QC QC ()labo4/www/thesis-top.files/12_m/li.pdf · qQQQQQQ=( , ,, ,, )T 01 02 10 20 12 21 kV dC dt...
4
t s C i i m /m V i i m m i i m /s Q ij i j m /s i N j N N δ ij Kronecker ij i j i S i V i i ji j ij j N ij i ij j N dC dt QC QC = − ( ) { } ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ − − ( ) { } ⎡ ⎣ ⎢ ⎤ ⎦ = = ∑ ∑ 1 1 0 0 δ δ ⎥ + m i S Q Q i ji ij j N ij ij j N = − ( ) = − ( ) = = ∑ ∑ 1 1 0 0 δ δ
Transcript of QC QC ()labo4/www/thesis-top.files/12_m/li.pdf · qQQQQQQ=( , ,, ,, )T 01 02 10 20 12 21 kV dC dt...
t s Ci i m /m Vii m mi i
m /s Qij i j m /si N j N
N δij Kroneckeri j i j
i Si
Vii
ji j ijj
N
ij i ijj
NdCdt
Q C Q C= −( ){ }⎡
⎣⎢
⎤
⎦⎥ − −( ){ }⎡
⎣⎢
⎤
⎦= =∑ ∑1 1
0 0δ δ ⎥⎥ +mi
S Q Qi ji ijj
N
ij ijj
N
= −( ) = −( )= =
∑ ∑1 10 0
δ δ
t m /m Δts Δt= s
Q21
q Q Q Q Q Q Q T= ( , , , , , )01 02 10 20 12 21
k V dCdt
m V dCdt
m V dCdt
m V dCdt
m T= + + + +( , , , , , , )0 0 11
1 22
2 11
1 22
2
cC C C C
C C C CC C C C
C
=
− −− −
− −− −
− −
1 0 1 0 1 10 1 0 1 1 1
0 00 0
0 00 0
0 1 1 2
0 2 1 2
0 1 1 2
0 −− −
⎡
⎣
⎢⎢⎢⎢⎢⎢⎢⎢
⎤
⎦
⎥⎥⎥⎥⎥⎥⎥⎥C C C2 1 2
cx k=
x c k= −1
C V C Viti i
t ti ji j
t tij
j
N
ij it t
ijQ C Q C= + −( )⎧⎨⎩
⎫⎬⎭
− −(− −
=
−∑∆ ∆ ∆1 10
δ δ ))⎧⎨⎩
⎫⎬⎭
+⎡
⎣⎢⎢
⎤
⎦⎥⎥=
∑j
N
im t0
∆
Cit
Fig.1 2-Zone Airfl ow Model
Q01
Q10
Q12 Q20
Q02
V1= m
C1m1
V2= m
C2m2
Table3 Gas Injection Pattern [m /s]
Table1 True Ventilation Rates [m /s]
Table2 Initial Concentation [ppm]
0%
5%
10%
15%
20%
25%
0 1 2 3 4 5
0%
5%
10%
15%
20%
25%
0 1 2 3 4 5
0%
5%
10%
15%
20%
25%
0 1 2 3 4 5
0%
5%
10%
15%
20%
25%
0 1 2 3 4 5
0%
5%
10%
15%
20%
25%
0 1 2 3 4 5
0%
5%
10%
15%
20%
25%
0 1 2 3 4 5
0%
5%
10%
15%
20%
25%
0 1 2 3 4 5
0%
5%
10%
15%
20%
25%
0 1 2 3 4 5
T=10
T=20
T=30
T=40
T=50
T=60
0%
5%
10%
15%
20%
25%
0 1 2 3 4 5
0%
5%
10%
15%
20%
25%
0 1 2 3 4 5
0%
5%
10%
15%
20%
25%
0 1 2 3 4 5
0%
5%
10%
15%
20%
25%
0 1 2 3 4 5
0%
5%
10%
15%
20%
25%
0 1 2 3 4 5
0%
5%
10%
15%
20%
25%
0 1 2 3 4 50%
5%
10%
15%
20%
25%
0 1 2 3 4 5
0%
5%
10%
15%
20%
25%
0 1 2 3 4 5
T=10
T=20
T=30
T=40
T=50
T=60
erro
r rat
ion
of
vent
ilatio
n ra
te
initi
al c
once
ntra
tion
patte
rn A
Fig.2 Error Ratio of Ventilation Rate with Concentration Decay Method
erro
r rat
ion
of
vent
ilatio
n ra
te
erro
r rat
ion
of
vent
ilatio
n ra
te
initi
al c
once
ntra
tion
patte
rn B
initi
al c
once
ntra
tion
patte
rn C
ventilation rate pattern 1 ventilation rate pattern 2 ventilation rate pattern 3
Inje
ctio
n pa
ttern①
Inje
ctio
n pa
ttern
②In
ject
ion
patte
rn ③
Fig.3 Error Ratio of Ventilation Rate with Constant Injection Method
0%
5%
10%
15%
20%
25%
0 1 2 3 4 50%
5%
10%
15%
20%
25%
0 1 2 3 4 50%
5%
10%
15%
20%
25%
0 1 2 3 4 50%
5%
10%
15%
20%
25%
0 1 2 3 4 5
erro
r rat
ion
of
vent
ilatio
n ra
te
Fig.4 Error Ratio of Ventilation Rate with Concentration Decay Method and Constant Injection Methodconcentration error [ppm]concentration error [ppm]concentration error [ppm] concentration error [ppm]
No Inverse
Matrix
concentration error [ppm]concentration error [ppm]concentration error [ppm]
No Inverse
Matrix
erro
r rat
ion
of
vent
ilatio
n ra
te
erro
r rat
ion
of
vent
ilatio
n ra
te
erro
r rat
ion
of
vent
ilatio
n ra
te
ventilation rate pattern 1 ventilation rate pattern 2 ventilation rate pattern 3
concentration error [ppm]concentration error [ppm]concentration error [ppm]
0
200
400
600
800
1000
1200
0 50 100 150 200 250 300 350 4000
200
400
600
800
1000
1200
0 50 100 150 200 250 300 350 4000
200
400
600
800
1000
1200
0 50 100 150 200 250 300 350 4000
200
400
600
800
1000
1200
0 50 100 150 200 250 300 350 400
0%
5%
10%
15%
20%
25%
0 1 2 3 4 50%
5%
10%
15%
20%
25%
0 1 2 3 4 50%
5%
10%
15%
20%
25%
0 1 2 3 4 50%
5%
10%
15%
20%
25%
0 1 2 3 4 5
erro
r rat
io o
f
vent
ilatio
n ra
te
concentration
[ppm]
time [s] time [s] time [s]time [s]
concentration error [ppm] concentration error [ppm] concentration error [ppm] concentration error [ppm]
Fig.5 Concentration Sampling Time and Ventilation Error Ratio in CaseA-2
t1=1/2n=100st2=1/n=200s
C1
C2
t1=50st2=100s
t1=200s t2=250s
t1=50s
t2=250s
T=10 T=20 T=30 T=40 T=50 T=60
0
100
200
300
400
500
600
700
800
900
1000
0 50 100 150 200 250 300 350 4000
100
200
300
400
500
600
700
800
900
1000
0 50 100 150 200 250 300 350 4000
100
200
300
400
500
600
700
800
900
1000
0 50 100 150 200 250 300 350 4000
100
200
300
400
500
600
700
800
900
1000
0 50 100 150 200 250 300 350 400
0%
5%
10%
15%
20%
25%
0 1 2 3 4 50%
5%
10%
15%
20%
25%
0 1 2 3 4 50%
5%
10%
15%
20%
25%
0 1 2 3 4 50%
5%
10%
15%
20%
25%
0 1 2 3 4 5
erro
r rat
io o
f
vent
ilatio
n ra
te
concentration
[ppm]
time [s] time [s] time [s]time [s]
concentration error [ppm] concentration error [ppm] concentration error [ppm] concentration error [ppm]
Fig.6 Concentration Sampling Time and Ventilation Error Ratio in Case① -2
T=10 T=20 T=30 T=40 T=50 T=60
t1=1/2n=100st2=1/n=200s
C2
C1
t1=50st2=100s
t1=200s t2=250s
t1=50s
t2=250s
