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Inquiri田 ab倒 1availab面ityof the repons sh凶 Idbe addr間宮dto Infonniluon Di:吋自由
Departmenl of Technic:aI Infonnauon, Japan Atomic: En町IYRes国n:hInstitute, Tokai.
mwa. Naka春日1,lbaraki.ken 319・11,Jap回.
。Japan.-¥'omic Ene噌恥出町hInslilule. 1鵬
編集量産発行 日本様子力僻究所
印 刷 いばらき 印刷側
JAER1-M 92-160
Flow Network Calculation Code for Heat, Mass and Momentum Transfer in A Multicomponent Gas Mixture Flow with Graphite Chemical Reactions
Hualining JC , Masurou OGAWA and Makoto HISH1DA
Department of High Temperature Engineering Tokai Research Establishment
Japan Atomic Energy Research Institute Tokai-EKira, Naka-gun, Ibaraki-ken
(Received October 2, 1992)
A flow network calculation code was developed to predict the thermo-hydraulic characteristics during a primary-cooling-pipe rupture accident in a high temperature gas cooled reactor such as the High Temperature Engineering Test Reactor (HTTR). The present calculation code deals with a natural convection of a multicomponent gas mixture (helium, nitrogen, oxygen, carbon monoxide and carbon dioxide) with graphite chemical reactions. One dimensional conservation equations of mass, momentum and energy for the gas mixture and equations of mass for gas species were solved by using a flow network model in the code. The calculation was performed for a flow channel system of an experimental apparatus simply simulating the cooling channels of the HTTR. The whole configuration of the flow channel is a reverse U shape, and the one vertical side of the reverse U shape consists of three parallel channels. Two of these channels are graphite ones. The entering flow rate, flow rates distributed to the parallel channels, generation volume of carbon monoxide and corrosion volume of the graphite could be calculated by the code.
Keywords: High Temperature Gas Cooled Reactor, Numerical Analysis, Flow Network Model, Reverse-U Shaped Flow Channel, Gas Mixture, Graphite Chemical Reactions, Pipe Rupture Accident
* Institute of Nuclear Energy Technology, Tsinghua University
I
JAERl-~ 92-1610
f1o~ ~.ett.rork Calculatiol!U Code for Heat. Mass aod Moment:um Transfer
io A Hult:icomponent Gas Mixt:ure Flow
留ithGraphite Chemdcal Reactions
会
Huaiming J~ • Masurou OGAVA and Makoto HISHIDA
Departlltent of High Temperature Engineering
Tokai Research Establisnment
Japan Atomic Energy Research Institute
Tokai-mura. Naka-伊 n.Ibaraki-ken
(Received October 2. 1992)
A flow network calculation code was developed to predict: t:he t:hermo-
hydraulic characteristics during a primary-cooling-pipe rupture accident
in a high temperature gas cooled reactor such as the Hlgh Temperature
Engineering Test Reactor (日τTR). The present calculatlon code deals with
a natural convection of a multicomponent: gas mixture (helium. nitrogen.
oxygen. carbon monoxide and carbon dioxide)留itbgraphite chemical reac-
tions. One dimensional cODservation equatioDs of mass. momentum and
energy for the gas回ixtureand equations of mass for gas species were
solved by using a flow network model in the code. The calculatlon was
performed for a flow channel system of an experimental apparatus simply
simulating the cooling channels of the HTTR.τhe whole configuration of
the flow channel is a reverse U shape. and the one vertical side of the
reverse U shape consists of three parallel channels. Two of these chan-
nels are graphite ones. 1be entering flow rate. flow rates distributed to
the parallel channels. generation volume of carbon monoxide and corrosion
volume of the graphite could oe calculated by the code.
Keywords: High Temperature Gas Cooled Reactor, Numerical Analysis, Flo日Network Model, Reverse-U Shaped Flow Channel. Gas Mixture.
Graphite Chemical Reactions, Pipe Rupture Accident
* Institute of Nuclear Energy Technology. Tsinghua University
JAERI-M 92-160
<IS92^I0lj2n-Sil)
^6Jc >iM:'?xlf* c-3?*. 65*, ' v ' ^ i . ~Stft*££\ :*.&(&&,£> 0>fE.**.£M£i5-5. ft/itf)
1. Introduction ................................................... 1 2. Nomenclature ................................................... 2 3. Numerical Analysis 3 3.1 Basic Equation 3 3.2 Flow Network Model 5 3.3 Algebraic Equation 7 3.4 Correlations of Heat and Mass Transfers and Pressure Loss ... 9 3.5 Rate of Chemical Reaction 11 3.6 Average Value in Branch 13 3.7 Initial and Boundary Conditions ............................. 13
4. Results and Discussion 15 5. Concluding Remarks 16 References 16 Appendix Computer Program 33
Japan Atomic Energy Research Institute (JAERI) is building the High Temperature Engineering Test Reactor(*) (HTTR) at Oarai Research Establishment. The HTTR is a high temperature gas cooled reactor with thermal output of 30MW and outlet coolant temperature of 950°C, employing the pin-in-block type fuel, and has the capability to demonstrate nuclear process heat utilization using an intermediate heat exchanger.
A primary pipe rupture accident is one of the most critical (important) design-base accident of the HTTR. The accident starts from a guillotine break of the primary coaxial double pipe in the primary cooling system as shown in Fig. 1. When the primary pipe rupture takes place, a gas mixture containing oxygen enters the inside of the reactor vessel (RV) through the breach of the inner pipe from the reactor containment vessel (RCV), and the oxygen reacts with high temperature graphite. The graphite chemical reactions may cause corrosion of graphite, temperature rise and generation of inflammable gas; carbon monoxide. It has already been assured by extensive safety analysis and evaluation under the conservative assumption that no serious damages are caused to the reactor core and the RCV during and after the accident^2).
On the other hand, it is of great importance to know the real phenomena of the accident in order to understand the safety characteristics of the HTTR and in order to carry out a safety design with higher accuracy. In the analysis of the accident of the HTTR, the TAC-KC computer code was used to analyze the thermohydraulic characteristics and the GRACE computer code was used to analyze the graphite oxidation < 3>. Thus, the thermohydraulics and the graphite corrosion were separately calculated by using the TAC-NC code and GRACE code, respectively. The assumptions were considerably conservative in the analysis. For example, it was assumed that only the reaction; C + •= O2 •* CO was taken into account as the chemical reaction of the graphite oxidation and no combustion of carbon monoxide was considered.
Accordingly, we developed a flow network calculation code to deal with heat, mass and momentum transfer with homogeneous (carbon monoxide combustion) and heterogeneous (graphite oxidation and Boudouard reaction) chemical reactions. The entering flow rate of the gas mixture, the corrosion volume of graphite and the generation volume of carbon monoxide were calculated in the code.
1
j.:-¥ERI-~1 ~~-Iω
1. lntroduction
Japan Atomic Energy Researcb Institute (JAERI) is building the Higb
Temperature Engineering Test Reactor(n) (H1TR) at Oarai Research Estab-
lishment. The HTTR is a high temperature gas cooled reactor with thermal
output of 30HW and outlet coolant temperature of 950・C.employing the
pin-in-block type fuel. and has the capability to demonstrate nuclear
process heat utilization using an intermediate heat exchanger.
A primary pipe rupture accident is one of the most critical (impor-
tant) design-base accident of the HTTR. The accident starts from a guil-
lotine break of the pr王国rycoaxial double pipe in the primaη cooling
system as shown in Fig. 1. When the primary pipe rupture takes place. a
gas mixture containing oxygen enters the inside of the reactor vessel
(RV) through the breach of the inner pipe from the reactor containment
vessel (RCV). and the oxygen reacts with high temperature graphite. The
graphite chemical reactions may cause corrosion of graphite. temperature
rise and generation of inflammable gas; carbon monoxide. lt has already
been assured by extensive safety analysis and evaluation under the con-
servative assumption that no serious damages are caused to the reactor
core and the RCV during and after the accident(2).
On the other hand. it is of great importance to know the real phe-
nomena of the accident in order to understand the safety characteristics
of the HTTR and in order to carry out a safety design with higher accu-
racy. In the analysis of the accident of the HTTR. the TAC-NC computer
code was used to analyze the thermohydraulic characteristics and the
GRACE computer code was used to analyze the graphite oxidation(りThus.
the thermohydraulics and the graphite corrosion were separately calcu-
lated by using the TAC-NC code and GRACE code. respectively. The assump-
tions町'ereconsiderably conservative in the analysis. For example. it l
was assumed that only the reaction; C + ~ 02 .. CO was taken into accollnt
as the chemical r~action of the graphite 0瓦idationand no combustion of
carbon monoxide was considered.
Accord~ngly. we developed a flow network calculation code to deal
with heat, mass and momentum transfer with homogeneous (carbon monoxide
combllstion) and heterogeneous (graphite oxidation and Boudouard reaction)
chemical reactions. The entering flow rate of the gas mixture, the cor-
rosion volume of graphite and the generation volume of carbon monoxide
were calclllated in the code.
JAEK1 M 92 «fa"»
2. Nomenclature
A : Coefficient of Eq.(3.15) B : Coefficient of Eq.(3.I5) Cp : Specific heat at constant pressure Da : Damkohler number d|( : Tube diameter of k th branch dp : Tube diameter of reference branch f : Friction factor f : Generation ratio of carbon monoxide mole fraction to carbon
dioxide one G : Flow rate (=pU) g : Gravitational acceleration (=9.807) k + : Chemical reaction rate constant M : Molecular weight m : Solid/gas chemical reaction rate (=mass flux) N'u : Nusselt number P : Dimensionless pressure p : Pressure Pr : Prandtl number Q : Generation heat due to carbon monoxide combustion R : Gas/gas chemical reaction rate Re : Reynolds number R„ : Gas constant (=8.314) Sc : Schmidt number Sh : Sherwood number T : Temperature TJJ : Absolute temperature t : Time V : Dimensionless velocity u : Velocity AV : Volume of node X : Dimensionless axial distance x : Axial distance Ax : Length of branch
Jレ-¥!::f{! :¥1 併せ ntiゆ
2. Xomenclature
A Coefficient of Eq.(3.15)
B Coefficient of Eq.(3.i5)
cp Specific heat at constant pressure
Da Oamk,δhler number
dk Tube diameter of k th branch
dO Tube diameter of reference branch
f Friction factor
f Generation ratio of carbon monoxide mole fraction to carbon
dioxide one
G Flow rate (~pU)
g Gravitational acceleration (:9.8U7)
k+ Chemical reaction rate constant
~I Molecular weight
m Solid/gas chemical reaction rate (=mass fl蹴}
Nu Nusselt number
P Di四ensionlesspressure
p Pressure
Pr Prandtl nu田ber
Q Generaticn heat due to carbon monoxide c白血bustion
R Gas/gas chemical reaction rate
Re Reynolds number
Rg Gas constant (=8.3J4)
Sc Schmidt number
Sh Sherwood number
T Te田perature
TK Absolute temperature
t Time
l' Oimensionless velocity
u Velocity
OV Volume of node
X Oimensionless axial distance
x Axial distance
Ox Length of branch
'} u
JAERI-M 92 160
Suffix b : Bulk C : Graphite i : Gas species j : The number of the node k : The number of the branch n : The number of the time step w : Wall 0 : Reference (Inlet or Atmosphere)
Greeks a : Heat transfer coefficient 8 • Mass transfer coefficient Ek : = dk' d0 n : Pressure loss coefficient 0 : Dimensionless temperature 6 : Angle of branch from gravitational direction \ : Thermal conductivity p : Density T : Dimensionless time v : Kinematic viscosity ui : Mass fraction
Here, all units used are the International System of Units (SI units).
3. Numerical Analysis
3.1 Basic Equation
One-dimensional transient equations of mass, momentum and energy conservation for a gas mixture are as follows:
i£ + JL 3t 3x
(3.1)
3u , 3u 3p ,4 , 1 _ ,.p I ul . . ,_ .. P "37 + p u 3x" = ' 3x " (d^ f + S| V^ u + P8 c o s e k ' ".2)
P ^ (cpT) + u (cpT) = S ka(T w - T) + Q, (3.3)
3
jt¥民間 ~1 92 ~ 1ω
Suffix
Bu1k
Graphite
Gas species
The number of the node
b
C
i
-τJLU品 The nu図berof the branch
The nu回berof the time step
Wall
n
百
Reference (1n1et or Atmosphere) o
Greeks
Heat transfer coefficient
'L'E.
n
n
e
e
---Z
E
C
---Z
S
A
g
-
A
F
I
f
e
e
o
o
c
c
r
s
e
s
,E
o
s-
n
a
e
r
r
t
o
u
d
s
s
a
J
E
s
k
e
a
d
r
M
H
Z
P
A
.,
....
K
E
a
B
Dimension1ess temperature
Ang1e of branch from gravitational direction
Thermal conductivity
n
。e
Density
Dimension1ess time
λ
p
T
Kinematic viscosity
Here, a11 units used are the 1nternational System of Units (S1 units).
Mass frac::tion
、Jw
Numerical Analysis 3.
Basic Equation 3.1
One-dimensional transient equations of mass, momentum and energy
conservation for a gas mixture are as fol1o日s:
(3.1) <lp • <l 瓦+五 (pu) = Sk mc'
(3.2)
(3.3)
bk
nu s
o
c
g
nv +
u
山一2
、.20
・“nH1
やゐ向"“-x
'A-AU
+
p
,
•. -L民
zu『-JU
,.、
U 去旬。 Ska{Tw-T) + Q,
3 ~
Dιx
qo
司、。u一x句。町、。u
nv +
u-t
ヘOTO
nv
ρ ー主 (CnT) + <lt '~p
JAHKI M 92 WW
here, k represents the number of the branch.
" di, A S k = : r - S - = f- . (3.4)
Ideal gas is assumed. The density of the gas mixture is given as:
* - R ^ • < 3- 5>
A one-dimensional transient equation of mass conservation for each gas species is in the following;
P — + cu —— = St pEfiuj,. - nit + Rj . (3.6)
The gas mixture in the accident may consist of five gas species; helium, oxygen, carbon monoxide, carbon dioxide and nitrogen. In the above equations, i=l, 2, 3, 4 and 5 show helium, oxygen, carbon monoxide, carbon dioxide and nitrogen, respectively.
We convert above equations to dimensionless ones by the following normalization:
X = — A ' d 0 d_k
A x k
c k = -p , V (3.7) d r
u ji\o g dz ' U = u^ * ( u ° =V p c ' i p = P o ~ p^in> [
G = D U ,
P ' , . 9 P 0 2 . (p' = p - Pa« -57 = POS cose k) J. (3.8)
PO u 0
T
t 1 " I E -
"0 j
4
帥
Utu -'¥1 犯止¥ERD
here, k represents the number of the branch.
Sb 'dK4. 一一一民 ・・..1.2 dk-1; ok
(3.4)
1he density of tbe gas mixture 1s given as: ldeal gas 1s assumed.
ロ}1ρ=一ー一
Rg Tk (3.5)
A one-dimensional transient equation of mass conservation for each g2S
species is in the following;
σω3~~
Dτf+cuτず'"5k pEi¥ι"'1 -wi> + I¥i ・ (3.6)
The gas mixture in the accident may consist of five gas species; helium.
oxygen, carbon monoxide, carbon dioxide and n主trogen. 1n the above equa-
tions, 1=1, 2, 3, 4 and 5 show heliu.古. oxygen, carbon monoxide, carbon
dioxide and nitrogen. respectil.'el}'.
1イeconvert above equations to dimensionless ones by the fol10町ing
normalization:
、x x =一千
dO'
dk
Ek 石' (3.1) L
均一九VA
IU , fr印 Ed 7} 一一 . ~uG .;一一一了一, ~p Po - ~min) Uo Pi;
G 口合u,
i)po p 一之二一i • (p' P -PO'τ;z pog cos"k) 。oUo
(3.8)
ノ
1
内 Ti:: ;;ァーー一 ,
"max
E 1: ーァー .
旦♀
Uo
JAEKI- M 92-16U
Da.
Dai
Re =
Pr =
Sc<
Xu =
4m c j t Po u 0 ejt
d c Eti
PO "0
d 0 U(j
v 0
PO C P0 v 0 Ao
vo D H e / i
a d 0
($i dg 1 ~ % e 7 i '
do Q
Shj =
Q* = PO u 0 cpO Tmax
PO ~ P « flpt = - cose k , > 5 k PO - Pinin
* 0
c * = . 2 . p cPo
J
(3.9)
The above normalization derives dimensionless equations from Eqs.O.l)-
(3.3), and (3.6);
^P . 3 , * t . \ r. TT + 3X ( p L ) " D a » C
8U 3U 3P °k p*IUl p'"-r- + p i » • ? £ * - • ? £ - (*f • T - 5 - 2 nc) , U + Ap6
*i 4 Sh
(3.10)
(3.11)
p * *_ ( C p * s ) + p*v £ ( C p * 9 ) = ± j f i j (0W - 9) + Q* (3.12)
P* ^rr + P*D - ^ =-r- B , -„ P*(u„, - ^i) + D 3 l U - 1 - 5) (3.!T
3.2 Flow Network Model
We can solve the differential equations of Eqs.(3.10)-(3.13) by using the finite difference method. However, much memory capacity and calculation time are necessary when the calculation is executed for the cooling channel system of the HTTR because of many cooling channels. Therefore a one-dimensional flow network model is applied to the problem. One cooling channel can be expressed by using a branch and the branch is connected to other branches at node in the flow network model. No distributions of variables are considered in the node, that is, the node is assumed as a point without volume. Thus, we can easily describe the complicated cooling channel system with these branches and nodes.
In the branch, we can obtain basic equations of momentum and energy
5
、l1lil-lili--apl
.Il:¥ERI ~I 9'.!-iW
D-・1
dτI
-e
h一旬
・1hu
Da.. 4mC ー一一司 C PO u(I E:k
Q会 doQ =
伺
P!I UO CpIJ 且max‘,
・1-E
R-u
phニハピ
d-P
一-4A
a
nu
(3.9) ρ。-1> flpt.ー一一一一-COS6", . 民1>0- P1I!in
Re一生 U()- , ¥10
,
内
u-uv-
nu-P一日
C
一Anv-
nur『
=
r
p
・p会 ρ
一一 , Pal
cf=三p-l' C
Pil
SC< _ V()
Ci 耳石i
I¥u = a dO =ーλo
The above normalization derives dimensionless equations from Eqs.(3.1)ー
(3.3), and (3.6);
(3.10) dp:l:. d , * -ー+~:. (p 00(;) Da ... aτ <lX ,~-, --W,
女 au 会<lU ilP dk ~ ,p会IUIPT+P U E王=ー五ー (4fト五五 E町正}τ主EU+APK (3.11)
(3.12)
(1 • 1 -5) (3.!~ ,
ρ*去勺:1:G) +ρ*U会(C/l3)会£もzf~畠。)+ Q企
安 dU.i 会,()c.;i 4 Shi 会
♂ ττ+山吉=τEEEZ P寓(Wwi-ωi) ... Dai
Flow Network ~Iodel
We can solve the differential equations of Eqs.(3.10)ー(3.13)by
using the finite difference method. However, much memory capacity and
calculation time are necessary when the calculation is executed for the
cooling channel system of the HTTR because of many coo11ng channels.
Therefore a one-dimensional flow network model is applied to the problem.
One cooling channel can be expressed by using a branch and the branch is
connected to other branches at node in the flow network model.
3.2
No dis-
tributions of variables are considered in the node, that is, the node is assumed as a point without volume. Thus, we can easily describe the
complicated cooling channel system with these branches and nodes.
In the branch, we can obtain basic equations of momentum and energy
5
JAKKI XI X tb"»
conservation for the gas nixture and of nass conservation for each gas species by integrating Eqs.t3.ll) to (3-E3) from the inlet of the branch to the outlet in tne X axis direction.
< W x " f-x = «*W tS + J C P * ) " - U*)"+!} ^ (3.14)
px - px+£x = A k G k + 3».
!«-kl „ £X A k - (4 fiXf + Z r J 5 + — j. (3.15) i
£>K+ix P x "
{(c p* C ) s + i ! C - (c p* C) s}G k (3.16)
r k Re Pr
+ U c p * C>» - (c p 3) n + 1l ^ ^
Uu>i)x+!x - (-i)xfck (3.1?)
4 Sh,- P*
If no chemical reaction takes place in the branch, Damkohler number in Eq.(3.14) is equal to zero. In the node, basic equations of mass and energy conservations for the gas mixture and of mass conservation for each gas species are expressed in the following.
I(d2 G ) k = I(Da w AX d 2 ) k . (3.18)
K G c p* C ) k = 0 (3.19)
I(C ^ i ) k = 0 (3.20)
Here, in Eq.(3.18), the gas flow rate entering the node is defined to be positive and the flow rate going out of the node to be negative. The
P signs of the heat flow rate of (Gc_ G) in Eq.(3.19) and the mass flow
6
t.j"j'
conservat fon f or tlle gas n.i::.:ture atllU lO,jf ロ.:nSS cOllllservatio.n f口reach gas
species by inte.;ratitrl>; Eq;s. U. U) to O. n:n llro,t!] the inlet of tite brand1
to the o,alet i目 Ü'e 瓦 ax.i~ directiot1l.
¥, 日前1':;J~\Et{ 1
(3.14) Gx・俳句 -cx=DaECEX+td}日ー山田ir!}祭
(J.15,)
Px -Px+ι;, = Akιk+Bk
iGld tJ¥ Ak = (4ιXf +午 ~.)τーァ-15+E...ι..似
G:'<+ιx {;x-会 Gk
Bk = { ~._~ --=i-> + (ιp"'"k- t: ~}~X ρ~: ... ・乙x p. x
d
(3.16) -h
G
E' x
、.FfJV
4胃
nr
E
pe
・、VH .、一+
V日、,
h
一
》
去
D-c
,a
、rqt
t. Xu 壷
一一ーとー::-{G.,.-'::) + IQ寓 }ιx
‘q, Re Pr 匝
,,, n~ト L 、 戸女!1X+ f{cp*o::,)R_ {句、 )U--"--~jτt一
(3.17) {(Wi)x+~x - (-i)xIGk
4 Shi p合ー
= ,一一一一一一一-(,~",-, -c..',) + !)a,}LX k Re SCi 'Wi -L ふ
n+l l p* UX + f(!.ci)n - (可} F ーでーー
If no che回icalreaction takes place in tile branch. Damkohler number
in Eq.(3.14) is equal to zero. ln the node. hasic equations of mass and
energv conservations for the gas mixture and of mass conservation for
each gas species are expressed in the following.
(3.18) i:(d乙 G)k=工(DawcιXd2)k'
(3.19) nu --k 、J
Pト
w
会
Da
c
pb
(
でム
(3.20)
Here, in Eq.(3.18}. the gas flow rate entering the node is defined to be
positive and the flow rate going out of the node to be oegative.
signs of the heat flow rate of (Gcp * 1:,) io Eq・(3.19)and the mass flow
rate of (GO in Eq.O.2®) are decided in the similar way as the flow rate. The node temperature and the node nass fraction are used as inlet values of the forarach for the outflow froai the node and the temperature and ctass fraction of the branch cutlet are used to calculate the node values.
Am experimental apparatus teas been manufactured to simulate the natural convection siraply during, the printary pipe rupture accident in the HTTB. The flow channel of the experimental apparatus is a reverse U shaped circular cube. Tlie one side of the reverse K tube is a hot region and the other is a cold region as shown in Fig. 2. The cold and hot regions sinulate the inlet cooling annular channel around1 the reactor core and the cooling channels in the reactor core, respectively. The Stat region of the reverse V tube consists of three parallel vertical channels. One of the three channels is a cold channel and the rest are hot channels. The hot channel is a graphite circular tube placed in an electric furnace which is represented as Test section A o»r C as shawn iu Fig. 2. The temperature difference between the three channels simulates the one in the radial direction of the reactor core. Figure 3 shows the flow network used here for nodeling the experimental apparatus. So.5 and 11 branches in Fig. 3 are graphite channels. The arrows in Fig. 3 denote the positive direction of the flow rate. The dimensions o>f the branches in Fig. 3 are shown in Table 3.
3.3 Algebraic Equation
In the present flow network shown in Fig. 3, the right-hand tern in Eq.(3.21) is necessary only vhen the node connects to Che \"o.5 or So. II branch. The other nodes do not require the right-hand term in Eq.11.21).
E(d 2G) k = (DaU(. &X d)k» (fc* = 5 or If) (3.21)
Here, the sign of G^ is defined as plus for the direction of the arrows shown in Fig. 3. For the pressure, in the closed circuit of the flow network model, the following equation is obtained from Eq.O.IS):
(These figures denote the branch numbers in Fig. 3.) The energy equations of the gas mixture at the branch and the node
are written as follows:
Gk^p* e>x«* - OfctCep* e ) s . &l + Cc p* e ) X l + 1 «J) (3.23)
+ (<cp*e>«»- C C / G ) ™ * 1 ! ^ ^
(cp* G ) X i I(Gk fi£) - EfCcp* 0 ) x M x f e <Gk gp - 0 (3.24)
respectively. In Eq.(3.23) the i th or (i+1) th node in the k th branch is selected as the node of inlet side, judging from the flow direction in the k th branch. In the energy equation at the i th node, k (k » 1,2,3,«") branches connect to the i th node as shown in Fig. 4. In Etq. (3.24), (c p* &)x+flx is the outlet value of the k th branch and (c p* 8 ) x
is the node value of the i th node, in Eq.C3.25), max(Xl,X2) denotes the followings;
if XI > X2, then max(Xl,X2) = XI if XI < X2, then nax(Xl,X2) = X2.
The equations of the ceass conservation for each gas species at the branch and the node can be expressed in the same manner as the energy equations.
Gk("i>x+Ax ~ Gk^ ui>x i o£ + ("i) X i + 1 S p (3.26)
4 Sl^ P " { c k Re S c > « i " ui> + D a i }
+ { ( U i ) n - (^)«H->}_S1^
8
J);W.Rn ¥n 9"1 -nb(~'
ln the present calcuUation three closed circu孟tsare chcs~n fr~ the flo~
(ui)x. HGk &p - Ef ( ( B I ) ^ ^ G k 5£} - 0 (3.27)
In the above equations of Eqs.(3.21) to (3-27), unknown values a»c in the following: (a) Mass flow rate of gas mixture in Che k ch branch ; Gfc (b) Outlet temperature of gas mixture in the k th branch » Tt» k (c) Outlet mass fraction of each gas species in the t th branch ; UQ (d) Temperature of gas mixture at the i th node ; TJJ j (e) Mass fraction of each gas species at the i th node ; UJJ j
Three simultaneous linear equations for the mass flow rate, temperature and mass fraction are obtained from Eqs.(3.2J) Co (3.27) by assuming that factors like A^ in EG,. (3.22) are tentatively constant, alchough those factors are functions of the flow rate, temperature or mass fraction. First, the flow rate is solved by an iteration procedure, then the temperature of the gas mixture and the mass fraction of each gas species are solved. Figure 5 shows the flow chart of the code. The calculation at the certain time step is repeated until Che converging conditions are satisfied, then it goes ahead to the next time step.
The present computer program is shown in Appendix.
3.A Correlations of Heat and Mass Transfers and Pressure Loss
Friction factor, heat transfer and mass transfer coefficients are given by the following .uations 1* :
x2 fapp(*2> ~ XJ fapp(xI> x ! x 2 X2 - Xj
4(x 2 - Xj) p u 2 Ap = ^ f X l_ X 2 -y- (3.29)
, , , D 3.44 , 1.25/(4x+) + 16 - 3 . W x * ,., -„* fann(x)Re = . + (3-30)
P P <x^ 1 + 2.1 x l0-"(x+)-2
APo-x = "J fappW 5! - (3.31)
9
.M屯ERI-M9tl-Jω
{い'i)lt1r(Gk占p-rH吋 )X+&tkGk 5ki '"'。 (3.27')
ln the above eq田ationsof Eqs.(3.21) to (3.27). unknown values aムよ 10 the
foUow1ng:
(a) ~æss flow rate of gas mixture 10 the k th eranch Gk
(b) Outlet temperature of gas mixture 10 the k th brancb Tu.k
(c) Outlet mass fract10n of each gas spec1es in the k tb branch ム!O.k
(d) Temperature of gas mixture at the i t:h n odeτNi.1
(e) ~bss fraction of each gas species at the i th node 山N.i
Three simultaneous linear equations for the mass flow rate. tempera-
ture and mass fraction are obtained frcm Eqs.(3.21) to (3.27) by ass~1ng
that factors like Ak 10 Eq.(3.22) are tentati、;elyconstant. although
those factors ar.e functions of the flo留 rate.temperature or mass frac-
t10n. First. the flov rate 1s solved by an iteration prccedure. then the
temperature of the gas m1ltture and the mass fract10n of each gas speci~s
are solved. Figure 5 snows the flov chart of the code.τhe calculation
at the certain time step is repeated unt11 the converg1ng cond1tions are
satisfied, then 1t goes ahead to the next time step.
The present computer program 1s shown 1n Appendilt.
3.4 Correlations of Heat and ~包ss Transfers and Pressure Loss
Fr1ction factor. heat transfer and mass transfer coefficients are
£ x _ X in Eq.(3.28) is a friction factor for a developing laminar flow through a circular tube. Pressure loss coefficients are shown in Table 1. a x.. x in Eq.(3.32) is a heat transfer coefficient for a thermally developing laminar flow. £X]-x? i" Eq.(3.36) is obtained from Eq.(3.32) on the assumption of analogy between heat and mass transfer. When we solve the algebraic equation, these factor and coefficients are implicitly dealt as constant values. These factor and coefficients are influenced by chemical reactions and are expressed by using dimensionless parameter in the following'5^.
fX1-XL io Eq.(3.28) 15 a frict10n factor for a developing laminar flow
through a c1rcular tube. Pressure l05s coefficients are shown in Table
1. "X1-X2 1n Eq.(3.32) 1s a heat transfer coefficient for a thermal1y
developing laminar flow. 8X1申 xzin Eq.(3.36) is obtained from Eq.(3.32)
on the assumption of analogy between neat and mass transfer. ~~en we
solve the algebraic equation. these factor and coefficients are 1mpl1c-
itly dealt as constant values. These factor and coeffic1ents are 1n-
f1uenced by chemical reactions and are expressed by lIsing dimensionless
parameter 1n the following(5).
10
JAERI-M 92-160
f = Fl(Re, Xj/d, X 2/d, Da, Daw) (3.40)
a = F2(Re, Pr, Xi/d, X 2/d, Da, Daw) (i.4l) 6i= F3(Re, Sc t, Xj/d, X 2/d, Daj, Daw £) (3.42)
In the calculation, only the parameters of Re, Pr, Scj and (X 2 - Xj) are considered to check, the calculation method.
3.5 Rate of Chemical Reaction
In the present numerical analysis, the following chemical reactions are considered:
C + 0 2 * C0 2 + 3.934 * I0 5 (J/mole) (3.a) C + |o 2 * CO + 1.105 * 10 s (J/mole) (3.b) C + C0 2 * 2C0 - 1.725 * 10 5 (J/mole) (3.c) CO + io 2 + C02 + 5.660 * 105(J/mole) (3.d)
Here, the positive sign represents an exothermic chemical reaction and the negative one an endothermic chemical reaction. It is said that the total chemical reactions of Eqs-O.a) and (3.b) are the primary ones. The chemical reaction of £q.(3.c) is called "Boudouard reaction". These three chemical reactions are solid(graphice)/gas reactions. The gas/gas reaction of Eq.(3.d) is the carbon combustion reaction.
The reaction rates of the solid/gas chemical reactions are expressed as follows^6':
= m c ( D _^_£_IJL ( 3. A 3 )
M 0 2 2 + f J2 " "«- M^~ 2 + 2f
mc 0 = - m c ( 0 - ^ ^rj - 2 m c ( 2 ) - ^ (3.44)
MC 1 + f c MQ -mc(l)^£i^4^ + B r ( 2 ) ! ^ (3.45)
(1) , « „ , 142000.,, p vD.5, M "W02>Q.?5 /•>/«.> m c 1 1 ' = -2560 exp(- -—=-) ( *- -) (-— . . ' ) (3.46)
Rg TK 1.013 » 105 «0 2 °- 2 0 9 5
«C(2) = -44.5 exp(- - ^ ^ ) - w C 0 2 (3-47)
U
JAE則一11.192-nω
f Fl(Re. X1/d. X2/d. Da. Dav)
Q = f.2(Re. Pr. Xi/d. X2/d. Da. Dav)
51= f3(Re. SCi' X!/d. X2!d. Da1' Dav1)
(3.40)
0.41)
(3.4.2)
In the calculat10n. only the para睡etersof Re. Pr. SCi and (X2・Kl)are
cons1dered to check the calculatioD method.
3.5 Rate of Chemical ReactioD
In the present nu国ericalanalys1s. the folloving chemical react10ns
are considered:
C + 02 .. C02 + 3.934 x 105 (J/mole)
C+争2.. C印0+1し1.10白5xωω回 k
C + CO2 .. 2CO -1.725 x 105 (J!I包Itole)
Cω0+争2..印2+ 5.660 x
(3.a)
(3.b)
(3.<:)
(3.d)
Here. the pos1tive s1gn represents an exothermic chemical reaction and
the negative one an endothermic chemicaI reaction. It is said that the
total che回icalreactions of Eqs.(3.a) and (3.帥 arethe primary ones.
The chemical react量onof Eq.(3.c) 1s called "Roudouard reactiontl• These
three chemical reactions are solid{graphite)!gas reactions. The gas/gas
reaction of Eq.(3.d) 1s the carbon combustion reaction.
The reaction rates of the soUid/gas chemical reactions are expressed
as fOllows(6):
(1)竺z之土工町 2= mc'" MC .2 + .2f
(1)竺 _f__ ?__(2)生E町 o= -mC'" Me T+f -Lmc'-' Mc
(1)主主 -L-+HtoFK02mC02 -mC'" ~Ic -T+f T mC 百C
mc(l) ・2560叶枝川t・01よ叩5)O. 5(志議dh75
町 (2)=ーω.5叶守守〉匂ω2
11
(3.43)
0.44)
(3.45)
(3.46)
(3.47)
JAKKI M 82 10»
f = 800 exp(- |5^) (3.48)
Da w j = — = — -r- aj (3.49)
mc' 1' and np' 2' are the graphite corrosion rates in the iti-pore diffusion control regime. In the present numerical analysis, we deal with the mass transfer control regime and the in—pore diffusion control regime. Thus, we did not give the chemical reaction rates because the chemical reaction control regime lies in the temperature region lower than 400 to 500°C. f of Eq.(3.48) is the generation ratio of carbon monoxide mole fraction to carbon dioxide one.
The following reaction rates in the carbon monoxide combustion reaction are used.
RCO = - R + ( 3 . 5 0 )
R°2= - ° - 5 R *i ( 3 - 5 1 )
R c ° 2 = R 16? ( 3 > 5 2 )
R+ = k+ P ( ^ - ) 0 - 5 W 0 2 ° - 5 (3.53)
,+ , ,«=> , 199720. . . . . . k+ = 7 v 10' exp(- -J—=r-) (3.54) Kg I K
The generation heat due to carbon monoxide combustion is considered in the present code by the equation:
RC0~ 0 = 5.660 * 10 5 rp—- (3.55)
"C0 2
The graphite wall temperature is increased by the graphite/oxygen chemical reactions. The graphite wall temperature after this increase can be used as the input data of the code instead of providing the generation heat of the graphite chemical reactions to the code. Thus, the heat is assumed not to be generated by the graphite/oxygen chemical reactions in the code. The absorption heat due to the graphite/carbon-dioxide chemical reaction was ignored because this chemical reaction occurs scarcely under the present temperature conditions less than 1400°C.
12
6200 f 800 exp(--~.ー}
'K
Da.. 4 da; a町.1 可τE石田主
士、ERI :¥t !l".! ntill)
(3.48)
0.49)
国C(l)and rnC(2) are the graphite corrosion rates 1n thc 1n-pore diffus10n
control regime. 10 the present numerical analysis.首edeal with the mass
transfer control regime and the 1n-pore diffus:on control regime. 1hus.
we did not give the che回icalreaction rates because the chemical reaction
control regime lies 10 the temperature region lower than 400 to 5000C. f
of Eq.{3.48) 1s the generation ratio of carbon mono誌主demole fraction to
carbon dioxide one.
The following reaction rates in the carbon monoxide combustion re-
action are used.
RCO '" -R+
~'o., R0
2= ー0.5R~ ーーニ
}ICO
~'co今RCOo= R~ 一一二
~ICO
R+ = k+ρ( .. ~一) Il.:,出印喝0.5""2
4ι 。 199120、kT = 7 ~ 10~ exp{-一一一一ー}
Rg T,,'
(3.50)
(3.5])
(3.52)
(3.53)
(3.54)
The generation heat due to carbon monoxide combus!:1oo 1s considereu
in the present code by the equation:
RCO民
o 5.660 x 105 ..-ーニ"'C02
(3.55)
The graphite wal1 temperature is increased by the graphite/oxygen
che田icalreactions. The graphite wall temperature after this increase
can be used as the input data of the code instead of providing the
generation heat of the graphite chemical reactions to the code. Thus.
the heat is assumed not to be generated by the graphite/oxygen chemical
reactions 1n the code. The absorption heat due to the graphite/carbon-
dioxide chemical reaction was ignored because this chemical reaction
occurs scarcely under the present temperature conditions less than 14000C.
12
JAER1-M 92-160
Thermal properties of each gas species and gas mixture in Kef.(7) were used in the present calculation.
3.6 Average Value of Branch
The outlet temperature and outlet mass fraction of the branch would be obtained if the one-dimensional transient basic equation is analytically solved. The basic equation, however, can not be solved because of the non-linearity. Accordingly, the average value of the branch was assumed to be expressed by the inlet and the wall values of the branch as follows:
0 = 0 W + (6 X - 8U){1 - exp(-CT)} ~
r _ 4 Ku U J ~ t k Re Pr
— £ ui = "Wi "*• ("be* " <»w,-)tl " exp(-C uH jr-
A •*• * u w
4 Sh ±
C " = E k Re SCJ_
The above inlet and wall values used were obtained at one iterative step before. The inlet value of the branch is equal to the value at the node to which the inlet of the branch connects.
3.7 Initial and Boundary Conditions
When the primary pipe rupture takes place in the HTTR, the helium gas coolant of about 4 MPa spouts out of the RV to the RCV. After the balance of pressure between the RV and the RCV, the gas mixture of air and helium enters the RV from the RCV by molecular diffusion and by a special type of weak natural convection^8'. Then, the natural circulation starts suddenly throughout the reactor after the weak air ingress period continuing for a certain time. We deal with this natural circulation here. Therefore, the flow condition just before the natural circulation should be an initial condition for the calculation in the HTTR. On the other hand, when we carry out the experiments the test is started by opening the slide valves at the inlet and outlet as shown in Fig. 2. Before the opening, the natural circulation is occurring in only the three parallel channels. The condition of this local natural circu-
(3.56)
(3.57)
(3.58)
(3.59)
13 -
JAERl-!¥1 92-1ω
Ther田alproperties of each gas species and gas m1xture主n Ref.(7)
were used in the present calculatioo.
3.6 Avera邑eValue of Branch
The outlet te悶peratureaod outlet mass fraction of the braoch官。uld
be obtained if the one-dimensional transient basic equation is analyti-
cally solved. The basic equation. however. can not be solged because of
the non-lioearity. Accordingly. the average value of tbe brancb was
assumed to be expressed by the inlet and the wall values of the branch as
fol1ows:
ー一句
宮島,、.,,T
F』,E
、却e
'・aIE 、.,u
nu z
nu ,,、+
w
nu =
-nu (3.56)
-r
=r
u-N一e-Dn
tUT-
-K
Eg-
z T
F』 【3.57)
Wi 匂 i1- {WxiーWwi)O-e貯 ωえ4 Sh~
C.. 一一一一ーιーωEk Re SCi
(3.58)
(3.59)
The above inlet and wa11 values used were obtained at one iterative step
before. The in1et value of the branch is eq四alto the va1ue at the node
to which the inlet of the branch connects.
3.7 lnitia1 and Boundary Conditions
~~en the primary pipe rupture takes place in the HTTR. the helium
gas coolant of about 4 ~æa spouts out of the RV to the RCV. After the
balance of pressure between the RV and the RCV. the gas mixture of air
and helium enters the RV from the RCV by molecular diffusion and by a
special type of weak oatural convection(吋‘Then.the natural circula-
tion starts suddenly throughout the reactor after the weak air ingress
period continuing for a certain time. We deal首iththis oatural circu-
lation here. Therefore. the flow condition just before the natural
circulation should be an initial condition for the calculation io the
HTTR. On the other hand. wheo we carry out the experiment. the test is
started by opening the slide va1ves at the inlet aod outlet as shown in
Fig. 2. Before the opening. the natural circulation is occurring in only
the three parallel channels. Tbe conditiot)s of this local natural circu-
13
JAEK1 - M 92 - 1&D
lation is the initial condition in the calculation for the experimental apparatus. However, since the objective of tme present study is to develop the analytical method, we gave a simple initial condition to the calculation as follows: (1) Nitrogen gas is filled in the all branches. (2) All flow rates are equal to zero. (3) Temperatures of only graphite branches are equal to, for example,
1000°C, and other temperatures are room ones. (4) All pressures are equal to atmospheric ones.
The following conditions are given as boundary conditions; (1) Two end branches connect separately to two infinite regions of a gas
mixture of nitrogen and oxygen with atmospheric pressure and room temperature.
(2) Wall mass fractions of oxygen, carbon monoxide and carbon dioxide in the graphite branch are obtained by solving the following equations.
s h o 2 p ™02
" Re-Sc^ iZ°2 ' " V - -^1T0 ( 3' 6 0 )
shC0 P* mC0 Re" - S ^ (-CO - «w C 0> = ^ «.61)
b h C 0 2 P ""COz Re S c C 0 2
( W C C 2 " ""COz* = p ^ ° - 6 2 )
It should be noted that the right hand sides of Eqs.(3.60) to (3.62) include wall mass tract* ns as expressed in Eqs.(3.43) to (3.47). Therefore, first, Eq.(3.60) of the wall mass fraction of oxygen is solved by Newton-Rapson method, then Eq.(6.62) is solved, and last the mass fraction of carbon monoxide can be obtained.
14
J;¥ERI -:1.1 !Y.! -]副》
lation is the initial condition in the calculation fOT the experimental
apparatus. However. since the objective of the present study 1s to
develop the analytical method. ve gave a simple initial condit1on to the
calculation as follows:
(1) Xitrogen gas is filled in the al1 brancnes.
(2) All flow rates are equal to zero.
(3) Temperatures of only graphite branches are equal to. for example, 10000C, and other temperatures are room ones.
(4) All preSStlres are equal to atmospberic ones.
The following conditions are given as boundar] conditions;
(1) Two end branches connect separately to two infinite regions of a gas
mixture of nitrogen and oxygen witb a~ospher主c pressure and room
temperature.
(2) Wall mass fractions of oxygen. carbcn monoxide and carbon dioxide in
the graphite branch are obtained by solving the following equations.
It should be noted that the right hand sides of Eqs.(3.60) to (3.62) in-
clude wall mass fractj.ns as expressed 1n Eqs.(3.43) to (3.47}. There-
fore, first, Eq.(3.60) Qf the wal1 mass fraction of oxygen 1s solved by
Newton-Rapson田ethod. then Eq.(6.6Z} is solved, and last the mass frac-
tion of carbon monoxide can be obtained.
14
JAERI-M 92-160
4. Result and Discussion
A steady state calculation was performed under the following conditions;
Graphite wall temperature : 1000°C Branch wall temperature : 20*C Gas temperature at inlet : 20°C Pressure at inlet and outlet : 1.01'* * 10 s Pa Oxygen mass fraction at inlet : 0.233 Nitrogen mass fraction at inlet : 0.767
The calculation results of Reynolds numbers in branches, temperatures at nodes, and mass fractions of oxygen, carbon monoxide and carbon dioxide at nodes are shown in Figs. 6-1 to 6-5. The Reynolds numbers in the branches with the same diameter and length differ from one another because of the difference of the bulk gas temperature. The flow rate at the outlet increased a little in comparison with the one at the inlet as shown in Fig. 6-1. This increase of the flow rate results from the gasification of the graphite due to the graphite/gas chemical reactions. The mass fraction of oxygen at the No.2 node (=0.207) is less than that at the No.l node of the inlet (=0.233) because the flow goes down in the cold branches of the No.14 to No.19. The mass fractions of carbon monoxide and carbon dioxide at the No.2 node are not equal to zero as well as the mass fraction of oxygen at the No.2 node as shown in Figs. 6-4 and 6-5.
A transient calculation was carried out under the same conditions as the above ones. Figures 7 to 10 show the calculation results of the flow rates at the No.5, No.17 and No.27 branches, the gas temperatures at the No.6 and No.18 nodes and the mass fractions of oxygen, carbon monoxide and carbon dioxide at the No.6 and the No.26 nodes, respectively. The abscissa of Figs. 7 to 10 is elapsed time. The time increment was 0.2 seconds in the calculation. It is found that the values calculated reach steady state after about 5 seconds. The results in the steady state calculation agreed with those of steady state in the transient calculation. In these figures the overshooting is observed at the initial stage shorter than few seconds of the elapsed time.
The calculation results will be compared with the corresponding experimental results to verify the method of the numerical analysis.
15 -
j:¥ERI -M 92 -]ω
4. Result and Discussion
A steady state calculation was performed under the fol10wing coodi-
tions;
Graphite町'a11temperature : 1000"C
Branch wall temperature 20=C
Gas temperature at inlet 20・cPressure at inlet and outlet 1.01、"105 Pa
Oxygen mass fraction at inlet 0.233
Nitrogen mass fraction at inlet 0.767
The calculation results of Reynolds numbers io branches. temperatures at
nodes, and mass fractions of oxygen. carbon monoxide and carbon dioxide
at nodes are shown in Figs. 6-1 to 6-5. The Reynolds nu曲 ersio the
branches with the same diameter and length differ from one another be-
cause of the difference of the bu1k gas temperature. Tbe flow rate at
the outlet increased a little in comparisoo with the one at the inlet as
shown in Fig. 6-1. This increase of the flow rate results from the gas-
ification of the graphite due to the graphite/gas chemical reactions.
The mass fraction of oxygen at the No.2 node (=0.207) is less than that
at the No.l node of the inlet (=0.233) because the flow goes down in the
cold branches of the No.14 to No.19. The四assfractions of carbon mon-
oxide and carbon dioxide at the No.2 node are not equal to zero as回ell
as the mass fraction of oxygen at the No.2 node as shown in Figs. 6-4 and
6-5.
A transient calculation was carried out under the same conditions as
the above ones. Figures 7 to 10 show the calculation results of the flow
rates at the No.5, No.17 and No.27 branches, the gas temperatures at the
No.6 and No.18 nodes and the mass fractions of oxygen. carbon monoxide
and carbon dioxide at the No.6 and the No.26 nodes, respectively. The
abscissa of Figs. 7 to 10 is elapsed time. The time increment冒'as0.2
seconds in the calculation. It is found that the values calculated reach
stιady state after about 5 seconds. The results in the steady state
calculation agreed with those of steady state in the transient calcula-
tion. ln these figures the overshooting is observed at the initial stage
shorter than few seconds of the elapsed time.
The calculation results will be compared with the corresponding
experimental results to verify the method of the numerical analysis.
15 -
JAKRI M 92 160
5. Concluding Remarks
The flow network computer code was developed to calculate heat, mass and momentum transfer in a natural circulation of a multicomponent gas mixture with graphite chemical reaction dee to air ingress. The entering flow rate, flow rates distributed to the parallel channels, generation volume of carbon monoxide and corrosion volume of the graphite were predicted by the present code. It was found that the numerical calculation method used in the code was basically effective for the analysis of heat, mass and momentum transfer in the gas mixture flow with solid(graphite)/ gas(oxygen or carbon dioxide) and gas/gas(carbon monoxide/oxygen) chemical reactions.
We have already carried out the experiments on the graphite corrosion at high temperature in the experimental apparatus as shown in Fig. 2. The results calculated by the code will be compared with those obtained in the experiment.
References
(1) S. Saito, T. Tanaka and Y. Sudo, Present Status of The High Temperature Engineering Test Reactor (HTTR), Nucl. Eng. Des., 132(1991), 85.
(2) Japan Atomic Energy Research Institute, Present Status of HTGR Research And Development, (1991).
(3) Japan Atomic Energy Research Institute, Present Status of HTGR Research And Development, (1989). (in Japanese)
(4) R.K. Shah and A.L. London, Laminar Flow Forced Convection in Ducts, Academic Press, New York-San Francisco-London (1978), 103.
(5) Y. Katto et al., Advances in Heat Transfer, Yokendou, Tokyo (1984), 183.
(6) M. Ogawa, Mass Transfer with Graphite Oxidation in A Gas Mixture Laminar Flow through A Circular Tube, J. Atomic Energy Soc. Japan, to be published.
(7) T. Takeda, B. Han and M. Ogawa, Thermal Properties of Multi-component Gas Mixture, JAERI-M 92-131 (1991).
(8) M. Hishida and T. Takeda, Study on Air Ingress during An Early Stage of A Primary-pipe Rupture Accident of A High-temperature Gas-cooled Reactor, Nucl. Eng. Des., 126 (1991), 175.
16
,I:¥ERI" ~I 92 -1ω
5. Concluding Remarks
The flow network computer code was developed to calculate heat. mass
and mo田entumtransfer in a natural circulation of a multicomponeot gas
mixture with graphite che由主calreactioo dじeto air ingress. The eotering
flow rate, flow rates distributed to the parallel channels. generation
volume of carbon monoxide and corrosion volume of the graphite were pre-
dicted by the present code. It田'asfound that the D'.lDlerical calculation
method used in the code 同'asbasically effective for the analysis of heat.
1i1ass and田omentumtransfer in the gas mixture flo官官ithsolid(graphite)!
gas(oxygen or carbon dioxide) and gas/gas(carbon monoxide/oxygen) chemi-
cal reactions.
We have already carried out the experiments on the graphite corro-
sion at high temperature in the experimental apparatus as shown io Fig.
2. The results calculated by the code wil1 be co国paredwitb those
obtained io the experiment.
References
(1) S. 5aito, T. Tanaka and Y. Sudo, Present Status of rne Higb Tempera-
ture Engineering Test Reactor (HTTR), 自国cl.Eng. Des.. 132(1991). 85.
(2) Japan Atomic Energy Research Institute, Present Status of HTGR Re-
search And Develop皿ent. (991).
(3) Japan Atomic Energy Research Institute, Present Status of HTGR Re-
search And Development. (1989). (in Japanese)
(4) R.K. Shah and A.L. London. Laminar Flow Forced Convection in Ducts.
Acade皿icPress. New York.San Francisco.London (1978). 103.
(5) Y. Katto et al.. Advances in Heat Transfer. Yokendou. Tokyo (1984).
183.
(6) M. Ogawa. t-lass Transfer with Graphite Oxidation in A Gas }Iixture
Laminar Flow through A Circular Tube. J. Atomic Energy Soc. Japan.
to be published.
(7) T. Takeda. B. Han and ~I. Ogawa. Thermal Properties of ~1ulti-component
Gas Hixture. JAERI-H 92-131 (1991).
(8) H. Hishida and T. Takeda, Study on Air Ingress during An Early Stage
of A Primary-pipe Rupture Accident of A High-temperature Gas-cooled
Reactor, Nucl. Eng. Des., 126 (1991). 175.
16
JAERI-M 92-160
Table 1 Dimensions of branches and Pressure loss coef f ic ients
Branch number
I Length (m) !
Diameter (m) 0 (deg) Pressure coefficient
1 2
i j 0.691 0.0549 0 1.5 1
2 0.7 0.0492 90 1.5 3 | 0.7025 0.0549 0 0 4 i 0.7025 0.0549 0 0 5 i 0.7 0.0549 o 0 6 1.085 0.0549 o 0 7 8
AND MOMENTUM TRAf.SFES IK A KULTI-COKPONENT GAS »«.»«O000Q6Q0 MIXTURE WITH GRAPHITE CKEttlCAL REACTIONS »«»««a00007Q0
».»»«00000800 KARCK 27, 1952 »*»»«GQOOOS>00
•»«»«oooo:ooo « . < . , > » . » i < > i > » » » » » < » < » > < t « t . t , . » . > » > < » > . i i i . » » > > I > 0 O C O H O O ...,.<»*<.*.<*.»«*».*«.**«»»*»*»*..*<*.**•*.**«*******><*»*»**•»**0000120a
N = THE K'JHBER OF NODES + 00001900 K = THE NUMBER 0? BRANCHES + 00002000 K = THE NUMBER a? GAS SPECIES ; HE=l,O2=2,CO=3,C02=4,N2=5 + 00002100 J = ITERATION TIKES * 00002200 DTI = INCREMENT OF TIKE STEP + 00002300 DT = INCREMENT OF TIME STEP + 00002400 TIME = ELAPSED TIKE OF CALCULATION + 00002500 Hi. = CONTROL CONSTANT FOR CALCULATIONS • 00002600
+ 00002700 H = LENGTH OF BRANCH • 00002800 D = HYDRAULIC DIAMETER - 00002900 Y = PRESSURE LOSS FACTOR + 00003000 F = FRICTION" FACTOR + 00003100 S H « ! = THE NL"-1 = ER CF THE NODE CONNECTING TO KTH BRANCH INLET + 00003200 NNC<K)= THE NUMBER CF THE NODE CONNECTING TO KTK BRANCH CUTLET + 00003300 CAT = VERTICALITY OF BRANCH + 00003400
* 00003500 TNI = TEMPERATURE OF GAS AT NODE (OLD) •» 00003600 TK2 = TEMPERATURE OF GAS AT NODE (NEW) + 00003700 TTN = TEMPERATURE CF GAS AT NODE + 00003800 TTNT = TEMPERATURE OF GAS AT NODE IN TIME ITERATION + 00003900 T01 = TEMPERATURE OF GAS AT BRANCH OUTLET (OLD) + 00004000 T02 = TEMPERATURE OF GAS AT BRANCH OUTLET (NEW) + 00004100 TTO = TEMPERATURE OF GAS AT BRANCH OUTLET + 00004200 TTOT = TEMPERATURE OF GAS AT BRANCH OUTLET IN TIKE ITERATION • 00004300 TA1 = AVERAGE TEMPERATURE OF GAS IN BRANCH (OLD) + 00004400 TA2 = AVERAGE TEMPERATURE OF GAS IN BRANCH (NEW) * 00004500 TWA = AVERAGE TEMPERATURE Or WALL + 00004600 TTA = AVERAGE TEMPERATURE OF GAS IN BRANCH * 00004700 TTAT = AVERAGE TEMPERATURE OF GAS IN BRANCH IN TIME ITERATION + 00004800
+ 00004900 PI = PRESSURE OF NODE (OLD) • 00005000 P2 = PRESSURE OF NODE (NEW) + 00005100 PP = PRESSURE OF NODE + 00005200 PPT = PRESSURE OF NODE IN TIME ITERATION + 00005300 PX1 = DIMENTIONLESS PRESSURE OF NODE (OLD) + 00005400 PXZ = DIMEiN'TIONLESS PRESSURE OF NODE (NEW) ^ 00005500 PA1 = AVERAGE PRESSURE OF BRANCH (OLD) + 00005600 FA2 = AVERAGE PRESSURE OF BRANCH (NEW) + 00005700
+ 00005800 UNI = CONCENTRATION CF GAS AT NODE (OLD) * C0005900 WN2 = CONCENTRATION OF GAS AT NODE (NEW) + 00006000
34
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C 00000100 C.a.事寧怠.a..・..・...寄.......a.a:奪a....a玄.s....c..sa怠・...奪"奪怠怠".怠...意志..寧8・..0000020(1C.a:...草....................禽...・Z事...・..s....ss..a....客 s・8・2・..........老2・".OCOOQ3COC.-:a:...怠 軍.,.,,"00000.:.00
C 00001300 C φ++令キ+++++令 ++...+...++φ+ 守...令 ++++-+++++φ++++...........+++++-++..や..+令~..令4静 φ....・事令+++令.. 00001400
C 令 ーーーー『ーーーーーーーーー-ーーーーーーーーーーーーーーーーーー・・ + 00001500 C ーー DEFI~!T!Q~ OF VARIABL~S ー・・ φ 00001600
c ーーーーーーーーーー---ーーーーーーーーーーーー・--ーーーーーーー + 00001700 C + 00001600 C 今 N THE ~!U円 õER ()F t;ODES .. 00001900' C + M THE ~UMBER OF 5RANCH主S ... 00002000 C K THE NU円BER ~F E~S S?~CIES ; HE=1 , 02=2 , CO=3, C02=4~ 目 2=5 + 000'02100 C J !TERATIOIi TI!':E5 .. 00002200 C .. OT1 INCREMENT OF TIME 5TE? .. 00002300 C OT I~cRE ;O: ErH OF iIME SoEP ... 00002400 C 令T!円 EL:'PSED il円E QF CA~CUlAT!ON + 00002500
C ‘ NL CCt.τROl CONSiANT FOR CALCULAT!ONS + 00002600 C ... 00002700 C H L 三 f!: G7~ CF a?A~~CH ・ 00002800C D HYCRAULIC D!'MEτE担 ‘00002900c y P司ESSuPE LCSS FACTGR .. 00003000
Tt-.:l T:円PERATURE GF G:'5 AT NODE C口lD)ï~2 T:~PERAïU~をさ口 (;AS Ai N口DE (~.!E~)
TiN iE何PERATURE CF GAS AT NOOE TTN1 TE~PERA1URE OF GAS AT NODE IN 11刊E ITERATIOtl 101 H~'PE 司AiURE O~ GhS ζT SRANCH OUTL~T (OLDl T02 TEMPERATURE OF GAS AT 8RANCH OUTLET CNEW) TTO TE 円 PEíiAT~rtE O~ GAS 且T BRANCH OUTLET iTOT 1EMPERATURE OF GAS Al BRANCH OUTLET IN TIME ITE買AT!ON1A1 AVERAGE TEM?E?ATURE OF GAS IN BRANCH (OLD) TAZ AV~RAGE TEM?ERATURE OF GAS lN BRAN::H (NEW)
TWA AVERAGE TE円PE百ιTURE OF WALl TTA AVERAGE TEMPERATURE OF GAS IN BRANCH TTAT AVERAGE TEMPERATURE OF GAS IN eRA~CH IN 11刊E ITERATIO~
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34
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FCRTRAN77 V12L10 DATE 9 2 - 0 9 - 2 1 TIME 2 0 : 4 2 : 0 3
C C c c c c c c r c c r
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UW>1 = CONCENTRATION OF GAS AT MODE + WWNT = CONCENTRATION OF GAS AT KOBE IB TIME ITERATION + uc: = cc.-cEf.-rsATiOK OF GAS AT SRA«CH OUTLET COLD) * '»02 = CONCENTRATION OF GAS AT eRANCK OUTLET CNEU5 * '*KC = CONCENTRATION CF GAS AT BRANCH OUTLET + WWCT = CONCENTRATION OF GAS AT BRANCH OUTLET IK TIME ITERATION • tf«: = AVERAGE CONCENTRATION OF GAS IN BRANCH tOLD) + KA2 = AVERAGE CONCENTRATION OF GAS IN BRANCH <KSV) • UAA = AVERAGE CONCENTRATION OF GAS IN BRANCH • tfAAT = AVERAGE CONCENTRATION Of GAS IN BRANCH"IN TIME ITERATION* k'WA = AVERAGE CONCENTRATION OF GAS AT UALL +
GA1 = AVERAGE MASS FLOW RATE IN BRANCH COLDJ + GA2 - AVERAGE MASS FLOW RATE IV BRANCH <NEt»> + GX1 = DIMENTIOHLESS AVERAGE MASS FLOtf RATE IN BRANCH CQLD> * GX2 = DIMENTIONLESS AVERAGE MASS FLOU RATE IN BRANCH {NEW} + GG = AVERAGE KASS FLOW RATE IK BRANCH • GGT = AVERAGE MASS FLOW RATE IN BRANCH IN TIME ITERATION + G". = KASS FLUX CF EACH GAS BIT GRAPHITE CHEMICAL REACTIONS • GM1 = KASS FLUX OF CARBON BY GRAPHITE CHEMICAL REACTIONS *
+ DI = DIFFUSION COEFFICIENT + CP = SPECIFIC HEAT OF GAS MIXTURE • CPtl = SPECIFIC KEA7 0? GAS MIXTURE AT NODE + CPO = SPECIFIC HEAT OF GAS MIXTURE AT BRANCH OUTLET * KU = VISCOSITY OF GAS MIXTURE • LAP. = THERMAL CONDUCTIVITY OF GAS MIXTURE + OEI = DEKSITY OF GAS MIXTURE AT KOBE + DEO = DE.'.'SITY OF GAS MIXTURE AT BRANCH OUTLET * SEA: = AVERAGE DENSITY 0? GAS MIXTURE IN BRANCH + SEAT = AVERAGE DENSITY Or GAS MIXTURE 1U BRANCH IN TIME *
ITERA~:O« *
RE - REYNOLDS NURSES C-R = GRASHOF NUMBER XU = NUSSELT NUMBER SC = SCHMIDT NUMBER SH = SHERWCOO NUK5ER
SAT s KASS TRANSFER COEFFI CIENT SI = PRODUCT MASS EY CHEMICAL RE ACTIONS Q = REACTION HEAT
C O = PRESSURE <=1.0E5 PA) C(2) I TEKPRERATURE < = 20 C3 CC3) = DENSITY <N2, 20 C, 0, .1 MPA) CfiJ = DENSITY CN2, 1000 Z, 0, .1 MPA) CCS) = VISCOSITY CN2, 20 C, 0. .1 MPA) CC6) = THERMAL CONDUCTIVITY CN2, 20 C, 0. .1 MPA; CC7) = SPECIFIC HEAT CN2y 20 C, 0. .1 MPA) CCS) = DIFFUSION FACTOR IS2.- 20 z. 0. .1 MPA) CC93 = DIFFUSION FACTOR <02, 20 c. 0. .1 MPA) CC10) - DIFFUSION FACTOR CCC, 20 c. 0. .1 MFA) c < : : > = DIFFUSION FACTOR CC02, 20 c. 0. .1 KPA) C C1 2 ) = DIFFUSION FACTOR CN2, 20 o 0. .1 MP A) CC13) = KINEMATIC VISCOSITYL CH2, 20 c. 0. .1 MPA) KCLW = MOLAR MASS OF GAS
・ GG Il VE~品GE M且55 iLOIll RJHE ru SRAtlCH .. 00007700 GGT 且VEP.I:GE 問ASS FLOW RAτE Hl BR且NtH IN TIME !TER血TI01l .. 00007800 G~ MASS FLUX OF EACH GAS BY GRAPHITE CHEMItAl 毘EACτ!O~5 .. OOOO?900
・ C阿 MASS FLUX OF CAR601l 6r GRAPH! τE CHEM!CAl REACTZO阿5 争 00008000+ ~ 00008100
01 DIFFUS!ON C OEFF!CIENτ.. 00008200 ・ C? S?ECIFIC HE且τOF GAS 凹 tXTUR~ + OOO~8300 4争 c?rl S? ξCiFIC NEAr OF GAS MlxrURE AT HODE .. 00008400 φC ? O SFEC!F!C H=:Aτ0; GAS M!XTURE A1 6RANC!I o~rlEτ.. OOOOS500
MU V!SCOSITY OF GAS MIXτU~=: + 0~008600 L;;~ THE.担問A.L C口問。UCτ!VITY OF GAS M[XTURE + 00005700
.. OE1 OENS!TY OF GAS 問rxτ!)自主 AT 1l0DE .. 00008800 DEO OENSI7Y QF GAS MIXτIlRE AT 8RANC!! a.tJlτlEτ 守 00008宇00
・ ~E 兵 ~VERhG~ DE~S!TY O~ G~S M!XτURE r~ BRA~C!! .. 0000争000‘ ZミιT rWERAGξOE町S!7r OF GAS MIXTURE In BRANCH IN TI問E ... 00009100 宇 !TEP.五ー :orl 4 00;'09苫00
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C 0 0 0 1 5 5 0 0 C i i i i i m i i i i i • i i i t i i i i i i i M t i » > i t i > i a l i i i M i » » » i i < i > i i i < i » » i O I I O ! S ( C O C * I I » I » » . « . C 0 G 9 5 ? 0 Q C«.... TO SOLVE TERPESATURE OF KOBE AMIB b....!*CH OUTLET •••••Q009SB00 C«*.*» .....Q0095900
O C C S O C 0 1 S U B R O U T T K E T E R P R T I ( T ) 0 0 0 9 6 Q O O <:.•»•• » » . » . O Q O 9 6 I Q O
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»S7(;;:=p:/4.o«Bc::;««2«BABscGA2ci2:;«cf,K(f.;ft:)}«cc2i CDNTIKUE DO 120 I=K-1,2»K S7 C ;=-P:/4.0«B :!-«)»• 2»DA=StGA2CI-».l).CFO(I-K)«CC2) C2K7!SL-E I F C G A 2 O / O A S S : G A 2 C I ) ) . L 7 . O . C ) 7KE>: AATll, -.)=•. .0 M U : / « ) = - ! . 0 EKO IF : = ( G A 2 C : ; / O A E E ( G A 2 C : > J . G E . O . O ) T H E K A A ; C , ; ) = I . O AATll,2.M!=1.0 END IF :=(GA2<X3/0A3SfGA2CK>>.GE.O.O: ThEN AATCN,*:-1.0 As-c:t,N.r!)=-:.c END :F I F ( G A 2 < K 3 / O A B S ( G A 2 C K 3 > . L 7 . 0 . 0 3 7 H E N AA71N,N>=1.0 A A T C J , 2 » K ; = I . O E N : :F
A A T C 2 , ! - N > = C S C ! - » K > » S T C 1 * M ) A A T C ? , M ) = C S £ K » l J « S T C J t » t J CONTINUE
DO 4 J 0 1 = 3 , 7 I F < G A 2 C I > / 0 A e S C G A 2 < I > > . £ . 7 . 0 . 0 . C R . G A 2 C I - l J / D * B S t G A 2 < ! - l J > .
• L T . O . O ) THEN A A 7 < I , I ) = S T < : - J ) A A T < : , : . N > = S T C I » W > GO TO 410 END IF A A T { ; , ; > = S T ( U AAT I I , 2 * K - 1 > = ST< I • « - ! ) C O N T I N U E
DO 4 2 0 i = 8 , 1 2 I f < G A 2 < l ) / D < < S S C G A 2 t I ) > . L T . 0 . 0 . 0 R . G A 2 ( i > l ) / 9 « B S C G A 2 < l + X > > .
« L T . 0 . 0 > THEN A A 7 C I , I ) = S T C I ) A A T C I , I * l * N ) = S ~ t i + l + K 5 GO TO 4 2 0 END I f A A T C I , r i = S T < i » l > A A T < I , I 4 N > = S T ( 1 » M > CONTINUE
| I | | g g | 8 S | 8 S o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o O O O O O O O O t J O O D CTOOOOOUOOQ O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O n H (J (4 u >4 n ,4 |j |4
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OIKEKSIGM hCM5,PCK>,l'«*),F:M),CAT<.»), " T I 1 ( » > , T I 2 ( K ) , T C I C K ) # T O 2 ( K : , T A : < K ; , - A 2 ( K > , T ! . I ( N ! » T N 2 ( N > , T W A ( H > » »PI (N)^F2(N)»PN;(N),P':2(K),PA:(K),PA2C«>, »GAlt*),GA2;K>,GAt?:: ,CGT(K)»TTAT(H),PPtK!,PPT(N),PATC«J-WAATtn,K) •D : C K < < : , C P C K > , D E : : K > , S E C ( K > , O E A : [ K > , S E A T C H > ^ C P T C K ) » • UM<K,<),Wf;2;K^<),CS:2»"1)»QtK)»AVEKCLC»')«CPO(M)^CPMf«>, »RE(K),GSCK>»Pat«;),SCCH#K!,SHtK#K>,SI CK, O , WWA t(T#K) » • WIICK, <),l.:2<K,K>,;."Cl(K,K>,W02t»,i;},WAl{K,K:,WA2(R-IC>, »AW<H,K),BUC*,IO,Cki(K,!O,0WCM,>;). AAU{2»r1-l,2«K5,SWC2»M, K ) , • C<13:,BATCK,K).X'..-C*),GX2<K>.NICM>,MQCH>, »WX:(2«.*-I,IC)»WX2(2»M-I»K:,TA(<) SEAL'S KNI(>'>*KKO<K:*Kll(K>,LAKCK) ,NU<K) .KOLUtK*!) CCMMCN/SIZE/H,3,?,F,NNI,NKa,CAT,07
. /C0MP/WI1,L.'I2,VC1,W02,UAI,WA2,WN1,IIN2,UAAT,WWA » /fL0W/GA1,GA2,GA,GGT, « /CUA'_/DI,CP,CPT,CPO,CPN>Mti,LAK,0EI,0EO,BEAI,OEA-- /KLUG/MOLW,AVE*0L,C » /SEFE/SE,C-a,PR,KU,SC.5H,a 00 200 L = 1,J 00 30 JJ=1,2»M-1 CO 30 KJ=1,2»«1 AAW( JJ#.<J)=C.O CONTINUE OC ISO 1 = 1,K :=CGA2CI>/DA=S(0A2CI)}.LT.C.0> ThEV i.'Jci;=«sD[:> NOC:J=KM (I) END IF IF (GA2(n/CABS<C-A2CI!3 .GE.C-.G) "t;K N: C:; = NN:ti) voc)=M«ic(i; EtiB 1 = DO 150 JJ=1,K A«'(1,JJ) = C O Brftl,J J) = 0 . 0 CW<:,JJ> = 0 . 0 D U C J J) = C O U'.2C:,JJ)=O.O W G 2 C , J j>=0.0 U K 2 ( N : C > , J J ) = O . O IF ( G A 2 ( 1 ) / B A B S ( G A 2 ( 1 > ) . G E . O . O ) T H E N WN1(1,1)=0.0 WN1<1,2)=0.233 UN1C1,3>=0.0 WN1 <1,4)=0.0
F0RTRAK77 EX V12L10 GSSPEC DATE 92-09-?: TIKE 20:42:03
0CC0C034 w«(;.5)=0.767 C0C0CC3S EKD IF C0000C36 := CGA2C!«}/DA3S(GA2Cf")) .LT.0.0) THEN CICCC037 k.':;;<N,i:=c.c C0CC0C38 wr;z (?l,c> = 0.Z55 C0CCCC3? u't.'t <K,3)=0.C coccc^^-c W M < N , 4 3 = 0 . 0 D^OOCO'.l UNI CN,53=0.767 00000042 END If 00 00 0043 »IlCI.JJ3=WNSfNKI3.JJ3 00DCC044 ISO CONTINUE
i «WA:CI.23»»O.5 s iu.i> = o.o SICI.2) = -0-5»RPLS S K I . 3 ) = -RPLS S K I . 4 ) = RPLS SKI,53 = 0.0 G(13=D(13»«2/CC(23«C(133^C[33.C<7)3»S.66OES»RPLS/M0LWC43 00 350 JJ=1.K SCCI.JJ)=MU(I)/DI(I.JJ>/DEA1(I) SHU.JJ3 = AMTC C RECI3. SCC1.JJ). HU3/DCI3 ) BATCI.JJ) = SH<I.JJ3*DK1.JJ3./DCI3 BWCI.JJ3 = 0.0 CWCI.JJ) = 0.0
IF ( I.E0.5.0R.I.E0.11 3 THEN BW(I.JJ>=4.0«SHCI,.JJ3»DK1.JJ3»HC13/D(1>/CC133 lF(KK.EO.l) C.CI.JJ)=BW<I.JJJ
ENDIF 1FCKK..EG.2) C . ' C I . J J 3 = 8 W < I . J J ) * H C I 3 « D < I ) / O T / C C 1 3 3 DWU.JJ3 = SI<:.JJ3«D<13«H<I3/CC33/C(133 IFOCK.EQ.23 DWC1.JJ3=DUCI.JJ3*H<I3»DtI3/DT/CC133.DEATCI3/CC3)
• t l/J o o o o o II • • II + ^ O O -s « K ii it ft - l + •> « *• -7 M H i > t ; s * / w u v »VJ i/iirt w w ^ O O U *j 3
H M O
• O M O O N
o o o o o o • II I) II ll II
« E r r t s: r* • N N » • w fg M rv M N
' - ' 3 3 3 3 3 W «X <t «4 « *t CO •< <X ct t <C
Z O O O •-• O </i i/> • - IA U1 IA
< 1.1 r> a o o o o ^ t 3 " 1U Ul HI 111 III i < Z M ' . > . i • t-( < -» -» -1 -1 -J • ' h O • ) " I '» T » ' t 2 w — ^- w ..- « ( O u. u. u. i
o o o a /-. • • • . <\j
o o o o *••
- u. < Z u. < *t
t O (V o o r- • • • • • (/) i i • K H I UJ h- u i 1- O c -» t~ - J O O
II II o o II n
o u O J U > a • -< rH _ J
" 1 - 1 - J
* - < * •
K E t n £ •^ "> 3 z: t H £ X * •> W i : r t V in ^ +
rg rg t\j rg ^ ,H M 3 E ru ry ry ry rg <-i t/i (M + ( V +• •c Z 2 z z < «« «t ' t u: 3 E H <J E <* w o O <3 13 ( J W U + -» 1 3 - j v
iX 3 3 3 3 3 w
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cu «t «t «c t *t CO -J to oa ni m «-• ^J W E CO 3 II m »H II <t o 1 o 1 r g rH *X * t «C < >-- U • - r*. < W V * •X z n a II S Q Q O o to II lO a 3 II 3 a UJ 3 Z • * * Kl O I A «-H •v r-« '"• ry - . *s. -^ ^ Ki 3 " . U tn C/l t n 1 CO z V? +
ll £ o n f, s\ ,> •>-* I I i n 2 (1 Z I A Z I I 1— II t-< Crt x: a a a o a £ + UJ M + rH /^ + rg
ui ni z Z Z 13 « r j fH K =) -1 3
u. (M u. r y i n I I z IA rw fy IM ry \ - i z U l ( M z Z I A fM a •" «* z *r z z 0> O «t «T «X < rw rv n> < U J o <M * t H H O
w -1 •-> o f ^ h - • J l O U O o « 1 - * } a X t - • J 13 a ^ w l^ Q ^ 3 a 3 s a z •^ 3 3 3 s 3 3 a 3 3 z 3 3 Z li- •X z <£ ** z a t O o O u- u. u. u. -t o •t -C o o < n o z <c «c o O r - <X •« O UJ n *-* *-* i-t •-< •-» ** UJ • -H <£. « t U i a U o a r-H >-a > i -i < + < < CJ o •-« r% < < t CJ m <c «c o o n ^ 1 «t <t 13
N K i g u i > 0 N C 0 0 ' O H M M g i n ' 0 N a ) l > 0 o ( \ l r t * l l A ' O t ^ t O O ' 0 0 U i I ) i a i 0 i f l i 0 i 0 i M > ( M ) . ( M H M > t > ^ O O O O O O O O O O O O O O O O O O O O O O O O O Q O O i i < - < < - < r < < - ' t - n < - < t < i - < t - < t - t i - ' ) < H O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O C J O O O O O O O O O O O O O O O O O O O O O O O O O O O C J O O O O O O O O O O O O O O o o o o o o o o o o o o o o o o o o o a o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o
K l g m - O N » 0 > 0
O O O O o o o o o o o o o o o o o o o o
O t> O O O O O O o o o o o o o o O O O O
o o o o o o o o o o o o o o o o o o o o o o o o o
• O N C O O O H C M M - J iA-or«.co (vj rg CM N i i c i f i K I i i M M M I O r* i-l i-i H TH tH r' rH il H |H Pt rt O Q O O O O O O O O O O O O O O O O O O O O O O O O O O D O O O O O O O O O O O 0 C 3 O O O O 0 0 O O O O O O O O O O O O O - - - — O O O O
C 00142200 00000164 DO 445 1=19,25 00142300 00000165 IFCGA2CI*1)/DA8SCGA2CI+1>).LT.0.0.0R.GA2CI+2)/DABSCGA2CI+2)>. 00142400
•LT.0.0) THEM 00142500 00000166 AAW<I,I)=SUCI*1,JJ) 00142600 00000167 AAWCl,l*2tN)=SW(I»2*M,JJ> 00142700 C0000168 GO TO 445 00142800 00000169 END IF 00142900 CC0C0170 AAWCI,2)=SWCI+2,JJ> 00143000 00000171 AAWCI/I*1+N)=SWCI+1+M,JJ) 00143100 00000172 445 CONTINUE 00143200 00000173 DO 455 1=1,M 00143300 OOOC0174 GX2CI)=GA2!I)»DC:>/CC3)/CU3) 00143400 C0000175 A A W £ I * N , I T N ) = G X 2 C I ) 00143500 0C0OC176 AS',.'CI*N,NICI) )=-GX2CI) 00143600 00000177 IFtGA2C5)/ABSCGA2C5)).GE.0.0) 00143700
IMPLICIT REAL'S (A-H.O-Z) PARAMETER < RG=8.314, K = 5. E?S=1.0E-6. XI0=1.0E-2« XIHIN=1-0E-DIMENSIOV SHC3/. S C I O . 0MG3(O. OKGytlO. AM0LCK*1) COMMON /MLWG/AMOL
S H C ) = AMTC ( R E . S C t 2 > . XBVO ) SH<2> = AI1TC ( R E . S C C 3 ) . X8YD ) S H ( 3 ) * AMTC ( R E . S C C 4 ! , x'BTD i TWK = TW * 2 7 3 . 1 5 F = a 0 0 . 0 » E X P ( - 6 2 0 0 . 0 / T U K ) AN = C . 7 5
0 » E X P ( - 1 4 2 0 0 0 . 0 / R G / T W K ) » C P / 1 . 0 1 3 E 5 > « « 0 . 5 C . 2 0 9 5 / A M C L : 2 > ; » « A K E X P < - 1 6 2 7 1 0 . 0 / R G / T L ' ! O
FNC = A 0 2 R « X I « » A N • A 0 2 L - X I - A 0 2 L - O M G 8 C 2 ) FKCO = A 0 2 R * A N » X I - « I A N - 1 . 0 > * A 0 2 L X I P 1 = X I - FNC/FNCO ERR = ABSt ( X I P 1 - X D / X I )
I F ( E R R . L T . E P S ) GO TO 2 0 0 I F ( X I P 1 . L T . 0 . C > X I P ! = X I M I N
FORT~A~77 EX V~2LI0 DA TE 92-a,9-2. T Hぞ 20:'-2:03
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