR, insertion of the rods improves the VC, but this cannot be credited as a VC mitigating action at EOC since all the rods are extracted. The decay and refueling of the EOC discharge isotope vector was modeled, and refueling was simulated with the appropriate TRU reload fraction. The next cycle isotope composition was in very good agreement with the isotope composition in the previous cycle. This indicates that converging the equilibrium isotope vector using a 2-D lattice calculation at the core-average VF was a good approximation. A 30% TRU reload fraction was used with the 125cm core. The leakage was *7.4%. The equilibrium cycle burnup dropped to *60 GWd/tiHM. The VC was slightly positive at EOC, and therefore, the design is not feasible with this TRU reload fraction (Table XIV). The lower burnup results in a nearly flat radial power profile across the core (Fig. 17). The short core has a more bottom-skewed power distribution with rods out compared to the tall core (Fig. 16). The 125-cm core has a lower discharge burnup than the 200-cm core. The effect of increased leakage outweighs the higher TRU reload fraction. The reactivity swing is low, as the fissile inventory ratio is quite close to unity, as with the RMPWR, due to the significant content of TRU isotopes with even mass number, which effectively behave as fertile neutron absorbers. This means that the burnup is sensitive to core leakage. However, while leakage improves 169 Lindley et al. REDUCED-MODERATION LWRs FOR TRU BURNING IN Th FUEL—II Fig. 16. Axial power distributions in 125- and 200-cm RBWR cores over active fuel length. TABLE XIV RBWR 125-cm Core Performance Discharge Burnup (GWd/tiHM) 59.5 EOC keff SOC DC (pcm/K) SOC VC (pcm/%Void) EOC DC (pcm/K) EOC VC (pcm/%Void) Cycle Length (years) 1.003 –3.5 –18.7 –3.9 z0.1 1.5 the VC, the axial reflector acts to limit this advantage, so the VC of the short core is more positive than predicted by the lattice calculation. Fig. 17. Radial power distribution in the 125-cm RBWR core. 170 The short core burnup is consistent with that expected from a 53% VF 2-D calculation with 7.4% leakage. From Fig. 8 in the Part I companion paper,1 the one-batch burnup is *38 GWd/tiHM. For the 200-cm core with 26% TRU reload fraction, 4.5% leakage, the one-batch burnup is *46 GWd/tiHM, so a four- to five-batch burnup of *75 GWd/tiHM is expected. The burnup calculated in the full-core analysis is significantly higher than this. This could be due to the relative influences of the high- and low-VF regions of the core. The highly voided region has nearly constant k? over the cycle, while the lower-voided region burns out relatively fast. The variation in spectrum over the core affects the evolution in power distribution and keff over the cycle, improving the neutron economy such that the cycle is longer than expected. These effects seem to be more significant for the tall, high discharge burnup core than the short, lower discharge burnup core. This requires further analysis. NUCLEAR TECHNOLOGY VOL. 185 FEB. 2014 Lindley et al. REDUCED-MODERATION LWRs FOR TRU BURNING IN Th FUEL—II In the high-leakage core, the relatively high reactivity top region of the core experiences higher leakage, so it might be expected to contribute less to the overall reactivity. This is consistent with the bottom-skewed power distribution of the short core. In the relatively low leakage core, the higher reactivity of the highly voided region may have a more significant beneficial influence on the overall neutron balance. In conclusion, a tall core appears more appropriate for the homogeneous RBWR design, although the high fullcore burnup requires further scrutiny. The maximum critical power ratio (MCPR) of this design was evaluated using Liu et al.’s correlation for RBWRs (Ref. 37), assuming careful enrichment balancing limits the local peaking factor in the assembly to 1.05 (as in current RBWR designs). Based on the results in Fig. 17, a radial power peaking factor of 1.2 is used, which is similar to existing RBWR designs. The core mass flow of the reference design is 7222 kg/s, which corresponds to an average mass flux of 842 kg/(m2?s). It may be possible and desirable to reduce this for the tall RBWR to reduce the pressure drop, but in general, the pressure drop is low for the RBWR core as it is short.38 Using the calculated axial power distributions, the MCPRs for the short and tall cores are 1.48 and 1.76, respectively. These large thermal-hydraulic margins are expected from the homogeneous core configuration and compare favorably with the U-Pu RBWR MCPR (Ref. 39). ACKNOWLEDGMENTS We would like to thank T. J. Downar and the rest of his group at the University of Michigan for help and guidance in setting up PARCS-RELAP5 models and guidance on investigating the reactor’s neutronic performance. We gratefully acknowledge the support of P. Smith and the rest of the ANSWERS team at AMEC for providing access and guidance on the use of WIMS 10. We would also like to thank P. Bryce and his colleagues at EDF Energy for providing access and guidance on the use of PANTHER. The first author would like to acknowledge the U.K. Engineering and Physical Sciences Research Council and the Institution of Mechanical Engineers for providing funding toward this work. REFERENCES 1. B. A. LINDLEY et al., ‘‘On the Use of ReducedModeration LWRs for Transuranic Isotope Burning in Thorium Fuel—I: Assembly Analysis,’’ Nucl. Technol., 185, 127 (2014); http://dx.doi.org/10.13182/NT13-53. 2. T. NEWTON et al., ‘‘Developments Within WIMS10,’’ Proc. Topl. Mtg. Physics of Reactors (PHYSOR 2008), Interlaken, Switzerland, September 14–19, 2008. V. CONCLUSIONS With sufficient RM, a Th-fueled LWR can operate on full TRU recycle while burning an external supply of TRU, e.g., recovered from reprocessing used fuel discharged from once-through LWR operation. In a retrofit PWR design, the core flow rate is reduced for the same RCP. Despite this, acceptable steady-state MDNBR and coolant inlet and outlet temperatures appear achievable. 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