ML20004D823

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

ML20004D823
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Site:	San Onofre
Issue date:	05/31/1981
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CEN-160(S)-NP, NUDOCS 8106100143
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San Onofre Nuclear Generating Station Units 2 and 3 Docket No. 50-361, 50-362 CEN-160(S)-NP

O CETOP-D CODE STRUCTURE AND MODELING METHODS FOR SAN ONOFRE NUCLEAR GENERATING STATION UNITS 2 and 3 MAY 1981 1

4 l

COMBUSTION ENGINEERING, INC.

NUCLEAR POWER SYSTEMS POWEP, SYSTEMS GROUP O WINDSOR, CONNECTICUT 06095 THIS DOCUMENT CONTAINS

i(8106 10 0 \LS $ P00R QUAUTY PAGES

- - = - --

()

. LEGAL HOTICE 4

This report was prepared as an account of work sponsored by Combustion Engir.eering, Inc. Neither Combustion Engineering nor any person acting on its behalf:

A. ftakes 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. Assumis any liabilities with respect to the use of, or for damages resulting from the use of, any information, 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

> used in the TORC code (Reference 1) for predicting the CE-1 minimum DriBR (MDriBR) 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 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 MDilBR's are compared, within design operating ranges, for t'he C-E S0;iGS 2 and 3 reactor cores. comprised of 16x16 fuel assemblies. Results, in terms of deviation between each pair of MD;1BR's predicted by the two models, show that CETOP-D with the inclusio,n of the " adjusted" hot assembly flow factor, can predict either conservative or accurate MDriBR's, compared with Detailed TORC.

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U TABLE OF C0flTEllTS ,

Title Page Section ABSTRACT i

11

> TABLE PF C0:1TEllTS LIST Of FIGUPdS iv Y

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 CORRELATI0ilS 2-1 0 2.1 Fiuid eroperties 2-1 2-1 2.2 Heat Transfer Coefficient Correlations 2.3 Single-phase Friction Factor  ?-2 2.4 Two-phase Friction Factor Multiplier 2-2 2.5 Void Fraction Correlations 2-3 2.6 Spacer Grid Loss Coefficient 2-4 2.7 Correlation for Turbulent Interchange 2-4 2.8 lietsroni Crossflow Correlation 2-7 2.9 CE-1 Critical ifcat Flux Correlation 2-7 3-1 3 flVMERICAL SOLUTI0ft OF Tile C0ilSERVATI0:1 EQUAT10flS Finite Difference Equations 3-1 3.1 3.2 Prediction-Correction Method 3-2 I 4-1 4 CETOP-D DESIGil MODEL 4.1 Geometry of CETOP-D Desgin Model 4-1 4.2 Application of the Transport Coefficient in 4-2 the CETOP-D Model 4.3 Description of Input Parameters 4-4

~' 5-1 5 TIIERMAL ttARG!!! AllALYSES USIf1G CETOP-D Operating Ranges 5-1 5.1 5.2 Detailed TORC Analysis of Sample Core 5-1 5.3 Geometry of CETOP Design Model 5-1

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TABLE OF C0!1TEtiTS (cont.)

.Q .

_Section No., , iltle_ Page No.

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

- 5.5 Application of Uncertainties in 5-2 CETOP-D 6 COIICLUSIONS 6-1 7 REFERENCES 7-1

) Appendix A CETOP-D Version 2 User's Guide A-1  ;

Appendix B Sample CETOP-D. Input /0utput B-1 e

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D

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LIST OF FIGURES O .

Figure No. Title Page No.

1.1 Control Volume for Continuity Equation 1-12 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-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 Geomet'yr for SONGS 2 and 3 5-3 5.2 Stage 2 TORC Channei Geometry for SONGS 2 and 3 5-4 5.3 Axial Power Distributions 5-5 5.4 Inlet Flow Distribution for SON 35 2 and 3 5-6 5.5 Exit Pressure Distribution for SONGS 2 and 3 5-7 5.6 CETOP-D Channel Geometry for SONGS 2 and 3 5-8 O .

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iv

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1 O LIST OF TABLES _

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1.,

Title Page No.

I Table No. .

Tuo 9hase Friction Factor Multiplier 2-8 2.1 Functional Relationships in the Two-Phase 2-9 -

2.2 Friction Factor Multiplier l

Comparisons Between Detailed TORC and CETOP-D ,5-9 i j 5.1 -

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LIST OF SYMBOLS _

• SYMBOL MFINITION 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 convectien 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 of 'I Engineering factor's HP A F Radial power factor, equal to the ratio of V R local-to-average radial power F

3 Ratio of critical heat flux for an equivalent uniform axial power distribution to critical

. . heat flux for the actual non-uniform axial power

. distribution.

F g. Total power factor, equal to the product of the

. loc.a1 radial and axial power factors F

z Axial power factor, equal to the ratie of the local-to-average axial power.

Gravitational acceleration g

G Mass flow rate h

Enthalpy k Thermal conductivity

%g Spacer grid loss coefficient K

gj Crossflow resistance coefficient K- -

Crossflow resistance coefficient i Effective lateral distance over which crossflow occurs between adjoining subchannels O

V MD.1BR Minimum departure from nucleate boiling ratio m Axial flow rate Ng,N Ny Transport, coefficients for enthalpy, pressure and velocity A Q J

O SYMBOL -

DEFINITION P

Pressure P

h 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

REF Reference crossflow width Tconj

Bulk coolant temperature T Saturation temperature sat Ty ,jj 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 w'jg Turbulent mass interchange rate between adjacent flow channels x Axial distance X Quality a Void fraction y Slip ratio o Density '

+ Two-phase friction factor multiplier 41 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 O Denotes hydraulic connection between subchannels

< end a J

Axial node number P

Denotes predicted value

I i 1

I 1 i l

4 a

1 O suecascarers Derrutricr< .

I

• i 1

J Denotes transported quantity between adjoining 4 I

4 lumped channels '

I

• Senotes transported quantity carried by I

1 diversion crossflow

! a t 1 Denotes effective value

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2  !

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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 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 desc71ption 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 model to account for the deviation of MONBR from that calculated by Detailed TORC.

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

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

which utilizes the same conservation equations as those in TORC, has been used in the Core Operating '..mit Supervisory System (COLSS) for monitoring MDNBR.

Ti4e CETOP-0 model u be described in this report has been developed to retain all capabilities the S-TORC model has in the determination of core thermal margin. It takes typically for CETOP-D to perform a calculation, as accurat21y as S-TORC, on a four-channel core represen-tation.

For the following reasons CETOP-D is as accurate as and faster-running than its predecessor, S-TORC.: (1) it uses " transport coefficients", serving

f. s as weighting factors, for more precise treatments of crossficw and turculent mixing betweco adjoining chanr 315, 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

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1 A finalized version of a CETOP-0 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 Conservatinn Ecuations A PWR core contains.4 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, mcmentum 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, characterited by averaged coolant conditions, and (2) l'mped u 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 rod subchannels).

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

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1.2.1 Conservation Eceations for Averaged Channels 1.2.1.1 Continuiry Ecuation 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 hac the. form: 3,

-m g+(mg+a dx) - w'jgdx + w'qdx + wgjdx = 0 (1.1)

~

Assuming the turbulent 1nterchanges w'gj=w'jg, the above equation becomes:

am g

= -

w

, gj (1.2) ox Considering all the flow channels adjacent to channel 1, and taking w g3 O as positive for f ows fro = 5 to 3. the coatiauity eauatioa becomes:

am g N

=- I w 3,..,N ax j=1 id ; i = 1, 2, (1.3) 1.2.1.2 Enercy E,cuation The energy equation for channel i in figure l.25, considering only one adjacent channel j, is:

8

-m hg g + (m hgg+ mgy h dx) - q'j xd - w'jj jh dx + w'93 gh dx+wjjh*dx=0 (1.4) 3x where h* is the enthalpy carried by the diversion crossflow w g.

The abcve equation can be rewritten, by using rq. (1.2) and w'j) = w'jg.

O as-U -

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

--e~ '

O ma O

ah "i ax "9 i - (h g-h)) w'j +(h g-h*)wjj (1.5)

Considering all adjacent flow channels, the energy equation becomes:

ah I q'I N w'II + NI w

II ax

= -

I (h-h)m i j (hi -h*) mg (1.6) mg 3,j g 3,j 1.2.1.3 Axial Mcmentum' Equation Referring to Figure 1.3b, the axial momentum equation for channel 1, considering only one adjacent channel j, has the form:

8

-Fjdx + p gAg - gA ogg dx - (p jj A .+ x pjgA dx) =

0 -mj ug + (m jug + d m jj u dx)-w'jjujdx + w'gj ju dx + wjju*dx (1.7)

~

where u* = 1/2 (uj+u ).

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

ap

-Fj - gA ojj-Ai ax *

• i"i * ("i-Uj)"'ij + u Njj (1.8)

Substituting the following definitions:

2 j j f jog AjKg$v$ mg uj s m ,g vp3 ; jF n(Avj 20e

+

(A b*

2ax i i i and Eq. (1.2) into Eq. (1.8), one obtains:

3Pg mg 2 uj f,4j Kg ;vg .

A i ax = -Aj ( g ) [ 20e +

2ax

+A j 3x vpg (A

)) ~ 9^i# i (.10) i i i O ,.

- (ui-uj ) "' u + (2"$ "*)"ij -

l'-4 -

./

Considering all adjacent channels, the axial momentum equation becomes:

3p g*~ m, 2 v4f4),

Kg g

v4 + ^i ax3

~

(Avp,}

ax

{ 20e g 2ax g

~ 9#1 N w (l.II)

- I (ug-uj ) gw'U - + NI (2u -u*) A i g

j=1 i j=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 p and p

• to Referring to the control volume shown g j the crossflow wg ).

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

"ij!"ij!

(p -p3) = Kij 2g s4 o.

g (1.12) where K gj is a variable coefficient defined in Reference 3 as 2

u i 1/2

+

K.)=(K"2 g + XFCONS ij 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 43 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.

l.2.2 Conservation Ecuations for Lumoed Channels 1.2.2.1 continuity Ecuation p

Since only mass transport is considered within the control volume, the continuity equation has similar fonn to that for averaged channel, i.e. ,

Eq. (1.3) .

4

1. 2.2.2 Energy Ecuation, Consider two adjacent channels i and j and apply the energy conservation to channel I within the control volume as shown in Figure 1.2.a. the energy equation has the form:

ah m y 3x i

=q'9- @4 (1,14) 4 3) w'93 + (hy -h*) wj )

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

_ turbulent interchange w'g3, hj w'.43 = energy transferred into channel i from j due to the turbulent interchange w'gj, h

g and h) are the fluid enthalpies associated with the turbulent interchange; h* is the enthalpy carried by the diversion cross-flow w and is determined g3 O as foiioms:

h* = li g i f w$ 3 >_ 0 (1.15) h* = li) if w g) < 0 1

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 g and'5) are defined as the radially averaged enthalpies of the boundary subchannels of lumped channels i and j respectively.

Since hg and b y are not explicitly Mlved ' n i the calculation, we define a transport cor2fficient fl Hto relate these parameters to the lumped channel counterparts h g and h) as follows:

h -h n=' i g (1.16) hg - h)

The parametergN is named the transport coefficient for enthalpy.

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

P l-6 . ._._ _ _ _ . _ - - _ _ , _ _ _ . -

h =

hg+h3, Iij + W3 e 2 2 (i.17)

O and g ', p I

F-h g

c

=

2 (1.18)

E-h j g

=

h 5-h (1*19) 2 which are followed by the approximations.-

hg=h +(E-h) j c

-h

= hi+h5*h 2 2N 3; (1.20)

, H hj=h c+(E.J - hc)

(1.21)

" hg+h3

• h) - hg 2 2N H

Inserting Eqns.(1.17)-(1.21) into Eq.1.14, the lumped channel energy O

equatier. is derived as:

h hg+h ah4 ,qi j_ ( g-h (hg -hy )n m9 +

N H

ij i 2 2N g ) hj where n = 1 if wgj > 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.

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. l 1

ap  !

A i =-F g -g::gA g-(ug-uj ) w' gj + (2ug-u*) w ax (1.23) b jj l

l-7

O where: A j = channel area, pg

= radially averaged static pressure, g = gravitational acceleration,

= coolant density, G = axial velocity carried by the turbulent interchange

"'ij u = channel radially averaged velocity F

4

= momentura force due to friction, grid form loss and density gradient As for h j and h), ug and u j can be regarded as the averaged velocities of the boundary subchannels of the lumped channels i and j respectively.

Definc the transport coefficient for axial velocity, tig, as follows:

u -u N~g -- -

3 (I' }

U ug-uj Using similar procedures in the approximation of h g and h) in terms of O hi , h 3, and r<a, es eescribed from E,. (1.17) to (1.22), we derive:

Ui+u3 + ~u, - uf (1.25) uj = 2 2N U

and

~

u g+u5 u.-u

+ (1.26)

)= 2 2%

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

ap u ,

j )n ij+(2ug -(uj +u.J + (ug-u A

i a

=-F j -A ggog - ( g-u g 3

) 'a ))w U U (1.27) where n is defined in Eq. (1.22) ,

l

( I l-8

O 1.2.2.4 Lateral Momenh Equation Consider the rectangular control volume in the gap region between channels i and j as shown in Figure 1.4.a. Assuming that the difference between the diversion crossflow momentum fluxes entering and leaving the control volume through the vertical surfaces sax is negligibly small, the formulation for lateral momentum balance is:

-F jj - pj sax + pg sax = -(p*stu

• V)x + (p*stu*V)x+3x (1.28)

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

O --

(94-93) = 33x F

is +

i s/t

^("**i3) ax 0.20 The term Fj3 / sax represents the lateral shear stress acting on the control volume due to crossflow and is defined as:

F j3 " w$3lw$$l (1,30)

K sax U g3 2p hbstituting Eq. (1.30) into Eq. (1.29), and taking the limit as ax40, (p

- "ij!"ij! I a Pj ) = K ij 2 g

s/1 ax ("**ij) (1.31) where: p = channel averaged pressure, K

gj = cross-flow resistance coefficient, w

gj

= deversion cross-flow between channels i and j, s = gap width beNeen fuel rods, .

= effective length of transverse momentum interchange,

.O 1 u* = axial velocity carried by the diversion cross-flow wg ),

assumed to be (uj +uj )/2

., u

C)

V The above equation is equally well applied to two lumped channels when each contains a certain number of s'ubchannels arranged as shown in Figure 1.4a gj and the gap width s should be In this case, the diversion cross-flow w expressed by :

W ij"(N) (cross-flow through gap between two ad.iacent rods) (1.32) s=(N) (gap between two adjacent roils) , (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 channels,parametersyg 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 4

two generalized lumped channels are governed by the following equation:

bj j! ,

a Mwjj) (1.34)

P i _ pj, g i.), 2 s 2gs p* 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

~

subchannels. This is because the control volumes chosen to model the transverse momentum transport in these two cases are identical. Since pg and p) are not explicitly calculated, we define the transport coefficient for pressure to relate these parameters to the calculated lumped channel

./ parameters pg and p) as follows: .

Np ,=

P-P5 1

(1.35)

Pg - pj 1

where pg and pj tre the radially averaged static pressures of the lumped channels i and j respectively. Inserting Eq. (1.35) into Eq. (1.34), we obtain the transverte mo:rentum equation for three-dimensional lumped channels as follows:

A V

Ei ~ Pj

,', l"i,!"ij #

t ( U * *h), g*g ti 'ij 2 sa x p g l-10

o 1.2.2.5 Transport Coefficients There are three transport coefficients Hfl ' N U and N p

in Eqs. (1. W . (1.20 and (1.35) which need to be evaluated prior to the calculation of conservation equations. Previous study in Reference 2 concluded that the calculated hj ,

m j , p g , and w jj are insensitive to the values used for flU and N . This conclusion p

, is further confirmed for the three-dimensional lumped channels. Therefore, the values of fi gand ft canp be estimated by a detailed subchannel analysis and used for a given reactor core under all possible operating conditions. It is, however, not the case for N H, whose value,is strongly dependent upon radial pow'er 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 N Hcan be calculated by using a deta. led subchannel TORC analysis to determine hj , h j, E ,g h; and fl forH use in the CETOP-D lumped channel analysis.

However an hiternate method is used in CETOP-D, utilizing the power distribution and *,he basic operating parameters input into CETOP-D to determine yfl for each axial finite-difference node. [

]

v l-11 i

O .

mg+ dx 8x

. . _ _ _ _A_ _ _ _ J, I A l

I 7 l

*Wjx i d

CHANNELi l I  ! CHANNELj CONTROL i l VOLUME $ l dx Wjidx ,

I i > W'jdx i

I I I m; l y

1 A

i e

O Figure 1.1 lO CONTROL VOLUME FOR CONTINUITY EQUATION t-n

m h; + m;h dx

. _ .:. _ _ A _. _ _ _ J.

II ^

i l l l I l l l

l 3-Llw;j'dx h

CHANNELi lCHANNELj CONTROL VOLUME I l l l I dx

= q{dx

• Jijx d l+

l  ; w;j#II;dx l l I 1 v I l m h; I I I

& !N P

- -l - T I BOUNDARY SUBCHANNELS (A) CONTROL VOLUME FOR LUMPED CI:ANNEL O

m;h; + m h;dx A

___1

^

i i I

l CONTROL I *ii

• VOLUME f l l CHANNELj

[

CHANNELi  ;

l l r q;dx dx Wjih;dx l

I

- wij h dx l m;h; [

! A f V (C) CONTROL VOLUME FOR AVERAGED CHANNEL Figure 1.2 CONTROL VOLUMES FOR ENERGY EQUATION

m ui + m;ugd x PiA; + d x p;A dx

, . _ _L _ _f _ _ _ _ l, i l ^

l lII l '

CONTROL / )l l- {Iil -*

w;ju'dx VOLUME I i l i I CHANNELi l I CHANNELj F;dx l V l l I

l SA ;p;dx g  ; I dx l I g l "jiUdj x

• - j--

l-wijUdix PdA;g i g g l

, l m u; l i

.q--

A a

b i

V BOUNDARY SUBCHANNELS PiA; (A) CONTROL VOLUME FOR LUMPED CHANNEL O m;u;+ 0 m u;dx 8X

. ._ _J L _ _ h _ _ _ _{

p ;A; + S__ p;A;dx CONTROL VOLUME j.

I

& w;;u'dx I

?

F;dx CHANNELi CHANNELj l

l 9 l gA;p dx dx i ,

I Wjiujd x j l l 9 r w;'ju;dx P idA;  ;

I m;u; I I

1 Pi A; l

_ g ._ _ _

Q (B) CONTROL VOLUME FOR AVERAGED CHANNEL Figure 1.3 CONTROL VOLUMES FOR AXtAL MOMENTUM EQUATION hjl4 >

O ..

x+dx .

_ Vx+ .1 x I I I  ; o l CONTROt i VOLUME I i

l OOOpOOO Pi s g p

-*j i O O O OiO O'O I I I I I psax ji. sax 3x 8 3

l*~I g l Pg Pj il CHANNELi CHANNELj CHANNELg i l l CHANNELj l

lt I

i

_j "

TOP VIEW b VX u SIDE VIEW x

(A) CONTROL VOLUME FOR LUMPED CHANNEL O

l N

l I I I

I i r----- ,

I 1 l l l  : l l l l

! l P'-

M W P-3 P3 -*} -> W ij P Pj dx e

, a I '

i l l l L __ _. _ ._ _ J CHANNELi CHANNELJ l CHANNELi CHANNELj

! JL d h A TOP VIEW SIDE VIEW "i "i (B) COf1 TROL VOLUME FOR AVERAGED CHANNEL O

Figure 1.4 CONTROL VOLUMES FOR LATERAL MOMENTUM EQUATION ,

O -

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

In CETOP-D, the following correlations are used:

2.1 Fluid Procerties Fluid procerties 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 O

The film temperature drop across the thennal boundary layer adjacent to the surface of the fuel cladding is dependent on the local heat flux, the temperature of the local coolant,, and the effective surface heat transfer coefficient:

DTF = TwaH - Tcool

=

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

h = 0.e@ (Re) (Pr) (2.2)

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

DTJL = (T sat -Tcool) * (*}

n V

e The initiation of nucleate boiling is determined by calculating the film temperature drop on the bases of forCCJ convection and nucleate boiling.

92-J1

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

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

2.3 Single-Phase Friction Factor The single-phase fric f on factor, f, used for detennining 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)

()

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

2.4 Two-Phase Friction Factor Multiolier A friction factor multiplier, o, is applied to the single-phase friction factor, f, to account for two-phase effects:

Total Friction Factor a 4t. (2.5) l CETOP-D considers Sher-Green and Modified Martinelli-Nelson correlations as listed in Tables 2.1 and 2.2.

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

For local boiling conditions, correlations by Sher and Green (Reference 11) l are used for determining o. The Sher-Green correlation for friction factor t

multiplier also accounts implicitly for the change in pressure drop due to l '(G,) .subcooled void effects. When this correlation is used, it is not necessary l to calculate the subcooled void fraction explicitly.

I For bulk boiling conditions, o is determined from Martinelli-Nelson results l

l of Reference 12 with modificaticns by Sher-Green (Reference 11) and by

j O .

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

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

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

a = B, + B) X + B2 X2+BX3 3 (2.6 )

where the coefficients Bnare defined in Reference 10 as follows:

(] For the quality range 0 1 X <0.01:

B, = B) = B 2 = B3 = 0; the homogeneous model is used for calculating void fraction: .

a=0 For X 1 0 Xv (2.7)

For X > 0 a=(j_g)[t7 xy e For the quality range 0.01 1 X <0.10:

B = 0.5973-1.275xlf p + 9.010x10-72 p -2.065x10 -10p3 B = 4.746 + 4.156x10 -2p -4.011x10 -5p2 + 9.867x10-9p3

~4 p2 -1.378x10~7p 3 9-@

B = -31.27 -0.5599p +5.580x10 B = 89.07 + 2.408p - 2.367x10 -3 p2 + 5.694x10~7p3 3

For the quality range 0.10 1 X <0.90:

O ~4 B = 0.7847 -3.900x10 p + 1.145x10~7p 2 - 2.711x10"IIp3

~4 B = 0.7707 + 9.619x10 p - 2.010x10 ~7p 2 + 2.012x10"Ilp3

-3 -7 2 ~I2p3 M B = 1.060 -1.194x10 p + 2.618x10 p -6.893x10

, _ _ , 2-3  ;

B = 0.s157+s.s0sxik4 p -1.938x10 ~7p 2 + 1.925:10"Il p3 3

For the quality range 0.90 1x1 1.0:

B,= B) = B2=B3 = 0; the homogenecus model given by Eq. (2.7) is used for calculating void fraction.

2) At pressures equal to or greater +.han 1850 psia, 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 vg 2.6 Spacer Grid Loss Coefficient The loss coefficient correlation for representing the hydraulic resistance n of the fuel assembly spacer grids has the form:

V Kg = 0) + Dp (Re)0 3 (2.11)

Appropriate values for D 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 correlat!cn:

5 (2.12) w'gj = G 0, (sREF ) A (Re)0 where: G = channel averaged mass flow rate O = channel averaged hydraulic diameter p

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-0.

2-4  ;

s 2.8 Hetsroni Cross Flow Correlation Berringer, et al, proposed in Reference 15 a form of the lateral momentum equation that uses a variable cotfficient for relating the static pressure difference and lateral flow between two adjoining open flow channels.

• 4 K

ij W ij!"ijl (Pt - Pj)

• 2gp* s 2 (2.13)

In Berringer's treatment, the varia.ble K gj accounts for the large inertial effects encountered when the predominately axial flow is diverted in the I lateral direction. g Reference 3, Hetsreni expanded the definition of K

jj to include the effects of M ear drag and contraction-expansion losses on the lateral pressure difference:

2 1/2 K

g= +( + (XFCOMS) 2 )

@q p 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 fica 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 suggested K. = 1.4 and XFCONS = 4.2 for rod bundle fuel assemblies.

These values are also used in CETOP-0.

2.g -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 +b P) b) ( )2 ((b+bP)( 3 4 6) ~( 6 ) ( x) (h7g))

10 0 6 6 10 (b7 P + b8 G/10 )

G O

J 10 6

O 2-5

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

O_~

p = 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, lb/hr-ft2 x = local coolant quality at CHF location, decimal fraction h = latent heat of vaporization, BTU /lb fg and bj = 2.8922x10-3 -

b = -0.50749 ' "

2 ,

b 3 = 405.32 b

4 = -9.9290 x 10-2 b = -0.67757 5

b. = 6.8235x10'4 -

o b = 3.1240x10'4 7

b* = -8.3245x10-2

.O 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 ) 6 0.87x10 to 3.2x10 6 inlet temperature (*F) 382 to 644 subchannel wetted equivalent 0.3588 to 0.5447 diameter (inches) -

subchannel heated equivalent 0.4713 to 0.7827 diameter (inches) heatedicnyth(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:'

9"CilF, Ecuivalent Uniform g FS=

V 9"CHF, fion-uniform C(J)

FS(J)=

y a(x)e-C(J) # -X)'x d

q"CHF,fion-uni form (1-e ~C(J)*IJ))o 4 V

T O .

where, for CE-1 CHF correlation, C(J) = 1.8 (I'XCHF)

• 1 6

(G/10 ) 0.478 The departure from nucleate boiling ratio, DNBR, is:

I 9"CHF, Ecuivalent Unifonn DNBR(J)=

FS(J) q ,,[g )

8 O

9 0

0 2-7 .i

O O TABLE 2.1 O

s TWO.Pfl ASE FRICTION FACTOR MULTIPLIER 3206 G > 0.7 x 106 1

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

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

FMN3 (X, P = 2000)

$" FMN3 (X,P) x 0R y g,gg I (X p) FMN3(X =0.4 P = 2000)

, $ = F AM (X, G, P = 2000) x f g(P,G. FMN3 (X, P = 2000) , IMN (X,P 3 = 2000) x Ff.tNg(X, P) 0 */DTF), g IMN3 (X, P = 2000)

$=1.0 WillCllEVER gg G < 0.7 x 106 e

$ = F AulX50.4, G =0.7, P 20005

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

LAHGEfl FMN3 (X,P) A pg3(X,P=2000)

FMf13(X* P) $ = F AM(X, G = 0.7, P = 2000) x x f4(G) FMN3 (X-4.0, P 2000) x x f4(G) MN3 (X, P = 2000)

FMN3(X,P = 2000) l '

x xg4 (g) g?j;((X, P) l FMN3 XJ = 2000) 2000 0

G 0.7 x 10

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

• OA. G. P = 2000)

$=1.0 $ = F AM(X, G. P = 2000) FMNg (X,P) F f.1N (X, P) "

, , 2 J (X+0.4, P = 2000)

FMN3 (X,P = 2000) FMN (X, P = 2000) p 2 F MNgX, P)

O '/D T F)* 2U.P = 2000)

(=1.0 - - - - - - -- - - - - - - - -- - .__ ___ - - -_ ___ ___

WHICI EYER G < 0.7 x 106 $ = FAM(X, G = 0.7, P = 2000) $ = FAM(X, G = 0.7, P = 2000) $ = F AM(X50 4, G 4 0.7, P42000)

LARGER x UAU1 b O xg4 (c) FMN2 (X,P) X Ull ,P =200M

$ = F AM(X, G = 0.7, P = 2000) x xf 4(G) pMN2 (X = 4.0* P = 2000)

FMNg (X, P = 2000) FMN (X,P = 2000)

• I 4(UI IMNZ{X P) x xf (G) 1850 2W, P = 2000)

G > 0.7 x 100 g= $ = FMNg (X, P) r l' 0 '2 (P, G) M 3f (P, GI = FMN2 (X,P) x f 3(P, G)

. D ) l 6=t.0 - - - - - - - - - - - - - - - - - - - - ---

[FMNg (x al - - - - -- -----

"' 6 g 3g p, , G < 0.7 x 10 g .FMNg(X,P) l g . g3 (p, g) xg3 (p,c) $=FMN 2 II*II"I IP*CI J

I 1

l14'7 0 0 0.02 0.2 l! EATING LOCAL aggtiyy* x 0.4 1.0 i 4 7 NO BOILING----- C OI LIN G - BULK B0lt ING r f1ME. FllNCTlufJAL ItELATIONSillPS ARE LISTED If1 TAOLE 2.2

O -

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

For local boiling:

f)=C(1+0.76(3 j P)[ ,)

u) 1 where Cj = (1.05) (1-0.00250*)

e* = The smaller of DTJL and DTF m = 1 - e*/DTF '

For bulk boiling:

0 yy0.75 6

- FAM = 1 + (G/10 )1+X

.X(0.9326 - (0.2263x10-3)P) '

l FMN1 =

1.65x10-3 + (2.988x10-0) P-(2.508x10 9) P2 + (1.14x10-II)p3 FM2 = X(1.0205 - (0.2053x10-3) p) 7.876x10~4 + (3.177x10-5) P-(8.722x10-9) P2 + (1.073x10 II)P3 FMN3 = 2 1 + (-0.0103166X + 0.005333X ) (P- 3206) f 2

=

1.36 + 0.0005p + 0.1 ( 66 ) - 0.000714P ( 0 )

6 10 10 6

f =

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

=

f 4 1 + 0.93 (0.7 - 6) 6 10

~

1 U

t 2-9

i -

3. NUMERICAL SOLUTIO:1 0F THE C0!1SERVATIO!! EOUATIONS, B

3.1 Finite Difference Ecuations The CETOP-D code solves the ceaservation equations described in Section 1 by the finite difference method. The flow chart shown in Figure 3.1 displays briefly the marching CETOP-D follows'in order to search for the

, minimum value and the location of D?iBR in a 4-channel core representation i

(c.f.Section4.1).

Equations (1.?.), (1.22), (1.27) and (1.35) which govern the mass, e'nergy and momentum transp3rt within channel i of finite axial length ax are Written in the following finite difference forms:

(1) Continuity Ecuation mg (J) - mg (J - 1) 3x

= -w gj(J) (3.1)

(2) Energy Equation '

r hj (J) - hg (J - 1) h3-h3 mg (J - 1) ~

Ax

=gj -- ...-

wjd "H

(3.2) h hwgjj+(g+h32 + -(hg2N- h3 )n) "ij '

g J-1 (3) Axial Momentum Equation O ns (J) - gi(J - i) o A

l ax F j - A gga g(J) .

s-u,uj) g U

3-1 L )

f 1 .

O .

u 2 (uj - u 3)n ,

2'J j wj j + ( 2j + u + 2N ) "ij (3.3)

U i J-1 (4) Lateral Momentum Ecuation pj (J - 1) - p[ - 1) w j3(J) wjj(J) g

=K ij -

p 2gs2 p*

+

g u*(J)wjj(J) - u*(J - 1)wjj(J - 1) 3 3x (3.4)

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

3.2 Predictioil - 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 accreate scheme for the solution ef mj , h j, w jj and pg at each axial level. The steps used in the CETOP-D solution are as follows:

The channel flows, m j , enthalpies h j , pressures p j and fluid properties are calculated at the node interfaces. The linear heat rates q', cross-flows , wjj, and turbulent mixing, wjj, are calculated at mid-node. The V solution method starts at the bottom of the ccre and marches upward using the core inlet flows as one boundcry condition and equal core exit pressures as another.

1 81.f2 J

O .

An initial estimate is made of the subchannel crossflows for nodes 1 These crossflows are set to zero.

and 2. ,

i

l W jj(l)*Wjj(2)=0 The channel flows and enthalpies at node 1 are known to be the inlet conditions. Using these initial conditions the marching tachnique proceeds to calculate the enthalpies and flows from node 2 to the exit node.

In this discussion "J" will designate the axial level "i" and 'j" '

O are used to desisaate chaaae's-Step 9

9 4

i_ _

1

_ . _ _ _ . _ _ ,33_._-_____,_.__,..____._,,....___..__.,____.

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

[..._ t.

1

O J

i e 4

1 1

4 +

i I

t 1

i i

3 i

1

!O l

i

(

i 1

l l

l ,

l l

O. The success of this non-iteretive, prediction-correctioe method iies in the

[ fact that the lateral pressure difference, p (J) j - p2(Ji, using the " guessed"  ;

diversion crossflow Wjj(J.+ 1)p, is a good approximation. Thus at each j node the axial flow rate can be accurately detemined. '

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

The conservation of mass and momentum equations are used to evaluate t'le diversion crossflows and, in turn, the flow rates at all locations. The axial momentum equation is used to determine pg - 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 frcm the TORC iterative numerical technique. In general, about[ [ in TORC to achieve the same accuracy as the prediction-correction method. In the TORC iteration scheme ,

the transverse pressures and the flows are only updated after the iteration, O

is completed. Therefore in marching up the core errors in the transverse pressures cause the errors in the flows and enthalpies to accumulate 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 accumulated errors in the downstream ncdes which often force the TORC method to continue.

to iterate.

O

, 3-5 ,_ , . _ _

j START I LJ 1r t' READ INPUT 1r PREDICT AND CORRECT C0CtANT PROPERTIES IN THE CORE AVERACE AND HOT ASSEMBLY CHANNELS AT ALL AXIAL NODES l'

'T PREDICT AND CORRECT COOLANT PROPERTIES IN THE HOT CHANNEL AT ALL AXIAL NODES 1

PREDICT NEW HEAT FLUX 1r CALCULATE CPF AND ONBR FOR THE HOT CHANNEL AT ALL AXIAL NODES v

NO IS MONBR OR QUALITY WITHIN THE LIMITS ?

N YES v

PRINT GUTPUT v

NO IS THIS THE LAST CASE 7 YES 1r l

STOP Figure 3.1 CETOP-D FLOW CHART 3-6

=. _ -

v J=2 O .

P PREDICT w;; , m; AT NODE J-1 u

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

v PREDICT h; AT NODE J + 1 v

COMPUTE COOLANT PROPERTIES O a-a+, "

H PREDICT w;j AT NODE J+1 v

CALCULATE p; p; AT NODE J u

CALCULATE w;j, m; , hi AT NODE J y

LAST NODE ?

O "s l

Figure 3.2 j

FLOW CHART FOR PREDICTION - CORRECTION METHOD

O)

4. CETOP-D 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 representaticn which

. g, will result in a best estimate of the hot channel flow properties and a preparation of input describing'the operating conditions and gecmetrical configuration

~

of the core. The CETOP-D model presented here provides an additional simplification

~

+-

to the conservation equations due to tfie specific geometry of the model. A

. description y of this simrif fication is included here together with an explanation:

~*

- n.

on the method for ge,nerating enthalpy transport coefficients in CETOP-D. '

4.1 Geometry of CETOP-D Desian Model

,,. .a Thc.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 - -

(,s) 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 t -

~ "

open for crossflow, but there is no turbulent mixing across th'e boundary.

Turbulent mixing is only allowed within channel 2. The outer boundaries'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 MDNBR hot channel 4. The location of the MONBR channel is determined from a Detailed TORC analysis of a core. Channels 2' and 2" are discussed in Section 4.2.

The radial power Yactor 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-0, the Chana.el 2 radial power distribution is normalized so the Channel 2 power factor is one. This is performed in CE10P-D so the Channel 2 power can easily be adjusted to any value. Initially, the inlet flow factor in O

(J the CETOP-D hot assembly is equal to the hot assembly relative flow obtained from the inlet fica distribution. If necessary, the inlet flow factor is later adjusted in the CETOP-D modcl to yield conservative or accurate MDNCR predictions as compared to a Detailed TORC analysis for a given range of operating conditions. __ , 4.) . _ , _ , _ _ . _ _

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

+Y 4.2 Application of Transport Coefficients in the CETOP-D Model i

. O' .

G l

e e

f O

f 8

P 4

4-2

,--,~ery.~- - , ,-v,,,.-w, ,,+,,..-,-,,,e,,

e d

• T 4

0 9

O 4-3

.I

~ ~

'i l'

u i .

I t

e

_ a 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 power 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 FR (i) is equal to:

p (j) _ power cenerate.1 in fuel assembly _,i (4.7)

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

N I F R(i) = N (4.8) 1=1 where N is the total number of assemblies in the core.

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

f (j ,3) , power cenerated in fuel red j of assembly i (4,g)

R power generated in an aserage fuel rod for an assembly containing M rods, one expects:

p)

(_

M t f g(i,j) = n r g(i) (4.10) j=1 4-4

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 power factor is used:

n .

., E c fg(f,j) fII)=d'I R

(4.11) n I 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

/ F(k)dZ-/

Z F(k)dZ Z

. o L /2 ASI =

(4.12) g FZ(k)dZ n

v where the axial pc'er 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'ilux supplied to char.nel i at elevation k is:

l 4 =(core average heat flux) R(f (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

. O f(i) = j=1 r. cj d (4.15)

V-is used to give ef fective heated perimeter in channel i. The

following c.<pression, derived from Eq's. (4.5) and (4.9), implies that i equivalent energy is being received by channel 1:

l

n D(i) fR (i) = dj=1 I c) fRII'3) (4*I6)

G C/ Engineering Factors 4.3.4 .

The CETOP-0 model allows for engineering factors (as described in Reference 1) due to manufacturing tolerances. Application of such factors

, imposes additional conservatism on the core thermal margin. Conventionally, engineering factors are used' as multipliers to effectively increase the radial peaking factors and diameters of rods surrounding the hot channel.

Alternatively, statistical methods are applied to produce a slightly increased DilBR 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 heat flux 4

O multiPiier tends to decrease DNBa in the foiiodins menner:

F DNBR = - < for f > 1 (4. )

where defines the DNBR before applying f and4 4 is the local heat flux.

(2) Enthalpy Rise Factor (f g) and Pitch and Bow Factor (fp )

i These factors are involved in the modification of the effective radial power factors and rod diameters for the fuel rods surrounding the hot

channel as follows

.m m

^

ffgP I cj Rf I4'd) E C I R(4'd)

F R I4) k d'I = 3"I d (4.18) m m ffgp E I J=1 c) j=1 t,

J m n

^

p f E G j IR (3,j) +~ j=1

r. c f (3,j) .

Q F R (3) , H j=1 n

j R

.n f I c + r ( '

H j=) 3 j=1 j v - - - - . _ . ---

G v . 1 and A

, l l D (4) = f HP -

' (4*I')

J=1 j .

3

^

m n

'D (3) = d (fH E C + E C. )

' ' ~ '

(4.20)

J=1 j j=1 J A A where FR .s and D's are the modified effective radial power factors a.nd rod diameters for channels 4 and 3, m is the number of rods on channel connection 4-3 and n'is the number of rods .

Again, the inclusion of f Hand f inp the core thermal margin prediction causes 4

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

O O

e

/

e e

e O

, 4-7 >

CHANNEL NUMBER >2 HOT ASSEMBLY = 1/4 OF ONE FUEL ASSEMBLY CHANNEL AVG. >pR s RADIAL POWER FACTOR 1

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

JOOOOOOO r

OOOO 2..

OO -

E 4

000 2.. 2 2" O ! to OO 2" ! 3 2' 2" l

E N

w 2" 2' 4 3 2' 2" h

!@ O 2" 2' 3 2' 2" s

! 00 2" 2 2" 1

i l

000 2" O

.O (D) CHANNEL 2 IN DETAILS ,

e -

Figure 4.1 CHANNEL GEOMETRY OF CETOP D MODEL 4LJt

(

5. THEP. MAL fMRGill AflALYSES US!!lG CETOP-D This section supports the CETOP-D model by comparing its predictions for a 16x16 assembly type C-E reactor '50:iGS 2 and 3) with those obtained from a detailed TORC analysis. Several operating conditions were arbitrarily

. elected for thi , der..onstration; they are repre ;entative of, but not the complete set of conditions which would ise considered for a normal OfB analysis.

5.1 Operatirg Ranges The thermal margin model for 3390 f1wt 50!{GS 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

% of 396,000 gpm Axial Power Distribution '

-0.3-+ 0. 3 ASI '

(~')

'~# '

5.2 Detailed TORC Analysis of Sample 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, 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 based on flow nodel test results, given in Figures 5.4 and 5.5. The results of the detailed TORC analyses are given in Table 5.1.

i 5.3 Geometry of CETOP Design ttodel The CETOP design model has a total of four thermal-hydraulic channels to model 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 which represents the average ccolant conditions far the remaining portion of the core. The boundary between channels 1 and 2 is open Q for crossflow; the rema?ning outer boundaries of channel 2 are assumed to be impermeabic and adiabatic. Channel 2 includes channels 3 and 4. Channel 3 lumps the subchannels adjacent to the f!D:lCR hot coannel 4.

5-1

() 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[ lof the core average value is appropriate for SONGS 2 and 3 operations within the ranges defined in section 5.1 so that 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.

().

O e

e O

5-2

f l

G 5 2

.8011 .8436

.7663 3 i CHANNEL NUMBE[R 1.18G 1.223 CHANNEL AVG 12' 13 7 8 4 -

RADIAL POWER - .

FACTOR -+ .7126 .9555 1.0G9 1.216 1.089 14 15 9 10 11 1.082 1.032 1.070 1.078 1.072

=

16 17 18 19 20 1.020 1.032 1.027 1.007 .9916

.8835 1 21 22 23 24 25 1.030 1.021 .9040 .9511 .8158 I

l l- I o 1 o I i I p _ ._ _ __ _l_ _p q_ __ _p __ _

l

, Gb , \

la1 @ _,_. - h-b -~ .0274 T 1 li l

~

l l.0305 I l l i t -l- - - -

-I- 4-- -i- -- - -

t- -

I l l Ie I i i l i I NOTE: CIRCLED NUMBERS DENOTE " LUMPED" CHANNELS Figure 5.1 STAGE 1 TORC CHANNEL GEOMETRY FOR SONGS 2 AND 3 5-3

w O - .

" em e e o e g e

t

+

.O M

e 1 O .

Figure 5.2 STAGE 2 TORC CifANNEL GEOMETRY FOR SONGS 2 AND 3

g .

_O _

O I

j 2.2 l g i 5 i g g g

~

! 2.0 -

A = +0.317 ASI ,

8 = 0.00 ASI . .

~

1.8 -

O C = .0.07 ASI A

- D =0.317 ASI . _

1.6 _

= A '

! O 1.4 -

3 o

$1.2 -

C -

m . ,

fm N -

• ~

,4 0 1.0 _

! s 5

x 0.8

! 0.6 -

l 0.4 I

0.2 '-

2 i -

1 l t t 't i i 1 '

1 1 I i

0 0.4 0.5 0.6 0.7 0.8 0.9 1.0 O . 0.1 0.2 0.3 t

i FRACTION OF ACTIVE CORE HEIGHT FROM INLET l

l 1

Figure 5.3 ,

{ '

! AXIAL POWER DISTRIBUTIONS j .

l '

l

9.

~

! ]

f I

i 1

l l

I-i-

t-i O

1

9. -

- .J Figure 5.4 O INLET FLOW DISTRIBUTION FOR SONGS 2 AND 3 5-6

O t

Q . ~

l .

l l

O I

E '

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

G G

4 O

O e

.O i O

Figuro 5.6

~

CETOP D CHANNEL GEOMETRY FOR SONGS 2 AND 3

. O (c"^""e' i "or snow">

5-8

O O O Axial Elev.

Operating Parameters MDNBR Quality at MDNBR ofMDNBR(in)

Detailed Detailed T0E CETOP-D TORC CETOP-D Core Core Avg. Axial Relative Inlet Relative Inlet Inlet fc#8tY Heat Flux Shape Flow.in Flow Flcw in Flow Detailed 6 Factor Pressure Ter.io , 10 1bm Btu Index location 1 Factor Location 1 TORC CETOP-D (psia) ( F) hr-ft br-ft 2 .( ASI)

2250 553 2.6394 284180 +.317 2250 553 2.6394 296290 +.000

~

2250 553 2.6394 281980 .070 2250 553 2.6394 .268050 .317 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 +.317 2415 571 2.3199 249920 +.317 2415 530 3.2712 384660 +.317 2415 571 3.0932 310600 +.317 TABLE 5.1 COMPARISONS BETWEEN DETAILED TORC AND CETOP-D

Q 6. CONCLUSION CETOP-D, when benchmarked against Detailed TORC for SONGS 2 and 3, 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 SONGS 2 & 3, and generally for applications in which the Design TORC methods have been approved (Reference 6),

9

/

a e

G O

e L

3 k- . ,

6-1

r~s - 7. REFERENCES V-

1. " TORC Code, A Computer Code for Determining the Thermal Margin of a Reactor Core", CENPD-ldl-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.

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, January, 1977. -

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

" Acceptance for Referencing of Topical Report 'CEMPD-206(P), TORC _

Code Verification and Simplified Modeling Methods".

t'h

(_) 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. , Universi ty of California Pubs.

Eng. 2, 1930, pg. 443.

10. Jens, W. H.; Lottes, T.A., Argonne National Laboratory Report, -

ANL-4627, May 1, 1951.

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

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

13. Pyle, R.S., "STDY-3, A Program for the Thermal Analysis of a Pressurized i

Water Nuclear Reactor During Steady-State Operation", UAPD-TM-213, June 1960.

14. "CE Critical Heat Flux Correlation for CE Fuel Assemblies with Standard 7_

Spacer Grids", CEMPD-162-P-A, September 1976.

i ( 'l . -

15. Berringer, R.; Previti, G. and Tong, L.S., " Lateral flow Simulation in an Open Lattice Core", AUS Transacticns, Vol. 4,1961, pgs. 45-46. .

i l .

2n

I

( [,' 5"

' ' ' ' ~

-,- .~- >1 -

_. _. " 5: '  ;-[ ..

l f

4

<>e > . .e mo.1,0~

TEST TARG'iT (MT-3) o'4 ,

- 1 1.0 lP@M y ilE R4 i,1 Q S I M +

i  ! a 1.25 1.4 1.6

=,

6" >

/ g

><  % ++

%$)

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"; f. ; 7 l. 7: J[ y i e , 1 ._ je ec: t ... - -

~

// d s

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~

IMAGE EVALUATION

. .oNNN\

TEST T~ARGET (MT-3)

I

!.0 5mHa

-- * @ HE

_i i ;"E:.:= L2g

^! A l.25-1.4 l 1.6

, _ i ==

6" *

~/ j

++

k+,7 b 4y,,7ff, -

4.%;,4 I

___ _C-__ _ _ _ _ _ _ _ _ ____________.-_______i_..

ll ,

+4 ...e. .

TEST TAR.GET (MT-3)

Relative -

6 s

. Parameters Address . Units Descriptions

,. e

\ -

HC 97 No: e s.

FSPLIT1 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 channel 5. Use 1.0 to specify infor-7 mation. -

NY 100 None Use 0.0 for not using the' relative locaticr.:

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 8 and pein-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 100% pcuer, hr-ftz -includes heat generated from rods and coo'l an t. 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 sF :

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

the design limit on Di;BR is reacnea.

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

1.0: To iterate on channel 2 radial peakir.

. factor. When this option is used the core heat flux in Channel I remains

. constant while all the Channel 2

~

radial peaking factors vary by the same multiplier until the 0N8 limit is reached.

,_s 2.0: Iterate on core flow l

( )

~ . -'

A-7

fT Relative  ;

Parameters Address ' Units Descriptions l

NZ7 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 ? id

+ J=1,NGRID types with the corresponding lose -

- . coefficient equations.

0.0 Normal grid with bui'. r 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) I'18 None Constant for Type 1 grid equation CBB(1) li None Constant for Type 1 grid equation CCC(l) 120 None Constant for Type 1 grid equation

(

CAA(2) 121 None Constant for Type 2 grid equation CBB(2) 122 None Const;nt for Type 2 grid equation CC(2) 123 None Constant' for Type 2 grid equ;cion 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

• 6 e

J A-8

(V~'s Relative Parameters Address Units Descriptions RAA2 129 None N

RAA22 130 , None GAP 2P 121 ft 1

. GAP 22 132 ft 2

A2P 133 ft A22 114 ft

'~

DD2P s ft

' bs 0022 136 ft 137 - 139 Hone For Future Work NDXPZ 140 None Number of axial power factors (Pecomend 41)

~

XXL(J) l41 - 190 None Rel'ative locations (X/Z)'of the axial J=1,NDXPZ ,,

power factors. If NY = 0.0 this input is not needed.

l l AXIAZ(J) 191 - 240 Nc.te Normalized axial power factors J=1, NDXPZ I

NFIND 241 -

None Speci.fy 1.0 to use the capability to change the hot assembly flow factor for differen:

regions of operating space. fpeci fy 0.0 to not use the capability. If 1.0 is specified, the following additional input it requi red.

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

O

(]

Relative  :

Parameters Address Units Descriptions I 243 g.p.m. 100% design core flow rate in g.p.m. divided REFLO 2 by core flow area ft FF(J)I 244-248 None Channels 2,3, and 4 inlet flow factor

- J=1,NREG for each region of operating so. ace. .

(Referred to as hot' assembly flow factor) 00J=1,HREG Provide for each region of operating space where: Ranges on 'raction of 1C 0% design core flow, inlet temperature K=(J-1)*12 system pressure, and AS: :

249 - 308

• s 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 n 2: lower limit < core flow 1 upper limit U

• 3: lower limit 1 core flow < upper limit

(

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

c BFR(J)I (251+K) None Upper limit fraction of 100% design core flow rate.

O

.- , - -- --,n,- --+ . _ - - -,-.-~,p, -----,w-- , ,.n,- ,, . ,-,

O Relative Address ' Units Descriptians Parameters ITI(J)I (252+K) None Types of inequalities applied ta limits of the inlet temperature range, same as IBF.

F Lower limit inlet temperature TIL(J)I .(253+K) .

TIR(J)I (254+r,) -

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.

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

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

IAS(J)I (258+K) None Types of inequalities applied to limits of the A.S.I. range (259+K) None Lower limit A.S.I. range ASL(J)I None Upper limit A.S.I. range

) ASR(J)I (260+K) 00 I

e v

Q

/3 V

1 A.4 Sample Input 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 transport coefficient at each node Hl.= Enthalpy in Channel _1 l

H2 = Enthalpy in Channel 2

~

1

-7 H3 = Enthalpy in Channel 3 H4 = Enthalpy in Channel 4 QDBL = core average heat flux, represents total heat generated from Q rods and coolant, wnere fuel tods are corrected (for axial densification) Stu/hr-ft 2,

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

- For no iteration, core flow iteration, and radial pea!.ing factor iteration, the he=t flux given in the input XLOC(2) is printed.

' POLR = for core power iteration, the ratio of the core average heat flux i

at the end of last iteration to the core overage heat flux at

. 100% power is printed.

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

TIN = Inlet temperature, F PIN = System pressure, psia GAVG = Core average mass velocity (610 lb/hr-ft )

- for core ficw iteration the mass velocity at the end of the

{) last iteration is printed.

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

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 MND3R at last iteration X-N = coolant quali,ty at location of DNB-N DNB-1 = hot channel MDNBR at first iteration X-1 = coolant quality at location of DNB-1 QUIX = QUIX file case number A

\_ / 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 additicnal 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 DNBR and Quality are not close to the actual values.

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

/~T HCH = MDNBR hot channel number, if 3 is or,inted this means

'w)

NN00 = MDNBR node location CESEC TIME = This paranieter is printed in the output when the CESEC code is linked with CCTOP-0.

I .

() FSPLIT = 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 flot, factor for different regions of operating space is used. The following paran,sters 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 f'. .s GIN = the calculated core average mass velocity , Ib/sec-ft 2 VIN ' inlet coolant specific volume, ft 3/lbn

• T

)

e i

)

O i

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- . - a a.u a - a-m--,,

O a

v i

O Appeneix a sempie ceroe-o input / output l

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f .l f

.= Np  % l' *%- i i 4 o

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$ .= 7 / - O i

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• 33

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• A 8 9  :

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. NNNNNNNNNN AM AA3 J" E 3 7 9 f l l CDDDDD&C D C  % D3 A9 D 3

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-.3 . "7. 3O. 2 . > . . . T. 3. Q>

i f

4 lZ 4 ft . m - 4 3 ". $ .= 3 0 3 9 i 4 a t ?P 3 3 A3 3 3 *l> b%D

f b ? ? ?. mi. %b /* b. N %

m. a. % % a 3 9 o A 3 ft f% oA J e I *99*999999 d D D 7 l .N. 3. J. :TP. y 7 . N. a l

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t 9 l ' l I *A f E  % 4 . # :: 8 I

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g I .- p 93 29 1 32 O i- A A a. 'A%

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= = = . '

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=NN99?

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h_,  !

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7. N.D.N N*=. N N% NwN

' I LPdDRdllBINil t

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i  ! l l i-N2 3e7p% 2 4 *= % 3 39%3% 3 2 == 3 A4 C*A3eAe77% C == 3 ? E 7NA 4 ==

l

• 3 3 r2 c*=73% 43 4N2% == 7 &N N == t l

@N2 0 2 == *e N% ** 9 e ? == A C CA7 32NC% == == D cCr#3pp% 1 3 4N e "P> NN% 3 = = 9 e e == 3 A = t 7 N s e 10 1 793 3L% $L%2C% 4P* ? 2 D * *e 7%?#fP% > % C =*** 3 = > b 323% e l

• e o e e o e e e o e o e o e e e o e o e o e e *

• e e e e e e e e o e e . o 3 l

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