Neutronic Calculations of TRIGA MARK-II with WIMS Cluster Options M. D. Usang∗1 , N. S. Hamzah1 , M. H. Rabir1 , M. H. Abdul Khalil, M. A. S. Salleh1 & M. P. Abu1 1 Malaysian Nuclear Agency
Abstract Neutronic calculations for RTP are made by using WIMS by utilizing several techniques. In this study, we explore the cluster options available in WIMS. In order to use this technique, the RTP core are split into several annulus containing both water and fuel. This enables us to determine the average flux at each annulus. This paper will demonstrate the required input card and general procedure for preparing WIMS input using the cluster option. Comparison of flux and multiplication factor between WIMS and experimental data are made and the amount of error estimated.
Abstrak Pengiraan neutronik bagi RTP boleh dilakukan menggunakan WIMS menerusi beberapa teknik. Dalam kajian ini, kita akan meneroka beberapa opsyen cluster yang terdapat dalam WIMS. Bagi menggunakan teknik ini, teras RTP akan dibahagikan kepada beberapa annulus yang mengandungi air dan bahan api. Ini membolehkan kita menentukan fluks purata bagi setiap annulus. Artikel ini akan menunjukkan kad input yang diperlukan dan prosedur penyedian input WIMS menggunakan opsyen cluster. Perbandingan fluks dan faktor pengandaan bagi WIMS dan data eksperimen akan dibuat dan jumlah ralat yang diperhatikan. Keywords: WIMS, modelling, TRIGA fuel, Neutronics
Introduction WIMS is a deterministic code for neutronic calculations introduced by the Atomic Energy Establishment of Winfrith, Dorchester. Its main utility is for generating cross section and also features several options useful for certain situations. For example, it is able to calculate flux, thermal reactivity coefficients, multiplication factors and even fuel burnup especially for highly absorbing elements [4]. Coupled with the fast execution speed, it is an excellent tool for building core designs, prior to developing a more complicated but realistic design using tools such as the Monte Carlo based MCNPX. Neutronic calculations for Reaktor TRIGA PUSPATI (RTP) by using WIMS can be done by one of the three approach. First is by homogenization of the core. Second is through multicell options. The final technique, through WIMS cluster options is the technique we decide to share in this paper. Neutronic parameters of interest are the infinite multiplication factor, kinf , neutron flux, Φ at various locations in the core. Apart from building a cluster model of RTP core, the cluster options are commonly associated with modeling fuel bundles and for calculating cross section for moderators.
Material Specifications In general, we can identify the material compositions of RTP core to consist of cladding, fuel and water. We assume all the control rods are withdrawn and are followed by fuel, typical in a full power reactor. The cladding materials is Stainless Steel 304 (SS304). Atomic densities for the cladding are listed in Table 1. The atomic densities and its WIMS ID are implemented in the code as argument to the MATERIAL card. Along with it is the supposed temperature and spectrum. Temperature for the clad are set to 310 K and the spectrum is 2. Detailed information on WIMS input preparation are left in the manual [2] due to the constraints of the paper. Aside from the cladding, another material with spectrum 2 is the Zirconium rod. The material ID, temperature, spectrum of Zirconium rod are similar to the zirconium in Table 2 but the atomic density is 0.042846 cm−3 b−1 . ∗ email:
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Table 1: Atom Densities and Material IDs for Clad Material Carbon Manganese Chromium Nickel Nitrogen Iron
WIMS ID 12 55 52 58 14 56
Atomic Density 0.000316 0.001730 0.018274 0.008904 0.000339 0.056844
Water are designated as coolant in this WIMS model, giving it spectrum 3 and temperature 309 K. The material is of course hydrogen and oxygen with an atomic density of 0.066856 and 0.033428 each. WIMS ID for hydrogen is 2001 and for oxygen is 16. Atomic density are calculated by the following formula. 0.6022ρi Ni = atoms. cm−3 b−1 (1) Ai Fuel materials are detailed out at Table 2 for fuel meat weighting 2654 g. Uranium content is 8.5% of total weight, equivalent 190 g. Uranium-235 enrichment of TRIGA fuel Uranium content is 20%. The spectrum is 1 and the temperature are 490 Kelvin. The hydrogen to zirconium ratio of 1.6 in TRIGA fuel has an inherent negative thermal reactivity coefficients of TRIGA at high temperature. Increasing fuel temperature made the heightened the vibration of hydrogen atoms. The increased vibration also increases the energy of neutrons that happens to collide with the hydrogen atom. Any neutron that happens to be thermal will have its energy increased and as a result, the probability for fission is reduced. With decreasing fission count, the reactivity will drop. This attribute is called Doppler Broadening of the neutron energy[3]. Thus, the hydrogen in Zirconium Hydride has different cross section in comparison with hydrogen in water. Thus, its WIMS ID is also different. Table 2: Atom Densities and Material IDs for Fuel Elements Material Uranium-235 Uranium-238 Uranium-239 Zirconium Hydrogen
WIMS ID 235.4 238.4 3239.1 91 2191
Atomic Density 0.000251 0.000990 1.0E-12 0.034143 0.054641
Geometry Specifications The core is divided into 7 sections defined by the ring of fuel positions and the centre thimble in the core. The centre thimble is also defined as the A ring and the case of a water filled centre thimble is considered. The first fuel ring is the B ring and successive rings are the C ring up to G ring. The exact annulus including the surrounding water of each ring from the core centre is illustrated in Table 3. Thus in our WIMS code, rings of water are first implemented before the fuel are placed in each ring. There is no need to model surrounding graphite given WIMS reflective boundary conditions. Each ring are drawn by the ANNULUS command card. Table 3: Annulus of Rings Ring A B C D E F G
Annulus (cm) 1.9114 6.0162 9.9635 13.931 17.902 21.874 27.000
Fuel Positions Number (Filled Position) 0 (0) 6 (6) 12 (12) 18 (18) 24 (24) 30 (30) 36 (0)
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Placement of fuel elements are made using the ARRAY and RODSUB command card. The ARRAY card determine the array parameters such as array type, angle of the first RODSUB and distance from the centre. Regardless of array type, all option arrange the array in a ring like manner, the only difference is on the determination of parameters such as RODSUB quantity and distribution of RODSUB on the array. RODSUB card are similar to the ANNULUS card, and the fuel elements are defined using this card on the array. RODSUB data for all fuel elements are defined in Table 4. Fuel arrangements are based on initial core configuration on which the last fuel ring remained unfilled. Table 4: RODSUB details Materials Zironium Rod Fuel Meat Air Gap Cladding
RODSUB (cm) 0.3175 1.8150 1.8240 1.8770
Neutronic Calculations and Result The infinite multiplication factor, kinf = 1.191021 is appropriate since we do not consider any leakage in the problem. Fuel elements in the same ring should have identical cross section and flux due to the symmetry of our core model. The average macroscopic thermal fission cross section, Σf (E) for each fuel elements is 0.095900 for the B ring, 0.094783 barn in the C ring, 0.094900 barn in D ring, 0.095154 barn in E ring and 0.098037 barn in the F ring. The normalized thermal flux, Φ(E) is 2.973430 × 10−4 ns−1 cm−2 in the centre thimble, 1.781364 × 10−4 ns−1 cm−2 in the B ring, 1.612312 × 10−4 ns−1 cm−2 in the C ring, 1.492325 × 10−4 ns−1 cm−2 in D ring, 1.286112 × 10−4 ns−1 cm−2 for E ring, 1.202948 × 10−4 ns−1 cm−2 on F ring and for the final G ring, the normalized flux is 2.341204 × 10−4 ns−1 cm−2 . Calculating the actual flux at the full power of 1 MW requires information on reaction rate. Reaction rate is the amount of fission induced by neutrons, N (E) in the particular volume (V ) of interaction. Since WIMS is a 2D code, the volume is anologous to its area. We may formalize this statement by defining reaction rate, RR as, RR = Φ(E) · Σf (E) · V = N (E) · Σf (E)
(2)
We are interested in the total reaction rate contributed by each ring. Reaction rate result can be utilized to calculate the normalized power, P . This is done by multiplying the reaction rate with the amount of energy released for each fission, ε = 3.20 × 10−11 W . With the normalized power, P we had just calculated, the normalization coefficent, η are immediately known by taking the ratio of our desired power and normalized power. P = RR · ε
(3a)
P0 η= P
(3b)
Please note that P 0 = 1M W/38.1cm is our desired power for each cm height. With the normalization coefficient, the actual reaction rate at fullpower is also revealed. Since only the flux varies with increased reaction rate, it is immediately obvious that the actual thermal flux can be calculated by multiplying the normalized thermal flux with the normalization factor. We summarized the value obtain from our calculations in Table 5. Table 5: Required parameters for calculating actual thermal flux. Parameter Total Reaction Rate (RR) Normalized Power (P ) Normalization Factor(η)
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Values 0.011922 3.8149 × 10−13 6.88 × 1016
We can now obtain the actual thermal flux for every ring. Table 6 details out the result of thermal flux calculation. B ring gave the largest thermal flux in the core with 2.0457 × 1013 n s−1 cm−2 . The centre thimble has a higher thermal flux than other positions in the core due to the water thermalizing most of the fast neutron going to the core centre. Table 6: Thermal flux at various locations in the core. Ring A B C D E F G
Flux (ns−1 cm−2 ) 2.0457 × 1013 1.2256 × 1013 1.1093 × 1013 1.0267 × 1013 8.8484 × 1012 8.2763 × 1012 1.6107 × 1013
Conclusion Our results for the centre thimble (A ring) and the pneumatic tube (G ring) corresponds with measurement data [1]. The measurement for the centre thimble yields a total flux of 5.05 × 1012 n s−1 cm−2 at the power 100 kW, equivalent to a total flux of 5.05 × 1013 n s−1 cm−2 at 1 MW. We can estimate the thermal flux from the ratio of normalized thermal flux and normalized total flux, 2.973430 × 10−4 Φ1M W = 13 5.05 × 10 6.8549 × 10−4 Φ1M W = 2.1906 × 1013 ns−1 cm−2
(4a) (4b)
This is only a rough estimation of the thermal flux. A better approximation should involve the calculation of average flux. Nevertheless, our quick estimate are sufficient to show that our WIMS result gave an acceptable value for the thermal flux. In the pneumatic tube located on the G ring, at G20 to be exact, thermal flux is 1.1 × 1012 n s−1 cm−2 at 100 kW. This is equivalent to 1.1 × 1013 n s−1 cm−2 at 1MW of power. In our WIMS result, thermal flux is 1.6107 × 1013 n s−1 cm−2 at G ring. Since our result is compatible with measurements, our model is further verified. Future studies can be more detailed in terms of geometry and may attempt to calculate the effective multiplication factor, kef f of the core.
References [1] Gui A. A. Ciri-ciri Reaktor TRIGA PUSPATI. Technical report, Unit Tenaga Nuklear, Jun 1984. [2] Atomic Energy Establishment, Winfrith, Dorchester. RSICC Computer Code Collection: WIMS-D4 (Winfrith Improved Multigroup Scheme Code System), 1991. [3] E. E. Lewis. Fundamentals of Nuclear Reactor Physics, page 46. Academic Press, February 2008. [4] I. Mele, S. Slavic, and M. Ravnik. Use and adaptation of wims code for TRIGA reactor calculations. Technical Report IJS-DP-6404, Jozef Stefan Institute, Ljubljana,Slovenia, 1992.
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TRICLUSW CELL 7 SEQUENCE 2 NGROUP 23 2 2 NMESH 70 NMATERIAL 22 NREGION 7 5 27 PREOUT INITIATE ANNULUS 1 1.9114 5 ANNULUS 2 6.0162 6 ANNULUS 3 9.9635 5 ANNULUS 4 13.931 6 ANNULUS 5 17.902 5 ANNULUS 6 21.874 6 ANNULUS 7 27.000 5 *water ARRAY 1 1 6 4.0514 0.26114 * B ring RODSUB 1 1 0.3175 1 *zr rod RODSUB 1 2 1.8150 2 *fuel meat RODSUB 1 3 1.8240 3 * air gap RODSUB 1 4 1.8770 4 *clad ARRAY 2 1 12 7.9810 0.0 * C ring RODSUB 2 1 0.3175 7 *zr rod RODSUB 2 2 1.8150 8 *fuel meat RODSUB 2 3 1.8240 9 * air gap RODSUB 2 4 1.8770 10 *clad ARRAY 3 1 18 11.946 0.0 * D ring RODSUB 3 1 0.3175 11 *zr rod RODSUB 3 2 1.8150 12 *fuel meat RODSUB 3 3 1.8240 13 * air gap RODSUB 3 4 1.8770 14 *clad ARRAY 4 1 24 15.916 0.0 * E ring RODSUB 4 1 0.3175 15 *zr rod RODSUB 4 2 1.8150 16 *fuel meat RODSUB 4 3 1.8240 17 * air gap RODSUB 4 4 1.8770 18 *clad ARRAY 5 1 30 19.888 0.0 * F ring RODSUB 5 1 0.3175 19 *zr rod RODSUB 5 2 1.8150 20 *fuel meat RODSUB 5 3 1.8240 21 * air gap RODSUB 5 4 1.8770 22 *clad MESH 10 10 10 10 10 10 10 * F RING MATERIAL 22 -1 303 2 12 0.000316 55 14 0.000339 56 0.056844 MATERIAL 21 -1 303 2 14 0.00001 MATERIAL 20 -1 403 1 235.4 0.000251 2191 0.054641 MATERIAL 19 -1 303 2 91 0.042846 * E RING MATERIAL 18 -1 303 2 12 0.000316 55 14 0.000339 56 0.056844 MATERIAL 17 -1 303 2 14 0.00001 MATERIAL 16 -1 403 1 235.4 0.000251 2191 0.054641
0.001730 52 0.018274 58 0.008904 \$
238.4 0.000990 91 0.034143 \$
0.001730 52 0.018274 58 0.008904 \$
238.4 0.000990 91 0.034143 \$
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MATERIAL 15 -1 303 2 91 0.042846 * d RING MATERIAL 14 -1 303 2 12 0.000316 55 0.001730 52 0.018274 58 0.008904 \$ 14 0.000339 56 0.056844 MATERIAL 13 -1 303 2 14 0.00001 MATERIAL 12 -1 403 1 235.4 0.000251 238.4 0.000990 91 0.034143 \$ 2191 0.054641 MATERIAL 11 -1 303 2 91 0.042846 * C ring MATERIAL 10 -1 303 2 12 0.000316 55 0.001730 52 0.018274 58 0.008904 \$ 14 0.000339 56 0.056844 MATERIAL 9 -1 303 2 14 0.00001 MATERIAL 8 -1 403 1 235.4 0.000251 238.4 0.000990 91 0.034143 \$ 2191 0.054641 MATERIAL 7 -1 303 2 91 0.042846 * B ring and centre thimble MATERIAL 6 -1 303 3 2001 0.066856 16 0.033428 MATERIAL 5 -1 303 3 2001 0.066856 16 0.033428 MATERIAL 4 -1 303 2 12 0.000316 55 0.001730 52 0.018274 58 0.008904 \$ 14 0.000339 56 0.056844 MATERIAL 3 -1 303 2 14 0.00001 MATERIAL 2 -1 403 1 235.4 0.000251 238.4 0.000990 91 0.034143 \$ 2191 0.054641 MATERIAL 1 -1 303 2 91 0.042846 FEWGROUPS 5 6 14 15 21 25 26 27 30 33 34 35 38 45 47 52 55 58 59 \$ 60 63 66 69 BEGINC REGION 1 1 2 2 7 7 12 12 17 17 22 22 27 27 THERMAL 15 VECTOR 15 23 BUCKLING 1.E-08 1.E-08 NO BUCKLING SEARCH BEGINC
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