ML20040D013

Nonproprietary Version of Revision 1 to CETOP-D Code Structure & Modeling Methods for San Onofre Nuclear Generating Station,Units 2 & 3

ML20040D013
Person / Time
Site:	San Onofre
Issue date:	09/30/1981
From:	ABB COMBUSTION ENGINEERING NUCLEAR FUEL (FORMERLY
To:
Shared Package
ML19297F285	List: ML20040D011 ML20040D013 ML20040D016 ML20040D018 ML20040D020
References
CEN-160(S)-NP, CEN-160(S)-NP-R01, CEN-160(S)-NP-R1, NUDOCS 8201290479
Download: ML20040D013 (77)

Text

r g'

-f

- a

+

N

'i>\\

i.

San Onofre Nuclear Generating Station Units 2 and 3 Docket No. 50-361, 50-362 Cell-160(S)-NP REV.1-NP CETCo-D CODE STRUCTURE AND MODELING hiETHODS FOR SAN ONOFRi NUCLEAR GENERATIflG STATION UNITS 2 and 3 J!*

Sept. 1981 i-i f.

COMBUSTION ENGINEERING, INC.

flVCLEAR POWER SYSTEMS POWER SYSTEMS GROUP l

WINDSOR, CONNECTICUT 06095 8201290479 820122 PDR ADOCK 05000361 A

PDR

\\

LEGAL fiOTICE This report was prepared as an account of work sponsored by Combustion Engineering, Inc.

fleither Combustion Engineering

~'

nor any person acting on its behalf:

A.

Makes any warranty or representation, express or 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.

Assuma's any licbilities with respect to the use of, f

or for damages resulting from the use of, any information,

{

apparatus, method or process disclosed in this report.

e e

f g

e 9

4 6

m mm

3 I

ABSTRACT The CETOP-D Computer Cude has.been developed for determining core thermal 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 differs from the TORC -

design model (described in Reference 5 and referred to herein as S-TORC, for " Simplified" TORC) by its simpler geometry (four flow channels) yet faster calculation algorithm (prediction-correction method).

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

To produce a design thennal margin model for a specific cere, 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, the CETOP-D and Detailed TORC predicted hot channel MDNBR's are compared, within design operating ranges, for the C-E SONGS 2 and 3 reactor cores, comprised of 16x16 fuel assemblies.

Results, in tenns of deviation between cach pair of MDNBR's predicted by the two models, shcw that CCTOP-D uith the inclusion of tnc " adjusted" het assenbly flcu factor, can predict either conservative or accurate MDNSR's, compared with Cetailed TORC.

l 6

i L

. _.,_ _,, ;. m-

-=

s 9

4 i

TABLE OF CONTENTS j

Section Title

. Page ABSTRACT-i' TABLE OF CONTENTS 11 LIST OF' FIGURES iv v

LIST OF TABLES vi LIST OF SYMBOLS 1

THEORETICAL BASIS 1-1 1.1 Introduction 1-1 1.2 Conservation Equations 1-2 1.2.1 Conservation Equations for Averaged Channels 1-3

~

1.2.2 Conservation Equations for Lumped Channels 1-5 2

EMPIRICAL CORRELATIONS 2-1 2.1 Fluid Properties 2-1 2.2 Heat Transfer' Coefficient Correlations 2-1 2-2 2.3 Single-phase Friction Factor 2.4 Two-phase Friction Factor Multiplier 2-2 4

I 2.5 Void Fraction Correlations 2-3 2-4 2.6 Spacer Grid Loss Coefficient 2.7 Correlation for Turbulent Interchange 2-4 2.8 Hetsroni Crossflow Correlation 2+7 2.9 CE-1 Critical Heat Flux Correlation.

2-7 j.

3 NUMERICAL SOLUTION 0F THE CONSERVATION EQUATIONS 3-1 l._,*

3.1 Finite Difference Equations 3-1 3.2 Prediction-Correction Method 3-2 4

CETOP-0 DESIGN MODEL 4-1, 4-1 4.1 Geometry of CETOP-D Desgin Model 4.2 Application of the Transport Coefficient in 4-2 the CETOP-D Model 4-4 4.3 Description of Input Parameters 5-1 5

THERMAL MARGIU ANALYSES USING CETOP-D 5-1 5.1 Operating Ranges 5.2 Detailed TORC Analysis of Sample Core 5-1 5-1 5.3 Geometry of CETOP Design Model

4 TABLE OF C0iiTEtiTS (cont.)_

Section flo.

, Title _

Page No.

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

C0llCLUSIONS 6-1 7

REFERENCES 7-1 Appendix A CETOP-D' Version 2 User's Guide A-1 Appendix B Sample CETOP-D Input / Output B-1 4

9 e

e.

9 8

9

t e

LIST OF FIGURES Figure No.

Title Page No.

1.1 Control Volume for Continuity Equation 12 1.2 Control Volume for Energy Equation 1-13 1.3 Control Volume for Axial Momentum Equation 1-14 1.4 Control Volume for Lateral Momentum Equation 1-15 3.1 CETOP-0 Flow Chart 3-3 3.2 Flow Chart for Prediction-Correction Method' 3-7 4.1 Channel Geometry for CETOP-0 Model 4-2 5.1 Stage 1 TORC Channel Geometry for SONGS 2 and 3 5-3 5.2 Stage 2 TORC Channel Geometry for SONGS 2 and 3 5-4 5.3 Axial Power Distributions 5-5 5.4 Inlet Flow Distribution for SONGS 2 and 3 5-6 1

l-5.5 Exit Pressure Distribution for SONGS 2 and 3 5-7 5.6 CETOP-0 Channel Geometry for SONGS 2 and 3 5-8 0

i iv

s 4

LIST OF TABLES Table No.

. Title Page flo.

2.1 Two-Phase Friction Factor Multiplier 2-8 2.2 Functional Relationships in the Two-Phase 2-9 Friction Factor Multiplier 5.1 Comparisons Between Detailed TORC and CETOP-D 5-9 e

S 9

V

4 LIST OF SYMBOLS SYMBOL DEFINITION A

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

Diameter of fuel rod De Hydraulic diameter DNBR Departure from nucleate boiling ratio DTF Forced convection temperature drop across coolant film adjacent to fuel rods DTJL Jens-Lottes nucleate boiling temperature drop across coolant film adjacent to fuel rods f

Single phase friction factor F

Force f f,f Engineering factors g p 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_

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

Axial power factor, equal to the ratio of the Z

local-to-average axial power.

g Gravitational acceleration G

Mass flow rate h

Enthalpy

'~

k Thermal conductivity K

Spacer grid loss coefficient g

K)

Crossflow resistance coefficient g

K=

Crossflow resistance coefficient i

Effective lateral distance over which crossflow occurs between adjoining subchannels MDNBR Minimum departure from nucleate boiling ratio m

Axial flow rate N,N.fl Transport coefficients for enthalpy, pressure g p u and velocity i

M

SYMBOL DEFINITION P

Pressure P

Heated perimeter h

Pr Prandtl Number PW Wetted perimeter q'

Heat addition per unit length q"

Heat flux Re Reynolds number s

Rod spacing or effective crossflow width s

Reference crossflow width REF T

Bulk coolant temperature oggj T

Saturation temperature sat T,,jj Surface temperature of fuel rod u

Axial velocity u*

Effective velocity carried by diversion crossflow v'

Specific volume V

Crossflow velocity w

Diversion crossflow between adjacent flow channels jy wh Turbulent mass interchange rate between adjacent flow channels x

Axial distance X

Quality a

Void fraction y

Slip ratio p

Density

.~

4 Two-phase friction factor multiplier tj Heat Flux c

Fraction of fuel rod being included in flow 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 k'

P Denotes Fredicted value

r O

+

SUPERSCRIPTS DEFINITION Denotes transported-quantity between adjoining lumped channels Denotes transported quantity carried by diversion crossflow Denotes ef fective value O

W

'9 e

9 4

e p

4 O

viii

~

1.0 THEORETICAL BASIS 1.1 Introduction The minimum value for the departure from nucleate boiling ratio (MONBR) which serves as a measure for the core thermal margin, is predicted for a C-E reactor by tre TORC code (Thermal-Hydraulics of a Reactor Core, Reference 1).

A multi-stage TORC modelling method (Detailed TORC), which produces a detailed three-dimensional oescription of the core thermal-hydraulics, requires about cp (central processor) seconds for each steady state calculation on the C-E CDC 7600 ccmputer. A simplified TORC modelling method (S-TORC, Reference 5),

developed to meet cractical design needs, reducts the cp time to about((saccads for.each calculaticn on a 20-channel core representation.

Such a simplification of the modelling method results in a penalty included in the S-TORC medel to j

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 noncanservatism 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 lame 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 1

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 l

its predecessor, S-TORC,: (1) it uses " transport coefficients", serving as weighting factor:, for more precise treatmentr. of crossficw and turbulent mixing between adjoining channels, and (2) it applies the " prediction-correction" method, which replaces the less efficient iteration method used in S-TORC, in the determination of coolant properties at all axial nodes.

1-1

A finalized version of a CETOP-D model includes an " adjusted" hot assembly flow factor and allows for engineering factors.

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

A statistical or deterministic allowance for engineering factors accounts for the uncertainties associated with manufacturing tolerances.

.~

1.2 Conservation Equations A PWR core contains a large number of subchannels which are surrounded by fuel rods or control 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, subchannels are said to be hydraulically open to each other and a PWR is said to contain an open core.

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 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 ficw channels.

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

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

1-2

1.2.1 Conservation Equations for Averaged Channels 1.2.1.1 Continuity Equation 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:

am j + (mj + ax dx) - w'jjdx + w'jjdx + w dx = 0 (1,1)

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

amj

=-w)

(1.2) j 3x Considering all the flow channels adjacent to channel i, and taking w jj as positive for flows from i to j, the continuity equation becomes:

am N

I ij ; i = 1, 2, 3,..,N (1.3)

I w

=-

ax j=1 1.2.1.2 Energy Ecuation The energy equatiQn for channel i in Figure 1.2b, considering only one adjacent channel j, is:

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

-m hj 5 + (m h5+

jj jj j

ax where h* is the enthalpy carried by the diversion crossflow w jj.

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

as:

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ l -_3 _

4 Ohi mi

=q'1. - (h -h ) v.'..+(h -h*)w..

(1.5) ax i

j 1]

i 1J Considering all adjacent flow channels, the energy equation becomes:

a b'.

q ' '.

N w'..

N wId (h -h ) m 'J + r

( h. - h* )

(1.6)

E

=

i j

1 m

ax m

j j_)

j g

3,)

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

(p Ajj+

p A dx) =

-F dx 4 p dA - gA p dx +

pA jg j

j j

jg j j

- n u dx)-w'),u dx + v'gj ju dx + w u*dx (1.7)

-m u 4 (m u

+

gj jj jg g

jj where uw = 1/2 (u +u,).

j J

By using the assaniption w' jj=w'j j, one has:

a p '.

=h mu (u -u )w'$3 + u*w )

(1.8)

-F - gA o

-A 4

j j

j jj j

gg 5

Substituting the f ollowing definitions:

2 Ar m

A vj f c5

• ~g.c j v ; )(~ '.' )

(l*9) m vpg j

j

~

g g

j;7,-;Fj s 2De.

u r

2h A

1 1

1 and Eq. (1.2) into Eq. (1.8), one nbtains:

Dpi m;

2 vj f;h Kgjv; vp;

~ 9^i i (*

}

• ^i S A

( A'1

~}

• ~ A (TC )

b A

i Ox i

2Dc.

2ax 1

1

- (u -u ) w'jj + (2u -u*)w )

j j

j j

1-4

9 Considering all adjacent channels, the axial momentum equation becomes:

g"-({m;)2 f eg + Kg v4 + ^i 3p vj vp,}

j j

3

~ 9#1 20e 2ar ax ax A

g j

N w'

N w

(1.11)

(ug-u ) A j

(2"i-"*)A E

+ E j=1 i

j=1 i

1.2.1.4 Lateral Momentum Equation For large flow channels, a simplified transverse momentum equation may be used which relates the difference in the channel-averaged pressures pg and p3 to the crossflow w ).

Referring to the control volume shown j

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

"ij!"ij!

(Pj-P ) " Kij 29 sd p.

(1.12) j where K is a variable coefficient defined in Reference 3 as jj 2

gj = (

2 u.

1/2 K

+ XFCONS

+

2 (1.13)

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

g 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.

1.2.2 Conservation Equations for Lumoed Channels l.2.2.1 Continuity Equation Since only mass transport is considered within the control volume, the continuity equation has similar form to.that for averaged channel, i.e.,

Eq. (1. 3).

1-5

1. 2.2.2 Eneroy Equation Consider two adjacent channels i and j and apply the energy conse'rvation to channel i within the control volume as shown in Figure 1.2.a. the energy equation has the form:

I ah

= q' j - (li -li ) w' j) + (h -h*) wjj (1.14) m g j

j j

where q' = energy added to channel i from fuel rods per unit time per unit length, w'$3 = turbulent interchange between channels i and j h w'$3 = energy transferred out of channel i to j due to the j

turbulent interchange w'$3, h w'$3 = energy transferred into channel i from j due to the j

turbulent interchange w'$3, h and h are the fluid enthalpies associated with the turbulent interchange; j

j h* is the enthalpy carried by the diversion cross-flow w and is determined jj as follows:

h* = li if wjj _0 (1.15) y j

h* = Ti if w ) < 0 j

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, n and T1 j

3 are defined as the radially averaged enthalpies of the boundary subchannels of lumped channels i and j respectively.

J Since h and h) are not explicitly mlved in the calculation, we define j

a transport coefficient N to relate these parameters to the lumped channel g

counterparts hj and h) as follows:

hj-h3 N

(1.16)

H"h-j - h)

The parameter N is named the transport coefficient for enthalpy.

g Using this ccefficient, one can assume the coolant enthalpy at the boundary:

1-6

hg+h.

E+E 3*

j 3

(1,17) h

=

c 2

2 m

and h

-h E-h (1.18) i c

2 h

-h (I*I )

h) - h c

2 which are followed by the approximations:

h4=h (i-h) c g

hg+h3+hg-h3; (1.20)

=

2

<. N g

hj=h +(fi - h )

c j

c

-(1.21) hg+h3 3-h4 h

=

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

h -h h

(h -h )n

= 4'j - ( j 3 ) w' jj +(h -( j +h.2'~~+

2N j

(1.22)

)

W m j N

j ij H

where n = 1 if wjj > 0 and n = -1 otherwise.

It should be noted that if channels i and j were averaged channels, N = 1.0 for this' case, Eq. (1.22) reduces to the Eq. (1.5) in Section g

1.2.1.2.

~

1.2.2.3 Axial Momentum Equation Consider two adjacent lumped channels i and j and apply the axial momentum-conservation law to channel i as shown in Fig. 1.3a.

3p j-g.jj-@j-E)w'jj+(2u-u*)w (1.23)

A

=-F A

i ax j

j jj 1-7

_7

~

v where:,A' channel area,

=

9 pg radially averaged static pressure,

=

g_

gravitational acceleration,

=

p coolant' density,

~

=

axial velccity carried by the turbulent interchange u.

=

"'ij

~

channel radially averaged velocity u

=

F g momentum force due to friction, grid form loss and

=

2 9 f'.

KGi i + A a mi ~)

i densi,ty gradieni, wnere F$=A$ (4i v

v i1 i

Di

{20e

+ 2ax ax (A

)]

9 4

if w.> 0 defined as the vel.ocity carried by diversion crossflow, {u*=u_i iJ-u*.

=

u*=uj if wgj<0 As for h and.h l

j j, u$ and uj can be regarded as the averaged velocities of the boundary subchannels of the luriped. channels i and j respectively.

l Define the transport coefficient for axial velocity, fl, as follows:

u u -u j

3 N

g (1.24)

=

u -u j

j Using similar proce ures in thie.japproxirNtion of E and h in terms of j

j h, h), and ti, as descrRed from,Eq.,(1.17{ 6 0.22), we derive:

g

~

4 u 7, "i 3

u, - u3 (1.25) i 2

2ti U

r

'~

and g + u) u u3-u4 w

u) =

2 2N (1.26)

+

U Inserting Eqs.'(1.25) and (1.26) into Eq. (1.23), results in thd axial momentum equation for, lumped channels:

a'pI j

(ui-u)n

= - F. - A gs.,.(:,jd ) w' jj +(2u -(u +u].

. u -u.

j A

_),) w,

a

-1 1,

ti j

i

.ax' 2

2l4 IU g

'0 (1.27)

+

s

.y.

where n is ~defingd in Eq. (1.22) s u m.

tr 1-8 s

%g 4 y

1.2.2.4 Lateral MomeFEm 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 dive'rsion crossflow momentum fluxes entering and leaving the control volume through the vertical surfaces sax is negligibly small, the formulation for lateral momentum balance is:

sax t p sax = -(p*stu

• V)

+ (p*stu*V) p3x (1.28) jj-iij

-F j

Making use of the definition of the lateral flow rate w.. = o* sV IJ Eq. (1.28) becomes, after rearranging:

F..

a(u*wjj)-

(1.29)

(II '# ) = s x' j

3 sI u

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

i *i ijlWij l f

w K..

(1.30)

=

sax IJ 2

29 s Substituting Eq. (1.30) into Eq. (1.29), and taking the limi t as ax-0, Jj. l w. l w

Jj 1

a (u*w..)

(1.31)

(P - p ) = K..

+

j IJ 2

s/t ax ij 29s where: ii = channel averaged pressure, K

= cross-flow resistance coefficient, jj w

=.deversion cross-flow between channels i and j, jj s

= gap width between fuel rods, t

= effective length of transver5e momentum interchange, u*

= axial velocity carried by the diversion cross-fic"..

w..,

IJ assumed to be (u +u )/2 j

j density of the diversion crossflow where 1,. ~r. ; ' "i j $

J p*

=

A * : 0,.

• w. <0 s

1-9 iJ t

The above equation is equally well applied to two lumped channels when each j

contains a certain number of subchannels arranged as shown in Figure 1.4a In this' case, the diversion cross-flow w and the gap width s should be jj expressed by :

I ij"(fi) (cross-flow through gap between two ad.iacent rods).

(1.32)

W s=(ti) (gap between two adjacent rods)

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

For the case of two generalized three-dimensional lumped j and p3 are regarded as the radially averaged static channels, parameters p pressures of the boundary subchannels of the lumped channels i and j respectively. As shown in Fig. 1.4a., the transverse momentum between two generalized lumped channels are governed by the following equation:

l l

(

• ij}

(1.34)

Id Id pi - p = K ].

2, s

+

j i

2gs 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 two cases are identical.

Since and p are not' explicitly calculated, we define the transport coefficient pg j

for pressure to relate these parameters to the calculated lumped channel parameters pg and p) as follows; p - pd I

(1.35)

N

=

p pj - Pj where p and p are the radially averaged static pressures of the lumped channels j

j i and j respectively.

Inserting Eq. (1.35) into Eq. (1.34), we obtain the transverse momentum equation for three-dimensional lumped channels as follows:

jjh l

1 3(u*wjj) pj-p W

ij O'M

• K

+

~

N 1j 2

sa x p

2gs p*

Ata

b..,

-- s 1.2.2.5 Transport Coefficients There are three transport coefficients fl ' "U and fl in Eqs.' (1.16), (1.24)

H 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;j are insensitive to the values used for t!g and il.

This conclusion j

j p

is further confirmed for the three-dimensional lumped channels.

Therefore, the values of fl and ri can be estimated by a detailed subchannel analysis end used g

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

It is, however, "not the case for fl, whose value is strongly deoendent upon radial power distribution g

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

A value of li can le calculated by using a detailed subchannel TORC analysis g

to determine h, h, h, hj and !!g for use in the CETOP-D lumped channel analysis.

j j

j However an alternate method is used in CETOP-0. utilizing the power distribution and the basic opert. ting parameters input into CETOP-D to determine fi for each g

axial finite-differen'ce node. [

~

] ~[

a ah-w h5

-g 4

W O

g

/

k y

1

(

s e

4 1

1-11

dm; mj+

dx dx

. _ _ _ _ _A_ _ _ _ J,

~

i a

I I

d l

• Wjix CHANNELi l

I i

CHANNELj CONTROL i

I VOLUME 9

1 dx i

wj;dx i

=

I I

i "Wjdx i

I mi l

U A

Figure 1.1 CONTROL VOLUME FOR CONTINUITY EOUATION 1-12

9 9

o-0 m;h; +

m;h dx dx

. _ _ _ _ A _ _ _ _ f, i

l l

l 4

i i

l i

I

-L ' w;j 'dx h

CHANNELi CHANNELj CONTROL l

1 VOLUME l

l l

I q;dx dx

=

I wj h dx,'

1-I

+

j I

I

-dl l

'I5 d wij i x I

\\

\\

\\

i M ll l

m h; I

I n,

u BOUNDARY SUCCHANNELS (A) CONTROL VOLUME FOR LUMPED CHANNEL m;h; +.$_ m h;dx dx A

I l

h CONTROL l

> "ij 'dx VOLUME l

l l

CHANNELi CHANNELj l

l

> q;dx l

dx-I

+

l wf;h;dx j

I I

I hd i

= wij j x I

I m;hi l

i I

I i

l A

U l

(G) CONTROL VOLUME FOR AVERAGED CHANNEL i

l Figure 1.2 CONTROL VOLUMES FOR ENERGY EQUATION L

m;u; + _$_ m u;dx dx 0

p;A; +

p;A;dx

. _ _L _ _f_ _ _ _ h,

^

i l

l l lI l

i l

w;;u'dx j

l-l-*

CONTROL / I I

l VOLUME I

i i

i I

CHANNELis I CilANNEL j F dx I V

i l

I gA; p ; dx dx

-l I

i I

1 1

I l

w;;G dx Yl e

j I

l-w;;G dx pidA; j jl j

l m;u-l i

!..h V

_ _ _g.

3 - - -

BOUNDARY SU3 CHANNELS Pi^i I

(A) CONTROL VOLUME FOR LUtaPED CHANNEL m u; + 0 m u;d.:

dX

. _ _h _ _.h _ _ _.

p ;A; +.$_ p;A;d::

CONTROL VOLUME

-e= w;;u'dx I

i* l CHANNELi CllANNEL j g

l gA;p dx dx l

d 4

l w; uj x j

l l

> w;'Iu;d::

.n' P idA;

~-

I m;ug i

i p;A; I

_gj = _ _ _ _ _ __

b (D) CONTROL VOLUAiE FOR AVERAGED CHAfJNEL Figarn 1.3 CONTROL VOLU:.iES FOR AXtAL i.iCf.iEi?TUM EQUATION 1-14

u'x+dx

?.,

g i

a i

l O O O o'O O O cOu1ROL i VOLUME I Pi s

I p

l j

i OOOOOOO i

I f

I i

pisdx iisdx dx j

• -l j

g p;

p Fii CHANNELi CHANNELj CllANNEL i l l CHANNELi g

l l

l I

I U

I TOP VIEW g

h V,

u SIDE VIEW x

(A) CONTROL VOLUf.*E FOR LUMFEO CHANNEL h

l l

l I

I I

i r-----

l l

I l

8 I

I I

l p'-

-*J Wpj dx l

pgM

> Wj f Pj l

i l

l l

l

-> V;j g

l L______a l

CilANNE L i

'CllANNEL j l

1 l

CHANNELi CilANNELi l

Y

'~

R d

d TOP VIEW SIDE VIEW "i

"j (B) CONTnOL VOLUME FOR AVERAGED CHANNEL Figure 1.4 CONTROL VOLUMES FOR LATERAL faOt.1ENTUM EOUATION 1-15

-.__-_-___._.--.m.

2.0 EMPIRICAL CCHRELATICMS CETOP-D retains the empirical correlations which fit current C-E reactors and the ASME steam tcble 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 of curve-fitted equations developed in References 7 and 8 for describing the fluid properties in the ASME steam tables.

In CETOP-D, these equations cover the subcooled and saturated regimes.

2.2 Heat Transfer Coefficient Correlations t

The film temperature drop across the thermal boundary layer adjacent to the surfeco of the fuel cladding is dependant on the local heat flux, the temperature of the lucel coolant, and the effective surface heat transfer ccefficient:

yg))

cool

-h -

( 'I)

DTF = T

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

0.8 0.4 h"0-g Sd k (Re)

(Pr)

(2.2)

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

60 (q"/10 )0.25 6

DTJL = (T

-Tcool)+

( 2'. 3 )

sat p/900 e

The initiation of nucleate boiling is determined by calculating the film temperature drop en the bases of forced convection and nuclecte boilir.g.

2-1

DTJL < DTF, nucleate boiling is said to occur.

2.3 Single-Phase Friction Factor The single-phase friction factor, f, used for determining the pressure 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) 2.4 Two-Phase Friction Factor fiultiplier A friction factor multiplier, e, is applied to the single-phase friction factor, f, to account for two-phase effects:

Total Friction Factor = 4f (2.5)

CETOP-D considers Sher-Green and Modified Martinelli-flelson correlations as listed in Tables 2.1 and 2.2.

For isothermal and non-l: oiling conditions, the friction factor n:ultiplier 4 is set equal to 1.0.

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

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

When this correlation is used, it is r.ot necessary to calculate the subcooled void fraction explicitly, for bulk boiling conditions, c is determined frca Martinelli.' elson resulta of Reference 12 uith modifications by Sher-Green (i'eterence 11) and by 2-2

~

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

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

1)

For pressures below 1850 psia, the void fraction is given by the

' ~

Martinelli-lielson model from Reference 12:

a=B + B) X + B X2+BX3 (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 = D) =B

=B

= 0; the homogeneous model is used for g

2 3

calculating void fraction:

a=0 For X 1 0 Xv (2.7) a For X > 0

" " (1-X)v7 + Xv g For the quality range 0.01 2 X.50.10:

-3

-72

-10 3 l

B = 0.5973-1.275x10 p + 9.019x10

-2.065x10

-2

-S 2 + 9.867d 0~9 3 B = 4.746 + 4.lS6x10 p -4.011x10 p

p I

-4 2

-7 3 (2.8)

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

B = 89.07 + 2.408p - 2.367x10~

+ 5.694x10~

3 3

p p

1 I

For the quality range 0.10 < X B = 0.7847 -3.900x10~ p + 1.145x10~

2

-II 3 p - 2.711x10 p

B = 0.7707

• 9.61?xlC~ p - 2.Ol M "-

2 I3 p 4 ?.^i">10 p

1 (2.9)

_2

_j p 8 = -1. 050 -1.19A x10 "p + 2. 610.< i o p

-6.833:a 0 )"p_,3 l

2

?-3

0.5157 + 6.506x10 p -1.938x10-7 2 + 1.925zl0-II

-4 B

p

=

3 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)

(1-X)vf+X vg 2.6 Spacer Grid Loss Coeffici_en_t_

The loss coefficient correlation for representing the hydraulic resistance of the fuel assembly upacer grids has the form:

K = 0) + D2 (Re)D 3

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

problem.

2.7 Correlation for Turbulent Interchance Turbulent interchange, which refers to the turbulent eddies caused by spacer grids, is calculated at channel boundary in the following correlation:

w'1J.. = if D (S

) A (Re)0 (2.12)

S e

REF where:

G = channel averaged mass flow rate D = channel averaged hydraulic diameter e

~

s = actual gap width for turbulent intcrchenge s

= reference gap width defined as total gap width pg7 for one side of a complete fuel bundle divided by the number of subchannels along this side Constants A and B era chosen as 0.0035 and 0 respectivel;. in the present version of CETOP-D.

2-4

4

2. 8 Hetsroni Cross Flow Correlation Berringer, et al, proposed in Reference 15 a form of the lateral momentum equation that uses a variable coefficient for relating the static pressure difference and lateral flow between two adjoining open flow channels.

jj j3lwj3l K

w (p g - p3) = 2gp*

2 (2.13) s In Berringer's treatment, the variable K accounts for the large inertial jj effects encountered when the predominately axial flow is diverted in the lateral direction.

In Reference 3, Hetsroni expanded the definition of K

to include the ef fects of shear drag and contraction-expansion losses jj on the lateral pressure difference:

uN UE

+ (K"2 + (XFC015) )

K)=

j 2

M The terms in Eq. (2.14) involving K= represent the lateral pressure losses due to shear drag and the contraction-expansions of the flow in the absence of axial flow, i.e., lateral flow only.

The third term on the right hand side of Eq. (2.14) represents the lateral pressure difference developed by 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.

Hetsroni suggeste'd K= = 1.4 and'XFCO:iS = 4.2 for rod bundle fuel assemblies.

These values are also used in CETOP-0.

~

~

2.9 CE-1 Critical Heat Flux (CHF) Correlation (Reference 14)

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

~'

b b) ([*)2 ((b+bP)(6)(b+bP) 5

-(

6 ) (x) (hfg))

3 4 6

q,,CH F 6

10 (b P + b

)

7 8

6) 10 2-5

2

-where: q"CHF = critical heat flux, B'J/hr-ft p

= pressure, psia d

= heated equivalent diameter of the subchannel, inches d

= heated equivalent diameter of a matrix subchannel with the same m

rod diameter and pitch, inches G

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

= local coolant quality at CHF location, decimal fraction h

= latent heat of vaporization, BTU /lb fg and b)

= 2.8922x10-3 b

= -0.50749 2

b

= 405.32 3

-2 b

= -9.9290 x 10 4

b

= -0.67757

-4 b

= 6,8235x10 b

= 3.1240x10'4 7

-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 0.5447 diameter (inches) l subchannel heated eouivalent 0.4713 to 0.7837 diameter (inches) heated length (inches) 84,150 To account for a nun-uniform axial heat flux distribution, a correction facter FS is used.

The FS factor is defined as:

9"CllF, Ecuivalent Uni form FS=

9 CHF, Ncn-uni for,

C(J)

X(J)

FS(J) =

()_g-C(J)X(J))

1. o q"(x)e-C(J)(X(J)-x)dx 2-6

f 3

where, for CE-l 'CHF correlation, C(J) =-1.8 (I XCHF)4.31ft'1 (G/10 ) 0.478 6

The departure from nucleate boiling ratio, Dt18R,-is:

DNBR(J) =

9"CHF, Equivalent Uniform I

FS(J)-

q"(J) i t

e I

b s

e 1

s i

i I

t

+

l' 2-7

_.-_ - _ _ _.. ~ _ _ _ _. _..... _ _ _ - _ _... _ _ _. _. _ _ _ _. _ _. _ _.. _,.. _ _ _ _ _. _ -... _ _ _. _ _ _

e TABLE 2.1 TWO.PflASE FRICTION FACTOR MULTIPLIER 3205 G > 0.7 x 106 i

g, y g.1(X = 0.4, G. P

• 2000)

I

$ = F A;.1(X, C, P = 2000)

Ff.1rJ3 (X, P = 2000)

FMN (X,P)

E15 (X t 0.4, PA 2000) 3 3

0R FufJ1 (X.P)

$ = FAM (X, G P = 2000) x f (P G, FMN3 (X, P = 2000)

,FMN3 (X, P = 2000) fiIN3 (X, P) x y

IM;J lX.P = 2000) 3 0 */DTF),

$ = 1.0 WillCHEVER G < 0.7 x 106 i

$ = F Af.1(X

• 0.4, G =0.7, P=2000) gg FUN)(X,P = 2000)

$ = F AI.1(X, G = 0.7,'P = 2000)

FMN (X,P) x LARGER 3

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

FMN3 (X *4.0, P= 2000)

FMN 1X* P)

FMN (X, P = 2000) 4 3

x x ! (G) 4 3

IMil) (X, P)

,g (g)

FM 4 (X,P = 2000)

I x

3 l

FMN3 (X, P = 2000) 2000 6

G > 0.7 x10 0 = F AM (X = 0.4, G.P = 2000)

$ = FAM (X, G.P = 2000)

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

X -.2[X, P = 2000)

F

$=1.0

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

FMN (X,P)

FMN2 (X* P)

I f.1TJ2 (X =0.4, P = 2000) g x

0R 3

NNI (X, P = 2000)

FMN (X, P = 2000)

FMfl (X PJ y

f (P G, y

NN3 (X.P = 2000)

/ F ),

~~~~-

4 = 1*0

~0.7 x 10[ ~ ~ ~ ~~$ = W.W. G = 0.7, P = 2000)-

VJHICHEVER

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

$ = F Af.It X= 0.4, G =0.7, P=2000)

IS If1N2 (X, P - 2000)

FMN (X, P) x 1

xf (G) 3

• ,4IgI IMN2 (X = 4.0, P = 2000) x

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

FfAN (X,P = 2000)

FMN (X,P = 2000) 3 3

x f (G) x _FMNg (X, F)

,g ggg 4

4 Ff,1N2 (X,P = 2000)

.1850 I

$=FMNg (X, P)

$=

i T.D TJL )

g, g (P, G)

M I (P, G)

$=FMN2 (X, P) x f (P, G) 1 +.

2 2

2 T,,3-DTJL I

$ = 1.0

~

0.042,P).1

~

• 3 l

@ = f (P, C) x f (P. G)

$=FMN2 (X, P) x f (P, C) 3 3

3 I

i' 14.7 0

11 0.02 O.2 0.4 1.0 g

QUALITY

• X HE ATING LOCAL BOILING -

BULK 8 OILING

] NO ColLING 3 NOTE: FUNCTIONAL liELAT10NSHIPS ARE LISTED IN TABLC 2.2

Table 2.2 Functional Relationships in the Two-Phase Friction Factor Multiplier (References 11,12,13)

For local boiling:

f) = C) (1 + 0.76 (3hP )- (10 )2/3-6 where C) = (1.05) (1-0.0025s*)

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

yy.75 o

FM = 1 + (G/10 )1+X

-3 6

(0.9326 - (0.2263do )p)

FMN1 =-

1.65x10-3 + (2.982x10-5) P-(2.528x10 9) P2 + (1.14x10-II)p3 FM2 =

X(1.0205 - (0.2053x10-3) p) l 7.876x10-4 + (3.177x10-5) P-(8. 728x10-9) P2 +-(1.073x10 Il)P3 2

FMN3 =

1 + (-0.0103166X + 0.005333X ) (P-3206) 2 = 1.26 - 0.0004P + 0.119 (I ) + 0.00028P (1 )

f 3 = 1.36 + 0.0005p + 0.1 ( G ) - 0.cc07149 ( G )

f 6

q 10 10 1 + 0.93 (0.7 - 6) f

=

4 6

10 2-9

t 3.

fiUMERICAL SOLUT10:1 0F THE C0riSERVATI0tl EQUATI0flS 3.1 Finite Difference Equations 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-0 follows in order to search for the minimum value and the location of DftBR in a 4-channel core representation (c.f. Section 4.1).

Equations (1.2), (1.22), (1.27) and (1.36) which govern the mass, energy and momentum transport within channel i of finite axial length ax are written in the following finite difference forms:

(1)

Continuity Equation a (J) - a (J - 1) j g

jj(J)

(3.1)

= -w 3x (2)

Eneroy Equation m (J - 1) j(J) - h (J - 1) h h4-h3 g

j

=gj p; H wjj

-s ax (3.2) h (h4 - h )n

- h w$3 + ( g + h.

3 2

2h

) "ij "

+

J-1 (3) Axial Momentum Equation p (J) - p (J - 1)

u. - ud j

j j - A go (J) wjj A

=-F j

3x g

j 3-1

t 4

u. + u.

(u. - u )n j

2u wjj. ( l j

2

+h

} "ij (3.3)

-~

U i

J (4) Lateral f1omentum Eouation jj(J) wjj(J) p$(J - 1) - p (J - 1) w N

ij 2,

p 2gs u*(J)w

+g jj(J) - u*(J - 1)w ;(J - 1) j-(3.4)

Where J is the axial elevation indicator and t.x 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 scheme for the solution of m, h, w and p at each axial level.

The steps j

j jj j

used in the CETOP-D solution are as follows:

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

j g

are calculated at the node interfaces.

The linear heat rates gj, cross-flows, w..

and turbulent mixing, w.., are calculated at mid-node.

The 1J 1J 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.

3-2

[

4 s

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

These crossflows are set to zero.

ij(1) = Wjj(2) = 0 W

The channel flov s and enthalpies at node 1 are known to be the inlet conditions. Using these initial conditions the marching technique proceeds to calculate the enthalpf es and floses from node 2 to the exit node.

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

Step _

N r

e e

4 M

WWd Imp n

3-3

.,.,.. ~..... -.......

..... -. -........ -.... -...... _.. -... -,.. ~..

9 I

r h

1 l

I

-)

~

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 crossficw,' Wjj(J + 1)p, is a good apprcximation.

Thus at each node the axial flow rate can be._ accurately detemined. _. _.

4 TORC on the other hand, initially assumes pj-pj = 0 at each axial location.

The conservation of mass and momentum equations are used to evaluate the diversion crossf1cus and, in turn, the flow rates at all locations.

The for the next iteration.

axial momentum equation is used to determine pj-pj The iteration stops when the change in the axial flow at each location is less than a specified tolerance.

Even though the prediction-correction method is a once-through marching technique, its results are sery 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 t.ressures and the ficus are only updated after the iteratian 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 fhe axial flows are corrected at each node before the next is calculateu.

Therefore the accummulated errors are greatly reduced.

It is the accumaalated errors in the downstream nodes which often fcrce the TORC method to continue.

to iterate.

~

e o

e 4

I 3-5

o START I

i U

READ INPUT o

PREDICT AND CORRECT COOLANT PROPERTIEG IN Tile CORE r

AVER AGE Ai D HOT ASSET.18LY CHAf;f!ELS AT ALL AXIAL f400ES y

PREDICT AND CORRECT CCOLAf T PROPERTIES IN THE HOT CHAf;NEL AT ALL AXIAL NODES PREDICT NEW HEAT FLUX y

CALCULATE CHF AND ONBR FOR Tile HOT CllANflEL AT ALL AXIAL NODES If NO IS f.1DNBR OR QUALITY WITH;U THE Lif.11TS ?

YES PRINT GUTPUT f

a l

NO IS Tills Tile LAST CASE 7 YES y

STOP Figure 3.1 CETOP D FLOW CliART 3-6

y J=2 v

PR EDICT w;j, m; AT NODE J 1 y

PREDICT w;j, w;j and m; AT NODE J u

PREDICT h; AT NODE J + 1 l

lf COMPUTE COOLANT PROPERTIES J=J+1 y

h PREDICT w;j AT NODE J+1 V

CALCULATE pi pj AT NODE J V

CALCULATE wjj, m;, h AT NODE J y

LAST NODE ?

YES n

Figure 3.2 FLOV/ CHART FOR PREDICTION CORRECTION METFIOD

___.____.__-.-&_m___

o 4.

CETOP-D DESIGN MODEL The CETOP-D code has been developed, using the basic CETOP numerical algorithm, to retain all the capabilities the S-TORC modelling method has.

Generation of design model involves selection of an optimal core representation which will result in a best estimate of the hot channel flow properties and a preparation of input describing the operating conditions and geometrical configuration of the core.

The CETOP-D model presented here provides an additional simplification to the conservation equations due to the specific gecmetry of the model.

A description of this simplification is included here together with an explanation son the method for generating enthalpy transport coefficients in CETOP-D.

4.1 Geometry of CETOP-0 Design Model The CETOP-D design model has a total of four thermal-hydraulic channels to model the open-core fluid pnenomena.

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 boundarief of the 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 MDMBR hot channel 4.

The location of the MDNdR channel is determined from a Detailed TORC analysis of a core. Channels 2' and 2' are discussed in Section 4.2.

~

The radial power factor and inlet flow factor for channel 1 in CETOP-0 is always unity since this channel represents the average coolant conditions in the core.

The Channel 2 radial power distribution is nonnally based upon a.

core average radial factor of unity.

However, prior to providing input in CETOP-D, the Channel 2 radial power distribution is normalized so the Channel 2 power factor is one. This is performed in CETOP-0 so the Channel 2 power 1

can easily be adjusted to any value.

Initially, the inlet ficw fcctor in the CETOP-D hot assembly is equal to the hot assembly relative flow cbtained from the inlet flow distribution.

If necessary, the inlet flow factor is later adjusted in the CETOP-0 model to yield conservative or accurate MDNBR predictions as compared to a Detailed TORC antlysis for a given range of

4.2 Application of Transport Coefficients in the CETOP-D Model ta O

e 9

e S

9 4

i I

e l

I l

i l

I l

i 4-2 I

i i

. - ~.., - -,.. - -, - _ _ - -,

- -. ~

f e

b 4

e w

I C

O h

g h

9 9

e

/

O h

0 e

0 e

N

j

.V s

'I t

I i

l l

4

'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 parameters, the following tems are discussed.

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

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

R p (j) _ power cenerated in fuel asse:bly i (4.7 )

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

N I F (i) = N (4.8)

R i=1 where N is the total number of assemblies in tne core.

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

f ($,j), power cenerated in fuel red j of assembly i (4,9)

R power generated in an average fuel rod For an assembly containing M rods, one expects:

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

.10) g R

j=1 4-4

j.y

'1 4

The CETOP '0 " code is'. bin t to allo'.. only:.orit.:r sJio t tower f at. tor for n

g

~,

each floa charnel, thus, for e channel containing n rods, the idea of s

x effective radial power factor is used:s x

n E ;ct f (I 'd )

R w.3'+

(4.11) f I'I d'I R

,h

+

+'

n

-T I

,E.

c',

, ;G,

~

a=1 a

.s,

,~

-~,'

s

.. ~

{-

t s

s.

where c is the fraction of the nd

j enclokad in channel'si. ~ s 1

s s.

4.3.2 ' Axial power Distributiens

. c;-

4 1he fuel rod axialipower distributioYis c,haracteriz'ed by the axial shape k.

index (ASI)', defined as

.I -

[

-h7

-m

~'

L /2 qs

,s

/

F (P.)d! - /, Fj(,k)dZ ^ 't

'Z o'

J.

L /2

' -d e

.s s1

-(4.12)

AS1,

=

t

1. lt T (kTdZ' g

Z

\\^

where the a::ial powertfacter at elevation 2k, F (k)c! 'l satisfies the nomalization 7

? N' b

condition:

s 3,

L.

g

~s 7

'(4.13)

/.

F (k)dZ = 1

. (...

-\\K 0

ss.

and L, dZ are total fuel length.ahd axial length increjent res !cctively.

,(

+

' 'N W.

The to'tal heat flux supplied to channil i at elevation k is:

s 4,,(core average heat flux) (f (i)) (F (k))

_(4.14)

R Z

s..

1 a

x Ef fec3.-f ve P.'od Diametcv, i

4.3.3 For a flow clianrel containing n rods of identical diameter d, the effective rod diameter defihed by:

n, j(i)=,Eg$d,ts (4.15) a,=e,;,-

A is used to give effective heatgd perimeter in channel i.

The g following expression, deSved frc ' W s. (4.ll) and (4.15), implies.that.'

.s

~

equivalentenergyisbeingrscc{.,.pdgychanneli:

.s 4-d A'

[. '

=

<y 9

n D(i) fgi)=dt cj (gU,j)

H.w,)

j=1 4.3.4 Engineerig Factors c

The CETOP-D model allcus for engince'ing factors (as described in Reference 1) due to manufacturing tolerances.

Appl hation of such factors imposes additional consevatism on the core thermal margin.

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

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

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

(1) Heat FYux Factor (f )

A slightly greater than unit heat flux factor f, acting as a heat flux 4

multiplier, tends to decrease DUBR in the following manner:

1 1

/

DNBR=C3[

, {liF for f

>1 (4. W ttj

,j o

where E defines the DNBR before applying f and 4. is the local heat flux, tj 8

l (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 reds surrounding the hot channel as follows:

m m

f E

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

R f

(4), g P j= _

j=1 j

g (4.1g)

II I

C.

\\

Hp 5

'j J=1 J=1 J

m n

c f (3,j) g c) fp' (3,j) + r f

I g

f (3),

j=1 j=1 j

g n

m f

i L.

+ 2 r,

H J

j=1 j=1 j

(-(

~...--

l and o (4) = f f d r c

(4.19)

HP j=)

j

^

m n

j)

(4.20)

D (3) = d (f I

C +

E C

H j=)

j j=1 where f 's and D s are the modified effective radial power factors and R

rod diameters fo. channels 4 and 3, m is the number of rods on channel connection 4-3'aad n is the number of rods Again, the inclusion of f and f in the core thermal margin prediction causes g

p

'a net decrease in Dl:BR in addition to that de scribed in Eq. (4.17).

l e

e e.

.4 v

9 e

9 O

y e

e e

o e

p' O

y 4-7

CHANNEL NUMBER

>2 HOT ASSEMBLY = 1/4 OF ONE FUEL ASSEMBLY CHANNEL AVG.

,F R RADIAL POWER FACTOR 1

CORE AVERAGE CHANNEL = ONE 1.000 FUEL ASSEMBLY (A) FOUR-CHANNEL CORE REPRESENTATION IMPERMEABLE AND ADIABATIC ]

JOOOOOOO OOOO OO 2..

m OOO O

2..

2 2"

5

! OO 2"

3 2'

2" U

w 2"

2 4

3 2'

y 5

2" 2'

3 2'

2" 5

2" 2'

2" 2"

(B) CHANNEL 2 IN DETAILS Figure 4.1 CHANNEL GEJMETRY OF CETOP-D MODEL AJ

5.

THEF. MAL MARGIN ANALYSES USING CETOP-0 This section supports the CETOP-0 model by comparing its predictions for a 16x16 assembly type C-E reactor (SONGS 2 and 3) with those obtained from a detailed TORC analysis.

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

5.1 Operating Ranges The thermal margin model for 3390 Mwt SONGS 2 and 3 was developed for the following operating ranges; Inlet Temperature 530 - 571*F System Pressure 1960 - 2415 psia Primary System Flow Rate,90-120

'a of 396,000 gpm Axial Power Distribution

-0.3-+0.3 ASI' 5.2 Detailed TORC Analysis of Sample Core The detail ~ed thermal margin analyses were performed for the sample core using the radial power distribution and detailed TORC model shown in Figures 5.1, and 5.2.

The axial power distributions are given in Figure 5.3.

The core inlet flow and exit pressure distributions used in the analyses were i

based on flow codel test results, given in Figures 5.4 and 5.5.

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

5.3 Geometry of CETOP Desian Model The CETOP design model has a total of four thernal-hydraulic channels to codel the opcn-core fluid phenomena.

Figure 5.6 shows the layout of these-channels.

Channel 2 is a quadrant of the hottest assembly in-the core (location 1).

and Channel 1 is an assembly unich represents the aver?ge coolant conditions for the remaining portion of the core.

The boundary betwee channels I and 2 is open n

for crossflow; the remaining outer boundaries of channel 2 are assumed to be impermeable and adiabatic.

Channel 2 includes channels 3 and 4.

Channel 3 lumps the subchannels adjacent to the MinBR Mt channel 4.

4 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 detailed analyses in Table 5.1.

It was found that a constant inlet flow split providing a hot assembly inlet mass velocity of[ ]of the core average value is appropriate for SONGS 2 and 3 operations within the ranges defined in section 5.1 so tFat MDNBR results predicted by the CETOP model are either conservative or accurate.

5.5 Application of Uncertainties in CETOP-D Engineering factors, which account for the system parameter uncertainties.

in SONGS 2 and 3, have been incorporated into the design CETOP-D model in accordance with the methods described in section 4.3.4.

4 e

a e

6 5-2

l E

6 5

2

.8011.843G

.7663 CHANNEL NUMBER 3

1 1.18G 1.223 12 13 7

8 4

CHANNEL AVG

.9555 1.0G9 1.216 1.089

.7126 AC OR 14 15 9

10

.11 1.082 1.032 1.070 1.078 1.072 1G 17 18 19 20 1.020 1.032 1.027 1.007

.9916 Si

.8835 21 22 23 24 25 1.030 1.021

.9040

.9511

.8158 F

l Il a

n l

I l

_l_ _ __ __ _l_ __ _j_

q_. _ 4 __ _

l I

I G0 i

1.0274 Y l'

i

.0305 l 1

--d l

l l

l l

_l_

q_ _ +l _ q_

t-1 I

I, I

i i

I i

I NOTE: CIRCLED NUMBERS DENOTE " LUMPED" CHANNELS 5

Figure 5.1 STAGE 1 TORC CHANNEL GEOMETRY FOR SONGS 2 AND 3 5-3

m 4

J 4-*

4 JA L

e.r

~

,.4-..- -

_a 4a-e-4 9

J s

e o

e i mee

• e = e e e i

1 e

O 4

i 4

i a

J 1

e

+

l l

l i

i o.

l I

i j

i

(

0%

~

6 I

I I

Figure 5.2' I

STAGE 2 TORC CHANNEL GEOMETRY FOR SONGS 2 AND 3 i

5-4

II<

<l l\\l

,1lJii lllll\\jl J41i e

0

~

~

J 1

C 9

t 0

g 8

t 0

i T

7. E N

t L

0 g

N

~

I MO D

R S

F NO G. T t

I

[

0 H T

i G

UB I

E I

H R

E 3 T R

F S A

E

E I

5 O e

D t

i 0 C

-; R V

F WO IT P

C

~

A L

4. F A

t 0

I i

O X

N A

O g

I T

A C

3. A t

0 R g

F 2

t I

I g

S S

0 I

I AS S A A A 7

1 7

1 3 0 0 3 0 0

+ 0 0 O.

1

= = = -

i 0

l ABCD 0

2 0

8 6

4 2

0 8

6 4

2 0

2 2

1 1

1 1

1 0

0 0

0 e S o < $ w g o c. s 5 X <

Tm lllI1 l

l1fl1'

e 4.

f

• e 4

I i

l 9

w g

f j

Figure 5.4 INLET FLOW DIST RIBUTION FOR SONGS 2 AND 3 5-6 l

1

k e

e 4

S 9

o k

e o

a E

e 4

m

~

Figure 5.5 EXIT PRESSURE DISTRIBUTION FOR SONGS 2 AND 3 5-7

-.n..x,_n.,..n.

o e

4 '

s e

+

hr w

0 e

O a

4 9

s 9

9 e

d.

e 4

e O

e s

M W.w d

=** er P

bm b

4 e

Figure 5.G CETOP-D CHANNEL GEOMETHY FOR SONGS 2 AND 3 (CHANNEL 1 NOT SHOWN) 5-8

~

Axial Elev.

Operating Parameters MDNBR Quality at MDNBR of MONSR (in)

Detailed Detailed TORC CE M -D WC QE W -D Core S

Core Avg.

Axial Relative Inlet Relative Inlet Inlet Heat Flux Shape Flow.in Flow Flow in Flow Detailed ocit Btu Index location 1 Factor Location 1 Factor TORC CETOP-D 6

Pressure

Temp, fl0 lbm)

(hr-ft2 ).( ASI)

(psia)

( F) 2 hr-ft q

2250 553 2.6394 284180

+.317 2250 553 2.6394 296290

+.000

~

2250 553 2.6394 281980

.070 2250 553 2.6394 268050

.31 7 1960 571 3.0674 262500

+.317 1960 571 3.0674 271390

+.000 1960 571 3.0674 262020

.070 1960 571 3.0674 248230

.317 2415 530 2.4534 307030 5.31/

2415 571 2.3199 249920

+.317 2415 530 3.2712 384660

+.317 2415 571 3.0932 310600

+.317 TABLE 5.1 COMPARIS0NS BETWEEN DETAILED TORC AND CETOP-D l

1 l

l l

+

6.

CONCLUSION CETOP-0, when benchmarked against Detailed TORC for SONGS 2 and 3, has been -

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

in the core.

Similar conclusions have been reached when CETOP-D results have been compared to TORC results for other C-E plants.

CETOP-D models thus are appropriate substitutes for Design TORC models (S-TORC) specifically for SONGS 2 & 3, and generally for applications in which the Design TORC methods have.been approved (Reference 6).

i i

I e

9 l'

1 6-1

7.

, REFERENCES 1.

" TORC Coo'e, A Computer Code for Determining the Thermal Margin of a Reactor Core", CENPD-16.1-P, July 1975.

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. 165-186.

3.

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

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

i 4.

Chiu, C. ; Church, J. F., "Three Dimensional Lumped Subchannel Model and Prediction-Correction Numerical Method for Thennal Margin Analysis of PWR Cores", Combustion Eng. Inc., presented at Am. Nuc.

Society Annual Meeting, Jan, 1979.

5.

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

6.

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".

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. Sc. Mech. Engrs., 70, 1948

~

pg. 695.

13.

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

14.

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

Derringer, R. ; Previti, G. and Tong, L.S., " Lateral Flow Simulation 15..

in an Open L attice Core", ANS Transactions, Vol. 4,1961, pgs. 45-46.

e

Appendix A CETOP-0 VERSI0ff 2 USER's GUIDE a

G G

0

A.1 Control Cards

' ~

Code Acc'ess and Cutput Control Cards A.2 Input Format _

1)

Read case control card Format (110, 70Al)

Case Number ~, 110 Alphanumeric information to identify case, 70A1 2)

Read Relative Addresses and Corresponding Input Parameters, Format (11, 14, 15, 4E15 8)

N1:

0 or blas.K, continue to read in the next card.

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

Successive case'. can be performed by adding input after the last card of each case.

The title card must be included for each case.

~

N2:

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

N3:

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

XLOC (N2):

correspcnding input parameters thru XLOC (N3):

A-2

A.3 1.ist of Input Parameters b'~'

Relative Parameters Address Units Descriptions Gilt 1

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

XLOC(2) 2 nillion-Btu.

Core average heat flux, during core nower-hr-ftd iteration this value is the initial guess TItt 3

F Core Inlet Temperaturo PREF 4

PSIA System Pressure fiXL 5

fione Use 0.0 to include the capability for adjusting the initial guess during

" iteration"*, so the nureber of it.crations may be reduced.

Specify 1.0 to not u:e the capability.

I flPOWER 6

ttse 1.0 to print more parameters during iteration in the event of convergtree problem.

Specify 0.0 to not sirint.

U 7-25 flone For future work GRJ DXI.(d )

26-(25+tiGRID) flone Relative Grid Location (X/Z), wherc X -is Jul,itCRID distance from bottom of active core to top of spacer grid, Z is the total channel axial length (relative nddr ens-77).

(25+flGRID+1 )-45 flone for future work 2

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

! = 1.4 ilPf.RlM(1 )

51-57 ft Heated Perimeter for Channel I l = 1,4 Parameters sup mscripted wit i 1 are not i icluded in CETOP-D Version 1.

• The term "ite(ation" can bc defined as e.ithcr iterction on corc power, core flow or on Chainel 2 radial :: caking factors b

A-3

e a

Relative Parameters Address Units Descriptions FR 58 Nor.e Maximum rod radial peaking factor wanted 4

for Channel 2.

During radial peaking factor iteration tnis value is the initial guess.

P1PB 59 None Ratio of the maximum rod radial peaking factor of Channel 2 to the Channel 2 average radial factor.

This ratic is based upon a power distribution normalized to the core RADIM1 60 None Effective radial peaking factor for Channel ~

RADIAL (I) 61 -6 3 None Effective normalized radial peakirg factor for Channel I (normalized to the Channel 2 I=2,4 l

avertge radial factor in the core ?cwer di:-

bution, if this is done correctly RADIAL (2; l

l will always be 1).

A channel nomalized l

radial peaking factor is determined by multiplying the nonnalized radial peaks in the channel by the correspondir g rod

's fractions depositing heat to the channel.

D(I)

P 1,4 64-67 ft Effective rod dian'eter for Channei 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 cro,3sflow between I =1,3 Channel I and Channel I+1. L l

b Number of axial nodal' sections in model, NDX 7i None maxinum of 49 (recomend 40)

NCHANL 72 None Number of Channels (always 4)

NGRIO 73 None Number of spacer grids (maximum number of F.

ITMAX 74 None Maximum number of iterations (reco =end 10). Insert 0.0 for no iteration then a MDNBR will be calculated for the input core power, core ficw and channel 2 radial peaking factor.

1 A-4

o,_

i o m i m. rnmr7arens. u,.a rrm.

l h

Relative

. Descriptions Paramters Address Units I

l-PDES 75 PSIA Reference pressure at which the core average mass flux is specified.

If the core inlet mass flux (GIti) is specifitd at (Tili,PI:EF) then PDES can be, set to 0.0.

If not, the code will corr:ct the inlet mass flux to Till and PREF by using PDES and TDES as reference

, conditions.

TDES 76 F

Refc.rence temperature at which the core average mass fl'ux is specified.

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

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

del 4ATX

'78 ft flydraulic diameter of a regular matrix chs,nel for use in calculating FPilCR in hot channel g

QFPC

, 79 lione fraction of power. generated in f.he fuel

. rod plus clad SKECDK 80 flone Engineering heat flux factor.

FSPLIT 81 lione Inlet flow factor for Channels 2, 3, 4 DDil(l) 82 ft

...

)

DD!l(2) 83 ft IIcated hydraulic diameter of channel 4.

COMIX 84 ft Partmeter used in the turbulent mixing correlation, determined by taki:ig the ratio of the number of subchannels alonc:

0 one side of a comniete fuci bun <.ie to the width on that side.

DDiBR 85

!!one Design limit on DriBR for CE-1 CliF correla'-

A-5

Relative Parameters Address

' Units Descriptions DNBRC0 86 None Initial value of the CNBR derivative with gespect power during core power iteration during core fi[cw iteration L 23 -

L

] and with rejs ect to ficw 4

DNBRTOL 87 None Tolerince on DNBR limit.

QUALMX 88 None Maxim;m acceptable coolant quality at MCNBR

. location.

QUALC0 89 None Initial value o.f the quality derivative with resppet power durin core pcwor

't iteration L and with respe:t to flow during co e flow iteration QUALTOL S0 None Tolerance on quality limit.

AHDAF

'91 None Ratic of core heat transfer area to flow area, used for scecifying a core saturation limit during overpcwer iteration.

Insert 0.0 far not using tha limit.

HTFLXTL 92 None Convergence window tolerance on the ratic 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 printe'd in the output when the CESEC code is linked with CETOP-D.

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

Insert 0.0 for CET0? to self-generate the transport coeffici.ents.

2

'AMATX 95 ft GAPT 96 ft D

g

A- -

(

Relative

.Parar.:cte rs Address Units Descriptions

\\

HC 97 None 5-FSPLITl 98 None Inle: flow factor for Channel 1 NX 99 None

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

Use 1.0 to specify infor-v mat,i on.

NY 100 None Use 0.0 for not using the' relative locaticns of the axial power factors as long as the axial power factors are input at the node interfaces.

Use 1.0 to specify lccations.

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.

XL0d(102) 102 nillion-BTU Core average heat flux at 100% pc.n",

hr-ftd includes heat generated frca rods end coo'l an t.

Fuel rods are corrected for axial densification.

XLOC(103)'

iO3 Hone QUIX file case number. The QUIX code is I

used in Physics to generate axial pcwer shi.:

NRAD.

104' Hone Option to " iterate" on the following until c

the design limit on DNBR is reachec.

0.0:

Iterate on core powe., if adaress (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 0:18 limit is reached.

l 2.0:

Iterate on core flow A-7

Delscriptions Relative Parameters Address Units I

~

~

N2Z 105 flone Use 0.0 to not print CESEC time (DTIf4E)

Specify 1.0 to print.

5 GRKIJ(J) 106-117 tione Option to input different spacer grid J=1,ilGRID types with the corresponding loss coefficient equations.

0.0 flormal grid with built in loss coeffid

.45 l

Type 1 grid with coeffig equation -

1.0 CAA(1) + CSD(1) * (Re)C Type 2 grid =

2.0 CAA(2) + CBB(2) ? (Re)CCC(2)

Type 3 grid =

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

CAA(1) l'18 flone Con'. tant for Type 1 grid equatic.i CBD(1) 119 flone Coa tant for Type 1 grid equation CCC(1) 120 flone Con; tant for Type 1 grid equatica h

Constant for Type 2 grid equation CAA(2) 121 flone CUB (2) 122 lione Constant for Type 2 grid equation CC(2) 123 flone Constant for Type 2 grid equation CAA(3) 124

!!one Constant for Type 3 grid equation

. CDB(3) 125 flone Constant for Type 3 grid equation CCC(3) 126,

tione Constant for Type 3 grid equation' 127-128 flone Recerved for additional input O

O A-8

4 Relative Parameters Address

' Units Descriptions RAA2 129 None s

RAA22 130 None GAP 2P 1 31 ft

'T

. GAP 22 132 ft 2

A2P 133 ft A22 134 ft DD2P 135 ft DD22 136 ft 137 - 139 Hone Tor Future Work NDXPZ 140 None Number of axial power factors (Recomend 41) l'1 - 190 None Rel'ative locations (X/Z)'of the a>ial XXL(J) 4 J=1,N0XPZ power factors.

If NY = 0.0 this 'nput is not needed.

AXIAZ(J) 191 - 240 None Normalized axial power factors J=1, NDXPZ I

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

Speci fy 0.0 to not use the cacability.

If 1.0 is specified, the follcwfng-additional input is requi red.

I NREG 242 None Number of operating space regions (maximum

~

is 5)

.A-9

7 Relative Parameters Address Units Descriptions REFLO 243 9.p.m.

100% design core flow rate in g.p.m. divided 1

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

(Referred to as hot assembly flow factor) 00J=i,liREG prc vide fo - each region of operating space where:

Rarges on raction of 100% design core flow, inlet temperature t

K=(J-1)*l2 system pressure, and ASf:

249 - 308 s

IBF(J)I (249tK)

None Types of inequalities applied to 14. nits of tra design core flow range 1: lover limit < co're flow < upper limit 2: lower limit < core flow < upper limit 3: lower limit _< core flow < upper limit

(

4: lower limit < core flow < upper limit BFL(J)I

'(250*K)

None Lower limit fracti.on of 100% design core

~

flow rate.

BFR(J)I (2El+K)

None Upper limit fraction of 100% design 3

core ' low rate.

e e

e

e Relative Parameters Address

' Units Descriptions ITI(J)I (252+K)

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

A TIL(J)I

.(253+K)

F Lower limit inlet temperature TIR(J)I (254+<)

F Upper limit inlet temperature IP'S(J)I (255+s)

None Types of inequalities applied to linits

'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 O

e e

4.

e o

e 5

O s

A.4 Samole Inout and Outout_

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.

CASE = CETOP-D case number NH = Enthalpy trarsport coefficient at each node H1,= Enthalpy in Channel i H2 = Enthalpy in Channel 2

~

H3 = Enthalpy in Channel 3 H4 = Enthalpy in Channel 4 QOBL = core average heat flux, represents total heat generated from densification) Btu /hr-ft{uel rods are corrected (for axia rods and coolant, wnere

- for cora power iteration, the heat flux at the end of the last iteration is printed.

For no iteration, core flow iteration, and radial peaking factor iteration, the heat flux given in the input XLOC(2) is printed.

POLR = for core nower iteration, the ratio of the core average heat flux at the enti of last iteration to the core average heat flux at 100% powe-is printed.

For no ite.ation, 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 s

6 2

GAVG = Core average mass velocity ( 10 lb/hr-f t )

- for core flow iteration the mass velocity at the end of the last iteration is printed.

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

w

-s 4

+

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 in Channel 2

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

DNB-N = hot channel MNOBR at last iteration

~

X-N

= coolant qual'i,ty at location of DNS-N -

~'

DNB-1 = hot channel MDNBR at first iteration y

X-1

= coolant avality at location of DNB-1 QUIX = QUIX file case number

s.

ITER = Number of " iterations" IEND = Specifies what type of limit or problem was encountered during " iteration".

(

, s 1 = MDNBR limit 2 = maximum coolant quality limit

' 3, 3 = no additional iteration is needed because the ratio of the preseat guess to the previous one is within the window tolerance HTFLXTL, address 92.

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

6 = the new guess produced by the code during iteration falls below zero.

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

s s ATR

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

HCH

= MCNBR hot channel number, if 3 is or,inted this means 4

MN00 = MDNBR node location CESEC TIME = This parameter is printed in the output when the CESEC code is linked with CETOP-0.

~

s s -

s i

FSPLIT = this is the inlet flow factor (in channels 2, 3, 4) chosen by the code i

for operating conditions specified ir. the inout.

This value is printed', '

when the capability for changing the inlet fic4 factor for different. regions of cperating space is used.

The following parpeters are,31so printed ;

to show that calcu? -:ted fraction of 100". desigd care flow $s within the operating space given in the input.

GAf1

= the calculated fraction of 100f. de:ign core flow 2%

G!ti

= the calculatrd core average mass velocit'/

lb/sec-ft x

s inlet coolant tpecificIolume, ft /lba 3

Vlf1 c'

i s

4 m

A T

e s

\\

w O

w

-g I

g

\\

e i

I o

s A-14

6 s

t Appendix B Sample CETOP-D Input /Cutput i

i t

e 1

N

?

e e

f i

i, t

8 l h

I i

i 1

i 6

e i

l I

l 6

I i

i i

e a

j f

+

{

l 8

6 e

t j

t t

l

'I l

l l

l 4

i i

t 1

I t

i

}

I 4

t a

5 i

t i

8 l-l 1

g i,

j e

6 1

f, 8

e I

I i

i I

l j

l 8

I g

)

t i

i i

I l

I I

l 1

i.

i i

+

j i

i 4

f l

l I

I I

a i

i 8

i i

8 i

i i

l I

i i

l-l I

i i

t I

l l

l l

f i

i l

I I

e i

1 i

l l

l s

l I

f i

l g

8 l

6 I

I 0

{

a t

l i

1 I

l 4

l

.t e

,i f

a e

l 8

t n

I t

i e

l l

4j e

4 i

4 i

i f

I s

f 4

s I,

I l

f t

i 1

1 e

4 i

A

+

.N.= N l 1

.= 7 /

• e 3

.

l i*

so p

=*A C%

N N%

3==

4.=

l l

't 3.N C 3 ** 7 N7

>

• 3 3

= 3*

3 N at 8

5

• ==

f a

e e e e e e e e o e o e e o e

e e. e e

3 3

= 3 3.

[

- A

?AAAAAAAAA

'3 A 3 33?3AA3 l

3N#,2A3=Az3

\\

N c3%

e3=N e.s c o r r e r t e N

= . e. 1. #. O. N. S. ?.

• >27.=*=*=.

• A.

?

i 3

'c j

t p

e i

e=

=

i i

i NC N=

A j i

l A

A 6

l

+

4K

> 3A 3 A 3

3 AN2

-N NNP P 3 AN =

7 AAM j

3 S.4 9

N3 3***

% 7

% A3 3

a 33 7 3320 j

. N. C.

2. *. N 3

==4 i

1 i

e.

e e e e e i-

[

j e,

i j

l

,,3

-33=

' a 3

i

. A

=

t

1. 1. 1. AAAAAAA 33 3 33 33A33 l

i.*

3 j

l' 6

NNNNNNNNNN JMAA3 /t 37n l

i A

==

3

{

l l

l s.

79*S7. :. r. ? = N. N. N3 i

O O

4 C4 C J C

• 3 i

l

3..C. N.,C c. o. %. z. r.

=

. e i

i J.

l i

i 4

)

e e

i i,,

23 iC

+ 7

• =

i 27

= CE

% 3*A N

M I

1 43 1

I j

g g=t g

i I

3 &t/N3 19fN P

,==

M73

)

e

,,,====*A CN 3 N% 3 I 3 3 NN

• 3 T3 2 3

234

+

i 4

• N a #. @* 3 N ? = = K =

8 2 *

• i

.==3 3.=3 * -

A A A A A f.A A A A 3 3 A3 3 3

• A *. 3 4 # =.=.=

1 3

& 8 n

e i

l 393A.3A/N CA j

i 1

g i

l

• * **

• 4 e *. 9 e

• u3 33

• O 3.* N 7 i

,a e

l l

l

3.==. N. e 3, A 4. %. C. ?.

• 7. ?. ?. =e =e7 i

e

.=

i y

A*

2 * %

t, = =. + %

+

A=

3 3e s

?== M 3 3*

3 32 C A

A A%

=

3 e

43 g

3

. * '6 *.t* A 8 A2 ?t

% L3 2 3 g

j N3 1 0=

a 3 ?. t N E. F 3 t

e e e e e e e e e e e e o e o e e o e e e 3 I

3 N.

A 3

3== 3 3 ee

• N 3 %.=

N 3

?

J Ne '

3 s

2 3AA/####A#33A333 3A3A33 e

4 3NNNNNNNNN3 3 3N3 3 3N3 A== 3 l

? 33 a*A3=N=%

3..=====3 e

== N, e A o. % e. ?.

o

• e ?. ? ?.=e A

3

. e e e

1 8

e e e 4 e

e

.=

e e

4 3 3 N c a==

• T74 C7*%

48 33 03

• E N c'*

A > A A.= N C 3 ? DN O3 # zN C D i. ? 3%C33===.E 3

N e M 3 A A 4 4 e'm a= *= ** & T E P P.3. 3. 3.== =.= N *

• 3. 3 4. A.= A.C..C..C. **= *.*. I=.C..? ? N N N N N N N N aw 33

= N ** Me?

A

~. =. =.

i N

f e

= c33 437 tN3 c=#% =A7 S tNc3et?e3=#ee==Ae*% -=AP*N = A 2.* e %

=9

=

.3. *==== N 9 3. 3..?

3..A..A..&..C.4..%.

.D..?. ?..?. N N N N N N N NN N 9 ?.

3 33 = =

Ne9*AAA4C O ** % % E C E P7

. =.

I

..e 3

i I

I I

l n

I p

k j

f I

r

- i

=

OT j

1 E9

}

(

I I

I $=

)

1

+

f a3 i

i e

l i

1 t

I,

,e l

l l

i M 7 l t'

l o

s.

3 I

4 l

t a

! 4o I,

i l

i 4

g

.as s

6 y

.7 3.% % 3 3 *, m % 37 -2,, CW,3c,-7,%. -3 7.7%,

m =.

t

• s 3 c%7 1 7== 7 3 7N C O Ct?3??% 37E 2C-2 3% &3 O N E ** = 7 % em %

==

sa *m % e

• 7== A c c p 7== -== n -r D

%

• e > N % ** 3== m e *== % A 3 C7 NseW t

> *8'l 3 3 K

'm L LL4 C% CP*?D D*=*7**fP/?**7%C***'t*7P3 2 23%

e

=e e o e o e e e o e e a e e e e e e e e e e e e o e e o e e e o e e e o e e e e e e 3

9 3 3 *W G *= 7 N fi r== 3 % 3*

O 7 N 3

• m J *" # E

==?**

D

• O 3 9 ** 3 "T Z - # 7 N #6 C7

=*

l

/* f* #6 A/t C 4am % % rt t C77 ? 3

• J === =* ** N N N % 9 4 ? *? U # # # 4 4 OC 3

l

/ / f P ? ? / f ? b P b f ? ? ? J'? e C C C 4 C C D & D44C D & C O C 4 D D D G

'S lN 4

g t

l l

?

l I

i "3

g

,6

}

g 0-g e

e, o l

i l

I g

q E

e g

8 i

%3?3 3 bK>$77NV 'n N ** % J' * ** t P P =% > C ** % ? 7 'M en 3 3 % f *w 3 O3b 6

1

• U 3% C 33# *== NC E C = 3 3 -3 C31*7 I 7 a=== **== *n 3 3== N 1 2 C 3

% *9 '8'l 7 1 43% O e O==.*.tm = **=m a ** - 3 3 4 #6 f CC7 4 O - P.% # N== & 3 3 a8'l 7 gi 7-N7 3 N # "* 3==== N - 3 C /* V3 4 *l : C4## CE-4N3: ? 3 N e== C 3A7 e

. N e e e e a e e e o e e e e e e e o e e e e e o e o e o e e o e e e e e o e e e e e 3

j Z3 ef7 3 E % C== f 7

== 2 C \\ C 7

• '9 % 31 CN&3P?7 7*E 2 7 7 7 e C== **

E e

J' ? P f. C C%% L : : '? ? 3 3== =*

• U %

• 't +

• 3 ?PPP& 0% %

ll* 7 3 3== =e 2

fbbbPf.?PPPPPP44 &GC

C CCD C &COCC444CQ& D D

• m ** am am 3

l.

j l

l l

I i

I i

e 6

t g

g

't

?

I t.

s, i

7 1 e

i 2-

'N l

a i

83 l

1 n e N 3 7 N t== % N 3 3 *J C % * =m A3T?Ng3TN7 > A > P *= % 3 f== c % $ 3 4 /*

• A

• %2% ** N e 3 N== 3 2*.# -== N 3 CC C N ** *

• C 3 2== A % C37AO% 3 C 7 4 /t 3 7

=

F"'"tN ** % C% 3==9==*.*=

c== % 3 gN%== c 0 ? 3% 7 % > > 3 y *= ? p77N%== 3 7 3

.q.

7 N.** A 7 J5 3 /t 37 0to33 c% A 3== 1P I E== 2== 3 r # au N N 3 *== - p 4 % %CN 2

e e e e o e o e o e e o e e e e o e e e e e o e o e o e e e e e e o e e e e e e e e e

'l te 3 *t O33 73 c *m % - A37 C== p 7 e== 3 3 r N 4== p $= 1 7 77 3 7 A O A *p p g **

D W

1. 1. 1. C C C ** % Cr7/ s 3 3====== N N *n M *'t 3 3AA/O C% % CE 7 3 3====== N 2

8 Q PrPPJ'??DD.rP OO& DD &Q DeD0 04DeO4D&44Cemm es* *m *m e=

3 g

y A

l 8

i I

1 I

{

-j 4

, =,

e i

l w3 I

l l

l g

4#

.j 1

l

{

g t

xv e

e N A* T T ** ?

3 f.i ** N ** 3 *6 7 3 9 EC 7 #.3 N 3 C "f 7 7 1 am T N ** %

'8'* OOo

* e eqtT &== E

• C ** *im N7 CL TN% N1*==== E N t P* C N== 7 c== 7 % 33932mm 33 j

N3-3== 3 3 C== *= N 4 3 3 3==== 0 # A & '8L 1==

g NNK% /== t s=

If 4 N.i 7 & f== 4 N l

j i

7. %. 3 7. C. 7 7 7.. 4 3 M. f

• C. C %

4. A. 3 9 3 7. C.7 3 7.A. T.#. # 1 9.D.N A 0.% N.%

1 e e o.

e e e

e e e e e

e 3

g 39C 3? ? *LesN43 7 E N4 33 &N O3 3 rN% - p = J== c N *w eoeDN3 3

/ ##CC f% % Cr?? 3 3 3 - - N N 'W * #6 -1 3 3 /* # C 3% % 1 S773 3==== N N e

' t =.3? b / P f in P P D J' ? P & C& G& C4& D 4OC D C & OO CD DC CC%

• w

• =*m *m 1

l I

i 4

+

I l

t o

I N

i

=e D I

3 A C l

Ars=3 7 verea3rrz% r P v e ? sr s cc e3 337 s*sts a rs-

• ~n n D-g

• AJe7N#-3mM*-L C% 43% 3#= 0*N*3rNN m33 c-N3% 43 3 i

%E-O% N4C /t %== T C A

• '5 C A *l 7 C7 3? ? 1 3 3 ** 7 - ** O N== ** A== N O C7 0

2

• t K ? ?== % e? ? 2== *'t # 4 A /t.t 3 *n N * *84 4

• m== 0== 4 r 7 3 3 7 3 7 N "T : KN f

e e o e e e e e e o e e e e e o e e e o e e o e e o e e e e e e e e e e e o e o e e 3

l l

I.

8

• S *^ t 3 /* 3 479 C N em *e f5 7 an %== A 7 W" % =* 7 7 7 D of'n % N% M S e C" 7 3 ft 39 0

• 33

==

J* l' I' C Cem *m % 5C7 7

.2 3 9== - N % % *%*% 3 3 4 ? ? C D * *m L L :* ? 3 -== N N N 3 >

1 J'? J'? b b b b J\\ D A P 4 D 3 OD D4 C O& D& OO4O DC 4D4 CC% *' am N % *m

• $ *\\

t i

I4 e

e e

l i

C e

i 8

i N

i 48 e

3 D

/

f * % M P % J' r > 3== 3 */ e 7 7

.t* 7 A 3m 2

I e

NP% O3 3== /* 3 1?T% 3.tl am3 *. 7 a N c m 3 N P N -s r e - s e p

• e 3 7 w r - s e. 3 N T.O. % ?--3

• rm:

=o au

3 3

c3?

=.

% &== 3 3 % em e g N== t N N % C ?

==%

e e c== e ** ** / em 3== % o o== N 3 # 9 4 7 *t

• J %

==

3 33077nC7D4A7 3== 7 C 7== p 7 9 3 A N 9 e j

=

3. ** ? *.* 3

? E ** N - N 1 am e e e e e e e e.

o e e o e e e e o e e e e e o e e o e q

t

. 3 e o e e e e o e 0

{

3 fN N%

D-2

-f33 C N.* - / ? * %3 - =- N,T.%-m,#PPr*%

• r97,373 I T N f ?. % %

J '

3 erroO%% 3x?>

3 -== N 3 1

o m

,goE.

h D F P /% P J>b p P b D D C4 G3&4D4& CC '

I I

//rsC z%% e x x ?.~ = 3 D&CD C 4>L 4 [U C a'

% *w % %

e :

I=

i 4

I I

2 9

{*

l 0

7 I

i no l

3 I

f' I

I l

a i*

J

.g-l

.ea r

2 g

,NC i5 I

2

=

, e =e A== c % en y g A e =. A S *g 3% N g *e % y at 7 N :=t y 3

3

)

3 0 3 **

• '% 3== =

• 't "U > c3 A7 m O 3 3 ** :* 3 N-% C o 9 art t t O N== *n el 3 Y3 e t4 l

E 7 3 = C ** 7 fl S /t ? O A

• e c ** *'*== A 3 m E "P.

.' L*

.J 3 =3 0rfeoe=g o g ee g 3 g== p 3 ? 3 e= N ; ye% c3 3% 3 N== M C D *t >

3*

3 e =e 3 #' *m 7 N C D *'t **== 4 3 *f % =* /4 ** C 3== 3 7 7 E O O / 3 *I 9 N N======== N ** =e

,= *

• e e o e e e e e e e e e e e e e e e e e e e e o e e e e e e e e e e e e e e o L=

g a

j N N 98% 9 =8% @ 3.#% /b [ CC O O ** % P= 8 C O O O O O O O Ms /. O & O O 4 O P* et8'*

I

'3 i

e et a

t t

4 i

i

=J 3 1

. and 134

'3 i

I I

l l

"j j

z--

z i

i i

.3 o e=

1 3.

t 6

y O N 'd 2 t i

g g

e-N-U#.~.,3-N,,,,%

eP3-Nece

%.? s-N-3,

.3 3-on s

}

---

NNNNNNNNNvececconeco3 3 ana e

c i

o~u 3

i e

3 e 2

i g

i a

8 4

I j

g i

i n

B-3

l ENCLOSURE 6

,