CANAL USER'S MANUAL
by
A.
Faya,* L. Wolft and N.
Todreast
J.
Energy Laboratory Report No. MIT-EL 79-028
November 1979
*Ph.D. Candidate, Department of Nuclear Engineering
tAssociate Professor, Department of Nuclear Engineering
t
Professor, Department of Nuclear Engineering
1_
____ ____I_
i
REPORTS IN REACTOP THERMAL HYDRAULICS RELATED TO THE
MIT ENERGY LABORATORY ELECTRIC POWER PROGRAM
A.
Topical Reports
A.1
A.2
A.3
A.4
A.1
(For availability check Energy Laboratory
Headquarters, Room E19-439, MIT, Cambridge,
Massachusetts,
02139)
General Applications
PWR Applications
BWR Applications
LMFBR Applications
M.
assoud,
"A Condensed Review of Nuclear Reactor
Thermal-Hydraulic Computer Codes for Two-Phase Flow
Analysis", MIT Energy Laboratory Report MIT-EL-79-018,
April 1979.
J.E. Kelly and M.S. Kazimi, "Development and Testing
of the Three Dimensional, Two-Fluid Code THERMIT for LWR
Core and Subchannel Applications", MIT Energy Laboratory
Report, MIT-EL-79-046, December 1979.
A.2
P. Moreno, C. Chiu, R. Bowring, E. Khan, J. Liu, N. Todreas,
"Methods for Steady-State Thermal/Hydraulic Analysis
of PWR Cores", Report MIT-EL-76-006, Rev. 1, July 1977
(Orig. 3/77).
J.E. Kelly, J. Loomis, L. Wolf, "LWR Core Thermal-Hydraulic
Analysis--Assessment and Comparison of the Range of
Applicability of the Codes COBRA IIIC/M1IT and COBRA IV-l",
Report MIT-EL-78-026, September 1978.
J. Liu, N. Todreas, "Transient Thermal Analysis of PWR's
by a Single Pass Procedure Using a Simplified Nodal Layout",
Report MIT-EL-77-008, Final, February 1979, (Draft, June 1977).
J. Liu, N. Todreas, "The Comparison of Available Data on
PWR Assembly Thermal Behavior with Analytic Predictions",
Report MIT-EL-77-009, Final, February 1979, (Draft, June 1977).
4,
34 4
ii
A.3
L. Guillebaud, A. Levin, W. Boyd, A. Faya, L. Wolf, "OSUB
A Subchannel Code for Steady-State and Transient ThermalHydraulic Analysis of Boiling Water Reactor Fuel Bundles",
Vol. II, User's Manual, MIT-EL-78-024, July 1977.
L. Wolf, A. Faya, A. Levin, W. Boyd, L. Guillebaud, "WOSUB A Subchannel Code for Steady-State and Transient ThermalHydraulic Analysis of Boiling Water Reactor Fuel Pin Bundles",
Vol. III, Assessment and Comparison, MIT-EL-78-025, October 1977,
L. Wolf, A. Faya, A. Levin, L. Guillebaud, "WOSUB - A Subchannel
Code for Steady-State Reactor Fuel Pin Bundles", Vol. I, Model
Description, MIT-EL-78-023, September 1978.
A. Faya, L. Wolf and N. Todreas, "Development of a Method
for BWR Subchannel Analysis", MIT-EL 79-027, November 1979.
A. Faya, L. Wolf and N. Todreas, "CANAL User's Manual",
MIT-EL 79-028, November 1979.
A.4
W.D. Hinkle, "Water Tests for Determining Post-Voiding
Behavior in the LMFBR", MIT Energy Laboratory Report
MIT-EL-76-005, June 1976.
W.D. Hinkle, ed., "LMFBR Safety & Sodium Boiling - A
of the Art Report", Draft DOE Report, June 1978.
State
M.R. Granziera, P. Griffith-, W.D. Hinkle, M.S. Kazimi, A. Levin,
M. Manahan, A. Schor, N. Todreas, G. Wilson, "Development
of Computer Code for Multi-dimensional Analysis of Sodium
Voiding in the LMFBR", Preliminary Draft Report, July 1979.
_
------
iii
B.
Papers
B.1
B.2
B.3
B.4
B.1
3. 2
General Applications
PWR Applications
BWR Applications
LMFBR Applications
J.E. Kelly and M.S. Kazimi, "Development of the Two-Fluid
Multi-Dimensional Code THEPRIT for LWR Analysis", accepted
for presentation 19th National Heat Transfer Conference,
Orlando, Florida, August 1980.
P. Moreno, J. Liu, E. Khan and N. Todreas, "Steady-State
Thermal Analysis of PWR's by a Simplified Method,"
American Nuclear Society Transactions, Vol. 26, 1977, p.
465.
P. Moreno,J. Liu, E. Khan, N. Todreas, "Steady-State
Thermal Analysis of PWR's by a Single Pass Procedure
Using a Simplified Nodal Layout," Nuclear Engineering
and Design, Vol. 47, 1978, pp. 35-48.
C. Chiu, P. Moreno, R. Bowring, N. Todreas, "Enthalpy
Transfer Between PWR Fuel Assemblies in Analysis by the
Lumped Subchannel Model," Nuclear Engineering and Design,
Vol. 53, 1979, 165-186.
B. 3
L. Wolf and A. Faya, "A BWR Subchannel Code with Drift
Flux and Vapor Diffusion Transport," American Nuclear
Society Transactions, Vol. 28, 1978, p. 553.
B.4
W.D. Hinkle, (MIT), P.M. Tschamper (GE), M.H. Fontana,
(ORNL), R.E. Henry, (ANL), and A. Padilla, (HEDL), for
U.S. Department of Energy, "LMFBR Safety & Sodium Boiling,"
paper presented at the ENS/ANS International Topical
Meeting on Nuclear Reactor Safety, October 16-19, 1978,
Brussels, Belgium.
M.I. Autruffe, G.J. Wilson, B. Stewart and M.S. Kazimi,
"A Proposed Momentum Exchange Coefficient for Two-Phase
Modeling of Sodium Boiling", Proc. Int. Meeting Fast Reactor
Safety Technology, Vol. 4, 2512-2521, Seatle, Washington,
August, 1979.
M.R. Granziera and M.S. Kazimi, "NATOF-2D:
A Two Dimensional
Two-Fluid Model for Sodium Flow Transient Analysis", Trans.
ANS, 33, 515, November 1979.
iv
ABSTRACT
This report gives a detailed description of the input data
and contains a listing of the computer program CANAL.
A
sample problem is also provided.
v
Brief History
In the fall of 1976 Louis Guillebaud performed the
first consistent check on the models and method of solution
employed by the computer program WOSUB
extension of the MATTEO code[4].
[1,2,3]
which is an
Alan Levin provided the
additional subroutines for calculating the heat transfer
coefficients and critical heat flux thus enabling WOSUB to
present data beyond the scope of the MATTEO code.
In the spring of 1977 William Boyd concentrated his work
on a parametric sensitivity study of the empirical parameters
of the WOSUB code and their effects upon the overall results
[3].
He was succeeded by Artur Faya who added to the code a fuel pin
model based on the collocation method
[1].
In the fall of 1977 Artur Faya started the development of
the CANAL code which is the subject of this report.
New
physical models were necessary because WOSUB results for some
important experiments were not satisfactory
[3].
Besides the
physical models of WOSUB tend to overestimate the transport of
vapor for bulk boiling conditions.
This in turn leads to
numerical instabilities in some cases.
The similarities between WOSUB and CANAL reside only on
the numerical scheme, heat transfer coefficient package and
fuel pin model.
CANAL and WOSUB differ in the following main
points:
· mixing model
· vapor generation rate
· liquid and vapor are treated as compressible
in CANAL and incompressible in WOSUB
· correlations
for fluid physical properties
. correlations for friction pressure losses
vi
L. Wolf supervised the foregoing efforts.
N. Todreas
assisted in the supervision of the final stages of
Artur Faya's work.
References
1.
L. Wolf et al. "WOSUB - A Subchannel Code for Steady-State
and Transient Thermal Hydraulic Analysis of BWR Fuel Pin
Volume I - Model Description", MIT-EL-78-023 (1978)
Bundles.
2.
L. Wolf et al. "WOSUB - A Subchannel Code for Steady-State
and Transient Thermal Hydraulic Analysis of BWR Fuel Pin
Bundles.
Volume II - User's Manual", MIT-EL 78-024 (1978)
3.
L. Wolf et al. "WOSUB - A Subchannel Code for Steady-State
and Transient Thermal Hydraulic Analysis of BWR Pin Bundles.
Volume III - Assessment and Comparison", MIT-EL 78-025 (1978)
4.
G. Forti and J.M. Gonzalez-Santalo, "A Model for Subchannel
Analysis of BWR Rod Bundles in Steady-State and Transient",
Int. Conf. Reactor Heat Transfer, Karlsruhe, Germany (1973)
vii
Contents
1.
Introduction
1
2.
Input Description
1
3.
CANAL Flow Diagram
8
4.
Description of Subroutines
10
5.
Sample Problem
12
6.
Listing of CANAL
18
7.
References
90
II
1
1.
Introduction
CANAL is a subchannel computer program for the steady-state
and transient thermal hydraulic analysis of BWR fuel rod bundles.
The physical models and numerical scheme used in the code are
described in /1/.
The purpose of this manual is to introduce the user into
the mechanism of running the code by providing information about
the input data and options.
2.
Input Description
The input data for CANAL is divided into sections by type.
The first card of
each section contains the section number
(four-digit integer) which defines the type of input to follow.
This permits the user to treat many problems in the same run
and only the sections which are changing from the preceding
problem need to be supplied.
A blank card must be the last
card of the first and each succeeding case in a deck of input
data.
Every case must begin with a title card with any
alphanumeric information in columns 5 to 72.
A negative
integer in columns 1 to 4 of the title card indicates that the
preceding was the last case.
INPUT DESCRIPTION
Card
Format
Case Control Cards
1
(I4,17A4)
ICASE, TITLE(I) (I=1,17)
ICASE
Problem case number
TITLE
Identification of the problem
Section 003 - NSUBS, NRODS and options
1
(214)
NSUBS, NRODS
NSUBS
Number of subchannels in the
lattice.
NRODS
Number of heating rods in the
lattice.
2
IUSYS,
ITRAN, ICHF,
ICISE,
ISHAP,
ICOUPL, IPRI, IPRL, NPTR, NSPAC
IUSYS
System of units indicator.
IUSYS=O, metric
=1, British
ITRAN
Type of transient.
ITRAN=O, steady-state
=1, mass flow transient.
=2, power transient
=3,
ICHF
CHFR Correlation indicator
ICHF=O,
ICISE
pressure transient
No CHF calculation
=1,
Hench-Levy
=2,
Barnett
=3,
CISE
Order number of a center subchannel for CISE CHF calculation.
(1014)
3
Card
Format
ISHAP
Axial power shape indicator
ISHAP=O,
=1,
ICOUPL
flat
tabulated
(Section 009)
If ICOUPL>0, thermal coupling
between fuel and coolant.
IPRI
If IPRI>O, print input data
IPRL
If IPRL>O,
long print out of
results.
NPTR
Printout of results every NPTR
times steps.
NSPAC
Number of axial locations
where grid spacers are present.
Section 005 -
1
Subchannel Layout
MSUB(I) , KISUB(I,K) (K=1,4)
MSUB
Total number of type I subchannels in the bundle.
KISUB
Adjacent subchannel identification
number for up to 4 subchannels
(in ascending order).
2
LIROD(I,K) (K=1,4)
LIROD
Adjacent rod identification number
for up to 4 rods
(614)
4
Card
Format
Section 007 - Subchannel Geometrical
and Hydraulic Parameters
(Read NSUBS sets of cards 1,2,and 3 sequentially)
1
A(I),
or m )
Subchannel flow area
DEQ
Subchannel equivalent hydraulic
(in or m)
(4E10.0)
PFRAC (I,K) (K=l,4)
PFRAC
Fraction of the perimeter of rod
LIROD(I,K)
3
(in
A
diameter
2
(2E10.0)
DEQ(I)
bounding subchannel I.
(4E10.0)
GAP(I,K) (K=, 4)
GAP
Gap width between subchannel I
and the adjacent subchannel
specified by KISUB(I,K)
4
(in or m)
(3E1().0)
ZTOT, DROD, ACISE
ZTOT
Bundle height
DROD
Diameter of heating rods (in or m)
ACISE
Flow area of subchannel ICISE (in2 or m
(in or m)
)
Section 009 - Fuel Rod
1
MROD(I) (I=1,NRODS)
MROD
(1814)
Total number of type I heating
rods in the bundle.
2
RPEAK(I) (I=1,NRODS)
RPEAK
Radial peaking factor for rod I
(1.)
(7E10.0)
5
Format
Card
(card 3 is needed if ISHAP>0)
3
(7ElO O)
SHAPEF(J) (J=1,JMAX)
SHAPEF
Axial shaping factor (1.).
(.card 4 and 5 are needed if ICOUPL>0)
4
(5E10.0)
RFS, CONDF, CPF, RHOF, HGAP
RFS
Fuel radius
CONDF
Fuel thermal conductivity
(BTU/hr-ft F or W/m C).
CPF
Fuel specific heat
(BTU/lb F or J/Kg C).
RHOF
Fuel density (lb/ft 3 or Kg/m 3 )
HGAP
Effective Gap Conductance
(BTU/hr-ft2 F or W/m
5
2 -
C)
(4E10.0)
RC, CONDC, CPC, RHOC
RC
Clad thickness.
CONDC
Clad thermal conductivity.
CPC
Clad specific heat.
RHOC
Clad density.
Section 011 - Calculational Parameters
(214)
JMAX, ITMAX
JMAX
Number of axial nodes.
ITMAX
Maximum number of iterations
to find the mass crossflows
2
DT, TMAX, EPSP
DT
Time increment.
TMAX
Total time of calculation.
EPSP
Convergence criteria to
equalize pressure drops.
(20).
(3E10..0).
6
Card
Format
Section 013 -
1
Fluidd Inlet Conditions
P, POWER, FINLET,
HINLET
(4E10.0)
P
System pressure
POWER
Power added to the bundle
FINLET
Inlet mass flow rate
(psia or N/m2).
(KW).
(Mlb/hr or Kg/sec).
HINLET
Inlet subcooling
(BTU/lb or J/Kg).
Section 015 - Transient Specifications
1
NTAB
NTAB
(I4)
Number of tabulated points.
(Card 2 is to be repeated NTAB times)
2
TTAB(N),
TTAB
(2E10.0)
VTAB(N)
Time;
first value must be
always 0.
VTAB
Value of the quantity specified
by ITRAN
(flow, pressure or
power) at time TTAB.
Section 017 - Empirical Parameters
1
(3E10.0)
YK, TETAM, CKNOT
YK
Parameter K
TETAM
Parameter
in the mixing model.
6M in the mixing
model.
CKNOT
Drift-flux concentration
parameter, C.
Card
2
Format
AFR, BFR, CFR
(3E10.0)
AFR
Parameters a, b and c, respec-
BFR
tively, in the friction factor
CFR
correlation
(f = aRe-b+C)
Section 019 - Spacer Coefficients
1
SPACL (N) (N=1,NSPAC)
SPACL
Distance from spacer axial
location N to the bottom of
the core.
(card 2 is to be repeated NSPAC times)
2
SPACER(I,N)
SPACER
Grid spacer coeffient for subchannel I at axial location N.
(1E10.0)
8
3.
CANAL Flow Diagram
Read Input Data
Preliminary Calculations
1
Evaluate Fluid Physical Properties
Set Inlet Conditions and Guess
Crossflows for First Axial Node
L
Solve Conservation Equations
'--
r.
--------
Criteria
P
i-
I
avl
|
no
?
Iterate to Obtain
New Crossflows
es
Compute Liquid and Vapor
Densities, set Inlet Conditions for Next Axial Node
and Guess Crossflows
MAX ..
Fuel Coupled?
Y
Compute Heat Transfer
-Coefficients, Compute
Fuel Temperature
Distribution
no
IF,
-
~~~
------------- ~---
I--`---
9
4.
Description of Subroutines and Functions
MAIN
Calls subroutines to read input data and
performs preliminary calculations
READ1
Reads the input data
RITE1
Prints out input data
RITE2
Short printout of the results
RITE3
Prints out local quantities
RITE4
Prints out CHF information
TSTEP
Controls time step
XMASS
Computes mass exchange between subchannels
XENGY
Computes energy exchange between subchannels
XMOMT
Computes momentum exchange between subchannels
CONSV
Solves conservation equations in each of the
subchannels
VAPSC
Evaluates the vapor source term
PARAM
Computes parameters that depend on physical
properties
CIRCUL
Finds the circulation paths
MULTI
Multiplies a square matrix by a vector
CONNCT
Sets the subchannels connection matrix
CHEN
Computes the heat transfer coefficient
CHF
Computes the critical heat flux
TURB
Computes the turbulent radial velocity
FREG
Computes the two-phase mixing multiplier
FUEL
Computes fuel temperature distribution
NODCO
Evaluates nodal coefficients employed in the
fuel pin model
FVS12
Evaluates Hermite cubic polynomials and
their derivatives
11
CONLIQ
Computes the thermal conductivity of the
liquid
CPLIQ
Computes the specific heat of the liquid
VISLIQ
Computes the viscosity of
SURTEN
Computes the surface tension
TTSAT
Computes the saturation temperature of water
as a function of pressure
ROL
Computes the density of the liquid
ROV
Computes the density of the vapor
HLIQS
Computes the enthalpy of saturated water
as function of pressure
HEVAP
Computes the latent heat of evaporation
POLY
Evaluates a polynomial of n
FFACT
Computes the single-phase friction factor
FIL02
Computes the two-phase friction multiplier
FIL02L
Computes the two-phase local friction
multiplier
the liquid
th
order
12
5.
Sample Problem
Fig. 1 shows the GE 9-rod bundle /2/.
The sample
problem is the GE run 2D1 where the power distribution is
uniform both axially and radially.
One can see that for
this particular case there is a 45 °
symmetry and the
analysis can be performed using a configuration of the
type shown in Fig. 2.
Other data of importance are
Pressure
1000 psia
Total bundle power
1064. KW
Inlet mass flow rate
0.01098 Mlb/hr
Inlet enthalpy
-259.2 BTU/lb
Total height of the bundle
Flow Area
Subchannel
-
·
6 ft.
Hydraulic Diameter
(in2)
(in)
Corner
0.0391
0.28028
Side
0.1824
0.4467
Center
0.1447
0.6465
--
--ii-
I
-'-----I--
12a
Fig.
1
- Geometry of the GE Nine-Rod Bundle
12k
-
.
.. .;.L
A.
C7
wsd-t?
2
Fig.
Snimple subchannel layout to describe
input
II_
_
_ _
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B
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data
13
Input for the Sample Problem
-
GE 201
0003
3
3
0
0005
8
I
0
0
0
4
3
.28028
.4467
.168
.e L65
.57
l
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1.'
30
0.
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0.
.001
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1 4
.32
0000
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1
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1.
1000.
L
2
1.
2
1
8
2
2
1
0007
0. 0391
.125
.1 35
.1 824
.5
.135
.I447
.5
.168
72
0009
4
0
0
1064000.
.01098
iO.
.25
1.3
259.2
0
14
Output for the Sample Problem
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IF (r , GT + 0 ) T W.. ( I.., J)
E::::EM
W
TC:l. ( L, ) =TC
- E NT R
I F( T .T.
)FLX (L, J)=HSP* (TWL.L -T Ul.
L)
HTP*t
'
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H ; cy
.
.:'
I...J
)Y- HS f-':
IHTPl... ( , J) =-ITF'
:)
)0 CONT I NUE
: F ( T GT
.
* 0 * ) CA...L
RCH
34
, H.
F AN:1
P
I::' ' (. F1:
L:' l-:Eoh: ):.i C FRTO 250.',')
C =T
20 .. 2 NR
3:R
F P
p (:::'!
r ) .fi:'TP R
A ) =
,
: PAF:IF
F:: : t ( L )
.2( C)ONTINUE FF,
X:l
i
22 J::2..:) .J fAX
22 CO3NTI NU E
TrO 24 J: 1 IJNA
J
I: F' (TQL..
(I
SE ' J)
L.E
O. )
TO 24
GO TO 2 5
24 CO NT I N UiE
25
(J)
LZT
LI. OT -DZF:LOTT
IF::L
( LtLE -O )EL.=O
1E=BDEQ ( ICISE )
G -FF: XI T/E
F A
GCIS:SE= TOT ( 1: CISE, JMAX)
CfLL.) GI
CHF (., , (G,X
C,HI NL ET,
250
L T_
(.'1:,1
RIT HL C I
i:1: CCi' R
CAIl.L RITE4
CONT INU
E.
iF: i i-.F
'R T
IF(
,
'P1L
3. GT.
C B,
ISE
RD
, CRT
NTS
PX,
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RI TE
IF( I TRAN o LE; 0 Rl ETU.N
IF (NT C.
G 0
( ) I::': FPR1L
T::: T+TI
GO: TO 1000
E N El~
__
GO
:.
,P
:I:T )
,';).,, ;D t 17
O 3 17
rINUE:
12 COiNfT:i
_I______
SE
E
- BZTOr
L CP I
2.
R
,
35
31.J Et .)I.MT
C
..........t.'. - ..
NI
ALRC
.FI..
EF I
ARCI
S ::
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I
IPRF.... NF'TR, NTAB.I.
TCASF:.
COMMON /INLET/ fP F'OWER F N.I.F:T HINl.ET
( 54) r,
I RD 13
(45,4) ,rLO: ( 45) LT
iN
COi:MMON /L.AYO:'T/KSUS(.IB(45) KSJB
( 35 ) :E I:O' ( 35 ) , I R,tCD ( 35, 4 )
I..C
I R : ( 35 4 ) ,MSU1B ( 45 ) .MRODZ
'
DEQ(45), GAI' (45s4) Fl-lA'T( 45., 4) ,! F'FRAC (.45,4) P
COMMON /EOM/A(45i)
30) AREA ZTOT lDRO , PRt)D
SP:ACER(45:
NC IRCS JMAX, iTTMAX
C'OMMiEN /NIJ'I/NSUES NRCDES T'S tJBS s,N'ROFSf:t,
COMMON /NU.MR/DZ1RZ fT DZD'T EF'SF'
T AB( 30 ) VTrA ( 30 )
COMMO.N /TRAkN/T,- TMAX
)
, I.1. ( 35 30) y'CL. ( 35 S
:'-.lX (35 y 30 )p RDF':W t')3
COMMON/ROt2DX:/
1I2)
iO
(
35,
30)
)COEl::.
TWL(3
(3
S5
5
0
FSF'... (35,30) ,lHrTPL
i
. OMM3ON/FU EL.1 /CONDF CONC, CPF 'CF'CY RHOF, RIOC ,A I...F'HF , AL F'I-AC HGAF , ,
*
R,
RGR
( 12 ) XCO ( 12) '
CS,I F7r:-SYFti , l Y El._ C !,D'EL.Fr lDFYE,. E .DXC
VtVJ C NOflT - EF'S EE, I.fE
COMMON/F'ARM/ AFFR, B'FR:, CF'1: Y ,rTETA
SI GMA ,
P RAND, V SC:L. C ON.L
'rsAr AT
fCON:PON/F'R OFi'/IVIA ' I I SAT T 9
' CF'PL . vYTSC(,V I7DHV]T P DFtIwr' GRAD.
( )pR
.P)
) ()
CC)MMON.t./f-'ES.S/F'rR
JB2D/rlTRu ( ' 30) AL.PHA (45 S30) ILIf (45 30) ,TL L (45 ,30 ),
CMr
0M ON/St
y
A,IWLTR(45,y30) ,DENSV(45v3 -i30)
T'tQLiAL..(45t30) ,X0tJA...(45y30) WV'TRF(45,f30)
GLIQ(45 30) GVAP(45 30)
y
* RENSL1(45 30) GTOT(45,"30@)
NV (80 80 )
ACI
( 80,80)
I NI ( 45 45 5AC
C'OMMON/CNN/NNN
DIMENSION RHOVA1f 4 ) RHI...
( 45)
DIMENS]:ON C(80) ,(0)
,
5) AJLI (45) GT(45)GN(45 ),YFI(45),
; IMENSION
,
AJ T(4 5)J A,..tA(4.'I
ASTR(45)
,
(45)
*ttVN (-45) , H_.IN (45) , tLN (45) AJN (45) ,,AJVN (45) AJLN
* FAC (45) , EDF'(45)) EIF'O ( 45) I:'rS (45)
BDIMENSTIONl.IWVT'(45) YWI...T(45) WT(45) ,WTOC(45) 1,H3fSTAR(45) ,TF'XM(45)
WViK (45,4),WILDK (45,4)
DIMENSION WTK(45,4)
DIMENSION FI(4)F'H(4)
.:,]X~
IT=:l.
PN=F'
C --
EVALUAJiTE PHYSICA....L F'PI:tOPF'ER;TIES
C
IF(TI...EO
)GO T
'O
15
HFO=HSAT
5
*
SA
L T=tl. I S
(L
15 FI1ATr" =HEVl tF( FP)
Hl AT -: EAF
tH ( F' )
H (3:-F11LAT+F;HSAT
T'SAT=TTSAT (F' )
COND:.N.l.:: CONI. JQ ( T'SATF ' )
CIL=CI-F'L. I ( PF')
v I SCL =v I SL I ( TSAT )
( TSAT )
SIGMA=-StRTEN
.cD
FPRAN: =CF'L* V I SCL./C ONDiL..
H!... =-I NI..ET
'+ HSAT
36
, '.1 i:iF,
I
.~,
fj 1i11.
£
RHC'f: I
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f:TN i
l V,
:: , G
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f
TT:ii : FT i::f:t
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I:
...
: N THOi
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/
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( : I I I =O.
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T ( I ) =-,.
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::
I
)
: =-H..E'r
. l f :AI
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id
I NIUE
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F*i.
. . .T
r.' i 1.
r.- ..
I.V=fIV'
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1)
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37
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:: F: ( I T , . . ) VFI FW:FN ( I )
Ft1-1i ( D
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:: L
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L UXt. (I,
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ccu
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t ... R:1:OY
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1
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p
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BiPS (II) BP
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ER : R
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S
ETP ( )
( I ) El:tF'
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25 CONTIUE
IF- T r :f . l:TMi AX 30 T
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:I:: (K(ONV GT OG)
)
TO 1. 000(
IF ( IT ~GtTo :T).
IO
TO 10:1.
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PAV >
NV=0ilO
C
.
C
----
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wrOT:=O
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F::f-t
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CFSSFL.(3OWS
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)(
tI''
+
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WJTTF-WT ( I:) -0 I *WTiN*OP
) ./DPAV
WT O)( IWTf ( i )
A
F I-JCI.
38
j>:}~~~~~~~~~~~~~~~~~
y:
l.t
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r
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:::i I - 3
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1:'.-I
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76
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)
:[ :i.:
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39
1.l1,
Of NTINUE
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, ,(J ) : PF.AVr
'1 ) S0 T : J-. N US
· ^ ( fF;:RT:R(I.,.)
y ) =W' ZTr]:
R)
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I
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i : '. s)v yfE P ). *
C:
7
I (=:I0)
T:
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(I... J T '
') -I N ( I: )
AFES, (:I:
,
fBl (L.( :1: .'
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L
(NI
:I: ) ( I)
(T... TIQ( r I:T J)::':
J
XTR
ffL... . ( I- J ) --.(
:
fL.JI .. ( tiN
I J)
M(
RH J VN (
1.A YI (,
J * -":1
GTO I, J ) Gi.. 1 ( 1 , J
C
)
it..
R
( ) *~tATI:A)N
.)
:J:
f
ARHOL*HLN
.!...A
I )
GVAP ( 1 ,
)
C.,
. ........... SEINE T
CONDITIONS FOR' NEXT AXIA
:I:F ( ) I
AJ :t: )
N
ATL 1: I)0 .
N(
SGT( I ): .3N (SI
J4 1 ) =HL.N ? ( .1:
Hi
T :.i: tI.)
F
IF
N ( .)
. EQ
.) J HI
RE T
F =J,
1N
'
"FIlT GUE:sS FOJR
....
C..
dt... T( I =:
)
·
( ,
0.
,.1ll HT ( I )=0
GO
r.-:Sl~~E
-
i' O J
MASS CROSS FLOWS
NODE
(
: ) )/G,|N
()/i-
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.
i
40
).
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0 I" )
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)
K ,W
DV K
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TIWff
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S U.B.CH11
R::'1:tOP /HV A 1S3AT,
;I::'I
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,4i
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C:OHf r N / O' 1: 7 I ON/ I UJSY , 3 :T: RF N r CH1F : C I SES :I:AP ,li i:1 F: L 3: F: R rI
* IrF"L. PN T R , NTAB, I CrASE
CO: MMON /1...AY
A C.li1
UTI/ U
i )A, , S
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,s
B 4:, , 4 ), RLRO El 4 5 ) IR...X
45
)
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4)
, Sl j(4 4 ')
itF.
MRO
, " 35) IR) l (I
: Rt X:
B.(3 ,4)
CO)IMMiON /
M/
( 4 ) D (.1 4
t
F:' ( 5 4 ) , ::Ji.E , ( 4 P4 ) ,AT
il5
14hC
C (F
45
* S'PACi3ER ( .45S3 ) A EA ZTOrT
t ,::'
COMM CNl f/N.M
UMI /NSUt.S , NODS"
l';,f:lOS
,
Yi '4S,. Xt'
YNCI
,TCS
TJMAUX:, Y
]s'i'
A Y MAX .I
:T MAX
COMMONI /N.H1R
./I.ZTry D ZT'
EPSP,Y EF>S1-':
COMMONi:/H X./Tl. 'L ts( 4S45
D:t f.ENS
i
ION WT"f'
K ( 5 ,4) ,W VK
4 4) , W i:l ; 4it 45) iW...M (45,r 4)
* MI.LDK( 4'-. 4)
DI MiENSN WT45) W. ' 1 i5) , W... r ( 45)
IM:E:
tl: E:_A:r:N ... ( 4 5 FrH
) R1 f l. i(4)
I ( 4 .5 ) G (G45)
lf :1.0 1 .I. N
B Ur S
C(OMO/
Mi3N
i: I::'
i
t
,
4 >
.KS::1tSUBt.
(I )
DO 9 K I=I KS
Wli..M :: )
WVD==.
; -1
= i
1) I•
'
i F(A. A(
i. LE
.GO TO 6
IF(AL..VFA(K) .LE-O,)GO TO 6
RHOV,=O
L= , o.5
5:
* Ri -1 L APC)
( ) 1)
+F;,l
F K) )
EHOL=O
5R)
EKKfI=(1•)
E :VMIX:-WVM=
- l'*TIL(IK)*(
I i
, 1- I
WT =f4'T I:.
IS=t:: I
I
1 !-* ) ( (K)-LF(I)
':
K -..W VA..
-
IIL
E3,K
+) E
::
I F ( .I G o 0 ) I:=::K
GWrHt-O'
T.O'Wf:/ ,ALrF
IS)
WLD.W-W
VD0..*Wv:Cr
GO TO 7
6 WL..
Ll:::: 1WT K(I I 1 )
7 WV:=WV+WVD
WVMK
KI(
WVDK(I
WLMl.K ( I
WL...DK f
( I'-)....
I
IFA
S ) ) RIVtALF
( IS)
)
KI=WVM
)
,K1 )W-VD
1 ) =WiL
,K
): WL.D
9 CONTI:EN l)E
WVT ( I ) =-WV
------
·~~
_ 1__11__
41
:1.)
Wl..T ( I )W
FZET FU
I;N
IEN[
WkTI
--
(I )
42
St.-1 T: o U T :i .:
FS ENEGY
COI l.rPUTE
i
l
I fW y
*
,J:..
7V
BETiEEN
fEXCANGE:
iY
ii tl
O L. : c4i1-11
'.lF
CI-NT
A
T A ,h
ISJBCHtNNIEL..S
(5 ''4) ,
( 4 ) L.R. (4, . ) L. It
YO1T/KS. 1J.I ( 4il ) , It:S
/LA'
CO)Nic_
! f :r ( 35) I LRO ( 3 ; 4)
SU (45) ,Mi i( iS:)
*, L.. i; k C (35; i 4 )
(45 4 )
4) , PHIEAT ( 45 4 ) 7 F:R'F
rtEQ
l, (45) GAP (4..A'
.
/.:f:1
, (4'5)
/
COtM)iN
:)
f:
;'
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X:
)
TT
h
P
:'
AR:r
,Fi'
) : Ai::'
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C
,* SEfr'
C O IM :N / f :i:X/ t.'UT I L. ( 45 .45
1:iiM
G A"
N(:1:1 L
C '
l . rTAT SAT' F:'R A N' V: I,:
-IA
f H
H...T....!......
l A I::'
F1)P:'/A.1
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F"
Aft
y
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i'
1 :
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AX
R O S NC I CS' RJ M A y I TMI
SU
' Nf
N US'f:NR:ICDS N
l/
COMMO)N /NUtJM
ET F:PSP'::
CO-MMOtJ /NtMR/uiiDl IDT- YZI:T
4 5
IS T Af R 4 5,
)
fltIt: )ENri ON r i*VoAuP (45) F.t t... :G:I (R45 ) Iu... (
4,, -) WL . ( 45 4 )
DI M ENItON W K i(4C
lS=: KSU t ( FI3
tO 9 K t. TIS:tJ( i
iS
::
f.
IF (t WL K( I: K :)I GT 0, ) ::=K
( S) *i LAftK ( iI 1i )
+ i-i.
..
'
W V El 1-
T
:1
K
.
.T0
.i
V D K( I y J.
-.·t1-i L.A T
1
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S=T;
)*f:Z
!K1
, GAP(
9 CNTINU.E
10to H iS- F.( ,
I
K
S::,
R ET U
QI ( ( 7*H..
K)
(
; ) --
t
t
l I )!
ti1...
-( I ) )
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0Ur
).
0
P I
_
43
SUBO.JB
R: UT3
C
c=
U.,
...
....
...
*
N E:
MI::UTES
M
MOM Tr (.W TV:OlK , L,..
ElK
OME:NT
EX-ANGED
VSYV
V V , .. G
B rETW
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,
ALF:A
B, MI::x
)
ADJACENT
S;... CH1ANNELS
COMi iON /L- AYOUt /rIKSLJ ( 4)
KSC UB (45 4) L-ROI: (45)
IRO3D (45 ,4)
L.fC IRC ( 35 4 ) MS(J. (4'..5 ) ,i
MROt ( 35) I:R7,D_(
(
I L RO E't (y
4)
COMMON /GEOM/A ( 45) DEQ (41.5 ) ,GAF (45 7 4) ,FHEAT ( 45, 4 ) ,PF'rtC (45 4 )
1 SFAiCER ( 45 ,30 )
F'AEA ,ZTOT TD ROD ,PFROD
I:iCOMMO:N /Nl fMI/NSJ!BS N ROtlS, NrTS UBS NTRO
r
DS
rNTRCS,j tX
[TMAX
CfOMMO
/NtIF:R/DZ y r
rZT, EPSP
COMMON/MIX /UTiL
(45 tS
DIMENSEON VSV(45) ,VSL (45)
(45) ALFA (45) YPXM (45)
DIMENSION WL.ttK (45 ,4) YWVDK (45,4)
1 ) 1 =:Ir.NSJB
S
..
S K1S LI (I
1DO 9 KI : ,KS
K=KIS LE (I K1)
F1-WVBTK( I,K 1 ) ST o
) IS=
I F ( AL.. FA ( .S)
GT e
) S= S+ WVDl K(
I"t
"
1)*VSV( ITS)/A L FA( IS)
Xi::' ( W .I-B I,
* VK:. +G T 0 ) S KS=S-!JW1. DK ( : K1:) *SL. ( IS ) / ( o -ALFA ( 1: S ) )
S: S+ U T IL:E (
K )* G ( ) G3( T )*GAP (I,
1
J )a [Zn
RET U N .
END
44
.:.
0:f......:
Cfl:
Cr.
1.N
A
i
,
(MiMi
;:: -'
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i.i 1
N U,'r
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r.
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r
i:
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T .
I'P. ': f..
- ( fU
W. Sl.L
- . 'T ) *', 99
.:t ( T'L4l... i.. T , *
) C TO 26
tf:T
'CTC
,,'TSAT)G
29
1 (1 A.4L..
T C0G
12
Hf.
I-'F
::fli ( . )
Nl i..t,,p...
1)r:
XXTT
' ND
.:'Tf IP
=- TW
r 1: ( WA TL. --TT GO
GW0N/ TO
T) (T
A
T)
r
H"T
P= ,( 2 3* (
.1. -C
.')']UA ,, S B!.:.
8 tl-tCOL/. I '
1 ( F: : fN 'Ot f,4 : '
3
C..........
XX';.'T :-:: A Rf' N EL L I
A .../ (
XT T =
·l -A **,.)
IF(XTT,..GEO,,,.5)
GO
G1O)
9
F: 1. 6
( 2*
S J; t.::i
9:
TR 8I
GO
XTT"F r '
I.F (HI
.IT..0. )tF:.-l
ltI1 1 S t=
-. i-
.... ...
;'Ai';ETE
PA
S
, 73
N f1- IC
'TCI:;
C)
;L) k
L::
k
(F t
f
F
:
F
:::Cl.:i...l: S I (3j
,J,1Y I I:f SJ, t: ElF S,
N :1
r
"IIt...
I F T IW
-. I' ' (
I F ( P1F :-
1:!8
0
*
T
Y.rK:,
... .
(TO
:1.Ci0'N D .../ .'
D
:iI''f
3i))
B L'S.
' I t'::
V9 :i:
i, FAi:
if-'(f .t. ... ,)fO,
) G:l TOf .3
7 C:O
NT1
E
H!-- F .
02 ,* ( ( M,'E/V : C...*
... )
t,'
0 IJ
[ : UC)
T 0'
'
)A . .
IT,
TA.'i( 3'f )
)
(
V
lf.SP,
UX
lI./,
FH
):
'~ , ':-
4),
I. : EIM
67
I -- UAt[. ) D,/'
D
FET P ( GN{ ( .1.
.... )
FC') I
'.'5 )
T F(F TF'
32 )A
)G.O
RT 1|- 0.
.=. -':0 .1.7- 0
3'.
"'
'"
J-'f3 4 O +5)
1:1.2
GO3 'f'
: .1 S=O,.
:
:I1.
70
7*17..tO ,
iA
. TP/3:
rP
E+
G0 TO 12
10 S=-:.
:t. I F.Tr L .
0. . )Gr
TO 0
HTFITFF
-EE*
( TWALL-TSA
L
A' )
9.9S
Go0 TO 26
30 ''NE W -TSAT+DE .1. L.TS
. ICI--C
I F L.A 1 =0
1.3
I1.=10:I'+1
IF(ICGT3T100) G TO 26
I-ITF'=X:'EE* ( 'TNEW-TSAT ) *'X 99.S
'
0. )=iSF
IF1:'
( G 4
LEE O
IF(1Ft1LJ3GE+0)
(30 TO 14
F't-XNFIEW=-IHSF'* ( I'TNEW-TL1IC ) + FIP* (' TNEW-TSAT )
G 1 TO 1 5
14 Pl I NEW= ( HSIP+TF' T )
( TNEW--TSAT )
C
tc
1S
J.
,
¢E,..:
.,
_
I
ESTF: F
0. C0 I
( A S ( F' INE!J-HF'..t.
F(TESTF'T001)
H. LE.- O
)
GO TO
FL..
f.6
1 ° F' H 0 L f- = ' T rN E
rttNE WA
T.T(:l
Z F ( P'ItI N E W-HFLI.J X ) 19 169 20
ITERATE TO OBTAIN (TWAtL-TST)
C ---.
C
19 TNEW-=TNEW+1.
GO TO 13
20 TNEW=TNEW-I>
GO TO 13
'
17 TEST2= ( PHIOLt-HFLUX ) / ( FPH INI-t-HEFLUX )
IF(IFLAG.E(+1) G30 'T
21
IF(TEST2GGT
T.0.) GO TO 18
IFLAG=1.
IF(PHINEW-HFLUJX)222Y23
22 PHF1-1Il
F'IOLD
F'IHI LO=PH I NEW
TH I=TOLD
TL O=TNEW
30C TO 24
23 PFHILO=PHIOLXC
PH-I I-I = Ft TN E W
TFHI=TNEW
T L..0 TO ...
1D
F
HIFH
/ T
IL.. ) ( TH- - TI .O )
24 S ...o f:'E
___
68
2.1
1I I ) .
*T! 1:i
W=: ( - 1::F
1 ',
.
E, 7 1-i 1 ) 1 1-:1:
Gif0 T' :.1
: '(t
1:': j tJ G'' F I... U )GO i '25 .t
F' iI . f:)= FP- : NE 1::
COll)
'T
1f1....C
f*P
'
24
G
iF(1] TT 24
.
'LI..( Vi.'T I- .W1
G0 T 0
6
F-':'*
(tT W
A L L-TL.T
I C.)
:1::F1I TU
1-T C=-PH t:TRiU/. ( TW4A L- -TL. [ f
GO T
2
(
J ,
1- 1 .tf
T 'f' (T A L -TS T
)
T
IF T
E 0) R:EijRN
H Flt.UX-F'S* T1W...L. -TL.
Fi...JXHFL UX
1i il t. t
: +) !rT-'*
TW.L
.-
TS AT)
FN :tI
Illlll__llp-i---
j·llliXI-i·_Xii-(LlsIIIIIP
69
St.B.JRUit:tI
p-f
NEj C
HG
-'
P XAAICS 'CE
,CISE, Ei. B, ATOT' y O: :l ';P;PAf
* f'KAX yHIINL.ET !- IL..AT ZTO.T, NTfRl'RDS CRITHL, CiT'if rF';'ITC')
..
IEA-T
FLUX USING THRE-E CORR:tED.~A rONS
Ci:MF:'I.'ITES CIt'T:CAL
-'CRIT/3t04 . /
ItlATB
HLAT/232o,
H:B N = -:N-L EET..23
/ 266
F'B=P/695.1
.B=G/1356.2
BLB=BL/0,3045
DEB=rE/0. 3048
GCISEB=GCISE/1356 .2
DATA
ACI SE=
ACrSE/0 09290
ATOTB=ATOT/0* 09290'
TRR=DRO./O030488
1
C
HENCH-LEVY
---
CORRELATION
C
C
S3-=.:XF (3. *.B)
S 2=-E XF (2 *GB )E
'TH13:= ( 37*S3- :. ) / (S3*53+1 )
rH2=(S2..-.*)/(o'2'21
T<,
,.,
S,,,, - 1 ) ( S 2* 3 St
+
.))
X =0 .7
213-2*T
T* 3
Ht3
X2=0 . 5 -) . 2699 rH3 Ft--+O
3+ 3a6 *'rH2 *TH2
IF(XGT.X1)tGO TO 5
t.r,~T
5
)
5
TF(X.GTX°)G
O TO 1.
CRITFHL= . E+06* ( 1 +9-3 . 3*X-O o 7*TH3*T.3 )
GC) TO 1.5
:1.
CR ITHL-=1 'E+06* (O .6 -0. /7*X-0 09*TI-H2*TH2 )
15 IF(FBNE1000.)
1 CITHL-=CRITIL(1 1-01*((P--600)/400 )**
.25)
C
C ---
CISE CORRELATION
AC=(1 + -Fff/PFRIT)/(1,
35*3C SEB) .**, 4 3333)
.C=68-,*(PCRiT/PR-1.
,
GCS),0.4,(
EB) I...,
r DiEB..
4 '-' ) -:. '
I,v:;1 ...............
CRIT =AC/PKRA]/ ( t...l+BC
.)/ATOTB*TL
NTRODS-AC
WBL= 1 . E +6* C ISET*ACI SEBl*HLAT*CR I T
IF(LB .GT
. )CRITC=WB/BL/B/
C
C
-B--
BARNETT COREELATION
AOTB=ATTB*
144.
ZTOTR=ZTOT/0,0254
S=NTRODS/FPKRA D/PKAX
DE=4 .ATOTB/3+ 14159/DR/S
DKNOT (DR*(R+DE))**0.5 DEQU I V=DKNOT-DR
AB=67 47* (tE**O. 68)
*G*019.2)
IR/3. 14159
-E
:.- .'
.
70
A= X
I F P.
. I.
..
744.EX
! 2*:.'
' -6 ,,5
N
.10 0 *>) A
': *-- L! l r /, .
B
; f t (i : - :. 261
. . * ( B *)
!.*G )!
:::
)
3 :1. 7)
C=
t.i
*, ( :I. : V** 1 ,*
41. l,)
(
B**O1.2 )
C RT TB- AB1-B*
+
iNB
1H
) ./( ::rC+ZTVI.
E 6.
1.
FETTUIR N
I3 JETl.D-!
... -11--.
...I
71
SUR.::,i:..tTI
,
NE
fC..---- COMF'UTES
TE
TR'l.".
r
, .. aJl
I, Gr
t.UFI..EINTr T'RANSVERSE
F'HP
RHfL.J: Q, XTR )
ELOCITY
C
COMMON /OF'TI ON/ I.JSYS
TRr,
I CIF pe .TCISE, ISHAP,
F:'R I COLUF'L, I
l
IFRL, NF'T v N'IAB,? :rCASE
COMMON /IN..ETP
T F fPWEF FTNL..ET, H I N tET
COMMON/MIX/UtILB ( 45 4)
COMMON /AYOUTl.r/KS.B
(45) ,KIStJB (4- 4) ,LROD(4'5) LIROD(45 4 ),
* LCIRC:,(35 4) MS1JB
()
(45) MROD(35) !,:I'RO.(35) ILROfrl (35 4)
COMMON /.M
IT/NSJRBS , NRO:.CS NTSI.JBS
i
NTRODS NCIRCS JMAX, I TMAX
COMMON /GEOM/A(45 ) IEQ ( 45 )
AP(
4 ) YPHEAT( 4 ) YPFRAC(45 ,4)
* SF'fC.ER(4530) .AREAZTOTDRODPRODr
COMMON /NUJMR/]DZ , riTlZDT
9 E SF'
COMMON /TRAN/TTMAXTTAP(30) ,VTA(30)
COMMON/PARM/ AFR iFR CFR, YK ,-TETAM VVJ CKNOT EF'S BEE ,DEE
COMMON /PROF'P/HVAP HSAT HLT. r TSAT F 'RAND VISC1. C'ONDL, SIGMA ,
* CPL, VISCV DIHVDT
rDHtSDT GRAD
DIMENSION A.JT(45),AJVAF(45)AnJLI(45)GT(45)YRHOVAF
5),
* RHOLIU(45)XTR(45)
DATA AKL1/0.0058/. R-1..46/
'CM=I.
DO 1 I=INSJUBS
REY=ABS(GT(I) )*DEQ( I )/VISI..
AJL I=AJLI-( I)
XN
AJV1=AJVAF'( I)
X =XTR( )
Gi3=GT( I )
*
7
RHOV=RHOVAP( I)
RHOL=RH-OLI Q ( I )
IF(TETAMGT i . )
* CALL. FREG(AJVJ1,AJL1 G1, XI,D1,REY RHOV RHOLTETAMCM )
KR=KSIJB ( I )
D
1 K=IyKR
K=KlrSUB(I Kf )
DMIXN=AKLI*(JAF'(I
,K1 )/DROD)**R
XM= (1.+( E () /DE ( I ) )**,
5) *(EQ ( I ) /DROD) / (REY**O
1)*DMI
- XM=XM/2 .
:- T: L. (
K= X(
,*A.JT T ( I >CJ
1 CONTINUE
DO 2 I=1,NSUBS
KR=KSU ( I)
DO 2 K1=1-KR-:
K=KISUB(IK:1)
IF(K.LTI)GO TO 3
LJTILD (IK)= (UTILD( I K)+U TILD(KYT))/2.
GO( TO 2
3 UTILD(IK)=IJTILD (KlI)
2 CONTINUE
RETURN
END
..
. .
...
.
- -:.?: -.:s
.
.
;
.
..
....
..
q
.
.
.-
.
.
a
.
. o;
.
*
*
-·.
.
-- e
..
....
·
.
,_. .
....
-;
..
.
...
.
72 -.
SUB"'"IiEf' :INE
C
.. ..-
Fi.c ( AJ)
yJ..
JI S,''T ARF A:I. A' 2
C
COPUTE
S TWOPSf:3
fL'JJ.SI-:
ff:C......C
BES
...........
' 'SHEMfE:
IOl...W
,(3
XIl
., 1- YI'E,
Y
FRHOV
l
R:H:
l.. TET1A M
1_ 1T
LJ
A'
MX:NG
iUl hLfTIPLIE
R UJS'3ING
OfJiMOfN/FtRfO /VAP
LST
HSAF'
H
TSAT F'RAN.I, ISCL CONi:L.'
* CF
C,
r.
L, XVTD HST
HT
G RA D
:ATA A1. A2/0,4 06/
CMAX=TETAM
CL=l.
CV=:I.
XrAT=0 , 57*FEY*,*0, 04717
A JLR=AJL*SQR:''T ( R H O31 G R f i:l .' ( RHOL. -RHOV) )
AJ V R=AJV*Q
-)F
'Rr ( RI-l
l./
G R/I:'Af/r.l/
E. ( RI-Lt L -RHOV )
TEST=A1A-A2 AJL...R
XC=Ai
J. /G:,QeRt''
(G -TRAl*,RHOLE
*t(E
RHOfl f-Ot)
) + A2
XC= XC/ ( SQRT ( RHOL../RHOV) A2)
IF(A J VR .GT , TEST) C T
11
CM=CL+t ( :iMAX-CL.. ) /XC*X
RET U RN
.
i NE rl.Jf
CM=Ci
f-XRAT
+ ( CMAX-CV ) ' (
RETURN
EN'[I
,CM)
1: GMA
) . (X/XC--XRAT)
·.... ,
.1
i
___1__111__111_1_____
73
SUBf.frPUT.TNI E,TFI.JlE
C
C:
C
HSP HT'
-TBC
(QF RI,
JL
W
CALCUILATES
FUEL. TEMPERATURE DISTRIBUTION
T--USING HERMITE C.JBIC POL.YNOMIALS
rTF
TCE
f; )
IN THE RtADIAL DIRECTION
ICISE, ISHAP,I COlJF' IPRI
COMMON /OPTTON/TUSYS I TRAN'ICHF
IPRL NPTR, NfTAICASE
COMMON /TRAN/TTMAXYTTAB(30) YVTAB(30)
FCPC RHOF, RHOC ALPHAF ALF'HAC HGAP,
COMMON/FUEL 1/CONiDF CON CCPF
* RCRG RCSRFSXRCI ELCDEL
ELF,DXFyDDCXC(1 ) XCO(12)
NT2 NODE NE)S
COMMON/FJEL'2/NF NC NF NF2 NT N
MGAP9 NF'A NPF
DIMENSION RD(50),TEMP (50) , TEMP(<0)OPQ2(50),TAIJX(50)
JC=2
CALL NODCO( QFPRIM HSF 9HTP ' TtBIULK p TWALL )
*
DO 21 I=IYNPA
C
C---
TEMPERATURE PFROFILE IN THE FUEL
IF(I.GT.NPF)
GO TO 300
D=(I-1 ) *DDF
'IJ=D/DELF
XHF=ELF*FLOAT ( I J )
SMALL=hES ( -XHF )
IF(D.EQ.O.)-GO TO 22
) GO TO 23
.E-1.
IF(SMALL,,.. E , 1o
I 1 =IJ+1
X ( )- IJcBEFI )/BELF
Y= ( D- (IJ+l i )'TEELF )/!ELF
G0 TO 100
22 X=O.
I =IJ+1
GO TO 100
23 X=I .
I .=I J
1.00 AT=O
-....DO
150 K....
K=I JC
-. DO TI'O
:-.-- -
:-.''...--
.. .. :-.:....
F=FLOAT(K)CALL FVS12 (FOXYVX)
CALL FVS12 (FPOYVY)
CALL FVS12 (F,1,XVIX)
CALL FVS12 (F,1YsVIY)
rY=(II-1)*JC+K
III=II*JC+K
AT=AT+XC(II)*VX+XC(II1)*VY
150 TI=T1+(XC(II)*V1X+XC(II1 )*V1Y)/IELF
IF(D.EQOo.) GO TO e8
Q2=- .*CONDF*'r
GO TO 200
88 Q2=O0
GO TO 200
XII
-
-
--
;···
x
74
'
TE r I : M :: A !.t
300
1,r:':t F iI...:IEI THEF ClA f) :1NG
:RCf- + : N-r- 1.) *tr:1f'
( B-RC I ) /BELC
tf j-=
1·i:=R:1+E5
:ILC*FL.f OAT ( . )
S;iA L.. A1..S (- H C)
IF (
EO RCIE) GO TO 24
IF(SMALL
LE
:L()1-0)
GO
Tro 25
I :1. NF+ 1 +L .J+ 1.
v ( -RC - I .. *tELC ) /DELC
Y= (Dr-RC I - ( IJ+1 ) bDEL.C) /ELC C
GO rTO 120
24 X=O.
Y-1
11=NF+1+IJ+1
GO
.25
fTO 120
X=1.
Y=O
I=N--FI+l+J
T1=
.
J
T1 -0,
DO 250 NK=IsJC
F=FLOAT'(K)
CALL FVS12 (FYOYXsVX)
CALL FVS1.2 (FPOYVY)
CAL.L FVS12 (F,1 XV1.X
CALL... FVS2 (F :1tY VY
!!:r= ( :I-1 )*JC+K
IT=I1 *JC+K
AT=AT+XC ( I )*VX+XC ( I I .)*'Y
250 T=T+ (XC ( I I )*VIX+XC ( I 1)*V1Y)/DELC
Q2=- ., CONEIbC*T1
200 RD(I)=B
TEMP(I )=AT
21 CONTINUE
TCENTR=T-EMP ( 1)
TEMFW=rTEMF' NF'A)
RETURN
END
:
...
I
..- o, .-.
.. ...
. .
.
..
_
_________
t,
75
C
C
()r
SUB.;(Ol' TINE NODO( ( PPRtM,
HF' HSF'
... EVAI.UATES NODAL..
COEFFICIENTS
tL
'¥WAt... )
COMMON /TRAN/TqTMAXTTAB(30)VTAB(30)
COMMON/FUEL 1/CONDF ,CONDC PCFF CPC HO Y RF
HOC ! AL.PHAF ALPHAC, HGAPF,
')
* RCRGRCSRFSRCIELCL,EL:~rI-DDtF,
XL.(J.(),,xcO(.
COMMON /NUMR/DZDTDZDTYEPS
COMMON/FUEL2/NF NC, NFNT2~N NT1 NT2,NODE, NEQS
*MGAPPNPANPF
COMMON /ROP/HVAPFHSATIHLATTATTAF'RANDVISCLCONILSIGMA,
CFPLVISCV DHVDT DHSDT, GRAD
D IE(12) ,XR(1
DIMENSION XA(12l')pFXB(12' ),XNO
2)'XT( 12)
DIMENSION WKAREA(3000)
J2=2
HFILM=HSPF+HTP
Q3=QRIM/3. 14159/RFS/RFS
Q2CS=Q3*RFS**:2/(2. *RCS)
f2GAP=Q3*RFS**2/(RFS+RCI)
IF(T.GT.0-) GO 10 2000
.TCS=TWALL
TCI=TCS+(03*RFS**2/( 2.*CONDC ))*A.OG(RCS/RCI)
TFS=TC I +02GAFP/HAP
XN=O.
DO 10 I:=I-N
10 XNODE'(I)=XN+(I-1 )*DELF
XN=XNODE(NF1 )+RG
DO 1. I=NF2, NT2
11 XNODE(1)=X^N+(l-NF ) *DELC
1..)
DO 12 I=IYNT1
IF(I.EP.NF1)-GO TO 12
DO 12 J=l,2
CF=(- -,-)-**J .
XR(K)=055*(XNDE(I)+XNODE.+(I'
) +CF*(XNODE( I+1I)-XNODE(I))/
1(2.*1.732)
K=K+1
12 CONTINUE
-2000 'DO 7 I=INEQS
DO 7J=tNEQS
....~IfI.7':--..
7 XAIJS)
=0.
L=NODE
I=NEQS
14 IF(I-NEOS)
15 ,16 16C
C --OUTER CLADDPNG
C
16 CKHD=CONDC/(HFILM*DELC) '
DO 5 K=IJ2
F=FLOAT(K)
CALL FVS12' (F.OO,0.VO)
CALL FVS12 (FO1.V1)
CALL FVS12 (F,1,0.oV10)
CALL FVS12 (Fy,l,,Vll)
XA(I,(NFFNC)*J2+K)=Vl+CKHt*Vli.
·~? ·-
..-..
"" '
·--··-·
76
"::
X A.r : ( iN: i:'
* C+f . .J= . t+ . C ) I
X ? ( ) : ( S P* 'i"- .J-H
t...
FT ' T '- '
'E
*J . 0
) / 1-f Z1 Ni
(:0 T 0 .1.3
:tF'(
-MAP)
17, 1.8 :1.
9
1.7 F::(
: '-1 I
2 ' .. s202 1
t5
C- --
:N TE R
ERF
I
P:
CNTSIN T HE Ct A:Et: .1NG
19 I1=(XR(L )-RCI)/DELC
v- ( XR(L )-IRCI-I 1 *ELC)/XEL.C
Y=(XR( 1 )-RC I-(L.+1)*.ELC)/DELC
IF(T.GT.O.) GO TO 202
2.:01. O(26 K=I-,J2..
F:=F C)AT ( )
.
CALL FVS. '2 (FOXVX)
CALL FVS12 (FOYVY)
I 1t+NF+f )*,2+K) =VX
XA (
26 XA( I ( I+NF+2)* 2+K)=VY
XB(I ) TCSf (S3*RFS**2/ ( *(.,ON.C ) )*ALOG (RCS/XR (L
GO T 203
202 CK=ALF'HAC*DT/D ELC
TOLE=O.
t.) 39 K=:L:J2
F=FLOAT(K)
CALL FV:i. 2. (FOrXVX)
CALL FVS12 (F, 1 X VI.X)
'X)
FVS12 (F2X
FVS12 (F (O!YYVY)
CALL
(F i YYV:.Y)
CALL
FVS 12 (F329YYV2Y)
CAl.l FVS12n
XA(I
(
I.+NF+1)*J2+K)=VX-CK*( (V1X/XR(L ))+(V2X/qELC) )
XA(I,(IIFNF+-2)*J2+))=
VY-CK*( (VY/XR(L ) ) (V2Y/ELC) )
IJ=( I 1+NF+I )*J2+K
IJ1=( I1+NF+2)*J2+K
39 TOLD=TOLtD+XCO(IJ>)*VX+XCO( IJ)*VY Xe^(I)=TOL.D
203 L-L-1
GO. TO
C ·-
C
tz:·;i
13
fD:z
G
rA
... FUEL-?CLADD.TNIG GAP
. . .
... ......
'.
*·-- - ----·iT-
C'
18 GAPC=CONtIC/( HGAP*tELC )
DO 27 K=iJ2
F=FLOAT ()
CALL -FVS12 (FYO
1.,V>
.
:
CALL FVS12 (FO
,V0)
CAL L FVS 12 (F,0,-1
VN)1.
CALL FVS12 (FIO.V.IO)
CALL
FVSt2 (F:v-
-
+YVINi)
XA(I (NF-i )J2+K)=V1
XA ( :['PNF*.J2+K)=VO
XA (
(NF. GAF'C*V.--(-V
) *,.2+K )
27 XA(I(,' NF+2)*J2+K)=GAFC*VN1-VN1
XB(I )=o
.
I- ·- -··-·-·--
77
I : -1
GA F'- i::CONIBF'/ ( HGA *'D
I... ')
t(C) 8 KI-1.yJ2
F=FLOAT (K)..
(F09,O)
CALL FVS12 (FOP1.V)
CALL FVS12
CALL FVS12 (FO9-1.PVN)
C.'ALL i-VS12 (F I O.Y V O)
1 1. Vll)
FVS1 2 (FPP
CAL.
XA(Iy (NF-:. )*J2+K)=V+GAAP
F*Vl1
XA( I NF*2+K ) =VO+(GAFPF*V10
XA( I (NF +I)*J2+K)=- .*VO
28 XA('
tNF+2)*J2+K)=-l.*VN1
XB(I)=O.
GO TO 13
·
*s
C
C ----- INTERIORF-OINTS INTHE Ft.fEL
C
2.1
=XR ( L )/ELF
X=( XR ( L )-I 1
ELF)/DELF
EL F
Y=(XR(I)-(I1+1 )*ELF)/)/ D
IF(TGT.O.) GO TO 205
'204 DO 29 K=-..12
:~
F=FLQAT(K)
CALL FVS12- (FOYXVX)
CALL FVS12 (FPOPYPVY)
XA ( I 1 *J2+)=UX
29 XA(Iy(I1+1).t2+K)=VY
X(I ) =TFS+3* (RFS**2-XR(L )**-2) / ( 4 *CONDEF)
G. TO 206
205 FK=AL.PHAF*DT/DEL.F
TOLD=O.
DO 42 K=-..yJ2
F=FLOAT(K)
CALL FVS12 (FO,.XVX)
CALL. FV2
8'
(F,1,XwV1X)
CALL FVS12 F ,2,X V2X)- CALL' FVS12 (FO Y VY)-:.
. . ---CALL FVS12-(F,
Y,2Y)
............
:
CAL. FVS12 (EV2.y.V2Y)
('L
XA(I,I1 *J2+K)=VX-FK*((V1X/XR(L ))+(u2X/XDELF))
XA(I (II1+)*J2+K)=VY-FK*(-(V1Y/XR(I_ ))+(V2Y/DtELF) )
IK=11*J2+K.
IKI=(II+l)*J2+K
42 TOLB=TOLrD+XCO (--IK) *VX-+XCO (-KI') *VY
XB-( I ) =TO..D+ALPHAF*TT*Q3/CONDF
206 L=L-1
13 CONTINUE
.
1=-1
GO TO 14 '
C
C
. -: .
.
.
C --CENTER LINE
C
20 DO 400 K=IFJ2
·III·------LI-LI---------------
r
-
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..
-
.
:,r " -7,
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78
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F'
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))
. :.V tJ.i.
XA(I,K)=VI
400 XA (I ,.,2-K)V INI
XB(I)=O
lO 45 I:.NEfQS
45 XT(I)=XB(I)
EPFS=
OE-7
CAILL' MET2
(XA
1 NEQS 12 X
6WKAREA IER)
DO 24 I=ItNEQS
24 XC(I)=XB(I)
RETURN
ENI
0
-
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··--
·-··
·
'-·' '
""-"'"-
·
I-·
·--
·"
····'
- -l- ------
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79
,LFi'tTINE FVS12. (F!,K.YX.u)
IF(X)
0.!20y20
,
10 C=-1GO TO 30
30 IF(K-1I)
40.
,.60
40 V=ABS(I--:. + )*(
.. -3.* X**2+[:*2.*X**-)+ABS(F-2+ )*((1 -C
C* X)**2)
GO TO 100
50 V=ABS(F-. )*(-6e*X+C*6&*X**2)TABS(F-2 )*(1 -C*X)*(1 -3,+*C*X)
GO TO 100
60 V=ABS(F-1.)*(12 *C*X-6)+ABS(F-2 )*C*(6.*C*X-4 )
100 RETURN
END
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DIrENSON XT AB(NFP) YTA (N'P)
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NF' 1 =NF'- 1
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NI=-N
IF((XGEXTAB(N)).AND( (X.LEXTAB(N+1)))GO TO 20
10 CONTINUE
(NI) )*(X-XTAB(NI))/(XTAB(NI+i)
20 Y=YTAB(NI)+(YTAB(NI+)-YTAB
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RETURN
30 Y=YTAB(NFP)
RETURN
' '
40 Y=YTAB(1 )
RETURN
EN
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· -- -- -- --- -·-- ---- ···· ···- ·- - - -- - -- --- -···---L. TES: T R FISI 13, ON
MARCIAI
2,1974
IE:
S
I1MENSION
.iUC:IBE PREC:ISION
A( 1A, P J ) Y l... ( itt,!) I1P , <..)
E
It.:I...
Q E
1
)
A t... .! , W:1 E .L: j 1, A ZE RO ONE FO tR
.
I TN S I X T
R N WREi
F I..
P I ( A BIG P St.1iM 1 I Wt , T TEE T n
AT
I)
ZERO ,ON!
)
sFOURE
F L.
S IXTN
I S XT I
1-O,1
H/ 0 D 1. y :1
16 r'0, . 0 625n0/
ZERO., ! ONE FODI.!,
SI XTN SI XTH./O0 0 1. 4t
.IN TIIAIT..::17 AT IO0
C :1.
.4 .O, Y
1i + , ()062
E:R
F
0
1F'N = N
WRE...
= ERO
D = ZERO
.IGA
ZERf:
DCIo 10 I
5 J3,--l,i
BO
,*
CI
F =
FP
' ABS! )
,.'
BF
. ,
C() NTI .1NUE
IF (GO ,GT,
IF
(IG
E(
E
ERQ IL.)
10 CONTINUE
-t t
,J
I
.t
.BIGA) BIGA = BIG
ZERO) GO TO 1..10
NE/ .IG
= J-14.
F(!Mt.
G) B .IG- F
)
JLT) TO
IGr
IJt...T
40
COif:UJTE
C
DOX:35 =:1:yJM1
S1) i I
1.....1.(
,..)
IM :::: I.....
I:' ( ElT ,..EQ.+
1A1 ::::
C1:.
(-
T -
-
----
)
(3GO TO 20
.,.5 K=
- . ,T M 1
D.T
O
~~~~-
O ) GO TO 2'5
WITH ACCI.!RACY
AE S(SLIM)
WI = ZERO
IF- ( IM1 ILT... T
r,---
.. ( IJ
I,)
L
-
( .T, J)
L..Ul(K,..)
I :=I, y
TEST
. -t-
J
-
86
frS ::: S N-T
C'1.
C;I
14: 1tTD(4 3t1T')
CONTI.N U E
C..
20
0J
-I
1t
W I +ASS
.1F .S 'M
)
AI:E
I / .!GA
1= AO14
:F T(fE' T.T
l..
WRE
=
TEST
WREL)
GO TO :3.
IF (lii
,I...T
1.) GO TO 35
]:tO (0 K=I
,T
M1
SUN.M =* SUJMti-... (Ii )
lp
Gl.K)U(K:11,
L..I.,.tJ:v .l)
- Sl.l M
k4CONTI
iN U:
35
4()
).i)
C NOiTI NILIE
30(
F'
ZEROf
C
CM'lTE
l
I:O 70 I=,.N
SUM
L.t.J(,
1:: (I GfT
..
1.(..I)
AN I L (IJ.)
I1,.!,
1
E.o
0)
GO
TO 55
WIT:
C
ACf.C.RACY TEST
C':1
7T AC SM)
AI
I...TI
..
) J T O 50
5 K,,. JM1
T = I.J(I, K)I...U(KJ)
SUlM
SL.M- T
11I:
W14Ir
:fABS ( T )
WI = WI+ABS(T)
CONT INU.!E
l...: ( 1T..) ='SUM.
WI
WAI+BAS(SUIM)
F
DO
. eff
C. 5 0
50
fi..
C
55
IF (I
ED, ZERO) AT
BIGA
.TEST = WI/A
IF (TE.ST ;GT4
'WRE..)
WREL.
TEST
G O TO 6 5i
1I : 1THCUT ACC(UJRACY
65
!..T 1.) GO T
:IF- ( JM.
-I
·
T E:ST
DC! 60 K:-*.,J1:
SUM
S.JM-L...(I)*...U(K,.;)
60
ClI
65
CONTINU.lE
L.. I. ,J 1 :1)
- SUJM
IASt(SUM)
= E(IJ:
...(I
IF
('
MAX
1
70
,GE
G
Q )>
TO 70
:1:
TI:1N
:INi
UF
CON
ES!
FOR:
_
ALGORTH
(3I :rITFM:IC
3NUilAIR:ITY
1
· _··I-······---·C-·-----l
-_
I
IL
7
C
w
1 35
f' 1 '1
Er,.GO
(Ji
'
l
. ..3'
.i.(1 'i'"'A':
t1 f' : I :::
D24
R..
j , EfXU.It.ri
I
itI
J
.
)
.F UfI i E) ' i 0 .T.0
C)0 tT 0 1*J.
809CH..
-. , 1 T F''FCE
I= X A
D
i.D(JP1',
5i. F
.:0j!11I o Ii.v TO
G'
85
GO(
TO 85
IEfiEN'f
C
UI)I]!.J*SI
TYJ
=1 X
T
P
I j.12( = .1
f 1. 0 ) GO TO 9 01
I.
IF.'N IF
NI
WA)
i. ,, HNQi
5
9 ~!
0
T:-.)
`T, TO 1
x:,'c.V--
.1
Ot
10
o
f
a~~i:V~fiE 1 'i'
IF' f rrT. E:X0)
G
Q = ,A4+1
IF (V cNE,
O TO 9005
y.''f,.10
E:.Fi
HIOH?1EFORN ACC.RACY
F
.FO,.O*(-IGT)
WA) G
TO 9005
= 129
ZER)
9000 CONTINIJE
:
-'1-
t
9005 RET.URN:N
l .
END
plllPPa·l·---·r-··112
-
G
F''T
GO TO 9000
IER
1.
1
-
_
THL
TEFT
I
ONTIN
2E
CONT INUlE
C
.10
1 ,1
'fPEfRROfR
TEST
.
88
¢
i:'-· .i.!F;'
1 I::'(~· · ·:· · ·UT '-MIJP·
--· -::,-I..
C M U R F....
: ........
..............
F MC:t.IJ
TI0 N
:REFi1NEM:.NT
^<rs
(,C
C
rt1
f!:D
Y '.'
..
...............................
OF:' SOL...TIO:!!
TO L...:NR
E:Q1.ATION.
::)
I: TR.
.L....
ST :!R;) I: M oX FE
cl... ... MI.IRFFG ( v ....
I
i: PVT
N :
s,rIIGTY 1RES
IER)
-- 'IECO1EFICEN
T MA''
MB IX, AX-T
WHERE A
IS N X N
T-HlE RIGIH-T HlAlND SIDE A VECITO.RIOF SIZE N
GIVEN N X N MATRIX, U.. IS THE LU
DE:COMP:OS ITI ON OF A AS S3I.:L':LI ED BY
C
¢
1·:
-:v1--
t
U.S AGE:
P AR AT-'RM-:
7 R-
C
B
C
.L
I.fi...
c
C.
IMSI... ROUTl. NE
I ::.VT
C
cCCU;
N
X
'.JUDATl'E
A GIVEN VECTOR OF FIVOT INDI:CES
OF SIZE N
AS Sl.JF'...:II E: B Y IMSI.J. iROUT 'EI.Nf!E
' MUt.DATF
-ORDER
OF A A ND UL
A ND AI..SO' S T E LENGTH OiF
,.
PVT,'rX,
RES
fROW Dl:MMENSE
:I:CON OF
C
AD
IX
A AND U... IN THIE
CAl..LI NG
PR:CGRAM
C
r
-
A GIVEN ViE:CTOR OF SIZE N, X IS AN ESTIMATE
TO THE'I S'I..
I.J
ON OF AX:., THE
I:: MPF'ROVED RESJUL T
OVERWR ITES THE I:NPUT VECTlOR X
Ar:':'F.tRXIMAT: NUMEI.ER OF I:GI::ETS :1:N THE ANSlIER
IWH:I:CH WERE
14E: IR
H.uNCH
ANE FI:O A::iF T:
MF:FR VIRO
MNT
-THE RFi:SUAL VECiTOR O: SIZE N U.SED AS A WORK
V.' CT OR
'AF;:1 'I
Vf
::'TiOR OF SIZE N
X
C_
_
: ;,
I
('
C
c,.U
C
f
,.
C··rt
:
Q
..R:;.:O0
!::'A:;,:A,,HE -TER
TERMINA..
E:RfOR
N
C
"
FAITL.ED.
C
C
Tk,
C
128
.
1. IND 1:CATIES
N
T-:i I'T :1VE :rT
MIF ROVEMEN
MATRIX IS
T
TOO I:...L
CONDITIONED ,.
:ri
·
.REC I
ION
' rE
MSI... ROUTINES
...fI:
P.JELM G i.JEI:;tTSTT
M
LA..NGUAGE
-
FORTRAN
LATEST REVISION
-
MARCH 221.974
C."
IMENS ION
rOUBL.E
F:'RE:::CISION
DATA
I E R=O
XNORM = ZERO
DO 1.
4t
.(
C:)IN Er
:: l.JE
IF (XNORFiM
IDGT =: 50
AMAX
M :l
NE
r.( 1)
SUM
ITMAX/v50/
ZERO/
I:1.t N
XNFRM
=4
8t
llI..( IAIY.)
A( IAY.)
XNIIRM YABI(
ZERO)
GO rTO 9005
20 DO 45 ITER=I,ITMAX
DC) 30 I::-:.N
SUM = DLE (B :: )
X(
G0O TO 2 0
))
.0/
v,X(1.)
YR-.S(I .) ,DX(
I.) IPVT( 1)
89
25 .J::::
. 1 y Ni
D
't):.;NI!
i. t .
CO
N'N
U.
f'TE
CAl..I...
TNt.
.
.XNR
H G.'I.i:,
-- '.'1f
3 5C
XI )5
= -- :1.
:PT
,N,:I','.t)X)
X (I)
CONT I Nt.E.
IF (.:TE
NE
1.) (tGOTO 40
I DG:t
G - .i
Tft D
OXORi1',1,,M
,NEo ZRl:)
I GT - -AL..Gt. .XNC./X)
: R .XNfld iMX
N lFi
IF (X:IN:) RM
l
. X OFI4) GO TO: 9-005.
,,':-'.,
(
4)(.:t
45
fC NTIl'f Ntl.f-
I TEI;
1.:,1AT :,Nt
C
D:IIt i'
Ti:
CONF iVE
IE. R e 129
90((0 C NTIN
r
.:
9005 RETU.JRN
END.-OI
C
C
A
···
:._::
C
41
II^ _
----1·····1·11-----_
·
7.
References
1.
A. Faya, L. Wolf, and N. Todreas, "Development of a
Method for BWR Subchannel Analysis,"
MIT-EL 79-027,
November 1979.
2.
Lahey, R.T. et al., "Out of Pile Subchannel Measurements in a Nine-Rod Bundle for Water at 1000 Psia,"
Int. Symposium on Two-Phase Systems,"
Haifa, Israel
Aug 29-Sept 2 (1971)
--`---
^-1"-1~^-ls-----1--"I'---"-