Some Definitions of Nuclear Fuel Pellet Density

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

Hydrogen to Heavy Metal Ratio (H/HM ratio)

Hydrogen to Heavy Metal Ratio or H/HM for short, is typical parameter in neutronic analysis of a nuclear reactor,  or more specifically, the Pressurized Water Reactor (PWR) type. Basically it is simply the ratio of moderator (water) to fuel/fissile material (U/Pu/Th) within one calculation cell. I will briefly show you how to calculate this H/HM.

Consider a standard Westinghouse PWR fuel: cylindrical fuel rod array, arranged in rectangular geometry, please refer to this link for the detail of its technical specifications.

Next, make sure that you have understood how to calculate the atomic number density, or otherwise learn it first from the following link:

Calculating_Number_Density [pdf | quickview]

Now suppose that the fuel has enrichment level of 3%, and 95% theoretical density, hence the atomic number densities are as follow:

Atomic number density of Uranium in the fuel: N_U = N_U235 + N_U238 = 2.3227E+22 atoms/cc

Atomic number density of Hydrogen in the moderator (water): N_H = 3.3456E+22 atoms/cc

And the volume fractions are as follow:

Fuel :   33.501 %
Coolant :   54.943 %
Structure :   11.555 %

And finally the H/HM ratio is calculated as follow:

That’s all, easy huh..?

Neutron lethargy

Neutron lethargy, or logarithmic energy decrement, u, is a dimensionless logarithm of the ratio of the energy of source neutrons to the energy of neutrons after a collision:

With that definition, the neutron lethargy increases as the neutron slows down, the gain in lethargy after a collision is:

End of story!

Read more about neutron basics here (PDF)

The IRIS Reactor Technical Specifications

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.

General Plant Data
Core thermal power	1000 MWt [ref.2-page35]
Power Plant Net Output	335 MWe [ref.2-page35]
Nuclear Steam Supply System
Number of coolant loops	Integral RCS [ref.2-page35]
Steam temperature/pressure	317/5.8 °C/MPa [ref.2-page35]
Feedwater temperature/pressure	224/6.4 °C/MPa [ref.2-page35]
Reactor Coolant System
Total core flow rate	36000 kg/s [ref.3-page53]
Primary coolant flow rate	4700 kg/s [ref.2-page35]
Reactor operating pressure	15.5 MPa [ref.2-page35]
Core inlet temperature	292 °C [ref.2-page35]
Core (riser) outlet temperature	330 °C [ref.2-page35]
Reactor Core
Fuel assembly total length	5.207 m [ref.2-page35]
Fuel inventory	48.5 tU [ref.2-page35]
Average linear heat rate	10.0 kW/m [ref.2-page35]
Average core power density (volumetric)	51.26 kW/l [ref.2-page35]
Specific power (= core thermal power/fuel inventory)	20.6186 kW/kg-HM
Fuel material	Sintered UO2 [ref.2-page35] Westinghouse standard PWR fuel
Fuel average density	96% Theoretical Density [ref.3-page203] UO2-TD = 10.96 g/cc
Rod array	Square 17×17 XL [ref.2-page38,ref.5-page155]
Number of fuel assemblies	89 [ref.2-page35]
Number of fuel rods/assembly	264 [ref.2-page35]
Fuel pellet diameter	8.19 mm [ref.1-page634]
Pellet-clad gap	0.082 mm [ref.1-page634]
Clad thickness	0.572 mm [ref.1-page634]
Outer diameter of fuel rods	9.5 mm [ref.2-page35,ref.5-page155]
Pitch (center-to-center)	12.54 mm [ref.1-page634]
P/D	1.32 [ref.3-page34]
Average H/HM ratio (Hydrogen to Heavy Metal ratio)	3.4 [ref.3-page34]
Volume fractions	33.50% fuel 54.92% moderator 11.58% structure
Volume ratios	fuel-to-moderator: 0.6099 moderator-to-fuel: 1.6396
Enrichment	4.95 Wt % U-235 [ref.2-page35]
Coolant average density	0.7295 g/cc [ref.6-page31] 0.727664 g/cc (calculated from enrichment and H/HM data)
Equilibrium cycle length	30-48 months [ref.2-page35]
Average discharge burnup	60 000 MWd/tU [ref.2-page35]
Reactor Pressure Vessel
Cylindrical shell inner diameter	6.21 m [ref.2-page35]
Wall thickness of cylindrical shell	28.5 cm [ref.2-page35]
Total height (including clossure head)	22.2 m [ref.5-page154]
Active core height (core barrel)	426.7 cm [ref.5-page156]
Active core inner diameter (core barrel)	241.27 cm [ref7-page45] calculated from core thermal power, power density, and active core height
Active core outer diameter (core barrel)	285 cm [ref.5-page157]
Steam Generators
Type	Vertical, helical coil tube bundle, once-through, superheated [ref.2-page35]
Number	8 [ref.2-page35]
Thermal capacity (each SG)	125 MWt [ref.2-page35]
Number of heat exchanger tubes (each SG)	656 [ref.2-page35]
Reactor Coolant Pump
Type	Spool type, fully immersed [ref.2-page35]
Number	8 [ref.2-page35]
Pump head	19.8 m [ref.2-page35]
Primary Containment
Type	Pressure suppression, steel [ref.2-page35]
Geometry	Spherical, 25 m diameter [ref.2-page35]
Design pressure/temperature	1300/200 kPa/°C [ref.2-page35]

References

1. Duderstadt, James J. and Louis J. Hamilton. (1976), Nuclear Reactor Analysis, John Wiley & Sons, Inc, New York.
2. IRIS@NuclearNews
3. MIT Master Thesis – Thermal Hydraulic Performance Analysis of a Small Integral PWR Core
4. J-NucEngDes – Carelli – The exciting journey of designing an advanced reactor
5. J-NucEngDes – Carelli et al. – The design and safety features of the IRIS reactor
6. Data from US NRC
7. Reactor dosimetry in the 21st century

Useful links

• IRIS official website
• IRIS – 2003 FINAL TECHNICAL PROGRESS REPORT
• IRIS@wikipedia
• Water density as a function of temperature and pressure
• IRIS dimension from google books

Standard PWR nuclear fuel assembly (17×17) technical specifications

Geometry	Square 17×17 matrix
Fuel assembly dimension	Square 214 x 214 mm
Composition per assembly	Total: 289 Fuel: 264 Control rod guide thimble: 24 Instrumentation thimble: 1
Fuel material	UO2 (U235,U238,Oxygen)
Cladding material	Zircaloy-4 98.23 weight % zirconium with 1.45% tin, 0.21% iron, 0.1% chromium, and 0.01% hafnium
Gap filler	Helium gas
Fuel average density	95 – 96% Theoretical Density UO2-TD = 10.96 g/cc
Moderator (coolant)	light water (H2O) average density 0.7295 gr/cc
H/HM ratio (hydrogen to heavy metal ratio)	1.7 – 3.4 (depends on enrichment level)
Enrichment	2.5 – 5 Wt % U235
Fuel pellet diameter	8.19 mm
Pellet-clad gap	0.082 mm
Clad thickness	0.572 mm
Outer diameter of fuel rods	9.5 mm
Pitch (center-to-center)	12.54 mm
P/D	1.32

Related Links

• Data from Oak Ridge National Laboratory
• Data from KAERI Nuclear Training Center
• Data from dspace@MIT
• Data from US NRC
• Zircalloy@wikipedia
• Water density as a function of temperature and pressure

Simple 2D Computational Fluid Dynamics (CFD) code

Here is a little example of 2D Computational Fluid Dynamics (CFD), the basic equation beeing used is the non-compressible Navier-Stokes equation. The code was written in C language, originally written by Professor Takayuki Aoki, TokyoTech GSIC.

• download the code here, extract, compile and run it on UNIX/LINUX platform, make sure that gcc and ImageMagick are correctly installed on your system
• learn more about CFD from TokyoTech OCW here
• See some results in YouTube here

ENJOY!

Another Free Code From Syeilendra : Calculation of Radioactivity Inside Human Body

The core of this freeware is The Fourth Order Runge-Kutta Method (FORK) which numerically solve the coupled differential decay equations. Download nucmed.doc , rename it to nucmed.zip, then extract. As usual, this code was written in Pascal under Borland Dephi 7.

Screenshots :

Keywords : runge kutta radioactivity decay nuclear medicine

Monte Carlo Simulation Applied To Infinite Slab Problem

In this article I want to share a little knowledge about a simple Monte Carlo Method which applied to solve the infinite slab problem. The basic idea of the Monte Carlo Method as it applied to the infinite slab problem is we want to know the distribution of particles that bombarded to the slab, as the particles performing a random walk. We can simulate this phenomena if we know the required physical variables of the system, in this case, the reaction cross sections. For further explanation, first please download montecarlo1.doc , rename it to montecarlo1.zip, then extract. Inside the “montecarlo1″ folder, you can find 2 explanation files, power point slide, and a computer source code. This source code is real implementation of monte carlo model in form of software, this code was written in Pascal Language of Borland Delphi 7.

Screenshot:

Keywords : freeware delphi pascal montecarlo physics simulation

Related files:

• Short_explanation.doc
• Flow_Chart_of_Monte_Carlo_Method.doc
• montecarlo_slides.ppt

Solusi Persamaan Difusi Neutron Satu Grup Pada Geometri Bola Dengan Menggunakan Metode S.O.R

Solution of One Group Neutron Diffusion Equation in Spherical Geometry With S.O.R Method

Read the manual: doc | quickview

Pada artikel ini saya ingin berbagi ilmu mengenai teknik memecahkan persamaan difusi neutron pada geometri bola (sferis), secara numerik dengan menggunakan program komputer. Reaktor nuklir yang akan dianalisis berbentuk bola sempurna dengan radius R, dan kuantitas yang dicari adalah profil distribusi flux neutron. Pertama silahkan download file “difusibola.doc“, kemudian rename menjadi “difusibola.zip”, kemudian ekstrak. Di dalam folder “difusibola” terdapat file “penjelasan.doc” dan folder “program”. File “penjelasan.doc” berisi teori dan penjelasan singkat mengenai persamaan difusi neutron dan solusi numeriknya, sedangkan folder “program” berisi implementasi real-nya berupa source code program komputer yang saya tulis dengan menggunakan bahasa Pascal pada Borland Delphi 7. Bila anda hanya ingin menjalankan programnya saja, dobel klik file “Project1.exe”, bila anda ingin melihat script-nya, dobel klik file “Project1.dpr”.

Berikut ini screenshot-nya :

Semoga Bermanfaat!

Keywords: reaktor nuklir nuclear reactor energy physics numerics persamaan difusi diffusion equation neutron delphi pascal jacobi program bola sferis spherical

Solusi Persamaan Difusi Neutron Satu Grup-Satu Dimensi

Solution of One Group-One Dimension Neutron Diffusion Equation

Read Me: Solusi_Persamaan_Difusi_Neutron_Satu_Grup_Satu_Dimensi.doc

Pada artikel ini saya ingin berbagi ilmu mengenai teknik memecahkan persamaan difusi neutron 1 grup 1 dimensi, secara numerik dengan menggunakan program komputer. Pertama silahkan download file “difusi1g1d.doc“, kemudian rename menjadi “difusi1g1d.zip”, kemudian ekstrak. Di dalam folder “difusi1g1d” terdapat file “penjelasan.doc” dan folder “program”. File “penjelasan.doc” berisi teori dan penjelasan singkat mengenai persamaan difusi neutron dan solusi numeriknya, sedangkan folder “program” berisi implementasi real-nya berupa source code program komputer yang saya tulis dengan menggunakan bahasa Pascal pada Borland Delphi 7. Bila anda hanya ingin menjalankan programnya saja, dobel klik file “Project1.exe”, bila anda ingin melihat script-nya, dobel klik file “Project1.dpr”.

Berikut ini beberapa screenshot-nya :

Semoga Bermanfaat!

Keywords: reaktor nuklir nuclear reactor energy physics numerics persamaan difusi diffusion equation neutron delphi pascal jacobi program software freeware