Solusi Persamaan Difusi 1 Group 2 Dimensi R-z
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Transcript of Solusi Persamaan Difusi 1 Group 2 Dimensi R-z
![Page 1: Solusi Persamaan Difusi 1 Group 2 Dimensi R-z](https://reader037.fdocument.pub/reader037/viewer/2022102813/546686f4b4af9fa5108b4672/html5/thumbnails/1.jpg)
Zaki Su’ud
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Persamaan Difusi 1 group)()(
1)()()()(. rrk
rrrrD feff
![Page 3: Solusi Persamaan Difusi 1 Group 2 Dimensi R-z](https://reader037.fdocument.pub/reader037/viewer/2022102813/546686f4b4af9fa5108b4672/html5/thumbnails/3.jpg)
Integralkan terhadap mesh (i,j)
ijijfeff
jijijia
ji
f
ji eff
ji
a
ji
Vk
VAdrrD
dVrrk
dVrrdVrrD
ij
1).()(
)()(1
)()()()(.
,,,,
,
,
,,
![Page 4: Solusi Persamaan Difusi 1 Group 2 Dimensi R-z](https://reader037.fdocument.pub/reader037/viewer/2022102813/546686f4b4af9fa5108b4672/html5/thumbnails/4.jpg)
Suku difusi
2/11
,,12/1
2/12/1
2/1
2/1
2/12/1
2/12/1,
).()(
).()().()(
).()().()().()(
iii
jijii
ii
i
i
jj
iiji
Arr
D
Adr
dDAdrrD
AdrrDAdrrD
AdrrDAdrrDAdrrD
![Page 5: Solusi Persamaan Difusi 1 Group 2 Dimensi R-z](https://reader037.fdocument.pub/reader037/viewer/2022102813/546686f4b4af9fa5108b4672/html5/thumbnails/5.jpg)
Suku difusi
2/1,1
,1,2/1,
2/12/1
2/1,
2/1
2/11
,1,2/1
2/12/1
2/1
2/1
).()(
).()(
jijj
jijiji
jj
ji
j
iii
jijii
ii
i
i
Azz
D
Adz
dDAdrrD
Arr
D
Adr
dDAdrrD
![Page 6: Solusi Persamaan Difusi 1 Group 2 Dimensi R-z](https://reader037.fdocument.pub/reader037/viewer/2022102813/546686f4b4af9fa5108b4672/html5/thumbnails/6.jpg)
Suku Difusi
2/1,1
1,,2/1,
2/12/1
2/1,
2/1
).()(
jijj
jijiji
jj
ji
j
Azz
D
Adz
dDAdrrD
![Page 7: Solusi Persamaan Difusi 1 Group 2 Dimensi R-z](https://reader037.fdocument.pub/reader037/viewer/2022102813/546686f4b4af9fa5108b4672/html5/thumbnails/7.jpg)
Persamaan Difusi yang telah didiskritisasikan
ijijfeff
jijijia Vk
Vij
1 ,,,,
2/1
1
,,12/1i
ii
jijii Arr
D
2/1,1
,1,2/1,2/1
1
,1,2/1
jijj
jijijii
ii
jijii Azz
DArr
D
2/1,1
1,,2/1,
jijj
jijiji Azz
D
![Page 8: Solusi Persamaan Difusi 1 Group 2 Dimensi R-z](https://reader037.fdocument.pub/reader037/viewer/2022102813/546686f4b4af9fa5108b4672/html5/thumbnails/8.jpg)
Persamaan Difusi yang telah didiskritisasikan
ijjiijjiijijijjiijjiij
ijijfeffjj
jiii
ji
jijiaiijjii
jjij
iiji
jjji
S
Vkzzrr
Vrrzzrr
zzrrzz
ij
1,1,1,11,
1/2ji,1
1/2ji,
1,j1/2,i1
j1/2,i
,1
,,,j1/2,i1
j1/2,-i
1/2ji,1
1/2ji,
j1/2,i1
j1/2,i
1/2ji,1
1/2ji,
j1/2,i1
j1/2,-i
,11/2-ji,1
1/2ji,
1,
1)A
D(-)A
D(-
) AD
AD
AD
AD
()AD
(-)AD
(-
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Syarat Batas
0)71,02/,(
0)71,02/,(
0
0),71,0(
0
tr
tr
r
tr
Hr
Hr
dr
d
zR
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Terapkan syarat batas i=1 , j bebas,
jjjjjjjjjj
jj
jjjjjjjjjjj
S
S
11,111,211111,11
,1,0
11,111,2111,011,11
)(
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Terapkan syarat batas(lanjutan)
IjjIIjIjIjjIIjjIIj
jI
IjjIIjjIIjIjIjjIIjjIIj
S
S
1,1,11,
,1
1,1,1,11,
0
bebas j , (max.)Ii
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Terapkan syarat batas(lanjutan)
1,1,11,
0,
12,21,11111,110,1
0
,1
iJiiJiJiJJiiJJiiJ
i
iiiiiiiiiii
S
S
bebasij
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Terapkan syarat batas(lanjutan)
1,1,11,
1,
11,1,1,11,
0
,1
iJiiJiJiJJiiJJiiJ
Ji
iJiiJJiiJiJiJJiiJJiiJ
S
S
bebasiJj
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Bentuk persamaan Matriks
- -
- -
-
- -
,,JI,
,1,,
2,11,21,2
1,11,21,1
JIJI
jijijiA
SA
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Fluks dan Sumber
JI
ji
JI
ji
S
S
S
S
,
,
1,2
1,1
,
,
1,2
1,1
S
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Algoritma Untuk Eigen Value1. Tebak harga fluks awal dan keff awal
2. Hitung Vektor Sumber 3. Cari fluks baru dari AΦ=S4. Hitung Sumber Fisi baru
5. Hitung Keff baru: keffm+1= keff
m(Fm+1/Fm)
ji
mjijfi
mF,
1,,
1
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Algoritma6. Cek konfergensi keff
7. Cek konfergensi fluks8. Bila belum konfergen kembali ke 29. Normalisasi fluks dengan power
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ANALISA BURNUP
B Decay +n
+n decay
C
A
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Cg
gC
gBBAg
gAagAA
A NNNNdt
dN
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Analisa Burnuphilang karena peluruhan radioaktif A
hilang karena tangkapan neutron oleh A
masuk karena peluruhan dari B ke A
masuk karena perpindahan dari C ke A melalui
tangkapan neutron
AAN
Ag
gAag N
BBN
Cg
gCcg N
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Analisa BurnupPersamaan burnup merupakan persamaan
differensial orde 1 terkopel dan biasanya dipecahkan bergantian dengan persamaan difusi.
Fluks netron dari hasil difusi digunakan untuk melakukan analisa burnup, selanjutnya perubahan komposisi akibat persamaan burnup pada gilirannya perlu dimasukkan dalam perhitungan kembali konstanta-konstanta difusi, penampang lintang reaksi, dsb.