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Nonproprietary Version, Responses to First Round Question on Statistical Combination of Uncertainties,Program:CETOP-D Code Structure & Modeling Methods, CEN-124(B)-NP Part 2
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Issue date:	05/31/1981
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LJ Response. to First Round Question on the Statistical Combination of Uncertainties Program: CETOP-D Code Structure and Modeling Methods (CEti-124(B)-NP Part 2)

May 1981 l

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l COMBUSTI0ft ENGIflEERING, INC.

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LEGAL NOTICE This report was prepared as an account of work sponsored by Combustion Engineering, Inc. Neither 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 cerchantability, 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. Assuce's any li:bilities witn respect to the use of, or for ca. mages resulting from the use of, any information, 1

apparatus, method or process disclosed in this report. .

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ABSTRACT s The CETOP-D Computer Code has been developed for determining core thermal margins for C-E reactors. It uses the same conservation equations as e used in the TORC code (Reference 1) for predicting the CE-1 minimum DNBR (MDNBR) in its 4-channel core representation.

9 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 thermal margin model for a specific core, either S-TORC or CETOP-D 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 Calvert Cliffs Unit 1, Cycles 5 & 6 and Unit 2, Cycles 4 & 5 cores, comprised of 14x14 fuel assemblies.

Results, in terms of deviation between each pair of MDNBR's predicted by the two models, show that CETOP-D with the inclusion of the " adjusted" hot assembly flow factor, can predict either conservative or accurate MDNBR's, compared with Detailed TORC.

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(~h - TABLt 0F CONTENTS

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Page Section Title ABSTRACT i

11 TABLE OF CONTEh. '

LIST OF FIGURES iv

v LIST OF TABLES vi LIST OF SYMBOLS 1-1 1 THEORETICAL BASIS 1-1 1.1 Introduction 1.2 Conservation Equations 1-2 1-3 1.2.1 Conservation Equations for Averaged Channels 1.2.2 Conservation Fquations for Lumped Channels 1-5 2-1 2- EMPIRICAL CORRELATIONS Fluid Properties 2-1 2.1 2-1 2.2 Heat Transfer Coefficient Correlations 2.3 Single-phase Friction Factor 2-2 2.4 Two-phase Friction Factor Multiplier 2-2 2-3 2.5 Void Fraction Correlations 2-4 2.6 Spacer Grid Loss Coefficient 2.7 Correlation for Turbulent Interchange 2-4 2-7 2.8 Hetsroni Crossflow Correlation 2-7 2.9 CE-1 Critical Heat Flux Correlation 3-1

. 3 NUMERICAL SOLUTION OF THE CONSE L .JION EQUATIONS Finite Difference Equations 3-1 l

3.1 3-2 3.2 Prediction-Correction Method 4-1 4 CETOP-D DESIGN MODEL 4-1 4.1 Geometry of CETOP-D Desgin Model i

4.2 Application of the Transport Coefficient in 4-2 I

the CETOP-D Model f 4-4 4.3 Description of Input Parameters 5-1

, (~N 5 THERMAL MARGIN ANALYSES USING CETOP-D t/ Operating Ranges 5-1 5.1 5-1

' 5.2 Octailed TORC Analysis of Sample Core 5-1 5.3 Geometry of CETOP Design Model 11

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TABLE OF C0t1TErlTS (cont.)

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Title Page flo.

! Section fio. -

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5.4 Comparison Between TORC and CETOP-D 5-2 Predicted Results

- 5.5 Application of Uncertainties in 5-2 l CETOP-D

' 6-1 6 C0!!CLUSI0i15 7-1 l 7 REFEREt1CES 1

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

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LIST OF FIGURES

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Figure No. Title Page No.

1.1 Control Volume for Continuity Equation 1-12 1.2 Control Volume for Energy Equation 1-13 I

1.3 Control Volume for Axii.1 Momentum Equation 1-14 1.4 Control Volume for Lateral Momentum Equation 1-15 3.1 CETOP-D Flow Chart 3-3 3.2 Flow Chart for Prediction-Correction Method 3-7 4.1 Channel Geometry for CETOP-D Model 4-2 5.1 Stage 1 TORC Channel Geometry for 5-3 Calvert Cliffs 1 and 2 5.2 Stage 2 TORC Channel Geometry for 5-4 Calvert Cliffs 1 and 2 5.3 Stage 3 TORC Channel Geometry for 5-5 Calvert Cliffs 1 and 2 5.4 Axial Power Distributions 5-6 5.5 Inlet Flow Distribution for 5-7 Calvert Cliffs 1 and 2 5.6 Exit Pressure Distribution for 5-8 Calvert Cliffs 1 and 2 4-Pump 0peration 5.7 CETOP-D Channel Geometry for 5-9 Calvert Cliffs 1 and 2 l

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- LIST OF TABLES I

Table No. Title Page flo.

i 2.1- Two-Phase Friction Factor Multiplier 2-8 1 5

2.2 Functional RO - :enships in the Two-Phase 2-9 !

Friction Factor Multiplier

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j 5.1 Comparisons Between Detailed TORC and CETOP-0 5 ' 's i

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. 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 tcmperature 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 of 'I Engineering factor's H 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 pcner distribution to critical heat flux for the actual non-uniform axial power

. distribution.

F Total power factor, equal to the product of the T 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

% Spacer grid loss coefficient G

Crossflow resistance coefficient K) g K- Crossflow resistance coefficient i Effective lateral distance over which crossflow occurs between adjoining subchannels O nDnBR ninimum denarture from nocicate boilins ratio m Axial flow rate N ,H ,ll ' Transport coefficients for enthalpy, pressure g p u and velocity W-

O SYMBOL -

DEFINITION P Pressure P

3 Heated perimeter 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

cool Bulk coolant temperature T

sat Saturation temperature T,3)j Surface temperature of fuel rod u Axial velocity u* Effective velocity carried by diversion crossflow v Specific volume V Crossflow velocity w

gj Diversion crossflow between adjacent flow channels wjJ .

Turbulent mass interchange rate between adjacent flow channels x Axial distance X Quality a Void fraction y Slip ratio o Density 4 Two-phase friction factor multiplier 4j Heat Flux c Fraction of fuel rod being included in flow channel SUBSCRIPTS f,g Liquid and vapor saturated conditions 1,j Subchannel identification numbers i ij Denotes hydraulic connection between subchannels

{)

i and j J Axial node number P Denotes predicted value n

. = ~ _ - . . . - - - ~. . -. . . . - . - . . . . . _ . . . - . .-. .- _ - . - . _ .- - .

r . .

j O ' SUPERSCRIPTS DEFINITION t-t- -

Denotes transported quantity between adjoining i lumped channels

Denotes transported quantity carriec by l- ;

i diversion crossflow

!' De' notes ef fective' value 4'

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

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

[_ [ 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 mod'l e to account for the deviation of f tDNBR frc. 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.

The CETOP-D model to be described in this report has been developed to retain all capabilities the S-TORC .nodel has in the determination of core thermal margin. Ittakestypically[ [ for CETOP-D l to perform a calculation, as accurately as S-TORC, on a four-channel core represen-tation.

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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 weig'hting factors, for morc precise treatments of crossflow 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, n -

( _)

1-1

Q,) -

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 Mv"BR due to model simplification. A statistical or deterministic allowance for engineering factors accounts for the uncertainties

. associated with manufacturing tolerances.

1.2 Conservatinn Ecuations .

A PWR core contains.4 large number of subchannals 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 flea 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) l' umped 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 t rom 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 rod subchannels).

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

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1.2.1 Conservation Ecuations for Averaced Channels 1.2.1.1 Continuity Ecuation Consider two adjacent channels i and j, as shown in Fig; e 1.1, which are hydraulically open to each other. The continuity equation for channel i has the form:

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-m j + (mg+ (1.1) dx) - w'jjdx + w'jjdx + wjjdx = 0

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Assuming the turbulent 1aterchanges w'jj=w'jj , the above equation becomes:

am j

=-w jj (1.2) 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'. =- E N w . ; i = 1, 2, 3,..,N (1.3) 3x j=1 iJ 1.2.1.2 Enercy Ecuation The energy equation for channel i in Figure 1.2b, considen ing only one adjacent channel J, is: e 3

-m hj g + (mj h; + mjjh dx) - q'jd x - w'jj jh dx + w'jj h;dx+wjj h*dx=0 (1.4) ax where h* is th. enthalpy carried by the diversion crossflow w;j.

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

(() as:

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"i g = q' j - (hj-hj ) w' jj+(hj -h*)wjj (1.5)

Considering all adjacent flow channels, the energy equation becomes:

q ' '. N w' N w..

B h '. J+E

= - I (h-h)m;I.

i j ( h1 . - h* ) m. Ll. (1.6) ax mg j_j j,j g

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1.2.1.3 Axial Moment;m' Equation Referring to Figure 1.3b, the axial momentum equation fer channel 1, considering only one adjacent channel j, has the form:

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-Fj dx + pj Aj - gA ojj dx - (p Ajj+ pgjA dx) =

-mj uj + (m juj + d m u jjdx)-w'jjuj dx + w'jj ju dx + wjju*dx (1.7) where u* = 1/2 (uj +u.).

J By using the assumption w'$3=w' jj, one has:

a p '.

-Fj - gAj pj-Aj 3x =h mu j j + (u j-u j)w'jj + u*wjj (1.8)

Substituting the following definitions:

2 Si "Pi ;F j f je5 AK j G i vi m uj s g, j a(Avj 2De.

+

2ax (A y}

(*

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

aPj m vj f j tj KGi"i a "Pi A; 3x = -Aj (Ag }2 20e.

b

2.a.x

A i Ox (h7 - 9^i# i ( .10) 1 1 1 Q - (u j-uj ) w'jj + (2u j-u*)wjj 1-4 ,

(O_)

Considering all adjacent channe.ls, the axial momentum equation becomes:

ep mg 2 vj f 9ej

K Gv ii*A 3 vpi ax j"~IT) 20e. 2ax i Tx-(A.i ) - 9#i i i N w' N w (1.11) 3 I (uj-uj) g,U. F I (2uj -u*)

j=1 1

J=l 1 1.2.1.4 Lateral Momentum Ecuation 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 jj. Referring to the control volume shown in Figure 1.4b, the fona of the raomentum equation is: .

"i'i"ij!

(pj -Pj) = Kij 29 sd o" (1.12) where K jj is a variable coefficient defined in Reference 3 as 2

i +

Kj .3 = ( + XFCONS 2 (1.13) ij For averaged channels the spatial acceleration term is not inclu&d explicitly but is treated implicitly by means of the variable coefficient, K jj.

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

,,relatively larce size.

1.2.2 Conservation Ecuations for Lumped Channels 1.2.2.1 Continuity Ecuation Since only mass transport is considered within the control volume, the continuity equation has similar form to that for averaged channe t , i.e.,

Eq. (1. 3) .

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n 1. 2.2.2 Energy Ecuation V '

Consider two adjacent channels i and j and apply the energy conservation to channel i within the control volume as shown in Figure 12.a, the energy equation has the form:

Bh mg

= q' g - (lij -Iij ) w' gj + (hg-h*) w gj (1.14) where q' = energy added to channel i from fuel rods per unit time per unit length, w'jj = turbulent interchange between channels i and j hg w'jj = energy transferred out of channel i to j due to the turbulent interchange w'..,

1J hj w'4) = energy transferred into channel i from j due to the turbulent interchange w'43,

! hj and h j are the fluid enthalpies associated with the turbulent interchange; h* is the enthalpy carried by the diversion cross-flow w$) and is detennined as follows:

h * = lij if w j3 > 0 h* = h. if w. . < 0 (1.15)

J 1J 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 , li$ and nj are defined as the radially averaged enthalpies of the boundary subchannels of lumped channels i and j respectively.

Since h; and h) are not explicitly solved in the calculation, we define a transport coefficient N to g relate these parameters to the lumped channel counterparts hg and h as follows:

j n=

H hi-hI (1.16) hg -Iij 73 The parameter Ng is named the transport coefficient for enthalpy.

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

1-6

h = h '. + h 3=. n'. + n.3 c 2 2 (1.17) fq L'

and p', ', p F-hj c

=

(1.18) 2 h -h i fij - h c

2 II*I9)

I which are followed by the approximations:

iij = ch +(i-h)

= h '. + h . + h. - h 2 2N (1.20)

, H Ii.a = hc +(fi.a - hc)

(1.21)

= hi+hj + h]. - h.

1 2 2t1 H

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

m j-ahi ,q i j-(jh -h ) W'jj +(hj -( j +h h

2

~+

(hj -h )n 2N ) *ij (1*22) where n = 1 if wj j >, 0 and n = -1 otherwise.

It should be noted that if channels i and j were averaged channels, Ng = 1.0 for this case, Eq. (1.22) reduces to the Eq. (1.5) in Section 1.2.1.2.

I

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

BP ax i = -Fj -g:g Aj-("uj- -uj ) w' jj + (2u j-u*) wj )

A i (1.23) l 1-7

O channel area, V where: A j =

pg

= radially avercged static pressure, g = gravitational acceleration, p - coolant density, 4

G = axial velocity carried by the turbulent interchange

"'ij u = channel radially averaged velocity F j = momentum force due to friction, grid form loss and density gradient As for h j and h), uj and uj can be regarded as the averaged velocities of the boundary subchannels of the lumped channels i and j respectively.

Define the transport coefficient for axial velocity, fi g, as follows:

' e -u.

N ~ (1.24)

U ,

i j Using similar procedures ir, the approximation of jh and h j in terms of hj , h j, and fl , as described from Eq. (1.17) to (1.22), we derive:

H uj -

U i+u3ui -u j (1.25) 2 2H g

and

~

u. + u.

1 u.-u

= +

2 2N U

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

ap u -u. , j +u. (uj-u j)n A =-F j -Aggag - ( j 3

)W ij+(2uj -(u + i a 2 2N U id (1.27) where n is defined in Eq. (1.22) -

                                                           - - - , 1.8- _ - . -              -      -           --     . - , _

O V 1.2.2.4 LateralMomedumEcuation Consider the rectangular control volume in the gap region between channels i and j as shown in Figure-1.4.a. Assuming that the differ 5nce between the diversion crossflow momentum fluxes entering and leaving the control volume through the vertica: surfaces sax is negligibly small, the fonnulation for lateral momentum balance is:

                 -F9 ) - pj sax + pj sax = -(p*stu

V)x + (p*stu*V)x+3x (1.28)

Making use of the defi'nition of the lateral flow rate , w.. = p* sV

1J Eq. (1.28) becomes,'after rearranging

F

                                           )      a(u'w$j)                              ,

(_p_jjP ) = s u$$

s/t ax (l . d)

The term F / sax represents the lateral shear stress acting on the control 43 volume due to crossflew and is defined as: I F'.3. = w$3lw$$l (1,30) sax K ]. 29 s 2 1 , Substituting Eq. (1.30) into Eq. (1.29), and taking the limit as ax+0, i (p W ijlWijl 1 3 _p_j) = Kij 2

s/t ax ("*ij ) U* I g i where: F = channel averaged pressure, Kgj = cross-flow resistance coefficient, w gj = deversion cross-ficw between channels i and j, i s = gap width between fuel rods, q t = effective length of transverse morrentum interchange, D u* = axial velocity carried by the diversion cross-ficw w jj, assumed to be (ug +uj )/2 1 k

O V The above equation is equally well applied to two ludped channels when each contains a certain number of s'ubchannels arranged as shown in Figure 1.4a In this case, the diversion cross-flow w jj and the gap width s should be expressed by: W jj:(N) (cross-flow through gap between two ad.iacent rods) (1.32) s=(N) (gap between two adjacent rods) (1.33) where N is the number of the boundary sut J ,nels contained in each of the lumped channels. For the case of two generalized three-dimensional lumped channels, parameters gj and p3 are regarded as the radially averaged static 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:

                                                         "ij!"ijl           +

t a(u*w43) (1.34) Pj - pj= Kij 2gs2 p* s

,                                                                                            ax 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 i                      subchannels.                .This is because the control volumes chosen to model the transverse momentum transport in these two cases are identical.                                                                   Since p; and pj are not explicitly calculated, we define the transpect coefficient l

for pressure to relate these parameters to the calculated lumped channel f parameters pj and pj as follows: i ' p1. - p3-N g' = (1.35) ! Pj - Pj l where p g and p3 cre the radially averaged static pressures of the lumped channels I i and j respectively. Inserting Eq. (1.35) into Eq. (1.34), we obtain the transver?_ momentum equation for three-dimensional lumped channels as follows: i O l pj-pj W 43lwjjl t {(u ) j N p

                                                    'i j        2      ,           s3 x 295 l                                                                                     1-10

O 1.2.2.5 Transport coefficients There are three transport coefficients Hfl ' "U and tip in Eqs. (1.16), (1.24) and (1.35) which need to be evaluated prior to the calculation of conservation equations. Previous study in Re#erence 2 concluded that the calculated hj , m j , p j , and w jj are intensitive to the values used for fl U nd tip . This conclusion is further confirmed for the three-dimensional lumped channels. Therefore, the values of fl Uand it canp be estimated by a detailed subchannel analysis and used for a given reactor core under all _ possible operating conditicos. It is , however, not the case for ?!g, whose value is strongly dependent upon radial power distribution 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 value of NHcan be chlculated by using a detailed subchannel TORC analysis to determine hj , h j, h ,j h and j fl forH use in the CETOP-D lumped channel analysis. However an hiternate method is used in CETOP-D, utilizing the pcuer distribution and the basic operating parameters input into CETOP-D to determine yfl for each axial finita-difference node. (

I l i l l \ i i a l' l-11 i

O . 4 m;+ dx dx

                                              - - - - _ _ A. _ _ _ __ ,I I                            l d

l

1 l

g > wijdx CHANNELi l

                                           '                            l   CHANNELj g

CONTROL t VOLUME $ l dx I

                                           !              , dx       c  .

I Wji I I # I j > w;jdx I I I Mi l I I t A f y ____I f 1 Figure 1.1 O CoNrnal volume ran coNrino,1y scu,1,cN

 *-#""h---   g    .,wg ,

9 e e

f

                                                  . _ _ _ _1__ _ _ _ J.

1 ^ l l l l i I i l l 3 - Llw;j'dx h cas,not / I CHANNELi lCHANNELj VOLUME I

                                                ,                                       l   l 1

1 l

                                                    - q;dx                       3 dx I

wf;hj dx , i ,-H w,31 ;,dx i i i i 7 l mih; I I

                                               !                    i       M          'ln                              v

_ _; _ _7 , BOUNDARY SUBCHANNELS (A) CONTROL VOLUME FOR LUMPED CHANNEL m h + _d mi h;dx dx A I

I i I I CONTROL v '""5 [l i CHANNELi l I

                                                                                             = *iih'dx CHANNELj                  i r gjdx                            l                               dx

} I wf;hj dx l - w;;h,ox 1 l m h; l l 1 i A , Y (] (B) CONTROL VOLUME FOR AVERAGED CHANNEL o Figure 1.2 CONTROL VOLUMES FOR ENERGY EOUATION

m;u; + _0_. m;u dx dx 0 P A; + p;A;dx O. V p 6x

                                        . _ _ L _ _f _ _ _ _ l.

i ' l ^ l l l ' I I ' CONTROL N w;u*dx l l l VOLUME I 1 I T l CHANNEL iti 8 I- CHANNELj F;dx ! T i ; i I gA;p;dx I 3 dx I I l

             .                                   *ji jd

l I l -- Wji Ui dx p o A; g l g ,

l m;u; i i

                                   !        A                             1                 Y q--          n    ,       ,        i BOUNDARY SUBCHANNELS Pi ;A' (A) CONTROL VOLUME FOR LUMPED CHANNEL m u; + 0 m;u dx dX l                                   .
                                       . _ _4_ _ _ j _ _ _ _1 i

j .- g I p ;A; + 0_ pA;dx CONTROL VOLUME l r wiju'dx i* CHANNELi CHANNELj

I gA;p jdx I dx I l I ,

                                  !                Wjiujdx            ;
                                                                          & w;'ju;dx P idA;   g i      m u;                         I 1        PI A;            I l
                                   -- - j- - - g---

p (B) CONTROL VOLUME FOR AVERAGED CHANNEL

   %J Figure 1.3 CONTROL VOLUMES FOR AXIAL MCMENTUM EQUATION 1-14

(G s u' x + A x - a _ Vx + 3x I I I ; a I CONTROt i VOLUME i i O O O Q',O O O Pi s I i p l

                         -*l              i I

O O O OiO O'O I I I I I;s A x EsAx ' j Ax I l* ~l P; pj l F ii CHANNELi CHANNELj CHANNEL i l l CHANNELi l ly l I i _j Y TOP VIEW h V, u' x SIDE VIEW (A) CONTROL VOLUME FOR LUMPED CHANNEL _ _ _I_ _ _ _ A l l I I I I i r----- , I 8 l l l t I i I 8 l l ! l p'. M W p. p; -*i --* w;j fpj AX ! : 1 I l l l l l L___ ___J l

                                    > V;j        y CHANNELi                  CHANNELj l                          I l                       CHANNELi                       CHANNELj
                       ,                         i              V I           T -          7L                                       tog view SIDE VIEW "i                         "j (B) CONTROL VOLUME FOR AVERAGED CHANNEL Figure 1.4 CONTROL VOLUf.iES FOR LA ERAL MOf.1ENTUf.1 EQUATION

                                           .                                                                             a Q                                                      .

LJ , 2.0 EMPIRICAL CORRELATICNS CETOP-0 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-0, 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-0, these equations cover tie subcooled and saturated regimes.

2.2 Heat Trans'er Coefficient Correlations The film temperature drop across the thermal boundary layer adjacent to the surface of the fuel cladding is dept: dent on the local heat flux, the temperature of the local coolant,, and the effective surface heat transfer ccefficient: DTF = Twall -T cool * (2*I) h For the forced convection, non-boiling regime, the surface heat transfer coeffi-cient h is given by the Ditti:s-Boelter correlation, Reference 9: l O.8 0.4 h=0 23 k (Re) (Pr) (2.2) For the nucleate boiling regime, the film temperature drop is detennined from the Jens-Lottes correlaticn, Reference 10: DTJL = (T sat (2.3) cool) = P/900

   <                                                                                 e (3)       The initiation of n cleate boiling is determined by calculating the film temperature drop on the bases of forced convection and nucleate boiling.

l b

                                                                   , , ,_ 2 , l _ .      , . _ _ _ , , _ _ _ _ _ _

  #     A V                                          .

J The initiation of nucleate boiling is determined by calculating the film temperature drop on the bases of forced convection and necleate boiling. When DTJL < DTF, nucleate boiling is said to occur. 2.3 Single-Phase Friction Factor v 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) Values for the coefficients AA, BB, and CC must be supplied as inputs. 2.4 Two-Phase Friction Factor Multiolier A friction factor multiplier, c, 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 Mar ~nelli-Nelson correlations as listed in Tables 2.1 and 2.2. For isothermal and non-boiling ccaditions, the friction factor multiplier 4 is set equal to 1.0. For local boiling conditions, correlations by Sher and Green (Reference 11) are used for determining ;. 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 to calculate the subcooled void fraction explicitly. For bulk boiling conditions, ) is determined from Martinelli-Nelson results of Reference 12 with modifications by Sher-Green (Reference 11) and by v

v . Pyle (Reference 13) to account for mass velocity and pressur? 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 belcw 1850 psia, the void fraction is given by the Martinelli-Nelson yodel from Reference 12:

c = B, + B) X + B2 X2+BX3 3 (2.6 ) where the coefficients Bn are defined in Reference 10 as follows: For the quality range 0 1 X <0.01: Bo = B) = B 2 =B 3 = 0; the homogeneous model is used for calculating void fraction: . a=0 For X 1 0 Xv (2.7) For X > 0

                     " * (1-x)y7 + xy g For the quality range 0.01 1 X <0.10:

B = 0.5973-1.275x10 -3 p + 9.010x10 -7 2p -2.065x1f l03

                                               -2 B = 4.746 + 4.156x10 p -4.0lix10 -5 p2 + 9.867x10 p

I -4 2 (2.8) B = -31.27 -0.5599p +5.580x10 p -1.373x10-7p3 2 B = 89.07 + 2.408p - 2.367x10-3 p2 + 5.634x10-7p3 3 For the quality range 0.10 1 X <0.90:

                                               -#              -7 2             -II 3 B = 0.7847 -3.900x10 p + 1.145x10                      - 2.711x10         p B = 0.7707 + 9.619x10 p - 2.010x10 -7p2 + 2.012x10-Ilp3                                          ,
                                              -3 B = 1.060 -1.194x10 p + 2.618x10 p -6.893x10
                                                              -7 2           -I p

2 2-3 _ _. . . _ ___ . _ . __ __ ._. _ __ _ _ _ . . ~ __ _ . _

B = 0.5157 + 6.506x1 p -1.938x10 -7p2 + 1.925::10-IIp3 3 For the quality range 0.90 < x < 1.0: B,='B) = B2 *0 3 = 0; the homogenecus model given by Eq. (2.7) is used for calculating void fraction.

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

Xv v

           "*               9
                                     ,   for p > 1850 psia                                  (2.10)

(1-X)vf+X v g 2.6 Soacer Grid Loss Coefficient The loss coefficient correlation for representing the hydraulic resistance of the fuel assembly spacer grids has the form: 3 (2.11) KG = D) + O2 (Re)D Appropriate values for O n must be specified for the particular grids in the problem. 2.7 Correlation for Tur'bulent Interchange Turbulent. interchange, which refers to the turbulent eddies caused by spacer grids, is calculated at channel boundary in the following correlation: w'jj = E 0, (s ) A (Re)B (2.12) REr-where: G = channel averaged mass flow rate 0,= channel averaged hydraulic diameter s = actual gap width for turbulent interchange s = reference gap width defined as total gap width REF for 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-D. 2-4

O - - 2.8 Hetsroni Cross Flow Correlation Berringer, et al, prcposed 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 ficw channels.

E W ij!Wij!

                          .             ij                                                     .

(Pt - Pj)

2gp* 2 (2.13) s In Berringer's treatment, the variable K jj accounts for the large inertial effects encountered when the predominately axial flow is diverted in the lateral direction. In Reference 3, Hetsreni expanded the definition of jj to include the effects of shear drag and contraction-expansion losses K

on the lateral pressure difference: u 2 1/2 K jj = + (K'2+ (XFCONS) 2 ) gW 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 ficw 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 tres' 2d explicitly in Eq. (1.31) by means of the momentum flux term. Hetsroni suggested K = 1.4 and XFCONS = 4.2 for rod bundle fuel assemblies. These values are also used in CETOP-r'. 2.9 CE-1 Critica! Heat Flux (CHF) Correlation (Reference 14) The CE-1 CHF correlation included in the CETOP-0 is of the following form: b (b +b P) q, bj( )2 ((b+bP)( 3 4 10 6) 6 ) ( x) (hfg)) 6 10 6 (b7 P + b8 G/10 ) 0 6) 10 2-5

2 where: q"CHF = critical heat flux, BTU /hr-ft O 9 = pressure psia d = heated equivalent diameter of the subchannel, inches d, = heated equivalent diameter of a matrix subchannel with the same { rod diameter and pitch, inches G = local mass velocity at CHF location, ib/hr-ft 2 x = local coolant quality at CHF location, decimal fraction h = latent heat of vaporization, BTU /lb 79 and bj = 2.8922x10

                                          -3                                    ,

b 2

                             = -0.50749         ,

b = 405.32

                                               -2 b         = -9.9290 x 10 b        = -0.67757
                                          -4 b         = 6.8235x10                   -

6 b = 3.1240x10'4 7

                                           -2 b

8

                             = -8.3245x10 The above. parameters were defined from source data obtained under following conditions:                                                                                     .

pressure (psia) 1785 to 2415 , local coo'lant quality -0.16 to 0.20, local mass velocity (1b/hr-ft2) 0.87x106 to 3.2x10 6 inlet temperature ( F) 382 to 644 subchannel wetted equivalent 0.3588 to 0.5447 diameter (inches) - l subchannel heated equivalent 0.4713 to 0.7837 diameter (inches) heatedlength(inches) 84,150 To account for a non-uniform axial heat flux distribution, a correction factor FS is used. The FS factor is defined as: ,

                                   ,    u alent Unifom FS=                                                                  ~

O ~ 9"CHr. reen-unirorm C(J) _ a(x)c -C(J)@(J)-x ) dx FS(J)= -c(J)x(J)3 , q ,.CHF,iton-uni form ()_e i t .

i . 4 . . i I! i I t i LO . where, for CE-1 CHF correlation, I f C(J) = 1.8 (I~XCHF) ft 6 (G/10 ) 0.478 f i i The departure from nucleate boiling ratio, DNSR, is:

i I

I DNBR(J)= 9"CHF, Ecuivalent Uniform I l

                              .                   p3 g                    q "(J) l J

l 1 . 4 I i I i i i I l l p l l 1 ) e !O l l l ( 2-7

O Taatt 2.' (aD ', TWO.Pil ASE FRICTION F A CTO R MULT(PLIER - I $ = F AM(X = 0.4, G, P = 2000) G > 0.7 x 106

                                                $ = F AM(X, G P = 2000)                                                                                                                x  FMfJ3 (X, P = 2000)
                             $=1.0                                                                                                         l FMN3 (X,P)                                   F MfJ3 (X 40.4, P = 2000)

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

                                                                                                                                                                                       ,   I f.1N3 (X, P) f; (P. G.               FMN3 (X, P = 2000)                                                                     , I "3 (X,P = 2000)

FMN3 (X,P = 2000) 0 */DIF), l

              $ = 1.0    WillCllEVER            g < g.y ,3 g6                                                                              i                                           $ = F AP.11X-0.4, G'O.7, P=2000)
                                                                                                                                           '                                                               e2000)

LAlGER

                                                $ = r AM(X, G = 0.7, P = 2000)                                                                     FMN3 (X,P)                          =  bN3         ,

IMU3(X P) $ = F AM(X, G = 0.7, P = 2000) x x f4(G) IMN3 { X-4.0, P42000)

                                                ,                                      ,g (g)                                                      FMN3(X, P = 2000)

FMN3(X, P = 2000) I

x _@E'l IX EI xI 4(G) g FMf43 (X P = 2000) 2000 G > 0.7 x106 $ = F Afd (X,G,P = 2000) $ = F AM (X, G,P = 2000) $ = F A't (X = 0.4 G.P = 2000)

                                                                                                                                                                                       ,   $Ny (X, P - 20001
                             $=1.0              $ = F AM(X, G, P = 2000)                                 Fr.tug (X,P)                          x    FMN2 (X, P)                             FMN2 (X-0.4,P = 2000) x g                                0R                                                                       IUN I(X,P = 2000)                          Fun 2(X, P = 2000)                     FMN IX, P) f,(P,G, EJ2 (X P = 2000) 0 */D T H.        _ _           _ _ , , , , _ _ ,,,,,,,, -'          -~~~~~~
              $=1.0      WHICllEVER                                                                                                                                                    $ = F AU(F. 0 4 C'3.7, P+2000)

'5" G < 0.7 x 106 $ = F AM(X, G = 0.7,P = 2000) $ = F AM(X,G = 0.7 P = 2000)

                                 ,3 FMN, (X* P)                                I U (X,   P)                       m   M M, P = m er                           LAHGER
                                                 $ = F AMIX, G = 0.7, P = 2000) x                           x f4(G)         x          2               , (c}

'- 2 M = 4 0. P = 200M FMN,(X P = 2000) ,,,30 (X, P = 2000) 2 m liN2 (X, P) , , gg F f.tN2 (X.P = 2000) 1850 I U "'7 " I U $=FMN3 (x, P)

                            ,9=                                                                                                                                                      l 1,J T-DTJL _)                  4 ,g 2(P,G)                                                                                                   $ = Ff.IINy (X,P) x 12 (P,G)
                                                                                                          " '2 (P, C)

[ut0TJLj I

              $ = 1.0                     ,   ~~~~~~--                                           - - - - - ___ __                            __                                                         - - - - -

Ftri(X=' g l a G < 0.7 x 10 6 $ = FMNg (X,P) 0 0 42, P) .1 1 h

I 3(P, G) , f3(p, c) $=FMN (X,P)xf 3(P,C) 1 l

14.7 0 0 0 02 0.2 0.4 1.0 llEATING LOCAL Q UALIT Y' X NO BOILING BOILING - -- BULK BULLING f;01E. F UNCTIONAL IIEL ATIONSillPS ARE LISTED IN TABLE 2.2

Table 2.2 Functicnal Relatienships in the Two-Phase Friction Factor Multiplier (References 11,12,13) , For local boiling: 10 6 2/3 f)=C)(1+0.76(3 9-P ) where C) = (1.05) (1-0.00250*) e* = The smaller of DTJL and DTF w = 1 - 0*/DTF For bulk boiling: 7x0.75 6 FAM = 1 + (G/10 )1+X (0.9326 e (0.2263d0-3)p) FMN1 = 1.65x10-3 + (2.988x10-5) P-(2.528x10 9) P2 + (1.14x10-II)p 3 M2= X(1.0205 - (0.2053x10-3) p) 7.876x10-4 + (3.177x10-0) P-(8.728x10-9) P2 + (1,073x10 Il)P3 2 FMN3 = 1 + (-0.0103166X + 0.005333X ) (P- 3206)

f 2

                       =      1.36 + 0.0005p + 0.1 ( G ) - 0.000714P ( 6 )

' 6 6 10 10 6

f 3 1.26 - 0.0004P + 0.119 (I0 g ) + 0.00028P ( ) f 4

1 + 0.93 (0.7 - G) 6 10 4 2-9

3. NUMERICAL SOLUTIO:1 0F THE C0:tSERVATIO! E00ATIOils O 3.1 .inite oirrer>nce ecuetions .

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 dicplays briefly the marching CETOP-D foilows'in order to search for the

   ,               minimum value and the location of DlSR in a 4-channel core representation (c.f. Section 4.1).
                                                                                                 ~

Equations (1.F.), (1.22), (1.27) and (1.36) which govern the mass, energy and momentum transp3rt within channel i of finite axial length ax are written in the following finite difference forms: (1) Continuity Equation mg (J) - m4 (J - 1) 3x

                                               = -w j3(J)                                          (3.1)

(2) Eneroy Equation s h4 (J) - b g(1 - 1) h.- mg (J - 1) = q! -< -4, h3 wjJ . Ax 1 ng

(3.2) h.+h. (h. - h j)n hw jjj+('2 + -jN ) "ij ' g l , J-1 l (3) Axial Momentum Eaustion Pj(J) - Pj (J - 1) uj - uj {s) Ag g =-F j - A gga g(J) - g ujj U 3-1

1 Q . u 2ug w$3 - ( 2j +2 u+ ("i 2N- "j)") Wi j (3.3) U j g.1 i (4) -Lateral Momentum Ecuation Pj(J-1)-p[(3-1) w j3(J) wj3(J) N p Id 2gs ,, 2 l

g u*(J)wj~ ,(J) - u*(J - 1)wjj(J - 1) s ax I2 4) Where J is the axial elevation indicator and ax is the axial nodal length. 3.2~ Prediction - Correction Method i In CETOP-D a non-iterative numerical schemd is used to solve the conservation (

equations. This prediction-correction method provides a fast yet accurate scheme for the solution of m j , hj , w jj and pg at each axial level. The steps used in the CETOP-0 solution are as follows

The channal flows, mj , enthalpies h j, pressures p jand fluid properties are calculated at the node interfaces. The linear heat rates gj , cross-flows, w. ., and turbulent mixing, w. ., are calculated at mid-node. The l 1J 1] solution method starts at the bottom of the core and marches upward ({]) using the core inlet ficws at one boundary condition and equal core exit pressures as another. 3-2 -.-

O . An initial estimate % made of the subchannel crossflows for nodes 1 and 2. These crossflows are set to zero. W ij(1)=wjj(2) = 0 The channel flows and enthalpies at node 1 are known to be the inlet conditions. Using these initial conditions the marching technique proceeds to cali:ulate the enthalpies and flows from node 2 to the exit node. In this discussion "J" will designate the axial level "i" and "j" ! are used to designate channels, t Step 5 l i t O I i- _ 3-3

O I-i i i l . 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" diversion crossficw, W93(J + 1)p, is a good approximation. Thus at each node the axial flow rate can be accurately detennined. U

   ~s
 %d TORC on the other hand, initially assumes p; - p) = 0 at each axial location.

The conservation of mass and momentum equations are used to evaluate the diversion crossflows and, in turn, the flow rates at all locations. The axial momentum equation is used to determine p9 - p3 for the next iteration. 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.p once-through marching technique, its results are very close to those from the TORC iterative numerical technique. In general, about _ _ in TORC to achieve the same Occuracy 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 4 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. 3-5

I START l 1r

                                    >        READ INPUT 1r PREDICT AND CORRECT COOLANT PROPERTIES IN THE CORE AVER ACE AND HOT ASSE?.18LY CHANNELS AT ALL AXIAL NODES l'
         't                             PREDICT AND CORRECT COOLANT PROPERTIES IN THE HOT CHANNEL AT ALL AXIAL N0 DES PREDICT NEW HEAT FLUX                              1r CALCULATE CHF AND ONBR FOR THE HOT CHANNEL AT ALL AXIAL NODES l

l ir NO IS MONBR OR I QUALITY WITHIN THE LIMITS ? YES U PRINT OUTPUT 1r d NO IS THIS THE LAST CASE ? YES 1r STOP l Figure 3.1 l CETOP D FLOW CHART 3-6

u J=2 O . v PR EDICT w;j , m; 1 AT NODE J 1 u PREDICT wgj, w;j and m; AT NODE J u v PREDICT h; AT NODE J + 1 u COMPUTE COOLANT FROPERTIES i J=J+1 u H PREDICT w;; AT NODE J+1 u CALCULATE p; pj AT NODE J l u CALCULATE w;j, m; , h; i AT NODE J l u i LAST NODE ? f ., q YES

} U i

I Figure 3.2 i FLOW CHART FOR PREDICTION CORR.iiION METHOD

p ' G .

4. CETOP-0 DESIGN MODEi_

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 prepara_ tion

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 geometry of the model. A l'~

                   . description y              of this simplification is included here together with an explanaticn on the method for gen,erating enthalpy transport coefficients in CETOP-0.                      ,

4.1 Ge_ometry of CETOP-D Desion Model _

                                                                                                              . .m 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 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 MONBR hot channel 4. The location of the MD?M channel is determined from a Detailed TORC analysis of a core. Channels 2' and 2" are discussed in Section 4'.2. . The radial power hactor and inlet flow factor for channel 1 in CETOP-D is always unity since this channel represents the average coolant conditions in the core. The Channel 2 radial power distribution is normally 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 CE10P-0 so the Channel 2 power can easily be adjusted to any value. Initially, the inlet flow factor in l

      ]            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 i                   later adjusted in the CETOP-0 model to yield conservative or accurate MD:!CR predictions as compared to a Detailed TORC analysis for a given range of

operating conditions. 4-1

t t 4.2 Application of Transport Coefficients in the CETOP-D Model i 1 c) - - l , 4 1 a e J I i I ) f , 5 i- " ( { i l Y l' l i i 1 l i t i I l' A + b f I ! i 8 I s r 9 l E 1 1 l i 6 O ! 4-2 I l [-

9 6 1-m o 5

            *T C-4-3

j . . i x,) i .i W 4.3 Description of Input Parameters A user's guide for CETOP-0, Version 2 is supplied in Appendix A. To , provide more information on the preparation of the input parameters, the following terms are discussed. 4.3.1 Radial Power Distributions The core radial pcwer distribution is defined by C-E nucleonics codes in terms of a radial power factor, FR(i), for each fuel assembly. The radial power factor F R (i) is equal to: p(j)[powergeneratedinfuelassemb1Li (4.7) R power generated in an average ruel assembly Assuming power generated in an average fuel assembly is equal to unity, the folicwing expression exists: , N 1 I F(i)=ft p' (4.8) l i=1 l l where ti is the total number of assemblies in the core. The radial power factor for each fuel rod is defined by: t f($ ) , power generated in fuel rod i of assembly i (4,g) l R power generated in an average ruel rod j for an assembly containing it rods, one expects: M (] 3 I f (i,j) = l-1 F (i) R R (4.10) l j=1 4-4 L

The CETOP-D code is built to allow only one radial power factor for each flow channel, thus, for a channel containing n rods, the idea of effective radial poscr factor is used: (]

                              .                          E       C   fj(f,j)                                    -

f RII)= d"I (4.11) n ,- E C ' j=1 j where c) is the fraction of the rod j enclosed in channel i. _. 4.3.2 Axial Power Distributions The fuel rod axial power distribution is characterized by the axial shape index (ASI), defined,as: . L /2 L

                                                         /         FZ (k)dZ - /                F(k)dZ Z
                                   .                        o                  L /2 ASI              =                                                                                     (4.12)

F7(k)dZ where the axial power factor at elevation k, FZ (k), satisfies the normalization condition: L

                                / = F Z(k)dZ = 1                                                                                     (4.13) o and L, dZ are total fuel length and axial length increment respectively.

The total heat flux supplied to channel i at elevation k is: 4 =(core average heat flux) (f g (i)) (FZ(k)) (4.14) 4.3.3 Effective Rod Diameter For a flow channel containing n rods of identical diameter d, the effective rod diameter defined by: n (4.15)

    .q                           6(i)=,E cd                     j V                                                ,) = 1 is used to give effective heated perimeter in channel i. The following expression, derived from Eq's. (4.5) and (4.9), iraplies that equivalent energy is being received by channel i:

n D(i) fR(i)=dI f (I'd) O " cj R . . (4'I6) 4.3.4 Engineering Factors The CETOP-D model allows for engineering factors (as described in Reference 1) due to manufactur ;olerances. 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 DNBR design limit, which is then input as parameter 85 (Appendix A). The former method req 3 ires further explanation on the treatment of engineering factors: (1) Heat Flux Factor (f ) A slightly greater than unit heat flux factor f , acting as a beat flux multiplier, tends to decrease DNBR in the following manner: DNBR = E- < CHF (4. )

                                     #*i 4        &i     for f+ > 1 where          defines the DNBR before applying f and9 4 is the local heat flux.

(2) Enthalpy Rise Factor (f g) and Pitch and Bow Factor (fp ) These factors are involved in the modification of the effective radial power factors and rod dir.acters for the fuel rods surrounding the hot channel as follows: m m

fIH E I Cj R(4'd) E ' f R(4'd) i F (4)~= P j=j = __=1j j R m m (4.18) I Hp E j . E

'C.

J=1 J"I J m n , f g I c) fR (3,j) +j=1r c f(3,j) R R (3) , j=1 j

                                    .n                   n

! f r . +r c N j=1 r.3 j=1 j

O *

and- . ,

D (4) = HP ffdI ; (4.19) j,j j . a m n D (3) = d (fH E C +I C ' (4.20) J=1 J j=1 J) A A where F R s and D's are the modified effective radial power factors a.nd rod diameters for channels 4 and 3, a is the number _of rods on channel connection 4_3andn'isthenumberofrods{ . Again, the inclusion of f Hand f inp the core thermal margin prediction causcs a net decrease in DNBR in addition to that described in Eq. (4.11). 9 e S l e e O 4-7

          .          .                                                                                              }

CHANNEL NUMBER --- >2 HOT ASSEP.'.3LY = 1/4 OF 4 ONE FUEL ASSEMBLY CHANNEL AVG.

                                                  " F" O                .a^oi^' rowen FACTOR 1

CORE AVERAGE 1.000 4 CHANNEL = ONE FUEL ASSEMBLY (A) FOUR CHANNEL CORE REPRESENTATION U! PERMEABLE AfID ADIABATIC ]

                                     .JOOOOOO 2.,                m 2"    2'      2

l

                                  <    O0                   2" i               I3     2'      2" C

w 2" 2' 4 3 2' y e p 3 3 U ; E 2" 2' 3 2' 2" 2" 2* 2.. (B) CHANNEL 2 IN DETAILS Figtne 4.1 CHANNEL GEOMETRY OF CETOP D MODEL

                                                     ---. $ 8, _ . _ _ _ _                              . _ , . - -

5. THERMAL MARGIN ANALYSES USING CETOP-D O'. This section w.eports the CETOP-D model by comparing its predictions for a 14x14 assembly type C-E reactor (Calvert Cliffs Units 1 & 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 normal DNB analysis.

5.1 Operating Ranges The thermal margin model for 2700 Mwt Calvert Cliffs Unit 1, Cycle 5 & 6 and Unit 2, Cycles 4 & 5 was developed for the following operating ranges: Inlet Temperature 450-580 *F System Pressure 1750-2400 psia Primary System Flow Rate, 77-120(4-pump)

                                % of 370,000 gpm                                      75       (3-pump)

Axial Power Distribution -0.527 .+0.527 AS I 5.2 _ Detailed TORC Analysis of Samole Core The detailed thermal margin analyses were performed for the sample core using the radial 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 inlet flew and exit pressure distributions used in the analyses were based on flow model test results, given in Figures 5.5 and 5.6. The results j of the detailed TORC analyses are given in Table 5.1. l 5.3 Geometry of CETOP Design Model _ i ! ~ The CETOP design 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 2 in Figure 5.1) and Channel 1 is an assembly which represents l ! the average coolant conditions for the remaining portion of the core, t The boundary between channels 1 and 2 is open 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 MDNBR hot channel 4. . 5-1 -

Q 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 4-pamp operation so that MDNBR results predicted by the CETOP model are either conservative .or accurate. A similar procedure to that described above shows that a CETOP-D hot assembly flow factor of [ ] is appropriate for 3-pump operation. 5.5 Application of Uncertainties in CETOP-D' t An allowance for the system parameter uncertainties in Calvert Cliffs Units 1 and 2 was derived statistically in Reference 6. This allowance has been incorporated into the design CETOP-D model in the form of a design MDi;BR limit equal to 1.23 replacing the original design limit of1.19. t 6 , t 0 - - 5-2 ,

E 1 1 2 V

1.1794 1.4500 CHANNEL NUMDER

( 6 7 ASSEMBLY AVG. RADIAL '3 4 5 , POWER FACTOR

1.0409 1.4191 1.G3G4 1.4350 1.1870

8 9 10 11 12 13 0.8172 1.3779 1.3458 1.1968 1.0208 0.9152 14 15 16 17 18 19 20 , 0.8163 0.G73G 0.9400 0.9928 1.325G 0.9360 0.829G 21 22 23 24 25 26 27 28 1.0419 1.3783 0.9393 1.1047 0.7593 0.814G 0.91G1 0.9458 i I I h n 1.3470 0.9933 0.7593 0.4196 0.7578 0.7903 0.7097 1.4204 l 1.6373

+ '

1.1980 1.3275 f _ _;_ _ _ 0.8132 0.7588 0.5855 0.5376 j 0.3079 1.1794 - R _L. - - - -@L I SI 1.022G 0.9425 0.92G4 0.7935 0.5300 0.4G99 0.3945

           --_               1.4353 1.4498 0.2182 1.1872                                             0.998G         0.6953              0.3083          0.3899                .{-

Q. - 0.9175 0.8419 ) ! i i I l NOTE: CIRCLED NUMBERS DENOTE " LUMPED" CHANNEL O e'Dere s.' STAGE 1 TORC CllANNEL GEOMETRY FOR CALVERT CLIFFS 1 AND 2 5-3 ? -- , _. . - . _ _ . _ _ _ _ - , _ _ _ . - - _ .

l CHANNEL NUMBER ~-5 2 1

                                                             ~
 . I 3     4 12   6              7            8

_) 13 9 10 11 14 15 16 i l l q- - + 1 Figure 5.2 STAGE 2 TORC CHANNEL GEOMETRY FOR CALVERT CLIFFS 1 AND 2 5-4

l I 1 t I i 1 . i i i l l ! l l f 1 ! i l l l _J l (N Q Figure 5.3 STAGE 3 TORC CHANNEL GEOMETRY FOR CALVERT CLIFFS 1 AND 2 5-5

O O - i . P i i I I a i 2.4 a i 1 ! +0.527 ASI --- ---- 2.2 -- l

                                                                                                                                                      -0.527 AS!
                                                                                                                                                    +0.337 ASI                                                                        .

2.0 - 0 000 ASI --- --

i -~~ s N 0.070 ASI - ! 1.8 -

                                                                                                  /'f           s N                                                                    <

f '

                                                                                       '                                N                                                                                                .

! c - , . g, 1.G .-

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                        '"         .I                            #"                                     /   '%_                                             /_

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's

! 0.S s ! / / / N ' ll[/y 7' N :s 0.4 :[. /

                                                                                                                                                                                        'N'N .s,~~.                            h
                                                                                                                                                                                                                      .;          Ng 0.2 y y  -

s

                                                                                                                                                                                                                                  ~ ,3 O

t 4 0 0.1 0.2 0.3 0.4 0.G 0.G 0.7 0.8 0.9 1.0 FRACTION OF ACTIVE CORE HEIGHT FROM INLET Figure 5.4 i AXIA1. POWER DISTRIBUTIONS

t O I t i l

                                                                                                     ,i i

l

q. ..

l _J O ei2ere s.s INLET FLOW DISTRl3UTl0N FOR CALVERT CLIFFS 1 AND 2,4-PUMP OPERATION 5-7

9. O !

 ,                                                                                              i.

I I r i 1 a i i 1. I f 9. l Figure 5.6 l EXIT PRESSURE DISTRIBUTION FOR CALVERT CLIFFS i AND 2,4 PUMP OPERATION l 5-8 L -

e a e * , ie O , I 1 1 I f d i 2 Figure 5.7 O CETOP D Cf:ANNEL GEOr.1ETRY FOR CALVERT CLIFFS 1 AND 2 (CHANNEL 1 NOT SHOWN) 5-9

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

p)

               %                                                                                                              (})           ,

Axial Elev. - Operating Parameters MDNBR Quality at MDNBR ofMDNBR(in) Detailed Detailed TORC CETOP-D TORC CETOP-D Core [ Avg. Mass Core Avg.' Axial Relative Inlet Relative Inlet Vel city Heat Flux Shape Flow.in Flow Flow in Flow Detailed Inlet Temp. 10 lbm Btu Index - Location 2 Factor Location 2 Factor TORC CETOP-D Pressure (psia) ( F) hr-ft br-ft 2 } *( AbI) - - - ~ - -- 1 2250- ' ' 548 2.5121 230111 +.527 2250 ., 548 2.5121 282026 +.337

2250 548 2.5121 248243 +.000 2250 548 2.5121 238397 .070 2250 548 2.5121 197362 .527 1750 465 2.1117 284825 +.337 1750 465 3.2910 391943 +.337 g 1150 580 1.8239 160408 +.337 1750 SSO 2.8425 204107 +.337

     ?'J0'       465       2.7569     331515     +.337 2400        580       2.4009     236406     +.337 2400        465        2.1117    320604     +.337 2400        580     .1.8239      199175     +.337                                                                                __.

TA3LE 5.1 COMPARISCNS BETWEEN DETAILED TORC AND CETOP-D i

6. CONCLUSION CETOP-D, when benchmarked against Detailed TORC for Calvert, Cliffs Unit 1

(]) Cycles 5 & 6 and Unit 2, Cycles 4 & 5, has been shown to produce a conservative and accurate representation of the DNB margin 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 Calvert Cliffs Unit 1, Cycles 5 & 6 and Unit 2, Cycles 4 & 5, and generally for applications in which the Design i TORC methods have been approved (Reference 16). I E o 4 .f O 6-1

U

7. REFERENCES . ,

o " TORC Code, A Computer Code for Determining the Thermal Margin ( ,) 1.

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.
               ?,  Hetsroni, G., "Use of Hydraulic Models in Nuclear Reactor Design",
)                  Nuclear Science and Engineering, 28, 1967, pgs. 1-11.
>              4. Chiu, C. ; Church, J. F. , "Three Dimensional Lumped Subchannel Model and Prediction-Correction Numerical Method for Thermal 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, January, 1977. .

              .6.  " Statistical Combination of Uncertainties, Part 2", CEN-124(B)-P, January, 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. l 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 Orop in Thin Rectangular Channels", Chem. Eng. Prog. Symposium Series, No. 23, Vol. 55, pgs. 61-73.

12. Martinelli, R.C. and Nelson, 0.8.; Trans. Am. Soc. Mech. Engrs., 70, 1948

   .                pg. 695.

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

I 14. "CE Critical Heat Flux Correlation for CE fuel Assemblics with Standard f Spacer Grids", CEllPD-162-P-A, September 1976.

15. Derringer, R.; Previti, G. and Ton g, L.S., " Lateral Flow Sinulation

\])

f in an Open t attice Core", ANS Tran , actions , Vol. 4,1961, pgs. 45-46. l . ! 7-1 L

1 O

    '"' 16. Letter dated 12/11/80, R. L. Tedesco (t4RC) to A.E. Scherer (C-E),
                " Acceptance for Referencing'of Topical Report CEilPD-206(P), TORC Code Verification and Simplified Modeling Methods".
                                    *T l

l n U u

e O . e ! Appendix A CETOP-D VERSION 2 USER's GUIDE O A-1

 - _ _ . . _ . . _ _ _ _ _ . . - - - -   - _ _ . - _ _ _ _ _ _ , _ _   "*~*%="TP='N*+e,.,y

O . A.1 Control Cards i 4 Code Access and Output Centrol Cards r 6 A.2 Inout Format

1) Read case control card, Format (Il0, 70A1)

. Case Number, Il0 Alphanumeric information to identify case, 70Al , 2) Read Relative Addresses and Corresponding Input Parameters, i 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 input after the last l 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 en this card. XLOC (N2): corresponding input parameters ! thru " l XLOC (N3): l Cs_) I l A-2

A.3 List of Input Parameters b Relative . Parameters Address Units Descriptions GIN 1 million-lbm Core average inlet mass velocity, during br-ftz core flow iterationi this value is the initial guess. XLOC(2) 2 million-Btu Core average heat flux, during core power br-ft4 iteration this value is the initial guess 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 d ~ing

                                                                 " iteration"*, so the number of iterations may be reduced. Specify 1.0 to not use the capability.

I 6 Use 1.0 to print more parameters during NPOWER 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 J=1, NGRID distance from bottom of active 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=1,4 l PERIM(I) 50-53 ft Wetted Perimeter for Channel I l I=1,4 HPERIM(I) 54--57 ft Heated Perimeter for Channel I I =1,4 l Parameters superscripted wit 1 1 are not ipcluded in CETOP-0 Version 1. l O *Tae term "itefation" flow or on Cha can de eerinee es eBtser iteration on core Power. cor inel 2 radial peaking factors l A _-3 ____ _ _ _

O- Relative . Address Units Descriptions Parameters \ s \ 58 None Maximum rod radial peaking factor wanted FR s for Channel 2. Curing radial peaking factor iteration this value is the - initial guess. PlPB 59 None Ratio of the maximum rod radial peaking factor of Channel 2 to the Channel 2 average racial factor. This ratio is based upon a power distribution normalized to the core RADIMI 60 None Effective radial peaking factor for Channel ' 61 -6 3 None Effective normalized radial peaking factor RADIAL (I) I=2,4 for Channel I (normalized to the Channel 2 average radial factor in the core power din bution, if this is done correctly .:AOIAL(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 red

   's fractions depositing heat to the channel.

0(I) . Effective rod diameter for Channel I, P i ,4 64-67 ft 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). 68-70 ft Gap width available for crossflow between GAP (I) I =1,3

                                           '                            Channel I and Channel I+1. [            .
                                                                                   )

71 None Number of axial nodal' sections in model, NDX maximum of 49 (recommend 40) 72 . None Number of Channels (always 4) NCHANL 73 None Number of spacer grids (maximum number of ': NGRIO ITMAX 74 None Mavimum number of iteratiens (recommend (,S/ 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. A-4 ._., - .- - - - -_, .

E n Relative ! Address ' Units Descriptions Parameters l PDES 75 PSIA Reference pressure at which the core average mass flux is specified. If

                            '                                               the core inlet mass flux (GIN) is specified
                          -                                                 at (TIN, PREF) then PDES can be , set to           ,

0.0. If not, the code ill correct

                                            '                               the inlet mass flux to (IN and PREF by using PDES and TDES as reference conditions.

TDES 76 F Referen.ce temperature at which the core average mass fl'ux is specified. . Can be set to 0.0 for the syne 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 MCNER in hot channel 79 None Fraction of power generated in the fuel QFPC

                                        -                                  . rod plus clad SKECDK             80                 None                    Engineering heat flux factor.

FSPLIT 81 None Inlet flow factor for Channels 2, 3, 4 00H(1) 82 ft [

83 ft Heated hydraulic diameter of channel 4. DDH(2) 84 ft

                                                                   -I         Parameter used in the turbulent mixing COMIX correlation, determined by taking the

[') , ratio of the number of subchannels along one side of a complete fuel bundle to the T width on that side. i DDNBR 85 I None Design limit on DNBR for CE-1 CHF correlat '

           .s Relative Address           ' Units                   Descriptions Pa rameters                                                                                         ,

DNBRC0 86 lione Initial value of the ONBR derivative with gespect power during core power iteration L and with rejs ect to flow 4 during core fl]ow iteration L ]- ONBRTOL 87 , None Tolerance on DNBR limit. 88 None Maximum acceptable coolant quality at MDNBR QUALMX

                                                    . location.

QUALCO 89 None Initial value o.f the quality derivative

                                 't                 with respegt power durin core power iteration L                     and with respect t      flow during c e flow iteration                       .

QUALTOL 90 None Tolerance on quality limit. AHDAF 91 None Ratio of core heat transfer area to flow area, used for specifying a core saturaticn limit during overpcwer 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 i teration .

DTIME 93 - Sec. CESEC time, this parameter is printed in the output when the CESEC code is linked with CETOP-D. CH(2) 94 None Average enthalpy transport coefficient in the total channel axial length between CHs. 2 and 3. Insert 0.0 for CETOP to self-generate the transport coefficients. 2 AMATX 95 ft GAPT 96 ft S O -

        % -~

Relative - 6

     /)     . Parameters          Address            . Units                       Description.s
                                                                                              \          -

3 HC 97 None s 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 channels. Use 1.0 to specify infor-
                                                                                                                  ~
                                           -7                            mation.                   /       -

NY 100 None Use 0.0 for not using the relative locations of the axial power factors as long as the 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 cnd 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 1003 powar, hr- f tz includes heat generated from rods end coolant. Fuel rods are corrected for axial densification. .- , XLOC(103)' 103 Hone QUIX file case number. The QUIX code is used in Physics to generate axial pcwer shr.: l HRAD. 104' Hone Option to " iterate" on the following until l i - the design limit on DNBR is reachec. l 0.0: Iterate on core power, if adcress ( (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 OMB l limit is reached. l 2.0: Iterate on core flow 1 (" i._ l I \ A-7

n V Relative . Parameters Address ' Units Descriptions I NZZ 105 None Use 0.0 to not : print CESEC time (DTIME) Specify 1.0 to print. GRKIJ(J) . 106-117 None Option to input different spacer grid J=1,NGRID types with the corresponding loss

                                -                    coefficient equations.

0.0 Normal grid with built in loss coefficie-

                                                     ^1.0  Type 1 grid with coefficient equation =
                                                      . CAA(1) + CSB(1) * (Re)CCC(l)
                              ,                      2.0   Type 2 grid -

CAA(2) + CSB(2) ? (Re)CCC(2)

3. 0 Type 3 grid =

CAA(3) + CBB(3) * (Re)CCC(3) CAA(1) 118 None Constant fer Type 1 grid equation CBB(1) 119 None Constant for Type 1 grid equation CCC(1) 120 None Constant for Type 1 grid equation CAA(2) 121 None Constant for Type 2 grid equation 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 v A-8

O Relative Pa ramete rs Address ' Units Descriptions RAA2 129 None s RAA22 130 . Ncre GAP 2P 131 ft v GAP 22 1 32 ft 2 A2P 133 ft A22 134 ft DD2P 135 ft DD22 136 ft 137 - 139 None For Future Work NDXPZ 140 None Number of axial power factors (Recorar.end 41) XXL(J) 141 - 190 None , Rel'ative 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 Nomalized axial power factors

J=1, NDXPZ I 241 None Specify 1.0 to use the capability to change NFIND -

the hot assembly flow factor for different j regions of operating space. Speci fy 0.0 to not use the capability. If 1.0 is specified, the following additional input is requi red. I Number of operating space regions (maximum NREG 242 None is 5) A U A-9 _ _ _ . __ __

Relative - Address Units Descriptions Parameters i REFLO 1 243 g.p.m. 100% design core flow rate in g.p.m. divided 2 by core flow area ft FF(J)I 244-248 None Channels 2,2. and 4 inlet flow factor

        -    J=1,NREG for each reg'an of operating sgace.

(Referred to as hot assembly flow factor) 00J=1,11 REG Provide for each region of operating space where: Ranges on "raction of 1(-0% design core flow, inlet temperature K=(J-1)*12 system pressure, and AS: : 249 - 308 IBF(J)I (249+K) None Types of inequalities applied to limits of the design core flow range 1: lower limit < core flow < upper limit 2: lower limit < core flow < upper limit

3: lower limit < core flow < uoper limit i

                  -                                              4: lower limit < core flow < upper limit BFL(J)I         ~(250+:1          None           ' Lower limit fracti.on of 100% design core 7

flow rate. BFR(J)1 (251+K) None Upper limit fraction of 100% design i core flow rate. l \ r

                                                      ~~._

( l l I 1 s-n

("> Relative Address ' Units Cescriptions Parameters ITI(J)I (252+K) None Types of inequalities applied to limits of the inlet temperature range, same as IBF. A

F Lower limit inlet temperature TIL(J)I .(253+K) . TIR(J)I (254+K) - F Upper limit inlet temperature IP'S(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 None Lower limit A.S.I. range ASL(J)I (259+K) ASR(J)I (260+K) None Upper limit A.S.I. range

O e l l e l l l l i l ! A-11

(OJ , A.4 Sample Inout 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. CASE = CETOP-D case number NH = Enthalpy transport coefficient at each node Hl.= Enthalpy in Channel 1 H2 = Enthalpy in Channel 2

                                    'T H3 = Enthalpy in Channel 3 H4 = Enthalpy in Channel 4 QDBL = core average heat flux, represents total heat generated from rods and coolant, wnere fuel rods are corrected (for axial densification) Btu /hr-ft .
                     - for core 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 power iteration, the ratio of the core average heat flux at the end of last iteration to the core average heat flux at i 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 GAVG u Core average mass velocity (610 lb/hr-ft2 )

                     - 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. I A-112

vs O . 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 MNDSR at last iteration

                                       ~ 'v X-N  = coolant quality at location of DNB-N DNB-1 = hot channel MONBR at first iteration X-1  = coolant qua'lity 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 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 iterations 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. ATR = Average enthalpy transport coefficient over the total channel axial length. . HCH = MONBR hot channel number, if 3 is Dr.inted this means . (- s_s . MN00 = MDNBR node location CESEC TIME = This parameter is printed in the output when the CESEC code is linked with CETOP-0.

r \

    ~lFSPLIT = this is the inlet flow factor (in channels 2, 3, 4) chosen by the code for operating conditions specified in the input. This value is printed when the capability for changing the inlet flow factor for different regions of operating space is used. The following parameters are also printed to show that calculated fraction of 100% design core flow is within the

, operating space given in the input. GAN = the calculated fraction of 100% design core flow GIN = the calculated core average mass velocity , lb/sec-ft VIN

inlet coclant specific volume, ft3 /lbm I

v J I P i f l s-A-14

b O . b i t

i i . I t e i 4 Appendix B Sample CETOP-0 input /0utput l l O B-1

     - _ . - - _ _ . - - _ _ _ . - _ _ _ _ _                                                       YF '"-WW         wyy- ,,,.y       ,,

I e p 1 i ! ' i 3 - i V I l 3 l 1 . 0 4 e l l l '

l i i e. g l .

4 i , l i i i I e 8 8 1 f. I !

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l, ! ', l l i

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i t j - 6 l 1 I l l I n e

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e ! l ! l g { ; i l . i l ' s i t l l s I

6

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