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Jarayonning mikrokinetikasi
2A—^—>3B -*2 >C
Aniqlanadi:
g * , g * , g R , A q R ,
S
a
‘-2
0 '
S
h
—
-3
k lx A
i
3
—
a”.
0
1
~ 2k>
XA
3
+3 k2xl
k 2 X H
g R = a r
g*A=~
2-r,
g S = 3 _-r:l - 3 •
rang(u)=
2
2 ta hal qiluvchi^ va V komponentalami tanlaymiz
„
r
_ '
r
1
gc
^ S
h
Muhim
munosabat:
bo‘lmagan
5
komponenta
uchun
stexiometrik
XC
=
X C } ~ \ ( X A ~
^0))-
\ (X B -
4°’)
V
= i \ z Pil - A H Pi
) - r y = 3 ( A
HBl)-r{
+ l ( - A
HC
2)-r2
Jarayonning matematik tavsifi (to‘g‘ri oqim).
i i \
A
^ » //
dx
a
Vr> p x
a
dv
L 1 ) xA - ^ + v - j 7 = - r g A ^ - j r = - f g A
— “-3 7
de
dt
] 2 )
- V
r
r l(
X
r
d v
d£
v dt
de
v L '
v de
2 9 8
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i.3) % =*<(o)~ ( * , - 4
o
)) 4 ( * «
2 .1 ) ^ = - 2
t
,
2.2) g* = 3 -r ,-3 -r
2
2.3) g «= r
2
3.1) r, = ktx2
A
3.2) r
2 = Ar2x^
4.1) &, = Axexp(- EJRT)
A.2) k2 = A
2 exp(- E2/R T)
5 > £ 4 f a :
at
L
6
)
dl
CpL
dT
V„
=>
de
vCpL
C„L
. «
L- . •/■ r afv
vC„L
v
dl
7) A? /;= 3 (-A //„)rl + (-A7/a )r
8) AqT = K T{Tr - T )
9) Cp =C%xA+C%xB+C%xc
10.1) Cj£ =aA+bAT + cAT
2
+dAr
10.2)
C %
=att + bBT +
c b
T 2
+ d BT
3
10.3) C“ = ar + &c;r +
+ dJ
2
Issiqlik tashuvchilarning oqimlari uchun tenglama:
11 \
<
Hj- - —!i
__L
a
qT}
’ dt
CPf LvT v
9 ’
n
+3 differensial tenglama.
Itnshlang‘ich shart:
(1 l') .r,(0) = x^0)
(12) x„(
0) = x f
(*)') \'(()) v(<))
((>') 'I (()) 7,(0)
2 9 9
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i
(ir) rr(o)=rr(0)
Kompyutyerda xususiy yechimni aniqlash uchun Koshi masa-
lasi yoki boshlang'ich shartli masala yechiladi - «o‘rin almashish -
urin almashish» issiqlik almashish apparatiga qarang (to‘g‘ri oqim).
3 0 0
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A x b o ro t m a trits a s i (to ‘g ‘r i oqim )
I " ' ' 1
v >
S(V
*r«)
rtm
n
d
4 /
4 /
*<0)
•O)
J‘
r,rc
N "
1
©
0
©
14
8
v >
©
©
©
4
©
7
5
5 *
•
q j *
i
T3
5 * .:
1 2
6 *
1
§
©
©
I I
\ p
1 5
7
1 0
8
fiS i)
©
9
9
©
♦
©
11
10*
9
$
6
1 1 *
©
©
< $ >
1 6
i )
4
< S >
< $ >
1
5 f
4 *
1
2
6
4
3
1 1
5
i
4
Hisoblash algoritmining blok-sxemasi (to‘g‘ri oqim)
Jarayonning matematik tavsifi (tcskari oqim).
Ideal o ‘rin almashish modelining komponentli balansi:
1
_
dv
dxA
dxA
V„
dv
dx.
VR R
X .
¥ V —
= — g A
4 d (
d i
L A
' R »
x , dv
~ d i~ w L 8 A ~ 7 d e
1
.
2
)
d*tt
d t
V,
L
dv
"d£
3 0 1
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1.3)
2
.
1
)
2
.
2
)
2.3)
3.1)
3.2)
4.1)
4.2)
5)
6
)
£
a
~
~
2
' r i
S
b
~ ^ ' r\ ~ 3 ' r2
'
l
= k \X A
r 2 = k 2X l
kx = Ax exp(- Ex / RT)
k
7 = A2 exp(- E2 / RT)
HP
L
d{vT)_
di
dT
=^> --- =
dt
t e + g t + g ? )
^ AaR +
■
Aa
1 =>
CPL ‘
CpL ■
~ ^ L -A a R +-El—Aar -
vCpL ■
vCpL ‘
L
V
dv
~di
7)
8
)
9)
AqR =3{-AHBX)rx+{-AHC{)r
2
AqT = K r {TT - T )
c = c
in d
x j + c ^ x ^ + c ; 11-
'
P
“
P
a
_ r
P
b
" r
P c
X
C
10.1) C >
n
p; = a A+ bAT +
ca
T
2 + dAT*
10.2) C ;; =aB +bBT + cBT
2 +dBT3
10.3) C £ =ac + bcT + ccT
2 + dc T3
Issiqlik tashuvchilaming oqimi uchun tenglama:
dL—
H - ( - A q T)
11
)
d t
CPr
L
vt
n+3 differensial tenglama, to‘g‘ri oqim bilan solishtirilganda
faqat (11) tenglama o ‘zgaradi.
BoshlangMch shartlar tizimi:
{I.V)X
a
{0) = 4 }
0-20
= &
(5') v(0) = v(o)
(6’)
T(0) = T(o)
3 0 2
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(ll') Tr (0) = Tp]
Kompyuterda xususiy yechimni aniqlash uchun chegara shartli
chegaraviy masala yechiladi - «o4rin almashish - o‘rin almashish»
issiqlik apparatiga qarang (teskari oqim).
Boshlang‘ich yaqinlashish:
fr (o)
Tenglamada chegaraviy shart quyidagi kattalikka aylantiriiadi:
7>(0), ya’ni kirishga issiqlik tashuvchi haroratining kattaliklari.
3 0 3
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A x b o ro t m a trits a s i (te s k a ri o q im )
-
v n
*.|TO
*(-) n«)
7<£) A jr
c .
«<0)
%
>vm
N ‘
H
n
: :
@
n
1
©
i§U
14
E 3
8
9
©
©
7
K ,
♦
t g i
5
5*
13
5-]
©
12
6"
1
b
©
©
< i l
15
7
“ 1 “ J
10
8
$
<0>
E 0
9
9
€
i
©
11
io»
©
6
ll*
n
|f|
< P
*
16
t
.) ♦
1
5'
i
*
2
6?
4
3
i r
|___
1
i
©
4
Hisoblash algoritmining blok-sxemasi (teskari oqim)
r(fl
M
tl)
Tr (e
= o)=> r r (o)
11’) tenglamaning yechimi:
3 0 4
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f u, = TT(L){T
7(0)}-'I<0) = 0
5.I.5.2. Nostatsionar rejimdagi quvurli reaktorlar
-(o)(0
x
0(t)
xr\[) \
£ = 0
£ = L
A - ± - + P
Asosiy qo‘yimIar:
Izotemiik rejim;
Bir parametrli diffuziyali model.
Matematik tavsifning tenglamasi:
V* dx _ P V R d2x
dx
R
L d t ~ L dl2 Vd£+ A{<)
* =
=
G*W
=T gA = ' V = S'W
I) ^ = D d
- \ - W ^
dt
d l
2
dl
-kx
1)
tenglama ikki mustaqil o ‘zgaruvchi t va e ga ega parabolik
tipdagi ikkinchi tartibli xususiy hosilali differensial tenglama
hisoblanadi va agar oqim uchun bir parametrli diffuziyali model
qabul qilingan bo'lsa, yagona oddiy reaksiya oqib o'tuvchi
reaktorning nostatsionar rejimini tavsiflaydi.
Topish lozim:
x = x(t,£)
t{0)
O ^ l Z L
Boshlang‘ich shart:
l') x(t{
0),e)= x{0)(i), o z e z L
Chegaraviy shart:
3 0 5
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\x(t,L) = x,(t)
Xususiy hosilalarda differensial tenglamalar tizimi (XHDTT) ni
yechish uchun hosilasi ma’lum [/(0),/<*)J va/yoki [0, L\ intervaldagi
chekli - farqli shaklda namoyon boMuvchi diskretlashtirish usulidan
foydalanish mumkin, natijada
1’) va 1” ) chegara shartli 1)
tengiama chekli tenglamalar tizimi (CHTT) dagi va/yoki oddiy
differensial tenglamalar tizimi (ODTT) ga aylanib qoladi.
Bu tenglamalar uchun diskretlashtirishning uchta variantdan
foydalanish mumkin:
1) £ mustaqil o ‘zgaruvchi bo‘yicha:
dx z XM ~ Xi
d£
A£
i
Natijada t mustaqil o‘zgaruvchili 1 - tartibli oddiy differensial
tenglamalar tizimi olinadi.
2) Mustaqil t o ‘zgaruvchi bo‘yicha:
d x „ x j + i ~ x j
dt ~
A£
j =
\,...m —
1
Natijada £ mustaqil o‘zgaruvchili 2 - tartibli oddiy differensial
tenglamalar tizimi olinadi.
3) £ va t mustaqil o ‘zgaruvchilar bo‘yicha:
&
z
x M
~
x i
d£
A£
i = \,...n-\
dx __x J+i- X j
dt ~
A£
j
= l,...m — 1
Natijada chekli tenglamalar tizimi olinadi.
Mustaqil o ‘zgaruvchi bo‘yicha diskretlashtirishning 1 - varian-
tini batafsil ko‘rib chiqamiz:
r = 0
t = L
|,
■ ■ ■ -■ ■ ■ - ■"
» ■ »H i
/7 = 0
1
2
"
/ 3 - 2 w - I
n
0 <£ da hosilalaming chekli - ayirmali keltirilishi quyidagi
ko‘rinishga ega:
3 0 6
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- « K a m c h i l i k l a r b o ‘y i c h a » h o s i l a :
dx:
~dt
- x
f-Af
M
- «Ortiqchalik bo‘yicha» hosila:
dx,
x,^ - x,
~
•*■/-+1
dt
M
- Ikkinchi hosila:
d
2x _ dl
_dx,
l'+M:
dP I'-Af
xi+1 2x, + X(_|
de:
—
M
M
Ushbu holda 1 ” ) chegaraviy shart quyidagiga teng:
*M ) = x0(/) = x0
x(t,L) = xL(t) = xn
Natijada xususiy hosilalarda tenglamalardan birini diskret-
lashtirish oqibatida t mustaqil o‘zgaruvchili va 1’) boshlang'ich
shartli, quyidagi diskret ko'rinishga keltirilgan oddiy differensial
tenglamalarning ( n - 1) tizimi olinadi:
/ = 1,...«-1
Agar chekli - ayirmali keltirishlarda «ortiqchalik bo‘yicha
hosila» hosilasidan foydalanilsa, unda boshlang'ich shartli oddiy
differensial tenglamalar tizimi quyidagi ko‘rinishga ega boiadi:
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