One of the most widely used correlations for evaluation of critical heat flux (CHF) in PWR is the Westinghouse-3 (W-3) correlation. For predicting the CHF condition in a non-uniform heat flux channel, we use these two steps:

1. The uniform critical heat flux is computed with the W-3 correlation
2. The non-uniform critical heat flux distribution is then obtained by dividing the uniform critical heat flux  by the F factor.

For uniformly heated channels, the critical heat flux is given by:

Where:

The axially non-uniform heat flux is obtained by applying a corrective F factor to the uniform critical heat flux:

Where:

Source: N.E. Todreas and Mujid S. Kazimi, Nuclear Systems I – Thermal Hydraulic Fundamentals, Hemisphere Publishing Corporation, New York (1990), page 558.

Useful links:

• Material from MIT
• Material from NCSU

Yeap.. akhirnya malam ini datang juga, ini malam terakhir saya di Umegaoka dorm, besok siang saya resmi move out from here and start a new life in a new place. I have been staying here since September 25 last year, and will officially move out tomorrow on September 16 this year, 357 exciting days have passed. Ya, 357 hari (or 356 malam) sudah saya habiskan di asrama ini.

Saya pindah ke tempat kost baru di deket kampus, di daerah Higashitamagawa, paling 20 menit-an jalan kaki dari kampus.

Selamat tinggal Umegaoka, n selamat datang Higashitamagawa!

New place, new spirit! O yeah!

–

• JANIS (Nuclear Data Library)
• OpenFOAM (Computational Fluid Dynamics)
• OpenFEM (Finite Element Method)
• Scilab (Numerical Mathematics, Matlab-like)
• Lazarus (Integrated Development Environment, Delphi-like)
• From French EDF
• MATPACK (German C++ Library)
• VE-Suite

–

test

Astaghfirullah ya Allah…

Hmmh.. ga disangka sy kena sindrom homesick lagi.. dulu pertama kena pas awal bulan Januari.. 3 bulan setelah sy sampai di Jepang, brarti 8 bulan yg lalu ya. Now one year has passed.. hhhhh.. rasanya bener2 sama persis ky wkt  itu.. kehilangan semangat.. gelisah ga keruan.. takut ga tau kenapa.. ngerasa waktu ko cepet sekali berlalu, rindu masa lalu, dll.. jadi ga bisa ngapa2in deh.. padahal tanggal 1 besok deadline submit report.. jumat depan kebagian presentasi lab lagi… hhh.. bener2 gawat klo gini nih.. T_T

Kayanya sih karena pengaruh suasana lingkungan juga.. ini kan akhir semester, banyak anak2 asrama yg move out, ada yg pindah ke tempat lain, n ada jg yang pulang ke negaranya. Kita disini emang hanya dikasih jatah setaun utk tinggal d asrama, makanya mereka pada pindah, sy juga insya Allah pindah bulan depan.

Di blok saya awalnya ada 6 orang, skrg yg satu udah pindah tempat, n yg tiga udah pulang ke negaranya, jadi skrg d blok sy cuma ada 2 orang, tp kemarin ngobrol ma dia katanya dia bakal move out hari senin depan.. yah.. minggu depan bnr2 sendirian deh.. sy makin gelisah lagi pas sadar klo ntar d tmp kost baru juga kan sy sendirian! hhh… emang enak kesepian ky gini di negri orang..

Emang udah saatnya cari pasangan hidup neh!

.. yg bisa mendorong ketika sy jatuh.. n bisa ikut senang ketika sy senang .. iiihh romanteeeezzzz!!

hhh.. ya gini jadinya klo orang lg error berat.. harap maklum deh ya..

The concept of equivalent hydraulic diameter [doc | quickview]

Source: Nuclear Reactor Analysis, Duderstadt & Hamilton, page 485

Rectangular array geometry (Light Water-cooled Reactor/LWR)

Triangular array geometry (Liquid Metal-cooled Reactor/LMR)

Just another self reminder..

The concept of equivalent hydraulic diameter [doc | quickview]

To design an NPP, calculations and analyses have to be performed (at least) to answer the following basic questions:

Core neutronics design

• Is the reactor critical?
• What is the core reactivity lifetime?
• What is the core power distribution (axial and radial)?
• Are the reactivity coefficients within acceptable limits?

Core thermal hydraulics design

• Can I remove the heat generated in the core while maintaining the fuel clad at an acceptable temperature during steady state operations?
• Will the fuel centerline temperature be acceptable under the same conditions?
• Can I prevent the fuel or cladding damage in the event of certain foreseeable accidents?
• How do system design and behavioral uncertainties impact the answers to the above questions?

Balance of plant design

• How much surface area does the steam generator require?
• What is the minimum steam generator tube thickness allowed?
• What will be the flowrate of the secondary systems fluids?

—

Osaka Castle

Alhamdulillah.. udah di asrama lagi, 5 hari kemarin nginep di Osaka, dari hari Senin (20 Juli) sampe haris Jumat (24 Juli). Saya ke Osaka sebagai partisipan Nuclear Engineering Experiment di Kyoto University Research Reactor Institute (KURRI), or tepatnya pake fasilitas riset yg namanya Kyoto University Critical Assembly (KUCA). KURRI ini salah satu badan riset nuklir univ Kyoto, tp lokasinya bukan di Kyoto, melainkan di Kumatori, Osaka. Cuma sayang banget, karena kegiatannya super padat, jd ga sempat jalan2.. hff.. padahal pengen banget liat Osaka Castle n Universal Studio.. hmm maybe next time…

Saya berangkat dari asrama hari Senin pagi jam 5.45, bareng satu temen dari Mongolia (Byambajav Munkhbat), terus kami ketemuan sama satu temen lagi dari Jepang (Masahiko Nakase) di stasiun Shin Yokohama. Terus kita naik Shinkansen, perjalanan klo ga salah sekitar 2 or 3 jam, trus di di stasiun Shin Osaka kita naik lagi kereta lokal sampe stasiun Kumatori.

Sebelum ke KUCA kami makan siang dulu di restoran kecil deket stasiun, kami makan okonomiyaki (mirip martabak telor bang solihin di monas, hehe..), ternyata lumayan mahal, sekitar 800 yen, tp gapapa namanya jg pengalaman. Setelah itu kami langsung menuju KUCA naik bis dengan ongkos 160 yen.

Okonomiyaki

Akhirnya kami sampai di KUCA Dormitory, tempat tinggal kami selama di Osaka. Hmm.. gedung asramanya punya 2 lantai, n keliatan udah tua, padahal sewanya lumayan mahal, semalem sekitar 1000 yen, asrama sy d Yokohama kan cuma sekitar 500-600 Yen. Kemudian kami check in, ternyata saya sekamar dengan Teaching Assistant kami, orang Indonesia, namanya M. Kunta Biddinika or mas Kunta, siip deh. Kami dapat kamar di lantai 2, kamarnya lumayan, yaa standar kamar di Jepang lah, ada TV, AC, westafel, bed, n yg paling penting: koneksi internet.

Hari Senin itu sebenernya libur, itu hari laut (marine day) di Jepang, makanya hari itu ya sbenernya ga ada kegiatan. Setelah menyimpan barang2 di kamar, kami berangkat ke gedung KUCA, deket banget dr asrama, cuma 5 menit jalan kaki. Kesan pertama saya begitu masuk kompleks fasilitas risetnya: “hmm.. ko ga kliatan so hi-tech ya..“, lagi2 gedung2 disana kliatan udah tua.

My KURRI ID Card

Hari itu acaranya cuma semacam acara pembukaan sederhana, ternyata pesertanya bukan hanya anak2 Tokodai, bbrp teman berasal dr univ Tohoku. Saat itu kami baru tau kalau ternyata seluruh penjelasannya akan diberikan dalam bahasa Jepang, waah sayang sekali.. mungkin krn mayoritas peserta adalah mahasiswa Jepang.  Padahal orang2 KUCA sbnernya bisa bhs Inggris juga, n tmn Jepang sy pun bilang sbnernya mereka pun ngerti klo penjelasannya pake English.

Sorenya kami pergi ke warung makan kecil di depan KUCA, pilihan makanannya ga banyak, saya cuma makan nasi pake ikan doang, n minum sugarless ice tea, pelayannya ramah, tau bahwa kami ga bs bhs Jepang dia pun berusaha pake bhs Inggris, walaupun agak susah.

@KUCA Dormitory

Malamnya pas mau mandi, baru saya tau ada satu masalah besar! ruang mandinya ternyata hanya ada satu n model ofuro! alias mandi bareng2! hiiih.. serem.. jadi saya pikir mending mandinya ntar aja di waktu2 yg kira2 ga ada orang mandi. Besoknya (Selasa subuh) sktar jam 4 subuh sy bangun n langsung mandi, “wah pasti ga ada orang yang cukup gila ampe mandi subuh2 gini” pikir saya. At first, everything went well, ga ada orang disana, eehh.. pas lagi asik2nya mandi, ada suara pintu dibuka! n tiba2 ada om2 gendut masuk!! bugil!!! yahhh.. sial bener.. akhirnya sy cpt2 kluar, kaburrr!!!

Di KUCA ini ada salah satu teman saya sedang kuliah S3, namanya M. Nurul Subkhi, dia ini sama2 dari Fisika ITB. Nah selama di KUCA ini saya pesan bento yg dimasak oleh istrinya Nurul ini, hmm.. sedaap hehe.. maklum dah lama juga ga makan masakan Indonesia.

Experimen “beneran”-nya dimulai hari Selasa. Jam kerja kami disana mulai jam 9 pagi sampai jam 5 sore. Ada 3 macam eksperimen yang akan kami lakukan disana:

1. Approach to Criticality, untuk memprediksi jumlah nuclear fuel plate yg diperlukan to achieve criticality
2. Control rod calibration, untuk tau control rod worth
3. Measurement of Reaction Rate Distribution, untuk tau distribusi fluks neutron

KUCA C-Core

Jadi “mainan” utama di KUCA ini adalah nuclear critical assembly, ga terlalu besar juga sih, yg kami pakai waktu itu adalah C-Core, assembly bermoderator H2O. Bagian utamanya terdiri dari 12 fuel frame yg tiap frame bisa diisi sampai maksimal 40 fuel plate. Ukuran fuel framenya 14 x 7 cm, jadi ukuran total assembly nya sekitar 28.4 x 42.3 cm, ga trlu besar.

Ternyata 2 profesor di KUCA ini orang Korea n mereka bnr2 fasih bgt bhs Jepang-nya, hmm.. kapan ya orang Indonesia ada yg jadi profesor nuklir di Jepang???

Hampir semua kegiatan intinya dilakukan hari Selasa n Rabu. Most of the time kami duduk d kelas dengerin penjelasan n di control room, doing data mining from there. Kami juga sempat dibawa masuk ke dalam reaktornya utk melihat secara langsung. Satu hal yg agak menarik adalah mereka menggunakan jemuran baju (yg plastik warna-warni itu lo) sbg penjepit pelat almunium utk menjaga constant gap witdth between fuel frames, ko bisa ya alat sederhana gt dipake di nuclear critical assembly???

Kami juga diberi kesempatan untuk mencoba melakukan fuel loading, masukin fuel plate ke dalam fuel frame. Setelah itu kami diminta menghitung jumlah fuel plate di dlm fuel frame, weh2 trnyata ga gampang loh. Orang2 KUCA ketawa aja liat kami kerepotan ngitung tu fuel plate, akhirnya kami disuruh pake ANFPNC alias Advanced Nuclear Fuel Plate Number Counter. Eehh.. taunya tu barang cuma sedotan biasa doang! weh2.. tu orang2 KUCA ketawa2 lagi, mereka bilang it’s just a joke. Saya surprise juga ko mereka bisa pake barang2 sederhana gt di fasilitas nuklir ky gt ya???

Munkhbat, me, and Sicheng @ control room

Hari kamis pagi acaranya experiencing reactor control. Jadi tiap student diberi kesempatan sebentar utk ngendaliin tu reaktor dengan cara control rod adjustment. Ada yg kebagian naikin n nurunin daya reaktor, sy kebagian nurunin daya dari 80% ke 40%. Ternyata ga gampang juga ngendaliin control rod, harus pake feeling. Siangnya acaranya group presentation, saya sekelompok dengan Munkhbat (Mongolia), Liu Sicheng (RRC), dan Kim Seon Tae (South Korea), tugas kami membahas mengapa data dari eksperimen ko beda dengan data dari perhitungan teoritis.

Experimental vs Theoretical

Setelah sesi presentasi, kami diminta untuk menyiapkan laporan eksperimen yang harus dikumpulkan besoknya (Jumat) jam 10 pagi, weh2 gilee.. kami cuma punya waktu semalam utk ngerjain laporan segitu banyak. Kelompok kami pun bagi2 tugas, saya kebagian ngerjain laporan chapter 1, fiuhh.. lumayan cape juga, malam itu kami lumayan ganbatte, walaupun sambil bercanda n ketawa2 keras semalaman, emang pada gila tu temen mongol n RRC hehe..  Munkhbat ngomel2 krn rencananya utk mabok2an pake bir Osaka malam itu jadi berantakan, n Sicheng malah ngeloyor santai n mau tidur aja katanya.. weh2.. saya baru tidur sktr jam 4 pagi n bangun sekitar jam 7 pagi.

Kemudian kami semua check out dari asrama dan menuju KUCA utk ngeprint n ngumpulin laporan. Hari itu acaranya cuma site visit, kami mengunjungi Kyoto University Reactor (KUR), yg trletak persis disebelah gedung KUCA, saat itu KUR sedang tdk beroperasi. Kami dibawa masuk ke dalam KUR dan diberi berbagai penjelasan, salah satunya adalah bahwa di KUR ini mereka punya fasilitas utk cancer treatment dengan metode BNCT.

And finally, KUCA experiment has come to the end, kami pun pulang hari jumat siang. Kami pulang bareng seorang profesor Tokodai, Prof. Yoshihisa Matsumoto. Di stasiun Shin Osaka kami makan siang okonomiyaki lagi, kami ditraktir Prof. Matsumoto, asiiik.. hehe..

Saya sampai d asrama Yokohama sktr jam 6 sore.. huff cape juga..

FIN

Image Gallery

Click to view the album (62 photos)

- – -

Baru aja nyobain nulis persamaan pake LaTeX, n ini dia persamaan LaTeX pertamaku!!

Sungguh saat2 yg bersejarah.. hihihi…

Persamaan apa hayo..??

Kemarin2 lg butuh data densitas Helium di dalem fuel rod nuklir, heran, udah kesana-kemari keliaran pake google ko ga ktemu2 yah.. ada yg punya datanya kah..? perlu neh..

Hmm.. apa itu termasuk data “rahasia” yah.. hmm aneh..

Yah daripada kerjaan mampet gara2 ga ada data, kepaksa bikin perkiraan sendiri deh.. sy pake persamaan gas ideal yg paling sederhana aja^[1]:

Harusnya sih persamaan gas ideal lumayan bagus untuk dipake ngitung densitas Helium, kan Helium gas monoatomik, jadi harusnya kelakuannya ya mirip sama gas ideal kan.. biar yakin benchmark dulu lah, sama data Helium pada keadaan STP^[2]:

• T = 273.15 K
• p = 101325 Pa

Nilai parameter lainnya:

• M Helium = 4.002602E-3 kg/mol ^[3]
• R = 8.314472 J/(K.mol) ^[1]

Trus itung deh..

Klo liat di wikipedia^[3], densitas Helium (STP) tu 0.1786 g/L, wah ternyata cocok ma perhitungan gas ideal!! siip!!!

Berarti sekarang saya bisa buat perkiraan yg lumayan akurat tentang densitas Helium di dalam fuel rod dong ya! data2 yang dipake:

• p = 3 MPa (dapet dr sebuah jurnal)
• T = 650 K (ada itungan nya, kpn2 di post deh..)

Itung..

Hmm.. berarti densitas Helium di dalam pellet-clad gap tu sekitar 0.00222185 g/cc dong ya..

Bener ga yah..? hmm…

Referensi:

1. http://en.wikipedia.org/wiki/Ideal_gas_law
2. http://en.wikipedia.org/wiki/Standard_conditions_for_temperature_and_pressure
3. http://en.wikipedia.org/wiki/Helium

Disclaimer:
Information presented in this article are based on publicly available data of the IRIS reactor project, as properly cited from the original source. This article is NOT part of the official IRIS project led by Westinghouse. For more reliable information, the reader should refer to any official websites and information sources of the IRIS project and/or the IRIS consortium. All trademarks and registered trademarks shown in this article are the property of their respective owners.

Neutronic Study of the IRIS Reactor Core

Syeilendra Pramuditya (シエイレンドラ  -  プラムディティア)
Energy Engineering Division
Research Laboratory for Nuclear Reactors
Tokyo Institute of Technology
JAPAN

Abstract

The neutronic analysis of the integral primary system PWR has been performed. The reactor analyzed is a modular, integral, light water cooled, low-to-medium power (~1000 MWth) reactor, which emphasizes proliferation resistance and enhanced safety. The comprehensive neutronics code system SRAC was used to develop a full-core model of the reactor core, and cross section data generated from JENDL-3.2 nuclear data library were used. The calculation results show that the core design has a relatively high power peaking factor, which is a disadvantage in terms of safety and thermal hydraulic performance. The reactivity coefficients are found to be negative, which indicates that the reactor core shows inherent safety features.

1. Introduction

Over the past decades, there have been several projects involving the integral reactor concept. Advantages of integral reactors include increased safety, more compact layout and reduced construction costs. Increased safety for integral reactors comes from the following design features: low power density, passive safety features of the containment, and of course the very key feature of the integral core configuration – no large pipe penetration into the reactor vessel. The elimination of all reactor coolant piping removes that piping from any loss of coolant accident (LOCA) possibility. The compact plant layout is derived primarily from the elimination of the reactor coolant piping and by placing equipment normally external to the RPV such as the steam generator (S/G), reactor coolant pump (RCP), and pressurizer (PZR) within the vessel. The elimination of the requirements for large on-site welds on reactor coolant piping, as well as the modular configuration of the reactor vessel assembly, is expected to lead to a shorter construction time. This, in conjunction with the overall smaller physical footprint, is expected to lead to lower construction costs. This work describes the neutronic calculation of the integral primary system PWR core, without thermal hydraulic feedback.

2. Reactor description

The reactor analyzed is the reference design of a modular, integral, light water cooled, low-to-medium power (~350 MWe) reactor, which emphasizes proliferation resistance and enhanced safety, currently known as the International Reactor Innovative and Secure or the IRIS reactor (Carelli et al., 2004; Carelli, 2009). A distinguishing characteristic of the IRIS reactor is the integral design: The steam generators (S/Gs), reactor coolant pumps (RCPs) and pressurizer (PZR) are all contained within the reactor pressure vessel (RPV) (Carelli, U.S. DOE Final Technical Progress Report-STD-ES-03-40, 2003). This configuration is different from a conventional PWR where the S/Gs, PZR, and RCPs are all mounted outside of the RPV, connected by reactor coolant piping of varying diameter, all located within a containment. Summary of the IRIS reference design is shown in Table 1.

Table 1. IRIS reference design

More detailed description and technical specification of the IRIS reactor could be found in the listed references.

3. Methodology

3.1. Reactor simulation codes

The methodology comprises two major parts, i.e. generation of group constants for various core regions, and whole core calculations. The Japanese Standard Reactor Analysis Code, the SRAC code system (Tsuchihashi et al., 1986), was used to perform the cell and whole core calculation. The SRAC code system was designed and developed at the Japan Atomic Energy Research Institute (JAERI, now JAEA) to permit overall neutronics calculation for various types of thermal reactors. The system covers generation of group constants, cell and core calculations including burnup. The SRAC code system is composed of the collision probability method (CPM) cell calculation code, named PIJ, and several whole core calculation codes. For the current study, we use the CITATION code for whole core calculation. The CITATION code evaluates the neutron multiplication factor, k-eff, by solving the neutron flux eigen-value problem by using finite-difference multigroup neutron diffusion theory approximation of the neutron transport equation, by direct iteration method. The code computes the effective multiplication factor, flux and power profiles in the core by using group constants generated by the PIJ code. In addition to this, the code can also be used to calculate reactivity feedback coefficients, effective delayed neutron fraction, and prompt neutron generation time (Fowler et al., 1971). Detailed description of these codes could be found in the listed references.

3.2. Neutron energy group

The JENDL-3.2 evaluated nuclear data library (Shibata et al., 1990) was used for CPM cell calculation and to generate the few group constants. Four energy groups were used in this work (Table 2).

Table 2. Energy group structure

3.3. Geometrical modeling

3.3.1. Modeling of the fuel cell

The reference core design of the IRIS reactor use the Westinghouse standard fuel assembly for PWR (Carelli, 2009), in which the fuel rods are arranged in 17×17 rectangular array (Carelli et al., 2004). Hence, the most appropriate geometrical model for cell calculation is the square cell, with several concentric circles representing regions for fuel, cladding, and moderator (Fig. 1).

Figure 1. Fuel cell modeling

3.3.2. Modeling of the reactor core

The IRIS reactor core consists of 89 fuel assemblies (FAs). Each fuel assembly contains 264 fuel rods and 25 control elements, arranged in 17×17 matrix (Carelli et al., 2004). The geometrical model for whole core calculations which was used in this work is mainly based on the work of Jecmenica et al., 2003, in which the core is modeled in 3D-XYZ geometry (Fig. 2). Active core height is 426.7 cm with uniform enrichment of 4.95 w/o 235U. The total core height, including top and bottom axial reflector regions, is 506.7 cm. Radial reflector was modeled using reflector cells of the same dimensions as FA.

Figure 2. Reactor core modeling

3.4. Core depletion analysis

The core depletion calculation can be divided into two main parts: (a) solution of the isotopic depletion equation, which requires information of the neutron flux; and (b) solution of the static multigroup diffusion equation for the neutron flux. Hence, we decoupled those calculations such that the depletion equations are solved over a specified time interval in which the power is assumed to be constant. Then, at the end of each time interval, the depleted densities and local average power level are used to calculate new group constants, and again, the multigroup diffusion equation is solved to determine a new neutron flux distribution and power distribution for the next time interval (Duderstadt and Hamilton, 1976; Zaki Su’ud, 2008).

3.5. Calculation of reactivity coefficients

Reactivity coefficients were determined by performing a sequence of static criticality calculations, using the CITATION code, to calculate the core effective multiplication factor, k-eff, for different parameters under consideration, i.e. fuel temperature, coolant temperature, and void fraction, as explained by Muhammad and Majid, 2008; Muhammad and Majid, 2009; and Duderstadt and Hamilton, 1976. The change in reactivity was calculated as follows (IAEA TECDOC-643, 1992):

(eq. 1)

Where k₀ is k_eff at the reference condition (888.586 K), and k₁ is k_eff at a specified condition. Reactivity coefficient is defined as change in reactivity for given change in parameter (Ott and Neuhold, 1985), and generally expressed as:

(eq. 2)

Here is any parameter that affects reactivity, and is corresponding change in reactivity.

4. Results and discussions

4.1. Criticality calculation

The group constants and infinite multiplication factor, k-inf, were calculated as a function of P/D (or H₂O/U) at a single calculational cell. In this work, P/D was increased from 1.05285 (corresponding to H₂O/U=0.59671) to 3.5797 (corresponding to H₂O/U=22.21507), while keeping all other parameters unchanged. The results are given in Table 3.

Table 3. k-inf as a function of P/D

The value of k-inf as a function of fuel pitch is plotted in Fig. 3.

Figure 3. k-inf as a function of P/D

The underlined values in Table 3 and the red dot in Figure 3 are calculation results for the current reference core design at its operating condition. Figure 3 shows that for current reference core, reactivity decreases as P/D decreases, this is corresponding to the decrease in reactivity as coolant density decreases, or as coolant temperature increases, which is a good point for safety performance.

4.2. Core power distribution

Power distribution and peaking factor are important parameters in terms of safety and thermal hydraulic performance. The maximum power density is found from the calculation at location (35, 1, 55), which is physically at the center of the core. The maximum power density is 175.225 Watt/cc, therefore, the calculated power peaking factor is 3.418.

4.3. Reactivity coefficients

4.3.1. Fuel temperature coefficient of reactivity

To calculate the coefficients for change of fuel temperature, only the fuel temperature was varied from 848.586 K to 948.586 K. The results of reactivity calculation for various fuel temperatures are given in Table 4 and plotted in Figure 4.

Table 4. Fuel temperature coefficient of reactivity

Tfuel (K)	keff
848.586	1.362786	0.266209	0.00087
868.586	1.361958	0.265763	0.000423
888.586	1.361173	0.26534	0
908.586	1.360401	0.264923	-0.00042
928.586	1.359604	0.264492	-0.00085
948.586	1.358848	0.264083	-0.00126

Figure 4. Fuel temperature coefficient of reactivity

The underlined values in Table 4 and the red dot in Figure 4 are calculation results for the current reference core design. Table 4 and Figure 4 show that the core reactivity decreases as the fuel temperature increases, this is due to Doppler broadening effect on the absorption cross section (Duderstadt and Hamilton, 1976), in which the energy range of neutrons to be absorbed in resonance is increased. Therefore, more neutrons are absorbed by the resonance, this will eventually lead to the decrease of core reactivity.

The reactivity coefficient for fuel temperature change from 848 K to 948 K, denoted as , is then determined as the slope of the curve in Figure 4:

(eq. 3)

Therefore, .

4.3.2. Moderator temperature coefficient of reactivity

To calculate the coefficients for change of moderator temperature, only the moderator temperature was varied from 544 K to 644 K. The results of reactivity calculation for various fuel temperatures are given in Table 5 and plotted in Figure 5.

Table 5. Moderator temperature coefficient of reactivity

Tmod (K)	keff
544	1.361577	0.265558	0.000218
564	1.361378	0.26545	0.000111
584	1.361173	0.26534	0
604	1.360987	0.265239	-0.0001
624	1.360788	0.265132	-0.00021
644	1.360583	0.265021	-0.00032

Figure 5. Moderator temperature coefficient of reactivity

Figure 5 shows that the core reactivity decreases as the moderator temperature increases, this is because an increase in moderator temperature, keeping the density constant, will lead to a hardened neutron spectrum, resulting in increased resonance absorption cross section. The hardened spectrum will cause an increase in the capture-to-fission ratio of 235U, which means a decrease in eta value, and hence a decrease in core reactivity.

The reactivity coefficient for moderator temperature change from 544 K to 644 K, denoted as , is then determined as the slope of the curve in Figure 5:

(eq. 4)

Therefore, .

4.3.3. Void coefficient of reactivity

To calculate the coefficients for change of void fraction in the coolant, the void fraction was varied from 0% to 10%. The results of reactivity calculation for various coolant void fraction are given in Table 6 and plotted in Figure 6.

Table 6. Void coefficient of reactivity

Void (%)	keff
0	1.361173	0.265340	0
2	1.356340	0.262722	-0.00262
4	1.351344	0.259996	-0.00534
6	1.345924	0.257016	-0.00832
8	1.340822	0.254189	-0.01115
10	1.335250	0.251077	-0.01426

Figure 6. Void coefficient of reactivity

Figure 6 shows that the core reactivity decreases as the coolant void fraction increases, this is because void formation in the coolant will decrease the average density of the coolant, and because coolant also acts as moderator in thermal reactor, this will lead to a spectrum hardening, and further causes an increase in resonance cross section, and hence reduces the core reactivity.

The reactivity coefficient for coolant void fraction from 0% to 10%, denoted as , is then determined as the slope of the curve in Figure 6:

(eq. 5)

Therefore, .

5. Conclusions

The calculation results show that the core has power peaking factor of 3.418, which is relatively high and could be considered as a disadvantage in terms of safety and thermal hydraulic performances. The fuel temperature coefficient of reactivity, coolant temperature coefficient of reactivity, and void coefficient of reactivity were all found to be negative. The Doppler coefficient was found to be more negative than the moderator temperature coefficient, which means that the fuel temperature change plays more roles on the inherent safety feature of the reactor core.

References

1. Carelli, M.D., 2009. The exciting journey of designing an advanced reactor. Nuclear Engineering and Design 239, 880-887.
2. Carelli, M.D., Conway, L.E., Oriani, L., Petrovic, B., Lombardi, C.V., Ricotti, M.E., Barroso, A.C.O., Collado, J.M., Cinotti, L., Todreas, N.E., Grgic, D., Moraes, M.M., Boroughs, R.D., Ninokata, H., Ingersoll, D.T., Oriolo, F., 2004. The design and safety features of the IRIS reactor. Nuclear Engineering and Design 230, 151–167.
3. Duderstadt, J.J., Hamilton, L.J., 1976. Nuclear Reactor Analysis. Wiley, New York.
4. Fowler, T.B., Vondy, D.R., Cunningham, G.W., 1971. Nuclear Reactor Core Analysis Code-CITATION, USAEC Report ORNL-TM-2496, Revision 2. Oak Ridge National Laboratory.
5. IAEA, 1992 IAEA, 1992. Research Reactor Core Conversion Guide Book. IAEA-TECDOC-643. International Atomic Energy Agency, Vienna.
6. Ječmenica, R., Trontl, K., Pevec, D., Grgić, D., 2003. IRIS Core Criticality Calculations. In: Int. Conf. Nuclear Energy for New Europe, Portorož, Slovenia. September 8-11. pp 105.1-105.5.
7. Muhammad, F., Majid, A., 2008. Reactivity feedback coefficients of a material test research reactor fueled with high-density U₃Si₂ dispersion fuels. Nuclear Engineering and Design 238, 2583-2589.
8. Muhammad, F., Majid, A., 2009. Reactivity feedbacks of a material test research reactor fueled with various low enriched uranium dispersion fuels. Annals of Nuclear Energy, In Press, Corrected Proof, DOI: 10.1016/j.anucene.2009.03.006.
9. Ott, K.O., Neuhold, R.J., 1985. Introductory Nuclear Dynamics. American Nuclear Society, La Grange Park, Illinois, USA.
10. Shibata et al., 1990 Shibata, K. et al., 1990. Japanese Evaluated Nuclear Data Library, Version-2, JENDL-3, JAERI 1319, JAERI, Tokai-mura, Naka-gun, Ibaraki-ken, pp. 319-11, Japan.
11. Tsuchihashi et al., 1986 Tsuchihashi, K. et al., 1986. Revised SRAC Code System: JAERI Thermal Reactor Standard Code System for Reactor Design and Analysis, JAERI 1302, Japan.
12. Zaki Su’ud, 2008. Neutronic performance comparation of MOX, nitride and metallic fuel based 25–100 MWe Pb–Bi cooled long life fast reactors without on-site refuelling. Progress in Nuclear Energy 50, 276-278.

Code package:

• The code [ncs.doc], written in Delphi (download, rename to “ncs.zip”, then extract)

The governing equation being used is the steady state neutron diffusion equation:

Numerical schemes being used are:

• Central finite difference for flux calculation
• Gauss-Siedel and S.O.R for flux calculation
• Power method for criticality calculation

Code package:

• Manual (English)
• Code [snr.doc], written in Delphi (download, rename to “snr.zip”, then extract)

Flowchart of the code:

Some previews:

Nuclear Fuel Pellet Theoretical Density (TD)
Fuel TD adalah nilai densitas fuel pellet pada kondisi ideal/sempurna, yang dihitung dengan persamaan umum berikut:

Fuel TD dihitung dengan asumsi bahwa seluruh volume fuel pellet terisi hanya oleh material fuel, dimana hal ini tidak terlalu tepat, karena sebenarnya di dalam fuel pellet pasti terdapat impuritas, baik itu porositas ataupun rongga2 udara yang sangat kecil, akibat proses fabrikasi yang tidak sempurna. Karena itu densitas fuel yang sebenarnya pasti tidak 100%, melainkan berkisar 94-96% dari fuel TD, dimana fuel TD adalah 10.96 gr/cc.

Nuclear Fuel Pellet Effective Density (ED)
Densitas fuel pellet yang sebenarnya biasa disebut dengan Fuel Pellet Effective Density (ED), dan dirumuskan sebagai berikut:

Nuclear Fuel Pellet Smeared Density (SD)
Fuel SD adalah nilai densitas fuel dengan asumsi bahwa fuel pellet menempati seluruh rongga di dalam cladding, dengan demikian kita asumsikan bahwa fuel pellet menempel dengan permukaan dalam cladding (diasumsikan tidak ada celah/gap). Hubungan antara TD, ED, dan SD adalah sebagai berikut:

Khusus untuk perhitungan cell homogenization dengan menggunakan code PIJ/BURN-SRAC, biasanya digunakan SD, yaitu dengan asumsi bahwa gap tidak terlalu mempengaruhi perhitungan, sehingga dapat diabaikan.

Sumber:

1. N. E. Todreas and M. S. Kazimi, “Nuclear Systems: Vol. I, Thermal Hydraulic Fundamentals,” Hemisphere, NY 1990, 3rd printing, Taylor & Francis, 2001, pp 33-35.
2. http://www.kntc.re.kr/openlec/nuc/NPRT/module2/module2_2/module2_2_2/2_2_2.htm
3. http://article.nuclear.or.kr/jknsfile/v34/A04803285970.pdf

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