ML20028A614
| ML20028A614 | |
| Person / Time | |
|---|---|
| Site: | Clinch River |
| Issue date: | 09/30/1982 |
| From: | Coffield R, Daschke K, John Miller WESTINGHOUSE ELECTRIC COMPANY, DIV OF CBS CORP. |
| To: | |
| Shared Package | |
| ML20028A612 | List: |
| References | |
| CRBRP-ARD-0257, CRBRP-ARD-257, NUDOCS 8211220428 | |
| Download: ML20028A614 (140) | |
Text
__
0 {LMFBR y,l CRBRP-ARD-0257
(%
m Clinch River Breeder Reactor Plant Nuclear sland SUPPLEMENTARY MANUAL FOR THE
{
F5RE-2M COMPUTER PROGRAM SEPTEMBER 1982 Prepared for the Project Mensyment Corporation as part of the U.S. Energy Research and Development Administration Liquid Metal Fast Breeder Reactor Demonstration Propam Any Further Distribution by any Holder of this Document or of the Data Therein to Third Parties Representing Ft,reip Interest, Foreip Governments, Foreip Companies and Foreip Subsidiaries or Foreip Divisions of U.S. Companies Should be Coordinated with the Director, Division of Reactor Re'earch and Development, U.S. Energy Research and Development Administration W Westinghouse Electric Corporation ADVANCED REACTORS DIVISION M 9-2 BOX 158 8211220428 821112 DR ADOCK 05000537 MADISON, PENNSYLV ANI A 15663 PDR
CRBRP-ARD-0257 SUPPLEMENTARY MANUAL FOR THE FORE-2M COMPUTER PROGRAM SEPTEMBER, 1982 1
J. V. Miller
- I R. D. Coffield K. D. Daschke J. S. Killimayer H. C. Anderson, III T. R. Reid Approved by:
4 R. A. Markley, MaWhger LMFBR Core T&H Analysis l
i i
- Westinghouse Nuclear Technology Division P.O. Box 355 Pittsburgh, Pennsylvani,a 15230 s
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l 0243E-58E:2 (S1320) 1 l
1
ABSTRACT F9RE-2M is a coupled thermal-hydraulics point-kinetics digital computer c designed to calculate significant reactor core parameters under steady state Variable inlet coolant conditions or as functions of til..e during transients.
The code calculates the reactor flow rate and temperature are considered.
l power, the individual reactivity feedbacks, and the temperature of coolant.
cladding, fuel, structure, and additional material for up to seven axial Various Plant Protection System trip functions can be simulated, positions.
and the control rod shutdown worth prescribed as a function of time from the By specifying appropriate hot channel / hot spot factors, the trip signal.
The transient behavior of an average, peak and hot fuel rod can be analyzed.
h heat of fusion accompanying fuel melting and the spatial / time variation of fuel-cladding gap coefficient (e.g., due to changes in gap size) are The feedback reactivity includes contributions due to the Doppler considered.
effect, coolant density changes and dimensional changes (includes bowing F9RE-2M is valid while the core retains its initial radial expansion).
geometry.
OI was renamed FSRE-2M following the The original F#RE-II computer model (2) incorporation of several major changes which were made to the program.
Since then, additional modifications have been made to the FSRE-2M mode These include updated modeling of gap conductance heat transfer, changes affecting material properties, modifications in transient coolant flow characteristics, simulation of inter-and intra-assembly flow and heat dl redistribution, reactivity feedback and decay heat modifications, mo e changes to allow for alternate fuel rod characteristics, program correcti These changes are and program improvements to provide user flexibility.
The required input variables described in this supplementary manual.
associated with these changes are also presented.
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TABLE OF CONTENTS N
i ABSTRACT 1
1.0 INTRODUCTION
3 INPUT VARIABLES AFFECTED BY PROGRAM MODIFICATION 2.0 11 GAP CONDUCTANCE HEAT TRANSFER 3.0 14 Radiation Heat Transfer Between Fuel and Cladding 22 3.1 3.2 Alternate Gap Conductance Model 27 Combination Gap Conductance Models 29 3.3 Requirement for Realistic Input Values 3.4 30 CHANGES AFFECTING MATERIAL PROPERTIES 4.0 30 New Thermal Conductivity Equations for Fuel 31 4.1 Thermal Conductivity of 8 C 4
32 Axial Variation in Fuel Conductivity Hot Channel 4.2 4.3 33 Factors Curve fit of the Sodium Properties 35 Curve Fit of the Specific Heat for Mixed Oxide Fuels 4.4 39 4.5 4.6 Alternate Specific Heat Table 40 MODIFICATIONS IN TRANSIENT COOLANT FLOW CHARACTERIST 5.0
'40 Pump Trip and Tirce Delay 40 5.1 Individual Flow Coastdown for Each Channel 5.2 44 SIMULATION OF INTER-AND INTRA-ASSEMBLY FLOW AND HEAT 6.0 REDISTRIBUTION 4b Flow Redistribution Simulation 48 Excess Energy) Simulation (Inter-and Intra-Assembly 6.1 6.2 51 Heat Transfer Typical Results Obtained by Including Inter-and 6.3 Intra-Assembly Flow and Heat Redistribution 53 REACTIVITY FEEP3ACK AND DECAY HEAT MODIFICATIONS 7.0 53 Alternate Doppler and Coolant Density Reactivity 55 Revised Channel Index on One Reactivity Feedback 7.1 7.2 Option 58 Alterne;e Decay Heat Model 62 7.3 Special Subroutine for Reactivity Feedback 7.4 63 MODEL CHANGES TO ALLOW FOR ALTERNATE FUEL ROD C 8.0 64
~
Alternate Fuel Geometry Option 66 8.1 Alternate Axial Power Shape 67 8.2 Axial Variation in Heat Generation Hot Spot Factor 8.3
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5131A-603A:2 jg (51320) 3
TABLE OF CONTENTS (Continued)
P*9%
70 9.0 PROGRAM REVISIONS 70 9.1 Revisions to the Calculation of Average Fuel Temperatures 73 Revisions in Derivation of a Gap Conductance Equation 9.2 75 PROGRAM IMPROVEMENTS TO PROVIDE USER FLEXIBILITY 10.0 75 Modifiy the Axial Power Shape During the Transient 10.1 76 Printout Interval Variation During the Transient 77 10.2 10.3 Option for Searching for Peak Values of Certain Critical Parameters 78 10.4 Storage of Data for Subsequent Retrieval for a Plotting Package 81
11.0 REFERENCES
A-1 INPUT DATA B-1 APPENDIX A SAMPLE INPUT LISTINGS AND MISCELLANE0US INFORMATION APPENDIX B C-1 APPENDIX C BUILT-IN TABLES OF SODIUM PROPERTIES
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5131A-603A:2 44g (51320) 4
1.0 INTRODUCTION
The purpose of this report is to describe changes which have recently These changes were made to incorporate made to the F9RE-2M computer program.
the additional models and/or to provide a greater degree of flexibility to i
d ls and user of the program and, in general, do not affect the bas c mo e The information contained in the original F9RE-II I
calculation methods.
III and in the subsequent document (2) which described early document modifications to program is therefore still applicable.
f Revisions which have been made to the program cover a wide variety o To facilitate locating changes related to a specific topic, the discussions of the modifications have been grouped into several major subjects.
Each of these categories comprises a separate section of this For example, there is a section dealing with gap conductance heat categories.
his subject report.
transfer (Section 3) in which several modifications related to Likewise, there are separate sections dealing with changes have been grouped.
dback,
to material properties, coolant flow characteristics, reactivity fee (Sections 4 to 8).
etc.
Other changes described in the report (Section 9) deal with corrections tions. These programming errors or revisions in the derivation of basic equa iable errors were generally conservative in nature and did not have an apprec imoact on the calculations.
d in Several of the modifications made to the FORE-2M program have i l ting the output provide the user with a greater degree of freedom in man pu a h
from the program or for making input modifications during the cours These changes are transient without resorting to the stop and RESTART option.
described in Section 10.
t Section 2.0 of the report lists all of the input data variables which ha i
Appendix A of the report is the complete been affected by the modifications.
There are on the order of 1700-1800 separate input variables irput data list.
While these many input variables may available for the FORE-2M program.
blem, it appear to offer an impossible task to the user in setting up a pro
(-
1 1
should be noted that a typical problem uses only a fraction of these The large number of input variable available results from the many variables.
Once a base deck has been possible options contained in the program.
established which describes the geometry of the reactor being considered, only a few variables are changed each time a different type of transient is studied.
Another f actor which reduces the number of input variables actually required Since the for a given problem is that any zero values need not be specified.
input storage locations are all automatically set equal to zero at the start Therefore, although the of the problem, only non-zero inputs need be listed.
input data list appears formidable at first glance, the frequent user of the program will soon discover that the amount of input data actually required for a given problem is quite manageable.
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2 0243E-58E:2 (51320) 6
INPUT VARIABLES AFFECTEU BY PROGRAM M001FICAT10NS 2.0 i bles
[
This sectior, contains a list and brief description of all the input var a A
5 E 2M program.
which have been affected by the modifications to the F R -As noted complete listing of all input variables is contained in Appendix A.
i d in the INTRODUCTION of this report, the amount of input data actu d by the for a specific case is generally much smaller than would be indicate This is because there number of possible input variables which are available.
ill is a rather wide range of options in the F8RE-2M program, many o not be used for any given problem.
d the variables A complete descriptier, of the model changes which have affecte listed on Table 1 is given in Sections 3 through 10.
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0243C-58E:2 (S1320) 7 l
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a TABLE 1 INPUT VARIABLES AFFECTED BY MODEL CHANGES Input Input Number Variable Description of Change Several new options on variable gap conductance 20 agap have been added.
A new option (6 =3) on " fuel" thermal k
conductivity has been added to cover the analysis 22 sk of B C control ds and a new Pu-UO2 equation from TID-26666 has been added (6k=4)-
4 Option for simulating inter-and intra-assembly flow and heat redistribution (6 =1).
31 as 5
(If Option on number of alternate power shapes.
N =1, an alternate axial power shape is supplied 32 N 3 for Channel 3; Input 8182) 3
-2) has been added which A new option (6ap= flow coastdown to be specified 58 6ap allows individual for each channel.
A new variable, emissivity of the fuel, has been 357 EMISF added.
A new variable, emissivity of the cladding, has EMISC 358 been added.
If the new input 20 option (saap=2) is used, the axial correction factors 6n gap conductance 827-847 Fh d in as the actual gap conductance in Btu /hr-ftpOF.
are now r New option on changing axial power shape during TSWAP is time (in seconds) at which 848 TSWAP problem.
alternate axial power shape (INPUT 849-855) becomes effective.
Alternate power factor for axial sections 1 849-855 ALTPdW(M) through 7 (see Section 10.1 of the text).
TJACK is New option on changing printout time.
time (in seconds) at which PJACK (INPUT 857) 856 TJACK becomes effective.
For time equaJ to or greater than TJACK (INPUT 856), this parameter becomes the maximum time 857 PJACK between printouts in place of PMAX (INPUT 71).
b 5131A-603A:2 4
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l TABLE 1 (Continued) f Input Input Number Variable Description of Change If the new Input 20 options are used, axial 948-954 RGAP(M,1) variations in radial gap size may be specified in 955-961 RGAP(M,2) 962-968 R6AP(M,3) inches (see Table 2).
Option indicator on fuel conductivity hot channel 969 FE(69)
If SE(69) > 0.0, axial variations in factor.
hot channel factors on fuel conductivity will be used.
If Input 969 is greater than zero, axial 970-976 FCSN(M,1) variations in the hot channel factor on fuel 1181-1187 FCfN(M,2) conductivity are specified (default value is 1.0).
1188-1194 FC#N(M,3)
If Option for alternate geometry for Channel 3.
IXIND=1, Inputs 7769 through 7790 and 8190 through 7768 IXIND 8206 must be supplied.*
Equivalent radius of coolant for alternate 7769 XRACL geometry.
Cladding inner radius for alternate geometry.
7700 XRACD Cladding outer radius for alternate geometry.
}
7771 XRACS Outer radius of fuel nodes n for alternate 7772-7781 XRAND (up to 10 geometry; 1 < n < M4AX.
values)
Radius of the central void for alternate geometry 7782 XRAVDB Volume of structure per unit length for alternate 7783 XVf5T geometry.
Volume of additional material per unit volume for l
7784 XVf,MT alternate geometry.
l Hydraulic diameter for alternate geometry.
7785 XDIHY Appropriate hydraulic diameter for calculating 7786 XDHT coolant heat transfer for alternate geometry.
i Characteristic structural dimension for alternate 7787 XDIST geometry.
it dimensions are in the s m units as used in original F9RE-Il
- All geom program-5131A-603A:2 5
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TABLE 1 (t6.itinued)
Input Input Description of Change Variable _
Number Characteristic structural dimension for alternate 7788 XDIMT geometry.
Structure surface-to-volume ratio of alternate 7789 XGST 9eometry.
Additional material surface-to-volume ratio for 7790 XGMT alternate geometry.
Axial variation in hot spot factor on heat generation for the alternate power shape in 7791-7797 PSm Channel 3 (Inputs 8182-8188)*
Option on alternate Doppler and coolant density (If 7798 IFEE8 reactivity feedback.
8160 and 8161 to 8181 must be supplied).
If IPtMP=1, flow coastdowns Option on pump trip.
begin at time of scram pl s pump delay (Input IPUMP u
77?9 8189).
Table of times (seconds) for flow coast-down values for Channel 2 and Channel 3 (Inputs 7800-7819 TIMEZ (up to 20 7820-7839 and 7840-7859). First value must be values) equal to 0.0.
Normalized values of flow coastdown for Channel 7820-7839 GPEAK corresponding to values of TIMEZ.
(up to 20 values)
Normalized values of flow coastdown for Channe 7840-7859 GHST corresponding to values of TIMEZ.
(up to 20 values)
Values of local flow rate in axial Section 1 of 7860-7879 (G/ Gin))
Channel 3 relative to inlet flow of Channel 3.
(up to 20 Values correspond to times specified in TIMEZ values)
(Input 7800-7819) 7880-7899 (G/G n)2 Same as 7860-7879 but for axial Section 2 i
Same as 7860-7879 but for axial Section 3 (G/G n)20 i 3 7900-7919 (up to values) f 1.0 will be used.
Tlf any value of P.'m is equal to zero, a value o i
5131A-603A:2 6
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TABLE 1 (Continued)
Input Input Number Variable _
Description of Change 7920-7939 (G/G n)4 (As above but for Section 4) i 7940-7959 (G/ Gin)5 (As above but for Section 5) 7960-7979 (G/Gn)6 (As above but for Section 6) i 7980-7999 (G/Gn)7 (As above but for Section 7) i Excess energy (BTV/sec) supplied to axial Section 1 8000-8019 QEXS (up to 20 values) of Channel 3.
Values correspond to times specified in TIMEZ (Inputs 7800-7819)
(As above but for Section 2) 8020-8039 (As above but for Section 3) 8040-8059 (As above but for Section 4) 8060-8079
( As above but for Section 5) 8080-8099 (As above but for Section 6) 8100-8119 (As above but for Section 7)
(
8120-8139 Alternate Doppler coefficient for Charnel 1 axial 8140-8146 FD/P(M,1)
Section 1 to 7 8147-8153 FD0P(M,2)
(As above for Channel 2) 8154-8160 FDdP(M,3)
(As above for Channel 3)
Alternate coolant density reactivity feedback 8161-8167 CEFBK(M,1) coefficient for Channel 1 Axial Section I to 7 8168-8174 C0FBK(M,2)
(As above for Channel 2) 8175-8181 CffBK(M,3)
(As above for Channel 3)
Alternate axial power shape for Channel 3.
8182-8188 XP8WR(M)
(1 1 M $ MMAX)
Pump trip delay (seconds); value added to scram time to determine flow coastdown if IPUMP = 1 8189 TPUMP Density of fuel (lbs/ft ) for alternate geometry 3
8190 XRH& L 5131A-603A:2 7
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TABLE 1 (Continued)
Input Input Number Variable _
Description of Change Liquidus temperature for alternate geometry 8191 XLIQ Solidus temperature for alternate geometry 8192 X59 LID 8193 XCAH
)
8194 XCBH Constants used in coolant heat transfer coefficient 8195-8201 XCCH(M) equation (see Inputs 321 to 332, Appendix A) 8202 XCHM I
8203 XCNH 8204 XCRH
)
Fractional density of as-manuf actured fuel for 8205 XRHB1 alternate geometry Fractional density of sintered fuel for alternate 8206 XRH02 geometry Option for alternate decay heat model (IDECAY=1) 8207 IDECAY Option of using core or Channel K as reactor power 8208 IREG If IREG=0, core average power is used; indicator.
(K=1, 2 or 3).
if IREG=K, Channel K power is used.
Fractional power of reactor associated with 8209-8211 FREG(K) regions corresponding to Channels 1, 2 and 3.
3 g,. REG (K)=1.0 k=1 Times (seconds) at which decay heat for individual 8212-8231 TDECAY channels will be specified (up to 20 values)
Fraction of power attributed to decay heat for 8232-8251 PDECAY(1)
Channel 1 for times corresponding to TOECAY.
(up to 20 values )
8252-8271 POECAY(2)
Decay power values for Channel 2.
(up to 20 values) 8 5131 A-603A:2 (51320) 12
F TABLE 1 (Continued)
Input Input Number Variable.
Description of Change 8272-8291 PDECAY(3)
Decay power values for Channel 3.
(up to 20 values)
Channel to which alternate specific heat of fuel 8282 IXCP applies.
Alternate fuel specific heat table (Btu /lb of).
8293-8312 XCPFIT (up to 20 values)
Temperature (oF) corresponding to alternate 8313-8332 XTEMP (up to 20 specific heat table.
values)
Option for selecting special reactivity feedback 8333 ISPEC subroutine.*
Index to determine which channel (i.e., 1, 2 or 3) 8334 IREX will be used with Inputs 165 and 320.
Indicator for start of decay heat curves (Inputs 8335 ISTART 8232 to 8291). If ISTART=0, time is measured from 4
steady state (t=0).
If ISTART=1, time is measured from point of scram.
Option for using curve fit of sodium properties:
8336 IPRWP IPREP=1 use curve fit IPROP=0 use tabular data Option for storage of data on TAPE 2 for 8337 IPLET subsequent use with a plotting routine. (IPL6T=1, selected data will be written on TAPE 2.)
Option for searching for maximum value of certain critical parameters.
(ITMAX=1, 2 or 3. depending 8338 ITMAX on which channel is of interest.)
Option for using curve fit of fuel specific heat:
8339 ICPF ICPF=1 use curve fit use tabular properties ICPF=0If ICPF=1, INPUTS 8340 through 8345 must be Note:
specified.
(
- See Section 7.4.
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9 5131A-603A:2 (51320) 13
TABLE 1 (Continued)
Input Input Number _
Variable Description of Change 8440 A(C )r
)
Constants used in curve fit of fuel specific heat p
4 C = A + B*T + C.T2 + D*T3 + E*T 8441 B(C )f p
p 1
8442 C(Cp)r where T is in OF.
8443 D(C )g
{
p 8444 E(C )f p
Effective heat capacity of fuel between the 8445 F(C )f p
solidus and liquidus temperatures.
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5131A-603A:2 10
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GAP CONDUCTANCE HEAT TRANSFER 3.0 l
One very important f actor in calculating the steady state and transient fu f the temperatures is the determination of the conductance and evaluation o In FORE-2M,
' esulting heat transfer coefficient for the fuel / cladding gap.
two options for calculating heat transfer across the fuel-cladding gap were r
For the first of these (Input 20 = 0), the user specif ted a single available.
i t value of gap conductance for the average channel which remained invar an Input multipliers on this constant value were throughout the transient.
k available (Input 355 and 359) to alter the values for the hot and pea These values also remain constant throughout the transient.
channels.
Likewise, this option allowed fixed, but axially varying, gap conductance I2) values to be input to all three channels via Input 827 to 847 d t e
For the second of the two options (Input 20 = 1), a variable gap con uc an is calculated based upon the local gap conditions existing at every po II) was based upon the work of Ross and This model the transient.The local gap coefficient for each position is calculated by:
I4)
Stoute
" gap * (" cont * "cond)
- F**
where:
is the overall gap conductance H
is the portion attributed to solid-to-solid conduction
" cont is the portion attributed to gap gas conduction H
15 the channel multiplier on gap conductance cond and F**
(F** = 1.0 for average channel; F** = Input 359 f or peak channel; and F** = Input 355 for hot channel.)
11
The individual components of the gap conductance are calculated as follows:
N "a
cont o
K Ncond " 6 + (gf + g )
9 c
where K, is the harmonic mean thermal conductivity of the fuel (K ) and y
cladding (K ) defined as:
p 2K K y 2 K, =
g}
g2 is the contact pressure (proportional to the interference P
between fuel and cladding); when P is zero (no interference),
c c
is zero.
the contributton of Hcont I4) determined to be approximately an experimental constant og 0.091 ft1/2, is the effective roughness of the two surfaces and is defined as:
6r
~ 2+6 2~ 1/2 6f c
6
=
r 2
are the respective roughnesses (in feet) of where 6f and 6c the fuel and cladding.
1s the Meyers hardness number of the softer material which is III taken to be on the order of three times the yield usually strength.*
- Reference 5 provides additional information on the selection of values for this paramater.
e 12 t
n e gap and h caicd ated h om n % e conhc M y of % e gas Kg 2
+S T,yg+C T,yg K
=A g
g g
g ts the where A, 8 and C are input variables and T,yg g
9 g
average local temperature of the gap.
is the accomodation distance (approx. 3.3 x 10-5 f t for helium (gf + gc) at 1 atmosphere)*
For a positive gap 1s the effective radial gap dimension.
69 6
=A +Bo (6f+6) c 9
g and for a zero gap 6 =So (6f+6) c g
is the calculated hot radial gap o
[
g I4) from is an experimentally determined constant which varies 2.5 at low interf acial pressure (#1400 psi) to 1.5 at high 6g interf acial pressures (#7000 pst).
- Ref erence 5 provides additional information on the selection of va this parameter.
13
RADIATION HEAT TRANSFER BETWEEN FUEL AND CLADDING 3.1 As can be seen from the equations, the Ross and Stoute model neglects radiant This is understandable because in their heat transfer across the gap.
experiments, the surfaces were in contact and typically measured gap 2 F conductances ranged from 500 to over 5000 Btu /hr-f t O. Figure 1 shows that for this range of values, the contribution due to radiation is quite small being on the order of a few percent at most.
When overall gap conductance is relatively low, however, the effect of radiant heat transf er becomes important and could account for as much as 20 to 50 percent (Figure 2) of the total heat transferred when the overall gap 2
Such a situation coula coeff icient is on the order of 100 Btu /hr-f t - F.
occur even with a pure helium atmosphere for large radial gap dimensions While dimensions of this magnitude are not (e.g., 0.015 inches or greater).
typical of fuel rods, the radial gap size in a boron carbide control rods (see Section 4.2) could, for example, be in the range where radiation heat transfer Fuel becomes an important factor for reasonably large values of emissivity.*
rods containing a large percentage of fission gases might also be in the range l
where radiant heat transfer could account for ten percent or more of the tota It was, therefore, considered prudent to modify the Ross and s
conductance.
The resulting equation is:
Stoute mooel to account for radiant heat transfer.
" gap * (" cont * "cond}
+ " RAD where is the radiant heat transfer component and the other terms are HRAD as previously described.
- It should be noted that while the emissivity of bright stainless steel is on
(
the order of 0.2 to 0.3, heating of the steel can quickly increase the emissivity to the 0.6 to 0.7 range (see Reference 6).
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5131A-603A:2 14
{51320) 18
4 nun St PERCENTAGE OF HEAT TRANSFERRED BY RADI ATION 5
=
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=
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= 4, I
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60 EFFECTIVE CURVE EMISSIVITY TgF) 50 1
1.8 1000 2
B.5 1000 E
E 3
1.8 000 E
4 e.5 000 E
40 2
Q= 100,000 8TU/HR FT
- g 5
N 30 E
E E
1
$g 20 l
5 5
t e
2 E
10 4
-3 I
I t
i 0
250 300 350 100 150 200 2 _ op TOTAL GAP CONDUCTANCE, BTU /HR-FT l-iyure 2 LII'ect of Radiasiim lleat Transfer as 4 ou Oserall Values of Gap Camd 44 N7-2 16
. ~
The contribution to the gap coefficient which is attributed to radiation can be derived by noting that:
(q/A )
f HRAD " (T -TI f
c and f + 460)4 - (T + 460)
(q/A ) = o F (T
c 7
where is the heat transferred by radiation q
is the surf ace area of the fuel Af is the Stefan-Boltzmann constant o
is the emissivity form f actor between the fuel and cladding F
15 the surf ace temperature of the fuel Tf is the inside surface temperature of the cladding Tc Since the emissivity form f actor is given by( )
A
-1 lf i
f
--1 p.
.. _. + -
A
\\"c cf c
the radiant heat transf er coefficient across the fuel / cladding gap can be written as:
o (Tf + 460) - (T + 460)#
2Af c
HRAD "
-y f ry 3-Af+A A
c
--1 Tf-T c
.G+{(
where the previously undefined syntols are:
the emissivity of the fuel cf the emissivity of the cladding cc the inside surf ace area of the cl, adding Ac
(:.
17
f + A )] is required to normalize the Theadditionalfactor[2A/(A f
radiant heat transfer to the mean area of the gap which is the parameter used c
in FPRE-?M as the reference heat transfer area.
Figures 3, 4, and 5 show some typical results obtained with and without radiant heat transfer for a boron carbide control rod subjected to a transient As can be seen, caused by insertion of the control assembly into the reactor.
the effect of radiant heat transfer has a marked impact on the results.
Figure 4, for example, shows that the maximum cladding temperature The extra heat transfer from by over 100 F when radiation is included.
0
) of radiation (prior to shutdown) decreases the stored heat (i.e., temperature the B C (see Figure 5) and thus less energy is available to be deposited 4
into the coolant during the transient.
18
150 NOTE:
's = 0.65 140 tg = 0.85
\\
130 \\
C o
my 120 S'-
cc
\\
110 n
N x
N 100
\\
\\
WITH RAOIATION N
O N
5y s0
%s%
{
WITHOUT at*
RA0lATION 80 70 I
I I
I I
I I
60 O
20 40 60 to 100 120 140 160 TIME (SECONDS)
Figure 3 Ty pical Variation in Transient B C/ Cladding Gap Conductance with and without 4
Radiation Heat Transfer Component f
34M7 3 l
)
19
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1E k
E E
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Eo
=
E u.
7 m
s
\\
=
z c
G
\\
-E-3 5
x w
\\
E=
E
\\
E
'i F
\\
1
-z N
E
=
i N
N N
.E E
i i
I i
g g
g g
E
=
~
a 3
?
(do) 3Hn1VW3dW310NI00V13 MnWlXVW NI N011VIHV A e-
- T N
l 34N7-4
(.
20 i
O NOTE:
c, = 6.65
-200
-400 C
t.
E -600 P<
5I -800
\\
- s. 1000
\\
3 a
\\
m
\\
x<E -1200
\\
WITH RADIATION E
\\
(T, = 2695'F) g y -1400 g
sc
%'~~
e.
y -1600 t
WITHOUT RADI ATION
-1800 (T, = 3060*F) 0 20 40 60 80 100 120 140 160
-2000 TIME (SECONDS)
Figure S Typical Variation in Masimum B C Temperature with and wi:Imot 4
Heat Iransfer Component
.\\4K7 S
(.
21
Al. TERNATE GAP CONDUCTANCE MODEL 3.2 In addition to modifying the Ross and Stoute gap conductance model to includ d to the radiant heat transfer (Section 3.1), a new model has also been adde This option (Input 20 = 2) allows the user to F9RE-2M computer program.
948-968) specif y an axial variation in the hot radial gap dimension (Inputs and to specify the overall steady-state gap conductance associated with each of these input dimensions using Inputs 827 to 847*.
Since the steady-state values are specified by the user with this option, the ht method of handling the transient variation in the gap conductance is somew a different, although quite analogous, to the procedure used in Ross and Stoute The basic gap conductance equation is given by model.
" cap = Hcont + Ncond + HRAD (Note that the F** multiplier is not used in this model since individual values of H are specified by the user.)
g3p specified, an iterative procedure to With the steady-state value of Hgap deta-mine the proper steady-state conductance is not required as in the However, once the initial temperature modified Ross and Stoute model.
distributinns have been determined, the steady-state values of HRAD and i
in the cont (if appropriate) are determined using the same equat ons asA H
modified Ross and Stoute model.
f rom the total, the remaining portion of the steady-state (S.S.) gap conductance is then assumed to be associated with conduction across the cap. Thus, I
- (Hcont + HRAD)S.S.
cond S.S. " " gap (H
827-847) are specified in
- When Input 20 = 2, the gap conductance (Inputs 8tu/hr-f t oF; o 2
foctors.
22
At any position and at any point in the transient, the gap conductances cont (if appropriate) are calculated in the and H associated with HRAD However, the identical manner as in the modified Ross and Stoute model.
portion of the gap conductance attributed to conductance across the gap is found by calculating the ratio between the steady-state and transient value of the parameters affecting conduction and multiplying these ratios by the The transient (T) value of the gas steady-state value of Hcond.
conduction portion of the gap conductance at any position is therefore given by:
K 6 + (gf + ge)
K 6 + (gf + g )
(Hcond}T " ("cond}S.S.
g g
g
-r
- S.S.
The difference is that the where the nomenclature is as defined previously.
The transient hot hot gap calculation is initialized using Inputs 948 to 968.
gap ( A ) for this option is givey by*:
g A
^
where is the input (hot, steady-state value of the radial gap RA0(M,K) dimension.
is the radial change in cladding dimension due to the change in AC average temperature from the steady-state value.
is the radial change in fuel dimension due to the change in AF average fuel temperature from the steady-state value.
The f act that the conduction portion of the gap conductance is obtained by the method described above makes this model somewhat empirical in nature.
- This equation reipaces equations (33) and (34) of Reference 1.
(.'
23
J j
However, the model will yield the same results as the modified Ross and Stoute model provided the input values of overall gap conductance are in perfect l
agreement with the corresponding hot, radial gap dimensions which are This model provides some additional user specified for this model.
flexibility for evaluating situations which may be considered non-typical of an idealized fuel rod (e.g., evaluating explicit experimental data where the apparent gap sizes differ from those expected).
To demonstrate the application of this new F9RE-2Pi capability, a typical For undercooling transient was analyzed for a large diameter, blanket rod.
this type of oxide rod, the transient release of stored heat affects the The power decreases rapidly early in the performance characteristics.
transient; however, the heat flux from the cladding remains relatively large.
In f act, the heat flux-to-flow ratio remains greater than 1.0 early in the Figure 6 shows flow coastdown and results in a cladding temperature increase.
the fkME-2M predictions with a fixed temporal value of gap conductance (Input The 20 = 0) and for a dynamically varying gap conductance (Input 20 = 2).
initial conditions used for the gap dimensions and gap conductance for the(8)and latter case were directly calculated with the LIFE-III computer code are listed below as a function of axial position from the bottom of the heated length (X/L = 0.0):
Radial Gap Gap Conductpnce*,
l Size *,(in.)_
Btu /hr-Ft OF Axial Position, X/L 1000.0 0.11 0 0005 4641.0 0.0005 0.28 1209.0 0.0030 0.39 347.0 0.0230 0.50 1703.0 0.0020 0.61 8389.0 0.0000 0.73 1000.0 0.0000 0.89
- Prior to shutdown.
('
$131A--603A
e 1
340 s
t 320 W
\\
N N
'k 2s0 NN.
260
\\
FIXED G AP C
CDNDUCTANCE
~'
[l#PUT 20=01 E{
220
/
200 1
=
V ARIABLE G AP
~
g CONDUCTANCE 5
s liNPUT 20 21 g
160
-j d
E 140 q
)
y 120 q
E I
100 q.
E k
80 60 40 20 1
I I
I I
I I
l' l
0 -
0 20 40 60 80 100 120 140 160 180 200 I
TIME (SECONDS) i Typical Effect of New Variable Gap Conductance Option'an Large Dia Blanket Rod Performance During an UndercoolingTransitnr Figure 6 3487-6 t
(
25
- i s
'\\
t ht As can be noted from the figure, the temperature predictions are somew a Dwe-to a gap conductance decrease (from its altered by using the new option.
j initial value) early in the trans....., the stored heat release is likewise
)
Later delayed in the transient and thus lower temperatures result initially.
in the transient, when the flow has decayed to lower values, more energ The this available and consequently smewhat higher temperatures result.
i is a
>fmportance of this example is simply to indicate that the new opt on de such
-viable means of linking F9RE-2M to a steady state fuel performance co
'as LIFE.
I j
i
)
)
i w
4 4
(
26
COMBINATION GAP CONDUCTANCE MODELS 3.3 In order to provide still more flexibility to the FDRE-2M user, some of the features of the two variable gap conductance models were combined into two For these models, the axial variation in the radial gap additional models.
dimension is specified (Inputs 948-968) and the gap conductance is calculated using the Ross-Stoute model modified with radiant heat transfer (Section The difference between the two additional models is that either c 3.1).
gap variations (Input 20 = -1) or the hot gap variations (Input 20 = -2) m Table 2 summarizes the pertinent information for all of the gap be specified.
conductance models.
These models allow the user tg analyze many additional types of gap condition For example, variations in cladding and fuel swelling, variable pellet diameters or combinations of these conditions may be simula that may occur.
Again, it is.noted that these models will yield the same with this model.
results as the other two models if the input conditions are in agreement, t
l 1
h 27
m l
~
TABLE 2
SUMMARY
OF GAP CONDUCTANCE MODELS IN FORE-2M Hot or Value of Type of Cold Gap Inputs Required Conductance Model Input 20 Variation Specified For Gap Model Used l
A 0
None (constant) 341 Constant 8
+1 With time Cold (feet) 350 Ross and Stoute*
i J827 to 847}
Alternate Model (Section 3.2)
C
+2 Time and space Hot (inches)
(948 to 968?,
D
-1 Time and space Cold (inches) 948 to 968 Ross and Stoute*
S E
-2 Time and space Hot (inches) 948 to 968 Ross and Stoute*
- With radiation heat transfer l
3.4 REQUIREMENT FOR REALISTIC INPUT VALUES A word of caution to the user of the variable gap conductance options in FfRE-2M may be appropriate at this point. An examination of the equation for H
and H will show that it is possible to have a zero or near zero cont cond denominator in these equations if certain input parameters are not properly specified. The denominator for Hcond, for example, is composed of three components: the acconnodation effect (gf + g ); the surface roughness g
eff ect 6, (6f + 6 ); and the radial gap dimension (6 ).
c g
and If the user would, for example, f ail to specify values for gf, ge So(Inputs 346, 348 and 349), the denominator of Hcond would be controlled completely by the radial gap dimension. If during the transient the thermal expansion of the fuel and cladding were such as to make the would become fuel / cladding gap dimension approach zero, the value of Hcond infinite.
To prevent an indefinite condition (i.e., division by zero), the FORE-2M and 6,to very sman values (i.e.,
program automatically sets gf, gc 10-25) if the user f ails to specify an input value for any of these However, this precaution does not prevent the value of Hcond parameters.
from still approaching an extremely large value if the radial gap dimension l
should approach zero. Thus, while the computer program will run, the answer may, in f act, be in error. To bring this potential problem to the attention of the user, a " CAUTION" message is printed out at the beginning of the output listing, instructing the user to check those input parameters which could The user may then wish possibly invalidate the gap conductance calculations.
to change the input values to more realistic values and rerun the problem.
l l
29
CHANGES AFFECTING MATERIAL PROPERTIES 4.0 In order to improve the computational efficiency of FpRE-2M, options have been incorporated into the program to allow the user to either specify tabular or curve-fit properties for the fuel specific heat and the sodium properties.
Several changes in the fuel thermal conductivity properties have also been made and axial variations in the associated hot channel f actor are now These changes are briefly discussed in the following subsections.
allowed.
NEW THERMAL CONDUCTIVITY EQUATION FOR FUEL 4.1 An additional equation (Input No. 22 = 4) has been added to the fuel thermal conductivity option. This equation is of the form:
'l 3'
K = FP A+BT +
where
= thermal conductivity, W/M OK K
T = temperature,OK 1.079 (1-P) pp,
2 (1.0 + 0.5P + 4.62P )
P = fractional porosity A = -6.0656 x 10'4
= 3.04212 x 10-4 8
= 0.75137 x 10-10 C
l If either thermal conductivity option 2 or 4 is selected, the initial and as-sintered densities must also be specified. (Inputs 858 and 859; also Inputs 8205 and 8206 if alternate geometry option is used.)
This new thermal conductivity equation for mixed oxide fuel is quite similar to the equation previously included (2) in the computer program and has been included to reflect the August 1977 revision to the Property Code 3112 equation in T!D-26666.(3)
(
30
4.2 THERMAL CONDUCTIVITY OF B C 4
In addition to being used to evaluate the transient behavior of fuel rods, the F9RE-2M program is frequently used to analyze other cylindrical, heat One such application is the transient analysis of boron generating elements.
To improve the flexibility of the computer program for carbide control rods.
this particular application, a new " fuel" thermal conductivity option (Input rumber 22 = 3) has been added. lihen this option is selected, the thermal conductivity of the B C pellets is evaluated using the following 4
I9):
equation
$) (0.1021e - 14.492)
K = (5.87 +.0095T) II 2.
where K is the local thermal conductivity, 8tu/hr-Ft O I
F T 1s the local, absolute temperature, OR
$ is the pore volume f raction e is the irradiation temperature, OF i.(
In the program, it is assumed that the initial or steady state temperature is Local, steady state temperatures at each radial the irradiation temperature.
and axial location are stored and the appropriate value is recalled when the transient B C thermal conductivity is required at any particular location.
4 l
l i
!(.
31
AXIAL VARIATION IN FUEL THERMAL CONDUCTIVITY HOT CHANNEL 4.3 In the previous version of the F9RE conputer program, a single input value (Input No.121) was used to specify a hot channel multiplier on the fuel This multiplier was used to either increase thermal conductivity.
(Fg > 1.0) or decrease (Fg < 1.0) the local fuel thermal conductivity in the " hot channel" (i.e., Channel 3).
A new option has been added which allows the user to specify an axial To use this option, the variation in the multiplier for all three channels.
user sets the fuel conductivity axial variation indicator (Input 969 > 0.0)
Since the and then specifies the appropriate correct f actors,FC9N(M K).
program automatically sets the def ault value of 1.0 if no value is given, only The values for the average those values which are not 1.0 need be specified.
channel (Channel 1) are input into locations 970 to 976; values for the peak channel (Channel 2) are input into locations 1181 to 1187; and those for the hot channel (Channel 3) use locations 1188 to 1194.
It is important to note that if this option is used, the original hot channel multiplier on fuel thermal conductivity (Input 121) will be overridden by the specified FCON values for Channel 3.
l l
l l
32
a w e
3 4.4 CURVE FIT OF THE 50010M PROPERTIES Calculation of values of the sodium properties is performed a significant Each calculation number of times during the course of a typical transient.
using the tabular input option requires a systematic search through the This procedure is appropriate table utilizing a linear interpolation routine.
time consuming and results in an inefficient use of the computer.
To provide the program user with the choice of using a more efficient method of determining the sodium properties, an option (IPR 99) has been added which allows the user to select a curve fit routine (INPUT 8336=1) for calculating The equations which have been programmed into the FORE-2M sodium properties.
program are quadratic temperature fits of the properties (10) listed in Appendix C.
The resulting equations are suonarized below:
l Thermal conductivity of sodium, Btu /sec-ft OF a.
2 K = 1.E072 x 10-2 -5.2 x 10-6T + 5.75 x 10-10 T
Thermal expansion coefficient of sodium, OF-1 2
a = 44.514 x 10-6 + 9.0125 x 10-9 T + 5.9375 x 10-13 T
b.
l 1
Dynamic viscosity of sodium, Ib/ft-sec c.
f For T > 6000F, 2
p = 3.741 x 10-4 -3.0008 x 10-7 T + 81.25 x 10-12 T
For T < 6000F, 2
p = 7.414 x 10-4 -1.564 x 10-6 T + 1.1675 x 10-9 T
d.
Specific heat of sodium, Btu /lb OF 2
= 0.34552 - 7.8906 x 10-5T + 3.3984 x 10-8 T
Cp l'
t 33 j
' ' ^ ^ " ' " - " - -. -.,, _
i 1
Density of sodium, Ib/ft3 e.
7.[
p = 59.588 - 8.0925 x 10'3. T - 1.0625 x 10-Sample calculations perfomed using both the tabular and curve fit method determining sodium properties indicate that the latter method will reduce the compute-execution time of a typical problem by nearly 15 percent.
l l
l 34
i i
CURVE FIT OF THE SPECIFIC HEAT OF MIXED OXIDE FUELS 4.5 For the same reasons discussed in the previous section, an option (ICPF) has been included which allows the user to specify whether a tabular set of fuel specific heat will be used (INPUT 8339=0) or whether a fourth degree polynomial describing the fuel specific heat will be utilized (INPUT 8339=1).
Unlike the sodium properties, however, the fuel specific heat is not unique j
The and may vary depending upon the composition of the fuel being analyzed.
user must, therefore, supply six constants (INPUTS 8340 to 8345) which define The model used is that described in the original the fuel specific heat.
FSRE-2M manual (2) where an " effective heat capacity" is used to describe the transition region between the solidus temperature and the liquidus temperature for mixed oxide fuels.
This effective heat capacity is detennined using the following expression:
C (,ff) = L/ i - (TL-T) p f
3 where is the effective heat capacity (Stu/lb O )
F C (,ff) p 3
is the latent heat of fusion (8tu/ft )
L is the average density of the fuel between the solidus and of 3
liquidus (lb/f t )
is the liquidus temperature of the fuel ( F)
Tg is the solidus (melting) temperature of the fuel ( F)
TS Table 3 shows three sets of values (-3o, nominal, +3o) for mixed oxide fuel heat capacity using the effective heat capacity for fuel melting and the tabular input option (INPUT 8339=0).
1 o
b 35 5131 A--603A
The following mixed oxide input information typifies the coefficients of the minimum, nominal and maximum (-3o, nominal, +3o, respectively) fuel It specific heat equations using the curve fitting option (INPUT 8339 = 1).
was found that a fourth degree polynomial fits the data (Reference 12) very well with a maximum of 1.6% error difference.
Maximum C Nominal C p
Input Minimum _C 7
7 5.9205 x 10-2 5.9841 x 10-2 6.0477 x 10-2 2.4780 x 10-5 2.3894 x 10-5 2.3008 x 10-5
[8340] (A)
-1.5593 x 10-8
-1.0643 x 10-8
-5.6927 x 10~9
[8341] (B) 4.7107 x 10-12 1.9322 x 10-12
-8.4621 x 10-13
[8342) (C)
-4.1776 x 10-16 1.9405 x 10'IO 4.2164 x 10-16
[8343] (D)
[8344] (E) 1.105 1.105
[8345] (F) 1.105 The heat capacity of the fuel at any temperature (T,'F) is then determined in the following manner:
a.
For T < TSOLIDUS
- g C (f) = A + B+T + C*T2 + 0*T3+ET4 p
T T $ LIQUIOUS b.
For TSOLIDUS 1 C (f) = F p
c.
For T > TLIQUIOUS C (f) = A + B*TSOLIDUS + C*T 50LIDUS+0*NSO 2
SOL 100S p
are the appropriate solidus and liquidus and T where TSOLIDUS LIQUIOUS From temperatures (Figure 7) defined respectively by INPUT 193 and INPUT 194.
sample calculations made using the curve fit option for fuel specific he 1s estimated that the computer execution time can be reduced 15 to 20 pe over the tabular option, depending on the number of fuel nodes used in a l
Of course, when using this option, it will be necessary particular problem.
for the user to determine the appropriate values of A B, C, D, E and F in order to properly represent the specific heat of the fuel being analyzed.
(
36 07av.;RF :7
TABLE 3 TYPICAL TABLE OF HEAT CAPACITY FOR MIXE0 OXIDE FUEL USING EFFECTIVE HEAT CAPACITY MODEL IN MELTING REGION (REFERENCE 12) e Heat Capacity, Minimum C Nominal C Maximum C P
Comments Tempgrature P
P
(+3,)
( F)
(-3o) 440.6 0.0664 0.0685 0.0706 1340.6 0.0751 0.0774 0.0797 2240.6 0.0792 0.0817 0.0842 Values Computed 3140.6 0.0873 0.0900 0.0927
)
4040.6 0.1056 0.1106 0.1156 From Reference 12 1
f 4500.0 0.1126 0.1287 0.1453 4940.6 0.1203 0.1523 0.1843 4999.0 0.1218 0.1560 0.1895 fEffectivevalue 5000.0 1.1050 1.1050 1.1050 5115.0 1.1050 1.1050 1.1050
)
for melting region fValuesforliquid
.(
5116.0 0.1218 0.1560 0.1895 7000.0-0.1218 0.1560 0.1895
)
fuel assumed equal to pre-melting value If this tabular procedure is used, an
- Special note to users of FORE-2M:
This value artificially high melting point (INPUT Value 117) must be used.
must be equal to or less than the highest temperature in the table of specific heat vs temperature (i.e., f rom the above table Tmelt y_70000F).
5250A--606A 37 (SIMO) 31
l 3000 2900 LIQUl0 SOLUTION NF AO
.louiDus 2000 O
2700 g
b SOLIDUS a
O E
SOLID SOLUTION sc 2600 A G t$
LEGEND 3
2500
- A OBSERVED SOLIDUS j
f dI 9 OfSERVED LIQUIDUS l
. SEE REFERENCE 12 O
(
2400 O onSERVED SOLIDUS
& osSERVED LIQUIDUS 2300 20 40 60 to Pu02 002 MOLE pug (PERCENT) 2 Figure 7 Phase Diagram for UO -PuO2 2
3487 7 38
ALTERNATE SPECIFIC HEAT TABLE 4.6 In many cases the propeeties of the fuel used in the blanket rods may be in the blanket and Pu-U in different than that of the driver fuel (e.g., 00 2 To cover this possibility in the event that the alternate the driver rods).
fuel geometry option is used (see Section 8.1), an alternate specific hea table is also available.
The tabular The option for the alternate specific heat (IXCP) is Input 8293.his, values of specific heat as a function of temperature associated with t option are Inputs 8293 to 8312 (specific heat values) and 8313 to 8332 A value of IXCP is selected to correspond to the (temperaturevalues).
For channel to which the alternate specific heat values will be applied.
example, if IXCP is equal to 2, the alternate specific heat table will be Normally, this option applied to the peak channel fuel (i.e., Channel'2).
- 3).
would be used with the alternate fuel rod in Channel 3 (i.e., IXCP=
However, note that it is not necessary to utilize the alternate fuel rod geometry option (Section 8.1) to specify an alternate table of fuel sp j
The alternate table of fuel specific heat may be used with or without heat.
the alternate geometry option.
39 5131 A--603A
MODIFICATIONS TO TRANSIENT FLOW CHARACTERISTICS 5.0 Several modifications related to the transient coolant flow behavior w These changes are included in the modifications to the F9RE-2M program.
discussed in this section.
5.1 PUMP TRIP AND TIME DELAY The flow coastdown in the F9RE-2 program was controlled by specification of a If the user wished time versus flow table (Inputs 196 to 225 and 226 to 255).
to begin the flow coastdown at a point in the transient other than time-zero, it was necessary to modify the shape specified in the table to achieve the desired coastdown.
This situation has been changed by the addition of a pump trip and delay time Now, if the user specifies a pump trip (Input 7799=1), the in the program.
That is, pump coastdown will not begin until a reactor scram has occurred.
226-255) will be referenced to the the times specified in the table (Inputs time of scram rather than to time-zero.
(
An additional time delay may also be included by specifying the desired dela When a value other than zero has been used, the interval using Input 8189.
times specified in the flow coastdown table will be referenced to the sum o With these changes, the user may now the scram time and the delay time.
include those features without having to generate a new set of table values for each type of transient.
INDIVIDUAL FLOW C0ASTDOWN FOR EACH CHANNEL 5.2 The number of options available for pressure drop and/or transient flow The new option (Input 58=-2) calculations (Input 58) has been increased.
allows the user to specify the relative flow rate between channels thro This is accomplished by specifying the following input.
the transient.
(
40
t sism; as (Optionforselectingindividual a) Input 58=-2 flow coastdown)
Time entries (seconds) for flow b) Inputs 7800-7819 TIMEZ coastdown in Channels 2 and 3.
First entry is equal to zero.
c)
Inputs 7820-7839 GPEAK(s)
Relative mass velocity in peak channel (Channel 2) associated with TIMEZ entries.
d)
Inputs 7840-7859 GHgT(t)
Relative mass velocity in hot channel (Channel 3) associated with TIMEZ entries.
Coolant mass velocity - Channel 1 e) Inputs 196-225 (G/G)j o
Time for Channel 1 entries 226-255 TIME If Inputs 196-225 are normalized, f) Input 166 G,
this is initial mass velocity in 2
Channel 1 (1b/sec-f t ),
Peak channel factor for mass F
g) Input 191 r
velocity in Channel 2.
Hot spot factor for mass velocity i
F h) Input 192 y
in Channel 3.
The mass velocity in Channel 1 is given by:
VEL 5C(l) = G (G/G)j o
o If G, is equal to zero, the values of G/G, are equal to the mass v in Channel 1 so that VEL 6C(1) = (G/G ))
o 41 0243E-58E:2 (51320) 36
For Channel 2, the mass velocity with the new option is then given by:
VEL 9C(2) = VEL 9C(1)
- F
- GPEAK(t) r and for Channel 3 VEL 9C(3) = VEL 9C(1)
F *GH6T(t) y Note that the correction f actor for the mass velocity in both Channel 2 and For Channel 2, the correction f actor is:
Channel 3 is composed of two values.'
F x GPEAK(T) r and for Channe' 3 F xGHST(T) y The flow coastdown for these two channels can be specified in either of two ways. First F and F can be set equal to 1.0.
In this case, the tabular
~
values of GPEAK and GHST represent the flow rate of Channels 2 and 3 relative r
y to Channel 1.
and F are selected to represent In the second method, the values of Fr y
The tabular values the relative (steady state) flow rate of the two channels.
of GPEAK and GHDT then represent the normalized values of the flow coast In this case, the initial entry on each of the in the representative channel.
two tables would be 1.0 at time zero whereas in the previous case the values at time zero would be equal to F and F.
r y
The other pressure drop / flow relationships available with Input 58 revnain same as previously documented.I2) These options are sunnarized below:
42
Value of Input 58 Option
-2 As described in this section
-1 No redistribution of flow. Flow in Channels 2 and 3 maintains same relationship to Channel 1 flow as exists in steady state 0
Original (l) F9RE-2 pressure / drop flow redistribution model Revised (2) FERE-2 pressure drop / flow
+1 redistribution model l
(.
t 43
SIMULATION OF INTER-AND INTRA-SUBASSEMBLY FLO 6.0 Coolant flow channels in the F8RE-2M program are not explicit duplicationf
- Rather, the configuration of the geometry used in most fast-reactor designs.
the actual flow area is represented by an equivalent annular flow passage as This simplified, one-dimensional schematically shown on Figure 8 representation is adequate for most situations and provides a reasonable approximation of the coolant flow characteristics surrounding a fuel rod.
Occasionally, however, situations arise in which the coolant flow adjacent to a fuel rod cannot be adequately characterized by one-dimensional axial flow.
Intra-subassembly cross-flow and heat transfer between adjacent flow passage i
may result in a substantial deviation from the one-dimensional approximat o Such a condition may occur at very low flow rates and/or when there is a la In order to nuclear or themal gradient in the vicinity of the fuel rod.
approximate such conditions, two models have been included in the FS program which simulate intra-assembly heat transfer and coolant flow These models are only applied to Channel 3 in the program-C redistribution.
(i.e.,thehotchannel).
(
5131 A-603A:2 44 (S1320)
- FUEL (Rg) f h
% CLADDING (R )
g COOLANT I
CHANNEL (RCH FLOW AREA: A = w(RCH - R,2) g k
[
EXAMPLE: EQUIVALENCE FOR SQUARE ARRAY
_g 2
Ag = s2 - wR
- R. CH"II '*
V Ne j
I I
DH " 4 A /P f
DH = 4 (s - r Rc ) / (2 x R,)
"D. H = (2/R ) (RCH -AI g
c
\\
\\
\\
\\
b Figure 8 Schematic of Fuel Rod Coolant Channel 3487-8
'(.~.
45
INTRA-ASSEMBLY FLOW REDISTRIBUTION SIMULATION
- 6.1 To simulate the channel cross-flow component, a parameter (G/G,)g has g
i been introduced which represents the local flow rate in ar.y axial section M f
relative to the inlet flow of Channel 3.
The values of (G/G,)g am g
A set of up to twenty input values introduced via Input nusbers 7860 to 7999.Theinpctvaluescorrespon(tothetimes f are supplied for each axial section.
specified by TIMEZ (Inputs 7800-7819).**
When this option is chosen (Input 31=1), the C.alculated inlet flow rate at any at that time to time in Channel 3 is multiplied by the value of (G/G,)g 4
The inlet flow obtain the corresponding local flow rate in axial section M.
rate in Channel 3 is calculated using any of the available pressure drop / flow redistribution options (Input 58) available.
The coolant enthalpy rise across the axial node is calculated using the local.
Thus, if the steady state value (i.e., the rather than the inlet, flow rate.
first value in the table) of (G/ Gin)N we m, for example. 0.9 at axial section 4, the modified temperature rise across the node would approximately***
be related to the norwal temperature rise as follows:
= AT/(G/G,) = 1.H AT aT 4
MODIFIED A similar relationship exists for the transient analysis procedure where the calculated inlet velocity of Channel 3 at any point in the transient is l
modified by the appropriate value of (G/ Gin)M to obtain the local velocity l
- Note that interassembly flow redistribution can be modeled by the Section 5.2 individual flow coastdown method or incorporated into the intra-assembly flow redistribution method of this section.
- Note that this is the same time table used for the individual flow co downs described in Section 5.2.
- Variations in the value of specific heat will alter the answer somewhat.
[
I l
5131 A-603A:2 46 (S1320)
It should be noted that the tables for (G/Ggn), e at that point in time.
For this option, not have a scram delay or pump trip associated with them.
the transient time and corresponding value of (G/G33) are, therefore, taken It should also be noted that in case the user directly from the input tables.
I fails to define sufficient data for this variable, the values for (G/G in M are def aulted to 1.0.
(
O 47
EXCESS ENERGY SIMULATION (INTER-AND INTRA-ASSEM 6.2 As part of the intra-assembly flow redistribution process, a certain amount o 1
energy is removed or added as the cross-flow component enters or leaves the In addition, heat may be transferred coolant node at a given axial position.
from one channel to an adjacent channel by conduction.
To address this problem using the present one-dimensional flow model in FdRE-2M, a term " excess energy" was defined which represents the radial heat-conduction and/or radial mass transport energy transferred into or out of a In this simulation model it is not important whether particular coolant node.
It is only this energy was transferred by conduction or mass transport.
necessary to define the quantity of energy which enters (positive value) or leaves (negative value) the coolant node over any time interval.
g (Inputs 8000 to 8139)* are supplied in a manner similar The variables QEXS to that of the previously discussed variable (G/Ggn)g. Up to twenty Again, the values of l
values are supplied for each axial node in Channel 3.
this variable are chosen to correspond to the times specified in the TIMEZ table (Inputs 7800-7819).
During the steady-state calculations, the coolant temperature rise over any t
axial coolant node is modified by the excess energy term as follows:
QEXSg
' C.EXS "
^C+A
-C G
f p
M Steady State where:
is the coolant temperature rise including the excess energy aTC.EXS term ( f)
- In units of Btu /sec I
5131A-603A:2 48 (51320) 42 L
is the coolant temperature rise without the excess energy term, ATC
('F) 2 A
is the coolant flow area, (ft )
f is the specific heat of the coolant evaluated at the mean C
temperature of the coolant node, (lb I
is the local mass velocity including the (G/Ggn)g Gg correction previously discussed, (Ib/sec-ft")
QEXS is the excess energy, (Stu/sec) g The modification to During the transient, a similar calculation is performed.
the coolant nodal temperature is performed as follows:
~
QEXS AT g
AT #
ATC,EXS C
pC Af
- AZM.
=
p
(
where the previously undefined synbols are:
is the coolant density evaluated at the mean temperature of the p
3 coolant node, (1b/ft )
is the length of the coolant node at axial section M. (ft)
AZg is the time interval over which the calculation is performed, AT (sec)
An excess energy ratio has been defined as:
Ratto = QEXS i
49
where is the amount of heat transferred directly to the coolant from the Q
fuel, cladding and other heat producing materials during steady state or over any time interval during the transient.
Values of this ratio are listed in the input at the same points in time as the other relevant data.
e 50
TYPICAL RESULTS OBTAINED BY INCLUDING INTER-AND INTRA 6.3 HEAT REDISTRIBUTION A typical hot channel, axial coolant temperature distribution as calculated with and without the intra-assembly flow and heat redistribution techniques For this analysis, described in the previous sections is shown on Figure 9.
input values for the (G/Gjn)g and QEXS terms were obtained from a g
detailed subchannel analysis code. As can be noted, good agreement is obtained between the F5RE-2M model and the detailed subchannel analysis code l
predictions.
Also shown on Figure 9 is the typical F@RE-2M prediction if the Section 6.0 In this latter case, the intra-assembly flow techniques are not applied.
maldistribution is set equal to a single value (spatially independent) which results in the F9RE-2M coolant temperature matching that of a. detailed subchannel analysis code at the point of maximum cladding temperature position As can be noted, this results in an (approximately X/L=0.69 on Figure 9).
The new overprediction of the coolant te:nperature above this axial position.
techniques of Section 6.0 allow the designer to eliminate this overconservatism in the hot channel modeling.
An interface is currently being established with the transient subchannel data to be analysis code, COBRA-WC,III) to enable (G/G I and QEXSg in M easily input to F9RE-2M on transient basis for low flow /high core temperature 4
transients (e.g., natural convection cooling), where these effects are Since COBRA-WC is a whole core detailed subchannel analysis code, important.
l term will which models all of the core assemblies in parallel, the QEXSg account for both intra-assembly and inter-assembly heat transfer.
j 5131A-603A:2 51 (51320)45 I
^
1
_ _[
800 w
LEGENO:
7 g
F$RE 2WIPREDICTl0N WITH GEXS" y
?
AND (C/G ), CAPABILITY
,E g
FWRE 2tl PREDICTl0N WITHOUT SECT 10N S.8 l
h
$gg
_g EXTENDED CAPAsiLITY
- s E
E k
DETAILEO SUSCH ANNEL AN ALYSIS CODE PREDICTION
=
400 g
5 8
u see 5
m W
Em E
200 Ep 5
E 100
^ ={
I b
I I
1.58 0.75 6
9.50
~
8.25 O.00 FRACTION OF HEATED LENGTH (x/L) 6.0 Modeling Capability) to that i
Figure 9 Comparison of F#RE 2M Coolant AxialTemperature Profile IWith and Without from Detailed Subchannel Analysis Code
i REACTIVITY FEEDBACK AND DECAY HEAT K)DIFICATIONS 7.0 Several changes have been made to the reactivity feedback and decay hea These modifications are all optfonal and can models in the FBRE-2M program.
II) into thi be used in place of the models which were originally programmed A description of these options are contained in the following code.
j subsections of this report.
ALTERNATE DOPPLER AND COOLANT DENSITY REACTIVITY FEEDBA 7.1 A new option for calculating the Doppler feedback and the coolant density If this option-is selected (Input feedback has been added to the program.
7798=1), the local Doppler feedback Ak (M,K) will be calculated using the following equation:
T (M,K) + 460.
f Ak(M,K) = FDOP(M,K)
In 7o(M,K) + 460.
(
where:
is the local Doppler feedback coefficient gp(M,K)
F T (M,K) is the local, average fuel temperature f
fuel temperature T (M,K) is the local, steady state average O
in is the natural log The local Doppler feedback coefficients (usually negaOve values) for each o the axial sections in the three channels are supplisd using Inputs 8140 to 8146; 8147 to 8153; and 8154 to 8160.
The local coolant density feedback for this option is calculated from
')*
Ak(M,K) = CFBK
,c
(.
53
j where.
)
CFBK(M.K) is the local coolant density feedback coefficient T (M,K) is the local coolant temperature e
((M,K) is the local, steady state coolant temperature i
The local coolant density feedback coefficients are supplied using Inputs 8161 I
Note that when this option is used to 8167; 8168 to 8174; and 8175 to 8181.
it is advisable to set the normal coolant density feedback coefficients (Inputs 414-420) equal to zero to prevent duplication of feedback.*
3 The local Doppler feedback contributions and the local coolant density feedback contributions are sumed to obtain the total reactivity feedback used in the kinetics calculations.
i f
- The original Doppler feedback calculation is automatically bypassed to prevent such an occurrence.
h-(5g20)2 5250A--606A 54
h
\\
REVISED CHANNEL INDEX ON ONE REACTIVITY FEEDBA!'K OPTION 7.2 Section 3.12 of Reference 2 describes two feedback mechanisms These feedback mechanisms were previously incorporated into F9RE-2M.
originally programmed to use the temperatures of the average chaMel (i.e.,
However, with tha Channel 1) in calculating the reactivity feedback.
I alternate geometry option now available (Section 8.1) it is possible that any one of the three channels may be the one of interest insofar as the radial and Therefore, the equations in the axial feedback mechanisms are concerned.
program have been modified to allow the user to select which one of the thre channels will be used for calculating these feedbacks.
Either The variable IREX (Input No. 8334) controls this selection process.
Channel 1, Channel 2 or Channel 3 can be selected by setting IRCX equal to 1
'.f the user neglects to specify the channel, the option will default 2, or 3.
A description of these feedback mechanisms and the equations to Channel 1.
used in the program are repeated here for completeness.
The two reactivity feedback mechanisms under discussion are an axial fuel Although other expansion feedback and a core radial expansion feedback.
feedback mechanisms analogous to these are contained in the program, these tw feedback options vary slightly in their method of application and require a more simplified input.
In the case of the axial fuel expansion feedback, the model uses the axially averaged fuel surf ace temperature (rather than the average fuel tempe That is, to compute the reactivity feedback.
(
55
^
l
' ~ MAX MAX b
T 'm) k I
[
T(d) d d
m-1 so m_
I m=1 s m.k a
(akFE)d = *FE MAX ml where:
is tte axial fuel reactivity expansion coefficient (ak/'F) 4FE over the active core length (Input 320) is the fuel surface temperature for axial increment m, Channel k T m,k s
A2,
is the length of axial increment m and superscripts (j) refers to the jth time step and the superscript (o)
The channel subscript (k) is selected using the refers to steady state.
variable IREX (Input 8334).
This option, as opposed to other fuel expansion in the program, is a simplified estimate of the reactivity feedback associated with (for example) the case of a " dished fuel p'ellet" in which the outer edge of the pellet If axial blankets are specified controls the stack length (for fresh fuel).
(Input numbers 55 and 56), only the active fuel length (axial sections 2 Note that a negative value of through 6) are considered in the equation.
is required to produce a negative reactivity component for an aFE expanding (increasing temperature) core.
In the case of core radial expansion, the model differs from others in the program in that the core expansion feedback is assumed to be proportional to The reactivity change is given by the average outlet coolant temperature.*
-T (ak)RE " *RE ut ut k
- The other model in the program utilizes a feedback mechanism which combines bowing, axial pressure differences, and changes in the radial temperature gradient across the core.
56 5250A--606A
,Aere is the radial core expansion coefficient (Ak/ F)
%E the channel outlet temperature (8 )
F Tc.out and the superscripts (j and o) are the same as described previously. Again, the channel selection (subscript k) is controlled with Input 8334. A negative
%E (Input 165) would give a negative reactivity feedback during value of a transient in which the core expanded due to an increase in temperature.
This feedback mechanism is particularly well suited for study of core expansion, core restraint, and similar reactivity effects which can be The associated with changes in the average coolant outlet temperature.
magnitude of the reactivity coefficient (%E) would obviously be selected with consideration for the type of fuel element support involved (i.e., free i
radial expansion or fixed-end fuel element support).
57 i
l
l 7.3 ALTERNATE DECAY HEAT MODEL The present method for determining the fraction of the reactor power which is attributed to decay heat is determinedII) using an empirical equation which contains several constants which are usually obtained from experimental data.
Frequently, the relative power resulting from decay heat is available from For example, such information may be available as a result of another source.
analyses performed for the purpose of establishing the nuclear characteristics of a reactor core.
To provide for this possibility, an optional decay heat model has been This option is activated using the variable included in the FORE-2M program.
IDECAY (Input No. 8207). When IDECAY is set equal to 1, the $mpirical decay heat model is bypassed and the decay heat fraction for the three individual channels is obtained from the following time versus decay fraction tables.
Description Inputs Variable 8212 to 8231 TDECAY(t)
Times at which decay heat fractions are supplied. (The first value in the table is 0.0.)
8232-8251 PDECAY(t,1)
Decay power fraction for Channel 1 corresponding to time values of f
TDECAY(t) 8252-8271 PDECAY(t,2)
As above, but for Channel 2.
8272-8291 PDEC AY(t,3)
As above, but for Channel 3.
The value of the time used to obtain the decay heat fraction can be referenced to the time of scram rather than the actual transient time.* Thus, if in a particular transient a scram were to have occurred at 0.1 seconds, the value f
of decay heat used at (for example) 1.0 seconds would be the decay heat value in the table corresponding to 0.9 seconds (i.e., T'= T - TSCRAM = 1.0-0.1=0.9).
Using ISTART=1, Input number 8335.
58 l
If a transient were to proceed without any scram occurring, the steady state value of decay heat, corresponding to time-zero in the tables, would be used throughout the transient.
The relationship between the prompt neutron power at steady state and the total power for this model is given by:
FISSIONS P* = P,(1-f)/8.6 x 10-10 3,,e 0
cm are respectively, the prompt fission rates and total 0
where P* and P The variable f power as previously defined by Equation (102) in Reference 1.
represents the steady state decay heat fraction and is determined by one the following methods:
If the " reactor power (Input 636)" and " total volume of fuel in core 1.
(Input 91)" are really representative of the total core, f is the weighted average of the decay heat fraction for Channels 1, 2 and 3.
3
, POECAY(1,K) = FREG(K) f=
where PDECAY(1,X) is the initial (steady state) decay heat fraction for Channel K and FREG(K) is the fraction of the total core power represented by Channel K.
8209, 8210, and 8211 and must t
The three values of FREG(K) are Inputs be selected so that:
59
3 FREG(K) = 1.0 Example: FREG(1) = 0.6 FREG(2) = 0.3 FREG(3) = 0.1 Total 1.0 If the program input for " reactor power" and " total fuel volume" are, l
2.
in f act, only that associated with the " average" fuel rod (i.e.,
Channel 1), f is then given directly by the steady state decay heat fraction of the appropriate Channel.
f(k) = PDECAY (1,K)
The selection of which of the above methods is used is controlled by the If IREG=0, the weighted average method is used; variable IREG (Input 8208).
The value of IREG is if IREG/0, the Channel K decay heat values are used.
also used to control the printout of the " prompt power" and " total power" during the transient as noted below:
IF IREG=0, Power printouts will be for Core Power IF IREG=1, Power printouts will be Channel 1 IF IREG=2, Power printouts will be Channel 2 IF IREG=3, Power printouts will be Channel 3 For the " Channel" power printouts (i.e., IREG>0), the printout will correspond appropriately to that of either an individual fuel rod; a subassembly; or a region of the core depending on the magnitude of the volume (Input 91) and power (Input 636) specified in the input.
1 Irrespective of which of the two methods are used, the individual deca The power fractibn for each of the three rods is determined separately.
is 9eneration rate in any one of the three. fuel rods at the end of time then given by:
(
60
P)(K) = P, = PDECAY(t,K) + 8.6E-10 PSTR where PSTR is the fission power which is determined using the kinetics equations programed into the FORE-2 program.II)
The average power over the time step for the fuel rod is given by:
fP(K)dt 3
f (K)
- j fdt The value of F (K) is used to evaluate the local, transient heat generation j
rate for the appropriate channel.
I I
i 9
(.
61 u
SPECIAL SUBROUTINE FOR REACTIVITY FEEDBACK 7.4 Although FSRE-2M contains a variety of options related to reactivity feedba there are occasions in the course of considering various design features when these standard feedback mechanisms are not sufficient to analyze a particular The designer may, for example, wish to study the effect of situation.
providing some mechanically or thermally actuated feedback mechanism i design.
To provide for this contingency, the FORE-2M program has been " partially" EC).
modified by the inclusion of a special feedback subroutine (subroutine SP At present, the subroutine is a dunmy routine which, if this option were selected (Input 8333=1), would return with a zero value of reactivity However, the purpose of including the subroutine is to facilitate feedback.
(if necessary) modifications of the code to accommodate a special feedback routine.
The subroutine SPEC has in CptMSN all of the steady-state and transient temperatures which would probably be required fcr cny conceivable reactivity These temperatures are the coolant inlet temperature feedback calculations.
and the follow 1.g temperatures for each axial position of each of the three channels:
1.
Coolant nodal average; 2.
Coolant nodal outlet; 3.
Fuel surf ace; 4.
Fuel average; 5.
Cladding average; 6.
Additional material.
l The length (AZ,) of each axial increment is also contained in the To use the model, it will obviously subroutine to allow for axial weighting.
be necessary to program the equation (s) required to simulate the desired However, this task is simplified with the special feedback mechanism (s).
subroutine and does not require any changes to the main program.
(.
62
MODEL CHANGES TO ALLOW FOR ALTERNATE FUEL R00 CHARACTER 8.0 This section discusses a group of changes made to the program to permit the user to specify an alternate set of characteristics for one or more of the In general, these changes three fuel rods analyzed by the F9RE-2M program.
will allow several of the specified characteristics (e.g., geometry) of the Channel 3 (hot channel) fuel rod to be significantly different than the Previously, many of these characteristics of the other two fuel rods.
parameters had to be identical for all three fuel rods.
The addition of these modifications now allows for the simultaneous analysis Such a of two entirely different types of fuel rods in the same study.
situation could arise, for example, in the study of a f ast breeder reactor which had driver fuel rods and blanket rods with different characterist The modifications discussed in this section and in other sections do n For to be used at the same time but can, in f act, be used individually.
example, the alternate decay heat model (Section 7.3) can be used regardless of whether or r9t the alternate fuel rod geometry model is selected.
('.
63
~ - - - - - - -
w w---
wy--
m
8.1 ALTERNATE FUEL GEOMETRY OPTION In the original version of the F9RE-2 computer program, the equations were all directed at obtaining the solution of a fuel rod transient involving three identical fuel rods. These three fuel rods were identified as an average rod And while (Channel 1), the peak rod (Channel 2) and the hot rod (Channel 3).
the heat generation rates and heat transfer characteristics of the three rods could be different, the geometry of all three fuel rods were the same.
Recently, it has been ot, served that with certain f ast reactor core geometries the feedback contribution of the blanket rods becomes a non-trivial portion of the overall feedback. And since the geometry of the fuel rods and blanket rods are not necessarily the same, the simultaneous treatment of more than one fuel rod geometry becomes desirable. This feature has, therefore, been included in these latest modifications to the F9RE-2M program.
To activate this option, it is merely necessary to set the option trigger (Input No. 7768=1) and supply a second set of geometric input variables (Inputs 7769 to 7790 and 8190 to 8206). This alternate geometry will then be
(
assigned to the fuel rod in Channel 3 (i.e., the " hot rod").
Channels I and 2 (i.e., the average and peak rods) will use the values of the geometry normally supplied in any problem.* Note that with this option, either two blanket rods and one fuel rod, or two fuel rods and one blanket rod may be analyzed in the The only restriction is that the geometry of the Channel 1 same transient.
and Channel 2 fuel rods is identical while that of Channel 3 is different.
The relative heat generation rates in Channels 2 and 3 are controlled using Inputs 179 and 180. Since the geometry of Channel 2 is the same as for Channel 1, the heat generation of Channel 2 is related to the heat generation of Channel 1 by the ratio of the power (P ) in the respective channels.
k Thus, for the peak channel (Channel 2),
- 0ther infonnation which has been explicitly defined for Channel 3 in the original code version (Ref. 2) is also automatically carried over for the alternate geometry (e.g., axial variation in central void size; Inputs 915-921).
b 64
+O=
r (Input 180) = (P /P )
P 2 3 For Channel 3, the differences in geometry must also be considered 50 that the correction factor on heat generation becomes:
H (Input 179) = (P /P )(Rf,g/Rf,3 P
3 3 where P
is the rod power of Channel K k
is the fuel radius of Channel K R f,k n
65
1 l
t ALTERNATE AXIAL POWER SHAPE 8.2 Frequently, the axial power shape of the fuel rods and blanket rods also An alternate axial power shape is differ enough to warrant consideration.
therefore available to supplement the alternate fuel rod option discussed in However, the alternate extal power shape can be uscif the previous section.
l even if the alternate geometry option is not used.
The option trigger for the alternate axial power shape is Input 32 (i.e.,
Up to seven relative values, corresponding to the number of Input 32=1).
18 As in axial sections (Input 8) are then supplied using Inputs 8182 to 8 8.
l the case of the regular axial power shape (Inputs 171 to 177), the va ues should be normalized so that:
IMAX
{
F,
- AZ 1.0
=
tHAX b A2 m=1 is The alternate axial power shape will be applied to Channel 3 if this opti The normal axial power distributton will be assigned to Channels 1 chosen.
and 2.
h t the Note that this alternate power shape option is entirely different t a With that option, the option described in Section 10.1 (Inputs 849 to 855).
h axial power shape (Inputs 171 to 177) can be modified at one point in t ll three transient. Since this transient alteration would apply equally to a channels (i.e., as a percentage change from the original shape), it is l
in suggested that both of these power shape options not be used simu order to avoid the possible introduction of an unwanted change in the p shape.
l l
l
(-
66 l
I
~
l AXIAL VARIATION IN HEAT GENERATION HOT SPOT FACTOR 8.3 To provide an additional degree of flexibility to the program user, a spatial variation in the f actor on heat generation for the " hot rod" (i.e., Channel 3)
This feature can only be used in conjunction with the is now available.
alternate power shape option (Inputs 32 and 8182-8188).
If the user wishes to use this feature, the axial variation in the hot spot f actor is supplied via inputs 7791 to 7797. If these inputs are supplied, this axial variation in hot spot f actor will be used in place of the normal hot spot f actor (INPUT 179) in computing the local heat generation rate in the Channel 3 fuel rod.
The local heat generation rate in each of the three fuel rods is then computed in the following manner:
Channel 1 (The Average Channel)
Q "' (M) = 948.05
- PIN
- A,
- FRFL/V9LFL 3
where:
is the average heat generation in the fuel of Channel 1 at Qy"'(M) axial section M. Btu /sec-ft is the input power (INPUT 636), Hw PIN is the ratio of local power to average power at axial A,
section M (INPUTS 171-177) is the fraction of power produced in the fuel FRFL 3
is the volume of fuel in the core (INPUT 91), ft V9LFL
(-
67 I
Channel 2 (The Peak Channel)
Q "*IM)
- 0 "'(M)
- P 2
1 r
where:
is the radial peak-to-average power density in the core Pr (INPUT 180)
Channel 3 (The Hot Channel) a)
If INPUT 32 is equal to zero:
0 "'IM)
- 0 "'(M)
- PH 3
1 where:
is the hot spot f actor used in calculating heat generation Ph in the hot channel (INPUT 179)
If INPUT 32 is equal to 1 and INPUTS 7791 to.7797 are not specified:
b)
WR(M)/A, Q "'(M) = Q "'(M)
- PH 3
3 where:
XPpWR(M) is the ratto of local power to average power for the alternate power shap'e (INPUTS 8182-8188).
If INPUT 32 is equal to 1 and INPUTS 7791 to 7797 are specified:
c)
Q "'IM)
- 0 "'(M)
- PS,* XPOWR(M)/A,
3 1
l 68
where:
is the local hot spot f actor on heat generation at PS, axial section M (INPUTS 7791-7797) for the alternate 8182-8188) power shape in the hot channel (INPUTS The addition of this feature permits the user to easily account for any spatial variation in heat generation uncertsinties which may occur.
(
5250A--606A 69
9.0 PROGRAM REVISIONS During the course of updating the FARE-2M program, several minor erro These errors were either a result of an incorrect deriva uncovered.
In general, the errors equation or were caused by a programming error.
ffect upon resulted in either conservative predictions or had little or no e the overall results.
REVISION TO THE CALCULATION OF AVERAGE FUEL TEM 9.1 II) was changing One of the model changes made to the original F9RE-2 program ithin a the location at which the temperature calculations were performed w If the original program, this location corresponded to the volume In the earlier revision to the model(2) fuel node.
weighted center of the fuel node.
it was shown that by changing the location a more accurate temperature calculation could be obtained.
Figure'10 is a schematic representation of the fuel node network Shown on the figure region fuel rod (up to 10 regions can be specified).
schematically are three sets of radii:
q
)
the radii describing the fuel node boundaries (user specified 1.
the location of the volume weighted nodal centers 2
d the radii at which temperatures are calculated using the improve 3.
location discussed above.
The relationship between the boundary radii and the radii at which l tion with a temperatures are calculated was derived by comparing an exact so u l
The resulting solution obtained using a finite element approximation.
I2) to be:
relationship was shown 2
2 R +1 p
n n
2 "m " 2 log (Rg)/R )
5250A--606A 70 I
(51320)18 1
FUEL ROD lj, tg
- tyg
=
r3 c
fg c
- fg=
I l
I I
I I
I I
I I
I l
I FUEL NODE I
l g
BOUNDARIES g
I i
l i
l i
I I
I 8
l*
/ Ali I
i i
l I
l VOLUMEWElGHTED j I
I I
l NODE CENTER I
I I
l I
l l
I I
i 1
i l
8
/
--i l
l I
RADil ATWHICH I
I I
TEMPERATURES I
I I
I ARE CALCUL ATED I
I I
I I
I I
I I
I i
I I
I I
I i
1 e
w Rg L.
I
+R2
- R3 1
Rg
=
l Figure 10 Schematic of Fuel Node Network in FWRE-2M 3487-10 l
(
71
While this modification to the program improved the temperature calculations, it introduced an error in the average temperature calculation since the average node temperature is associated with the volume weighted node ce While this error did not significantly change the overall results obtained from the program,* the value of the average temperature listed in the F9RE To correct this deficiency, the average temperature of output was in error.
each fuel node was determined by a parabolic interpolation of the two adj For the example shown on Figure 10, for example, the fuel temperatures.
average fuel temperature of node 2 would be given by:
2 2
T =T3 - (T3-T) f-R a
2 2
2 R2-R1 where:
and R are the temperatures calculated at R3 2
T and T y
2 is the radius at the location corresponding to the volume weighted and a2node center and is defined by I
2+r2 r
a2" 2
- Since the Doppler calculation uses a transient temperature chan an absolute value, the difference between the va change in the fuel temperature was not affected appreciably.
(~.
72
4 REVISION IN DERIVATION OF A GAP CONDUCTANCE EQUATION 9.2
[
In performing the recent program modifications, it was noted that one of l
equations in the original F#RE-2 version of the variable gap conductance This equation was related to the decrease contained a minor derivation error.
in gap dimension resulting from fuel melting if the volume of molten fuel The equation
- was given in the form exceeded the central void volume.
2
+1)R N
AV R
(AVmit g
j melt f b(melt)
ARmelting "
Z ZR f
where:
is the total fuel volume Af is the area of molten fuel is the fuel radius Rf is the radius of the central void R
is the change io radius due to fuel melting g
ARmelting is the fractional change in fuel volume associated with AValt melting is the number of fuel rings which have melted N
The equation is derived by comparing the change in fuel volume asso l
melting with the amount of molten fuel that can be accommodated by the cen The excess molten fuel volume is then assumed to contribute to a change void.
in the radial expansion of the fuel rod.
N Letting f = h E
, we have for a unit length of fuel f m=1 2
= wR2 + 2,R AR w(R2 - R )f ult g
f 2
N AV R
(AV
+1)R mit f Mt g {,j b(melt)
Z ZR ARmelting f
- Equation 34 of Reference 1.
(.
73 5250A--606A
Comparison of this equation with the previous equation shows that the now contains a term 1/f rather than the value of unity 2
multiplier on R contained in the original equation. This error would have resulted in a slight underprediction of the expansion characteristics of the fuel if the following four conditions existed:
The original variable gap conductance model (Input 20=+1) was used.
1.
A central void was specified or occurred as a result of sintering.
2.
3.
Fuel melting occurred.
The molten fuel volume exceeded the volume of the central void.
and 4.
In the event that all of the above conditions existed, the result would have been that the calculated fuel temperatures would have been overpredicted.
This error has been corrected in the modified version of the computer program.
e 74
d-PROGRAM MODIFICATIONS TO PROVIDE USER FLEXIBILITY 10.0 In addition to the changes made to obtain model improvements, several feat have been added to the F9RE-2M program which do not affect the basic calculations but which were added to provide some additional flexibility for The use of these additional features allows the user to either j
obtain specific information or to have the ability to manipulate the output the user.
These features have been without having to stop and RESTART a problem.
included as options since it may not be necessary nor desirable to use them for many cases.
MODIFY THE AXIAL POWER SHAPE OURING THE TRANSIENT 10.1 Certain types of analyses require that the axial power shape be changed at For example, for a control rod insertion some point in the transient.
transient, the axial power shape changes when the rod is inserted from an initially withdrawn position.
i The analysis of this type of transient has previously been performed using the The insertion phase of the transient RESTART option in the computer program.
Then the program is stopped, the axial shape appropriately modified, is run.
and the remainder of the transient analyzed.
To provide more flexibility for the user, a new option has been added whic allows the axial power shape to be modified without stopping the problem.
Input number 848 is a new variable (TSWAP) that defines the time at wh The alternate axial power shape alternate power shape will become effective.
is defined by the variable ALTP5W(M)*.
(Inputs 849-855)
After the time TSWAP has been reached, the local heat generation is c by multiplying by the ratio of the alternate shape factor to the original 171-177) as shown below.
shape factors (POWRAT(M), Inputs for x $ TWSAP, ALTP9W(M)/P9WRAT(M) dified) = Q"'
- where 1 5 M I Pf4AX 75 t
c., r n.
,ar.
PRINTOUT INTERVAL VARIATION DURING THE TRANSIENT 10.2 t t ) can be Printout intervals (i.e., the period of time between prin ou s However, once controlled by several different input variables in F9RE-2M.
i d and is either a these variables are selected, the printout interval is f xe between function of the number of timesteps (Input 34) or a specified time printouts (Input 71).
In many transients, there may be a period of time during which the h ges occur change quite rapidly while during the remainder of the transient c an Thus, while it may be important to have frequent printouts i ht during the one portion of the problem, the same printout interval m g more slowly.
i f the transient.
produce a needless amount of output during the slower port on o h
the A new option has therefore been added which permits the user to c a If a non-zero value is input to printout interval during the problem.
d at location 856, it will represent the point in time, specified in secon s, This new printout which a new printout interval will becomd effective.
blem interval is specified as Input 857 and will override Input 71 once th time exceeds the value of Input 856.
l l
(~.
76 1
OPTION FOR SEARCHING FOR PEAK VALUES OF CERTAIN CR 10.3 In order to reduce the amount of output data, the user of F9RE-2M usually does Rather, he selects a not print out the results from each calculation.
printout interval (INPUT 71) which will result in a reasonable quantity of Frequently however, particularly for transients in which the output data.
values of the parameters change rapidly (e.g., rapid reactivity transients),
[
this procedure will f ail to specifically print out the maximum value of The user must then attempt to estimate the certain critical parameters.*
magnitude and time at which the maximum values of these parameters could oc To avoid the possibility of errors in this procedure, an option has been added (INPUT 8338) which will key the FIRE-2M program to search for and record the time of occurrence and maximum values of: 1) reactor power; 2) maximum fuel centerline temperature; 3) maximum cladding 1.D. temperature; and 4) maximum The user can select either Channel 1 (INPUT channel coolant temperature.
8338=1), Channel 2 (INPUT 8338=2) or Channel 3 (INPUT 8338=3) as the cha The program on which the search for maximum temperatures will be performed.
will then identify the time and axial location at which the maximum values of these parameters occur.
Since this option will increase the computer execution time slightly
(<0.5%), it is recomended that this option be bypassed (INPUT 8338=0) for slow transients were interpolation will usually produce satisfactory results.
l
- Suc'h a condition usually occurs in the first few seconds of a transient.
( -
STORAGE OF DATA FOR SUBSEQUENT RETRIEVAL FOR 10.4 An option has been included in the latest version of F8RE-2M which storage of selected parameters for possible use in a subsequent plottin The original F#RE-2 program (1) did have a plotting package in it, but this was later removed because it was somewhat incompatible with th package.
blestinghouse coreputer f acility.
d 5)
The present version of FARE-2M stores 169 selected variables (Table This storage is initiated by setting option IPLIIT (INPUT 8337) l to on TAPE 2.
equal to 1; if the option is not desired, this variable should be set equa zero (INPUT 8337=0).
Once the option is selected, the user must then save the data tape for Rather subsequent use by specifying the appropriate " CATALOG TAPE 2" con ible with than write a generalized plotting routine (which may not be compat every computer facility), it is sugaested that each f acility write its own l ting it as plotting program, retrieving the data stored on TAPE 2 and manipu a The 169 variables are stored on TAPE 2 in a series of strings, There will be required.
l indexed according to the index numbers shown on Tables 4 an41 5 f
"N" strings (each 169 words in length) where "N" correspondi to the n The dimension of computer printouts that were obtained during the problem.
y this "dunny" array is therefore given by DUPMY (N,169) whe e N can var l
) in a given between 1 (steady state) e d the maximum number of printouts (IMAX The following metho! (for example) could then be used to retrieve problem.
the data:
I' DO 100 N=1, IMAX READ (2) (DUMMY (N,I),I=1,169) 100 l
l l
78 b
5250A--606A
TABLE 4 VARIABLES STORED ON TAPE 2 FROM F8RE-2M RUN CORE DEPENDENT PARMETERS Parameter _
1_dex Number _
n TIME (sec) 1 Total Core Power (N )
2 Prompt Core Power (k )
2 3
Channel 1, Coolant Mass Velocity (Ib/sec-ft )
2 Channel 2 Coolant Mass Velocity (Ib/sec-ft )
4 2
Channel 3, Coolant Mass Velocity (Ib/sec-ft )
5 6
Channel 1. Coolant Outlet Temperature (OF) 7 Channel 2. Coolant Outlet Temperature (DF) 8 Channel 3, Coolant Outlet Temperature (OF) 9 Maximum
- Cladding Temperature (OF) 10 Total Core Reactivity (d) 158 Programed Reactivity (*)
159 Total Feedback (A) 160 Doppler Feedoack (*)
161 Cladding OD Temp. (*F), Channel 3, Axial Mode il l
162 Cladding OD Temp. (*F), Cnannel 3. Axial Node #2 163 Cladding 00 Temp. (*F), Channel 3, Axial Node #3 164 Cladding 00 Temp. ('F), Channel 3 Axial Node #4 165 Cladding OD Temp. ('F), Channel 3, Axial Node #5 166 l
Cladding OD Temp. (*F), Channel 3 Axial Node #6 167 Cladding OD Temp. (*F), Channel 3, Axial Node #7 168 Coolant Inlet Temperature 169 5250A--606A 79
(-
(51320) 32
TABLE 5 VARIABLES ST(RED ON TAPE 2.FR(M FIRE-2M RUN CHANNEL DEPENDENT PARAMETERS Index Number Axial Sections 1 to 7 Channel 1
2 3
4 5
6 7
Parameter 1
11 12 13 14 15 16 17 2
60 61 62 63 64 65 66 FuelCenterlineTemperature(OF) 3 109 110 111 112 113 114 115 F
1 18 19 20 21 22 23 24 2
67 68 69 70 71 72 73 Average Fuel Temperature (d )
3 116 117 118 119 120 121 122 1
25 26 27 28 29 30 31 2
74 75 76 77 78 79 80 Fuel Surf ace Temperature (OF) 3 123 124 125 126 127 128 129 1
32 33 34 35 36 37.
38 i g 2
81 82 83 84 85 86 87 Cladding I.D. Temperature (OF) 3 130 131 132 133 134 135 136 1
39 40 41 42 43 44 45 2
88 89 90 91 92 93 94 Average Coolant Temperature (DF) 3 137 138 139 140 141 142 143 1
46 47 48 49 50 51 52 2
95 96 97 98 99 100 101 Outlet Coolant Temperature (OF) 3 144 145 146 147 148 149 150 2
1 53 54 55 56 57 58 59 2
102 103 104 105 106 107 108 Surf ace Heat Flux (8tu/hr-ft )
3 151 152 153 154 155 156 157 3
162 163 164 165 166 167 168 Cladding 0.0. Temperature (DF)
+
)
11.0 REFERENCES
J. N. Fox, 8. E. Lawler and H. R. Butz, "F#RE-II, A Computational Program for the Analysis of Steady-State and Transient Reactor Performance,"
1.
GEAP-5273, September 1966.
Modified Version of the J. V. Miller and R. D. Coffield, "FSRE-2M:
FORE-II Computer Program for the Analysis of LMF8R Transients,"
2.
CRBRP-ARD-0142, November 1976.
" Nuclear Systems Materials Handbook," Vol. I, TID-26666, 1975.
3 3.
A. M. Ross and R. L. Stoute, " Heat Transfer Coefficient Between U02 and
~
.g 4.
Zircaloy-2," AECL-1552 (CRFD-1075), June 1962.
1 R. B. Baker, " Calibration of a Fuel-to-Cladding Gap Conductance Model for 5.
Fast Reactor Fuel Pins," HEDL-TME-77-86, May 1978 G. G. Gubareff, J. E. Janssen and R. H. Torborg, Thermal Radiation 6.
4 Properties Survey, Second Edition, Honeywell Research Center, Minneapolis, Minnesota, 1960.
7.
W. H. McAdams, Heat Transmission, McGraw-Hill Book Company, New York, 1i 1939, pp. 54-55.
" LIFE-III Fuel Element Performance Code " ERDA-77-56, July 1977.
8.
" Compilation of Boron Carbide Design Support Data for LMFBR Control 9.
Elements," HEDL-TME-75-19, 1975.
G. H. Golden and J. V. Tokar, "Thermophysical Properties of Sodium,"
10.
ANL-7323, August 1967.
T. L. George, R. A. Masterson and K. L. Baseshore, "A Modified Version of COBRA for Whole-Core LMFBR Transient Analysis," Trans. Am. Nucl. Soc. 32, 11.
pp. 531-532 (1979).
R. L. Gibby, L. Liebowitz, J. F. Kerrisk, et al., " Analytical Expressions 12.
for Enthalpy and Heat Capacity for Uranium-Plutonium 0xide,"
i HEDL-TME-73-60. June 1973.
{'
5250A--606A 31 (51320) 29
~ \\'
f e
O APPENDIX A INPtIT DATA
(
\\
A-1
a A.1 INPUT DATA The particular input for the data cards is discussed in Subsection A-3.
The format for the other cards are:
Case Card:
Column Contents 1
) independent case designation
( dependent case designation 2-6 F7RE*
7-9 User's initials I
Column 2-34 10
/ are Optional 11-14 Case Number 15-27 Blank 28-34 Date 9999~ Card (Sentinel Card):
Columns Contents 1-4 9999 5-80 Blank Last Card:
Columns Contents l
1-5
) LAST Columns 6-9 are Optional 9
Because of tape-handling difficulties when a wrapup is requested, only single cr.ses can be run in this version of the code.
l All the input data cards have the same format.
Columns 1 to 4 must l
be a right adjusted integer corresponding to the input location for the first input value to the right of column 4.
Columns 5 to 80 contain input valu.:, in free form; that is, there is no requirement that a particular input appear in specified columns.
Free form requires that
(~
A-2
f-each number be separated by one or more spaces or by a comma, from its neighbor.
The input values in columns 5 to 80 are loaded in consecutive order, with the first value corresponding to the location in columns 1 to 4.
Input locations 1 to 60 are integer number.
Input locations beyond 60 must be external fixed point (F Field) or floating point (E Field) numbers:
that is, a decimal point must be used.
Repeat and skip options offer acditional input flexibility. The expression 1.0 ARna, for example, assigns 1.0 to n consecutive locations. The a is to typographically emphasize that a blank must be used.
Similarly, the expression ASna skips n consecutive input locations. All input values are preset to zero at the start of the program.
As such, the user can input values for only the locations to be changed from zero. Any alphanumeric input in columns 5 to 80 contained within parentheses is edited in the printed output, but otherwise is ignored.
This allows the user to insert comments in the input deck to identify particular portions of the input.
Appendix B contains a listing of the input for a sample problem. The input options and card format are illustrated ir, this listing.
There is no requirement that the data cards be in any particular order.
Because of this capability, it is possible to use a basic input deck with the modifications for the particular problem included before the sentinel card. The last card of a given input variable overrides l
previous data.
A.2 RESTART i
l The user has the option in F$RE-2M for a final and two intermediate wrapups, and for a restart.with changes in input from any of these wrapups.
Table A-1 contains a list of input values that cannot be changed on restart.
Because of the restart capability, the flexibility of FfRE-II has been l
l greatly extended.
A typical use might be the coefficients of reactivity l
terms which are single value input. For the particular transient
(.
- Inputs 7768, 7798, 7799, 8207, 8208, 8292, 8333 to 8335, and 8336 to 8339 are exceptions to this rule.
A-3
(
problem under consideration, the user might discover that the coefficients vary over too large a range to be approximated by a single number.
This functional variation may be approximated to any degree of accuracy by repeatedly running for a specified tire step and restarting with the new revised reactivity coefficients.
The input deck for a restart is as follows:
Independent case card Data cards for Ir:put locations 29 and 52 Sentinel card Dependent case card Data cards with changes in input values Sentinel card Last card A.3 DESCRIPTION OF INPUT DATA Table A-2 describes the input data for the FORE-211 program.
Not all of the variables are required for any given problem. The actual amount of input '
data required depends upon the options selected for a particular case.
It should be noted that core flow and inlet temperature as a function of time must be input to the code.
These data are typically calculated with a plant simulation model which analyzes the coupled thermal / hydraulics of the primary, intermediate and steam loops.
A-4
TABLE A-1 VALUES NOT TO BE CHANGED AT RESTART Location _
Definition 1
Number of delay groups 7
Number of radial core regions
.8 Number of vertical core sections 9
Number of radial fuel nodes l
18 Lumping conditions 21 Number of channels 27 Additional material input 76 Equivalent radius of the coolant 77 Cladding inner radius 78 Cladding outer radius 79-88 Radii of the fuel nodes I
90 Core outer radius 91 Volume of fuel in the core 94-100 Length of core axial sections I
l I
(
A-5
1 m
)
TABL6 2:
INTEGER VARI ABLES, LOCATIONS 1 to 60 INPUT FOR FORE-2ft Nodal and Tabular Options Input Number Variable Range Units Remarks l
1 IMAX 1 1 IMAX < 6 Number of delay groups i
2 IffiAX 1 < IMMAX < 3 Number of terms in empirical fit to fission product decay [see Equation (102) of Ref.1),
Number of mass velocity entries 3
INUli 2 < INUti < 30 Number of effective multiplication factor 4
ISMAX 2 < ISilAX < 30 entries (if this is input) f 5
JMAX Maximum number of time steps Number of T entd es j
6 KNUM 2 < KNUf41 0 3
c I
Number of radial core regions 7
LMAX 2<L<7 (L f 0,1)
Number of vertical core sections
?
8 HMAX 1<M<7 e
Number of radii at which fuel temperatures 9
NHAX 1 < N < 10 are calculated Number of power entires (if this is input) j 10 NUtiPWR 2 < nut 4PWR < 30 Number of entries due to sodium voiding 11 Ni4VglD 2 < NMVil0 < 30
-(if this is an input) 12 NMSCRM 2 < l#iSCRM < 30 Number of ak poinh due to scram (if I
this is an input)
'~
13 NMC##t.
2 < NMCIA. < 30 Number of bulk coolant boiling entries (if this is an input)
\\
Number of cladding burnout entries l
14 Nf4 CLAD 2 < NMCLAD < 20 (if this is an input) l
(
15 N14 TERM Channel to which temperature limits should be applied (1, 2 or 3),
if 0, average channel will be used (including coolant temperature scram).
m
^
I INpVT FOR FORE-2M Nodal and Tabular Options Input Number Variable Range Units Remarks 0
Equals O means use calculated w which 16 6
f g
i assumes parabolic profile 1
Equals 1 means use input values for w g i
(locations 820 - 826) 17 6
1 Cantilevered at inlet, pinned at exit bow 2
Simply supported' at both ends 3
Cantilevered at exit, pinned at inlet 4
Cantilevered at exit, free at inlet i
5 Cantilevered at inlet, free at exit O
No bowing 18 6
1 If coolant, cladding, structure and 9
additional material are not lumped 0
If lumped 19 6
1 For extrapolation procedure (for feedback est approximation) 0 Otherwise (I}
20 6
(1 or 2)
For variable conductance from fuel to gap cladding O
Constant conductance (see location 341)
(1)
If 6,p=1, the Ross and Stoute model, modified to include radiant heat transfer, is used.
g If 6,p=2, axial variations in conductances and radial gap dimensions are specified for each of the g
three channels using Inputs 827 to 847 and 948 to 968 (see Reference 3 for a description of the model used with this option).
If o,p = -1 or -2, the Ross and Stoute model (including radiant heat transfer) is used. Inputs 948 to 968 g
are used to specify either the cold (6
= -1) or hot (o,p = -2) radial gap dimension.
gap g
INPUT F0PE-2M Nodal and Tabular Options i
input Number Variable Range Units Remarks
+
21 6
1 Calculate temperatures for average h
channel only 2
Calculate temperatures for average and peak channels i
3 Calculate temperatures for average, peak and hot-spot channels 22 6()
0 Use curve fit for fuel conductivity k
(InputNo. 118-120) 1 Uses table (Input No. 861-900) 2 Uses original TID-26666 Pu-UO conductivity 2
[
3 Uses irradiated B C conductivity from 4
HEDL-TME-75-19 4
UsesTID-26666(Rev.1,8/1/77)Pu-UO2 conductivity 1
Use power table 23 6 p.r 0
Otherwise 1
If scram table of reactivity is input scram 0
Otherwise 1
If sodium void reactivity table is input void 0
Otherwise (1)
If o = 2 br 4 is used, Inputs 858 and 859 must be specified.
If alternate geometry option (Input 7768) k is used, Inputs 8205 and 8206 must also be specified.
e m
INPUT FOR FORE-2M Code Options input Number Variable Range Units Remarks 26 6
1 If user has specified step size step 0
For calculation of step size 27 6
1 If additional material is used u
0 Otherwise (if 6 = 0, G must be 0.0) u u
28 6
1 If h
= 3 should be calculated at time cof of void (set to 1 if no voiding table) 0 Otherwise 29 6
1 If this is a restart restart 0
Otherwise 30 6
0 If average fuel temperature is based on ave core only 1
If average fuel temperature is based on
>a core plus_b.1,ankets
?
31 6
0 Option on coolant cross-flow component and excess energy.
If 6 1, Inputs 7860 s
to 7999 and 8000 to 8140,=must be supplied 1
32 N
0 Number of a,xial power shapes.
If N =0, s
s only one shape supplied (Inputs 171-177).
1 If N =1, an alternate shape must be l
s l
supplied for Channel 3 (Inputs 8182-8188) 1 I
i l
INPUT FOR FORE-211 l
i Edit Options Input Number Variable Range Units Remarks l
33 6
1 Print the long edit IO"9 0
Do not print the long edit 34 NML8NG Number of steps / printout (long edit) l 35 6
1 Print section 0 (precursor concentrations) gp; 0
Do not print section 0 36 6
1 Edit average channel only, sections E and F 7p2 (Fuel and Radial Temperatures) 2 Edit average and peak channels 3
Edit average, peak, and hot-spot channels 0
Edit all channels calculated 37 6
1 Print fuel Equivalents temp 0
Print fuel Temperatures P
3B liSKIP
<MMAX Total number of axial sections to be bypassed in the edit of sections E and F 5
39-45 HDELZ Axial section to be bypassed in the edit of sections E and F 46 6
1 Print out section G (Coolant Temperature Sp3 and Velocity) 0 Do not print section G
'l Print section H (Cladding surface heat flux) 47 ogp4 0
Do not print section H 1
Print section 1 (Coefficients and Gap Con-l 48 67p5
- ductance)
Do not print section I 0
i
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JNPUT TOR FORE-2M OperOptions Input Nunter Variable Range Uni ts Remarks l
1 i
1 52 KNTNV If your case is a restart:
O means continue problem where original one left off l
1 Means continue problem from first wrapup 2
Heans continue problem from second wrapus i
53 IVARY(I)
Option for variable void See Section 3.2:
Reference 2 54 ISINTR(I)
Option for fuel sintering 55 B
Number of axial blankets at bottom of core Bot 56 B
Number of axial blanbets at top of core l
Top 57 6
0 High-density coolant (liquid metal) 1 Low-density coolant (gas or steam) k coolant 5B 6
-2 to +6 Option for' pressure drop (2) 3p 6 ry Option for axial flux weighting 59 A
0 Axial weighting per input 171-177 1
Axial weighting per input 941-948 60 6
Option for melt routine:
melt Calculates percentage molten fuel 1
0 No calculation II)To obtain correct heat balance for core of non-uniform axial hole size in pellet ( rescribed but not calculated by code, e.g.,
" cored pellets"), a proper. heat balance requires using [ 3] and [54] = 1.
i j
(2)See Section 2.2 of this addendum and Section 3.9 of Reference 2 for a description of the pressure drop /
flow redistribution options.
l C
Decimal Variable locations Greater INPUT FOR FORE-2M than 60 Times and Termination Controls input No.
Variable Range Units Remarks 61 DELP Maximum fractional power change per step 62 DELT Initial step size (must always be input) see 63
, Hf%X sec User's maximum step size (input only if I
6
- I stsp 64 TfMX (1) sec Maximum running time of transient F
T)1ax 65
'F Upper limit for temperature of fuel node 1 Tf" 66 "F
Lower limit for temperature of fuel node 1 T'N 67 F
Upper limit for fuel boundary node 68 T'iin N
.F Lower limit for fuel boundary node U
69 T
.F Upper limit for coolant temperatures iax 70 T
"F Lower limit for coolant temperatures Hax 71 P
sec Maximum time between printouts 72 TSMin sec liinimum time step size (recommend 10~)
73 Blank 74 Blank (1) NOTE:
An additional time limit on computer running time is established with the control cards which precede the FORE-2M input deck. The program has a built-in 10-second delay on this specified value to permit the printing of the output.
Fo' short running problem (TMAX < 30 seconds), the delay is reduced to r
8 3 seconds.
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9 9
0 1
2 3
4 0
0 0
0 0
r N
e t
7 7
7 7
7 8
9 9
9 9
9 1
1 1
1 1
m u
o p
e n
G i
Pa i
,4
.l.f I.I 1
m I
i e
INPUT FOR FORE-2M Material Properties Variable Range Units Remarks input Number 106*
Fe Hot spot factor for thermal conductivity 4
of the cladding - multiplier Input 107 for Channel 3 g
107 Ke (or A)
B.tu/Sec-Ft 'F Thermal conductivity of the cladding Btu /Sec-Ft *F ga(conduct,ivgty of the structure 1
108 K
3 Btu /Sec-Ft *F Thermal conductivity of the additional I
109 K
material (must be non-zero) u l
Btu /lb *F Specific heat of the cladding 110 C,
l Btu /lb *F Specific heat of the structure 111 C
j 3
Btu /lb *F Specific heat of the additional material 112 C u 3
lb/ft Fuel density 113 of 3
Ib/ft Cladding density 114 p,
3 Ib/ft Structure density 115 o,
l lb/ft Density of additional material 116 o
Fuel melting temperature (see note on pg.37; u
C
'F 117 T
0 Btu /Sec-Ft *F
'}
thermal Constants used in calculatin$y if quadratic 118 K
2) conductivity of the fuel (on l
Btu /Sec-Ft *F g
fit selected input 22=0)
)
119 K
j 2
Btu /Sec-Ft *F3J 120 K
Hot spot factor for fuel conductivity j
121*
F k
- Indicates hot spot factor.
t l
^
INPUT FOR FORE-2M Material Properties Input Number Variable Range Units Remarks 122 B
Btu /Sec-Ft *F Constants used in calculating fuel con-ductivity at melting (only if quadratic i
3 123 C
Btu /Sec-Ft *F fit selected Input 22=0) g IRT 3
124 B
Btu /Ft Fuel heat of fusion j
125-144 C'
Btu /lb *F Specific heat of fuel versus 145-164 T'
'F Tempera ture ak/*F Core radial expansion coefficient 165 app 166 G,
Lb/Sec-Ft Initial flow rate in average channeIIII i
167 M
1.0 to 7.0 Channel 3 axial claddina section for which input 168-170 apply
>0 HCF of cladding at 167 axial section(2)
[
168 F3 HCF of film at 167 axial section(2) i 169 F
>0 2
Ratio of flux at exi)23$o flux at midpoint 170 F
>0 I
of 167 axial section\\
1 I
196-225.
(1) If G, = 0, absolute flow rates as a function of time must be specified using Input l
(2) Internally set to 0.0 if not specified.
l l
n INPUT FOR FORE-2M Power and Flow Factors Input Number
~
Variable Range Units Remarks 171-177 A
1 3m1 titAX Ratio of peak power to average power for axial section m IO y
Fraction of power due to gamma and neutron heating 179*
P Hot spot factor used in calculation of heat H
generation rates in hot spot channel l
180*
P Radial peak-to-average power density I
ratio in core N
181-190 Y"
I Y A" = Af Ratio of heat generation rate in fuel node n
n=1 n to fuel average heat generation rate 191*
F Peak channel factor used in calculating r
O
?
G k=2 (mass velocity for channel 2) j 192*
F Hot spot factor used in calculating v
gc,k=3 (mass velocity for channel 3) t 193 TS9LIO
- F Solidus temperature of fuel 194 TLIQ
- F Liquidus temperature of fuel 195 TPLAS
- F Temperature at which fuel becomes plastic
S INPUT FOR F9RE-2I1 Coolant Flow Characteristics input Number Variable Range Units Remarks Lb/Ft -Sec ')
Coolant mass velocity for average channel I
196-225 G'
versus 226-255 T'
see Time 256-285 T'I"I'
'F h
Coolant inlet temperature c
$"S 286-315 T'
h sec Sum of the local loss coefficients in 316 B
OR, k=2 peak channel (orifice, inlet, outlet and local effects)
')
Constants needed to calculate COMP, 317 C
)
criterion for Reynolds number i
Suggested values: C = 0.316
)
I e = 0.25 318 e
h 319 D
ft Hydraulic diameter of coolant passage H
320 a FE (1) If input 166 is specified, a normalized f' low rate (G/G ) should be used.
g 9
e
INPUT FOR FORE-2M_
Coolant Heat Transfer Coefficient Inputs Input Number Variable Range Units Rema rks 321 Ag
)
322 Bg 323-329 C,,
g Constants used in coolant heat transfer 330 MH coeff-icient equation 1 1 m i M Max.
331 NH 332 RH 333 D
ft Appropriate diameter for use in calculating HT the coolant heat transfer coefficient 334*
F Hot spot factor for calculating coolant h
P heat transfer coefficient G
335 d
ft Characteristic structure dimension (see s
Subsection 3.4.4 of Reference 1) 336 d
ft Characteristic dimension of the additional material (see Subsection 3.4.4'of Ref.1) 337 G
ft'I Structure surface-to-volume ratio 3
338 G
ft" Additional material surface-to-volume u
ratio (if 6u-0, G must be 0.0).-(see Sub-section 3.4.4 of ReYerence 1) 339 h
Btu /Sec-Ft
- F Coolant heat transfer coefficient for c,3 hot spot channel at time of void (used only if 6cgf = 0)'
340 DEC$ljP Option for decoupling additional material DECOUP = 1.0 Decouples 1, 2, 3 DEC5UP = 2.0 Decouples 2, 3 DECWUP = 3.0 Decouples 3
- Indicates hot spot factor.
^
+
INPUT FOR F9RE-2fi Gap Conductivity Inputs Input Number Variable Range Units Remarks 341 h
Stu/Sec-Ft
- F Heat transfer coefficient of fuel cladding f
gap (355, and 359 need be considered inif location 20
- 341, thissection) 342 A
Btu /Sec-Ft *F
]
9 Constants used in equation for calculating 2I thermal conductivity of the gap (see 343 B
Btu /Sec-Ft 'F 9
Equation 38 of Reference 1) 344 C
Btu /Sec-Ft 'F3) g 2
345 a
ft Constant used in gap conductivity equation (see Equation 37'of Reference 1) 346 8,
Constant used in gap conductivity equation (see Equations 39 and 40 of Reference 1) 347 E,
lb/in Modulus of elasticity of the cladding ft Average jump distances for the fission 348 gc gas at the cladding and fuel surfaces, ft respectively 349
.gf (R,-R) cold ft Cold cladding radius minus cold fuel radius 350 f
351 6
ft c
Arithmetic mean roughness heights of cladding and fuel, respectively 352 6
ft f
2 353 f
lb/ft Meyer hardness of material (use hardness value for the softer of the two materials)
MELT Volume increase of fuel due to melting 354 aV Hot spot factor to calculate gap 355*
F 9
coefficient Indicate..s hot spot factor.
INPUT FOR FORE-2M Gap Conductivity Inputs input Number Variable Range Units Remarks 356 2
c Ib/in Elastic yield point of cladding y,p, 357 EMISF 0 - 1.0 Emissivity of the fuel surface 358 EMISC 0 - 1.0 Emissivity of the clad inner surface 1
359+
F,p Peaking factor for gap coefficient for g
peak channel
)
l l
Y l3
~
- Indicates peaking factor.
is INPUT FOR FORE-2M Feedback inputs Input Numbar Variable Range Uni ts Remarks 360 C
Relative worth of axial fuel expansion 7
(see Equation 90 of Reference 1)
F-I Linear thermal expansion coefficient of 361 as structure in the radial direction
-I 362 a'
'F Ef fective coefficient of thermal expansion s
used in calculation of increase in core radius
~I 363 o
'F Structure coefficient of thermal expansion (see Subsection 3.5.3'of Reference 1)
-I 364 a
- F Linear thermal expansion coefficient s,ax of structure in the axial direction (see Equation 97 of Reference 1) 1 Fit coefficients for fractional expansion 4
365 E
1 e0 366 E
h
'F
(
of cladding from 70*F.
Of the form
-1
=
el
(
l 2
Ee0 + E j T+Ee2 T
367 Ee2
,1
'F-2
,1 e
368 Ef0 1-
}
~
Fit coefficients for fractional expansion 369 E
'F~I of fuel from 70*F.
Do not include dis-i 7j 1
I continuity due to melting in this fit 370 E
)
I' 2
f2 371 Eu0
)
1
'F-1 1
Fit coefficients for fractional expansi.on 372 Eul I
(
of additional material from 70*F
-2 373 E
I
'F u2 d
l l
INPUT FOR F9RE-2M Feedback Inputs Input Number Variable Range Uni ts Remarks 374-404 Blank 405 R
Core radius coefficient T
Core height coefficient 406 H
I 18i MMAX t
t I
6k 1 < m < MMAX e6p,)m Density coefficient of reactivity of the 407-413 (p
cladding for section m Density coefficient of reactivity of the 414-420 (o
o )m 1 imi MMAX c
c coolant for section m d
Density coefficient of reactivity of the 421-427 (of
)
1 s m s iAX w
,f,
fuel for section m P
ro Density coefficient of reactivity of the 428-434 (p
I 1 1 m 141AX u
m u
additional material for section m I
6k Density coefficient of reactivity of the j
435-441 (as 6o )m 1 im1 HIAX s
structure for section m 442-471 k.s Table for effective multiplication
~
p versus Time 472-501 T,
sec 502-531 ak'oid ak due to sodium voiding versus Tire y
since initiadon 532-561 T' id sec vo 562-591 ak' ak due to scram versus Time since
~
scram initiation 592-621 T'
sec scram 622 H
ft Distance between core inlet and exit support plates
INPUT FOR FORE-2l4 Feedback Inputs Input Number Variable Range Units Remarks Radians Measurement of the core lower support 623 Y
plate's angular deflection from the o
horizontal (at steady state) 624 Z
ft Distance from core inlet support to actual core inlet l
input constants used in Doppler feedback 625 A
~
Dop equations 626 8
1 Dop I
627 b
g Spatial, power weighting factor, radial 628-634 P
1 < t < LMAX direction Doppler correction for temperature 635 CD profile
?
G INPUT FOR FORE-2M Power Inputs Input Number Variable Range Units Remarks 636 P
F1W Input power in
)
Normalized Power Versus 637-666 P'
t 667-696 T'
Time p
see 697-699 A*
1 < im < IMt1AX t"
Terms used in empirical expression for g
~
decay of fission products 700-702 a*
1 < im < IMMAX t"
Terms used in empirical expression for I
~
~
decay of fission products (cannot be equal to 0.1) 703-705 a$,
1 i
1 mi IMMAX sec Terms used in empirical expression for decay of fission products A,
706 5
fissions /cc-sec Source w
707 T
see Length of time prior to start of problem o
for which the reactor operated at the constant power, Pg 708-713 s
1 < i < IMAX Delayed neutron fraction, i group th g
th 714-719 yj 1 < i < IMAX sec" Decay constants of i group 720 v
Neutrons per fission 721 i
sec Neutron lifetime 722-727 C
1 < i < Il1AX cc' Delayed neutron precursor concentration i
th for i group 728 ck Small constant determining appropriate solution to power equations 729 c
Criterion for power and energy accumulation P""
(suggestedinput: 1.0 x 10- )
. = _ _
4 1
INPUT FOR FORE-2M Miscellaneous Input Number Variable Range Units Remarks Convergence criterion for initial fuel 730 eT temperature calculations Constant used to indicate location to 731 A a calculate coolant temperature Tferam "F
Scram initiation temperature 732 733 c
Scram constant to determine start of Scram scram reactivity T, Boil 7
Coolant's bulk boiling temperature 734-753 e
2 i
versus absolute pressure 754-773 P'
lb/in C
i i
774-793 T,Burnoutj op Cladding burnout temperature versus e
2 i
absolute pressure lb/in
?
794-813 P
Fraction of channel frictional pressure 814 f
Z drop inlet to void 81 5 P
lb/in Static head pressure at channel inlet St lb/in Pump head pressure at channel inlet I
816 P,p p
vapor
.F Fuel temperature at which vaporization 817 T 7 occurs typically 10~4 Conver!enceweightingfactorforgap 818 W
coeffi ient in steady state f
Blank 819 Regional weighting factor for core radial 820-826 W
temperature profile (must be input if E
6 = 1) 7
l_NPUT.
F0r M_
Miscellaneous Input Number Variable -
Range Units Remarks If Input 20 = 2 Axial correction for gap coefficient, (F )1 1<m<-
MMAX 827-833 h
these values are Channel 1. M = 1, 7 2
BTU /HR-FT - F Axial correction for gap coefficient, (F }2 1<m<-
MMAX 834-840 h
Channel 2, M = 1, 7 If Input 20 = 0 (F)3 1<m<-
MMAX these are correc-Axial correction for gap coefficient, 841-847 h
Channel 3, M = 1, 7
.tion factors If TSWAP > 0.0, this is time at which 848 TSWAP
> 0.0 seconds alternate power shape (849-855) becomes effective 849-855 ALTPOW(M) 1 < m < HMAX Alternate axial power shape factor to use with TSWAP
}"
856 TJACK If TJACK > 0.0, this is time at which y
-> 0.0 seconds Input 857 becomes effective Alternate printout interval; overrides 857 PJACK seconds Input 71 when time is greater than TJACK Fa n
858 og 0 - 1.0 Initial density r ti al ac al 859 o
0 - 1.0 Sintered density s
eti i
860 T
F Sintering temperature s
861-880 Kf BTU /FT-Sec-F1 Table for fuel conductivity versus temperature (input only if 6 equals 1) f' k
F 881-900 TQ 0
^
input F 20RE-2M i
Miscellaneous j
input Number Variable Range Units Remarks i
(2)
Axial variation in central void for 901-907 R
0<r<
Hole-1
- r ft 1
Channel 1; M = 1, 7 908-914 R
0<r<
r ft Axial variation in central void for Hole-2 3
l Channel 2; M = 1, 7 915-921 R
0 1ri r ft Axial variation in central void for Hole-3 g
Channel 3; M = 1, 7 Fraction of power generated in the Note: Not an input variable; 922 cladding.
calculated by the code 1
923-925 F (1,2,3)
>0 Velocity correction factor for AP G
calculation, for Channels 1, 2, and 3 l
>0 Friction factor correction for 926-928 F
fr(1,2,3) g, Channels 1, 2 and 3 oo 929-931 K
20 Exit loss coefficient for Channels.1, exit (1,2,3) 2 and 3 932-934
'ain(1,2,3) 0 - 1.0 Area ratio for inlet of Channels 1, 2 and 3 4
0 1,0 Ared ratio for exit of Char.nels 1, 935-937 oout(1,2,3) 2 and 3 Z(1,2,3) ft Height of fluid above active core for 938-940 H
Channels 1, 2, and 3 941-947 AFFIT 1 < m < MMAX Axial flux weighting factors for input m
No. 59 = 1 (2) NOTE:
If the specified hole size exceeds the radius (R ) at which the temperature of the first g
node is calculated, a warning message will be printed out at the beginning of the transient output.
~.-
1T
_' ^
.m 31PUT F0n r0RE-2M
~
l L
Miscellaneous I
Hot radial gap dimensions for variable gap I 948-954(1)
RGAP(H,1) 1 < m < MMAX inches conductance option 2 (input 20 = 2) s
- 9"E
- ** *
- 9"E 955-961(1)
RGAP(H,2) 1 < m < MMAX inches conductance option 2 (Input 20 = 2) 962-968(l)
RGAP(M,3) 1 < m < HMAX inches Hot radial gap dimensions for variable gap c6cductance option 2 (Input 20 = i2)
If value greater than 0.0, axial variation 969 9E(69)
>0,0 in fuel conduct ()*vity factors need be spec-ified [FCON(M.K J 970-976(2)
FCON(M'1) 1 < m < NHAX Axial variation in fuel conductivity correction for Channel 1 [if SE(69)>0.0) 977-980 y
(Not Currently used) 3 l
I i
i (1) If Input 20 = -1, the cold gap dimension is specified in inches.
(2) Default values for Inputs 970-976, 1181-1187 and 1188-1194 are 1.0.
. _ =.
.o S
INPUT FOR F9RE-2M l
Built-in Tables Input Number Variable Range Units Remarks 981-1000 K
Stu/Sec-Ft Thermal conductivity of coolant e
versus temperature
.)
1001-1020 T
p c
I Coolant coefficient of expansion 1021-1040 a c versus temperature 1041-1060~
T
- F c
lb/ft-sec Oynamic viscosity of coolant 1061-1080 pc versus temperature 1081-1100 T
'F c
1101-1120 c
Btu /lb *F S ecific heat of coolant versus c
1121-1140 T
F c
1141-1 MO P
Density of coolant versus c
temperature 1161-1180 T
'F c
Axial variation in fuel con-i 1181-1187 FCON(M,2) 1 < m 1 MAX ductivity correction for Channel 2
if 9E(69)>0.0 Axial variation in fuel con-1188-1194 FCON(M,3) 1 1m1 MAX ductivity correc. tion for Channel 3
ifSE(69)>0.0 I
i 1
l l
i
-s INPUT FOR FORE-2M Alternate Geometry Input Number Variable Range Units Remarks 7768 IXIND 0 or 1 Alterrate geometry option.
If IXIND=1.
Inputs 7769-7790 and 8190-8206 must be supr, lied 7769 XRACL ft Equivalent radius of coolant for alternate geometry 7770 XRACD ft Cladding inner radius, alternate geometry 7771 XRACS ft Cladding outer radius, alternate geometry 7772-7781 XRAND ft Outer radius of fuel node, alternate geometry, 1 < n < NMAX 3,
4, 7782 XRADVS ft Radius of central void, alternate geometry 2
ft Volume of structure per unit length of 7783 XVOST fuel 2
ft Volume of additional material per unit 7784 XV9MT length of fuel 7785 XDIHY ft Hydraulic diameter for alternate geometry
INPUT FOR FORE-2M Alternate Geometry Input Number Variable Range Units Remarks 7786 XDHT ft Appropriate hydraulic diameter for calculating heat transfer for alternate geome try 7787 XDIST ft Characteristic structural dimension for alternate geometry 7788 XDIMT ft Characteristic dimension of additional material for alternate geometry
-1 7789 XGST ft Structure surface-to-volume ratio of alternate geometry
?
-I U
7790 XGMT ft Additional material surface-to-volume ratio for alternate geometry 7791-7797 PS Hot spot factor on heat generation for m
the alternate power shape in Channel 3; 1 1 M i MX
- If any value of PS, is equal to zero, the normal hot spot factor (Input 179) will be used.
I
1 no i
o 2
tw t
p co m
l el 0
u e
Sf 4
p n
1 n
lt 8
o a
ae 1
t h
il s
=
C xn Ai k
P 0
i c
M 2
r a
U 8
o ne 2
3 b
P 7
f i h d
I t
n n
e m
s n
e o
o e
fa t
w to) i i
f I r u
o atZ t
t s
c p
d 3
r E
c c
k n
t eM e
e r
ed
.s t e I
s l
wvI S
S am ai pt e
oiT e
nl i a r
c n
lt l
l rp r
o c
n fae a
a R
ep ts f
a l s i
i t u n
w h
l eu x
x l s pi s
o C
ar(
A A
a mg e
l c
e ue m
f r
o33 r
r
,b pb i
)
o l
o o
1 t
dZ f
ll f
f
=t nn eE fee Bs ow f
zM e
onn e
e E u o
o iI v
nn v
v E m nd lT o
saa o
o F
ot e
a b
ehh b
b I1 i s l9 me a
uCC a
a 8
ta b3 rs l
f1 po a1 ou s
aff s
s I8 Oc T8 N(
A Voo A
A s
s t
M d
i 2
n n
o E
U c
R e
O s
F TU P
N I
e 1
1 gn r
r 0
0 a
o o
R 1-1 0
0 sre tem 1
2 3
a e
=
=
e r
l
)
M M
M a
b r
)
)
)
)
P a
(
T n
n n
i B
P Z
K
(
-i i
i w
r E
M E
A T
G G
G o
a E
U M
E S
/
/
/
l V
F P
I P
H G
G G
F I
I T
G G
(
(
(
dna kc a
b r
d e
e b
9 9
9 9
9 9
e m
1 3
5 7
9 1
F u
8 8
8 8
8 9
N 7
7 7
7 7
7 e
t t
8 9
0 0
0 0
0 0
a u
9 9
0 2
4 6
8 0
n p
7 7
8 8
8 8
8 9
r n
7 7
7 7
7 7
7 7
e I
t l
A
- l l
l ll
INPUT FOR FORE-2M Alternate Feedback ar.d Flow Parameters Input Number Variable Range Units Remarks Values of local flow rate in Axial Section 4 7920-7939 (G/ Gin)M=4 of Channel 3 relative to the inlet flow of Channel 3 (use TIMEZ)
As above for Axial Secdon 5 7940-7959 (G/ Gin)M=5 As ab ve r Axial Section 6 (G/G')M=6 7960-7979 in As above for Axial Section 7 79S0-7999 (G/ Gin M=7 8000-8019 QEXS(M=1)
BTU /sec Excess energy supplied to Axial Section 1 of Channel 3 P
8020-8039 QEXS(M=2)
BTU /sec Same as above for Axial Section 2 8040-8059 QEXS(M=3)
BTU /sec Same as above for Axial Section 3 Same as above for Axial Section 4 8060-8079 QEXS(M=4)
BTU /sec 8080-8099 QEXS(M=5)
BTU /sec Same as above for Axial Section 5
^
l l
INPUT FOR FORE-2M l
{
Alternate Feedback and Flow Parameters Input Number Variable Range Units Remarks 8100-8119 QEXS(M=6)
BTU /sec Excess energy supplied to Axial Section 6 of Channel 3 8120-8139 QEXS(M=7)
BTU /sec Same as above for Axial Section 7 8140-8146 FDOP(M,1) aK Alternate Doppler coefficient for Channel 1, Axial Sections 1 to 7 8147-8153 FDOP(M,2) aK Alternate Doppler coefficient for Channel 2, Axial Sections 1 to 7
?
8154-8160 FDOP(M,3)
AK Alternate Doppler coefficient for Channel 3, Axial Sections 1 to 7
!N 8161-8167 C0F8K(M,1)
AK/ F Alternate coolant density reactivity coefficient for Channel 1, Axial Sections 1 to 7 8168-8174 C0FBK(M,2) aK/ F As above for Cnannel 2 8175-8181 C0FBK(M,3) aK/ F As above for Channel 3 Alternate axial powr shape for Channel 3 8182-8188 XPOWR(M)
(1 s M s M AX) 8189 TPUMP seconds Pump trip delay if IPUMP=1
3 re f
d le s
e n
r l
nn ae u
e a
rt t
u h
r ta c
f C
o r
n a
f o
tr f
d r
f ae u
e o
l et n
r f
e l
hl ay e
u e
a mr t
f u
t t
n le f
nf se i
u f
ao am s
o y
s f
o f
l k
o onX f e f r f
e ooA og ot r
o r
e ciM e
am uy ry tM ye ym e
y t r ur na tt to t
at tt iu1 ia i e R
i re ae q
sn sg s
em rm dem nr n
n po eo e
ee ee e
me pe ss1 dt dt d
eg mg ut l
a t
e n1 l a l n e
e t e se a
ar t
st t
ti y nr ne a
ua sa ncr oo ot n
dn un ait if il r
i r d r tfe t
ta e
ue ie sf m cl c
t qt l t neo ae ar l
il ol ooe ru ro A
La Sa Ccg Ff Ff s
3 t
t M
0 0
i f
2 n
/
F F
1 1
E U
s R
b O
l F
R
^
O F
TU P
N I
e gna R
e l
)
ba L
D M
1 2
i F
I
(
r O
Q L
H H
H H
H H
0 0
a H
I O
A B
C M
N R
H H
V R
L S
C C
C C
C C
R R
X X
X X
X X
X X
X X
X yr te r
m e
1 o
b 0
e m
2 G
u 8
N t
t 0
1 2
3 4
5 2
3 4
5 6
e a
u 9
9 9
9 9
9 0
0 0
0 0
m 1
1 1
1 1
1 2
2 2
2 2
r n
8 8
8 8
8 8
8 8
8 8
8 n
p e
I t
lA 21"
INPUT FOR FORE-2M Alternate Decay Heat Input Number Variable Range Units Remarks 8207 IDECAY 0 or 1 Option for alternate decay heat model 8208 IREG 0,1, 2 or 3 Option on using core or Channel K as reactor indicator for the IDECAY=1 option. If IREG=0, average core power is used; if IREG=K, Channel K power is used.
(see footnote) 8209-8211 FREG(K) 3 Fractional power of reactor associated E FREG=1.0 with regions corresponding to Channels K=1 1, 2 and 3 for determining average core power for the IDECAY=1 option.
8212-8231 TDECAY Second Table of time for alternate decay heat
?
values ti 8232-8251 PDECAY(1)
Fraction of power attributed to decay heat i
in Channel 1 8252-8271 PDECAY(2)
As above, but for Channel 2 8272-8291 PDECAY(3)
As above, but for Channel 3 FOOTNOTE:
IREG also is used to control printout of transient power (see Section 7.3) if the IDECAY=1 option is used.
9 INPUT FOR F9RE-2M Alternate Fuel Specific Heat Table and Other Miscellaneous Items Input Number Variable Range Units Remarks 8292 IXCP 0,1, 2 or 3 Channel to which alternate fuel specific heat applies 8293-8312 XCPFIT BTU /lb-F Alternate fuel specific heat 8313-8332 XTEMP F
Temperatures corresponding to alternate specific heat 8333 ISPEC Option for selecting special rcactivity i
feedback subroutine 8334 IREX 1, 2 or 3 Channel to which Inputs 165 and 320 apply 8335 ISTART Indicator for start of decay heat curves (Inputs 8232 to 8291).
If ISTART=0, time is measured from steady state (t=0).
If ISTART=1, time is measured from point of scram.
IPR 9P=0; tabular sodium properties will 8336 IPR 9P O or 1 be used.
IPR 9P=1; built-in curve fit of Appendix C sodium properties will be used.
T.
INPUT FOR FORE-2M Alternate Fuel Specific Heat Table and Other Miscellaneous Items Input Number Variable Range Units Remarks 8337 IPLOT 0 or 1 IPL9T=0 bypasses this option.
IPL9T=1, selected transient results will be written onto TAPE 2 for subsequent use in plotting package 8338 ITMAX 0,1, 2, or 3 ITMAX=0 bypasses this option.
ITMAX=1, 2, or 3: program will print out time of occurrence and maximum value of reactor power and maximum values of fuel cladding and coolant temperatures for either Channel 1, 2 or 3.
ICP =0; tabular specific heat of fuel is 8339 ICP 0 or 1 f
f used (INPUTS 125 to 164).
ICPf=1; curve fit of specific heat of fuel will be used (INPUTS 193. 194 and 8340 to 8343mustbespecified).
8340 A(C )f BTU /lb *F Constants for curve fit of specific p
heat of fuel 2
2 3+E T4 8341 B(C )f BTU /lb-F C =A+BT+CT+DT p
p 3
C(C )f BTU /lb *F 8342 p
4 8343 D(C )f BTU /lb *F p
5 8344 E(C )f BTU /lb *F 8345 F(C )f BTU /lb *F Effective specific heat of mixed-oxide fuel p
P between the solidus and liquidus temperatures i
APPENDIX B MISCELLANEOUS INFORMATION AND SAMPLE DECK STRUCTURE FORMATS
(
B-1
4 B.1 M15CEttANEOUS INFORMATION The purpose of this section is to assist the user in the preparation of input for running the modified version of the FERE-II computer program.
The present program includes a restart option which allows for possible restarts at three distinct points (user specified) in the transient.
This option can be used to either study a parametric variation in some variable (for example, scram reactivity rates) from some point in tne transient or it can be used to continue a problem from the final timestep of a previous run. This latter usage is quite effective for long running problems (for example, a continuous rod withdrawal from
" fero" power).
The problem can be run for a short time to see if it is progressing properly, and then can be restarted and run to completion.
The WRAPUP-RESTART option can also be used in long running problems to assure that a set of restart variables are available in case of an inadvertent 7roblem termination (e.g., " time estimate exceeded"). The I
restart variables are stored on TAPE 1 and read from TAPE 4 if a restart is desired.
In FDRE-2M, the " hot channel factors" are used to decrease the value of a variable rather than to directly increase the temperature rise associated with that factor.
For example, the hot channel factor on enthalpy rise is used to decrease the flow in the hot channel rather than to directly increase the temperature rise of the coolant in the hot channel. Likewise, the hot channel factors on film, gap and thermal l
conductivities are used to decrease the nominal value of these variables.
Therefore, because of the manner in which they are applied, the hot channel factors used in F9RE-2M are the reciprocals on the normal hot channel factors.
The exceptions to this rule are the factors on heat j
l 9eneration (IHPUT 179 and 180) which are applied directly.
b B-2
)
Another point to consider in running a F9RE-2M transient is that the hot channel is treated as a complete and separate channel and that some factors will affect more than one variable. The factor on heat generation in the fuel will, for example, also affect the enthalpy rise since the excess heat due to the increased heat generation will be transferred to the coolant. Care must be exercised that a duplication of such factors is avoided. As an example, since the normal hot channel factor on enthalpy rise (FaH) includes the factor on heat generation (F3g), the appropriate factor to include in the FQRE-2M program (F, Input number 192) would be y
y=[F F
aH A list of the hot channel factors available in FORE-2 is given below
~
and noted by a'n asterick in the input listing (Appendix A).
Input
(
Number Symbol Definition 106 F*
Hot-spot factor for thermal conductivity of clad 121 F
Hot-spot factor for fuel conductivity k
179 P
Hot-spot factor used in calculating heat g
generation rates in hot channel (normally FRX FaQ) 180 P
Radial peak-to-average power density ratio p
in core (i.e. F )
R 191 F
Peak
- channel factor used in calculating I
flow rate in peak channel 192 F
Hot-spot factor used in calculating flow y
rate in hot channel 334 F
Hot-spot factor for calcula+.ing coolant h
heat transfer coefficient 355 F
Hot-spot factor for gap coefficient g
359 F
Peaking factor for gap coefficient in S *E peak channel
- In FORE-2M, Channel 1 = Average Channel; Channel 2 = Peak Channel; and Channel 3 = Hot Channel.
B-3
'B.2 INPUT DECK STRUCTURE The binary tape of the modified FIRE-II program is cataloged at the Advanced Reactor Division as WMF9RE2M. Tables B.1 through B.5 show the structure of input decks for various options of the program.
The
" control cards" listed before the input deck are required for a specific computer system and could therefore differ from site-to-site.
(
B-4
TABLE B-1 STRUCTURE OF A REGULAR PROBLEM (NO RESTART)
ATTACH (A WMFORE2M, ID = SARDC, MF = MFA)
SETCSRE(ZER9)
A.
789
)f9RE*XYZ*1234 12-15-75 (Data) l l
(See Table B-5) l
{
(Data)-
9999
)LAST B-5
TABLE B-2 STRUCTURE OF A WRAPUP PROBLEM (PREPARATION FOR RESTART)
ATTACH (A, WMF9RE2M, ID = SARDC, MF = HFA)
SETCDRE(2ER9)
A.
CATAL9G (TAPEl,WMNAMEIT,CN= CASE. ID= USER, SC=S) 789
)f9RE*XYZ*5678 12-15-75 (Data) l (Input 49 = 1, 2 or 3) l (Input 50 and 51
- (
Specify Timesteps for l
Wrapups)
(Data) 9999
)LAST
(
B-6
TABLE B-3 STRUCTURE OF A RESTART PROBLEM ATTACH ( A, WMFORE2M, ID = SARDC, MF = MFA)
ATTACH (TAPE 4, WMNAMEIT, ID= USER, MF=MFA)**
SETCpRE (ZER$)
A.
789 12-15-75
)FSRE*XY2*6942 See input for restart - Appendix A
(
9999 12-15-75 (FSRE*XYZ*6942 (Data)
(Only data which is to be changed need be specified) l (Data) 9999 i
)LAST l
l
- WMNAMEIT must correspond to tape name previously reserved l
from WRAPUP l
B-7
TABLE B-4 STRUCTURE OF A RESTART PROBLEM WITH ADDITIONAL WRAPUP ATTACH ( A, WMF9RE2M, ID = SARDC, MF = MFA)
ATTACH (TAPE 4, WMNAMEIT, ID= USER, MF=MFA)
SETCSRE (ZERS)
A.
CATALOG (TAPE 1,WMNEWHAME, CN=NEWCASE, ID= USER, SC=S) 89
) FORE *XYZ*7865 12-15-75 Restart data input 9999 (FORE *XYZ*7865 12-15-75 (Data)
(For additional wrapups, inputs 49, 50 and 51 must be specified)
(Data) 9999
)LAST (1) The name of the new restart tape may be the same as old restart tape provided a PURGE (,WMNAMEIT, ID= USER, PW= CASE) preceeds the statement.
(
B-8
1 1
TABLE B-5 INPUT DECK STRUCTURE FOR F#RE-2d (See Appendix A)
A) Regular Problem - no restart 1)
Independent Case Card 2)
(Data) l l
- 3) 9999 (Sentinel Card) 4)
)LAST' *
(Last Card)
B) RESTART Problem 1)
Independent Case Card
) Restart variables u
1
- 4) 9999 (Sentinel Card)
- 5) Dependent Case Card 6)
(Data) l l
Data which is being changed I
l 7
9999 (Sentinel Card) 8
)LAST * (Last Card) o B-9
1 APPENDIX C BUILT-IN TABLES OF SODIUM PROPERTIES
\\
From G. H. Golden and J. V. Tokar, "Thermophysical l
Properties of Sodium," ANL-7323; Argonne National Laboratory, August, 1967 i
i NOTE: These values may be over-ridden by using all or part of f
INPUT values numbers 981 through 1180.
,(-
i C-1
BUILT-IN TABLES OF SODIUM PROPERTIES Thennal Conductivity e
Temperature T vs.
g of Sodium, K c 200*F
.014055 BTU /sec-ft *F 300
.013572 400
.013089 500
.012619 600
.012164 700
.011717 750
.011497 800
.011283 850
.011069 900
.010858 1000
.010447 1050
.010247 1100
(
.010047 1200
.009661 1300
.00928 1400
.00892 1500
.008567 1600
.008225 1700
.007894 1800
.007575 NOTE: These values may be over-ridden by using all or part of l
INPUT values numbers 981 through 1020.
' (.
C-2
BUILT-IN TABLES OF 5001UM PROPERTIES Thermal Expansion, Coefficient of Sodium, a Temperature, T c
ys, c
~I 46.34 X 10-0
- F 200 *F 47.28 300 48.22 400 49.18 500 50.15 600 51.12 700
- 51. 62 750 52.11 800 52.61 850 53.11 900 54.12 1000 54.63 1050 55.14 1100 56.18 1200 57.23 1300 58.28 1400 59.36 1500 60.44 1600 61.54 1700 62.66 1800 l
l NOTE: These values may be over-ridden by using all or part of INPUT ylaues numbers 1021 through 4060.
l l'
(
C-3
BUILT-IN TABLES OF SODIUM PROPERTIES Dynamic Viscosity of Sodium, y vs.
Temperature, T c c
200*F 0.0004753 f/ft-sec 300
.0003699 400
.0003026
.0002565 500
.0002233 600
.0001983 700
.000188 750
.0001788 800
.0001706 850 900
.0001632 1000
.0001505 1050
.000145 1100
.00014 1200 I
.000131 1300
.0001234 1400
.0001168 1500
.000111 1600
.0001059 1700
.0001013 1800
.0000972 NOTE: These values may be over-ridden by using all or part of INPUT values numbers 1061 through 1100.
I C-4 i
s
BUILT-IN TABLES OF SODIUM PROPERTIES Specific Heat of Sodium, C vs.
Temperature, T c
c 0.3311 BTU /f *F 200*F
.3250 300
.3194 400
.3146 500
.3105 600
.307 700
.3055 750
.3042 800
.3030 850
.3020 900
.3006 1000
.3001 1050
.2998 1100
.2998 1200
.3004 1300
.3017 1400
.3036 1500
.3063 1600
.3096 1700
.3136 1800 l
These values may be over-ridden by using all or part of l
NOTE:
INPUT values numbers 1101 through 1140.
1~
C-5
BUILT-IN TABLES OF S0010M PROPERTIES Density of Sodium p
vs.
Temperature, T c
c 3
57.965 f/FT 200'F 57.157 300 56.344 400 55.527 500 54.705 600 53.881 700 53.467 750 53.053 800 52.638 850 52.222 900 51.389 1000 50.971 1050 50.533 1100 49.716 1200 48.878 1300 48.038 1400 47.198 1500 46.357 1600 45.517 1700 44.677 1800 t.
NOTE: These values may be over-ridden by using all or part of INPUT values numbers 1141 through 1180.
i C-6
-