My first LaTeX equation!

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

Sungguh saat2 yg bersejarah.. hihihi…

Persamaan apa hayo..??

Helium density in pellet-clad gap of nuclear fuel rod

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

Are you really sure that you wanna enroll in a Ph.D program..?!?!?

Source: http://www.cs.purdue.edu/homes/dec/essay.phd.html

The Basics

A Doctor of Philosophy degree, abbreviated Ph.D., is the highest academic degree anyone can earn. Because earning a Ph.D. requires extended study and intense intellectual effort, less than one percent of the population attains the degree. Society shows respect for a person who holds a Ph.D. by addressing them with the title “Doctor”.

To earn a Ph.D., one must accomplish two things. First, one must master a specific subject completely. Second, one must extend the body of knowledge about that subject.

Mastering A Subject

To master a subject, a student searches the published literature to find and read everything that has been written about the subject. In scientific disciplines, a student begins by studying general reference works such as text books. Eventually, the student must also search scholarly journals, the publications that scientists use to exchange information and record reports of their scientific investigations.

Each university establishes general guidelines that a student must follow to earn a Ph.D. degree, and each college or department within a university sets specific standards by which it measures mastery of a subject. Usually, in preparing for Ph.D. work in a given field, a student must earn both a Bachelor’s and Master’s degree (or their equivalent) in that field or in a closely related field. To demonstrate complete mastery of the subject, a student may be required to complete additional graduate-level courses, maintain a high grade average, or take a battery of special examinations. In many institutions, students must do all three.

Because examinations given as part of a Ph.D. curriculum assess expert knowledge, they are created and evaluated by a committee of experts, each of whom holds a Ph.D. degree.

Extending Knowledge

The essence of a Ph.D., the aspect that distinguishes Ph.D. study from other academic work, can be summarized in a single word: research. To extend knowledge, one must explore, investigate, and contemplate. The scientific community uses the term research to capture the idea.

In scientific disciplines, research often implies experimentation, but research is more than mere experiments — it means interpretation and deep understanding. For Computer Scientists, research means searching to uncover the principles that underlie digital computation and communication. A researcher must discover new techniques that aid in building or using computational mechanisms. Researchers look for new abstractions, new approaches, new algorithms, new principles, or new mechanisms.

To complete a Ph.D., each student must present results from their research to the faculty in a lengthy, formal document called a dissertation (more popularly referred to as a thesis). The student must then submit their dissertation to the faculty and defend their work an oral examination.

Relationship To Products

In some cases, the results of scientific research can be used to develop new products or improve those that exist. However, scientists do not use commercial success or potential commercial profits as a measure of their work; they conduct investigations to further human understanding and the body of knowledge humans have compiled. Often, the commercial benefits of scientific research are much greater in the long-term than in the short-term.

Research Activities

Computer Science research can include such diverse activities as designing and building new computer systems, proving mathematical theorems, writing computer software, measuring the performance of a computer system, using analytical tools to assess a design, or studying the errors programmers make as they build a large software system. Because a researcher chooses the activities appropriate to answer each question that arises in a research investigation, and because new questions arise as an investigation proceeds, research activities vary from project to project and over time in a single project. A researcher must be prepared to use a variety of approaches and tools.

A Few Questions To Ask

Many of you are trying to decide whether to pursue a Ph.D. degree. Here are a few questions you might ask yourself.

1. Do you want a research career?

Before enrolling in a Ph.D. program, you should carefully consider your long-term goals. Because earning a Ph.D. is training for research, you should ask yourself whether a research position is your long-term goal. If it is, a Ph.D. degree is the standard path to your chosen career (a few people have managed to obtain a research position without a Ph.D., but they are the exception, not the rule). If, however, you want a non-research career, a Ph.D. is definitely not for you.

2. Do you want an academic position?

A Ph.D. is the de facto “union card” for an academic position. Although it is possible to obtain an academic position without a Ph.D., the chances are low. Major universities (and most colleges) require each member of their faculty to hold a Ph.D. and to engage in research activities. Why? To insure that the faculty have sufficient expertise to teach advanced courses and to force faculty to remain current in their chosen field. The U.S. State Department diplomatic protocol ranks the title “professor” higher than the title “doctor”. It does so in recognition of academic requirements: most professors hold a Ph.D., but not all people who hold a Ph.D. degree are professors.

3. Do you have what it takes?

It is difficult for an individual to assess their own capabilities. The following guidelines and questions may be of help.

Intelligence:

In your college and graduate courses, were you closer to the top of your class or the bottom? How well did you do on the GRE or other standardized tests?

Time:

Are you prepared to tackle a project larger than any you have undertaken before? You must commit to multiple years of hard work. Are you willing to reduce or forego other activities?

Creativity:

Research discoveries often arise when one looks at old facts in a new way. Do you shine when solving problems? Do you like “brain teasers” and similar puzzles? Are you good at solving them? In school, did you find advanced mathematics enjoyable or difficult?

Intense curiosity:

Have you always been compelled to understand the world around you and to find out how things work? A natural curiosity makes research easier. Did you fulfill minimum requirements or explore further on your own?

Adaptability:

Most students are unprepared for Ph.D. study. They find it unexpectedly different than course work. Suddenly thrust into a world in which no one knows the answers, students sometimes flounder. Can you adapt to new ways of thinking? Can you tolerate searching for answers even when no one knows the precise questions?

Self-motivation:

By the time a student finishes an undergraduate education, they have become accustomed to receiving grades for each course each semester. In a Ph.D. program, work is not divided neatly into separate courses, professors do not partition tasks into little assignments, and the student does not receive a grade for each small step. Are you self-motivated enough to keep working toward a goal without day-to-day encouragement?

Competitiveness:

If you choose to enroll in a Ph.D. program, you will compete with others at the top. More important, once you graduate, your peers will include some of the brightest people in the world. You will be measured and judged in comparison to them. Are you willing to compete at the Ph.D. level?

Maturity:

Compared to coursework, which is carefully planned by a teacher, Ph.D. study has less structure. You will have more freedom to set your own goals, determine your daily schedule, and follow interesting ideas. Are you prepared to accept the responsibility that accompanies the additional freedoms? Your success or failure in Ph.D. research depends on it.

A few warnings:

Students sometimes enroll in a Ph.D. program for the wrong reasons. After a while, such students find that the requirements overwhelm them. Before starting one should realize that a Ph.D. is not:

Prestigious in itself

Almost everyone who has obtained a Ph.D. is proud of their efforts and the result. However, you should understand that once you graduate, you will work among a group of scientists who each hold a Ph.D. degree. (One faculty member used to chide arrogant graduate students by saying, “I don’t see why you think it’s such a great accomplishment — all my friends have a Ph.D!”).

A guarantee of respect for all your opinions

Many students believe that once they earn a Ph.D. people will automatically respect all their opinions. You will learn, however, that few people assume a Ph.D. in one subject automatically makes you an authority on others. It is especially true in the science communicaty; respect must be earned.

A goal in itself

A Ph.D. degree prepares you for research. If all you want is a diploma to hang on the wall, there are much easier ways to obtain one. After you graduate, you will have occasion to compare your record of accomplishment to those of other scientists. You will realize that what counts is the research work accumulated after a scientist finishes their formal education.

A job guarantee

When an economy slows, everyone can suffer. In fact, some companies reduce research before they reduce production, making Ph.D.s especially vulnerable. Furthermore, once a person earns a Ph.D., many companies will not hire that person for a non-research position. As in most professions, continued employment depends on continued performance.

A practical way to impress your family or friends

Your mother may be proud and excited when you enroll in a Ph.D. program. After all, she imagines that she will soon be able to brag about her child, “the doctor.” However, a desire to impress others is insufficient motivation for the effort required.

Something you can “try” to find out how smart you are

Sorry, but it just doesn’t work that way. Unless you make a total commitment, you will fail. You will need to work long hours, face many disappointments, stretch your mental capabilities, and learn to find order among apparently chaotic facts. Unless you have adopted the long-range goal of becoming a researcher, the day-to-day demands will wear you down. Standards will seem unnecessary high; rigor will seem unwarranted. If you only consider it a test, you will eventually walk away.

The only research topic you will ever pursue

Many students make the mistake of viewing their Ph.D. topic as a research area for life. They assume each researcher only works in one area, always pursues the same topic within that area, and always uses the same tools and approaches. Experienced researchers know that new questions arise constantly, and that old questions can become less interesting as time passes or new facts are discovered. The best people change topics and areas. It keeps them fresh and stimulates thinking. Plan to move on; prepare for change.

Easier than entering the work force

You will find that the path to successful completion of a Ph.D. becomes much steeper after you begin. The faculty impose constraints on your study, and do not permit unproductive students to remain in the program.

Better than the alternatives

For many students, a Ph.D. can be a curse. They must choose between being at the top among people who hold a Masters degree or being a mediocre researcher. The faculty sometimes advise students that they must choose between being “captain of the B team” or a “benchwarmer” on the A team. Everyone must decide what they want, and which profession will stimulate them most. But students should be realistic about their capabilities. If you really cannot determine where you stand, ask faculty members.

A way to make more money

While we haven’t heard any statistics for the past couple of years, graduate students used to estimate the “payoff” using the starting salaries of Ph.D. and M.S. positions, the average time required to obtain a Ph.D., the value of stock options, and current return on investments. For a period of at least five years that we know, the payoff was clearly negative. Suffice it to say that one must choose research because one loves it; a Ph.D. is not the optimum road to wealth.

The good news:

Despite all our warnings, we are proud that we earned Ph.D. degrees and proud of our research accomplishments. If you have the capability and interest, a research career can bring rewards unequaled in any other profession. You will meet and work with some of the brightest people on the planet. You will reach for ideas beyond your grasp, and in so doing extend your intellectual capabilities. You will solve problems that have not been solved before. You will explore concepts that have not been explored. You will uncover principles that change the way people use computers.

The joy of research:

A colleague summed up the way many researchers feel about their profession. When asked why he spent so many hours in the lab, he noted that the alternatives were to go home, where he would do the same things that millions of others were doing, or to work in his lab, where he could discover things that no other human had ever discovered. The smile on his face told the story: for him, working on research was sheer joy.

Source: http://twofish.wordpress.com/2006/07/26/becoming-a-phd

What does being a Ph.D. mean?  People aren’t Ph.D.’s assume that it’s just a like a masters or undergraduate degree, where you go through the factory assembly line and come out at the other end with a piece of paper that gets you some money and prizes.

But that’s not the case.  You don’t *get* a Ph.D., you *become* a Ph.D.  If you have a Ph.D., it’s not a statement about a piece of paper or certification, it’s a statement about who you are, what you have seen, and how you look at the world.  The certification really doesn’t matter much.  My degree is almost useless as a ticket for money and prizes, but it is a statement about who I am and what I’ve seen.  If you want to erase my degree, go ahead, I don’t think it matters that much.

Being a Ph.D. affects all of my relationships.  It affected who I married, and what my children are like.  I can’t separate my “work life” or my “school life” from my “personal life.”  As you can see, being a Ph.D. affects my feeling toward other people, and it’s part of my marriage.  My wife is a Ph.D. candidate in early childhood education.  An essential part of our marriage involves professional collaboration and respect.  I learn about educational theory from her.  She uses me as a peer briefer to look over her data.  We’ve created more together than children, we’ve created some new insights as to how the world works.  (See next year when her dissertation comes out.)  The professional collaboration I have with my wife is part of our love, it’s part of our marriage, it’s part of how we are, and it’s something that people on the outside of academia don’t quite understand.

Let me give you an example of how bizarre my world might seem to someone who isn’t living in it.  Right now I’m studying the dynamics of volatility smiles.  I’m getting any grades or certifications from this.  I’m not taking any formal courses.  I’m just reading and learning.  Now the stuff I’m reading is also stuff that MFE’s can read, but suppose some were to tell me that the obstensible purpose for what I’m reading is “useless.”  In other words, someone tells me that I’m destined not to have a job on Wall Street.

I….  wouldn’t…. care……

If it turns out that it is *impossible* for me to make any money on what I’m studying.  I’d still study it about as hard.  Because it is interesting.  It’s cool math.  It challenges my mind.  It makes me a better person when I understand how foreign exchange volatility smiles work.  And in my life, the important thing isn’t destination, it’s the journey.  When I think I understand something, my first reaction is to go and find something new that I don’t understand.  When I seem to have mastered a skill, I go and find something I’m incompetent at.
None of that has anything to do with whether or not I become a quant or not, and it’s really hard to explain to headhunters and HR people.

Source: http://www.lysator.liu.se/~matca/phd

The cost of a PhD

There is a cost to everything and the PhD is no exception. I experienced a slipped disc and associated loss of nerve function. Two years later (2000), I still haven’t gotten all of it back. For those who do a lot of programming, it is common with neck and shoulder problems. Of course, staring at a monitor for eight hours a day (or more, much more), will not be good for your eye sight. Then you have the problem that being a PhD is more of a lifestyle than a job; you mix work and free time in such a way that you end up having only work. This is not good, as it leads to higher stress. High stress levels during prolonged time will have such effects as reducing your empatic ability, make you develop depressions, diabetes, etc. I’ve experienced all of those.

My advice to PhD students

Learn to say ‘NO!’.

It is very important that you are able to set limits on your work load, because nobody else will. For example, when you meet your professor one evening and he says ‘There is a conference you should attend. The deadline for an extended abstract of 600 words is at 2400 tonight.’ you have the right to say ‘There is no possibility that I can meet that deadline.’ – and you should.

Working hours

Keep a strict tally of how many hours you work and when. Outside the university, some computer consulting companies have made a point of 6 hours a day. When you find out that you are working 60 hours a week, stop. In the university world, your time is free at no cost to others; from my experience the university do not care if you burn out.

Vacation

Really do take your vacation. Some PhD students, including me, claimed to take vacation but just kept on working. It is essential for your health to have a change and relax.

Avoid the ‘Grad student algorithm’.

This is an expression from the days of fractal coding of images. It means that you take a picture, a workstation and a grad student and lock them into a room until the job is done. It is the repetitive nature of the task which is really annoying; you are a highly talented and skilled person and you should not be doing “manual” labour.

Stay fit!

You only have one body and it must last you a lifetime. As a PhD, you will most probably work long hours, live under stress, spend too much time at a keyboard, etc. Then you need physical exercise or you will end up a wreck. Spend some time investigating what a slipped disk and diabetes, really means.

Insist on a decent workplace

You need a desk that can be raised so you can work standing up at times. The best working position is usually your next – keep it dynamic and don’t get stuck. You need a personalised chair, too. The left-over from the last inhabitant will most certainly not fit your body.

Run yourself.

Your supervisor will provide some guidance, but you need to be the main force behind your work. You will have to take the initiatives and keep the project moving forward.

Stay focused

It is very easy to get sidetracked – and it is hard to say what is really a sidetrack and what is a fruitful investigation, especially in advance.

So..?!?!?

A Romantic Nuclear Storiette…

Neutronic Study of the Medium Size Integral PWR 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

Nominal reload strategy	Two-batch
Number of fresh FAs	40–45
Actual number of batches	1.98–2.22
FAs with 4.95% 235U enrichment	40–45
FAs with reduced 235U enrichment	-
Cycle length (Years)	3.0–3.5
Average discharge burnup (MWd/tU)	48–53,000
Lead rod average burnup (MWd/tU)	< 62,000

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

No.	EU (eV)	EL (eV)	Group type
1	1E+7	6.74E+4	Fast
2	6.74E+4	130	ResolvedResonance
3	130	2.38	Unresolved Resonance
4	2.38	1E-5	Thermal

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

Pitch (mm)	P/D	k-inf
10	1.05285	1.137346
11	1.15814	1.269726
12	1.26342	1.358791
12.54	1.32028	1.395168
14	1.47399	1.462823
16	1.68457	1.505699
18	1.89514	1.515622
20	2.10571	1.504098
25	2.63213	1.423757
30	3.15856	1.30966
32	3.36913	1.260744
34	3.5797	1.211802

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.

A good research topic in nuclear engineering

Kemarin sensei saya ngasih semacam special lecture utk anak2 lab nya, n disela2 lecturenya beliau sempat cerita tentang sebuah unsolved problem in nuclear engineering. Jadi gini, untuk menaikan daya reaktor kan dilakukan dengan cara positive reactivity insertion, alias control rods withdrawal, once the desired power level has achieved, the operator will stop the control rods withdrawal, and it is expected that the power increase will promptly stop, so that the reactor becomes steady again. But in actual operation, that’s not happen! the power increase continues for about 4-5 days, why??? my sensei said that, up to now, belum ada orang yang berhasil menjelaskan fenomena ini secara saintifik dan memuaskan, beliau bilang belum ada yg benar2 paham about the physics behind this phenomena. Nah, makanya klo ada yang iseng mo nyoba2 memecahkan teka-teki ini, dijamin deh, kerjaan ente bakal jadi paper n masuk jurnal internasional! Oia tp buruan, karena saat ini, fenomena ini sedang diteliti jg oleh salah satu student sensei saya yg saat ini sedang internship di Westinghouse Electric Company, LLC, USA, jd harus buruan, jgn sampe keduluan ma dia tu!!

Ada yg berminat kah???

Calculation code for nuclear cross section

Code package:

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

Calculation code for spherical nuclear reactor

The geometry of the reactor is spherical:

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:

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

AccessPlus: payah…

hhhh…. kartu accessplus di hp ngadat lagi… udah 2 kali kejadian kaya gini nih.. temen2 ada yg pake accessplus juga ga utk nelp ke Indonesia?? aneh betul.. bahkan nada panggilnya pun kaga ada bro?!? padahal pulsa masih 1600 yen, lumayan kan, tp pas di cek pulsa terus berkurang tiap kali ane coba nelp!! padahal kan ga nyambung?!? ini juga pake accessplus juga lg kepaksa, saldo di skype tinggal 6 yen..

karena kesel juga ya akhirnya sy nelp lah ke acplus.. yg nerima mba2.. eh pas diangkat malah dia ikutan ngomel2.. katanya “oh iya tu mas.. acplus emang suka gitu tu.. error emang.. mas ada kartu lain ga?” sy jawab ya ga ada, trus dia bilang lagi “iya mas, walaupun saya di acplus, tp sy klo nelp jg pake kartu lain..” nah loh?!? tobat.. tobat… bukannya ngasih solusi or penjelasan.. eh malah dia nyuruh ganti kartu aje…. yahh.. gimane si, masa karyawan perusahaan begitu ye…. aneh2 aje emang….

Neutronic Study of the Medium Size Integral PWR Core

Cell Calculation
The fuel assembly design is similar to the Westinghouse 17×17 XL Robust Fuel Assembly design and AP1000 fuel assembly design[Ref.3]. Cell homogenization calculation to get the group constants is carried out by using SRAC code. Once we have the group constants, then k-eff for a single calculational cell can be calculated as follow,

Where for finite cylinder, the geometrical buckling is formulated as,

The neutron energy is divided into 4 groups, and because this is a thermal reactor, so I arranged it as 1 fast group and 3 thermal groups, shown in the table below,

Energy Group Structure

Fast 1	1.00000E+07 – 2.38240E+00 eV
Thermal 1	2.38240E+00 – 4.13990E-01 eV
Thermal 2	4.13990E-01 – 1.09630E-01 eV
Thermal 3	1.09630E-01 – 1.00000E-05 eV

Some results of cell calculation are as follow.

Figures below depict k-eff for a single calculational cell under geometrical buckling 4.51658E-4 cm^-2

Core Calculation
The summary of the reference design is shown below[Ref.4],

Reference Design

Nominal reload strategy	Two-batch (partial reload)
Number of fresh fuel assemblies	40–45
Actual number of batches	1.98–2.22
Fuel assemblies with 4.95% 235U enrichment	40–45
Fuel assemblies with reduced 235U enrichment	-
Cycle length (Years)	3.0–3.5
Average discharge burnup (MWd/tU)	48–53,000
Lead rod average burnup (MWd/tU)	< 62,000

And here is the schematic cross sectional view of the reactor core^[Ref.3]:

For SRAC-CITATION calculation purpose, the core geometry is approximated as multi-region concentric cylinders, as follow,

Core geometrical approximation for SRAC-CITATION calculation

The reference core employs two-batch partial reload, which means that at the end of each cycle (3 – 3.5 years), about half of the fuel assemblies (40 – 45 FAs) are replaced with fresh fuels. By employing such reloading strategy in a 3 year cycle, the result is shown in the figure below,

The in-core power distribution of cycles after the first cycle depends on the fuel reloading pattern, which means the positioning strategy for fresh FAs. One possible option is to divide the active core radially into 2 equi-volume regions, and then replace the FAs in the outer region with fresh FAs, as illustrated in the figure below,

For the reloading pattern as explained above, the in-core power distributions are as follow,

Or another option is to divide the active core radially into 4 equi-volume regions, as illustrated in the following figure,

In that case, the power profile will become as follow,

References

1. Duderstadt, James J. and Louis J. Hamilton. (1976), Nuclear Reactor Analysis, John Wiley & Sons, Inc, New York.
2. Carelli, 2003 M.D. Carelli, IRIS, a global approach to nuclear power renaissance, Nuclear News 46 (10) (2003), pp. 32–42.
3. Carelli et al., 2004 M.D. Carelli et al., The design and safety features of the IRIS reactor, Nuclear Engineering and Design 230 (2004), pp. 151–167.
4. Carelli, 2009 M.D. Carelli, The exciting journey of designing an advanced reactor, Nuclear Engineering and Design 239 (2009), pp. 880–887.

Akhir pekan yang sungguh indah!

huff.. cape juga.. gila banget weekend kali ini, hari jumat kmarin sensei bilang klo sy hrs submit report, sy bilang “iya sensei, sy submit deh, tp minggu depan ya..” eh sensei malah bilang “wah hari senin sy ga ke lab, tp sy bsk sabtu ke lab, kamu ke lab kaga?” waduh.. masa sy mau bilang engga, jadilah sy bilang “i.. iya sensei, sy k lab deh besok..” hmpff pdhal hrsnya sabtu kan libur.. jadilah besoknya sy k lab, sepii.. but wait, trnyata sensei udah dtg duluan! buset dah, jd ga enak.. ^_^’ jadilah sy bertapa d lab dan saling beradu pandang mesra dengan layar LCD 17 inci.. hikz.. T_T

akhirnya malam pun tiba.. n sy tunggu biar sensei pulang duluan, biar sopan maksudnya.. n akhirnya sampailah jam 9 mlm, n sensei blum menunjukan tanda mau pulang!! and then I gave up.. sy pulang duluan aja dah.. gudbay sensei..

n sampailah sy d dorm, trus dinner, liat berita d metro tv n sctv, dll dll.. n then jam 12 malam datanglah email itu, email dr sensei! beliau br pulang jam 12 mlm! masalahnya itu kan mlm minggu! senseiku yg hebat.. luar biasa… beliau bilang klo beliau mau ngasih sebuah dokumen utk sy, n nanya mau dtg ga hari minggu bsk, buset lg.. brarti sensei hr minggu pun ke lab dong yah….. hhh.. sy bilang “kaga deh sensei.. punten yah..”

krn hrs kejar setoran, jadilah hr ini sy mahasiswa yg rajin.. seharian ngerjain tugas.. sampe ga sempet mandi.. hiiihh jijay… ngapain siy yg gt aja diceritain ke seluruh dunia coba…

Alhamdulillah.. tugasnya bisa selesai “on time”, dgn hati masih dagdigdug sy tekan tombol send d browser sy tepat jam 21.55, only 5 minutes to the deadline…  hasilnya?? i don’t know.. smoga aja sensei cukup hepi dgn report sy…. huff.. ngantuk…

what.. a.. beautiful.. week.. endhh……….

FIN

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 on the link below:

Calculating_Number_Density.pdf

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..?

Silabus Kuliah Fisika FMIPA ITB

Saya heran juga, kenapa sampai saat ini (2009/5/4) di website resmi fisika itb ko ga ada silabus kuliah nya ya?? padahal kan itu termasuk penting banget, bahkan di internet kayanya ga ada loh silabus kuliah fisika itb, udah saya coba google berkali2, tetep ga ktemu2! aneh..

Jadi barangkali ada yang kebetulan lagi nyari, silahkan download di link berikut (versi ini udah agak jadul):

Silabus_Kuliah_Fisika_FMIPA_ITB.pdf

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)

Medium Size Integral PWR Technical Specifications

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 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

Useful links

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