Serpent

Annals of Nuclear Energy 117 (2018) 25–31

Contents lists available at ScienceDirect

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

Analysis of a small-scale reactor core with PARCS/Serpent F. Fejt ⇑, J. Frybort Czech Technical University in Prague, V Holesovickach 2, Prague 8, Czech Republic

a r t i c l e

i n f o

Article history: Received 15 November 2017 Received in revised form 22 February 2018 Accepted 3 March 2018

Keywords: Lattice physics Few-group cross section generation Transport correction B1 leakage VR-1 reactor PARCS Serpent

a b s t r a c t Cross section homogenization is a challenging task that has been implemented mainly for full-core calculations of nuclear power plants. Small-scale reactors started to be a main point of interest for this kind of analysis during last few years. This paper presents a suitable homogenization strategy for a small core of VR-1 reactor (28.6
28.6 cm) realized by Serpent 2.1.28. Homogenized macroscopic data are used in PARCS_v3.2 core simulator for calculations of multiplication factor and radial flux distribution in the core. The PARCS results are compared to reference results calculated by Serpent 2.1.28. Reasons for observed inconsistencies between these two calculation modes are discussed. Ó 2018 Elsevier Ltd. All rights reserved.

1. Introduction Few group diffusion codes utilizing few-group cross section data are commonly applied to power reactors in order to obtain information about soluble absorber critical concentration, power (eventually flux) distribution, and burn-up characteristics. A good match between calculated values and predictions is ensured thanks to a large size of the core, which is more in line with mathematical and physical limitations of the diffusion theory. However this assumption is not valid for small research reactors or even small core configurations in general. Similar procedures of cross section generation and core modeling, that are sufficient for power PWR (Leppänen and Mattila, 2016)/VVER (Miglierini et al., 2014) reactors, result in a significant difference (from hundreds to thousands pcm in keff – see Ref. Rais et al. (2017) for small research reactor or Ref. Baiocco et al. (2017) for general small configuration) between a few group diffusion calculation and a lattice physics code in the case of small-scale reactors with high relative neutron leakage. The goal of the paper is to present a homogenization strategy that leads to an good agreement with expected results even in cores that are more complex than Siefman et al. (2015). All cross section data (in two group energy structure with a breakpoint at 0.625 eV) are generated in Serpent. Special cross section differ-

⇑ Corresponding author. E-mail address: [email protected] (F. Fejt). https://doi.org/10.1016/j.anucene.2018.03.002 0306-4549/Ó 2018 Elsevier Ltd. All rights reserved.

ences are listed in following chapters. Both the multiplication factor and the flux distribution is examined in the core configuration. 2. Description of VR-1 reactor The training reactor VR-1 is a zero-power open-pool type nuclear reactor with operation focused on education and training. Nuclear fuel assemblies are of IRT-4 M type and the core is moderated and reflected by demineralised light water. The stainless steel reactor vessel has radius of 1.15 m and height of 4.7 m. The reactor core is located at the bottom of the vessel, and it is fully water reflected. The radial size of the core depends on a core configuration, and it ranges from 28.6
28.6 cm (4
4 positions in the core lattice) to 42.9
35.75 cm (6
5 positions) with pitch of 7.15 cm. 2.1. IRT-4M fuel assemblies The IRT-4 M fuel assemblies are available in three variations at VR-1 reactor. The maximum number of fuel tubes is eight. Fuel assemblies with six tubes allow insertion of control rods. Fuel assemblies with four tubes are also available, but they are not used in the studied reactor cores. All square fuel tubes are concentric with rounded corners as can be seen in Fig. 1 (top view) – the fuel layer (U (19.7% enrichment) + Al) with thickness of 7 mm in the middle of each tube is confined in Al alloy cladding (approx. thickness of 4.7 mm on both inner and outer side of the fuel layer). Axial composition of the 8-tube fuel assembly can be seen in Fig. 2. All presented dimensions are within manufacturing tolerances and

26

F. Fejt, J. Frybort / Annals of Nuclear Energy 117 (2018) 25–31

Fig. 1. Serpent model (top view) of 8 and 6-tube fuel assembly (green – fuel layer, red – cladding). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 3. Serpent model (side view) of control rod (CR).

modeled in PARCS, but it is homogenized with the rest of a active control rod section, i.e. cross sections data for a control rod are generated to one colorset based on Serpent model including this follower. An effect of an insertion/withdrawal of a control rod is evaluated based deviation of fully inserted and fully withdrawn colorsets – partly inserted control rods are processed internally in PARCS code. In a case of large-scale reactor, similar construction part occupies a relatively small portion of the core in comparison to small research reactors where they can affect a significantly core characteristics. 3. Codes for the analysis 3.1. PARCS

Fig. 2. Serpent model (side view) of 8-tube fuel assembly (green – fuel layer, red – cladding, blue – water, cyan – stainless steel). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

they were confirmed by good long-term agreement between experiments and criticality calculations (Bily and Sklenka, 2014).

2.2. Control rod UR-70 Each control rod at VR-1 reactor is of UR-70 type and consists of a thin Cd cladding wrapped around an inner Al rod. Both of them are confined in a stainless steel tube. The bottom part of the control rod ends with a bottom plug as can be seen in Fig. 3. This CR bottom plug represents a problematic part in a homogenized core modeling because the cross section is mostly affected by Cd cladding, and therefore each axial layer is distinguished based on a presence of this Cd cladding. The follower itself is not explicitly

PARCS is a three-dimensional reactor core simulator which solves the steady-state and time-dependent, multi-group neutron diffusion and low order transport equations in orthogonal and non-orthogonal geometries. PARCS (Downar et al., 2012) uses cross section data generated by lattice physics codes such as SCALE/TRITON (Rearden and Jessee, 2016), HELIOS-2 (Wemple et al., 2008), CASMO (Rhodes et al., 2006) or Serpent (Leppänen et al., 2015). This study utilizes the Serpent code, which produces comparable results for fuel assembly calculations as other lattice physics code (Novak et al., 2017). PARCS includes several different solvers, e.g. finite difference, analytic nodal method, and fine mesh SP3. The most basic one (finite difference) is used to solve the examined problem. Since assembly discontinuity factors are not integrated in finite difference method, spatial nodes must be sufficiently small to achieve a precise solution of the neutron diffusion. Size of the spatial nodes, in general distinguished into radial and axial dimension, represents a balance between an accuracy of a calculation and a time requirement. Initial number of axial nodes is listed in Table 1. Behavior of multiplication factor (VR-1 reactor core in Fig. 7) related to axial nodes is shown in Table 2 – final axial node height can be calculated from height of axial layer in Fig. 2 and the final number of axial nodes per layer in Table 1. Same analysis is also done for x,y-nodes, and the results are shown in Table 3.

27

F. Fejt, J. Frybort / Annals of Nuclear Energy 117 (2018) 25–31

3.2. Serpent

Table 1 Axial setting of VR-1 reactor core. ID Axial Layer (see Fig. 2) 1

2

3

4

5

6

7

2

2

2

8

8

8

Initial number of nodes 20

2

2

2

Final number of nodes 80

8

8

8

Table 2 Axial convergence of VR-1 reactor core based on multiplication (Nx) of initial axial number of nodes. Asterisk indicates final axial setting. Nx

keff -keff [pcm]

Time [a.u.]

1 2 3 4* 5 6 7 8 9 10

50.3 19.8 9.9 5.3 3.3 2.4 1.5 0.8 0.4 0.0

1.0 2.3 5.2 8.1 8.2 14.2 13.8 16.2 20.0 20.9

N10

Nx

Serpent is a three-dimensional continuous-energy Monte Carlo reactor physics burnup calculation code (Leppänen et al., 2015). Serpent is used for a spatial homogenization of all fuel and nonfuel sections in the core. All Serpent results are listed with one standard deviation, i.e. 68% confidence level. Since VR-1 research reactor is a zero-power type, there is no fuel burning in the SERPENT/PARCS model. A significant improvement in cross section homogenization is brought by Serpent(v2.1.27 and later) and its new function that defines transport correction for the calculation of diffusion parameters. This new function (trc) helps to mitigate differences in transport cross sections caused by inappropriate replacement of in-scatter method with out-scatter method which appears to be not valid in a case of small-scale cores. The inscatter method is represented by Eq. (1) (Yamamoto et al., 2008)

P g0

Rtr;g ¼ Rt;g 

Rs1;g0 !g U1;g0 U1;g

ð1Þ

where

Rtr;g is transport cross section of g-th energy group, Rt;g is total cross section of g-th energy group, Rs1;g0 !g is P1 scattering cross section from g0 -th to g-th energy

Table 3 Radial convergence of VR-1 reactor core based on x,y-number of nodes per each core position (node size equals 7.15/# Nodes [cm]). Asterisk indicates final radial setting. # Nodes

keff -keff [pcm]

Time [a.u.]

10 11 12 13 14 15 16 17 18 19 20⁄ 21 22 23 24 25

81.1 64.6 51.9 42 34.2 27.8 22.6 18.2 14.6 11.5 8.9 6.6 4.6 2.8 1.3 0.0

1.0 1.3 1.7 2.1 2.9 3.6 4.4 5.4 6.4 7.4 7.7 8.4 8.4 9.0 9.7 10.0

N25

Nx

group, and

U1;g is P1 component of angular flux, i.e. neutron current. The assumption of equality between in-scatter and out-scatter method is represented by Eq. (1)

X

X

g0

g0

Rs1;g0 !g U1;g0 

Rs1;g!g0 U1;g

ð2Þ

Substituting Eq. (2) into (1) yields the final out-scatter approximation of transport cross section

Rtr;g  Rt;g 

X

Rs1;g!g0

ð3Þ

g0

Since Serpent uses the out-scatter approximation (Leppänen et al., 2016), it is necessary to correct transport cross sections via trc option. Energy-dependent transport correction factor f ðEÞ required by trc option is defined by Eq. (4).

Time requirements listed in both Tables 2 and 3 represent sum of all procedures, i.e. input/output processing, memory allocation, and calculation, thus the time requirement is not proportional only to the number of nodes.

f ðEÞ ¼

Rtr ðEÞ Rt ðEÞ

ð4Þ

Correction procedure subtracts the transport cross section (outscatter method) for hydrogen from a material mixture, multiplies

1.2 1

f(E)

0.8 0.6 0.4 0.2 0 1e−09

1e−08

1e−07

1e−06

1e−05 0.0001 0.001 Energy [MeV]

0.01

0.1

1

10

Fig. 4. Energy-dependent transport correction factor f ðEÞ. Plotted data are provided by Rais et al. (2017).

28

F. Fejt, J. Frybort / Annals of Nuclear Energy 117 (2018) 25–31

the total cross section for hydrogen with f ðEÞ function (see Fig. 4), and adds it back to the mixture as it is represented by Eq. (5).

Rtrc tr;mix ¼ Rtr;mix  Rtr;H þ Rt;H  f ðEÞ

fl

ð5Þ

fl

fl

A detailed description of calculation and application of transport correction factor can be found in Herman et al. (2013). 4. Few group cross section generation Basic part of a cross section generation in this paper follows a general practice for large power reactors with the exception that Serpent calculations are conducted in 3D geometry as opposed to general practice of 2D infinite lattice calculations. The outline of a homogenization scheme can be seen in Fig. 5. All fuel assemblies are homogenized in a x,y-infinite lattice (x,y-reflective boundary condition) with z-infinite light-water reflector above and below the fuel assemblies. Cross-section data for axial layers 4 and 7 (Fig. 2) are homogenized only from 10 cm of water to utilize the proper neutron spectrum closest to the fuel assembly. It is necessary to incorporate B1 leakage correction due to a significant spatial leakage (Leppänen et al., 2016). Even though utilizing the full-core model to create an actual leakage spectrum may be more accurate, VR-1 reactor assembles several highly different core configurations every year, and therefore it is not possible to rely on a unique fullcore leakage spectrum. All predictions should be based on data obtained from a general leakage spectrum. Energy structure cas70, that is pre-defined in Serpent (Leppänen, 2017), is used as an intermediate multi-group structure for calculation of the leakage-corrected critical spectrum. Each type of the fuel assembly is spatially homogenized into 7 axial layers as can be seen in Fig. 2, thus producing 7 sets of macroscopic data. Effect of a control rod is derived from a fully inserted and a fully withdrawn case. Data for non-fuel sections (reflector and power-measurement channels) used in the model are generated from a hypothetical core in Fig. 6 that resembles a typical core configuration at VR-1 reactor with the same axial layer structure as fuel assemblies. The 3 water reflector layers used for cross-section homogenization

fl

Fig. 6. Hypothetical full-core model utilized for generating cross-section data for non-fuel elements (blue, green elements). Yellow elements are not utilized in the examined core configuration. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

are surrounded by additional water representing the water in the reactor pool. This general model, by its nature, produces the nonfuel data that may be applicable to different configurations of VR-1 reactor. All cross section data are generated in two-group structure with energy breakpoint at 0.625 eV.

5. Multiplication factor comparison 5.1. Infinite fuel lattice calculation The first step in the Serpent-PARCS homogenization procedure testing comparison is examination of data generated for a fuel assembly with following boundary conditions: x,y-infinite lattice of fuel assemblies, z-actual model of fuel assembly with infinite light-water reflector above and below the fuel assemblies. All calculation including such boundary conditions are going to be marked with ð1; zÞ. The reference result is from the Serpent code. PARCS is conducting calculations with data generated by Serpent. This first step in the analysis is testing the basic assumption that diffusion calculation by PARCS with Serpent-generated data should give the similar results as the Serpent calculation. This discrepancy is introduced due to the complex axial structure of the model (see Fig. 2), general limitation of diffusion theory (a presence of a highly absorbing material) and its energy group approach. PARCS results match the reference Serpent results with a sufficient accuracy (Dk1;z 6 20 pcm). Only presence of a highly absorbing material increases the discrepancy between results of these two codes to about Dk1;z ¼ 137 pcm. The good agreement of reference and PARCS results proves that geometry settings in PARCS are fully adequate to this task. 5.2. Core calculation

Fig. 5. Outline of homogenization scheme.

The next step in the analysis is focused on comparison of fullcore calculations for a configuration shown in Fig. 7. This core configuration contains a typical set of absorbing rods: safety rods B1 through B3, experimental rods E1 and E2; and finally also absorbing rods for core power control R1 and R2. The keff is calculated for three control rods settings: all CRs inserted, all CRs withdrawn, and the critical state (B1: 680, B2: 680, B3: 680, E1: 341, E2: 680, R1: 404, R2: 680 where position 0 represents a fully inserted CR and 680 a fully withdrawn CR).

29

F. Fejt, J. Frybort / Annals of Nuclear Energy 117 (2018) 25–31

culation. This might lead to a fact that a possible source of this error is a radial flux distribution at the fuel/non-fuel boundary. The control rods with a similar position and surroundings (E2/R2 and E1/R1) remain the similar control rod worth even in PARCS (679/670 pcm and 1192/1199 pcm). 5.3. Light-water transport cross section correction

Fig. 7. Radial view of examined VR-1 reactor core.

As opposed to infinite lattice calculation in Table 4, the actual core must be calculated with B1 corrected data as can be seen in Table 5. The Dkeff between PARCS and Serpent for critical state is 551 pcm. This result is in line with observed PARCS/Serpent differences for small-scale reactors published in Baiocco et al. (2017) (526 pcm) and (Rais et al., 2017) (418 pcm). The keff for cross section data with infinite spectrum exhibits significant discrepancy and these data are not applicable to this kind of problems. Besides keff other information like control rod worth are necessary for a reactor core operation. The differences between PARCS and Serpent calculations in Table 6 are 10
lower than the difference of keff for the critical state. This knowledge suggests that a similar difference of keff can be found in both states (before and after a control rod is inserted to the core), therefore this discrepancy does not propagate to the control rod worth to its full extent. It also suggests that the source of difference between PARCS and Serpent results is not in control rods, but in non-fuel regions. The control rod discrepancy proves to be in a close connection with a position of a control rod and DUth (Eq. (6)) in a given location (Fig. 11). The control rods located at the edge of the core (E1, E2, R1, and R2) show the highest overestimation together with the highest flux deviation. On the other hand, the control rods B1, B2, and B3 are within/very close to a range of 3  r of Serpent calTable 4 Multiplication factor for fuel assemblies in ð1; zÞ model – Serpent (S) and PARCS (P). FA

S (1  r)

P

PS

6 6 (CR out) 6 (CR in) 8

1.50997 ± 3e5 1.50822 ± 3e5 1.20036 ± 4e5 1.53034 ± 3e5

1.51005 1.50838 1.20173 1.53054

8 ± 3 pcm 16 ± 3 pcm 137 ± 4 pcm 20 ± 3 pcm

Table 5 Serpent (S) and PARCS (P) Multiplication factor for core configuration with control rod positions – CS (critical state), IN (all CRs inserted), OUT (all CRs withdrawn). Rods

S (1  r)

P (B1)

P ð1; zÞ

P (B1)  S

CS OUT IN

0.99999 ± 5e5 1.01315 ± 5e5 0.91562 ± 5e5

0.99448 1.00552 0.91025

1.02577 1.03743 0.93427

551 pcm 763 pcm 537 pcm

Table 6 Serpent (S) and PARCS (P) control rod worth comparison. Rod

S [pcm]

P (B1) [pcm]

D [pcm]

DUth [%]

B1 B2 B3 E1 E2 R1 R2

1,939 ± 7 1,957 ± 7 1,947 ± 7 1,132 ± 7 627 ± 7 1,146 ± 7 620 ± 7

1911 1941 1941 1192 679 1199 670

-28 -16 6 60 52 53 50

3.2 2.4 2.1 14.4 9.6 12.6 9.5

The necessity of transport-corrected cross section is demonstrated in Table 7. Cross section data generated by Serpent with no trc option distinctly underestimate keff in PARCS calculation (4; 386 pcm). The impact of transport-correction on keff heavily depends on core dimension (Rais et al., 2017), i.e. the discrepancy grows with a decreasing core dimension. 5.4. Stochastic cross section generation Stochastic nature of Monte Carlo cross section generation brings a question about data consistency. In order to explore this phenomena, PARCS calculation is run 5 times with different cross sections colorsets – each colorset is generated by a separate Serpent run. Each Serpent simulation is run with 800 active cycles of 800,000 neutrons each and 50 inactive cycles. The final PARCS results in Table 8 appears to be very consistent, and it evidences that Serpent keff standard deviation covers a deviation of PARCS results and it also confirms that the Serpent calculation settings are adequate for the calculation model. The same behavior is also observed in Jo et al. (2018) where ‘‘The absolute uncertainty is defined as one standard deviations of the k-eff’s predicted by the 10 SIMULATE-3 runs”. 6. Radial flux distribution Basic information about group flux distribution in PARCS is given by Fig. 8 for the fast group and Fig. 9 for the thermal group: the highest fast neutron flux is in the core center and thermal neutrons are produced mainly in the water reflector regions. The flux data presented in this section are averaged values for the fuel node (the axial layer 1 in Fig. 2). Following Figs. 10 and 11 show flux differences for fast and thermal neutrons, respectively. The differences were calculated according to Eq. (6). Uncertainty for the flux tallies in Serpent is less than 1% for fuel assemblies and less than 1.5% for the first radial water reflector layer.

Table 7 Effect of trc option in Serpent on PARCS keff – CS (critical state), IN (all CRs inserted), OUT (all CRs withdrawn). Rods

PARCS (B1)

PARCS (B1), no trc)

CS OUT IN

0.99448 1.00552 0.91025

0.95614 0.96682 0.87444

Table 8 Multiplication factor for repeated cross section generation runs – critical state, Serpent keff ¼ 0:99999 ± 5e5. Run

PARCS (B1)

1 2 3 4 5

0.99448 0.99449 0.99447 0.99448 0.99449

F. Fejt, J. Frybort / Annals of Nuclear Energy 117 (2018) 25–31

15

0.093

0.177

0.239

0.243

0.178

0.092

4

0.221

0.530

0.732

0.750

0.533

0.221

0.9 0.8 0.7

3 2

0.251

0.253

0.731

0.741

0.994

0.994

1.000

0.988

0.745

0.727

0.254

0.250

0.6 0.5 0.4

1

0.219

0.527

0.738

0.719

0.522

0.219

0

0.091

0.176

0.239

0.234

0.174

0.091

0.3 0.2

Radial flux distribution [-]

1 5

5

2.90

4.60

2.70

2.70

4.80

2.50

4

8.30

13.60

12.60

8.30

9.60

9.00

3

6.40

-0.20

-2.10

-7.00

8.60

5.40

2

5.60

8.40

-3.20

-2.40

-0.30

6.20

1

9.10

9.50

7.60

14.40

13.10

8.10

0

2.50

4.80

2.60

2.40

4.40

2.70

B

C

D

E

A

B

C

D

E

F

F

Fig. 8. Homogenized radial flux distribution (PARCS) relative to maximal value – fast group.

0.763

0.987

1.000

0.783

0.523

4

0.622

0.384

0.446

0.452

0.423

0.638

0.9 0.8 3

0.991

0.501

0.535

0.554

0.452

0.985

0.7 2

0.982

0.447

0.524

0.530

0.499

0.987

1

0.633

0.418

0.440

0.422

0.376

0.615

0

0.517

0.772

0.981

0.961

0.748

0.509

A

B

C

D

E

F

0.6 0.5

Radial flux distribution [-]

0.516

Fig. 11. PARCS/Serpent deviation of homogenized radial flux distribution – thermal group.

Macroscopic transport cross section Position

Fast

Thermal

Channel Reflector

Non-fuel elements 0.0967 cm1 0.2755 cm1

0.546 cm1 2.148 cm1

8-tube FA 6-tube FA

Fuel elements 0.2356 cm1 0.2382 cm1

1.104 cm1 1.269 cm1

0.4

Fig. 9. Homogenized radial flux distribution (PARCS) relative to maximal value – thermal group.

5

16.30

5.10

3.90

3.60

3.80

14.80

4

0.30

-7.00

-3.80

-5.40

-6.80

-0.50

3

6.10

-5.40

-4.50

-4.50

-6.30

6.10

2

6.40

-6.10

-4.40

-4.50

-5.60

5.90

5

1

-0.50

-6.70

-5.30

-3.60

-7.00

0.30

0

0

14.80

3.90

3.70

4.10

5.20

16.30

A

B

C

D

E

F

15 10

PARCS/SERPENT [%]

20

-5 -7

Fig. 10. PARCS/Serpent deviation of homogenized radial flux distribution – fast group.

!

DUx;i;j

-5 -7

Table 9 Transport-corrected cross section (layer 1) for fuel and non-fuel elements.

1 5

5 0

0.1 A

10

PARCS/SERPENT [%]

30


P U x;i;j ¼
S  1  100% Ux;i;j

ð6Þ

where
P is a homogenized flux calculated by PARCS in a given core U position,


S is a region averaged flux calculated by Serpent in a given U core position, x is a group 1 (fast) or group 2 (thermal) neutron flux, i; j is a core position.

There can be found a significant flux discrepancy due to several aspects that should be focused in future analyzes of small-scale research reactors. (i) B1 correction in just one of the possible methods (Dorval, 2016), and a closer examination may bring a more suitable approach for a small-scale reactor. (ii) Commonly the highest discrepancy is found at the boundary of core/reflector. Since the core consists of only 4
4 positions, all fuel assemblies can be considered to be at this boundary. (iii) Highly absorbing material affects all positions in the core because of its close proximity. (iv) The measuring channels at positions A1, A4, F1, and F4 are hollow and full of air that act as a void region, and it deforms the neutron flux shape. Distinctive features of a channel position and a reflector can be seen in Table 9 where transport cross section for the homogenized layer 1 is compared. Significant flux differences were observed also in Clerc et al. (2014), and their proposed solution is a optimization of transport cross section (in a case of diffusion solver) of a radial reflector. The application of this method on VR-1’s core will be examined in future work. 7. Summary This paper presents a step-by-step procedure of cross section homogenization that leads to results which are in line with published information. Even though VR-1’s core is the smallest core that has been examined so far, and a connection between size and discrepancy matches an observation in Rais et al. (2017), a multiplication factor and its difference is comparable to other small-scale reactors. Reaching similar discrepancy is conditioned on utilization of two important cross section generation procedures: B1 leakage correction and hydrogen transport-correction. Lacking any of these two aspects causes a high keff error. A close inspection can reveal a fact that ð1; zÞ type of homogenization (as opposed to B1 method) overestimates keff , while no transport-correction underes-

F. Fejt, J. Frybort / Annals of Nuclear Energy 117 (2018) 25–31

timates keff , and yet their combination does not reach an accuracy of B1 and transport-corrected cross sections. Core multiplication factor differences and especially effects of control rods are influenced by the distribution of neutron flux discrepancies. Neutron flux calculated by PARCS in the central part of the core is mainly underestimated, while within the reflector it is overestimated. A comparison of a homogenized flux is negatively affected by reflector parameters. Since such high differences were observed even for a larger system, it brought a necessity of finding a proper solution. One of them is optimization of radial reflector cross sections which can have a positive impact on both keff and a neutron flux. This approach is going to be focused in the future work. Acknowledgments This work was supported by the project Research Infrastructure No. CZ.02.1.01/0.0/0.0/16_013/0001790, financed from European structural and investment funds and Czech Republic funds. References Baiocco, G., Petruzzi, A., Bznuni, S., Kozlowski, T., 2017. Analysis of a small pwr core with the parcs/helios and PARCS/Serpent code systems. Ann. Nucl. Energy 107, 42–48. Bily, T., Sklenka, L., 2014. Measurement of isothermal temperature reactivity coefficient at research reactor with irt-4m fuel. Ann. Nucl. Energy 71, 91–96. Clerc, T., Hbert, A., Leroyer, H., Argaud, J., Bouriquet, B., Ponot, A., 2014. An advanced computational scheme for the optimization of 2d radial reflector calculations in pressurized water reactors. Nucl. Eng. Des. 273, 560–575. Dorval, E., 2016. A comparison of monte carlo methods for neutron leakage at assembly level. Ann. Nucl. Energy 87, 591–600. Downar, T., Xu, Y., Seker, V., 2012. PARCS v3.0 U.S. NRC Core Neutronics Simulator – Theory Manual. RES/U.S. NRC, Rockville, Md.

31

Herman, B.R., Forget, B., Smith, K., Aviles, B.N., 2013. Improved diffusion coefficients generated from Monte Carlo codes. American Nuclear Society – ANS; La Grange Park (United States). Jo, Y., Hursin, M., Lee, D., Ferroukhi, H., Pautz, A., 2018. Analysis of simplified bwr full core with serpent-2/simulate-3 hybrid stochastic/deterministic code. Ann. Nucl. Energy 111, 141–151. Leppänen, J., 2017. Casmo 70-group structure.http://serpent.vtt.fi/media-wiki/ index.php/CASMO70-groupstructure. Accessed: 2017-09-20. Leppänen, J., Mattila, R., 2016. Validation of the serpent-ares code sequence using the mit beavrs benchmark hfp conditions and fuel cycle 1 simulations. Ann. Nucl. Energy 96, 324–331. Leppänen, J., Pusa, M., Viitanen, T., Valtavirta, V., Kaltiaisenaho, T., 2015. The serpent monte carlo code: Status, development and applications in 2013. Annals of Nuclear Energy 82, 142–150. Joint International Conference on Supercomputing in Nuclear Applications and Monte Carlo 2013, SNA + MC 2013. Pluri- and Trans-disciplinarity, Towards New Modeling and Numerical Simulation Paradigms. Leppänen, J., Pusa, M., Fridman, E., 2016. Overview of methodology for spatial homogenization in the serpent 2 monte carlo code. Ann. Nucl. Energy 96, 126– 136. Miglierini, B., Mazzini, G., Ruscak, M., 2014. 3d neutronic analysis of vver1000/v320 using parcs code. In: Proceedings of the 2014 15th International Scientific Conference on Electric Power Engineering (EPE), pp. 727–731. Novak, O., Chvala, O., Luciano, N.P., Maldonado, G.I., 2017. Vver 1000 khmelnitskiy benchmark analysis calculated by serpent2. Ann. Nucl. Energy 110, 948–957. Rais, A., Siefman, D., Hursin, M., Ward, A., Pautz, A., 2017. Neutronics modeling of the crocus reactor with serpent and parcs codes. Rearden, B.T., Jessee, M., 2016. SCALE Code System. ORNL/TM-2005/39. Rhodes, J., Smith, K., Lee, D., 2006. Casmo-5 development and applications. PHYSOR2006, ANS Topical Meeting on Reactor Physics. Siefman, D.J., Girardin, G., Rais, A., Pautz, A., Hursin, M., 2015. Full core modeling techniques for research reactors with irregular geometries using serpent and parcs applied to the crocus reactor 85, 434–443. Wemple, C., Gheorghiu, H.N., Stamm’ler, R., Villarino, E., 2008. The helios-2 lattice physics code. Proceedings of the eighteenth symposium of atomic energy research, p. 620. Yamamoto, A., Kitamura, Y., Yamane, Y., 2008. Simplified treatments of anisotropic scattering in lwr core calculations. J. Nucl. Sci. Technol. 45, 217–229. http:// www.tandfonline.com/doi/pdf/10.1080/18811248.2008.9711430.