ML20030A833

Nonproprietary Version of Response to First Round Questions on Statistical Combination of Uncertainties Program: CENTOP-D Code Structure & Modeling Methods (CEN-139(A)-NP)

ML20030A833
Person / Time
Site:	Arkansas Nuclear
Issue date:	03/31/1981
From:	ABB COMBUSTION ENGINEERING NUCLEAR FUEL (FORMERLY
To:
Shared Package
ML19277A045	List: 2CAN078107, Forwards Proprietary & Nonproprietary, Responses to First Round Questions on Statistical Combination of Uncertainties Program.... Proprietary Rept Withheld (Ref 10CFR2.790). Affidavit Encl ML20030A833
References
NUDOCS 8107290078
Download: ML20030A833 (78)

Text

_ _ _ _ _ - _ - _ _ _ _

I l

l i'

i I

i i

i Responses to First Round Questions i

on the Statistical Combination of Uncertainties l

Progrant: CETOP-D Code Structure and j

liodeling Methods i

(CEN-139(A)-NP) l MARCH 1981 i

i l

COMBUSTION EllGINEERIftG, INC.

i l

l

[

r 8107290078 810715 PDR ADOCK 05000368 P

PDR y

i

LEGAL fl0TICE This report was prepared as an account of work sponsored by Combustion Engineering, Inc. Iteither Combustion Engineering nor any person acting on its behalf; i

A.

liakes any warranty or representation, express or j

implied including the warranties of fitness for a particular purpose or merchantability, with respect to the accuracy, completeness, or usefullness of the information contained in this report, or that the use of any information, apparatus, method, or process disclosed in this report may not infringe privately owned rights; or B.

Assumes any liab.lities with respect to the use of, or for damages resulting from the use of, any information, apparatus, method or process disclosed in this report.

e e

I

- 1 l

d ABSTRACT

)

The CETOP-D Computer Code has been developed for determining core thermal 1

1 margins for C-E reactors.

It uses the same conservation equations as used in the TORC code (Reference 1) for predicting the CE-1 minimum DNBR l'

(MDNBR) in its 4-channel core representation.

The CETOP-D model to be presented in this report di ffers from the TORC design model (described in Reference 5 and referred to herein as S-TORC, j

for " Simplified" TORC) by its simpler geometry (four flow channels) yet faster j

calculation algorithm (prediction-correction method).

S-TORC utilizes the comparatively less efficient iteration method on a typical 20-channel geometry.

To produce a design thermal margin model for a specific core, either S-TORC or CETOP-0 is benchmarked against a multi-stage TORC model (Detailed TORC described in Reference 1) which is a detailed three-dimensional description of the core thermal hydraulics.

In this report _, tiie CETOP-D and Detailed TORC predicted hot channel MDNBR's are compared, within design operating ranges, for the C-E AN0-2, cycle 2 reactor core, comprised of 16x!6 fuel assemblies.

Results, in terms of deviation i

between -each pair of MDNBR's predicted by the two models, show that CETOP-D with the inclusion of the " adjusted" liot assembly flow factor, can predict

~

either conservative or accurate MDNBR's, compared with Detailed TORC.

~

i e

4 1

3

I t

TABLE OF C0flTErlTS J

Section Title Page i

't ABSTPACT i

TABLE OF C0t4TEllTS ii LIST OF FIGURES iv LIST OF TABLES V

LIST OF SYMBOLS Vi 1

THEORETICAL BASIS 1-1 1.1 Introduction l'-1 1.2 Conservation Equations 1-2

.l.2.1 Conservation Equations for Averaged Channels 1-3 1

1.2.2 Conservation Equations for Lumped Channels 1-5' 2

EMPIRICAL CORRELATIO.'1S 2-1 2.1 Fluid Properties 2-1 2-1 2.2 Heat Transfer Coefficient Correlations 2.3 Single-phase Friction Factor 2-2 f~

Two-phase Friction Factor Multiplier 2-2 2.4 l

2.5 Void Fraction Correlations 2-3

~2.6 Spacer Grid Loss Coefficient 2-4 2.7 Correlation for Turbulent Interchange 2-4 i

2.8 Hetsroni Crossflow Correlation 2-7 l

2.9 ^ CE-1 Critical Heat Flux Correlation 2-7 l'

3 NUMERICAL SOLUTI0ft 0F THE C0f1SERVATIO1 EQUATI0 tis 3-1 3.1 Finite Difference Equations

3-1 3.2 Prediction-Correction Method 3-2 4

CETOP-D CESIG!! MOPEL 4-1 4.1 Geometry of CETOP-D Desgin Model 4-1 l

4.2 Application of the Transport Coefficient in 4 l the CETOP-D Model 4.3 Description of Input Parameters 4-4 5

THERf'AL MARGIf1 A!!ALYSES USIfiG CETOP-D 5-1 5.1 Operating Ranges 5-1

~

5.2 Petailed TORC Analysis of Sanyle Core 5-1 5.3 Geometry of CETOP Design Modci 5-1 ii

i TABLE OF CONTENTS (cont.)

Section No.

Title Page No.

5.4 Comparison Between TORC and CETOP-0 5-2 Predicted Results 5.5 Application of Uncertainties in 5-2 CETOP-D 6

CONCLUSIONS 6-1 7

REFERENCES 7-1 Appendix A CETOP-D Version 2 User's Guide A-1 Appendix B Sample CETOP-D Input /0utput B-1 J

e 4

e e

l l

t l

L

4

!=

i LIST OF FIGURES i

Figure No.

T'tle Page No.

1.1 Control Volume for Continuity Equation 1-12 2

+

1.2 Control Volume for Energy Equation 1-13 1.3 Control Volume for Axial Momentum Equation 1-14 i _

1.4 Control Vclume for Lateral Momentum Equation 1-15 3.1 CETOP-0 Flow Chart

'3-3 3.2 Flow Chart for Prediction-Correction Method 3-7 t

4.1 Channel Geometry for CETOP-D Model 4-2 5.1 Stage 1 TORC Channel Geometry for ANO-2 Cycle 2 5-3 5.2 5tage 2 TORC Channel Geometry for ANO-2 Cycle 2 5-4 5.3 Stage 3 TORC Channel Geometry for ANO-2 Cycle 2 5-5 5.4 Axial Power Distributions 5-6 5.5 Inlet Flow Distribution for ANO-2 Cycle 2, 5-7 4-Pump Operation 5.6 Exit Pressure Distribution for ANO-2 Cycle 2, 5-8 i

4-Pump Operation 5.7 CETOP-D Channel Geometry for ANO-2 Cycle 2 5-9 l

4 iv

. ~.

}

i

(

j LIST OF TABLES Table flo.

Title Page flo.

1 i

2.1 Two-Phase Friction Factor Multiplier 2-8 2.2 Functional Relationships in the Two-Phase 2-9 Friction Factor Multiplier 3.1, Comparisons Between Detailed TORC and CETOP-D 5-L 6

1

• 4 O

e 9

e h

1 1

i A

LIST OF SYMBOLS

?

SYMBOL DEFINITION i

A Cross-sectional area of flow channel CHF Critical heat flux d

Diameter of fuel rod 1

De Hydraulic diameter DNBR Departure from nucleate boiling ratio DTF Forced convection temperature drop across coolant film adjacent to fuel rods

j DTJL Jens-Lottes nucleate boiling temperature drop across coolant film adjacent to fuel rods f

Single phase friction factor F

Force f,f ' p ngineering factors-H F

Radial power factor, equal to the ratio of R

local-to-average radial power F

Ratio of critical heat flux for an equivalent 3

uniform axial power distribution to critical heat flux for the actual non-uniform axial power distribution.

F T

Total power factor, equal to the product of the local radial and axial power factors i

F Axial power factor, equal to tne ratio of the local-to-average axial power.

g Gravitational acceleration G

Mass flow rate h

Heat transfer coefficient h

Enthalpy i

K Spacer grid loss coefficient

~

g K

' Crossflow resistance coefficient jj K.

Crossflow resistance coefficient j

t Effective lateral distance over which crossflow occurs between adjoining subchannels l

MDNBR Minimum departure from nucleate boiling ratio m

Axial flow rate N,N,N Transport coefficients for enthalpy, pressure g p u l

and velocity I

SYMBOL DEFINITION P

Pressu_re P

Heated perimeter h

Pr Prandtl Number.

PW Wetted perimeter q'

Heat addition per urit length q"

Heat flux Re Reynolds number s

Rod spacing or effective crossflow width s

Reference crossficw width REF T

Bulk coolant temperature cool T;at Saturation temperature

~

T Surface temperature of fuel rod wall u

Axial velocity u*

Effective velocity carried by diversion crossflow v

Specific volume V

Crossflow velocity w)

Diversion crossflow between adjacent flow channels j

wj3 Turbulent mass interchange rate between adjacent flow channels x

Axial distance x

Quality a

Void fraction y

Slip ratio

~

Density p

l 4

Two-phase friction factor multiplier

$i Heat Flux c

Fraction of fuel rod being. included in flow j.

channel SUBSCRIPTS f,g Liquid and vapor saturated conditions i,j Subchannel identification numbers ij Denotes hydraulic connection between subchannels.

i and j J

Axial node number P

Denotes predi'cted value

d SUPERSCRIPTS DEFINITION J

Denotes transported quantity between adjoining

~

lumped channels l

Denotes transported quantity carried by diversion crossflow Denotes effective value J

4 e

4 im 9

e Viii

J

?

ij 1.0 THEORETICAL BASIS lj l.1 Introduction The minimum value for the departure from nucleate boiling ratio (MONBR) l l

which serves as a measure for the core thermal margin, is predicted for a C-E reactor by the TORC code (Thennal-Hydraulics of a Reactor Core, Reference 1).

i+

A multi-stage TORC modelling method (Detailed TORC), which produces a detailed three-dimensional description of the core thermal-hydraulics, requires about li

[ [ cp (central processor) seconds for each steady state calculation on the C-E CDC 7600 computer.

A simplified TORC modelling method (S-TORC, Reference 5),

developed to meet practical design needs, reduces the cp time to about seconds for each calculation on a 20-channel core representation.

Such a simplification of the modelling method results in a penalty included in the S-TORC model to account for the deviation of MDNBR from that calculated by Detailed TORC.

Present TORC /CE-1 methodology includes in S-TORC an adjusted hot assembly inlet flow factor to eliminate the possible nonconservatism in the MDNBR predic-tion produced by S-TORC.

An even simpler code, CETOP, (C-E Thermal On-line Program, Reference 4),

which utilizes the same conservation equations as those in TORC, has been used in the Core Operating Limit Supervisory System (COLSS) for monitoring MDNBR. The CETOP-0 model to be described in this report has been developed to retain all capabilities the S-TORC model has in the determination of core thermal margin.

Ittakestypically[

[ for CETOP-D to perform a calculation, as accurately as S-TORC, on a four-channel core represen-tation.

~

For the following reasons CETOP-D is as accurate as and faster-running than its predecessor, S-TORC,: (1) it uses " transport coefficients", serving as weighting factors, for more precise treatments of crossflow and turbulent i

mixing between adjoining channels, and (2) it applies the " prediction-correction" method, which replaces the less efficient iteration method used in S-TORC, in l

l the determination cf coolant properties at all axial nodes.

i t

4

.\\

i A finalized version of a CETOP-D model includes an " adjusted" hot assembly s

flow factor and allows for engineering factors.

The hot assembly flow factor l3 accounts for the deviations in MDNBR due to model simplification.

A -stati stical lI or deterministic allowance for engineering factors accounts for the uncertainties I

associated with manufacturing tolerances.

1

]

1.2 Conservation Equations s

A PWR core contains : large number of subchannels which are surrounded by fuel rods or contros rod guide. tubes.

Each subchannel is connected to its neighboring ones by crossflow and turbulent interchange through gaps between fuel rods or between fuel rods and guide tubes.

For this reason, j

subchannels are said to be hydraulically open to each other and a PWR is said to contain an open core.

1 The conservation equations for mass, momentum and energy are derived in a control volume representing a flow channel of finite axial length.

Two.

types of flow channels are considered in the represention of a reactor l,

core:

(1) averaged channels, characterized by averaged coolant conditions, and (2) lumped channels, in which boundary subchannels, contained within the main body of the channel, are used in the calculation of interactions with neighboring fluv. channels. An averaged channel is generally of t

j.

relatively large size and is located far from the location at which MDNBR occurs. With the help o f boundary subchannels, a lumped channel describes 1

in more detail the flow conditions near the MDNBR location, and is of relatively small flow area (e.g. a local group of fuel rod subchannels).

To be more specific about the differences between the modelling schemes of the two channels, their conservation equations are separately derived.

/

~

1-2

I L

1.2.1 Conservation Equations for Averaged Channels 1.2.1.1 Continuity Equatidn Consider two adjacent channels i and j, as shown in Figure 1.1, which are hydraulically open to each other.

The continuity equation for channel i has the form:

ami dx + w dx = 0 (1.1) j + (mg+g dx) - w'jjdx + w'jj jj

-m Assuming the turbulent interchanges w'j =w' $, the above equation becomes:

I

~

amj = -w (1.2) jj ax Considering all the flow channels adjacent to channel i, and taking wjj as positive for flows from i to j, the continuity equation becomes:

a m'.

N I

w. ; i = 1, 2, 3,..,N (1.3)

~

= -

ax j=1 iJ 1.2.1.2 Energy Equation The energy eqt.ation for channel i in Figure 1.2b, considering only one adjacent channei j, is:

0 m h d) - q'jdx - w'jj jh dx + w'jj jh dx+w h*dx=0 (1.4)

-m h; +'(m hjj+

g jj j

ax where h* is the enthalpy carried by the' diversion cros.sflow wjj.

.The above equation can be rewritten, by using Eq. (1.2) and w' gj = w'jj,

as:

• ~-

• w

-.y.,

.. ~ - - -

_s-i.

'ah d

I (1.5)

"i

= q' $ - (h -h ) w' jj+(h -h*)wjj j j j

gx Considering all adjacent flow channels, the energy equation becomes:

J w'II + N ah q ' '.

N wId I

E (h -h*)

(1.6)

(h-h)m I

=

i m

i j ax m

g j_)

j g

3) i I

l 1.2.1.3 Axial Momentum Equation i

Referring to Figure 1.3b, the axial momentum equation for channel i, considering only one adjacent channel j, has the form:

8

-F dx + p dAj - gA pjg dx - (p A; -

p A dx) =

j j

j jj i

j g + [ m u dx)-w'jj j jj w'jj ju dx + w u*dx (1.7) u dx +

j j + (m u

-m u jj where u* = 1/2 (u +u.).

j J

j l

By using the assumption w'jj=w'jj, one has:

ap.

(1.8)

• i"i + (u -u )w';) + u*wjj

-F - gA p$g-Ai ax j

j j

Substituting the following definitions:

2 AKgvj)(~ MAT }

(*

f a(Avjjcq m vpg ; F j

g j

j j

u s 2Ax-20e.

j 3,

j 1

1 1

(1.2) into Eq. (1.8), one obtains:

-and Eq.

j v'p ;

f 4; Kgjvj 3

DP m

2 vj A gxi- = -A (g;,- )

[7De.

2n

+ A; 3x (3- )] - gA pjg

+

(1.10) j j

i 1

1 1

- (u -u ) w'jj + (2uj-u*)wjj l

j j l

\\

1-4

4 i

i j

Considering all adjacent channels, tk axial momentum equation becomes:

2 f tj + K ap j"~({m j

vj G vi.

3 vpi j

i 20e 2ax i

ax (A

}

~ 9Pi

+A i

ax 3

j j

l n

w' n

w (1.11)

(2u -u*) 4 l

,E (u -uj) A

+

j j

i j=1 i

a=1 i

1.2.1.4 Lateral Momentum Ecuation

[.

1 For large flow channels, a simplified transverse momentum equation may be used which relates the difference in the channel-averaged pressures

)3 to the crossfiow w Referring to the control volume shown pq and p3 g.

in Figure 1.4b, the form of the momentum equation is:

"ij!"ij!

(p -p3) = Kij 29 s( p*

(1.12) j where K is a variable coefficient defined in Reference 3 as jj I'

2 "i

j j = ( K"

+ XFCONS

+

K 2

(1.13) ij For averaged channels the spatial acceleration term is not included explicitly but is treated implicitly by means of the variable coefficient, K ).

j i.

Because the coefficients K-and XFCONS were empirically determined for rod bundles, Eq's. (1.12) and (1.13) are appropriate for channels of

.relatively large size.

i 1.2.2 Conservation Equations for Lumoed Channels 1.2.2.1 ' Continuity Equation l

. Since only mass transport is considered within the cor trol volume, the i

continuity equation has similar fcm to that for averaged channel,-i.e.,

i Eq. (1. 3).

g

...,n,

,n

--..w

,~a-,

-.v.--.

w

- -, -.~~

l

1. 2.2.2 Energy Equation 4

!~

Consider two adjacent channels i and j and apply the energy conservation to l

channel i within the control volume as shcwn in Figure 1 2.a. the energy

'i equation has the form:

Bh

= 9' j - (Ii -li ) w' $3 + (h -h*) wjj (1.14)

I mj3 j

j j

i where q' = energy added to channel i from fuel rods per unit j

time per unit length, w'jj = turbulent interchange between channels i and j j

h *;'jj = energy transferred out of channel i to j due to the j

turbulent interchange w'1J, 1

_b.w'.. = energy transferred into channel i from j due to the I',

J 1J t-turbulent interchange w'jj, j

h and h are the fluid enthalpies associated with the turbulent interchange; g

3 h* is the enthalpy carried by the diversion cross-flow w and is determined jj y

as follows:

h* = li if wjj_ > 0 (1.15) j h* = h.

if w.. < 0 J

1J j-At elevation x, the enthalpy_ carried by the turbulent interchange across the boundary between channels i and j is modeled as the fluid enthalpy of the boundary subchannels of the donor lumped channel.

Thus, Ti. and Ti.

1 J-are definea as _the radially _ averaged enthalpies of the boundary subchannels i

of lumped channels i and 'j respectively.

and h) are not explicitly Solved in the calculation, we define Since h j l

a transport coefficient N to relate these parameters to the l aped channel H

counterparts h and h as follows:

j 3

h.

--h.

N (I*

)

H" h.-h.

1 J

{

The parameter N is namcd the transport coefficient for enthalpy, H

i Using this coefficient, one can' assume the coolant enthalpy at the boundary:

~

I M

h. + h

h. + n 1

3=

1 3

(1.17) h

=

c 2

2 and

h. - h i

l E-h

• 1 3

(1.18) j c

2

h. - h.

'I j

h) - he" 2

1 which are followed by the approximations:

i l

E=h *(i-h}

j c

c h.+h.

h. - h3; (1.20) 1 3+

l~

=

2 2t4H h.=h

+(fi. - h )

ij J

c J

c (1.21)

h. + h].

h.-h.

1 J-1

+

=

2 2flg Inserting Eqns.(1.17)-(1.21) into Eq. 1.14, the lumped channel energy equation is derived as:

Y i

h -h h +h.

(h -h )n

= 9'j - ( j j

j

}

"ij

+

m gj id i-2N j

H where n = 1 if w ) > 0 and n = -1 otherwise.

j It should be noted that if channels i and j were averaged channels, l

N = 1.0 for this case, Eq. (1.22) reduces to the Eq. (1.5) in Section g

l 1.2.1.2.

~

1.2.2.3 Axial Momentum Equation Consider two a'djacent lumped channels i and j 'and apply-the axial momentum

(

conservation law to channel i as shown in Fig. 1.3a.

4 -g.;j j-(u -u ) w'gj + (2u -u*) w )

(1.23)

A

-=-F A

9 j

j j

j i

1-7

where: A channel area,

=

j i

p.

radially averaged static pressure,

=

1 g

gravitational acceleration,

=

p coolant density,

=

0 axial velocity carried by the turbulent interchange

=

ij channel radially averaged velocity u

=

Fj momentum force due to friction, grid form loss and

=

density gradient As for h and h, u and u can be regarded as the averaged velocities j

j j

j i,

of the boundary subchannels of the lumped channels i and j respectively, i

Define the transport coefficient for axial velocity, N, as follows:

g u -u.

N ~

j I

U (1.24) u -u j

j Using similar procedures in the approximation of h and h in terms of j

j I

h, h), and N, as described from Eq. (1.17) to (1.22), we derive:

j H

i "i + "j # "i j

(1.25)

-u uj -

2 2NU and 4

u '. + u.

u.-u (1.26)

+

u) =

2 2NU Inserting Eqs. (1.25) and (1.26) into Eq. (1.23), results in the axial momentum equation for lumped channels:

) W'jj+(2u -(u,+u.

(uj-u )n ap u -u.

j j -A go; - ( j 3

} ) "ij

~

A

=-F j

+

i a

g g

2 2N U

U

.(1.27) where n is defined in Eq. (1.22) -

l f'

l-8

I i,

1.2.2.4 1.ateral Momerfum Equation Consider the rectangular control volume in the gap region between channels i and j as shown in Figure 1.4.a.

Assuming that the difference between the diversion crossflow momentum fluxes entering and leaving the control 4

volume through the vertical surfaces sax is negligibly small, the fonnulation for lateral momentum balance is:

-Fjj - pj sax + p$ sax = -(p*stu

• V)x + (p*stu*V)p3x (1.28) r Making use of the definition of the lateral flow rate j

w.. = p* sV 1J Eq. (1.28) becomes, after rearranging:

F a(u*wjj)

(_

)=

43

)

P -P j j sax s/t ax (1.29)

~

The term F / sax represents the lateral shcar stress acting on the control j3 volume due to crossflow and is defined as:

F..

w..lwj3l K

sx ij,

2 (1.30) g Substituting Eq. (1.30) into Eq. (1.29), and taking the limit as ax+0, W

lW l

jj

(

- j) " ij 2

sI a (u*wjj)

(1.31) 3 where: F = channel averaged pressure, Kjj = crost-flow resistance coefficient, w ) = deversion cross-flow between channels i 5nd j, j

s

= gap width between fuel rods,

= effective length of transverse momentum interchange, t

u*

= axial velocity carried by the diversion cross-flow w jj, assumed to be (u +u )/2 g

j l

The above equation is equally well applied to two luniped channels when each contains a certain number of subchannels arranged as shown in Figure 1.4a J

and the gap width s should be In.his case, the diversion cross-flow wjj expressed by :

(1.32) jj (f!) (cross-flow through gap between two ad.iacent rods)

W l

=

s=(ft) (gap between two adjacent rods)

(1.33) where il is the number of the boundary subchannels contained in each of the lumped channels.

For the case of two generalized three-dimensional lumped i

l channels, parameters 'p and p are regarded as the radially averaged static

~

j j

pressures of the boundary subchannels of the lumped channels i and j i

respectively. As shown in Fig. 1.4a., the transverse momentum between two generalized lumped channels are governed by the following equation:

t 3(u*wjj)

"ij!"ij~l j

(1.34)

Pj - p = Kij 2

s

+

29sp*

ax h

i-It should be noted that the transverse momentum equation for the generalized lumped channels i and j in Fig.

1.4a is the same as that for the boundary subchannels.

This is because the control volumes chosen to model the transverse momentum transport in these 1.wo cases are identical.

Since are not explicitly calculateu, we define the transpect coefficient-p; and pj for pressure to relate these parameters to the calculated lumped channel and p as followS:

parameters pg j

p'. - p.l (1.35) 11

=

p pi - pj are the radially averaged static pressures of the lumped channels where p; and pj i and j respectively, inserting Eq. (1.35) into Eq. '(1.34), we obtain the transver; roxentum equation for three-dimensional lumped channels as follows:

'(u*w

)

j jlw;.j. _.

+ _......; ;_.

(1.36) p-p.

w j

- - -. _J.

=g p

295 p*

1 1-10

i i

j I

1.2.2.5 Transport Coefficients There are three transport coefficients fl, [1 and fl inEqs.(1.16),(1.2/,)

g U

p and (1.35) which need to be evaluated prior to the calculation of conservation equations.

Previous study in Reference 2 concluded that the calculated h,j m, p, and w are insensitive to the values used for fl and fl. This conclusion j

g jj g

g is further con irmed for the three-dimensional lumped channels.

Therefore, the f

l values of fl nd ft can be estimated by a detailed subchannel analysis and used 0

p for a given reactor core under all possible operating conditions.

It is, however, not the case for ti, whose value,is strongly dependent upon radial power distribution g

and also a function of axial power shape, core average heat flux, channel axial elevation, coolant inlet temperature, system pressure, and inlet mass velocity.

a A value of fi can be calculated by using a detailed subchannel TORC analysis g

j j

5 g and ?!g for use in the CETOP-D lumped channel analysis.

to determine h, h, h, h Ilowever an alternate method is used in CETOP-D, utilizing the power distribution and the basic operating parameters input into CETOP-D to determine fl for each g

axial finite-di fference node. [

c 1

i l

O 4

L l-11

k l

m; +

dx 8x

_ _ _ _ _h____j i

I i

I l

l

> w;;dx l

I CHANNELi l

l l

l CHANNELj CONTROL i

i l

dx VOLUME I

I I

wj;dx c

l 1

I

" W'jdix I

i I

t I

m; l

N V

i i

i y-l l

l r

1 i

i Figure 1.1 CONTROL VOLUME FOR CONTINUITY EQUAT'ON 1

1

.I

- ---~_-.

't - l '

t 0

mh+

m;h;dx i

dx

.____4_..____,

i l

i l

l i

I i

1-= ' w;;h'dx i

2 CHANNELi lCHANNELj CONTROL l

l l

VOLUME I

dx d

9i x i

I wf;h dx

(

+

1 j

d w;;Ii;dx l

{

i l

l 1

I l

mhj i

l I

I f

U r

+

I 3OUNDARY SUBCHANNELS

)

(A) CONTROL VOLUME FOR LUMPED CHANNEL m h; + _$_ m;h dx i

dx

. _ _ _ _ _b _ _ _ _.5, i

h l

I I

[l l

II l

CONTROL i

VOLUME l

l CHANNELi CHANNELj I

l

' = q;dx l

dx

~

l l

wj;h dx j

~

l

& w;j ;dx h

I I

I m h; j

l It i

i l

(B) CONTROL VOLUME FOR AV ERAGED CHANNEL I

I Figure 1.2 CONTROL VOLUMES FOR ENERGY EOUATION i

m u;+ 0 m;u dx dx d

p;A dx p;A; + _dx I

.-L3 l

l h

l l

j I

l i

j

,g wjju'dx CONTROL / I I

VOLUME I

i l

i I

CHANNELil i

I CHANNELj F;dx !

F I

U i#i dx I

dx A

I I

I I

Ud

• ji j X l

G dx l -

Wji l

PdAj l

g i

m u-l

)

k I

'I

'1-T T--

BOUNDARY SUBCHANNELS A

Pi ;

i (A) CONTROL VOLUME FOR LUMPED CHANNEL m u; + 0 m uj x d

dX i

~

bL - -.1 -

- - {

p ;A; + _d_ p;A dx CONTROL I

I VOLUME

'l

& w;ju'dx I

I i*

I CHANNELi CHANNELj p

gA;p;dx I

dx

'~

d

+ - -

wj;uj x

~

> w[ju dx I

P idA; g

I m;u; I

A I

l l._ _ _4_.

P_

i; (B) CONTROL VOLUME FOR AVERAGED CHANNEL l

l Figure 1.3 CONTROL VOLUMES FOR AXIAL MOMENTUM EQUATION f

1-11

t x+dx I d il V + dx I

I x

__w ik I

l OOOQlOOO CONTROt i i

O O d bio di O I

I l

I i

Ps4x ->I iis4x dx i

j

• ~l l

Pi Pj Fii CHANNELi CHANNELJ CHANNELil l CHANNELj g

i I

I I

I N

I TOP VIEW

^:

~~

Vx u' x SIDE VIEW (A) CONTROL VOLUME FOR LUMPED CHANNEL l

1 I

i

[

I r-----

I

]

l l

l 1

I l

i g

l P'-

W Pj PiM

-'* Wj f Pj OF i

i 1

l l

l l

l l

L______J I

il I

• V

\\

~

CHANNELi CHANNELj l

l l

CHANNELi CHANNELj I

L

(

d A

TOP VIEW SIDE VIEW "i

"j (B) COtJTHOL VOLUME FOR AVERAGED CHAiJNEL Figure 1.4 l

rottTF11 Vn'I!?tP;FD3+" TE R AI f.'nt.1FNTtlM FOf I A T'nN

e i

2.0 EMPIRICAL CORRELATIONS CETOP-D retains the empirical correlations which fit current C-E reactors and the ASME steam table routines which are included in the TORC code.

In CETOP-D, the following correlations are used:

2.1 Fluid Properties Fluid properties are determined with a series of subroutines that use a set oi curve-fitted equations developed in References 7 and 8 for describing the fluid properties in the ASME steam tables.

In CETOP-D, these equations a

cover the subcooled and saturated regimes.

2.2 Heat Transfer Coefficient Correlations i

The film temperature drop across the thermal boundary layer adjacent to the surface of the fuel cladding is dependent on the local heat flux, the temperature

.o l

of the. local coolant, and the effective surface heat transfer coefficient:

(2.1) f DTF = T

-T

=

wall cool I

h i

For the forced convection, non-boiling regime, the surface heat transfer coeffi-cient h is given by the Dittus-Boelter correlation, Reference 9:

0.8 0.4 h=

(Re)

(Pr)

(2.2)

For the nucleate boiling regime, the film temperature drop is determined from the Jens-Lottes correlation, Reference 10:

DTJL = (T

-Tcool)*

(*}

sat l

e The initiation of nucleate boi. ling is cetermined by calculating the film temperature drop on the bases of forced convection and nucleate boiling.

i fl

The initiation of nucleate boiling is deter,nined by calculating the film temperature drop on the bases of forced convection and nucleate boiling.

i When DTJL < DTF, nucleate boiling is said to occur.

2.3 Sinole-Phase Friction Factor The single-phase friction factor, f, used for detennining the pressure i

drop due to shear drag on the bare fuel rods under single-phase conditions is given by the Blasius form:

f = AA + BB (Re)CC (2.4)

Values for the coefficients AA, BB, and CC must be supplied as inputs.

i.

2.4 Two-Phase Friction Factor Multiplier A friction factor mulciplier, 4, is applied to the single-phase friction factor, f, to account for two-phase effects:

Total Friction Factor = 4f.

(2.5) i' CETOP-D considers Sher-Green and Modified Martinelli-Helson correlations as f

listed in Tables 2.1 and 2.2.

For isothermal and non-boiling conditions, the friction factor multiplier l-4 is set equal to 1.0.

For local. boiling conditions, correlations by Sher and Green (Reference 11) are used for determining o.

The Sher-Green correlation for friction factor multiplier also accounts implicitly for the change in pressure drop due to subcooled void effects.

When this correlation is used, it is not necessary tn calculate the subcooled void fraction explicitly.

For bulk boiling conditions, 4 is detennincd from Martinelli-Nelson results-raf">+?

wi+h sedificc;iens by Sher-Green (Reference 11) and by i

i Pyle (Reference 13) to account for mass velocity and pressure level dependencies.

2.5 Void Fraction Correlations The modified Martinelli-Nelson correlation is used for calculating void fraction in the following ways:

1)

For pressures below 1850 psia, the void fraction is given by the Martinelli-Nelson model from Reference 12:

i a=B + B) X + B X2+BX3

!j (2.6 )

g 2

3 where the coefficients B are defined in Reference 10 as follows:

n For the quality range 0 1 X <0.01:

B = B) = B

=B

= 0; the homogeneous model is used for g

3 calculating void fraction:

a=0 For X 1 0 Xv (2.7)

For X > 0 o " (j_x)yf + xy g

For the quality range 0.01 1 X <0.10:

2

-3

-7 2

-10 3 B = 0.5973-1.275x10 p + 9.010x10 p -2.065x10

-2

-5 2 + 9.867x10'9 3 B = 4.746 + 4.156x10 p -4.011x10 p

p I

(2.8)

-4 2

-7 3

~

B = -31.27 -0.5599p +5.580x10 p -1.378x10 p 2

~

B = 89'.07 + 2.408p - 2.367x10-3 2 + 5.694x10-3 p

p 3

l for the quality range 0.10 1 X <0.90:

~4

-7 2, 9.711x10-II 3 B = 0.7847 -3.900x10 p + 1.145x10 p

p

-4

-7 2 + 2.012x10 " p3

~

B = 0.7707 ^ 9.619x10 p - 2.010x10 p

M

-3

-72

-12 3 B = 1.060 -1.194x10 p + 2.618x10

-6.893x10 p

y

d 1

3 l

2 + 1.925zl0 p

-4 0.5157 + 6.506d0 p -1.938x10 p B

=

3 l'

For the quality range 0.90 < x < l.0:

• 0

= 0; the homogeneous model given by Eq. (2.7) is B,= B) = B2 3

a' used for calculating void fraction.

2) At pressures equal to or greater than 1850 psia, the void fraction is given by the homogeneous flow relationship (slip ratio = 1.0):

Xv for p >_ 1850 psia (2.10) 9 (1-X)vf+X vg 2.6 Spacer Grid Loss Coefficient The'los: coefficient correlation for representing the hydraulic resistance of the fuel assembly spacer grids has the form:

(2.11)

K = 0) + D2 (Re)D 3

g Appropriate values for D must be specified for the particular grids in the n

problem.

2.7 Correiation for Tudbulent Interchange Turbulent interch'ange, which refers to the turbulent eddies caused by spacer grids, is calculated at channel boundary in the following correlation:

w'jj = G D (s

) A (Re)0 (2.12)

S e

REF where:

G = channel averaged mass flow rate D,= channel averaged hydraulic diameter s = actual gap width for turbulent interchange

= reference gap width defined as total gap width s REFfor one side of a complete fuel bundle divided by the number of subchannels along this side Constants A and B are chosen as 0.0035 and 0 respectively in the present version of CETOP-0.

'9 4

+

t 4

.i 2.8 lietsroni Cross _ Flow Correlation Berringer, et al, proposed in Refe'rence' 15 a form of the lateral momentum equation that uses a variable coefficient for relatin3 the static pressure

. difference and lateral flow between two adjoining open flow channels.

ij ijlWijl K

W (2.13)

(Pj - Pj) = 29;,*

2 s

accounts for tiie large inertial In Berringer's treatment, the variable K$j ~

effects encountered when the predeminately axial flow is diverted in the lateral direction.

In Reference 3, lietsroni expanded the definition of K

to include the effects of shear drag and contraction-exparision losses jj lJ on the lateral pressure difference:

2 1/2 jj =

+ (-

+ (XFC0 tis)

-)

M K

2 The terms in Eq. (2.14) involving K-represent the lateral pressure losses due to shear drag and the cnntraction-expansions of the flow in-the absence of n 'l flow, i.e., lateral flow only.

The third term on the right hand

^7 Eq. (2.14) represents the lateral pressure difference developed by v

the _ centrifugal forces as the axially directed flow is diverted laterally.

This term accounts implicitly for the flow inertia effects that are treated explicitly in Eq. (1.31) by means of the momentum flux term.

Iletsroni suggestcd K= = 1.4 and XFC0tlS = 4.2 for rod bundle fuel assemblies.

~

These values are also used in CETOP-0.

CE-1 Critical lleat Flux (CilF) C_orrelatinn (Reference 14) 2.9 l

The CE-1 CilF correlation included in the CETOP-D is of the following form:

j(*)

((b+bP)(0)(bibP) b

~I 6) x) (hfg))

h 3 4 6

I0

_J O 9,,Cilf 6

}0W (hP+b

/0) 7 8

(L) 6 10 2-5 P

~

2 where: q"CHF = critical heat flux, BTU /hr-ft p

= pressure, psia d

= heated equivalent diameter of the subchannel, inches 4g l

d,

= heated equivalent diameter of a matrix subchannel with the same rod diameter and pitch, inches 2

G

= local mass velocity at CHF location, lb/hr-ft ~

i x

= local coolant quality at CHF location, decimal fraction h

= latent heat of vaporization, BTU /lb fg

-3 and b

= 2.8922x10 j

b

= -0.50749 2

b

= 405.32 3

-2 b

= -9.9290 x 10 4

b

= -0.67757 5

~4 b

= 6.8235x10 b

= 3.1240x10'4

~2 b

= -8.3245x10 8

The above parameters were defined from source data obtained under following

~

conditions:

pressure (psia) 1785 to 2415 local coolant quality

-0.16 to 0.20 2

6 6

local mass velocity (lb/hr-ft )

0.87x10 to 3.2x10 inlet temperature ( F) 382 to 644 subchannel wetted equivalent 0.3588 to 0 3447 diameter (inches)-

subchannel heated equivalent 0.4713 to 0.7837 diameter (inches) heated length (inches) 84,150 To account for a non-uniform axial heat flux distribution, a correction factor FS is used.

The FS factor is defined a:::

CHF, Equivalent Uniform FS=

9" CHF, Non-uniform

-C(J)@(J)-x(J-l)) dx c(J)

"(x)e q"CHF,Non-uniform (1-e"C(J)*U))

F5(J)=

o i

~.. -

l.

i i l where,.for CE-1 CHF correlation,

'C(J);.=1.8(1~XCHF)4.31 I

ft')

i (G/10 ) 0.478 6

l 4

The departure from nucleate boiling ratio, DNBR, is:

.I

-+'

DNBR(J) =

9"CHF, Equivalent Uniform I

FS(J)~

. q,, g )

e 1

i i

r i

I.

1 i

).-

h i

t 4

i e

e I

t-p w

er e

?-7

i L_____._

L l

l l

TABLE 2.1 l

TWO PIIASE FRICTION F ACTOR MULTIPLIER 3206 G > 0.7 x 106 i

$ = F AM(X = 0.4, G, P = 2000)

$ = F AM(X, G, P = 2000)

FfAN (X, P = 2000) 3 x

FMN3 (X, P)

FFAN (X =0.4, P = 2000) 0R FMN3 (X,P)

$ = F AM (X, G, P = 2000) x 3

MN3 (X, P = 2000)

IMN3 (X, P) f (P,G, FMN (X, P = 2000) x g

3 0 */D T F),

fMN3 (X,P = 2000) g Q=1.0 WillcifEVER G < 0.7 x 106 1

0 = F AM(X=0.4, G=0.7, P=2000) gg

$ = F AM(X, G = 0.7, P ' 2000)

FMN (X,P)

IIAU3 (X, P = 2000)

LARGER x

FMN (X,P)

$ = F AM(X, G = 0.7, P = 2000) x x f (G)

WN3 (X=4.0, P*2000) 3 4

l x

x f (G)

FMfd3 (X, P = 2000) l 4

IfAN3 (X, P)

,g (g)

TMN (X,P = 2000)

I x

3 4

l F MfJ3 (X, P = 2000) 2000 G > 0.7 x 106

= F AM (X, G, P = 2000)

$ = F AM (X , P = 2000)

$ = F AM (X = 0 A, G,P = 2000)

! " Ff,1rJ, IX, P = 2000)

$=1.0

$ = F AM(X, G, P = 2000)

FMN IX, P)

FMNy (a, ')

F MfJ3 (X*0.4, P = 2000) g R

FMNg (X, P = 2000)

FMN2 (X, P = 2000)

FPANy (X. P)

I F f,1N3 (X, P = 2000) f' 0 */DT F)*

$ = 1.0 WillCitEVER G < 0.7 x 106

$ = F AM(X, G = 0.7, P = 2000)

$ = F AM(X, G = 0.7, P = 2000)

$ = F AM(X=0.4, G=0.7, P=2000)

IMN2 (X, P = 2000) x

• f (G)

FMN2 (X, P) x f (G)

FfAfJ2 (X = 4.0, P = 2000)

L AP.G E R 1

x

$ = F AM(X* G = 0.7, P = 2000) 4 x

4 FFAN3 (X, P = 2030)

FMN (X, P = 2000) x f (G)

FMN2 (X, P)

,g (g) 4 4

FfAfJ2 (X, P = 2000) 1850 0

G > 0.7 x10 g.

$=FMNg (X, P)

I'

= f (P, G)

, g (p, g)

, pg p) p 3

D l

$=,.0 i

, M N ',X.

6 G < 0.7 x 10

$=FMNg (X,P)

" g g.12, F) -1, I

x f (P, G)

$ = FMN (X, P) x f (P, G)

$=f3 (P, G) 3 3

3 I

1 14.7 O

O 0.02 g

L O C '. L Q U ALITY* X 0.2 0.4 1.0 It E ATIN G NO B0iLING7 BOILING BULK BOILING r

~

c fj 0T E: FUNCTIONAL 'IEL ATIONSillPS ARE LISTED IrlTABLE 2.2

Table 2.2 Functional Relationships in~

the Two-Phase Friction Factor Multiplier (References 11,12',13) i 1

For local boiling:

f)=C(1+0.76(3

)(

)

")

j 0

where'C) = (1.05) (1-0.f)0250*)

0* = The smaller of DTJL and DTF w = 1 - 0*/DTF For bulk boiling:

7X.75' 0

(G/10 ) M 6

x(0.9326

-(0.2263x10-3)p)

FMN1 =

1.65x10-3 + (2.988x10-5) P-(2.528x10 9) P2 + (1.!4x10-II)p FP42 =

X(1.0205'- (0.2053x10-3) p) 7.876x10~4 + (3.177x10~b)' P-(8. 728x10-9) P2 + (1.073x10 II)P3 2

FMN3 =

1 + (-0.0103166X~+ 0.005333X ) (P-3206) 1.36 + 0.0005p'+ 0.1 ( 0 ) - 0.000714P ( G )

f

=

2 6

6 10 10 1.26 - 0.0004P + 0.119 ( - ) + 0.00028P (-

)

f

=

3 1 + 0.93 (0.7 - 0) f

=

4 6

10 t

r

-~

3.

NUMERICAL SOLUT10il 0F TIIE CONSERVATI0il EQUATIONS 3.1 Finite Difference Equations

a The CETOP-D code solves the conservation equations described in Section 1 by the finite difference method.

The flow chart shown in Figure 3.1 displays

~

briefly the marching CETOP-D follows in order to search for the minimum value and the location of DNBR in a 4-channel core representation

(

(c f. Section 4.1).

3 Equations (1.F.), (1.22), (1.27) and (1.36) which govern the mass, e'nergy I

and momentum transport within channel i of finite axial length Ax are I

written in the following finite difference forms:

tl 4

(1)

Continuity Equation m (J) - m.(J - 1) j 1

jj(J)

(3.1)

= -w (2) Energy Equation

- h (J) - h (J - 1)

h. - h, j

j m (J - 1)

, Ax 1- -

j

=gj

11 "wjj

-4

~

(3.2) h.+h.

(h. - h )n 3

jjj&('2 hw

) "ij

+~

J-1 (3) Axialj' Lomentum Equation e

p (J) - p (J - 1) j j

u'.

- u-A 3

5 - A ga;(J) g..-.ujj

=-T j.

g

==

j u

I 3-1

i k

a

("i ~'"j)") W j Zu wjj + ( j + u u

2

.(3.3)

+

2N i

j 2

U j

g.1 3.

(4) Lateral Momentum Equation 3

i g3(J) wjj(J) p (J - 1) - p (J - 1) w j

N ij 2 s p*

9 p

u*(J)wjj(J) - u*(J - 1)wjj(J - 1) g (3.4)

+

s ax Where J is the axial elevation indicator and ax is the axial nodal length.

3.2 Prediction - Correction Method In CETOP-D a non-iterative numerical scheme is used to solve the conservation

)

equations.

This prediction-correction method provides a fast yet accurate i-scheme for the solution of m, h, w and p at each axial level.

Thc: steps j

j jj j

l

~

used in the CETOP-0 solution are as follows:

(

The channel flows, m, enthalpies h, pressures p and fluid properties j

j j

are calculated at the node interfaces.

The linear heat rates q'., cross-flows, wg, and turbulent mixing, wjj, are calculated at mid-node.

The solution method starts at the bottom of the core and marches upward using the core inlet flows as one boundary condition and equal core exit pressures as another.

l 3-2

d An initial estimate is made of the subchannel crossflows for nodes 1 and 2.

These crossflows are s'et to zero.

l jj(1)=wjj(2)=0 w

The channel flows and enthalpies at node 1 are known to be the inlet conditions. Using these initial conditions the.narching technique proceeds to calculate tha enthalpies and-flows from node 2 to the exit node.

4 k

In this discussion "J" will designate the axial level 'i" and "j" are used to designate channels.

Step i

M 1

9 f

i.

l I

t 4

3-3 j

i i

i 1

I i

4

+

The success of this non-iterative, prediction-correction method lies in the fact that the lateral pressure difference, p (J) - p2(J), using the " guessed" j

diversion crossflcw, Wjj(J + 1)p, is a good approximation.

Thus at each node the axial flow rate can be acct:ritely determined.

t i

lj TORC on the other hand, initially assumes pg - p3 = 0 at-each axial location.

The conservation of mass and momentum equations are used to evaluate the diversion crossflows and, in turn, the flowI rates at all locations.

The axial momentum equation is used to determine p - p for the next iteration.

g j

The iteration stops when the change in the diversion crossflows at each location is less than a specified tolerance.

Even though the prediction-correction method'is a once-through marching technique, its results are very

~ close to those from the TORC iterative numerical technique.

In general, about((

[inTORCtoachievethesame-accuracy as the prediction-correction method.

In the TORC iteration scheme the transverse pressures and-the flows are only updated after the iteration is completed.

Therefore in marching up the core errors in the transverse pressures cause the errors in.the flows and enthalpies to accummulate up the core.

In the prediction-correction scheme the. transverse pressures and the axial flows are corrected at each node before the next is calculated.

Therefore the accummulated errors are greatly reduced.

It is the accummulated errors in the downstream nodes which often force the TORC method to continue.

to iterate.

O e

4 l-

~

l START l

i d U

D

<1E AD INPUT l..

U PREDICT AND CORRECT COOLANT PROPERTIES IN THE CORE 5

AVERAGE AND HOT ASSEMBLY CHANNELS AT ALL AXIAL NODES U

PRE 0lCT AND CORRECT COOLANT PROPERTIES IN THE HOT CHANNEL AT ALL AXIAL N0 DES 4 -

PREDICT NEW HEAT F LUX y

CALCULATE CHF AND ONBR FOR THE HOT CHANNEL AT ALL AXIAL NODES U

N0 IS MONBR OR QUALITY WITHIN THE LibilTS ?

YES p

~

PRINT OUTPUT It NO IS THIS THE LAST CASE 7 YES If STOP Figure 3.1 CETOP D Ft.OW CllART 3-6

J=2 I

u PREDICT wij, m; AT NODE J 1

.i 1r PREDICT wij, w;j and m; AT NODE J 9

PREDICT h; AT NODE J + 1 y

COMPUTE COOLANT PROPERTIES J=J+1 y

h PREDICT w;j AT NODE J+1 It CALCULATE p; p; AT NODE J CALCULATE w;j, m;, h; AT f! ODE J ifs LAST NODE ?

YES y

Figure 3.2 FLOW CHART F03 PREDICTION CORRECTION METHOD

4.

CETOP-D DESIGN MODEi.

The CETOP-D code has been developed, using the basic CET0r riumarical algorithm, to retain all the capabilities the S-TORC modelling method has Generatica of design model involves selection of an optimal core representation which

(

will result in a best estimate of the hot channel flow p~nerties and a prepara, tion of input describing'the operating conditions and geometrical configuration of the core. The CETOP-D model presented here provides an additional simplificatior to the conservation equations due to the specific geometry of the model.

A description of this simplification is included here together with an explanation' y

...c.

~

on the method for generating enthalpy transport coefficients in CETOP-D.-

4.1 Geometry of CETOP-D Desicn Model The CETOP-D design model has a total of four thermal-hydraulic channels to model the open-core fluid phenomena.

Figure 4.1 shows a typical layout of these channels.

Channel 2 is a quadrant of the hottest assembly in the core and Channel 1 is an assembly which represents the average coolant conditions 'for the remaining portion of the core.

The boundary between channels 1 and 2 is

~

open for crossflow, but there is no turbulent mixing across the boundary.

~

Turbulent mixing is only allowed within channel 2.

The outer boundaries of' the m total geometry are assumed to be impermeable and adiabatic. The lumped Channel ~2 includes channels 3 and 4.

Channel 3 lumps the subchannels adjacent to the MDNBR hot channel 4.

The location of the HDNP,R channel is determined from a Detailed TORC analysis of a core. Channels 2' and 2" are discussed in Section j.2.

The radial power ' factor and inlet flow factor for channel 1 in CETOP-D is always unity since this channel represents the average coolant conditions in l

the core. The Channel 2 radial pawer distribution is normally based upon a core average radial factor of unity. However, prior to providing input in CETOP-0, the Ch.mel 2 radial power distribution is normalized so the Channel 2 power factor is one.

This is performed in CETOP-D so the Channel 2 power can easily be adjusted to any value.

Initially, the inlet flow factor in the CETOP-D hot assembly is equal to the hot assembly relative flow obtained from the inlet fica distribution.

If necessary, the inlet flow factor is later adjusted in the CETOP-D model to yield conservative or accurate HDMCR l

predictions as compared to a Detailed TORC analysis for a given range of operat inq con '.t ions.

4-}

=.

4.2 l Application of Transport Coefficientt in the CETOP-D Model i

a 38 e

e iO j.

O.

4 4

+

h

)

i f

I I

i 1

(4 '

i i

1'j' i

i

(.

f i.

l t

l l

1 4

3 4-2

m I6 4

l 4

9

• 9 b

o i 8 a

' d

)

i *

{~

e e

o I

l M

4-3 l

P

s

?

-1

}

. l 3

I 1

d:..

I

}

1,... g -

i*

1 i-1 4.3 Description of Input Parameters A user's guide for CETOP-D,. Version 2 is supplied in Appendix A.

To.

provide more information on the preparation of the input'paramete 3,'the following terms are discussed.

!j 4.3.1

. Radial Power Distribution The core. radial power distribution is defined by C-E nucleonics codes in terms of a radial power factor, F (i), for.each fuel assembly.

R The radial power factor F (i) is equal to:

R p (j) _ power generated in fuel asserrbly_i

. (4.7)

R power generated in an average-fuel assembly Assuming power generated in an average fuel assembly is equal to unity, the following expression exists:

l N

I F (i) = N (4.8)

R

.i=1 where H is the total number of assemblies in the core.

The radial riower factor for each fuel rod is defined by:

f (;'3), power generated _in fuel rod,1,of assembly i (4,g)

R power generated in an average f uel red l-

.for an assembly containing M rods, one expects:

M E f (i,j) = M F (i)

(4'10) p R

j=1 l

4 t, L

The CETOP-0 code:is built to allow only one radial power factor for each flow channel, thus, for a channel containing n rods,.he idea of -

effective radial power factor is used:

l

/

n I

C ff(i,j) i f (I)= )*I (4,11)

R

,E C,

J=l J-where c3 is the fraction of the rod j enclosed in channel i.

4.3.2 Axial Power ~0istributions The fuel ro'd axial power distribution is characterized by the axial shape index (ASI), defi6cd as:

L /2 t

I F(k)dZ-/

F(k)dZ Z

Z ASI.

O L /2 (4.12)

=

F (k)dZ Z

g where the axial power factor at elevation k, F (k), satisfies the normalization Z

condition:

.L

/ = F (k)dZ = 1

~(4.13)

Z o

and L, dZ are total fuel length and axial length increment respectively.

The total heat flux supplied to channel i at elevation R is:

4 =(core average heat flux) (f (i)) (F (k))

(4.14)

R Z

4.3.3 Effective Rod Diameter For a flow channel containing n rods of identical diameter d, the effective rod diameter defined by:

n

'g(i)=,L cj (4.15) d J=l is used to give ef fective heate,! perimeter in channel i.

The follwing expression, derived from Eq's. (4.5) and (4.9), it.iplies that equivalent energy it be ng received by channel 1:

n c) f (I 'j )

(4.16)

D(i) fR (i) = d E R

J=1 4.3.4 Enginecring Factors The CETOP-D model allows for engineering factors (as described in Rcference 1) due to manufacturing tolerances.

Application of such factors imposes additional conservatism on the core thermal margin.

Conventionally, engineering factors are used as multipliers to effectively increase the radial peaking factors and diameters of rods surrounding the hot channel.

Alternatively, statistical methods are applied to produce a slightly increased DfiBR design limit, which is then input as parameter 85 (Appendix A).

The former method requires further explanation on the treatment of engineering factors:

(1) Heal. Flux Factor (f )

A slightly greater than unit heat flux factor f,. acting as a heat flux multiplier, tends to decrease DriBR in the folloIving manner:

y fg 7

,)

(4, g)

DitBR CHF CHF f 4j 4j 4

where defines the DilBR before applying f and 4j is the local heat flux.

CHF t

4j (2) Enthalpy Rise Factor (f ) and Pitch and Bow Factor (f )

g p

These factors are involved in the modification of the effective radial power factors and rod diameters for the fuel rods surrounding the hot channel as follows:

m m

f E

C I (4'd) cj R(4'd) ff E

R

^

gP 0"I

-d (4.18)

F (4) -

d*I

=

R m

m I

ff 5

'j c,

Hp J=1 J=1 J

m n

c f(3,j) f I

c fg (3,j) + r

^

R 3

(3), _g, j=1 j=1 j

fg n

m 4

I c

f

).

N i.3 j=1 j=1 j

t.. (.

T.

b

,_&m, 4s-.J G+

L-4-

A

d and (4.19)

D (4) = f f d E-c H.P j,1 j

m n

^

D- (3) '= d (fp' I d: + E C'

)

(4.20)

J=1 j j=1 j where s and D's are the modified effective radial' power factors a.nd I

rod diameters for channels 4 and 3, m is the number of rods on channel connection 4-3 and n is the number of rods 72 and i 'in the core thermal margin prediction causes Again, the inclusion of fH p

a net decrease in DNBR.in addition to that described in Eq. (4.11).

i 4

I i

1

/

e i

4-7

CilANNEL NUM3E t-

• 2 e !!OT ASSEMCLY = 1/4 OF ONE FUEL ASSEMDLY CilANNEL AVG.

pR RADI AL PO'.*/ER FACTOR d

'1 CORE AVERAGE I-1.000 CilANNEL = ONE FUEL ASSEf.iULY -

j-

?

(A) FOUR CilANf1EL CORE REPRESENTATION IMPERMEABLE AtlD ADI ABATIC 0000000t O O '-

OOOO 2

i.

<co 2"*

2 2.,

i i ;;;

9 co

.o 2"

2' 3-12" m

j T

/ 3 2"

O

=

m 2"

2' 3

4 2'

m 3

l w

2" 2'

3 2'

2"

~

j 2

2*

2

O XD O O O 2..

(B) CllANilEL 2 IN DETAll 1

Fipre 4 ;

CilAfJNEL GEO:.'li'l!!Y 01 CEU i' D f.iODEl.

ti- ',

j t

5.

THERMAL MARGIN ANALYSES USING CETOP-D

{>

This section supports the CETOP-D model by comparing its predictions for.a 16x16 assembly' type -C-E reactor (ANO-2):with those obtained from a detailed TORC analysis.

Several operating conditions were arbitrarily selected for this. demonstration;:they are representative of, but not the complete set of conditions which would be considered for a nonnal DNB analysis.

5.1 Operating Range:

The thermal margin model for 2815 Mwt ANC-2, Cycle 2 was developed for the following operating ranges:

Inlet Temperature 465 - 605*F

. System pressure.

1750 - 2400 psia Primary system flow rate 193,200 - 386,400 gpm Axial power distribution

-0.527 - +0.527 ASI 5.2 Detailed TORC Analysis of Sample Core The detailed thermal margin analyses were performed for' the sample. core using th.adial power distribution and detailed TORC model shown in Figures 5.1, 5.2, and 5.3.

The axial power distributions are given in Figure 5.4.

The core exit pressure and inlet flow distribution used in the analyses were based on flow model test results, given in Figures 5.5 and 5.6.

The results of the detailed TORC analyses are given in Table 5.1.

~

GeometryofCETdPDesianModel 5.3 The CETOP de. sign model has a total of four thermal-hydraulic channels to model the open-core fluid phenomena.

Figure 5.7 shows the layout of these channels.

Channel 2 is a quadrant of the hottest assembly in the core (location 8) and Channel 1 is an assembly which represents the average coolant conditions for

(-

the remaining portion of the core.

The boundary between channels 1 and 2 is open g

for crossflow; the remaining outer boundaries of channel 2 are assumed to be j

impermeable and adiabatic.

Channel 2 includes enannels 3 and 4.

Channel 3 lumps 1

r-the subchannels adjactnt Lc the Mf::CR hat channel

-1.

i l'

5-1

?

s

' 9

~ "

5.4 Comparison Between TORC and CETOP-D predicted Results The CETOP model described above was applied to the same cases as the detailed TORC analyses in section 5.2.

The_results from the CETOP model analyses are compared with those from the cetailed analyses in Table 5.1.

It was found that a constant inlet flow split providing a hot assembly inlet mass velocity of.80 of the core average value is appropriate for 4-pump operation so I

that MDNBR results predicted by the CETOP model are either conservative or

,I accurate.

A similar procedure to that described above shows that a CETOP-D hot assembly 3

flow factor of is appropriate for 3-pump operation.

5.5 Application of Uncertainties in CETOP-D An allowance for the system parameter uncertainties in ANO-2 cycle 2 was derived statistically in Reference 6.- This allowance has been incorporated into the design CETOP-D model in the form of a design MDNBR limit equal to 1.24, replacing the original design limit of 1.19.

i 9

m 4

(

s

-P C

4

.)

9.

t 24 16 8 l

.~

CHANNEL NUMBER 0.8736 1.1237 1.1734 7

ASSEMBLY RADIAL 37' 31 23 15 7

POWER FACTOR

+ 0.7252 1.0676 1.1592 1.2056 1.2470 41 36 30 22 14 6

0.6704 0.8274 1.0757 1.0296 1.2052 1.0447 43 40 35 29 21 13 5

0.7252 0.8245 0.6465 0.8348.

1.2389 0.9651 1.0816 42 39 34 28 20 12 4

1.0713 1.0757 0.8383 0.8081 0.9062 0.9278 0.9186 1

38 33 27 19 11 3

1 1.0270 1.2387 0.9046 1.2315 0.9420 1.2414 1

1591 0.8680

___+

]

32 26 18 10 2

1.1215 l 1.2054 1.2026 0.9661 0.9262 0.9445 1.000S 0.8244

- - - l- -- + - -

i 25 27 9

1 l

l 1.0414 1 1

1.0803 0.9162 1.2425 0.8241 I-Q. -

!.2455 !

1.1715 0.5126 I

I I

i NOTE: CIRCLED NUMBER DENOTES " LUMPED" CHANNEL Figure 5.1 STAGE 1 TORC CHANNEL GEOl.1ETRY FOR ANO 2, CYCLE 2 5-3

. - ~..

I I

(

i

,i 7-l

-l 4

1 3

i i

?

J I

i 1

i i

.J-i j.

i.

<1-

!~

i t

1 l.

e i

t i

j i

4 4 -s-Figure 5.2

(

STAGEm iORC CHANNEL GEOf.1ETRY FOR ANO 2, CYCLE 2, LOCATION U 5-4

~.

I I

3 t

1 1

i i

i

)

I i

i l

I i

l l

i I.

i Figure 5.3 STAGE 3 TORC CHANNEL GEOMETRY FOR ANO-2, CYCLE 2 5-5 I

e

,,.4 V,, O~~Ml"~.'-7i 4

/

I i

i 1

e i

e l

~~

//

/

l,

/

/

o I

l./

/

j d

o

/

l

/

/I e

(

/

~

/

[

d

/

i

\\

l I

/

6 9

/

ow

/

/

\\

4 1

2

=j

/

/

el 1

/

0 N

/

O. C u.

O

/

/

g b

o e

[

I

[3 I

l g

I s

/

O C

~

1 g

W e

t-i I

f

(*.

p I

\\

cW C

e C.

EbU33 y

I

.9 E f

s o

I 6 N.5 o o

/

g

(

N *l M O tw manoo

/

ddddd

/

G k

a c

+

+

y 6 4

/

./

\\

u.

/

\\

l O

/

\\

f

\\

2

/

\\

O

/

I 9e

~

/

\\

x

/

u.

I I

I s)

N

~

~

e s

x

\\

\\\\.

' s.

\\

- o s's

%~%

\\

%,g I

I

.._ I

'2 k

I I

v.

o!

c.

9 q

-r.

ei c.

q q

v, c!

a c4 m

ei r

e o

o a

,,e,,,

1 j

Figure 5.5 INLET FLOV/ DISTRIBUTION FOR ANO-2, CYCLE 2 4. PUMP OPERATION

o 4

t 9

sl'

.' )

Figure 5.6 EXIT PRESSURE DISTR 180 TION FOR ANO-2, CYCLE 2 4 PUMP OPERATION 6-P

4 i

a

\\

em a

I 6

e d

b e

O e

MID M

Figure 5.7 CETOP D CHANNEL GEOMETRY FOR ANO 2, CYCLE 2 (CHANNEL 1 NOT SIlOWN) r n

i a

i L_.

Axial Elev.

Operating Parameters MDNBR Quality at MDNBR-of MDNBR (in)

Detailed Detailed TORC CETOP-D TORC-f CETOP-D Core 1

Avg. Mass

' Inlet Vel city Core Avg.

Axial Relative-Inlet Relative Inlet lleat flux Shape-Flow in flow flow in Fiw Detailed 6

' Pressure Temp.

10 1bm}

Btu Index location 8 factor Location 8 factor TORC CETOP-D-i (psia)

("F) 2

.ASI

))

{ } '.80

[

}

[ ]-

.80

~

r-R

-R

?250 553.5 2.598 267437

+.527 1.172

~~

1.144

.134

'.112 52.4 56.1

~

2250 553.5 2.598 312561

+.337 1.169 1.066

.153

.169

.142.2.

142.2 2250 553.5 2.598 278307

+0.00 1.186 1.137

.017

.020 108.5 116.0 2250 553.0 2.598 264238

.070 1.169 1.135

.028

.039 138.4 138.5 2250 553.5 2.598 225343

.527.

1.195 1.164,

.076

.066 131.0 131.0 1750 605 1.407 122096

+.527 1.172 1.155

.181

.194 71.1 74.8 1750 553.5 1.547 168322

+.527 1.181 1.178

.073

.089 63.6 67.4 2400 605 2.868' 227330

+.527 1.209 l

1.181

.069

.051 52.4 56.1 l50 46S 2.868 392894

+.337 1.166 1.068

.108

.123 142.2 142.2 1

6 30 465 1.724 314014

+.337 1.140 l'.048

.164.

.143.

142.2 142.2 2400 605 2.390 238744

+.337 1.162 1.067

.203

.213' 142.2 142.2 2400 605 1.434 120256

.527 1.180 1.178

.064

.069 134.7 134.7 2400 553.5 1.562 162529

.527 1.203 1.183

- 065

.055 131.0.

131.0 TABLE 5.1 COMPARISONS BETWEEN DETAILED TORC AND CETOP-D

=

T 1

~

i f5 6.

CONCLUSION i

CETOP-D, when benchmarked against Detailed TORC for ANO-2 cycle 2, has been l.

shown to produce a conservative and accurate representation of the DNB margin

.lj in the core.

Similar conclusions have been reached when CETOP-D results have

{

been compared to TORC results for other C-t olants.

CETOP-0 models thus are appropriate substitutes for Design TORC models (S-TORC) specifically fo'r AN0-2 cycle 2, and generally for applications in which the Design TORC

l methods have been approved (Reference 15).

• i i

)

t

$4 i'

4 l

r t

1 1

e i

7.

REFERENCES 1.

" TORC Code, A Computer Code for Determining the Thermal Margin of a Reactor Core". CENPD-161-P, July 1975.

1

~

2.

Chiu, C., et al, "Enthalpy Transfer Between PWR Fuel Assemblies in Analysis by the Lumped Subchannel Model", Nuc. Eng and Des.,

53 (1979), p.165-1B6.

j

- 1 j

3.

Hetsroni, G., "Use of Hydraulic Models in Nuclear Reactor Design",

j Nuclear Science and Engineering, 28, 1967, pgs. 1-11.

4.

Chi", C.; Cbvrch, J.

F., "Three Dimensional Lumped Subchannel l

Mocel and Prediction-Correction Numerical Method for Thermal Margin Analysis of PWR Cores", Combustion Eng. Inc., presented at Am. Nuc.

t Society Annual Meeting, Jan, 1979.

J 5.

" TORC Code, Verfication and Simplification Methods", CENPD 206-P, January, 1977.

6..

" Statistical Combination of Uncertainties, Combination of System Parameter Uncertainties in Thermal Margin Analyses for Arkansas Nuclear One Unit 2"., CEN-139 (A)-P, November, 1980.

7.

McClintock, R.B.; Silvestri, G.

J., " Formulations and Iterative Procedures and the Calculation of Properties of Steam", ASME, 1968.

8.

McClintock, R.B.; Silvestri, G.J., "Some Improved Steam Property Calculation Procedures", ASME Publication 69-WA/PWR-2.

9.

Dittus, F.W. ; Boelter, L.M.K., University of California Pubs.

Eng. 2, 1930, pg. 443.

10. Jens, W. H.; Lottes, P.A., Argonne National Laboratory Report, ANL-4627, May 1.1951.

11.

Sher, N.C. ; Green, S. J., " Boiling Pressure Drop in Thin Rectangular Channels", Chem. Eng. Prog. Symposium Series, No. 23, Vol. 55, pgs. 61-73.

12.

Martinelli, R.C. and Nelson, D.B.; Trans. Am. Soc. Mech. Engrs., 70, 1948 pg. 695.

13.

Pyle, R.S., "STDY-3, A Program for the Thermal Analysis of a Pressurized Water Nuclear Reactor During Steady-State Operation", UAPD-TM-213, June 1960.

14.

"CE Critical Heat Flux Correlation for CE Fuel Assemblies with Standard Spacer Grids", CENPD-162-P-A, September 1976.

15.

Berringer, R.; Previti, G. and Tong, L.S., " Lateral Flow Simulation in an Open Lattice Core", ANS Transactions, Vol. 4, 1961, pgs. 45-46.

.,r-

.~-._-

n y

-n_-

.x,--

v-

.--,y

16.

Letter dated 12/11/80, R. L. Tedesco (NRC) to A.E. Scherer (C-E),

" Acceptance for Referencing of Topical Report CENPD-206(P), TORC Code Verification and Simplified Modeling Methods".

I i

e t

=

d 4

4 o

Y t

~

E n

-4 1

t i

4 e

i 4

Appendix A CETOP-0 VERSION 2 USER's GUIDE

~

i t

l e

e 4-l

I A.1 Control Cacds

~

1 Code Access and Output Control Cards A.2 Input Format.

1)

Read case control card, Format (110, 7nA1)

Case Number,110 Alphanumeric information to identify case, 70Al 2)

Read Relative Addresses and Corresponding Input Parameters,

~

Format (11,'I4, 15, 4EI5.8)

N1: 0 or blank, continue to read in the next card.

Otherwise any value in this location indicates end of input for the case.

Successive cases can be performed by adding iaput after the last card of each case.

The title card must be included for lach case.

N2: Specifies the first relative address for data contained on this card.

H3:

Specifies the last relative address for data contained on this card.

XLOC(N2):

corresponding input parameters thru XLOC (N3):

^

t l

A.3 List of Input Parameters Re', a ti ve Pa rameters Address Units Descriptions t

GIN 1

million-lbm Core average inlet mass velocity, during hr-fts core flow iterationi this value is the initial guess.

XLOC(2) 2 million-Stu Core average heat flux, during core power br-ftz iteration this value is the initial guess U

TIN 3

F Core Inlet Temperature PREF 4

PSIA System Pressure NXL 5

None Use 0.0 to include the capability for adjusting the initial guess during

" iteration"*, so the number of iterations-may be reduced.

Specify 1.0 to not use the capability.

I NPOWER 6

Use 1.0 to print more parameters during iteration in the event of convergence problem.

Specify 0.0 to not print.

7-25 None For future work GRJDXL(J) 26-(25+NGRID)

None Relative Grid Location (X/Z), where X is t

J=1, NGRID distance from bottom of act? 'e core to top of spacer grid, Z is the total channel axial length (relative address 77)

(25+NGRID)-45 None For future work 2

A(I) 46-49 ft Flow Area for Channel I I = 1,4 PERIM(I) 50-53 ft Wetted Perimeter for Channel I 1

I = 1,4 HPERIM(I) 54-57 ft Heated Perimeter for Channel I

~

I = 1,4 Parameters superscripted wita 1 are not i 1cluded in CETOP-D Version 1.

I

• The term "ite[ation" can-be defined as epther iteration on core power, core flow or on Cha mel 2 radial peaking factors

o 4

i Relative Parameters Address its Descriptions I

.s FR 58 None Maximum rod radial peaking factor wanted 4,

s for Channel 2.

During radial peak.'ng factor iteration this value is the initial guess. -

PIPB 59 None Ratio of the maximum rod radial peakint; i

factor of Channel 2 to the Channel 2 a

average radial factor.

This ratio is based upon a power distribution normalized to the core f

RADIM1 60 None Effective radial peaking factor for Channe'

,J RADIAL (I) 61-63 None Effective normalized radial peaking factor

!=2,4 for Channel I (normalized to the Channel 2 average radial factor in the core power di bution, if this is done correctly RADIAL (2 will always be 1).

A channel normalized radial peaking factor is determined by multiplying the normalized radial peaks in the channel by the corresponding rod fractions depositing heat to the channel.

~

D(I)

!= 1,4 64-67 ft Effective rod dianr te.- for Channel I, determined by multiplying the rod diameter with the rod fractions depositing heat to the Channel (assuming diameter of all rods in Channel are the same).

~

GAP (I) 68-70 ft Gap width available for crossflow between Channel I and Channel I+1. [

I=1,3

~

)

NDX 71 None Number of axial nodal' sections in model, maximum of 49 (recommend 40)

NCHANL 72 None Number of Channels (always 4)

NGRID 73 None Number of spacer grids (maximum r. umber of ITMAX 74 None Maximum number of iterations (recommend 10). Insert 0.0 for no iteration then a MDNBR will be calculated for the input core power, core flow and channel 2 radia peaking factor.

l f

L Relative Parameters Address Units Descriptions

~

I 1

PDES 75 PSIA Reference preskure at which the core

,i average mass flux is specified..If i--

the core inlet mass flux (GIN) is specified at(TIN, PREF)thenPDEScanbe,setto 0.0.

If not,.the code will correct the inlet mass flux to TIN and PREF by using PDES and TDES as reference conditions.

0 TDES 76 F

Referen.ce temperature at which the core average mass fl'ux is specified.

Can be set to 0.0 for the same reasoning stated above.

Z 77 ft Total channel axial length, where active length of fuel is corrected for axial' densi fication.

DEMATX 78 ft Hydraulic diameter of a regular matrix channel for use in calculating MDNBR in hot channel QFPC

, 79 None Fraction of power "terated in tha fuel

. rod plus clad Engineering heat [ lux factor.

SKECDK 80 None FSPLIT 81 None Inlet flow factor for Channels 2, 3, 4 l _

DDH(1)

~ 82 ft l,'

]

(

DDH(2) 83 ft Heated hydraulic o

' >r of channel 4.

-I COMIX 84 ft Parameter used in

• urbulent mixing correlation, determi. ed by taking the i

ratio of the nt...oci

,f subchannels along one side of a complete fuel bundle to the width on that side.

i DDNBR 85 None Design limit on DNBR for CE-1 CHF correlat

1 l

\\

}

Relative Parameters Address Units Descriptions DNBRCO 86 None Initial value of the DNBR derivative with

[espect power during core power iterati r

during core fl]ow iteration ljs ect to flow and with re 4

j DNBRTOL 87 None

' Tolerance on DNBR limit.

QUALMX 88 None Maximum acceptable coolant quality at MDNBR

.. location.

QUALCO 89 None-Initial value o.f the quality derivative with resp yt power durin core power iteration L and with respect to flow during c e flow iteration [

i QUALTOL 90 None Tolerance on quality limit.

AHDAF 91 None Ratio of core heat transfer-area to flow area, used for specifying a core saturation limit during overpower iteration.

Insert 0.0 for not using the limit.

HTFLXTL 92 None Convergence window tolerance on the ratio of the present guess to the previous one during " iteration".

This tolerance is used to reduce oscillation during iteration.

DTIME 93 Sec.

CESEC time, this parameter is printed

~

in the output when the CESEC code is linked with CETOP-D.

~

CF(2) 94 None Average enthalpy transport coefficient in the total channel axial length between CHs. 2 and 3.

Insert 0.0 for CETOP to sel f-generate the transport coefficients.

2 AMATX 95 ft GAPT 96 ft

,n-

--n.:-n v

\\

l Relative 6

j

. Parameters Address Units Descriptions

\\

HC 97' None s

1 FSPLITl 98 None Inlet flow factor for Channel 1 NX 99 None

'Use 0.0 to not print enthalpy transport coefficient factors and enthalpy distribu-tion in chant.els.

Use 1.0 to specify infor mat, ion.

/

NY 100 None

, Use 0.0 for not using the' relative locatior.

of the axial power factors as long as the

'4 axial power factors are input at the node interfaces.

Use 1.0 to specify locations.

NZ 1 01 None Use 0.0 to write output on tape 8 and prin:

one line of information, use 1.0 to write

(]'

output on tape 8 and print all output.

XLOC(102) 102 nillion-BTU _

Core average heat flux at 1005 power, hr-ft2 includes heat generated from rods and coo'l ant.

Fuel rods are corrected for axial densification.

~

XLOC(103) 103 lione QUIX file case number. The QUIX code is us'ed in Physics to generate axial pcwer sh IIRAD.

104' lione Option to " iterate" on the following until the design limit on NiBR is reached.

0.0:

Iterate on core powe'., if address (74) is 0.0 there is no iteration.

1.0: To iterate on channel 2 radial peakin factor. When this option is used the core heat flux in Channel 1 remains constant while all the Channel 2 radial peaking factors vary by the same multiplier until the DNB limit is reached.

l 2.0:

Iterate.on core flow A-7

+.

Relative Parameters Address Units Descriptions

{

3 l

Use 0.0 to not print CESEC time (DTIME)

I NZZ 105 None Specify 1.0 to ' print.

(

GRKIJ(J) 106-117 None Option to input different spacer grid types with the corresponding loss J=1,NGRID coefficient equations.

0.0 Normal grid with built in loss coeffici.

Type 1 grid with coeffi i f equation =

'1. 0 CAA(1)+CSB(1)*(Re)CbCfk Type 2 grid =

2.0 CAA(2) + CBB(2) ? (Re)C G(2)

Type 3 grid =

3.0 CAA(3) + CBB(3) * (Re)CCC(3)

CAA(1) 118 None Constant for Type 1 grid equation CBB(1) 119 None Constant for Type 1 grid equation CCC(l) 120 None Constant for Type 1 grid equation

(

Constant for Type 2 grid equation CAA(2) 121 None CBB(2) 122 None Constant for Type 2 grid equation CC(2) 123 None Constant for Type 2 grid equation

~

CAA(3) 124 None Constant for Type 3 grid equation CBB(3) 125 None Constant for Type 3 grid equation CCC(3) 126 None Constant for Type 3 grid equation 127-128 None Reserved for additional input I

6 e

f A-8

Relative Parameters Address Units Descriptions l*

RAA2 129 None s

RAA22 130 None i

GAP 2P '

1 31 ft GAP 22 1 32 ft 2

A2P 133 ft

'~

A22 134 ft DD2P 135 ft DD22 136 ft 137 - 139 None For Future Ucrk NDXPZ 140 None Number cf axial power factors (Reconmend 41)

XXL(J) 141 - 190 None Reiative locations (X/Z)'of the axial J=1,NDXPZ power factors.

If NY = 0.0 this input is not needed.

AXIAZ(J) 191 - 240 None Normalized axial power factors i

J=1, NDXPZ I

None Specify 1.0 to use the capability.to chanc NFIND 241 the hot assembly flow factor for different regions of operating space.

Specify 0.0 to not use the capability.

If 1.0 is specified, the following additional input :

requi red.

I NREG 242 None Number of operating space regions (maximum is 5) i

$-9

t Relative r

Parameters Address Units Descriptions i

I REFLO 243 g.p.m.

100% design cohe flow rate in g.p.m. divide <

2 by core flow area ft FF(J)I 244-248 None Channels 2,3, and 4 inlet flow factor J =1,NREG for each region of operating space.

(Referred to as hot assembly flow factor) l 00J=1,itREG Provide fo'- each region of operating space where:

Ranges on 'raction of 100% design core flow, inlet temperature i

K=(J-1)*12 system pressure, and AS1 :

t 249 - 308 4

s 4

IBF(J)I (249+K)

None Types of inequalities applied to limits of the design core flow range 1: lower limit < core flow 5, upper limit 2: louer limit < core flow < upper limit 3: lower limit 5 core flow < upper limit s

4: lower limit < core flow < upper limit i'

BFL(J)I

'(250+K)

None

' Lower limit fraction of 100% design core flow rate.

BFR(J)I (251+K)

None Upper limit fraction of 100% design core flow rate.

L -

i l

q l

l i

l Relative Pa rameters Address Units Descriptions ITI(J)I (252+K)

None Types of inequalities applied to limits of the inlet temperature range, same as IBF.

TIL(J)I

.(253+K)

F Lower limit inlet temperature TIR(J)I

- (254+K)

F Upper limit inlet temperature IPS(J)I (255+K)

None Types of inequalities applied to limits

'of the system pressure range, same as IBF.

PSL(J)I (256+K) psia lower limit system pressure

'PSR(J)I (257+K) psia Upper limit system prdssure IAS(J)I (258+K)

None Types of inequalities applied to limits of the A.S.I. range ASL(J)I (259+K)

None Lower limit A.S.I. range ASR(J)I (260+K)

None Upper limit A.S.I. range A

e 9

e

t i

A.4 Sample Input and Output A sample input and output are attached using the model given in Figure 5,7. A~

definition of the titles used in the output is shown below.

,I l..

CASE = CETOP-D case number NH = Enthalpy transport coefficient at each node Hi = Enthalpy in Channel 1 H2 = Enthalpy in Channel 2 H3 = Enthalpy in Channel 3 H4 = Enthalpy in Channel 4 QDBL =-core average heat flux, represents total heat generated from densification) Btu /hr-ft{uel rods are corrected (for axial rods and coolant, where

- for core power iteration, the heat flux at the end of the last 4

iteration is printed.

For no iteration, core flow iteration, and radial peaking t

factor iteration, the heat flux given in the input XLOC(2) is printed.

POLR = for core power iteration, the ratio of the core average heat flux at the end of last iteration to the core average heat flux at 100% power is printed.

~

For no iteration, core flow iteration, and radial peaking factor iteration the ratio of XLOC(2) to the heat flux at 100% power is printed.

TIN =

Inlet temperature, F

PIN = System pressure, psia 6

2 GAVG = Core average mass velocity ( 10 lb/hr-ft )

- for core flow iteration the c:s velocity at the end of the last iteration is printed.

ASI = Calculated axial shape index based upon axial shape factors input.

i i

i

• J NRAD = 0, core power iteration, if address (74) is 0.0 there is no iteration

!~

1, Channel 2 radial peaking factor iteration 2, core flow iteration PIMAX = maximum rod radial peaking factor ',n Channel 2

- for radial peaking -factor iteration the max. peak at the end of the last iteration is printed.

DNB-N = hot channel MNDBR at last iteration X-N

= coolant quality at location of DNB-N U

DNB-1 = hot channel MDNBR at first iteration X-1

= coolant quality at location of DNB-1 QUIX = QUIX file case number ITER = Number of " iterations" IEND = Specifies what type of limit or problem was encountered during " iteration".

1 = MDNBR limit 2 = maximum coolant quality limit 3 = no additional iteration is needed because the ratio of the present gu'ss to the previous one is within the window tolerance e

HTFLXTL, address 92.

H 4 = core saturation limit 5 = iteration has terminated because the maximum number of iterations has been reached.

6 = the new guess produced by the code during iteration falls

~

below zero.

This may occur if the derivative on DNBR and Quality are not close to the actual values.

ATR

= Average enthalpy transport coefficient over the total channel axial length.

HCH

= MDNBR hot channel number, if 3 is pr.inted this means

[

l MN00 = MDNBR node. location CESEC~ TIME = This parameter is printed in the output when the CESEC code l

1s linked with CETOP-D.

t '-

i

}

I FSPLIT. = this is thefinlet flow factor (in channels 2, 3, 4) chosen by the code for operating conditions specified'in the,ing This value is printed

~'

when.the capability for changing the inlet fis, : actor for different regions of operating space is used.

The following parameters are also printed

.I -

to show that calculated fraction of 100% design core. flow is within the l

operating space given in the input.

the calculated fraction of 100% design core flow GAN

=

2 the calculated core average. mass velocity, Ib/sec-ft GIN j

=

l;

-VIN 3

inl'et coolant specific volume, ft /lbm

'l 6

U.

5 k

4 6

'~

1 f

s.

i f

i f

4 m

~

~w g-

'1 e

I i

I i

a 1,

4 Appendix B Sample CETOP-0 Input /0utput 1

e 4

O W

O e

s a-]

b k.

k h*

I

- - - - - = = =. =-

--- ** +-+-~~ -

-=

,=

4 Ayu-/C)(O 2 e plp*P tlP. PdO*4 t N A L - (. 0 7 0 4 91 ) ---

C A.4 t e - - - -- e 7 0 --

~ - - - - - -

I Nuof-

--- ce

,4 g I

~

a q

(

I l.t127 551.55o1 551.5501 558.ssol SSI.'Sul 551.5501 551.5501 2

1.5163

-. %5 ). 5 0 7 6 - --- 55 4 ; t 7 6 7 55eso430-

-- SS4.13 MS

-- 55 4. o n67 --- - 552;915 4 - - - - - - ~ ~ - - - - - - - -

3 t.6217 SSh.2990 557.7566 557.5010 557.69M9 557.3na) 55c,n9ee 4

t.0215 5%9. 7 %9 8 --- - 5 6 '. 0 P 5 3

- 561. 7 3on - -- 562;0716 561. e u M M -

- - 5 5 F e 317 0 --- --- --

4 2.l*%)

565.6135 5%n,***7 566.3902 566.7396

'jhS.87Me 559 96g

); # F e. 7 S e F ; ? ts.,

171 r5ves.:

573236M9 SFt;5eSt

%FMF345

~.n27 591 7

n---------

F 4.2971 573.959 576.314#4 575.9353 576.3054 5 7 4. #.5 n 6 SnS.A296 M

%.SF/9-

- 5 7h;19/ t --

% *! !. 0 519 - - -- S M 0 ; 6 9 4 2 -- - So l.0516-

'i 7 9.17 M e - -- S e M. S c 3S "-

9 7.llM2 S et o. q u ?

$95.7532 SMS.4e99 Sc5.7h03 5 A 3.ht 10

%Ft.36%M 3o Ia.o657 S a e. F b.2 -

,590.17 l 1 --- -- - 590.1322 5 9 0. I M 2 9 --- - S n F. *S n 2 - --- S74;22Su - - - - - - - - - - ----

11 s?..'421 5 A M 9 9 e' d 594.7mpn S94.6936 594.7M24 S8/.1//I SFF.0463 82

-- #9.JFe3 5944176#6 599stA2c 599.o77=

N99,tSSg

$9ng46Mt SF9sagio

.r.

13 60.5977 597.lo26 605.4956 603.4505 603.e391 600.5213 Sa2.SMo9 la

-183.13n4 col. ant?

607.7166 -- --

607.7?dS 607.6290-604.5no6

-- - 5 sa S. 2 M 4 4 -----

-- - -- l IS

-St.Il00 6 0 5. 4 t.14 6tl.FF64 6tt.M378 611.6426 60M.3Fa6 SM7.9479 16

-5d.6195

. 60w.n%2n

-- h t S. M i e 9

-615.9242 - - - 635.6367 682.3nM2 S90.5643 --- -

--l 17

-/M n? Set 613.e95 619.M601 639.9867 619.6117 636.1533 59 3. 2 te 95

-. I a - - - - 2 5. M ie

• 9 ilFr4993 e2%vado; 123r96Fe 623:5042 619;9h90

^95t" W

, p 19

-2d.FF75 671.1533 62F.9159 6?F.9746 627.o379 623.ehob 598.coi2 20

-74.1543. -

625.3n94 ---- -- - 6 31 8 214

-638.9A92-631.3955 627.7527 6 01. 0 9 0 6 -- ---. --- ----

21

-25.o955 6?v.2MM9 615.A559 636.0253 635.3578 631.6275 6n3.7336 27

-7%.e620

• 13.3417

--- -- 6 3 9. A 9 71 --- - 6 a n. o 6 g 5. -.

639.33?S

-- 635.5S20 euh.et97 - - --

3 25

-/9.837 637.aore 644.0522 6ers.2040 643.822F 639.5925 609.1490 24 - -

-47.113%

641.s7ee s o n,.4161 6en,es99 e.47.6427 64517212 198r84394 25

-16.9057 6 e:S. R? b5 652.6933 652.M260 658.9568 647.93%6 014.7659

/6

-44,t956

- - -- 6 s o, t a l e - -- - A5 7. 0 9 6 4

---. 6 5 7. 2 n 9 A - -- -- a S h 2 9 8 2 ---- - 6 S 2. 2 410 ----- - h l 7. 6 M H 8. -- - - - - - - - - -

27

-S%.2/Il osa.%n92 663.6733 6 61. 7 e,71 Ano.MlFS nSh.haq7 620.6763

g.

2M

-a,2. 5 7 6 7 -. 659 ta77 666.4339

.no6.a983.-.. e.n5.5tsa

.#.63.2513

- 62 5.7 Sl 6 -- - -.-- -- - -

/4

-77.SM55 663.AM74 671.3264 673.3942 670.3Mu9 665.9326 020.90e6 30

-- - l / 7. 91 s t 4.

a.7ps?

626.gost tFA 3ame 6Fs.29t=

679r 773

• 4 0 er l e 6.a 7

31

-229.5362 673.7161 681.5153 651.58 28 vHO 4521 675.7979 633.e936 g.

32

- 2 ess. 9 5 M e

---. 6 7 M. M M i s.. -

6AA.9046

- - 6 8 6. ad 2 7 4 -.--. -- 6 3 5. M o 2 7

- n e d. u T 4 8 --- 6 l b. 9 3 8 9 - - ---- - - - - - --

31

-57a.na59 6A4.1995 692.e733 692.4MS7 691.3226 6at. 2M70 640.4337 3d S"*

1. ^58

~'*"****Id-

'--698.u589 698.02'8

- a vei.M I S2---

691. F o lm

- 643.97/4 - -

t 3%

lla. 2Ms s o's. s.

3 5 7813.710#l 7o3.6911 7o2.4315 697.1733 647.5649 36.....

273.62ns_.

Tou.uASA na u.d w /;t

?oo.as7e 7 s,a.15 E e 702:5740 651.9464 37 ApM.2290 705.7172 115.0945 7tS.nno6 7 3 3.6 A S4 707.3165 654.5u92 g-39

- 7/. 2 3 %..

7 n. M Ato _.

720.3342 7 2 0. a u t F = -.. -- 7tA.9034.

- 7 9 2.n298, e *. F. A 4 % 2 ---.----

39

-16.0092 715.hM27 72%.0152 725.2078 721.5A95 717.3938 660.6090 a0

-2S.9911

.._. 739. goon.. -... 7 2 A 5 9 6 3 -- - 7 29. t 7 9 0

.. 7/7 a2:5 - - -723.7837.-

nn3.237=

.. ~

7 at

./n./ u t 775.Ina7 731.e430 759.Aue9 729.8419 723.M697 664.Ma%I 8'bt5 hin 6 A v r.

AMI N64 4 f 3 PtMat f X-N D este - 1 it -; outr IfLH I Esau A r ne n e Ma on CASL o imL

! ! '4 s

j

.g a y o 25 e rs a3a,

1,3451 553.5 7750.

2.59ti n o. 0 6825.--

.o 3.a982 L

. 0 229 - 2.1

• a6

.oeF2 n.

=..-..I

.11.2 a. Se 1

Cf St C 1 I Mt a 30.no

- - - - - -. - - - -.. - - - - - - - - - - - l

-...~.

. a-.

,. -- - - - - - - -.._.__,,_,j

..(

e

..g

' ~ ~

e70 aml-2 CYCt.E 2 g F*utte UP. Nf tM I N a t,. (~ 0704S3) l-

-42;%*aat tA**5e

'Al f, 2 25 t;.

26 29.e> 24 4

.It9 2069 30t9

... -..,,9g,....... s n c 9.-

6nta 30 3 g, p.,,

34 4%.7764 4717 9667

--- - --~~ - - - - - - ' - ' - -

as a v. 7%.in n 0dphn

.0 n7925 --

.04 3 R15 50 5524.ea$

6.271 532

.t23tl

- 4 4 --' S 7 2 c. n a -

'., - 4 0

.fF99 0 M 5 t ".,

SR 618.gv:2 t,ogeo 1.0000 1.0

~ ~ - - - ~ ~

~ ~ ~ - - ~ ~ - -

67 6 5 3. e.5 % t 0

- - - t ; o 7 2 t o -------

bu 677,sgo%7 3,8742

.oRR9M 027135

- - --*-~~~~

6M 7p.onn166

- - -.102%0

--.04058 71 F 3:49, 4

I t '.

10 7 % ---7 6 0. -

n.

77 Mut?,e750 0 392 st 25 975 1.00000

-- - - - ~~ - - - - - -

- - - - - ~ ~

el Me.hou 0.04006 - ---.t:5 7 02

- 92.A439 MS Ant./so

.4 005 750

~

A9 925 005 1133434 - - - l.001 94 410.04 0.000000 0.0000 0.0000 94 8011.000 f.

l.

^.

in2 leis.ta9a56 0.0 0.0 3.

- - ~. -

los

Iogg, g,.

...- -..g,-.

t4 llo till.

3.

l.

l.

tia 3 t e.

.. 3.

3p

)

tIo 1Po.%9 0

O.

- l?9 3528.on200 1.074ne

. inst' 26414 135 Ith.ooF342

.0100'a56

.?t3a36 33IntI i

3 tuo toons.

141 1940.000 6375 0625

.oA75 145 143.112%..

-.1 3 7 5. --

.th25-1875 -

l#9 152.2t25

.23T5

.2625

.2875

_.153_156.3125 4175 2 8.J '-

3AJS IS7 16u.4325 4375 4625 4 8t F 5

=--

- + - - - - - - --

th.

Ies.5125

. 5 3 7 5.....

%h25 5AF5-165 16 8.e. t 25 6175 6625 6875 lb9 172.7125 7575. - -... 7 6 7 5 -..- -

. 7 s T 5 - - -

3375

.A675

.MMT5 175 tTh.Mi/5 377.

Ino.9l25

,937s

. u s. 2 e 9474 tel

? Hit.opo

- - - - - - - ' - ~ ~

198 198.3900 7 0 0 0....

-.8756 9600.-.

19%

19et.no%

t.050 1.050 1.025 199 2n28.o20 1.u05 0050 -.

9750..

~ _... _..

205 2nv.,96 in 9eSo 9550

.*100 207 2 t o.9 50c.

.nana 93ue 9$$a 211

?!4.9%0 9656 9M50 1.00%

I 215 2168.025

. 1.050.

1.000..

3.1 1 0 -.- -. - -.

219 222t.len 1.175 1.205

1. 2.4 % -

l.2an f l et s. - -.

225 22o1.255

1. 2 #. 0

??F

/405.194 99%0

.A250 5700

__. 2 3 8 238.5700 t 91 9ttu.

-..-6 e

w ap b-

&.