Modeling of the SPERT transients using Serpent 2

Annals of Nuclear Energy 125 (2019) 80–98

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Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene

Modeling of the SPERT transients using Serpent 2 with time-dependent capabilities Alex Levinsky a,⇑, Ville Valtavirta b,1, Frederick P. Adams a,2, Vinicius N.P. Anghel a,2 a b

Canadian Nuclear Laboratories, 286 Plant Road, Chalk River, Ontario K0J 1J0, Canada VTT Technical Research Centre of Finland, Finland

a r t i c l e

i n f o

Article history: Received 27 April 2018 Received in revised form 29 August 2018 Accepted 30 September 2018

Keywords: Time-dependent Monte Carlo Serpent Pressurized water reactor Reactor kinetics Reactor transient Reactor period

a b s t r a c t Monte Carlo multi-physics modeling of reactor transients is being made feasible by the advancement of computer capacities. Developments have recently been made in the area of dynamic Monte Carlo methods, and corresponding new algorithms have been implemented in a number of transport codes. In particular, a time-dependent simulation mode has been implemented in the Serpent 2 code. This paper is focused on time-dependent simulations of the SPERT experiments. The results of reactor-physics simulations are presented. The modeling has been performed using Serpent 2. The results of the reactor physics simulations without fuel temperature feedback are in very good agreement with the experimental data. Crown Copyright Ó 2018 Published by Elsevier Ltd. All rights reserved.

1. Introduction Code-coupled simulation tools are needed to effectively perform safety analysis of reactor accidents and incidents, where feedback phenomena play a very important role. This is the area of interest for almost all the organizations in the nuclear industry, namely reactor designers, utilities and nuclear safety regulators. As a result, in the last decade, multi-physics coupled calculations and enhancement of reactor analysis and simulation tools have become two of the most important research areas under development. NURESAFE (Chanaron et al., 2015), NURESIM (Chauliac et al., 2011), and CASL (Turinsky and Kothe, 2016) are examples of large projects that have focused on the development of high-fidelity coupled simulations. One of the main applications of the coupled simulations is transient analysis, which may involve modeling of experiments, normal plant operation or accident scenarios. Traditionally, the reactor physics side of coupled simulations has been represented by deterministic or hybrid methods (Sjenitzer, 2013). The use of Monte Carlo techniques has been lim⇑ Corresponding author at: Westinghouse Electric Company, Cranberry Twp, PA 16066, USA. E-mail address: [email protected] (A. Levinsky). 1 Mailing address: VTT Technical Research Centre of Finland, Ltd., Kivimiehentie 3, Espoo FI-02044 VTT, Finland. 2 Mailing address: Canadian Nuclear Laboratories – Chalk River Laboratories, B889, Stn Keys, Chalk River, Ontario K0J 1J0, Canada. https://doi.org/10.1016/j.anucene.2018.09.038 0306-4549/Crown Copyright Ó 2018 Published by Elsevier Ltd. All rights reserved.

ited by their high computational costs, but multi-physics modeling of transients in Monte Carlo codes is now feasible due to the ongoing advancement of computer capacities. Algorithms must be developed for the time-dependent calculations, implemented in Monte Carlo codes, and evaluated for performance against the available experimental data, before practical use can be made of that new capability. The goal of the work presented in this paper is to perform time-dependent simulations of the SPERT experiments (Stacy, 9810) using the Serpent 2 code (Leppänen, 2015). Results of reactor physics and coupled reactor-physics – fuelperformance simulations are presented in this paper. A brief introduction to the current status of the Monte Carlo codes with timedependent capabilities is given in the first section of the paper. Some information regarding the SPERT reactor is provided in the second section, with an emphasis on the experiments that will be presented in this paper. Descriptions of the SPERT I and SPERT III experiment models created for Serpent are included in the third section. The verification of models is discussed in the fourth section. The modeling of the transients and the discussion of the results are presented in the last two sections.

2. Current status of the Monte Carlo codes with time-dependent capabilities The Monte Carlo method of simulating particle transport is based on a statistical approach. Individual neutrons are simulated

A. Levinsky et al. / Annals of Nuclear Energy 125 (2019) 80–98

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Nomenclature b

vd;i vp

DT ki

m / P

t

t;f ;s

BWR DT

delayed neutron fraction the emission spectrum of delayed neutron precursor family i the energy spectrum of prompt fission neutrons time step decay constant of family i average neutron yield at fission neutron flux total, fission, and scattering cross sections neutron speed Boiling Water Reactor decay delay

by sampling events from known probability distributions that describe the behavior of a system given an initial state. The expected behavior is found as an average, and random outcomes are generated until the average outcome converges to within an appropriate variation (Tuttleberg, 2014). Since approximations that are typically required by deterministic methods can be avoided in the Monte Carlo approach, a potentially more accurate solution of the transport equation may be obtained. A complex set of phenomena must be resolved by a Monte Carlo code with time-dependent capability. They are described by the coupled system of the time-dependent Boltzmann equation for neutron transport expressed as Eq. (1) and the equations for the delayed neutron precursor concentrations defined by Eqs. (2) and (3) (Sjenitzer and Hoogenboom, 2015):

1 @/ðr; X; E; tÞ þ X 5/ðr; X; E; tÞ þ Rt ðr; E; tÞ/ðr; X; E; tÞ @t ZZ vp ðr; E; tÞð1 bðr; E0 ; tÞÞmðr; E0 ; tÞ Rf ðr; E0 ; tÞ/ðr; X0 ; E0 ; tÞ ¼

tðEÞ

0

þ Rs ðr; E0 ; tÞ/ðr; X0 ; E0 ; tÞdE dX0 þ Sd ðr; X; E; tÞ þ Sðr; X; E; tÞ ð1Þ ZZ @C i ðr; tÞ ¼ ki C i ðrÞ þ bðr; E0 ; tÞmðr; E0 ; tÞ @t 0 Rf ðr; E0 ; tÞ/ðr; X0 ; E0 ; tÞdE dX0

Sd ðr; X; E; tÞ ¼

1 X ki C i ðr; tÞvi ðEÞ 4p i

ð2Þ

ð3Þ

The following issues must be addressed by a Monte Carlo code in order to perform time-dependent reactor physics calculations (Sjenitzer and Hoogenboom, 2015): Modeling of delayed neutron population; Treatment of branching neutron chains; Explicit treatment of time-dependence instead of the implicit treatment present in eigenvalue and source-detector (fixed source) calculations; Imposition of initial conditions. Applying time-dependent changes to the system. Algorithms that allow time-dependent calculations have been implemented to some extent in several Monte Carlo code, namely TART, MERCURY, TRIPOLI4, MNCP5, GEANT4, OpenMC, T-ReX and Serpent 2. The next sections will provide a brief review of the methodologies for the time-dependent calculations implemented in these codes. All the discussed codes are parallel.

E kdyn LT mn Nabsorption Nproduction PWR S Sd SPERT ti

neutron energy dynamic neutron multiplication factor total neutron lifetime neutron mass neutron loss rate neutron production rate Pressurized Water Reactor external source delayed neutron source Special Power Excursion Reactor Tests time interval between collisions

2.1. TART and MERCURY One of the first Monte Carlo codes having time-dependent capability was TART (Cullen, 2012), a coupled neutron-photon, three dimensional radiation transport code, which was developed by Lawrence Livermore National Laboratory (LLNL). TART was followed by MERCURY, also being developed by LLNL (Mercury Code Team, 2016 and Procassini et al., 2010). 2.2. T-ReX The T-ReX (Transient-Reactor eXperiment simulator) code is an extensive update to TDKENO (Mausolff et al., 2018). It has been developed as a transient analysis tool. The T-ReX code has a few geometric limitations, and minimal theoretical approximations. It employs the Improved Quasi-Static (IQS) method to solve the time-dependent Boltzmann transport equation with explicit representation of delayed neutrons (Mausolff et al., 2018). The detailed description of the algorithms implemented in T-ReX can be found in Mausolff et al. (2018). 2.3. TRIPOLI and MCNP A novel methodology to perform time-dependent calculations using a Monte Carlo code was proposed by Sjenitzer (2013). In this methodology, the issues listed above can be addressed by the following techniques (Sjenitzer and Hoogenboom, 2015): Forced decay of precursors in each time interval is used to get enough statistics per tally bin. The expected weight of a delayed neutron is used for precursor population control. Simulation of branching process is done via branchless method. A particle is stopped at the time boundary, and a new path length is sampled from there, using the updated cross-section data. Tally normalization is done using the number of starting neutrons and the time bin size. Precursor and neutron distributions are used as a source for a dynamic simulation. They are obtained from the steady-state calculations performed for a critical system. For parallel calculations, all particles get a new unique particle number from which a random seed is produced at the beginning of each time interval. These technique were used to implement a time-dependent capability in the MNCP5 code version 1.51 (X-5 Monte Carlo Team, 2003) and the TRIPOLI4 code (TRIPOLI-4 Project team, 2010). The detailed description and results were published in Hoogenboom and Sjenitzer (2014).

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2.4. GEANT4 The GEANT4 simulation toolkit (Agostinelli, 2003) was extended to simulate time-dependent neutron populations with a goal to use it in reactor physics applications (Russell, 2012 and Wesley, 2016). This version of GEANT4 was called Geant4 STOchastic Reactor Kinetics or G4-STORK. For time-dependent calculations, the following characteristics were implemented in the G4STORK code (Wesley, 2016): The code starts from an initial guess of the equilibrium neutron position and energy distribution. Individual neutrons are tracked through the geometry as a function of time steps provided by the user. At each time step, the effective neutron multiplication factor is calculated using dynamic criticality method. In the calculation keff is assumed to be constant over each time step, which is true if the reactor geometry does not change during the time step. Consequently, short time intervals are preferable for this approach. A large neutron flux is required to get enough neutron productions and losses within the time interval in order for keff to be statistically significant. At each time, Shannon entropy is determined, and the neutron population is renormalized to the initial number of neutrons. The neutron population is taken to be converged when the Shannon entropy of the neutron spatial distribution is constant between simulation iterations. The kinetic energy of a neutron relative to a nucleus is handled by the on-the-fly Doppler broadening algorithm. Delayed neutrons, like the prompt neutrons, are created instantaneously following the fission process. Cases that simulate transients on the order of one tenth of a second can be run in a reasonable time frame. However, significant acceleration of the code would be required in order to simulate longer transients. 2.5. OpenMC The OpenMC code (Romano and Forget, 2013) has been under development since 2011. time-dependent modules in the code were implemented in the code recently (Mahjoub and Koclas, 2015). The particulars of this approach are the following (Mahjoub and Koclas, 2015): Delayed neutrons are handled via group decay constants. The cumulative density function is calculated using the inversion method for sampling. The decay delay DT is obtained via Eq. (4).

DT ¼

1 logðrÞ; ki

ð4Þ

where r is a random number 2 [0, 1]. Particle tracking is a function of time. An appearing time T 0 , a lifetime LT , and a disappearing time T f are used in the code for this purpose. The lifetime of each neutron is obtained using the kinetic energy. The total lifetime of a particle is defined as a sum of time intervals between the collisions.

LT ¼

X X Li qffiffiffiffiffi ti ¼ i

i

2E mn

ð5Þ

The disappearing times for prompt and delayed neutrons (T nþ1 0;p and T nþ1 0;d respectively) are defined using Eq. (6). n n T nþ1 0;p ¼ T 0 þ LT n n nþ1 T nþ1 0;d ¼ T 0 þ LT þ DT ;

ð6Þ

where n is the index of the incident neutron, and p and d correspond to prompt and delayed neutrons, respectively. The approach used to track neutrons is completely independent of time intervals and neutrons are followed during their travel through the cell without any interruption. A set of variables is calculated for each small time interval, Dt. The reaction rate in each time interval is given by the Analog Estimator. The flux is obtained by dividing the total reaction rate by the total macroscopic cross section of each material in which the neutrons undergo collisions. The homogenized cross sections are calculated by dividing the reaction rate by the obtained neutron flux. The distances traveled by neutrons in each interval of time are added by the Track-length Estimator. The total distance traveled by neutrons is equal to the integrated flux of particles. The integrated flux can be obtained by adding tracks. The adiabatic approximation for the cross sections is used. Reactor data is obtained by solving the steady state transport equation with parameters describing the instantaneous conditions of the reactor cell. 2.6. Serpent 2 Serpent is a Monte Carlo neutronics code developed at VTT Technical Research Centre of Finland (Leppänen, 2015). Serpent 2 uses a hybrid MPI/OpenMP approach for parallelizing the calculation. One of the major applications of the Serpent 2 code is coupled multi-physics calculations (Valtavirta et al., 2016). Hence, it is important that the code acquires an ability to perform timedependent transient modeling. The Serpent 2 code was selected for the time-dependent simulations of the SPERT experiments based on its high flexibility, the advanced level of its time-dependent capability implementation, and its ability to be coupled with thermal hydraulics and fuel performance codes. A more detailed description of the dynamic simulation mode in Serpent 2 can be found in Valtavirta et al. (2016), but the main parts of the dynamic simulation mode are also described here: Transient simulations with Serpent are based on starting the simulation from known live neutron and delayed neutron precursor source distributions and tracking both neutrons and precursors through space and time in a continuous manner (i.e. without time discretization). The simulations are typically divided into timeintervals for periodic population control that is applied to the neutron and precursor populations. In order to obtain the initial distributions for live neutrons and delayed neutron precursors a time-independent criticality source simulation is first executed. During this simulation, positions of neutrons and delayed neutron precursors are recorded to a file in order to later be used for a transient simulation: 2.6.1. Initial neutron source For the initial neutron source Serpent stores neutrons at random times during their lifetime. This is achieved by saving neutrons during a criticality source simulation at tentative interaction sites. However, the interactions of neutrons are not distributed uniformly in time, but depend on the neutron energy and the local interaction cross section: The mean path length between two interactions (mean free path) for a neutron with energy E traveling over a path, where the interaction probability is constant over the path length, is

kmean ðEÞ ¼

1

Rtot ðEÞ

;

ð7Þ

where Rtot is the total macroscopic cross section over the path. The time it takes for the neutron to travel this path length gives the mean time between two interactions


t mean ðEÞ ¼

kmean ðEÞ 1 ¼ ; v ðEÞ Rtot ðEÞv ðEÞ

ð8Þ

where v ðEÞ is the velocity of the neutron. This means that the mean interaction frequency depends on the energy of neutrons as

f mean ðEÞ ¼

1 ¼ Rtot ðEÞv ðEÞ: t mean ðEÞ

ð9Þ

If neutrons are stored at sampled interactions and the stored neutron source is to represent the physical neutron source in the system at a random time, each neutron should be stored with a probability proportional to P / 1=ðRtot ðEÞv ðEÞ). Serpent saves neutrons at tentative collision sites with the probability of

P¼A

w

v Rpath

;

ð10Þ

where w is the weight of the incoming neutron,

v

is its velocity,

Rpath is the macroscopic cross section used in sampling the pathlength to the tentative collision site and A is a normalization factor depending on the minimum neutron speed and the minimum cross section to keep the probability P below unity for all cases. Here Rpath can be either the local material total cross section if surface tracking is used or a majorant cross section if delta tracking is used. For each live neutron, the location, direction cosines, the neutron energy and the weight of the neutron are saved. The total live neutron population is also tallied for normalization using an implicit estimator for

Z Z

Nphys: live ¼

V

E

1

v

/ð~ r; EÞdEdr3 ;

ð11Þ

where the integral is of the one over velocity multiple of scalar flux over the whole geometry and energy range. 2.6.2. Initial precursor source The initial precursor source for a transient simulation is saved during the criticality source simulation either on a regular mesh or as a point distribution. The tallying of the initial precursor source is based on tallying the production rate of each delayed neutron group, assuming steady state for the precursor population and calculating the stable population for each group by dividing the production rate for the group with the decay constant of the group. As for the point distribution source, the implicit estimate of precursor production rate for group g due to one interaction by a neutron representing a source population of w neutrons per second is

bg ð~ r; EÞmð~ r; EÞRf ð~ r; EÞ w; C_ þg ¼ Rtot ð~ r; EÞ

ð12Þ

where bg ð~ r; EÞ is the fraction of fission neutrons being delayed in group g; m is the number of fission neutrons produced per fission, Rf is the macroscopic fission cross section and Rtot is the macroscopic total cross section. Assuming a steady state, the stable precursor concentration supported by this production rate is

bg ð~ r; EÞmð~ r; EÞRf ð~ r; EÞ Cg ¼ w; kg Rtot ð~ r; EÞ

ð13Þ

where kg is the decay constant of delayed neutron precursor group g. At each interaction site, the production rates are calculated for each group according to Eq. (12) and point precursors are stored for each group with information on the position of the precursor, the precursor group as well as the initial concentration represented by the precursor (Eq. (13)). In order to limit the number of precursors stored to the source to a manageable level, Russian roulette is played before storing the precursor with a survival probability of

Psurv: ¼ P

C_ þg bg ð~ r; EÞmð~ r; EÞRf ð~ r; EÞ ; ¼P w Rtot ð~ r; EÞ

83

ð14Þ

where P is a user given constant. 2.6.3. Transient simulation The transient simulation is started by setting up the initial neutron and delayed neutron precursor distributions based on the previously stored data. The weights of the neutrons are normalized so that the initial neutron population corresponds to the one tallied in the criticality source simulation used for the source generation. If mesh-based precursor tracking is used, the initial emission rate will automatically match that of the source generation simulation. In the case of point precursors, the weight of the precursors read from the file is scaled so that the emission rate from the precursors read into memory matches that of the source generation simulation. During each time interval of the transient simulation, a primary source is first generated based on 1. The live neutron population that survived until the end of the previous time interval (or the initial neutron population for t ¼ 0). 2. The delayed neutrons that should be emitted during the time interval from the precursors that survived until the end of the previous time interval (or the initial precursor population for t ¼ 0). A user given number of primary particles is sampled from these two source distributions keeping the statistical weight of the primary particles roughly constant. This means that ratio between the sampled live neutrons and emitted neutrons is approximately equal to the ratio of physical live neutrons and emitted neutrons:

Nphys: Nslive live : s Nemit Nphys emit

ð15Þ

These primary particles and any secondary (etc.) particles they produce are then tracked until their absorption, leakage or their arrival at the next time-interval. Furthermore, the delayed neutron precursor population is allowed to decay during the time-interval based on the exponential decay law. During the transient simulation, the fission reactions only produce prompt neutrons. Delayed neutron emission is handled in an implicit manner instead: the implicit estimate of precursor produced for group g due to one interaction by a neutron representing a source population of win neutrons is

dC g ¼ bg m

Rf w ; Rtot in

ð16Þ

where bg ; m; Rf and Rtot represent the values at the interaction site and energy. A part of this precursor population will decay into delayed neutrons before the end of the interval while the remaining part will survive the interval as precursors. These parts can be represented with

dC emit ¼ dC g 1 exp kg ðt EOI t int: Þ g

ð17Þ

and

dC surv: ¼ dC g exp kg ðt EOI t int: Þ ; g

ð18Þ

where tint: is the interaction time and t EOI is the time at the end of the current time interval. Russian roulette is played for the part that should be emitted during the interval to determine whether to sample an additional delayed neutron to be tracked or not whereas the part that survives the interval is either added to the end-of-interval precursor concentrations (mesh based precursor tracking) or added

84


as a separate point precursor after a round of Russian roulette (point precursor tracking). At time interval boundaries population and weight control is applied to the neutron distribution and the point precursor distribution if it is being tracked. The neutron population and weight control is achieved by using Russian roulette and stochastic splitting to obtain N slive neutrons with a statistical weight representing =N slive neutrons each (see Eq. (15)). The point precursor distriN phys: live bution is normalized into a constant number of particles (by default 10 times the number of primary source particles) with an equal emission during the upcoming time-interval. 2.6.4. Time-dependent transformations Serpent 2 also supports time-dependent geometry transformations which can be used, for example to model control rod movement. The user can supply initial translations, velocities and accelerations for different surfaces and/or geometry universes to produce the desired movement. Serpent will update the geometry at each time-interval boundary based on the supplied kinematic parameters.

Fig. 1. SPERT I. 592C Fuel Rods Lattice Arrangement (part of Figure B-1 in Grund (1964)).

3. SPERT experiments The Special Power Excursion Reactor Tests (SPERT) Project was a series of reactor experiments beginning in 1954 and continuing into the late 1960s at the National Reactor Testing Station, now the Idaho National Laboratory (Stacy, 9810). It was a thorough investigation into the kinetic behavior of nuclear reactors, with a broad and long-lasting relevance to the nuclear industry. SPERT experiments provided key benchmarks for the validation of early reactor kinetics tools, have continued in that role ever since, and include the transients that are simulated in the present work. Open literature descriptions of the SPERT facilities and experiments are dispersed among a number of different publications and reports. The details of the SPERT I and SPERT III experimental installations are carefully systematized in this section based on the rigorous review of all the accessible sources of information. The majority of the available geometrical data are in inches. It was necessary to convert them to centimeters to build input models for Serpent. As a result, a significant number of digits after a decimal point is given in order to preserve the exact dimensions in inches. 3.1. SPERT I series of experiments The SPERT project produced experimental data on behavior of various kinds of nuclear reactors. The experiments used from the SPERT I campaign are a subset of the self-limiting power excursion tests of a well-moderated, low-enrichment UO2 SPERT I core in 1961, as described in Spano et al. (1962), Spano (1963), Scott et al. (1963), Spano (1964). The SA592C set of experiments used here, with a SPERT I core of 592 fuel rods, have the long, thin fuel rods constrained in the middle by a horizontal aluminum square lattice. The SPERT I core includes fuel rods arranged at square lattice pitch of 1.684 cm as shown in Fig. 1. As seen in this figure, the SPERT I core was fourfold symmetric. The SPERT I experiments have not yet been included in a benchmark. The NEA guide for evaluating experiments (Nuclear Science Committee, 2013) was therefore used as a general basis for the description that follows. The documentation from the SPERT I SA592C experiments was found to be missing some data necessary for purposes of a benchmark. The required data was derived from other sources. Different sources for the data show slightly different values, hence data consistent in a majority of sources was chosen. Documents for other SPERT experiments (the destructive OC experiments OC-290C and OC599C (Grund, 1964) and MARTY

experiments (Ball et al., 1961) were consulted, because the fuel in the SA-series experiments was used in those experiments as well. The SPERT I experiments differed from each other by the placement of the temperature sensors, and by the vertical positions of the control rods and the transient rod. Both the control rods and the transient rod were adjusted to set up each reactor power transient. The fuel was heated by the power released during the transient. The power was observed to rise quickly in the initial phase, reach a maximum, and then decrease due to negative temperature feedback, attributed mainly to the Doppler broadening of resonances in the 238U neutron-capture cross section. Significant data such as time, power and fuel sheath temperatures were recorded over the course of the experiments. Maximum power and time to reach maximum were derived from the recorded data (Spano et al., 1962). The same arrangement of fuel rods and the same supporting structure were used for all experiments. The lattice pitch was square, with cells having 1.68402 cm sides. Light water was used as the moderator. The core assembly was formed by populating the central lattice sites with fuel rods, while the surrounding lattice was left empty (moderator only). Each fuel rod in the reactor has a total length of 181.61 cm including top and bottom end plugs. The active height of 169.86 cm (66 78 in.), was chosen in order to be consistent with the rest of the parameters of the fuel. The overall core was 450 cm high, with the control and transient rods section being 374.64 cm high. The fuel pin structure is shown in Fig. 2. The figure is shown only to indicate how the fuel is put together, as the dimensions are found to be slightly different when a consistency check is made. Where the material data listed were contradictory among the references, the data from Spano et al. (1962), Spano (1963), Scott et al. (1963), Spano (1964) and earlier Babcock & Wilcox

Fig. 2. SPERT I. 592C Cross-Sectional View of the Fuel Rod (in.) (Fig. 4 in (part of Figure B-1 in Grund (1964)).


85

Table 1 SPERT I Fuel Pin Parameters. Parameter

Value

Fuel Fuel Density Fuel Mass in a Pin Total U Mass in a Pin 235 U Mass in a Pin Enrichment of Uranium Clad MaterialType Clad Outer Diameter Clad Thickness Clad Inner Diameter Active Fuel Height

UO2 Powder UO2, 9.45 g/cm3 1600 g 1409 g 56:7 0:1 g 4.01 0.05 wt% 304 Stainless Steel 1.27 cm (0.5 in.) 0.07112 cm (0.028 in.) 1.12776 cm (0.444 in.) 169:86 cm (66 78 in.)

Length of Clad

181:61 1:27 cm (71 12 12 in.) Aluminum 0.640 cm (0.252 in.) 5 in.) 5.87375 cm (216 4.94 cm (1.945 in.) 0.98552 cm (0.388 in.) 0.762 cm (0.300 in.)

End Cap Material Length of each End Cap Helium Space and End Cap Length Helium Space Length Helium Space and End Cap Diameter Diameter of Each End Cap

Table 2 Aluminum Alloy 6061-T6 Element

Nominal Mass Fraction(MF) (%)

Si 2/3 of Max Fe Admissible MF Cu MF0.32 Mn Nominal Cr Nominal Aluminum

0.6 0.46 1.0 0.2 Balance

experiments (Ball et al., 1961) was used, as it came from different sources, which were mutually consistent. Table 1 gives the parameters of a fuel pin and Table 2 gives the structural aluminum alloy composition. The UO2 fuel was modeled as a cylinder with a length of 169.926 cm and a diameter of 1.13 cm. The cladding had an inner diameter of 1.13 cm and outer diameter 1.27 cm. It is modeled as 304 stainless steel with a density of 7.93 g/cm3 (Parisi and Pecchia, 2014). The aluminum end plugs shown in Fig. 2 were modeled with outside diameter 1.27 cm, inside diameter 0.98 cm and an internal length of 4.94 cm, which contained helium gas. The outer face of the plug was a cylinder of solid aluminum. The control rod is made out of four blades moving as a unit. Each blade is built as shown in Fig. 3. The transient rod has a cruciform cross-section and is made out of a poison section and an aluminium follower, as shown in Fig. 4. The length of travel from the maximum insert position and the ejected position is equal to the length of the poison section of the rod. The whole reactivity worth of this rod is about 3 dollars. Spano (1963), Scott et al. (1963). Data on the fuel material is given in Spano (1963, 1964). The fuel rods contained UO2 with a nominal enrichment of 4.02 wt.% 235 U/U and a density of 9.45 g/cm3 . The data from analysis is somewhat variable, due to the measurement errors. These references do not include errors on the measurement, but a later reference does (Parisi and Pecchia, 2014). These errors were added to the table to give an estimate of the uncertainty involved. Another reference on the composition of the fuel gives two slightly different compositions. One is identical to the composition listed and the other is from another analysis, which included additional data on impurities such as fluorine and moisture, and yields 4.01 % concentration of 235U. The additional impurities were estimated to contribute less than 5 104 cm1 in macroscopic absorption cross section. The

Fig. 3. SPERT I. 592C One of the Control Rod Blades (Figure A-16 in Grund and Norton (1963)).

isotopic enrichment determined from chemical and physical analyses is listed in Table 1. The composition of the stainless steel from this experiment was not available. For a closest approximation, the composition from the fuel sheath in the similar but destructive SPERT experiment (Grund, 1964) was used. The material that was used in that experiment is the same as the material in the experiments we investigate. The composition was obtained from a chemical analysis of the materials actually used in the experiments in Grund (1964)) and listed for cladding steel in Table A-V. The density of the stainless steel was not provided in Grund (1964), but the density of this type of stainless steel was found in a well-documented benchmark experiment that used the same fuel (Parisi et al., 2014; Parisi and Pecchia, 2014). An aluminum-boron alloy containing 7 wt% natural boron in a form of B4C was used for reactivity control devices (Grund and Norton, 1963)). Since the density for this material was not given, a physical approach was followed in determining its value. The micrographs presented in Heffner (1963) show that the boron carbide and the aluminum form a physical mixture, and not an intermetallic compound or a ”proper” alloy. Consequently, the density is deduced from the information available on aluminum (Boyer and American, 1992) and boron carbide. The temperature at the beginning of the experiment was approximately 20 °C (293.15 K) (Spano et al., 1962; Spano, 1963). For all configurations described in this report, the experiment was conducted as follows:

86


Fig. 4. SPERT I. 592C Transient Rod Blade (in.) (Figure A-17 in Grund and Norton (1963)).

The reactor was brought to a critical state with the transient rod outside the active core. The critical position of the control rod was recorded. The control rod and the transient rod were raised slowly in concert, with the reactor kept critical. At the end of the rise, the control rod transient position was recorded. Once the control rod reached the transient position, the transient rod was quickly withdrawn from the core. The transient was recorded, and then the reactor was tripped. 3.2. SPERTIII series of experiments The SPERTIII reactor facility was planned as a facility for the study of reactor behavior and safety under operating conditions typical of pressurized-water and boiling-water reactors (Heffner and Wilson, 1961). The SPERT III facility was deactivated in 1968, but was not decommissioned until 1980 (Stacy, 9810). Its test results were adopted as a foundation to underlie the safe design of the many American PWR and BWR reactors that were built and are still in operation. A detailed description of the SPERT III installation, derived from the review of numerous reports and papers, is provided in this section.

The SPERT III reactor facility was based on a pressure vessel resembling a PWR reactor vessel, only smaller in scale. Its height was 724 cm (23 feet 9 in.), but its interior diameter was only 122 cm (48 in.) (Heffner and Wilson, 1961). Operation up to a pressure and temperature of 17.2 MPa (2500 psig) and 616 K (650 °F) was enabled by the shell thickness of 8.26 cm (314 in.) thick steel, including a 18-in. interior layer of 304L stainless steel. The shell was made by rolling and welding sheets of steel around an inner cylinder that had been precisely machined. Outside the shell was 10.2 cm (4 in.) of ‘‘foamglass” thermal insulation and 15.2 cm (6 in.) of lead shielding. Inside the shell were four concentric thermal shields with a combined thickness of 14.6 cm (534 in.), to absorb the heat from the fission neutrons and gamma radiation. Inside the shields was the core skirt, which formed a cylinder 1.59 cm (58 in.) thick around a core region 8.13 cm (32 in.) across; it also served as a thermal shield. The thermal shields and core skirt were 304L stainless steel. The arrangement of these concentric elements is illustrated in Fig. 5, with dimensions given in Table 3. Other dimensions are based on (Dugone, 1965). The thermal shield values are based on Fig. 8 of Olson (2015), which is consistent with the shield thickness values listed in Montgomery et al. (1965), and the spacing shown in Fig. 44 of Heffner and Wilson (1961).

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F

60.96 cm (24.00 inches)

F

F

F

F

F

25

25

25

25

25

25

F

25

25

25

25

N

25

25

25

25

25

W

25

25

N

25

25

F

25

W

25

16

16

25

25

25

F

F

25

25

25

16

16

25

E

25

F

25

25

S

25

25

E

25

25

25

25

25

S

25

25

25

25

F

25

25

25

25

25

25

F

F

F

F

F

F

F

F

F

F

F

F Fig. 6. Operational Loading of Fuel Assemblies in SPERT III E-Core.

Fig. 5. Concentric Arrangement of SPERT III Reactor Vessel.

Table 3 SPERT III Reactor Vessel Parameters. Parameter

Radius [cm]

Diameter [in.]

Reactor Core Skirt Interior Reactor Core Skirt Exterior

40.64 42.23

32 3314

First Thermal Shield Interior

43.50

First Thermal Shield Exterior Second Shield Interior

45.72 46.83

3414 36 3678

Second Shield Exterior

49.37

3878

Third Shield Interior

50.48

3934

Third Shield Exterior

53.66

4214

Fourth Shield Interior

54.93

4314

Fourth Shield Exterior

60.0

Reactor Vessel Interior Reactor Vessel Exterior

61.0 69.2

4714 48 5412

‘‘Foamglass” Insulation Exterior

79.4

6212

Lead Radiation Shielding Exterior

94.6

7412

A bottom grid 7.62 cm (3 in.) thick and a top grid 17.78 cm (7 in.) thick, both of 304L stainless steel, were supported by the core skirt. Sixteen boxes were shaped to fill the gap between the cylindrical core skirt and the active core region. The filler pieces were boxes formed from 0.318-cm (18 in.) 304L stainless steel sheet; coolant flowed through them. The core region was composed of sixty-eight square grid sections (Stacy, 9810). The core region lattice pitch of 7.62 cm (3.000 in.) was defined by holes in the top and bottom grids (Heffner and Wilson, 1961). The transient rod was a four-bladed device that fitted through a cruciform hole in the bottom grid (Heffner and Wilson, 1961). The lower section of the blades was an absorber made of stainless steel containing 1.35 wt% 10B, and the upper section was ‘‘18–8” stainless steel. The upper section moved down to take the place of the absorber as it was driven down out of the core to initiate a transient; the bottom of the absorber remained below the active region. The transient rod was always present in the core. In both sections of the transient rod, the material of the blades was 0.475 cm 3 (16 in.) thick. The arm length of the blades is shown to be 6.38 cm 9 in.) in Fig. 8 of Stacy (9810), for an overall width of 7.62 cm (216

(5.125 in.). Section 2.4 of Heffner and Wilson (1961) states the width to be 5.025 in., and Appendix A of Heffner and Wilson (1961) states the width to be 5.25 in., but (Olson, 2015; Dugone, 1965; Montgomery et al., 1965) agree with a width of 518 in. Mounting points and coolant flow channels for fuel assemblies were provided by fifty-six holes 6.36-cm (2.505-in.) in diameter in the bottom grid. Mounting points and coolant flow for four smaller fuel assemblies in the centre were provided by four holes 5.41-cm (2.130-in.) in diameter. Coolant flow between the fuel assemblies was provided by other holes 2.54 cm (1.00 in.) or smaller, as seen in Fig. 16 of Heffner and Wilson (1961), which is excerpted here in Fig. 7. To assist with perspective, Fig. 7 may be compared with Fig. 6. The eight control-rod guide tubes are shown in Fig. 7 (highlighted yellow), mounted over eight 6.59-cm (2.596-in.) square holes in the bottom grid plate. In the centre of Fig. 7, a loose assembly of guide tubes (highlighted green) is shown around the cruciform transient rod (highlighted red) and the four surrounding grid sections. The positions of both control-rod and transient-rod guide tubes are confirmed in Fig. 8 of Heffner and Wilson (1961), in which the guide tubes 3 are described as being made of 16 in. 304L stainless steel. In a later reference, (Dugone, 1965), the guide tubes are described as being made of Zircaloy-2. Note that the guide tubes are not described in Olson (2015), but their existence is mentioned. The top core grid is shown in Fig. 17 of Heffner and Wilson (1961). The fuelassembly holes in the grid appear to be large and square, leaving little material between holes, but details were not found in the available references. The SPERT III reactor was initially operated with a core that had assemblies of plate fuel containing highly enriched uranium (Montgomery et al., 1965), which was later referred to as the C– core. The C–core was replaced by the E-core, which had 60 new fuel assemblies with pins containing pellets of low-enriched UO2 in stainless-steel cladding (Dugone, 1965). Fifty-two 25-pin assemblies were fabricated (Dugone, 1965). However, the operational Ecore comprised forty-eight 25-pin fuel assemblies (marked 25), four 16-pin assemblies (marked 16) and eight paired control rods (marked N, E, W and S) in sixty grid sections (Combustion Engineering Inc., 1961b), as shown in Fig. 5. The eight outermost grid sections contained square filler pieces. The fuel pins for the E-core fuel assembly were repurposed from a previous low-power reactor experiment (Combustion

88


Fig. 8. Nominal 25-Pin Fuel Assembly.

Fig. 7. Layout of Guide Tubes and Filler Pieces in SPERT III Core (Colour Highlights Added to Guide the Eye). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Engineering Inc., 1961a). More details may be found in Combustion Engineering Inc. (1961b), with the fuel pin shown in drawing PL2D2598. Basic fuel-pin parameters provided in Olson (2015) were found to be consistent with the primary references. The fuel enrichment and density are listed in Crocker (1964), along with the mass of 235U per pin; the detailed fuel-pin parameters adopted from the references are shown in Table 4. The spring was made of 0.152-cm (0.060-in.) diameter Haynes 25 alloy wire, with 12.5 turns wound to an outside diameter of 1.04 cm (0.410 in.) and a free length of 5.59 cm (2.20 in.) (Combustion Engineering Inc., 1961b). In Crocker (1965) the spring expansion space is listed as 2.50 in., which would include the length of endcaps inside the fuel sheath. Autoclave test results indicated that the clad would resist collapse under operating conditions in SPERT III (Crocker, 1965). However, 15% of fuel pins were later found to have localized fuel cladding collapse onto the pellets (Taxelius, 1968a). The 25-pin assembly was described as a square can of 0.064 cm (24-Ga., 0.025-in.) 304L stainless steel, 7.557 cm (2.975 in.) across the outside, with holes in the walls totaling 774 cm (120 squar-

Table 4 E-Core Fuel Pin Parameters. Parameter

Value

Fuel Pellet Material Enrichment of Uranium Fuel Pellet Diameter Clad MaterialType Clad Outer Diameter Clad Thickness Clad Inner Diameter Active Height (Fuel Pellets) Length of Clad End Cap Material Outside Length of each End Cap Inserted Length of each End Cap Length of Recess in each End Cap Diameter of Recess in each End Cap Insulator in Recess of Bottom End Cap Length of Space for Spring Spring Material Spring Mass (Calculated from Dimensions) Fuel Pin Length (end-plate-to-end-plate)

UO2, 10.5 g/cm3 4.80 0.05 wt% 1.067 cm (0.420 in.) 348 Stainless Steel 1.184 cm (0.466 in.) 0.051 cm (0.020 in.) 1.082 cm (0.426 in.) 97.28 cm (38.30 in.) 103.63 cm (40.80 in.) Type 347 Stainless Steel 0.640 cm (0.252 in.) 0.635 cm (0.250 in.) 0.945 cm (0.372 in.) 0.762 cm (0.300 in.) Al2O3 5.08 cm (2.00 in.) Haynes Alloy 25 5.8 grams 104.85 cm (41.28 in.)

e in.) to permit cross-flow (Dugone, 1965). The five-by-five array of fuel pins in the assembly were fixed on a square lattice pitch of 1.486 cm (0.585 in.) by upper and lower endplates. Provisions were made for nine of the pins to be removable through the endplates. The endplates are shown without description in Fig. 4 of Houghtaling et al. (1965), reproduced here as Fig. 8. Posts on the endcaps of the fuel pins were fitted into small holes in the endplates. The upper (left) and lower (right) end boxes are shown in Fig. 8, along with the holes that were cut through the endplates between the fuel pins for coolant flow. No exact specifications for the cutouts in the endplates were found in the available references. Intermediate grids were also inserted in the assembly at heights of 33.0 cm (13 in.) and 67.3 cm (2612 in.) (Dugone, 1965). The upper and lower end boxes fit into openings in the top and bottom core grids. The 16-pin assembly was described as similar to the 25-pin assembly, containing a four-by-four array of the same type of fuel pins on the same spacing (Dugone, 1965). The square can was made of 0.063-cm (0.025-in.) 304L stainless steel, but was only 6.289 cm (2.476 in.) across the outside (Dugone, 1965). Provisions were made for four of the pins to be removable. Descriptions or illustrations of the arrangement of endplates and end boxes specific to the 16-pin fuel assemblies were not found in the available primary references. Each control rod had a square upper poison box section made of 0.472-cm (0.186 in.), ‘‘18–8” stainless steel containing 1.35 wt% 10 B, and a lower fuel pin section with a four-by-four array of fuel pins on a square lattice pitch of 1.486 cm (0.585 in.) (Dugone, 1965). Based on Fig. 3 of Taxelius (1966), the upper grid plate was 3.09 cm (1.32 in.) thick. The fuel section had a square can of 0.063-cm (0.025 in.) 304L stainless steel 6.340 cm (2.476 in.) across the outside (Heffner and Wilson, 1961). In Dugone (1965), the control-rod box width is said to have been 2.496 in., but that is presumed to include the 0.010 inch-thick rubbing pads on the box wall. In Cao et al. (2015), the control-rod fuel-section box is listed as 6.2890 cm (2.476 in.) across, but the 16-pin assembly is listed as 6.3398 cm (2.496 in.) across, which is the reverse of Dugone (1965). The thickness of the fuel-section can was not found in the available primary references, but by applying the method of Cao et al. (2015) to the 2.80-square-inch flow area (Dugone, 1965), it was derived to be 0.184 cm (0.072 in.). Flux suppressors were placed inside the assembly between the absorber and the fuel to suppress the neutron flux (Dugone, 1965). The material was stainless steel 0.076 cm (0.030 in.) thick, with 1.35 wt% 10B content, The flux suppressors are visible in Fig. 9 of Dugone (1965), which is reproduced here as Fig. 9. Greater detail appears in Fig. 6 of Taxelius (1966), which is adapted with colour highlighting in Fig. 10. The upper and lower flux suppressor plates (pink) were assembled into interlocking three-by-three grids


Fig. 9. E-Core Control Rod Assembly.

Fig. 10. Details of Flux Suppressors in Control Rod Assembly.

above and below the upper endplate (blue). The lower flux suppressor plates fitted between the fuel pins (gray), while the upper flux suppressor plates fitted between the thicker walls (orange) of the poison box section. The upper flux suppressor was 2.54 cm (1.00 in.) tall and the lower flux suppressor was 6.906 cm (223 in.) 32 (Dugone, 1965) tall, separated by the upper endplate 3.35 cm (1.32 in.) thick (Taxelius, 1966). The flux suppressor plate width was listed as 2.184 in. for the upper suppressor and 2.340 in. for the lower suppressor, presumably to fit between flanges of the endplate, which were not described in the available references. An incident in which a flux suppressor plate broke loose and fell to rest on top of the uppermost intermediate grid is described in Taxelius (1966). The position of the plate in Fig. 3 of Taxelius (1966) suggests that the nominal height of the intermediate grid was measured from the upper surface of the bottom endplate to the bottom side of the intermediate grid. Fig. 4 of Taxelius (1966) suggests that the control rod position was measured from a ‘‘zero” with the control-rod fuel below the active core; (Potenza, 1966) states that a 26.5-inch control-rod withdrawal corresponds to 21.8 in. of fuel drawn up into the active core. Thus, the top of the fuel would be 11.9 cm (4.7 in.) below the active core at ‘‘zero” withdrawal. The 60 fuel assemblies of the SPERT III operation E-core (including the eight control rods) contained a total of 128 pins (Potenza, 1966). The mass of 235U per pin is listed as 38.5 grams in both

89

(Olson, 2015 and Dugone, 1965). Interpreting the 1271.5 kg mass for uranium in Table II of Potenza (1966) as total UO2, each pin would contain 805 grams of uranium, or 38.6 grams of 235U at 4.8 wt% 235U/U enrichment. Based on the fuel pellet diameter specification of 1.0668 cm (0.420 in.) and the fuel length of 97.28 cm (38.30 in.) (Combustion Engineering Inc., 1961a), the volume of UO2 in each element would be 86.95 cm3. The mass of UO2 at 10.50 g/cm3 would be 913.0 grams, containing 804.7 grams of uranium and 38.6 grams of 235U. Manufacturing tolerances of 0.10 g/ cm3 on pellet density and 0.15 in. on length of fuel (Combustion Engineering Inc., 1961a) were set, implying a range of 0.4 grams for 235U in each fuel pin. Consistency is thus shown between (Combustion Engineering Inc., 1961a and Potenza, 1966), while (Olson, 2015 and Dugone, 1965) are found to be within the tolerances. Reactor experiments on the E-core in the SPERT III facility began with an approach to critical as fuel was installed, and calibration of the control rod worth (Potenza, 1966). That was followed by static measurements including the transient rod worth and the temperature coefficient of reactivity (Potenza, 1966). The static experiments provide a basis for benchmarking of numerical models of the reactor. A neutron source was used for subcritical multiplication measurements during the approach to critical. Measurements were made both with control rods fully inserted and with control rods fully withdrawn, as in Fig. 4 of Potenza (1966). Control-rod differential reactivity worth was determined from period measurements using temperature as a reactivity shim (Potenza, 1966); gadolinium poison in the coolant was used as a reactivity shim in confirmatory measurements (Taxelius and Potenza, 1967). The calibration curve for control rod reactivity worth is shown in Fig. 11, measured using gadolinium nitrate as a reactivity shim, as reproduced from Fig. 2 of Taxelius (1968c). The transient rod reactivity worth as a function of its position is shown in Fig. 12, which reproduces figure B-4 of McCardell et al. (1969). The measured temperature defect – the integral decrease in system reactivity with increasing system temperature – may be seen in Fig. 13, from Fig. 3 of Taxelius (1968c). The temperature coefficient was measured against control rods (Taxelius and Potenza, 1967). Results for the operational core at 70 °F and 550 °F are shown in Table 5, which is based on Table II of Potenza (1966) and other data from (Taxelius and Potenza, 1967). Note the small differences between the values in Table 4 and the figures that were produced later. When material compositions based on a simple interpretation of the standards and specifications were used in the Serpent model, the value of keff calculated in Serpent for the most-reactive condition (control rods fully withdrawn at room temperature) was initially lower than nominal. Material compositions were therefore investigated for possible variation within tolerances. The manufacturing specification for the uranium dioxide fuel was 4.80 wt% enrichment with a tolerance of 0.05 wt%, and a sintered density of 10.50 wt% 0.10 wt%. Each of these terms represents an uncertainty of roughly 1% in 235U mass, in addition to the tolerance on fuel length. Manufacturing deviations in the direction of lower 235U content might be expected, given the high cost of 235 U in the 1950s and the greater difficulty of sintering to higher density, but there was also a requirement to weigh all fuel during assembly. The 38.5-gram 235U mass per fuel pin reported in Olson (2015, 1965) might reflect a deviation of 0.26%, but would be well within tolerances. The nominal fuel composition was retained. The material standards for the fuel-pin clad and fuel-pin endcaps were 348 and 347 stainless steel, respectively. The nominal compositions are similar, with 9–13% nickel and 17–19% chromium, and only an upper limit specified for manganese. In the lower limit of zero carbon content, the niobium and tantalum con-

90


Fig. 11. Measured Control Rod Worth in SPERT III E-Core.

Fig. 12. Measured Transient Rod Worth in SPERT III E-Core.

Fig. 13. Measured Temperature Defect in SPERT III E-Core.

A. Levinsky et al. / Annals of Nuclear Energy 125 (2019) 80–98 Table 5 Selected Nuclear Parameters for SPERT III E-Core Parameter

At 294 K (70 °F)

At 561 K (70 °F)

Excess Reactivity Temperature Defect Shutdown Reactivity Shutdown Reactivity with Transient Rod Total Reactivity Worth of Transient Rod Control Rod Critical Position Temperature Coefficient Control Rod Worth Near Critical Control Rod Worth Near Critical Void Coefficient

+14.2 $ – 10.3 $ 15.0 $ 4.7 $ 14.55 in. 0.4 ¢/°F 1.55 $/in. 1.6 $/in. 0.34 $/L

+2.5 $ 11.7 $ 22.0 $ 26.7 $ – 28.25 in. 5.5 ¢/°F 0.41 $/in. – 0.48 $/L

Table 6 Stainless Steel Compositions for SPERT III E-Core, Weight Percent. 304L SS

347 SS

348 SS

69.45 19.0 10.0 1.0 0.5 – 0.015 0.023 0.015

72.38 17.0 9.0 – 1.0 0.5 0.05 0.045 0.03

72.38 17.0 9.0 – 1.0 0.5 0.05 0.045 0.03

Element of Alloy/ mass fraction [wt%] Iron Chromium Nickel Manganese Silicon Niobium Carbon Phosphorus Sulphur

tent could also be zero. The model was therefore revised to eliminate tantalum and manganese and to reduce niobium and carbon. Lower-limit values were also adopted for nickel and chromium, and identical compositions were used for 347 and 348 stainless steel. These changes largely resolved the discrepancy in reactivity calculations. A significant quantity of 304L stainless steel was also used in the SPERT III E-core, including the box walls, endplates and intermediate grids of the fuel assemblies. The specifications for manganese, nickel and chromium in 304L are similar to those for 347 and 348. The 304L composition in the model had nickel and chromium content at the midpoint of the specified ranges. One might better refine the balance between alloy contents for the 347, 348 and 304L stainless steels in the fuel assemblies, with better information or other assumptions, but little impact on the results would be expected. The compositions used in the model are shown in Table 6. 4. Models of the SPERT experiments in Serpent 4.1. SPERT I model The data for building and testing a model for the SPERT I slightly enriched UO2 experiments was obtained from several sources (Spano, 1963, 1964; Parisi et al., 2014; Spano et al., 1962; Scott et al., 1963; Parisi and Pecchia, 2014). The sources (Parisi et al., 2014) and (Parisi and Pecchia, 2014) were used for material composition of the fuel sheath, because the SPERT I experiment reused fuel used in the aforementioned references. The references Spano et al. (1962), Scott et al. (1963) give data both on the set-up of the control and transient rods and on the reactor period and effective multiplication factor for these setups. Models were built for the initial states of 26 experiments, and effective multiplication factors were computed for all of them. In all simulations, the effective multiplication factor was found to be roughly 11 mk higher than the experimental value. Calculated

91

results were consistent for both the Serpent (Leppänen, 2015) and the MCNP (Hoogenboom and Sjenitzer, 2014) codes and two different cross section libraries. A possible cause of the constant mismatch between experiment and simulation may be that some type of neutron absorber was not included in the material descriptions given for the experiments. To simulate the unknown absorber, a very small amount of 10B was added to the water until the simulation agreed with the experimental keff result for one of the experiments. To simulate transient conditions, the models were modified by moving the cruciform rod so that the reactor core becomes critical, while keeping the control rod at the position corresponding to the computed keff . The cruciform rod is then ejected from the active core and the transient is computed. The value of the reactor period may be found after the higher order modes die off, which needs at least 0.2 s to be simulated after rod ejection. To reduce the computer resource requirements for the simulation, only water close to the active core was modeled. The reduction of the amount of water was chosen such that the value of keff is changed by less than 0.1 mk compared to a simulation including the whole water pool.

4.2. SPERTIII model The SPERT-III E-core model was based on the specified nominal core parameters, including the reactor-vessel data listed in Table 3 and the fuel-pin data listed in Table 4, as well as specific values discussed in the text. Other model parameters were estimated by inspection of illustrations, and approximations were made where reasonable and necessary, as discussed below. The axial compression spring in the fuel pins contains cobalt, which is a neutron absorber and might affect the neutron flux locally. The fuel pin description of Table 4 is complete, but the spring was approximated as a homogeneous mixture of Haynes Alloy 25 and air. The approximation was made necessary by the complex helical geometry; good coverage is provided by the diameter of the spring being almost the same as the fuel and the wire diameter being 37.5% of the coil spacing. A vertical section through the fuel pins of the control rod is seen in Fig. 16, with the homogenized spring material shown in purple, and a white space for void in the endcap. The figure was prepared using graphical output from Serpent 2 for the model that was developed. The yellow blocks show the poison plates in the absorber section, and the vertical orange bars show the upper and lower flux suppressors. The upper endplate is shown by the light green block, and the Zircaloy-2 walls of the guide tube are shown by the dark green bars on left and right. There were holes in the walls of the fuel assembly boxes around the fuel pins, as shown in Fig. 8. Based on calculation of wall volume over the fuel pin length of 41.4 inches, the walls were represented by a homogeneous mixture of 25% water and 75% stainless steel. The caps at the ends of the fuel pins had stainless steel posts, which were set into holes in the endplates. Since the posts and endplates were similar alloys, both posts and holes were neglected as a simplifying approximation. A horizontal section through the northeast quadrant of the core model at the level of the intermediate grids is seen in Fig. 14; the fuel section of the control rod is aligned with the active core. Due to a lack of detailed information, the intermediate grids were represented by interlocking bars similar to the flux suppressors. 1 The bars were 304L stainless steel sheet 0.063 cm (16 in., 16 Ga.) thick and 1.27 cm high (1/2 in.). In the lower left corner of Fig. 14, the dark green squares around the 16-pin fuel assemblies and control rods represent Zircaloy-2 guide tubes. Based on examination of Fig. 16 of Heffner and

92


Fig. 14. Horizontal Section Through Intermediate Grids in SPERT III Core Model.

Wilson (1961) (reproduced here as Fig. 7), the 16-pin fuel assembly guide tubes are represented as 0.318 cm (1=8 in.) thick. The Zircaloy-2 boxes have 6.350 cm (21=2 in.) inner and 5.985 cm (23=4 in.) outer dimensions, with blocks to represent the walls connecting the boxes. The cruciform stainless steel transient-rod follower is partially visible between the four 16-pin fuel assemblies. Clearance between the box and the edge of the 3-in. grid section was 0.063 cm (0.025 in.). The gap for the blades of the transient rod is 1.143 cm (0.450 in.) wide, slightly narrower than the slots in the lower core grid (0.470 in.). The gap for the transient rod would be made even narrower if the guide tubes were made any thicker, and that was judged not to be an accurate representation. The upper endplate was nominally 1.32 in. thick. Based on scaling from the upper endplate by inspection of Figs. 8 and 9, the lower endplate was represented by a plate 2.08 cm thick (0.82 in., 12 in. less than the upper endplate). The endplates had channels for coolant flow, and the upper endplates had provision for fuel pins to be removed. The top endplate was therefore represented by a slab only 2.54 cm thick; the flow channels were represented by an array of 1-in. holes aligned between the fuel pins, with nine holes for the 16-pin assembly and sixteen holes for the 25-pin assembly. A horizontal section through the lower end plates in the northeast quadrant of the core model is shown in Fig. 15; the fuel section of the control rod is aligned with the active core. The fuel section of the control rods was represented in a manner similar to the 16-pin fuel assemblies. The walls of the assembly box were thicker and the flux suppressors were added, as in Fig. 16, but the fuel pins and end plates were given the same representation as in the 16-pin fuel assemblies, with nine holes for coolant flow. A vertical cross-section of the core model is shown in Fig. 18, with the steel of the core skirt, thermal shields and vessel wall shown dark blue, and the 9 vol% mixture of stainless steel in coolant shown light blue. The section plane is occupied by one control rod with absorber section (yellow) above the core, as well as the 16-pin and 25-pin fuel assemblies. One blade of the transient rod is also visible, with the stainless steel follower (green) in the core and the absorber section (yellow) below the core. The lengths of the end boxes of the 25-pin and 16-pin fuel channels are defined by the gap between the bottom core grid and the lower assembly endplate, and the gap between the upper endplate and the top core grid. The bottom end box height was estimated to

Fig. 15. Horizontal Section Through Endplates in SPERT III Core Model.

Fig. 16. Top of Control Rod Fuel Pins in SPERT III Core Model.

be 5.08 cm (2.00 in.), based on inspection of Fig. 8. The upper end box was modeled with the same height. Overall, the model distance between the upper surface of the bottom core grid and the lower surface of the top core grid was 119.635 cm (47.10 in.). The upper and lower end boxes were each represented by a homogeneous horizontal layer 5.08 cm (2 in.) thick, containing a mixture of 9 vol% 304 L stainless steel with coolant. Based on the ratio of areas for a 2.505-inch-diameter hole in a 3-inch-square grid section, the lower core grid was represented by a homogeneous three-inch-thick layer of 46 vol% 304L stainless steel with coolant. The upper core grid was represented by a seven-inch-thick homogeneous layer of 19 vol% 304L stainless steel with coolant, based on the proportions for a square grid with wall thickness 10% of the grid spacing, as a rough estimate. The regions above the top core grid and below the bottom core grid were simply represented by coolant. The core skirt, thermal shields, vessel wall and intervening coolant layers were represented by cylinders of steel with the diameters from Table 4, extending vertically above and below the core grids. Sensitivity testing showed that reactivity calculations were sensitive to the presence of the coolant layers. The filler pieces were represented by a single 0.318-cm-thick wall of 304L stainless steel around the active core, surrounded by a homogeneous mixture of 9 vol% 304L stainless steel in coolant, as a simplifying approximation. As another approximation, the representation of


93

Fig. 17. Gamma Attenuation in Thermal Shields.

filler pieces, core skirt, thermal shields, and vessel wall extended above and below the active core region. Based on Fig. 44 of Stacy (9810), which is reproduced here as Fig. 17, few neutrons would reach the reactor vessel wall; fewer of those would be expected to return to the core. The short-dashed line for gammas produced by neutron capture is reduced tenfold from the core skirt to the fourth thermal shield, and a hundredfold outside the reactor vessel wall. Hence, structures outside the vessel were not represented in the model. Analytical data on the compositions of SPERT III or E-core reactor components were generally not found in the available primary references. Engineering standards are specified for most components, but the range for implementation of some specifications can leave a significant uncertainty for reactivity. Material representations based on standards were therefore refined in the process of model verification.

5. Comparison of the Serpent models and steady-state calculations 5.1. SPERT I As discussed previously, a small amount of 10B was added to the water to correct for a uniform bias in experimental and calculated values for the neutron multiplication factor. The amount was the same for all experiment simulations. A comparison of the keff results computed using the SPERT I model with 10B added in water and the experimental results reported in Spano et al. (1962) and Scott et al. (1963) is shown in Fig. 19. The linear fit slope for keff versus rod height is close for the computed and the experimental data: 0:784 103 cm1 for experiment and 0:759 103 cm1 for the adjusted Serpent calculation.

94


14

Excess Reacvity (Dollar)

12 10 8 6 4 Measured E-Core Control-Rod Reacvity

2

Control-Rod Reacvity in Serpent 2

0 10

15

20

25

30

35

40

45

Control Rod Posion (Inch) Fig. 20. SPERT III. E-Core Control Rod Reactivity Curve at Room Temperature. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Temperature [Kelvin]

Fig. 18. Vertical Section Through Centre of SPERT III Core Model.

257° 14

307°

357°

407°

457°

507°

557°

607°

543°

633°

1.025 Experimental Serpent

12

Excess Reactivity [Dollar]

1.02

k

eff

1.015 1.01 1.005

10 8 6 4 Measured E-Core Temperature Defect

2

1 25

30

35 40 Rod Position (cm)

45

50

Temperature Defect in Serpent 2

0 3°

93°

183°

273°

363°

453°

Temperature [Degree Fahrenheit] Fig. 19. Comparison of Experimental to Serpent Results for Effective Multiplication Factor for SPERT I Core SA592C.

Fig. 21. SPERT III. E-Core Reactivity as a Function of Temperature.

5.2. SPERT III Having established a SPERT III E-core model that agreed reasonably well with measured reactivity values, the reactivity terms associated with the transient rod, control rods and temperature were verified. The total worth of the transient rod was 4.7$ according to the experimental data, and the rod worth in the Serpent model is found to be 4.6$. The calculated reactivity curve for control-rod position is shown in Fig. 20 (red dashed line), compared with the measured curve (solid black) as in Fig. 11. As discussed above, the control rod movement was measured from a zero position with the top of the control-rod fuel at 4.7 in. below the active core. The reactivity curve was measured at room temperature, nominally 21 °C (70 °F). In Fig. 20, discrepancies of roughly 300 pcm in reactivity and 0.5 in. in control rod position are visible. The temperature effect on reactivity of the SPERT III E-Core is shown in Fig. 21. The curves are aligned at room temperature and at high temperature. At some points between, the error bars of Fig. 13 are exceeded by the difference between the calculated curve and the measurement. Visible artefacts in the calculated reactivity at low temperature are due to the large spacing between temperature nodes in the nuclear data library that was used for the calculation; the reactivity discrepancy may be partly related. Near 400 K, the difference in temperature defect between calculation and measurement in Fig. 20 is 100 to 300 pcm.

Note that a measured excess reactivity of 13.1 dollars in the maximum-reactivity state at room temperature is indicated in Fig. 11, while Fig. 13 indicates a measured excess reactivity of 13.8 dollars at room temperature, and Table 5 lists an excess reactivity of 14.2 dollars. Since measurements were made with diverse techniques, a reasonable target for model accuracy may be defined by that range of results. The reactivity calculations in Serpent 2 for the model that represents the SPERT III E-core core, as shown in Figs. 20 and 21, are found to be well within that range. By that measure, the accuracy of the Serpent 2 model that was developed to represent the SPERT III E-core is found to be adequate for simulation of the transient measurements. 6. Transient simulations and discussions 6.1. SPERT I transient modeled using Serpent 2 Since the SPERT I reactor core is not large (about 2 m or so), the point kinetics approximation (Rozon, 1998) may be appropriate. The Serpent code (Leppänen et al., 2014) computes the in–hour equation parameters using three different approximations. The approximation chosen for comparison to the experimental results is that of Nauchi and Kameyama (2010), as it provides all the parameters for computing the reactor period.


6.1.1. Initial reactor period The experimental results for the reactor period were obtained immediately after the rod was ejected from the reactor core. The ejection took about 0.3 s, an interval over which the temperature feedback did not have enough time to develop. Hence, these results can be compared to the results obtained from Serpent without temperature feedback. A transient was computed for one case where the position of the control rod was 34.7726 cm. The computed value for the inverse reactor period a, 20 s1 was close to the value computed by Serpent from static parameters of the reactor, 20.1377 s1, and different from the experimental value 29.9 s1. The reactor period was chosen to be long enough so that its measured value would be less influenced by transients resulting from the cruciform rod removal from the core. The discrepancy in time constant between experiment and calculation might arise from a rod position error of a few millimeters, as seen in Fig. 22. Possible sources for such a difference therefore include experimental uncertainty in control-rod and transient-rod positions, as well as some unknown isotope in the material composition Fig. 23. 6.2. SPERT III transient modeled using Serpent 2 In the SPERT III facility, transient tests were conducted by rapid withdrawal of the transient rod. The reactivity insertion was fixed by the initial position of the transient rod, which was determined from the reactivity calibration curve, as shown in Fig. 12. The initial critical condition was achieved by adjustment of the control rods. The initial positions of control rod and transient rod in transient tests were not specified in the available primary references. Tran-

400

Experimental Serpent

α (s−1)

300

200

100

0 25

30


45

50

Fig. 22. Comparison of Experimental to Serpent Results for SPERT I Core SA592C.

4

10

Experimental Serpent

2

α (s−1)

10

0

10

−2

10

25

30


45

50

Fig. 23. Comparison of Inverse Reactor Period between Experiments and Serpent Results for SPERT I Core SA592C.

95

sient tests were initiated at ambient temperatures and with no coolant flow, in which state the effect of coolant heating was relatively small and could be neglected (Taxelius, 1968b). Tests were also performed at elevated initial temperature, typically 394 K (250 °F), to provide a baseline for tests at high initial power (Taxelius, 1968b), conditions more representative of power reactor operation. Transient test T-32, in the series with high initial temperature and low initial power (McCardell et al., 1969), was selected for simulation in Serpent 2, based on low flow rate and moderate reactivity insertion. Test conditions for T-32 were an initial power of 50 W with coolant flow of 73 cm/s (2.4 feet/s) at 400 K (260 °F) and 10.3 MPa (1500 psi) (McCardell et al., 1969). The width of the transient peak was roughly 0.1 s; coolant would move only a few centimeters in that time. The peak power level below 70 MW would not be expected to lead to coolant voiding, and avoids additional complications. Thus, T-32 represents a simple case where thermalhydraulic effects could reasonably be approximated without flow. A net reactivity insertion of 1.09$ was introduced by removal of the transient rod. In Figure D-43 of McCardell et al. (1969), which is reproduced here as Fig. 24, the measured power, integrated energy and derived reactivity may be seen over an interval of 1.7 s during the transient, which captures the time of interest. The reactivity insertion led to a reactor period of 21.8 ms, before reactivity feedback from thermal effects. It is worth to notice that after the peak power the system is still delayed super critical. Termination of prompt fission chains due to the system no longer being prompt super critical leads to the observed decrease in power.

6.3. SPERT III Transient Modeled Using the Serpent 2 Code The T-32 experiment was initially simulated using the Serpent 2 code with the time-dependent capability, but without taking the fuel temperature feedback effect into account. Firstly, the critical system state with the control rods and transient rod positions as close as possible to the experiment had to be found. The total criticality change of the reactor due to the transient rod movement is 8.25 mk. The initial position of the transient rod was found, knowing the total worth of the rod, which is equal to 4.63$ in the Serpent model and 4.7$ according to the experimental data (McCardell et al., 1969). The estimation of the control rod assembly position was made using the control rod reactivity curve (see Fig. 20). The steady-state calculations were performed to produce the neutron source files with prompt and delayed neutrons. The model, as configured to represent initial conditions, was then run with the Serpent code in time-dependent mode. The run was configured to leave the reactor in steady state for the first 0.02 s, to confirm that the initial neutron multiplication factor was close to 1.0. The subsequent movement of the transient rod was represented by an acceleration of 5080.0 cm/s2 for 0.09 s (see Fig. 25), at which time the transient rod was stopped outside the core. The total duration of the transient was 0.72 s, divided into 720 time intervals with a duration of 1 ms. The calculations were performed on 4 nodes (SuperServer 2028GR-TR), with 28 cores (dual Intel Xeon E5-2697) and 128 GB of RAM per node. Six batches were simulated with a neutron population of 4:32 106 neutrons per batch. The calculations took 130 h. The results of simulations and their comparison with the experimental data are shown in Fig. 26. The initial 0.02-s offset is not shown on the graph. The simulation did not include fuel temperature, thermomechanical or thermalhydraulic feedback effects. Consequently, the reactivity would be expected to increase up to a certain value and then remain at that value; with reactivity remaining constant and positive, the power would be expected to increase exponentially.

96


Fig. 24. Reactivity, Power and Energy as a Function of Time During the T-32 Transient in the SPERT III E-Core (McCardell et al., 1969).

Fig. 25. Initial (a) and Final (b) Positions of the Transient Rod in the T-32 Expriment.

The simulated reactor reactivity increases due to the transient rod injection, and then plateaus for the rest of the transient. Two domains of time dependence in the experimental reactor power profile may also be discerned. The first part is indicated by the power increase before feedback effects start to influence the reactor behavior, while the second is indicated by the decrease of power due to feedback effects. The simulated reactor power profile is seen to align with the first part of the experimental power profile. A reactor period of 27.1 ms was obtained from the Serpent calculations for the first part, where a reactor period of 21.8 ms was observed in the experiment (McCardell et al., 1969). However, the reduction of power in the second part of the experiment is simply not seen in the simulation, because thermal feedback effects are not modeled.

A very small adjustment of the control rods position was performed to get a reactor period closer to the experimental value. The new simulations led to a reactor period of 17.7 ms. It was deemed impractical and unnecessary to further reduce the difference between simulated and experimental values, since the experiment was bracketed closely by simulations that differed very little. In order to facilitate a comparison to the experimental reactivity curve the reactivity during the simulation was estimated in the following manner: The k-eigenvalue equation can be formulated for the whole reactor using

h/; Rc i þ h/; Rf i þ LEAK ¼

1 h/; mRf i þ h/; pRs i; k

ð19Þ

97


70.00

1.4

28.0

Power (SERPENT) Exponenal Fio Power

60.00

Reacvity (SERPENT)

1.2

1

40.00

0.8

30.00

0.6

20.00

0.4

10.00

0.2

0

0.00 0.00

0.20

0.40

0.60

Energy (MW s)

50.00

Reacvity (Dollar)

Power (MW)

Energy

0.0

0.80

Time Since the Beginning of Transient (s)

Neutron Mulplicaon factor (a.u.)

Fig. 26. Comparison of Reactivity, Power and Energy Simulated in Serpent with the Experimental Data (T-32 Transient).

1.0140 1.0120

1.0100 1.0080 1.0060 1.0040

k_eff (SERPENT)

1.0020 1.0000

0.9980 0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

Time Since the Beginning of Transient (s) Fig. 27. Neutron Multiplication Factor (keff ) Simulated in Serpent.

where h/; xi represents the integral of the reaction rate x/ over the whole reactor and all energies, LEAK is the neutron leakage rate and the cross sections Rc ; Rf ; mRf and pRs represent the capture, fission, fission neutron production and scattering neutron production cross sections respectively. While the k-eigenvalue equation itself does not hold for the transient simulation we do tally the different reaction rates for each time interval and calculate

k¼

h/; mRf i h/; Rc i þ h/; Rf i þ LEAK h/; pRs i

ð20Þ

to obtain an estimate which is equal to the neutron multiplication factor if the flux is in the fundamental mode but will differ from it for a time when the system is perturbed. The reactivity estimates are based on k in the usual manner

q¼

k1 : k

Smoothing was applied to the time profile shown in Fig. 26 for the reactivity. The ‘‘raw” profile of k is plotted in Fig. 27. One may observe ‘‘noise” in the time profile, and the noise increasing with time in the transient. According to one hypothesis, the noise grows due to the increase of the variance in the population size when the time increases. A detailed discussion of the subject can be found in Valtavirta (2015).

7. Summary The results of the simulations show that Serpent 2 in the timedependent mode adequately models the reactor physics aspects of the transients performed in the SPERTI and SPERTIII experiments. The static results for the constrained core SPERT I experiments were found to be close to those of a corrected model that included an addition of 10B to the moderator. The reactor period calculated from static parameters without temperature feedback is close to the initial reactor period as measured in the experiment. Serpent can be used as a standalone code to simulate that part of a transient. The experimental data also showed the effect of later temperature feedback. Reactor power was measured, from which the reactivity and total energy release were calculated. To simulate temperature feedback for comparison to those experimental results, coupled simulations must be performed. The T-32 transient in the SPERT III E-core was modeled using the Serpent 2 code as a standalone code without temperature feedback. The results of these calculations are in a very good agreement with the initial experimental data. The transient simulation yielded a reactor period close to the theoretically calculated and measured values. We consider the inclusion of temperature feedback to the dynamic simulation as a logical next step for this work.

98


Acknowledgments The authors thank the staff of the Canadian Nuclear Laboratories Library for their help and assistance. This study was funded by Atomic Energy of Canada Limited, under the auspices of the Federal Nuclear Science and Technology Program. This work was partly conducted within the McSAFE project which is receiving funding from the Euratom research and training programme 2014–2018 under grant agreement No 755097.

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Montgomery, C.R., Norberg, J.A., Wilson, T.R., Summary of the spert-i, -ii and -iii reactor facilities. aec research and development report. Technical Report IDO16418, Reactor Technology, U.S. Atomic Energy Commission, 1965. Nauchi, Y., Kameyama, T., 2010. Technique for Iterated Fission Probability and Reactor Kinetic Parameters Using Continuous-Energy Monte Carlo Method. J. Nucl. Sci. Technol. 47, 977–990. Nuclear Science Committee. Evaluation guide for the international reactor physics experiments evaluation project (irphep). Number NEA/NSC/DOC(2013) 2. Nuclear and Energy and Agency, May 2013. Olson, A.P., 2015. SPERT III E core: Facility Specification, Research Reactor Benchmarking Database: Facility Specification and Experimental Data. IAEA, ISBN 978-92-0-151714-2. Parisi, C., Pecchia, M., B& W Spectral Shift Control Reactor Lattice Experiment: A484 Uranium Rods Critical Experiment with Infinite Radial Reflector. 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Russell, L., Simulation of Time-Dependent Neutron Populations for Reactor Physics Applications using the Geant4 Monte Carlo Toolkit. Master of Science Thesis. PhD thesis, McMaster University, 2012. Scott, Jr., R., Wasserman, A.A., Schmitt, R.C., Transient Tests of the SPERT I Lowenrichment UO2 Core - - Data Summary Report. Technical Report IDO-16752, AEC Research and Development, September 3 1963. Sjenitzer, B.L., The Dynamic Monte Carlo Method for Transient Analysis of Nuclear Reactors. PhD thesis, Technische Universtiteit Delft, 2013. Sjenitzer, B.L., Hoogenboom, J.E., 2015. Dynamic Monte Carlo Method for Nuclear Reactor Kinetics Calculations. Nucl. Sci. Eng. 175, 94–107. Spano, A.H., 1963. Self-limiting-limited Power Excursion Test of a Water-moderated Low-enrichment UO2 Core. Nucl. Sci. Eng. 15, 37–51. Spano, A.H., 1964. Analysis of Doppler-limitedPower Excursion in a Watermoderated Low-enrichment UO2 Core. Nucl. Sci. Eng. 19, 172–186. 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Valtavirta, V., Uncertainty Understanding in Coupled Time-Dependent Monte Carlo Simulations with Serpent 2, 2015. Valtavirta, V., Hessan, M., Leppänen, Delayed Neutron Emission Model for Time Dependent Simulations with the Serpent 2 Monte Carlo Code –First Results, 2016. Wesley, F., Benchmarking of G4STORK for the Coolant Void Reactivity of the Super Critical Water Reactor Design. PhD Thesis. PhD thesis, McMaster University, 2016. X-5 Monte Carlo Team. MCNP – A General Monte Carlo N-Particle Transport Code, Version 5. LANL, 2003.

Modeling of the SPERT transients using Serpent 2

Modeling of the SPERT transients using Serpent 2

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