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# Archive for November, 2010

## Sodium volumetric thermal expansion coefficient

Posted by Syeilendra Pramuditya on November 30, 2010

Read also this: Liquid Sodium Thermodynamic and Transport Properties

The volumetric thermal expansion coefficient of Sodium is around 0.0002 /K, it depends on temperature and pressure, and the following is a brief description.

Some Liquid Metal-cooled Fast Reactor (LMR) designs employ Sodium as coolant material in its primary heat transport system. And one of the important physical properties of Sodium used in thermal hydraulic analysis is the volumetric thermal expansion coefficient (usually denoted by the Greek letter Beta).

Beta is expressed as follow: $\beta=-\frac{1}{\rho}\frac{d\rho}{dT}$ $\beta=\textrm{Volumetric thermal expansion coefficient} [K^{-1}]$ $\rho=\textrm{Density} [kg/m^3]$ $T=\textrm{Temperature} [K]$

By using the above formula, we can now evaluate $\beta$ if we know the dependency of density on temperature. This dependency is available in form of tabular data or empirical correlations. I will use the following correlation, which I obtained from a reliable source: $\rho(P,T)=a_0+a_1T+a_2T^2+a_3T^3+a_4P$ $\frac{\partial \rho(P,T)}{\partial T}=a_1+2a_2T+3a_3T^2$ $\beta=-\frac{1}{\rho}\frac{d\rho}{dT} =-\frac{a_1+2a_2T+3a_3T^2}{a_0+a_1T+a_2T^2+a_3T^3+a_4P}$ $a_0=1011.597$ $a_1=-0.22051$ $a_2=-1.92243\times 10^{-5}$ $a_3=5.63769\times 10^{-9}$ $a_4=2.26\times 10^{-7}$

So by using the above empirical formula, now you can easily evaluate the value of $\beta$ at any “valid” temperature and pressure.

As an example, here is the plot of $\beta$ as a function of temperature, keeping the pressure constant at 101325 Pa (equal to 1 atm): We can see that the relation between $\beta$ and temperature “looks” linear, so for pressure value of 1 atm, $\beta$ can be approximated by the following simplified equation: $\beta(T,P = 1~atm)= 2.135\times 10^{-4} + 9.77\times 10^{-8} T$

So how accurate this formula is?

Well, Wikipedia says that the relation between volumetric and linear thermal expansion coefficient can be approximated as $\beta \simeq 3\alpha$, and this link and this link say that the linear coefficient is around $7\times 10^{-5}$, which implies that the volumetric coefficient should be around 3 times of that value, or about $0.00021~K^{-1}$. And this link says that the value is $0.000226~K^{-1}$.

So the above formula is quite good, I think.

Posted in nuclear engineering | Tagged: , , | 3 Comments »

## [SOLVED] Installing PGPLOT on Mandriva 2010

Posted by Syeilendra Pramuditya on November 29, 2010

I just finished the installation of PGPLOT on my UNIX machine, my operating system is Mandriva 2010. I followed the installation instruction described here.

But when I tried to run the sample code by the following command:

[user@machine pgplot] $./pgdemo1 I got the following error message: ./pgdemo1: error while loading shared libraries: libpgplot.so: cannot open shared object file: No such file or directory After googling around for a while, I found the solution. So find a file named “.bashrc” in your home directory (/home/yourusername), and open it, add the following lines at the end of the file: LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/usr/local/pgplot
export LD_LIBRARY_PATH

In case you don’t have the .bashrc file, just create one then, and put the following lines into it:

# .bashrc

# User specific aliases and functions

# Source global definitions
if [ -f /etc/bashrc ]; then
. /etc/bashrc
fi

LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/usr/local/pgplot export LD_LIBRARY_PATH When I tried to run the sample code again: [user@machine pgplot]$ ./pgdemo1

Graphics device/type (? to see list, default /NULL): /GIF
version=v5.2.2
state=OPEN
user=psyeilendra
now=29-Nov-2010 10:04
device=pgplot.gif
file=pgplot.gif
type=GIF
dev/type=pgplot.gif/GIF
hardcopy=YES
terminal=NO
cursor=NO
Plot dimensions (x,y; inches):      9.99,      7.99
(mm):    253.70,    202.90
%PGPLOT, Writing new GIF image as: pgplot.gif_2
%PGPLOT, Writing new GIF image as: pgplot.gif_3
%PGPLOT, Writing new GIF image as: pgplot.gif_4
%PGPLOT, Writing new GIF image as: pgplot.gif_5
%PGPLOT, Writing new GIF image as: pgplot.gif_6
%PGPLOT, Writing new GIF image as: pgplot.gif_7
%PGPLOT, Writing new GIF image as: pgplot.gif_8
%PGPLOT, Writing new GIF image as: pgplot.gif_9
%PGPLOT, Writing new GIF image as: pgplot.gif_10
%PGPLOT, Writing new GIF image as: pgplot.gif_11
%PGPLOT, Writing new GIF image as: pgplot.gif_12
%PGPLOT, Writing new GIF image as: pgplot.gif_13
%PGPLOT, Writing new GIF image as: pgplot.gif_14

It works well now, and here is one sample result, generated as a GIF image:

I also tried to compile a Fortran sample code:

Source code (rename to pgsample.f)

which calls some PGPLOT functions, then I compiled it by the following command:

[user@machine pgplot] $g77 -fno-backslash -lpgplot -o pgsample.exe pgsample.f [user@machine pgplot]$ ./pgsample.exe

It works well too, it generates a GIF image file named “pgplot.gif”:

A complete explanation of available PGPLOT functions can be found here.

Posted in whatever | Tagged: , , | 1 Comment »

## Lah.. kemana belanjaan gw??

Posted by Syeilendra Pramuditya on November 27, 2010

Ck ck ck.. kasihan juga liat kulkas saya yang nyaris tidak ada isinya, jadilah tadi siang saya pergi ke toko dekat kos2an untuk belanja..

Setelah selesai membeli beberapa bahan masakan, sy pergi ke sebuah supermarket (namanya OLYMPIC) untuk membeli beberapa barang lainnya, n sepeda sy taruh d tempat parkir sepeda..

Karena bakal repot juga kalo belanjaan sy bawa masuk, jd ya sy tinggal saja itu belanjaan d keranjang sepeda.. setau sy disini memang sudah biasa seperti itu, sy sering liat sepeda2 d tempat parkir keranjang nya penuh dgn belanjaan.. yaa aman laah, Jepang gt loh hehe..

Sekitar sentengah jam kemudian saya keluar dan segera menuju tempat parkir sepeda, hmmh??? lah koq keranjang sepeda saya sudah kosong blong! blas semua isinya lenyap! belanjaan kuuuuu!!

Ya ampuuun masa d sini ada maling seh?!? yang justru bikin heran ya barang2 yg dicolong itu, isinya kan cuma bahan2 makanan yg bs dibilang g seberapa harganya, cuma sayur, minyak, snack, dll, total hanya sekitar 500 yen-an, setara dengan harga satu porsi makan siang, belanjaan itu dibungkus plastik tipis warna putih, jadi isinya ya kelihatan lumayan jelas dari luar, ck ck ck pasti tu maling lagi kelaparan.. kasihan.. hmm.. orang mana dia ya..

Ternyata d negeri makmur seperti ini ada ajaa orang2 bermental maling.. emang dimanapun ga boleh lengah kynya..

Alhamdulillah.. yg hilang hanya barang2 yg tidak seberapa harganya..

*hmm.. penasaran jg itu maling orang Jepang or orang asing ya.. kynya g mungkin orang Jepang deh.. hmm..

Posted in just a story | 3 Comments »