ML20010H477

Fibwr:Steady State Core Flow Distribution Code for Bwrs, Computer Code Users Manual.

ML20010H477
Person / Time
Site:	Vermont Yankee
Issue date:	07/31/1981
From:	Ansari A, Gay R, Gitnik B NUS CORP., RENSSELAER POLYTECHNIC INSTITUTE, TROY, NY, YANKEE ATOMIC ELECTRIC CO.
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ML20005B488	List: ML20005B487 ML20010H469 ML20010H477
References
NP-1924-CCM, NUDOCS 8109240516
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FIBWR: A Steady-State Core Flow D;stribution Code for Boiling EPRI EPRI NP-1924-CCM Water Reactors Computer Code Manual P,o,ect 1754.,

Computer Code User s Manual 3 aui,,98, l

Keywords Core P f pass Flow Core Flow Distribution Core Pressure Drop l Core Void Distribution '

Steady-State Hydrauhcs I

'ared by Kee Atomic Electric Company

.mingham, Massachusetts

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r FIBWR: A Steady-State Core Flow Distribution Code for Boiling Water Reactors Computer Code User's Manual d N P-1924-CCM Research Project 1754-1 Computer Code Manual, July 1981 Prepared by YANKEE ATOMIC ELECTRIC COMPANY 1671 Worcester Road Framingham, Massachusetts 01701 Principal Authors B. J. Gitnick s NUS Corporation, Rockville, Maryland R.R. Gay Rensselaer Polytechnic Institute, Troy, New York R. S. Borland Science Applications, Inc., McLean, Virginia A. F. Ansari Yankee Atomic Electric Company, Framingham, Massachusetts Prepared for Electric Power Research Institute 3412 Hillview Avenue Palo Alto, California 94304 EPRI Project Managers J. A. Naser B. A. Zolotar Code Development and Validation Program Nuclear Power Division

EPRI PERSPECTIVE PROJECT DESCRIPTION This computer code manual, together with the companion report, EPRI Final Report -

NP-1923, FIBWR: A Steady-State Core Flow Distribution Code for Boiling Water Reactors--Code Verification and Qualification Report, documents the FIBWR steady-state BWR hydraulic computer code. This code was developed to calculate the steady-state flow and pressure distributions in the BWR core by taking into account the ietailed description of the complex BWR flow paths.

PROJECT OBJECTIVE The objective of modeling the complicated flow paths in tLe BWR core and explicitly the leakage flow to the bypass is to accurately predict tae flow and pressure dis-tributions throughout the core. These distributions have a determining influence on the moderator density distribution in the care. The moderator density in turn has a strong effect on the power distribution and, hence, behavior of the core.

PROJECT RESULTS The FIBWR code has been used successfully to predict data from the Frigg test loop and Vermont YanKe?. This computer code will be useful to utility engineers for various BWR applications. Some of the potential steady-state applications are:

1. Determination of the moderator density distribution for nuclear simulator codes such as SIMULATE

2. Initialization of input parameters for transient codes such as RETRAN, VIPRE, and COBRA

3. Calculation of the power and corresponding flow of the limiting assembly hot channel when et thermal limits

4. Determination of pressure load.ngs on internal structures such as the support plate and fuel channel walls Joseph Naser, Project Manager Nuclear Power Division iii l

_ _ _ _ _ . _ _ _ _ . _ _ . _ _ _ _ _ _ _ _ . _ _ _ _ __ ___ J

' ABSTRACT A user's manual for the steady-state core flow distribution code (FIBWR) is described. FIGWR is a computer code developed for the steady-state thermal-hydraulic analysis of BWRs. Sevcral models for calculating various pressure drop components and void distributions are incorporated as ue.er options. This report describes the theory, required input, and the code output and shows a sample problem run with FIBWR. The companion volume describes the verification and qualification performed with FIBWR.

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ACI 0WLEDGMENTS This work was johtly funded by Yankee Atomic Electric Company (YAEC) and Electric Power Researcn Institute (EPRI), under the program management of Dr. Burt A. Zolotar.

The authors are indebted to Dr. Burt A. Zolotar of EPRI for facilitating this study and for providing many helpful suggestiens. We wish to thank Mr. Bruce C. Slifer of YAEC for initiation of this development work and for providing nany useful suggestions and careful review. Mr. Peter Versteegen of Science Applications, Incorporated (SAI) is acknowledged for providing a source listing of the FAVII; code, which formed the nucleus of FIBWR. Last but not the least we wish to thank P.obert Rowell of YAEC for providing computer related support.

vii

f CONTENTS Section Page 1 INTRODUCTION 1-1 2 CALCULATIONAL METHOD 2-1 3 FIBWR REPRESENTATION OF THE REACTOR CORE 3-1 4 DESCRIPTION OF FIBWR EQUATIONS AND MODELS 4-1 4.1 Quality and Void Fraction 4-1 4.2 Friction Pressure Drop 4-8 4.3 Local Losses 4-12 4.4 Acceleration Pressure Drop 4-16 4.5 Elevation Pressure Drop 4-17 4.6 Bypass Flow 4-17 4.7 Water Tubes 4-19 5 CALCULATIONAL DETAILS 5-1 5.1 Water Properties 5-1 5.2 Minimum Flow Requirements 5-1 5.3 Convergence Techniques 5-2 5.4 System Energy (Heat) Balance 5-4 l

5.5 Heated Cora Dimensions and Node Heights 5-7 6 I.1PUT DESCRIPTION 6-1 6.1 Input Deck Format 6-1 6.2 Detailed Description of FIBWR Input Variables 6-3 6.3 Sample Input 6-23 7 FIBWR OUTPUT DESCRIPTION 7-1 7.1 General Format 7-1 7.2 Ir.put and Case Initialization (NALL > 0) 7-2

~.. Intermediate Calculations 7-2 1

7.4 Case Summary 7-3 7.5 Sample Output 7-3 8 REFERENCES 8-1 ix

I 4

i ILLUSTRATIONS Number Pagee 4-1 Void Fraction vs. Quality rt 1000 psia, G=lx106 lbm/hr ft2 49 j 4-2 Form Loss Multiplier Comparisor at BWR Conditions 4-15 I 4-3 Geometry Input 4-18 5-5 Control Volumes and Flows for the BWR Heat Balance 5-5 l

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I TABLES Number Page 2-1 FIBWR Execution Methodology Descriptt;. aw Convergent Case 2-2 4-1 Void Model Constant - 4-7 6-1 Available Options in FIBWR 6-20 xiii

i SUPNARY This report describes the FIBWR computer code, which was developed to provide an accurate and convenient steady-state core hydraulic simulator for BWR core reload design and licensing calculations.

In a BWR, the power distribution is closely coupled to the coolant density.

Because BWRs are undermoderated, the neutron flux and power are strongly influ-enced by local variations in the steam void distribution, which is a direct function of the power-flow distribution in the core rey.on. Thus, a synergistic relationship between flow and power exists in a BWR core. FIBWR provides the capability to accurately predict the flow distribution for a given power distri-bution. The total flow entering the lower plenum splits into an active component and a bypass component. The active component (referred to as active flow) flows up through the fuel channel. The bypass component (referred to as leakage or bypass flow) flows through the interstitial regions that surround the fuel channel.

The leakage rate to the bypass is dependent on the pressure drop across the core, which is in turn dependent on the active-bypass flow split. A BWR hydraulic simulator must accurately predict the pressure drop, flow, and void distributions over a large range of power-flow operating conditions.

The FIBWR code incorporates a detailed geometrical representation of the complex flow paths in a BWR cc.de and explicitly models the leakage flow to the bypass.

FIBWR includes a selection of widely used and recently developed models avail- _

able at user option to calculate the following: (a) void fraction in both the subcooled and bulk boiling regions, (b) the location of the onset of subcooled boiling, (c) flow quality as a function of equilibrium quality, (d) single-phase friction factor, (e) two-phase friction multiplier, and (f) two-phase local loss multiplier. These models have been reviewed and qualified against the latest multirod pressure drop and void data. The FIBWR code has been verified by analytic studies and comparisons to other thermal-hydraulic codes. Benchmark S-1

__ _____. _ _ _ . _ _ . - . _ _ . _ _ . . _ _ . _ _ . _ . _ _ . _ _ _ _ _ _ = _ _ _ . . _ _ _ . _ _ _ _ . .

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i comparisons of FIBWR predictions with measured data for the Vermont Yankee reactor have shown excellent agreement.

{ This work was partially sponsored by EPRI under RP1754-1, with Yankee Atomic T 4 E?ectric Company being the prime contractor.

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Section 1 INTRODUCTION The FIBWR code evaluates the flow and void distribution within a boiling-water reactor (BWR) : ore by solving the steady-state one-dimensional equations of con-tinuity, momentum, and energy. FIBWR computes the coolant mass flow rates in each channel and in the bypass region for either a given total core mass flow or specified total core pressure drop.

FIBWR has great flexibility to handle the varied geooetrical configurations of currently operating BWRs. The FIBWR code models the core of a BWR as up to one hundred parallel flow channel types plus a bypass region. Each channel type has a user-specified geometry and power distribution. The detailed geometric modeling of each fuel assembly includes the effects of the inlet orifice, fuel support piece, lower tie plate, unheated fuel regions, grid spacers, water tubes, upper tie plate, and chimney. Three bypass flow paths located after the orifice but before the active fuel region and up to eight bypass flow paths dependent on the core support plate pressure differential are allowed. All bypass flows are lumped into a single flow region representing the average bypass; however, as a supple-mental calculation, a hot bypass region may be calculated using user input power and flow penalty factors.

Since there are numerous models available in the literature that describes void and pressure loss relationships of two-phase flow, several options have been incor-porated which, in the opinion of the authors, represent the best of the widely known models. The user may select among several models for each of the following:

initiation of subcooled boiling, relation of flow quality to equilibrium quality, relationship of void fraction to flow quality, single-phase friction factor, two-phase multiplier for frictional losses, and the two-phase multiplier for local (form) losses. The FIBWR code computes the acceleration, frictional, local, and elevation pressure 16sses in each channel based upon the above models and sums I them to arrive at the axial pressure distribution in the channel. The code defaults l to the reconnended models; however, the user has the option to specify Jifferent models.

1 1

1-1

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{ The fcilowing assumptions Are basic to the solution methodology:

1. Static pressure at the inlet and outlet plenums is uniform fcr all channels, 4

2. Subcooled or saturated inlet conditions, i 3. One-dimensional upward vertical flow in each flow channel,

4. Const' ant, uniform pressure for the evaluation of water procerties.

The assumptions simplify the numerics of the equations considerably. For steady-state conditions at high system pressures, the impact on calculational accuracy of these assumptions is slight. Although it is well known that one-dimensional a equations cannot completely describe the complex patterns of two-phase flow, the effects of these patterns have been incorporated in the thermal-hydraulic models and input coefficients for predicting flow quality, void fraction, and pressure drop.

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Section 2 CALCULATIONAL METHOD The pressure drop and flow distribution is obtained by an inner / outer iteration technique. The methodology used is illustrated in Table 2-1. Typically, the code is required to determine the core pressure drop and flow distribution for a given core flow. An initial estimate cf core pressure drop is input by the user or internally calculated. On the inner storations, the flow in each channel type is adjusted until the desired pressure drop is reached. During this process, the variation in leakage flows to the bypass and the water tubes is calculated, and the total flow which passes through the orifice, lower and upper tie plates is obtained. When converged to the estita.3d pressure drop, the flows from each of the channels and the bypass regions a'e summed to obtain the total core flow, which is compared against the required core flow. The outer iterations adjust core pressure drop until convergence is obtained. Alternately, the user may require the code to determine the core flow for a given core pressure drop. Here the calculational scheme is identical, with the exception that only inner iterations need be performed.

2-1

4 Table 2-1 FIBWR EXECUTION METHODOLOGY DESCRIPTION FLOW CONVERGENT CASE Step

1. An estimate of the core pressure drop is user input or automatically computed using total core parameters such as the total mass flow rate and power level.

The initial estimate of the channel flow splits is made on the basis of the inlet orifice coefficient for each channel. If the pressure drop guess is user input, the initial guess of channel mass flows will be equal in all chan-nels. Saturated water density is assumed for the bypass.

2. For a given channel the energy equation is solved, by integration up the chan-nel to yield the axial fistribution of equilibrica quality.

3. The flow quality and void fraction distributions are calculated in the channel as a function of the previously computed eauilibrium quality.

4. The heated region pressure drop is evaluated next by integration of the two-phase flow momentum equation up the channel.

5. The pressure differentials for the leakage paths are determined, and the water tube flows and bypass flows are evaluated. The pressure drops for the unheated regions are computed consistent with the total flow, which passes through the orifice, tie plates, and other unheated zones. The heated and unheated region pressure drops are now summed to obtain the channel pressure drop.

6. The channel pressure drop computed above is compared to the core pressure drop.

If they are not equal to within a user-specified degree of accuracy, a new estimate of channel inlet velocity is made, and execution returns to step 2 above. If the pressure losses agree, execution again proceeds to step 2, but this time the hydraulic conditions in a new channel are calculated. When the conditions in all channels in the core have been calculated, the bypass eleva-tion head is reevaluated, and execution proceeds to step 7 below.

7. Now that all channel mass flows are known, the total computed channel mass flow is compared to the required core mass flow (user input). If the values agree to within the required ac uracy, execution proceeds to step 8, below. If not, a new core pressure drop is guessed, and execution once again returns to step 2, where the whole process starts once again.

8. Now that all core hydraulic conditions are known, the output summary and other parameters such as CPR are calculated and printed.

i 2-2 FP 9

Section 3 FIBWR REPRESENTATION OF THE REACTOR CORE The FIEWR code does not solve for each fuel assembly discretely; rather, up to or.e hundred characteristic channel types are used to represeit the hydraulic and power distribution variations preseat in the core. The use- must specify the geometry, power distribution, and number of channels present in the core of each characteristic channel type. If the user requires a detailed hydraulic solution for each assembly, a " character!stic channel analysis" may be performed to deter-mine the core pressure drop, and subsequent pressure drop convergent cases may be run to analyze the individual channels. It is therefore essential to salect characteristic channels that have the same geometry, leakage coefficients, hy-draulic resistance coefficients, and representative axial and radial power distri-butions of the channels they typify.

The input defines the characteristic channels in detail. Hydraulic descriptions of the orifice, lower tie plate, grid spacers, upper tie plates, and, where appli-cable, water tube inlet and outlet holes are represented as being separate and distinct local losses. Bypass leakage coefficients describe the fuel support-lower tie plate flow path, channel-lower tie plate flow path, and lower tie plate holes for each channel type. Additionally, the user may input bypass leakage coefficients for up to eight "conunon" bypass leakage paths (i.e., leakage paths whose flow is solely dependent on the core support plate pressure drop). For each channel, tne active flow area and water tube areas, and the axial elevations of the local restrictions (e.g., tie plates, grid spacers) are input. The axial elevation data describes five axial zones for cach channel: the height from the core support plate to the bottom of the rodded section, the lower unheated rodded section, the active fuel section, the upper unheated rodded section, and the upper unheated unrodded section (chimney). The grid spacer elevations are input as a fraction of the active fuel length. The elevation of the orffice below the core support plate is an additional input which is common for t.ie core.

The power distribution data are presumed known and are supplied as input to the FIBWR code. The input is supplied as radial peaking factors and axial peaking factors (normalized power distributions) for each channel type. The number of 3-1

axial nodes is an input; up to 25 axial nodes are allowed. The axial peaking factors. input should be node-averaged values. The code searches for the highest and lowest active fuel elevations; the axial nodes uniformly span the distance in between. An option is available to adjust the input axial power factors to the reference active fuel length for cores with mixed length fuels. Both radial and axial powers factors must be normalized to unity. The code checks the nor-malization, and the case terminates if the normalization is in error by more than 0.05 percent. An option is available to proceed with the calculation regardless of input errors or power distribution misnormalization.

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Section 4 DESCRIPTION OF FIBWR EQUATIONS AND MODELS The total pressure drop for each chani.al is calculated as the sum of the individual pressure drg components: friction, local (form) loss, acceleration (momentum change), and eievation. Acceleration and elevation can be evaluated once the flow quality and void fraction have been determined. The friction and local loss terms require input coefficients and models to account for two-phase effects.

The details of the models contained in the FIBWR code are discussed below.

4.1 QUALITY AND V0ID FRACTION FIBWR calculates both the thermodynamic equilibrium quality and the flow quality.

Equilibrium quality, <X eq> , is determined from the following relationship:

<X,q> = (H9-Hsat)/Hfg ,

(4-1) where H j is the bulk enthalpy of the node of interest. <X eq > can be positive or negative. This is the quality that would be obtained if the flowing mixture were removed adiabatically, thoroughly mixed, and allowed to reach thermodynamic equilibrium. The flow quality is tF true fraction of vapor that exists in the flowing mixture, defined as the ratio of vapor mass flow to total mass flow.

It is always positive and less than or equal to unity. Typically, flow and equili-brium qualities are nearly equal for the high void elevations of a BWR fuel channel; they differ in those regions where subcooled boiling conditions exist. FIBWR uses the EPRI (1_) model to predict the point of bubble Ceparture; the Saha-Zuber (2_) and Levy (3_) models c.re available as options.

The EPRI subcooled void formation model (1), developed by Lellouche and Zolotar, is based on a mechanistic model. FIBWR contains Zolotar's simplified version of this model, which has been shown to be in agreement with the mechanistic model for steac;y state conditions. According to the EPRI model, the temperature, Tdeparture' at which subcooled void formation begins, may be found by:

2 B YB -4AC (4-2)

TSAT - Tdeparture " 2A 4-1

where,

A = 4HB (HDB + HHN)

B = 2H08 (HHN + HDB[2)+8q"HB (HHN + HOB) 2 C = q" (4H B 9"

• NDB) given T = temperature 0F 2

i q" = wall heat flux at point of departure - Btu /hr-ft p = Pressure - psia Re = single phase Reynold's number D = hydraulic diameter - ft h

Pr = Prandtl number K = thermal conduct' 'ty - btu /hr-ft OF and, HHN = CHN(Re)0.662 Pr K/D h 0

HDB = CDB(Re)0.8 Pr .4 K/D h HB = exp P 630 (0.072)2 4

where,

• 0.023 for channels and tubes C

Dd 0.033c +0.013 for rod bundles and annuli "J0.2 .

for channels and tubes HN 10.2Df4RODD h for rod bundles and annuit c = fraction of area available for flow

=A fjg, Afjg,+ Arod i RODD = heated rod radius - ft 2

Afjg,= flow area - ft ll i

4-2

I Arod = Nrod

• RODD2

- ft 2 Nrod = number of heated rods The following calculational precedure is used to determine the flow quality once the equilibrium quality distribution is known. For each node, starting at the channel inlet the calculational procedure is,

1. Evaluate T departure using Eq. 4-2, from which h departure and

<Xegdeparture> may be calculated.

2. If the mixture enthalpy is less than hdeparture' ** < flow > to zero and proceed to the next node.

l 3. If h departure is less than h inlet then set <Xegdeparture> equal to l <Xeginlet>*

4. Compute the flow quality using the hyperbolic tangent profile fit:

<Xfj g> = <Xeq) - <Xeqdep> l-Tanh(1 - l Aq ,)

1- <Xegdep> l-Tanh(1 - ) Aq ,)

5. If the difference between the flow and equilibrium qualities is less than 0.001 then they are set equal to each other for all subsequent nodes.

6. Evaluate the next node by returning to Step 1.

i The equations for the Saha-Zuber and Levy models can be found in their original j references, or 1, Table 5-1 of Lahey and Moody (4_). For these models, FIBWR uses

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an exponential profile fit of the form suggested by Levy (_3_) to calculate the l flow quality:

l

[<X >

)

<Xfj,,) =

<X,q) - <X,q>eparture exp

<X > ~I I (4-3) d eqdeparture) .

Once the flow quality has been determined, a void-quality relationship is used to determine the void (vapor volume) fraction. The relationship between the void 4-3

fraction and quality in a flowing system is dependent .pon the phasic densities and the relative velocities of t!.e two phases. The fundamental void quality rela-tion (exact) is:

<gy a

<X>

+ S *Lb(1-<X>)

where

<a> - void fraction S elip ratio =

• = mass-averaged vapor velocity 7L mass-averaged liquid velocity

<X> - flow qua? ity pg , og - densities of vapor and liquid .

Hence, in order to relate void fraction to quality, one need only know the slip ratio, S. The homogeneous model assumes a constant slip ratio of 1.0. However, because S is difficult to define for a system in general, it has been customary to define two more basic parameters, Cg and V gj.

Cg , the concentration parameter, quantifies the effect of the radial void fraction and velocity distributions, while Vg ), the drift velocity, is a measure of the local velocity differences between the phases. An alternate (exact) void quality relation was derived by Zuber and Findlay (5_):

<X> (4-5)

<a> =

C P P9 v d g <X> + pi (1-<X> +

g s -

We are now left with the task of defining Vgj and gC instead of S in order to relate void fraction to quality. Most experimenters have chosen to correlate Cg and Vg ) instead of slip ratio.

Cg has a value of unity if the liquid and vapor phases are uniformly distributed.

If the vapor is concentrated in the high velocity or central flow regions, the con-centration parameter is greater than 1. It is less than 1 if the opposite is true.

4-4

l Historically, a value of C, = 1.13 has been found appropriate for fully developed annular flow. In fact, both the Zuber-Findlay (5_) and Levy (6) void-quality models specify a crnstant C, equal to 1.13. However, gC must be a functica of flow regime,

and should tend towards one in single-phase vapor flow.

The drift velocity, V ),g may be modeled by considering a bubble rising in a liquid.

A balance of forces gives the terminal rise velocity as u=K t 3

'Dk 2 sine , (66)

C L

i where a = surface tension, lb /ft f

2 g = gravitational constant, 32.174 lb,/sec ID -ft g = 32.174 m c

lb f-sec 2 K3 = experimental constant e = angle with the horizontal.

For vertical flow it is often ass 7ned that the drift velocity is proportional to the terminal rise velocity.

Lellouche and Zolotar Q) recommend ' iterative technique, referred to as the EPRI model, to determine C, and Vg ). Co , the concentration parameter, is determined as follows:

C =

o LfAN where A = Kg - + (1-Kg) <a>"

r= 1 + 1.57 9 p / (i. - Ky)

' 0 / h 9 p K

g

= K j + (1-Ky ) g 4-5 1

- ,,-- - w,-, , - - - , - , . - - . - - - - --

e ,--e- - -- - e

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

4 K g = MIN (K ' , Kf) i F I Kg, 5 1+exp[-Re[103 K

G, J 0.8 for cylinders, annuli and rod bundles

! 1 (0.72 for channels j

J1 <a> = 0.0 lN" 11 - exp [- Cy<a>] <a> > 0. 0 4P c C

1 = p (p -P) l c

P = critical pressure, psi c

P = pressure, psi

. The drift velocity, Vg ), is given as:

I L g) 99c sine (1-<a>) / (4-8)

Vgj = 1.41 2 L _

This is equivalent to Eq. 4-6 for the bubble terminal rise velocity i_f,K f 3

is set equal to 1.41 (1 <a>)3/2, In the above equations, C o and V g ) are functions of the void fraction, va>. To facilitate the iterative solution, these equations are rewritten as follows:

given YF = (1-<X>) 1+g I4'9) i L -

N -

then A

LN

• 0.2 (4-10)

(1 + YF/X>)LN

<a, =

q A

i LN < 0.2 (1 + YF[X>)C1 4-6

+m-sv- my i-- r w-- -%s__.mry-% 1'y'T* b * - ' - - - - - - , - - p--

c r-3 ----+i----~

l The void fraction.o), is adjusted until the new value is within 0.001 of the pre-

vious value, or the maximum number of iterations (20) has been exceeded.

Dix (7) developed a model for C, which goes to zero as flow quality goes to zero (as in subcooled boiling where the bubbles cling to the heating surface) and which also goes to 1 as quality goes to 1 (as in single-phase vapor flow), and is greater than 1 for annular flow. The Dix model is:

C g =61+(f-1)b (4,73) where b = (p /p )0.1 5

g g

<x> l

g. ,

<X> + Pg (1-<X>)

' pg For the drift velocity, Dix chose the value h

E 4 C Sin i

(4-12)

' Vg ) = 2.9 pg which is equivalent to Eq. 4-6 with K3

• 2*9 l.

The recommended model in FIBWR is the model proposed by EPRI. The homogeneous, Dix, l Zuber-Findlay, and Levy models are available as a user option. The Zuber-Findlay and Levy models, define gC and K3 (Eq. 4-6) as empirical constants. The relationship between the models for the values of C o and K3 is shown in Table 4-1 below:

Table 4-1 VOID MODEL CONSTANTS Appropriate Choice of Parameters Model Cg K 3

EPRI variable 1.41 (1 <a>)

Dix variable 2.9 Homogeneous 1 0 Zuber-Findlay 1.13 1.41 Levy 1.13 1.18 4-7

A graphic comparison of the void quality as predicted by several of these models is presented in Figure 4-1.

4.2 FRICTION PRESSURE DROP The frictional pressure losses are correlated in terms of the single-phase velocity head:

2 2 apfric " I 42 -phase friction (4-13) gP ct where f = the single-phase Darcy-Weisbach friction factor, 2

2g P the single-phase velocity head, cL 2

G = mass flux, Ib,/sec-ft ,

3 og = liquid density, lb,/ft ,

I b,- f t g = 32.174 c

abf -sec 2'

and c2 = the multiplier to account for two-phase effects.

Three models have been included in FIBWR to predict the friction factor f. The recommended model is the well-known Dlausius (8) relationship:

f = A Re B (4 14) where A and B = input coefficients.

Re = the single-phase Reynolds number .

The second model is a fit to the Moody curves (8_):

6 f = 0.0055 1.0 + (20000c/Dh + 10 /Re) B-15) 4-8

" l I I I I I I I I I l Homogeneous 80 - ** EPRI .-

ber Findlay 70 - # *** #

60 -

1. *I -

50 -

[ -

Fraction

(%) /*

40 -

/. * -

?

• l.*/

30 -

g B -

/

20 -

10 -

1 I I I I I I I l l I 2 4 6 8 10 12 14 16 18 20 Flow quality (%)

Figure 4-1. Void Fraction vs. Quality at 1000 psia, G=lx106 lbm/hr ft2

where c is the surface roughness, and D is the hydraulic diameter.

h The third model is the Cot; brook equation (8,):

-.I__ . 1,74 2c 18.7' (4-16) gfi 2 tog 10

.{ , Re [.

This expression must be iteratively evaluated.

2 There are four te-phase friction multiplier (42-phase friction) models in FIBWR.

The recommended model is the modified Baroczy (9_, ,1_0) which is graphically presented in Figures 5-16 and 5-17 of Lahey and Moody (4). The second model is the homogen-eous flow relationship:

2 fO t h 4 -phase friction " I

• 2

{~ (4 17}

The third model is the Jones-Dight (1_1_) fit to the Martinelli-Nelson curves (12_):

~

2 ~*

4 -phase friction " **P 2 g ak ( w) (4~IO) where w = in[100(<X >+ 0.01)]

• k* =0 C

ki (P/10CO)I The matrix of (untruncated) coefficients Cki is as follows:

1 k 1 2 3 4 0 2.5448316 -0.51756752 0.10193956 -0.0080606798 1 -7.8896201 1.9550200 -0.37233785 0.026160876 2 15.575870 -0.96886164 -0.19025685 t 060288725 3 -17.340906 -4.6129079 2.2654839 -0.32426871 4 10.409842 8.4910340 -3.4925414 0.46553847 5 -3.2044877 -5.9583098 2.3299085 -0.30333482 4-10 I

e

.n

l l

l 6 0.42484805 1.8989183 -0.72534973 0.093379834 7 -0.010804871 -0.22867680 0.086169847 -0.011021915 The fourth model is the Martinelli-Nelson with a mass flux end pressure correction:

2 2 n

1. 2-phast friction * #M artinelli (4-19)

Nelson where 1.36 +

P

+ 0.1 ( 6)- { ( ), 5 0.7 O

0mi 6

t i 1.26 0.4P + C.119 (10 ) + 0.28P ,)0 I G > 0*7 1000 G 2000 *T ' 6 10 l

The fifth rr.odel is the Chisholm (13) relationship:

(4-20)

-phase friction = 1 + (r (1) Ef (<XWX>)) N ,<x , M _

where

. B - constant as in Blausius relationship i e.g., f = A(ReB)

{og)0.5 fy)-B/2 A

T= l 1 1l-9) lYt}

o = liquid or vapor density, lbm /ft 3or gg/m3 p = liquid or vapor viscosity, Ib,/ft-sec or Kg/m-sec G = mass flux in Kg/sec-m2 E, m are input constants. (see Reference (l_3_)

3 for typical values of E and m).

Figure 5-18 of Lahey and Moody (4) presents a graphic comparison of several of i

the two-phase friction multiplier models.

4-11

4.3 LOCAL LOSSES The local pressure drop is defined as the irreversible pressure loss associated with an area change, such as an orifice, tie plate, or grid spacers. The general local pressure drop equation is similar to that for friction pressure droi.:

2 2 Aplocal " K 0 4 2-phase local (4-21) 2geog where K = the single phase form loss coefficient G

2gg = the single-phase velocity head, 2

2-phase local = the two-phase multiplier for local losses.

The loss coefficients are determined empirically or from hanavooks of hydraulic resistances, such as Idel'chik (14), and are user input. The FIBWR model assumes that the local losses are zero thickness restricticns. This implies that the K should reflect the net static pressure loss superimpdsed on the fully developed pressure gradient:

Orifice, tie plate, or grid spacer

__ _ Static pressure profile Static - I ' if no orifice or spacer pressure l present l

l

~ 'L / '

s

., I c

2 2

OP

• K 2g P 2-phase local ct I l 1

~ ,,, 4 I t',

I i I i

1

'l 1

I Actual *.tatic pressure Height profile 4 .12

t l

It should also be noted that the G in the above expression is based on the channel flow area. Coefficient values for orifices, tie plates, and spacers which are based on the restriction flow area must therefore be corrected:

2 A

KI=Kactual channel flow 2 @-22)

A restriction i

Similarly, the coefficients for inlet and outlet holes for the water tubes must be corrected:

2 A

water tube (4-23)

KI=Kactual 2 A

inlet or outlet water tube holes The FIBWR code has three models for the two-phase local loss multiplier.

The default model is the riodified homogeneous expression:

• -phase local = 1 + (E) <XH -1 (4-24) f where l

E = an empirical adjustment factor. A separate value of E may be input for spacer grids anJ the upper tie plate.

The homogeneous expression is obtained by setting E equal to 1.0.

The second model is a version of the Janssen (15) model modified by Weisman (16).

l Janssen's local loss multiplier for short restrictions is:

+!-phaselocal

• D 2 (625)

,90 1<X><a3'(<a><,l>;+(1-<X>)2(1-<a>)

2 3 I oC 2 -2C t<X>2 1

o (1 <a3>)2 _ (I-* 5>)2 h #"3" *"5"

/

+ (1 -<X>)2 1 oc ~(1-oC)2-1-<a " - ( C)*

3 (I-#"5') _ ,

4-13

where ca3 >- void fract e at vena contracta

<a5>- flow channel vt, .3 fraction

<X> - flow e ity oC - net reduction in flow area factor, i.e.,

vena contracta area / original flow area

=1/(1+/K)

Weisman has developed a correlation for obtaining <a >. His correlation is 3

<a3*** vc> + A(< homo'-**vc')

where

<:tx vc>= evaluated flow channel void at the fraction vena con-tracta flow velocity A=K with the restriction that 0 s A 5 1 andtheconstants(experimental):

K = - 1.8ca 5>+ 1.05 b = 3.1 (<a5> .36) h = empirical length to diameter ratio of restriction, which is input to the code.

It can be shown that Janssen's model reduces to the homogeneous model if both <a3' and <a5 > are set equal to <ahomogeneous>, calculated by assuming slip equals one.

ThethirdmodelistheRomie(R)orslipexpression:

P<X$

i (4-27)

• 2 2-phase local " K<T> l-<a> +(1-<X>)2 4-14

l l

It also can be shown that Janssen's model reduces to the Romie (slip) model if

< 3> i s set equal to <a5

Figure 4-2 presents a comparison of the three two-phase local loss multiplier nodels.

I I I i i i i i l l l l l s

3.5 - l ~

l p

%/ /

- s -

G = 1 x 106 lbm/hr ft2 /

P= 1000 psia ' #

pf 3.0 -

. / -

ol4l .'

/

l s zS\ ' _

o /

/

S h>#k .

2.5 -

/ B -

2 - ' -

20 *

,s' 1

/ -

l f[

1.5

~

/ ~

I I I I i l i I l I l l l 3

0 0.05 0.1 0.13 l

l Quahty l

l Figure 4-2. Form Loss Multiplier Comparison at BWR Conditions I

4-15

. _ = . . _. - .

1 4.4 ACCELERATION PRESSURE DROP The acceleration pressure drop includes the reversible pressure change experienced I at contractions and expansions, or resulting from the acceleration of the fluid during the boiling process (density change). The reversible pressure change from a flow area change when the fluid is in single phase is:

2 G

apACC " II ~ OA) 29 p g (4-28)

I where A = {2 initial = final flow ared flow area 2

G 2

2

=the single-phase velocity head with respect to the final 9PcL flow area.

When two phases are present:

( )

opACC "c g (Al+AI 2 P M I l ^l (4-29) 2 i

where, pM, the momentum density is defined by:

L ,<X>2 , (1-<X>)2 _

pg p <a= pg (1-<p) (4-30) g

<a>= void fraction at A2

<X>= flow quality at A 2 and other terms are as previously defined.

The basic formulation for the acceleration pressure change due to density change is 2

G I I (4-31) apACC . g c PM PM

- OUT IN-4-16

. __ . . _ . . . .~

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

where the momentum density, g p , is evaluated at the inlet and outlet of each axial nede. Other terms are as previously defined. The total acceleration pressure drop in boiling water reactors is on the order of a few percent of the total pres-sure drop.

4.5 ELEVATION PRESSURE DROP The elevation (gravitational) pressure drop is evaluated as follows:

AP,j ,y = p AZ (4-32) where l

p = og(1-<a-) + p g <a>

4.6 BYPASS FLOW Due to the low flow velocity, the pressure drop in the bypass region above the core support plate is essentially all elevation head. Thus, the sum of the core support plate differential pressure and the bypass region elevation head is equal to the core differential pressure.

The flow through the typass flow paths is expressed by the form:

W=Cg APb^C2AP 4+C 3AP 2 p.g The leakage paths to the bypass for a typical BWR geometry are shown in Figure 4-3. The pressure drops used to evaluate the above expression are functions of channel pressure differential (Pactive - Pbypass), and are evaluated at the lower tie plate-fuel support piece interface, the lower tie plate holes and the channel-lower tie plate interface (paths 6, 9, and 8 of Figure 4-3). The other paths (with the exception of the control rod coolant flow, which is input) are functions of the pressure differential across the core support plate. These paths are re-ferred to as the " common paths." The quantity of paths number 1, 2, and 5 is

! equal to the number of control rods. The quantity of path number 10 is equal to the number of spring plugs. The quantity of path number 3 is equal to the number of instrument and source locations. There is one path number 4. In order to simplify the use of the code, the user may renumber these common paths and lump several of these paths together. The number of such paths and the coefficients C1 through C4 are user input.

3 4-17 l

i

J The coefficients for these paths may be analytically or empirically determined, and should include the effects of long-term service. Long-term service mdy result in a net decrease or a net increase in total core leakage flow. Experience indi-cates that crud deposition to some extent should be expected in some of the leakage TOP OF CORE f

ZCHI ZUHA e

' Spacer height = HFSG*ZHET ZHET HFSG n +1

....r.

4 n ,

Note: Bottom entry peripheral fuel supports 1

are welded into the core sup; ort plate.

For these bunoles, path numbers 1.2.5 and 7 do not exist.

! o ZUHB

+ - Channel 0

1 "9 l tie p ate SP"I"9 PI"9 A Core 6 support ZGEO l

i g3 4 Bottom o of core g -.

_ /.___

Fuel support _ N In-core

/ guide tube llk l-Shroud Ib (Controlrod '

ge*de tube 0

'"9 fuel th + ZGEO

1. Control rod guide tube--fuel support

2. Control rod guide tube--core support plate Fuel length = ZUHA + ZHET + ZUHB 3. Core support plate--in-core guide tube

4. Core support plate--shroud l, .

5. Cortrol rod guide tube--drive housing 7 6. Fuel support--lower tie plate Control rod 7. Control rod drive coo 1%g water drive housing 8. Channel--lower tie plate

.I

9. Lower tie plate holes

10. Spring plug--core support Figure 4-3. Geometry Input.

4-18

[

t

flow paths. The result will be a decrease in leakage flow where the deposition ,

occurs. 01 the other hand, long-term channel pressure loading is expected to result in some amount of permanent channel deformation yielding an increase in t

leakage flow through path number 8. The bypass leakage coefficients, Cy through C4 , for the Vermont Yankee BWR have been documented (18).

The total bypass flow is the sum of the flows through each of these paths. On each outer iteration, the bypass enthalpy and void distribution are recalculated, and the bypass elevation head is reevaluated. After FIBWR converges on the channel and bypass flow distribution, the enthalpy and void distribution of a user-defined i hot bypass region is calculated. The results of the hot bypass region calculation

? appear in a supplementary edit. Tynically, the hot bypass region calculation is used to determine the onset of boiling in a particular bypass subchannel.

The mass flux used in the hot bypass region calculation is the total bypass mass

. flux times and input flow factor. The power deposition in the hot bypass is the '

average bypass power deposition per channel times an input factor. These factors may be bounding values or may be evaluated with a subchannel thermal hydraulics code. It should be noted that due to the lower density head, cross-flow redistri-bution will tend to quench a boiling subchannel. If significant boiling is experi-enced in the hot bypass region, a more detailed calculation should be used to j determine the hot bypass void distribution profile.

The user may omit the bypass calculation and input the bypass flow. The code will then assume that all bypass flow passes through the common paths; for example, no leakage flow must pass through the fuel channel orifices. No bypass enthalpy rise calculations are performed if this option is selected.

~

4.7 WATER TUBES l

FIBWR calculates the water tube flow consistent with the pressure drop of tie active coolant parallel to the tube. The entrance and exit elevations are input with reference to the start of the heated region of each channel. The water tube i is assumed to start at or above the bottom of the reference length, but may extend up into the upper unheated region. The FIBWR code models the water tube pressure drop in a similar manner to the active coolant, with the exception that the homo-7 geneous void relationship and two-phase local loss multiplier 'odels are used i

dould the water tube experience bulk boiling. No friction loss multiplier or two-phase corrections to the acceleration pressure drop are included; if the flow rate is lev enough to allow the water tube water to boil, these pressure loss components will not be significant.

4-19 I

m- - - - - , g- -. p, -,,,e- -rwn-,,-, y,,p.,w ww ,- --m- , , , , - , n,,,,,w, ,,ymar-- er w.4n.----,ew. n.--v, e - w-,

r-

Section 5 CALCULATIONAL DETAILS E

5.1 WATER PROPERTI,S The water properties consistent with the 1967 ASME steam tables are evaluated using the STHLIB routines from RELAP4. The STHLIB routines require an external file of water properties; this file is expected to be supplied to FIBWR on TAPF15.

A complete description of these routines is presented in Appendix 0 of Reference 17.

5.2 MINIMUM FLOW REQUIREMENTS During the iteration process, the program continually checks to ensure that the flow does not fall below the minimum flow. This minimum flow is calculated to l ensure that a very high (>.99) quality is not reached and the steam leaving the top of the channel does not become superheated. The minimum flow is:

W (5-1)

MIN

• O B hf + .99hfg - hlN) where

Qg = the channel power deposited in the active flow, Btu /Sec h

f

= saturated liquid enthalpy, Btu /lb l

( hfg = latent heat of vaporization, Btu /lb l

h lN

= inlet enthalpy, Btu /lb I If, during iteration for a given required pressure drop, the program makes a flow guess less than the minimum flow given in the above equation, the program will first calculate the pressure drop for the minimum flow. If this pressure drop is less than the required pressure drop, the iteration for the flow continues.

If the minimum flew pressure drop is greater than the required pressure drop, the required pressure drop is changed to this new value. In this way, the program will not allow cLyergence on a required core flow or pressure drop that will 5-1

i result in one or more channels with exit enthalples greater than that of saturated steam. If, on a flow-required run, the program finds it cannot converge on the flow without going below the minimum channel flow limit, it converges to the minimum possible total flow, with at least one or more channels operating at the channel minimum. The following warning is printed to the user: " WARNING - CHANNEL XXX ,

NOT CONVERGED AS CORE PRESSURE DROP REQUIRES INLET VELOCITY BELOW MINIMUM."

Similar minimum flow requirements exist for the water tubes and the bypass region flows.

5.3 CONVERGENCE TECHNIQUES The basic iteration problem is to force the channel types that the user specifies for the core to converge to a given pressure drop. If the user is making a re-quired pressure drop run, each channel type will be forced to conv.arge to the uscr-specified pressure drop, provided the minimum flow requirement is met. If the user is making a required total flow run, the first guess for pressure drop that the channel types are converged to is either input by the user, or the program makes the first guess. This pressure drop guess must then be corrected until the total flow requirement is met, but the lowest level iteration problem is to find the flow required to produce a given channel pressure drop. To start the iteration process, the code will guess an initial mass flow rate for each channel.

If the first guess does not produce the required pressure drop, a second flow guess is generated from the following simple ratio:

G2=Gi 3p . (5-2) where the subscripts indicate the iteration number.

l For the second iteration, a simple linear interpolation method is used:

[o p n-1 Ap rea'd

\

. (5-3)

Gn +1 = Gn-1 ~ ion-1 -oG )-n 'kp npn-1 / ,o where, again, the subscripts indicate the iteration, the (n+1) being the next iteration.

l l

l 5-2 r

-= var-wp- --,-----r g y w.-.  %- m-- ..-e,,*9ey%yp-,g ,,-rp'-9.a--4 y- --,,4-PT""*N-7"' T'-I'b'MM'WTr' PW F i"W '

"W '1 "Y -'-M" - - * " - "'# 5*

i t

)

On the third and subsequent iterations, the following polynomial extrapolation method is used:

Gn = A + Bapreq'd + Cap req'd (5-4) where

~ "~ n-2 n C= - (apn ^P }

^"P n APn -1 aPn-2'APn_

l I B= Gn-2-Gn-1 +A p CfA\pn-2 n-1 Pn Pn-1 and A=Gn BAp -C op n-2 n-2, For the required flow case, the individual pressure drop converged channel flows are added up, the leakage flow fraction added on, and the total compared to the required total flow. If they are not within user-specified convergence limits, a new pressure drop guess is made and the channel types converged to this new guess. If the total flow fails to match the required total flow, an iterative procedure for core pressure drop similar to that for channel flow is used.

Under certain conditions, the pressure drop versus flow curve for the reactor l

channel may become very flat, or may not even be single-valued, with several pos-sible channel flows giving the same pressure drop. This seems to be true particu-larly at low flow conditions. In a tightly orificed channel, typical of current designs, this is highly unlikely. However, the program may have difficulty con-verging swiftly in some situations. If the user input maximum number of iterations is exceeded, a warning message will be printed and the run terminated. The user l may increase the maximum number of iterations permitted and force the program to converge. Alternately, the user can either relax the convergence criterion, or disable the bypass leakage calculation option. The program can then be rerun l

using the converged core pressure drop from the relaxed convergence or no bypass option case as the input guess.

5-3

)

i l

5.4 SYSTElc ENERGY (HEAT) BALANCE The FIBWR code has the option of computing the core irilet enthalpy by solving an energy balance on the system composed of the reactor vessel, recirculation loop piping, and cleanup demineralizer piping (shown in Figure 5-1). Flows entering this system are the reactor feedwater flow, Wpy, and the control rod drive system flow, W cr. The only flow leavirn the system is the primary steam flow, W STM' Nonflow energy inputs to the system are the core thermal power (CTP) and recircula-tion ptsnp power, Qp; nonflow energy losses are the radiative power loss, QRM' and the net cleanup demineralizer power loss, Q cu. The energy balance can be expressed as follows:

CTP = Q p jg,+ Q cu + ORAD ~ OP (5-5) where CTP = C (W STM NSTM + NDC N OC - HIN coreI '

N FW FW ~ Ncrcr)'

H N N Oflow = C (W STM STM ~ N and C is a conversion factor from Btu /see to MWt(0.001055), and the subscript DC refers to the flow at the entrance to the downcomer (i.e., the core exit flow that is continuously recirculated rather than discharged from the vessel as steam).

The system energy balance for inlet enthalpy is thus H H +

DC DC + NFW pg + Wcr ep H H (5-6)

IN Ncore " (gP~Ocu ~ ORAD) .

For two recirculation loop reactors, Q canp be expressed as:

Qp= (PUP 01 + PUP 02) PUEF (5-7) 5-4

i i

Exit I

steam Downcomer and fl0W recirculation

system _. ___.r mW STM p STM H l ll P

dome 1 Radiative 1 I power l g Steam separators loss 4't QRAD ll and dryers l

g y h ll 1 L l l g l _ __ _ _J ______a l

Feedwater WFWH pg ,

flow

?

7 If.____.._____3 Upper plenum g

g ll ,

d b ___a g lL.

3 fr---- -----1 l ll y I 8

core 1 Cleanup O cu Y][g glg I I

system Core power loss l li g g P

! [ fg I l Recirculation Q P s N ll l pump l V' sl JL g power loss L._ .. .! l . _ ._ _ _1 p_.._ _ _

I 1 M HW  !

l l IN core l I I I I I Lower 4, g plenum 3 g L__________ ________J NcrHct Control rod coolant flow Figure 5-1. Control Volumes and Flows for the BWR Heat Balance 55

l l

where

' PUP 01, = ptspp 1 and 2 moter powers, NW

. PUP 02 PUEF = assumed efficiency of each pump O CU = C[WCU(hCU IN - hCUOUTl I The downcomer entrance flow is simply:

N DC "N core ~NSTM " N core ~N FW ~

cr

• The downcomer enthalpy is:

H DC

=H +CMfg 9 - M-O where CUC is the steam carry under fraction, and the superscript " dome" implies that the saturation enthalpies must be evaluated at the dome pressure:

P dme

=P eore - DPCD . (5-10) 1 J

where DPCD is the pressure differential between the core and the dome.

Note that the following variables are required'to evaluate HIN based on Eqs. 5-5 through 5-10.

Flows: WFW' Ncr' N cu Temperatures: Tyg, Tcr, Tcu IN, Tcu OUT Pressures: DPCD Pump Parameters: PUP 01, PUP 02, PUEF Carry Under Coefficient: CUC Radiative Power Loss: QRAD 5-6

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

All of the above, with the exception of DPCD, PUEF, QRAD, and CUC are directly measured and edited by the NSSS process computer. PUEF, QRAD, and CUC are assumed to be constants, and can be obtained from the process computer data bank. The NSSS process computer measures PD0ME, fr m which DPCD may be evaluated if P core is known. Typically, DPCD is 15 psi at full power, full-flow conditions. The variation of DPCD for part-load conditions may be evaluated with a code such as RETRAN (10).

5.5 HEATED CORE DIMENSIONS AND NODE HEIGHTS When the fuel assemblies specified have varying active fuel lengths, FIBWR auto-matically selects a uniform reference heated core length for all channels. The reference core starts at the bottom of the active fuel zone of the lowest channel and extends to the top of the active fuel zone of the tallest channel. Nodes uniformly span the reference core. Input axial power distribution data should be midnode values for the reference heated core. This method is consistent for axial power data from 3-D simulator calculations or process computer edits. How-ever, design or scoping axial power distributions are typically quoted with respect theachchannel'sheatedlength. For user convenience, the FIBWR code contains an option, 10P(5) = 1, whereby the input power distribution is interpreted as uniformly spanning the individual channel's heated length. If a particular channel's dimen-sions differ from the reference core dimensions, its input axial power data will be renormalized to preserve its power distribution for the revised node structure.

i i

5-7

Section 6 INPUT DESCRIPTION 6.1 INPUT DECK FORMAT A FIBWR problem consists of a title card, coment cards (optional), data cards, and a terminator card. A listing of the cards is printed at the beginning of-each problem. The order of the title, data, and comment cards is unimportant except that the "ast title card or the last data card with a duplicate card number will be used.

When a card format error is detected, a line is printed that contains a dollar sign ($) located under the character causing the error and a comment giving the card column of the error. An error flag is set to terminate the run after process-ing the balance of the input data.

Title Card j A title card must be entered for each problem. A title card is identified by an equal sign (=) as the first nonblank character. Thetitle(theremainderof the title card) is printed as the first line of every page. The title card is normally placed first in the problem.

l Coment Cards j An asterisk (*) or a' dollar sign ($) appearing as the first nonblank character identifies the card as a comment card. Any information may be entered on the remainder of the card. Blank cards are treated as coment cards. The only process-ing of comment cards is printing of contents. Coment cards may be placed anywhere l in the input deck.

l Data Cards

The data cards contain a varying number of fields which may he integer, floating point, or alphaaumeric. Blanks preceding and following fields are ignored.

I t 6-1 l

l

l The first field on a data card is a card number which must be an unsigned integer and must agree with a card number present in the list of card t;9es (pages 6-5 through6-21). If the format of the card number or the data items on the remainder of the card do not agree with the required format, an error flag is set. Conse-quently, data on the card are not used, and the card will be identified by the card number in the list of unused data cards. Valid cards, describing additional geometries not required for the channel types of the case being executed, will also be included in the list of unused data cards. After each card number and the accompanying data are read, the card number is compared to previously entered card numbers. If a matching card number is found, the data entered on the previous card is replaced by the data on the current card. If the card being processed contains only a card number, the card number and the data on the previous card are deleted. If a card causes replacement or deletion of data, a statement is printed indicating thz the card is a replacement card.

Coment information may follow the data fields on any dua ca.-d by preceding the comment with an asterisk or dollar sign.

A number field is started by either a digit (0 through 9), a sign (+ or -), or adecimalpoint(.). A comma or a blank (with one exception subsequently noted) terminates the number field. The number field has a number part, and, optionally, an exponent part. A number field without a decimal point or an exponent, or both, is a floating-point field. A floating-point field without a decimal point is assumed to have a decimal point immediately in front of the first digit. The exponent denotes the power of ten to be applied to the number part of the field.

The exponent part is a sign or an E or D, or an E or D and a sign followed by a number giving the power of ten. These rules for floating-point numbers are identical to those for entering data in FORTROI E or F formatted fields except that no blanks (one exception) are allowed between characters.

Floating-point data punched by FCRTRAN programs can be read. To permit reading of floating-point date. a blank following an E or D denoting an exponent is treated

! as a plus sign. Acceptable ways of entering floating-point numbers are illustrated j by the following si:' fields, all containing the quantity 12.45.

l 12.45,+12.45 1245+2 1.245+1, 1.245El 1.245E+1 l

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l A field starting with a letter is an alphanumeric field. The field is terminated by a comma, a blank, or the end of the card. All characters except commas and j blanks are allowed. I ferminator Cards The input data for FIBWR problems are separated by slash cards: the final problem is terminated by a period card instead of a slash card. The slash and period cards have a (/) and (.), respectively, as the first nonulank character. Comments may follow the slash and period on the slash and period cards.

When a slash card is used as a terminator, the list of card numbers and associated data used in a problem is passed to the next problem. Cards entered for the next problem are added to the passed list er act as replacement cards, depending on the card number. The resulting input is the same as if all previous slash cards were removed from the input to the problem set.

6.2 DETAILED DESCRIPTION OF FIBWR INPUT VARIABLES In the following description of the data ci ds, the card number is given along with a descriptive title of the data contained in the card. Next, the arder of the data (Word 1, 2, ...), the format (I, R, or A), the variable name, and the input data requirements are given where applicable. The format of the field, integer, real or floating, or alphanumeric is indicated by I, R, or A, respectively. Please note that for common bypass path cards, geometry set cards, and channel type data cards, the common path number, the geometry set number (referred to in this section as II), and channel type numbers (referred to as JJ) are included as part of their i

respective card numbers.

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Card Word Format Description 100000 Problem Dimension 1

I NCHAN (>0) Total number of channels in core.

2 I NCT (>0, $100) Number of characteristic channel t> Pes.

3 I NSTEP (>0,$25) NSTEP is the number of axial nodes in the active core.

4 I NGSET (>0, $100) Number of geometry sets.

200000 - 200002 Options 200000 1 I IOP(1) MODCAL 2 I 10P(2) IINLT 3 I IOP(3) ICHEK 4 I 10P(1) NALL 200001 1 I IOP(5) IFLUX 2 I 10P(6) NFLOP0 3 I IOP(7) NBYPC 4 I 10P(8) NWATR 5 I IOP 9) NCHF 200002 1 I IOP 10) NSCQ 2 I IOP 11) IVOID 3 I 10P(12) IFRIC 4 I 10P(13) IPHSQ 5 I 10P(14) NFORM 6 I 10P(15) NKP Table 6-1 presents definitions of the above variables.

6-4

1 Card Word Format Description 200003 1 I ITLIM 2 R FERR 3 R CALMD ITLIM - Iteration limit This limit defines the maximum number of inner and outer iterations. The inner loop calculates the channel inlet velocities for a given core pressure drop, while the outer loop adjusts the given core pressure drop in order to satisfy the given total core flow. The convergence criteria are given by FEPR.

FERR - Fractional error Convergence criteria on flow and pressure drop. It is specified in terms of a fraction of the total. For the outer iteration loop convergence is checked on(Wf-WReq'd)fgReq'd <FERR and for the inner iteration loop (Pf -

PReq'd)jpReg'd <FERR, where W is the total e. ore flow, pg is the channel K T

pressure drop and I is the iteration counter. For the water tube model, con-vergence is based on (Pf - P g)/Ph <FERR where Ph is the water tube pres-sure drop and Ph is the channel pressure drop parallel to the water tube.

CALMD - Core pressure drop The definition of this variable varies; see IOP(l). The current version of FIBWR has two mode options. CALMD is only necessary when 10P(1) is 1. In this case it represents the given core pressure drop in psi and C0FL repre-sents an estimate o' the core flow. When IOP(l) is 0 and CALMD is a number greater than zero, CALMD will be used as an initial estimate of the core pres-sure drop in psi, bypassing the internal estimating routine.

l l Card Word Format Description 200004 1 R FCHE t 2 R FCHM l

FCHE, FCIE - Coefficients for CHISHOLM Model FCHE and FCHM are the E and M factors required for the CHISH0LM Two phase friction multiplier model (IOP (13) = 15). Typically, FCHE is set to 2400 and FCHM to -1.0 for BWR-conditions.

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Card Wo.'d Format Description 300000 System Parameters at Rated Conditions 1 R CPOW 2 R C0FL 3 R PS (>l4.0,$3200.)

4 R CIN CPOW - Core power (Kdt,106 Btu /hr, 106 Btu /hr-ft 2, W/cm2)

This item specifies the rated core power. It is used in conjunction with PCTP ta arrive at the proper power for the problem at hand. The units are specified by 10P(6).

C0Ft - Core flow (106 lbm/hr, 106 lbm/hr-ft 2, kg/m2-sec)

This specifies the rated core flow and is used in conjunction with PCTF to atrive at the proper flow for the problem at hand. The units are specified by IOP(6).

PS - b stvi pressure (psia)

The system pressure at which the core water properties are to be evaluated.

Don.2 water properties are evaluated at PS-DPCD (See DPCD on card 300004).

CIN - Inlet condition (OF, Btu /lbm, quali.ty)

This item specifies the inlet temperature, enthalpy, or subcooling to the core, depending on the option specified in 10P(2). It is used to specify the inlet enthalpy. If IC;'(2) is 1, 2, or 8 this variable is ignored.

6-6

Card Word Format Description 300001 System Parameters at Current Conditions

'1 R PCTP (>0.0) 2 R PCTF (>0.0) 3 R BPF 4 R CRFL PCTP - Percent power The value for CPOW is the nominal power value. It is adjusted by the percent power figure to obtain the actual power.

PCTF - Percent flow The value of C0FL is the nominal flow value. It is adjusted by the percent flow.

BPF - Bypass fraction This is the fraction of the total recirculation flow that does not go through the heated region of the fuel assemblies. If 10P(7) is 21 this value is cal-culated internally and BPF is an initial guess.

CRFL - Control rod drive coolant flow This is the 3 mount of ficw entering the core from the control rod drive housings (100 lb/hr).

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Card Word Format Description 300002 1 R FPGR 2 R FPGC 3 R FPCB FP3R - Fraction of power deposited in fuel rods Fraction of power that is conducted'through clad and deposited in active coolant. Used in calculating the appropriate heat flux for subcooled boiling and for the critical heat flux ratio, if requested.

FFit - 'raction of power deposited in bypass region Part of the power is generated in the water of the bypass flow, control rods, and channel walls, and eventually manifests itself in an enthalpy rise of the bypass flow. This fraction is specified by FPGC.

FPCB - Bypass conduction factor Fraction of the power deposited in the bypass region (FPGC) which has been conducted through the channel walls. Channel wall heat conduction, therefore, equals FPCB* FPGC* CHANNEL POWER. Used to calculate the channel wall heat flux for subcooled boiling in the bypass region.

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6-8

t The following two cards provide information required to perform the system energy (heat) balance. The units of the feedwater, control rod and cleanup flows inputs are OF if IOP(2) = 1, and Btu /lb of IOP(2) = 2. For all other values of 10P(2),

the data items on these card are ignored..

Card Word Format Description 300003 and 300004 Heat Balance Inputs

300003 1 R FWFL Feedwater flow rate (106 lb/hr) 2 R TFWF Temperature /enthalpy of feed water (OF, Btu /lbm) 3 R TCRF Temperature /enthalpy of control rod drive flow (OF, Btu /lbm) 4 R CDFL Cleanyp and demineralizer (CD) ficw (100,.Ib/hr) 5 R TCUIN Input temperature /enthalpy to CD (OF, Btu /lbm) 6 R TCUOT Exit temperature /enthalpy from CD (OF, Btu /lbm) j i 300004 1 R CUC Carry under fraction 1 2 R PUP 01 Recirculation pump 1 power (MW) 3 R PUP 02 Recirculation pump 2 power (MW) 4 R PUEF Recirculation pump efficiency 5 R QRAD System thermal losses (MW) -

6 R DPCD Core to dome pressure drop (psi) n t

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Card Word Format Description 400000 Common Geometry Input 1 R ALPLEN.

2 R ZSTU 3 R AINLT 4 R ACHIM 5 R DECH 6 R APLEN 7 R BHDIAM 8 R BAREA ALPLEN - Channel entrance flow area (in2)

Lower plenum flow area per channel. Used to account for acceleration losses from the lower plenum to support tube. If not defined or set to zero, ALPLEN is set equal to AINLT.

ZSTU - Support tube length (in)

See AINLT for further information.

AINLT - Fuel support piece flow area (in2)

This variable can be used to account for acceleration, elevation, and friction losses in the fuel support piece. The flow for each fuel assembly enters from the inlet plenum into the support piece. AINLT is generally used in conjunc-tion with ZSTU. When not defined or set to zero AINLT is set equal to AF(I).

If ZSTU is zero then only an acceleration pressure drop will be calculated from AINLT to AF(I).

ACHIM - Chimney flow area (in2)

The chimney is defined as the section of the fuel channel above the fuel bundle upper tie plate. For this section a friction and elevation pressure drop are calculated.

DECH - Chimney equivalent hydraulic diameter (in)

This variable is used to evaluate the friction loss in the chimney section.

It is used in conjunction with ACHIM and ZCHI(I). If DECH is input as 0.0, then it defaults to DE(I).

APLEN - Channel exit flow area (in2)

This is the upper plenum flow area per channel which is to be used in calcu-lating the exit pressure change due to deceleration. When this variable is not specified or set to zero APLEN is set to AF(I).

BHDIAM - Bypass hydraulic diameter (in2)

Defines the bypass flow hydraulic diameter. Used in the evaluation of total

. bypass region fluid properties.

BAREA - Bypass flow area (in2) l Total of core bypass flow cross-sectional area.

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Card Word Format Description 1

400001 - 40000NBYPC Common Bypass Paths ,

1 I .NPATH Number of paths of this type 2-5 R Cl-C4 Coefficients for determination of path flow Above information is repeated NBYPC (IOP(7)) times. The bypass flow is cal-culated by the following formula:

C 4

G =Cy %'+C2 y

dP g +C 3 dP g I I I where: GI is the bypass flow for path I in Ib/hr and dPI is the delta pres-sure for path I in psi. The core support plate pressure differential is used to evaluate the leakage flow for all common bypass paths.

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l Card Word Format Description 401100 Geometry Data for Set Il 1 A IDGE0M 2 R AF 3 R DE 4 R RODN (>0.0) Number of fuel rods 5 R RODD (>0.0) fuel rod outer diameter 6 R TDE IDGE0M -'Hollerith geometry set identifier Geometry set input must be supplied for each unique hydraulic type (e.g.,

dimensions, leakage paths, orifice, and other loss coefficients). IDGE0M is an input 10-character hollerith identifier; the first character must be alphabetical, or be preceded by "10H."

AF(II) - Fuel assembly flow area (in2)

This array defines the active flow area of the rodded section of the whole assembly. The inlet velocity calculated by the code corresponds to this flow area. If AF(II) is set to zero, all calculations for this channel type are omitted.

DE(II) - Fuel assembly equivalent hydraulic diameter (in)

This variable defines the hydraulic dia.neter of the bundle located in channel II. This equivalent diameter is based on the wetted perimeter and is used to evaluate friction losses, and in critical heat flux correlations.

DE = 4X cross-sectional wetted perimeter flow area TDE(II) - Fuel assembly thermal diameter (in)

Thermal diameter: ,

TDE = 4X cross-sectional heated perimeter flow area The input is required for critical power ratio (CPR) calculations.

6-12

I Card Word Format Description '

40I101 Heights 1 R ZGE0 2 R ZHUB 3 R ZHET 4 R ZUHA 5 R ZCHI ZGE0(II) - Reference length (in)

This is a reference length to account for different geometries that may exist in the same core (see Figure 4-3). This number is only used'to calculate an

(

additional elevation head.

ZUHB(II) - Unheated rodded length below active fuel (in)

See Figur ,-.3 for explanation.

ZHET(II) - Active fuel rod length (in)

Heated length of the fuel rod. See Figure 4-3 for explanation.

ZUHA(II) - Unheated rodded length above active fuel (in)

See Figure 4-3 for explanation.

ZCHI(II) - Chimney height (in)

• See Figure 4-3 for explanation.

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1 Card Word Format Description 40I102 1 - NGRD R HFSG(II,J) l HFSG(II,J) - Spacer grid location II = channel number; J = relative spacer grid location within II. The spacer grid midpoint location is specified in terms of a fractional length of the active length (heated) of channel (II) with reference to bottom of the active length.

Card Word Format Description 40I103 Local Loss Coefficients (single phase) 1 R ORC 0 ORIFICE 2 R TIC 0 LTP 3 R GRC0 GRIDS 4 R EXCO UTP.

ORC 0(II) - Single-phase orifice coefficient The orifice pressure loss coefficient includes the losses due to the flow direction changes before and after the orifice and is based on the rodded flow area, AF(II).

TIC 0(II) - Lower tie plate loss coefficient TICO is based on the rodded flow area, AF(II).

GRC0(II) - Single-phase spacer grid loss coefficient a Within a given assembly, it is assumed that each spacer grid has the same single-phase loss coefficient, based on the rodded flow area, AF(II). The pressure losses occurring under two-phase conditions are accounted for by a.

two-phase multiplier.

EXC0(II) - Exit loss coefficient This coefficient takes into account the single-phase irreversible pressure losses of the upper tie plate and any obstructions beyond the upper unheated section of the fuel rod. The loss coefficinnt is based on the fuel assembly flow area, AF(II). The pressure losses occi.~rring under two-phase conditions are accounted for by a two-phase multiplier.

6-14

Card Word Format Description 401104 Friction and Form Multiplier Data 1 R AA 2 R BB 3 R ELDG 4 R ELDE AA(II) - Coefficient l Used in conjunction with BB if BLAUSIUS friction factor equation is used (see BB) or interpreted as the roughness (micro inch) if the Moody curve approximation or the COLEBROOK model is used (IOP(12) = 2 or 3).

BB(II) - Second coefficient for the BLAUSIUS relation l If the BLAUSIUS relation is chosen (IOP(12) = 1) the friction factor equation, f = AA ReBB, is used.

ELDE(II), ELDG(II) - Form model coefficients Coefficients for the upper tie plate (ELDE) and grid spacers (ELDG) for when the modified homogeneous (10P(14) = 1) and Janssen (IOP(14) = 2) two-phase form multiplier model is used.

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Card Word Format Description

40!!05 Water Tube Data 1 R NWTB 2 R ZWHIN 3 R ZWH0T 4 R WTUID Inner diameter of water tube-(in) 5 R WTU0D Outer diameter of water tube (in) 6 R PCIWT 7 R PCEWT 8 R FPGW NWTB(II) - Number of water tubes The number of water tubes in an assembly of geometry type II.

ZWHIN(II) - Height of entrance to water tube (in)

Defines the elevation of the entrance to the water tube with reference to the bottom of the heated length for geometry type II. Assumes a single entrance.

ZWH0T(II) - Height of exit from water tube (in)

Defines the elevation of the exit from the water tube with reference to the bottom of the heated length for geometry type II. Assumes a single exit.

PCIWT(II), PCEWT(II) - Coefficients for entrance and exit effects Coefficients used to evaluate the losses for entrance to (PCIWT) and exit from (PCEWT) the water tube. The water tube flow area is the reference area for these loss coefficients. m, s

FPGW(II) - Fraction of power deposited in water tube 1

Fraction of channel power deposited per water tube. Used to calculate enthalpy rise in water tube.

f 6-16

Card Word Format Description 20I106 1-4 R Cl-C4 Bypass path 6 See card 400001 for usage 40I108 1-4 R Cl-C4 Bypass path 8 of C-coefficients.

'01109

, l-4 R Cl-C4 Bypass path 9 See Figure 4-3 for path definition.

Card Word Format Description 500000 Hot Bypass Region Definition 1 R HBAREA 2 R HBFFAC 3 R HRADP 4 R HDIAMB HBAREA - Hot bypass flow area (in2)

Cross-sectional area for bypass flow in the hot bypass region. Used in cal-culation of hot bypass region fluid properties. If HBAREA is not defined or

• set to zero, the hot bypass region calculation is anitted.

HBFFAC - Hot bypass flow factor Ratio of hot hypass mass flux to average bypass mass flux (lb/hr-ft2 ). Used in calculatica of hot bypass region fluid properties.

HRADP - Hot bypass radial power factor Ratio of power deposited in the hot bypass region to the power deposited in the bypass region per channel.

HDIAMB - Hot bypass region hydraulic diameter (in2)

Defines the hydraulic diameter which will be used in the evaluation of the hot bypass region fluid properties.

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Card Word Format Description 50JJ00 Power and Channel Type Data for CT JJ -

1 R NCHN 2 R RADP 3 A IDCHAN NCHN(JJ) - Channels per channel type This is an array of channels present for channel' type JJ. The sum of NCHN(JJ),JJ = 1, NCT must equal NCHAN.

RADP(JJ) - Radial power distribution This is the axially integrated relative channel power (including bypass and water tube power depositions). This value goes with AXP(K) to generate a three-dimensional power distribution. The values should be normalized over the whole core to an average of 1 (1.0 + 0.0005 is allowed as input when ICHEK, 10P(3), is equal-to zero).

IDCHAN(JJ) - Hollerith descriptor for each channel type Chani.el types are distinguished by power peaking or R-factor differences.

IDCHAN is a 10-charact+r alphanumeric descriptor; it must begin with an alpha-betic charae.ter, or be pre:Eded ay "10H."

6-18

t Card Word Format Description 50JJ01 1 I NORF 2 R PEKL 3 R RFAC 4 R HINN NORF(JJ) - Geometry set designator array  !

NORF defines the geometry set to be used in conjunction with channel type JJ.

PEKL(JJ) - Local peaking f actor Maximum power of a fuel rod in the given assembly relative to aC other rods at the peak axial power node. Used only to evaluate the Critical ;5at Flux ;

Ratio. l RFAC(JJ) - R-factors R-factors of the given assembly to be used in conjunction with the Critical Power Ratio correlation.

4 HINN(JJ) - Inlet enthalpy of channel JJ I J HINN(JJ) need only be input for each channel if 10P(2) = 8 (IINLT = 8). The lowest inlet enthalpy specified for all channels is used as the inlet en-thalpy of the bypass region.

Card Word Format Description 50JJ02 1-25 R AXP(K,JJ) Axial shape

AXP(K,JJ) - Axial power distribution i

The relative axial power distribution can be used for design or exploratory calculations. This variable works in conjunction with RADP(JJ) to specify the local relative power. Input of AXP may take two forms (see 10P(5)), with reference to the channel (JJ) heated length or with reference to the inter-nally calculated reference heated length. Values should be normalized over I the core to a value of 1 (1.0 +- 0.0005 is allowed as input when ICHEK,

! 10P(3), is equal to zero).

As a user convenience, the AXP array need cnly be specified for the first channel type. If omitted, the AXP values of the last channel type for which i the AXP array was specified will be used. If the 3-D power distribution is j to be read in (e.g., IOP(5) = 2), the A.XP values will be replaced by values read from the external file.

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t Table 6-1 i AVAILABLE OPTIONS IN FIBWR l IOP(l) Calculational Modes (MODCAL) *0 - The core pressure drop is calculated for a given core flow.

CALMD is not necessary, 1 - The core flow is calculated for a given core pressure drop.

CALMD (in psi) is required.

10P(2) Inlet Conditions (IINLT) *0 - CIN is inlet enthalpy (HIN) in Btu /lbm.

1 - Inlet enthalpy (HIN) is calculated from given flows and temperatures.

2 - Inlet enthalpy (HIN) is calculated from given flows and enthalpies.

3 - CIN is inlet temperature, OF.

4 - CIN is inlet subcooling in Btu /lbm.

5 - CIN is inlet subcooling in OF.

6 - CIN is inlet subcooling in OC.

7 - CIN is inlet quality.

8 - Inlet enthalpy is input for each channel in Stu/lbm.

10P(3) Input Checking (ICHEK) *0 - Exit or. ur: acceptable input value.

1 - Bypass cnecking of input and execute.

2 - Check input deck; do not execute.

10P(4) Printout 1 - Summary of results only (NALL) *0 - Results (channel edits + summary) only 1 - Results + input echo 2 - Results + input echo + steam tables 3 - Results + input echo + nodal pressure drop components 4 - Results + input echo + nodal pressure drop components +

steam tables 5 All of above + increasing amounts of intermediate calculation results (warning: these options may generate avoluminousoutput).

10P(5) Power Distribution (IFLUX) *0 - Power distribution calculated from input AXP and RADP arrays.

1 - Correct AXP array based on the channel length and position relative to the lowest and tallest channel geometries in the core.

2 - Three dimensional distribution input (not operational at this time).

• Default values are indicated by an asterisk.

6-20

Table 6-1 (continued) 10P(6) Power and Flow Input Units (CPOW and C0FL)

(NFLOPO) and flow in 106 lbm/hr

• 0,1-PowerinMW{

2 - Power in 10 Btu /hr-ft2 and flow in 106 lbm/hr-ft2 3 - Power in MW 2 4-Powerin10gandflowjn106lbm/hr-ft and flow in 106 lbm/hr 5-Powerinw/cmgtu/hr-ftand flow in kg/m2.sec IOP(7) Bypass Models

, (NBYPC) *0 - No bypass calculation. The user input bypass fraction and core flow are used to determine the bypass flow.

>C - Number of common bypass paths (must be58) 10P(8) Water Tube Calculation Indicator (NWATR) *0 - No water ~ tube flow calculation 1 - Water tube flow and enthalpy rise calculated j IOP(9) Critical Power / Heat Flux Correlations (NCHF) *0 - No critical power calculations wi'.1 be performed.

1 - Reserved 2 - Janssen-Levy 3 - W-3 with Tong's bulk boiling f factor i 4 - W-3 with Tong's subcooled boiling f factor 5 - B&W2 with B&Ws' subcooled boiling f factor 10P(10) Subcooled Boiling Model (NSCQ) *0,1 - EPRI model 2 - Saha-Zuber model 3 - Levy's model 4 - Equilibrium model IOP(ll) Void Fraction Correlations (IVOID) *0,1 - EPRI model i 2 - Dix 3 - Levy void fraction

4 - Zuber-Findlay

! 5 - Hccogeneous 10P(12) Single-Phase Friction Factor Correlations (IFRIC) *0,1 - Friction f actor is calcelated from f + AA*RE**BB where the coefficients AA and BB are read in (BLAUSIUS relationship).

2 - Uses built-in friction factor approximation of Moody diagram.

3 - Colebrook equation 1

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i Table 6-l'(continued) i l

10P(13) Two-Phase Frictica Multiplier (IPHSQ) *0,1 - Baroczy 2 - Homogeneous 3 - Martinelli-Nelson without mass flux correction 4 - Martinelli-Nelson with mass flux correction 5 - Chisholm model (note: card 200004 is required) i IOP(14) Two-Phase Form Losses

!. (NFORM) *0,1 - Modified homogeneous model 2 - Modified Janssen model 3 - Romie slip model 10P(15) Kinetic and Potential Effects in Energy Equation (NKP) *0,1 - Effects are ignored.

2 - Kinetic and potential energy effects are included in inter-mediate enthalpy calculations used for the subcooled boiling model.

6 l 6.23 SAMPLE INPUT Section 7.1 LISTING OF INPUT DATA FOR CASE I l

l 1 e FI8eR MODEL FOR vtR*0NT v&NMEE SA*pLE PROPLEM 2 e 3 ***** PROGRAM DIMENSIONS. OPTIONS. CONVERGENCE 4 e 5 100000 368 4 24 6 6 200000 0 4 0 4 7 200001 0 0 3 1 0 8 200002 0 0 0 0 00 9 200003 50 0.0001 0.0 10

• 11 e 12 esente RATED CONDITIONS *****ee**e*

13 e 14 300000 1593.0 48.0 1035.0 20.0 15 300001 100.0 100.0 0.11 0.023 16 300002 0.98 0.02 0.00e00 17

• 18 e 19 eeee MEAT BALANCE DATA eeeeeeeeeeeeeeeeeee 20 300003 6.41 372.0 100.0 0.0641 534.0 430.0 21 300004 0.0020 2.8263 2.R263 0.93 0.6 15.0 22 e 23 e 24 400000 24.04 4.563 7.31 27.233 4.338 45.46 4.554 11283.2 25 e 26 ELE AK AGE (DEFFICIENTS FOR CHANNEL INDEPENDANT LEAaAGE FL0e PATMS 27 400001 89 3774.0 0.0 0.0 0.0

• CONTROL 400 DEPENDANT PATM3 28 400002 30 114.0 0.0 0.0 0.0

• INSTRU"ENT TUBE DEPNONT PATMS 29 400003 1 26496.0 0.0 0.0 0.0 e SMNOUO=PERIPMERAL PATM 30 e GEOMETRY SET =1 FOR CENTRAL 7x7 FUEL 38 400100 CEN=7 15.535 0.5765 49.0 0.563 0.7170 32 400101 7.7 1.25 144.0 17.932 2.43 33 400102 0.132 0.271 0.411 0.551 0.690 0.830 0.970 34 400103 29.65 7.58 1.21 1.35

• ORIF+LTP+3 FACER +uPPR GRIO LOSS COEFFS 35 400104 0.1892 =0.2041 1.0 1.0 36 400106 75.0 0.0 0.0 0.0 e FutL SUPPORT =LTP LEAuAGE COEFF 37 400108 0.0 702.0 0.0 3.7106

• FINGER SPRING LEauaGE ccEFF 38 400109 1783.0 0.0 0.0 0.0 e LTP MOLES 39 e GEOMETRY SET =2 FOR PERIPMERAL 7a7 Futt 40 400200 PER=7 15.535 0.5765 49.0 0.563 0.7170 41 400201 7.' t.25 144,0 17.932 2.43 42 400202 0.1J2 0.271 0.611 0.558 0.690 0 0.970 43 400203 164.76 7.58 1.21 1.35

• ORIF+LTP 830 +UPPR GRIO LOSS COEFFS SPACER 44 400204 0.1892 =0.2041 1.0 1.0 45 400206 75.0 0.0 0.0 0.0

• FUEL SUPPORT LTP LEanAGE COEFF 46 400208 0.0 702.0 0.0 0.7106 e FINGER SPRING LEANAGE COEFF 47 400209 1783.0 0.0 0.0 0.0 e LTP MOLE 8 48 e GEOMETRY SET-3 FOR CENTRAL exa Futt 49 400300 CEN=8 15.516 0.5162 63.0 0.493 0.6261 I 50 400301 7.7 1.25 144.0 t 872 2.49 51 400302 0.131 272 0.431 6 551 0.691 0.831 0.971 52 400303 29.58 7.56 1.38 1 e ORIF+LTP+ SPACER +UPPR GRIO LOSS COEFF8 53 400304 0.3892 =0.2041 1.0 ,0 54 400305 1 2.0 146.0 0.425 t,s*3 75.1 0.5 0.0003 e *ATER Tust INFO 55 400306 75.0 0.0 0.0 0.0

• FufL SUPPnRT=LTP LEANAGE COEFF 56 400338 0.0 702.0 0.0 0.7106 e FINGER SPRING LEamAGE COEFF 57 400309 1783.8 0.0 0.0 c.0 e LTP MOLES LEANAGE COEFF 58 e GEOMETRY PET =4 FOR PEPIPMERAL 838 FutL 59 400400 PER=8 15.516 0.5862 63.0 0.493 0.6261 60 400401 7.7 1.25 144.0 17.872 2.49 61 400402 0.138 272 0.411 0.351 0.691 0.831 0.971 62 400403 164.38 7.56 1.38 t.41

• ORIF+LTP+8 PACER +UPPR GRIO LOSS COEFFS 6-23 l

l

Section 7.1 63 400404 0.1892 =0.2041 1.0 1.0 64 400405 1 2.0 146.0 425 493 75.1 0.5 0.0003 e MATER TUBE INFU 65 400406 75.0 0.0 0.0 0.0 m FUEL SUPPORT =LTP LEAwaGE COEFF 66 400408 0.0 702.0 0.0 0.710e e F1hGER SPR!hG LEAMAGE CCEFF 67 400409 1783.0 0.0 0.0 0.0 e LTP MOLES Lean &GE CCEFF 68 e GE0=ETRY SET =5 FOR CENTRat ex88 FUEL 69 400500 CEN=8R 15.8248 0.5324 62.0 0.483 0.6728 70 400501 7.7 1.25 150.0 11.872 2.49 71 400501 7.7 1.25 144.0 17.872 2.49 e CHNG IN SI8R GE0m DUE TO SIMUL ATE CARD ABOVE 18 REPLACEMENT CARD.

72 400502 0.126 0.261 0.395 0.529 0.664 0.798 0.932 73 400502 131 .272 .411 551 692 .831 971 e CHNG DuE 10 Simulate CARD A80VE IS REPLACEuthT CARD.

74 400503 30.77 7.86 1.24 1.46 e ORIF+LTP+8 PACER +UPPR GRIO L008 COEFFS 75 400504 0.1892 . 2041 3.0 1.0 76 400505 2 2.0 152.0 531 0.591 63.4 1.3 0.0007 e w&TER TuBF INFO 77 400505 2 2.0 346.0 0.531 0.591 63.4 1.3 0.0007

• CMhG OUE TO 31"ULATE CARD A80vt Is REPLACEMENT Caro.

78 400506 75.0 0.0 0.0 0.0 e FUEL SUPPORT =LTP LEagaGE CCEFF 79 400508 0.0 702.0 0.0 0.7106 e PINGER SPRING LEARAGE COEFF 80 400509 3783.0 0.0 0.0 0.0 e LTP MOLES LEenAGE COEFF 81 e GE0utTRY SET *4 FOR PERIPHERAL 8X8R FUEL 82 400600 PER=8R 15.8248 0.5324 e2.0 0.483 0.6728 83 400601 7.7 1.25 150.0 11.872 2.so 84 400602 0.126 0.261 0.395 0.529e ORIF+LTP+8 0.664 0.798 0.932 85 400603 170.99 7.86 1.24 1.46 PACER +uPPR GRgD LOSS COEFFS 86 400604 0.1892 =0.2041 1.0 1.0 87 400605 2 2.0 152.0 0.531 0.598 63.4 1.3 0.0007 e MATER TuSE INFO 88 400605 2 2.0 146.0 0.53 0.591 63.4 1.3 0.0007 CNNG Out 70 37! state CARD ABOVE 15 REPLACEMENT CARD.

49 400606 75.0 0.0 0.0 0.0 e FutL SUPPORT =LTP LEAnaGE COEFF 90 400608 0.0 702.0 0.0 0.7106 e FINGER SPRING LEAnaGECOEFF 91 400609 1783.0 0.0 0.0 0.0 e LTP MOLES LEAMAGE COEFF 92 e puutR DISTRIBUTION DATA 93 500100 68 0.90588 CEh=7x7 94 500101 1 1.14 1.050 95 500102 5775 5775 1.1 1.1 1.22 1.22 1.15 1.15 96 9 1.18 1.10 1.07 1.07 l.03 1.03 1.06 1.06 97

• 1.1 1.1 1.1 1.1 0.92 0.92 0.5775 0.5775 94 500200 80 3.1 CEN=8E8 99 50020t 3 1.14 1.050 100 500300 60 0.6 PER=8x8 tot 500301 4 3.340 1.050 102 500400 160 1.14 CEh=4X8A 103 500401 5 1.14 1.050 104 .

6-24

i i

Section 7 FIBWR OUTPUT DESCRIPTION 7.1 GENERAL FORMAT FIBWR output optionally consists of three distinct sections, input and case initial-ization, intermediate and characteristic channel calculations, and a results sumary. By manipulating user option 10P(4), NALL, various sections of output may be generated including extensive intermediate calculation edits. To facilitate the explanation and understanding of the FIBWR output format, a sample output (which correspeads to the. sample input of Section 6.3) is given at the end of this chapter. Note that the print option 10P(4) is set equal to 4 for this case.

The first item in each FIBWR case output is a card image echo of the input deck as submitted. This is followed by monitor messages from the input procassing rou-tines, when necessary, to identify replacement (overlayed) cards and data cards not used for that particular case. Referring to the sample input of Section 6, if the user establishes a " base" input deck with data available for several cases (e.g., geometry sets) and executes a case whic.h uses some, but not all the input data, the unused cards will be referenced. The user should review that section to verify that the unused cards in the case are actually unnecessary. The re-quired amount of storage for input and a processing flag value are returned from the input processing routines and printed. FIBWR is currently .limensioned to

! allow 4000 words of storage for user input. A value other than zero for the re-turned processing flag indicates a fatal error in input processing. The descrip-tion of the error can be found with the input monitor messages.

Page headings are given for the remaining output. The heading contains the case i

sequence number, case title (user input), run date, and page number. Through-out the formatted output, the internal variable name has been included in the data heading to aid the user.

l The balance of output, in order of appearance, is described below. Optional i sections of output, based on the calculational model chosen, are enclosed in 7-1 1

l

parentheses. Sections affected by the value of 10P(4) contain the value of NALL for which they appear.

7.2 INPUT AND CASE INITIALIZATION (NALL> 0) j

1. Core wide and general case input values. Card series 100000 and 300000, card 400000.

2. User option (IOP) array. Card series 200000. Option values, as input or default, are identified. A text section follows which defines several optional input variables and indicates the models and correlations chosen.

(3.) Optional heat balance calculation data. Cards 300003 and 300004.

4. Characteristic channel data. Composite of channel-type data (50JJ00 series) and geometry-type data (40I100 series).

(5.) Common bypass path coefficients. Cards 400001-40000NBYPC.

(6.) Characteristic channel dependent bypass coefficients. Cards 40I106, 401I08, and 401109.

7. Characteristic channel spacer grid location array. Card 40IIO2.

(8.) Axial power distribution arrays. Card 50JJ02.

9. Radial power distribution array.

10. Relative power distribution (S) array. Calculated from the radial and axial power distribution arrays and normalized to the reference channel heated length (see 10P(5)). As an option the S array may be input directly (see IOP(5)).

11. Average radial and axial distribut_ ion factors. Output as a check on user normalization of input power distribution arrays.

12. NALL = 2 or NALL > 3. Water properties for subcooled and saturated conditions. Summarizes the 25-point interpolation table used internally. Calculated for the temperature interval from core input temperature to saturation temperature at the given core pressure.

7.3 INTERMEDIATE CALCULATIONS (13.) Heat balance calculation results. Values are civen in internal units. Printed if NALL > 0, and IINLT = 1 or 2.

14. Initial guess on core pressure drop. Value input as variable CALMD or as calculated by subroutine GUESS.

(15.) Iteration monitor. IOP(1) = 0. Selected results of outer iteration i calculations. Data given are (L to R) Outer Iteration Number, i

7-2

Converned Core Pressure Drop for that iteration, Calculated Core Flow, Relative Convergence Value, Bypass Region and Water Tube Flow, and the Estimated Core Pressure Drop, used as the required core pressure drop for the next outer iteration.

The remaining intermediate results describe converged calculations for each charac-teristic channel.

16. NALL > 2. Nodal pressure drop components. Pressure drop components and two-phase multipliers are given for each axial node.

(17.) NALL > 2. Water hole calculations. Values calculated for water tube from inlet to exit (user input dimensions).

18. NALL > 2. Pressure drop components for unheated channel regions (refer to Figure 4-3). Values calculated for combinations of channel, water tube, and bypass mass flows, where appropriate.

Friction factors and two-phase multipliers are also included.

19. Results for each characteristic channel. Nodal fluid properties and conditions are sumarized. Power depositions, active and bypass flows and pressure drops are given (bypass flow includes an average amount of comoi. bypass flow). Top of node values are given for fluid properties, quality and voids, and channel wall pressure drop differentials. The path 6-9 leakage flow rates are printed.

7.4 CASE SUNiARY (20.) Bypass flow calculations. Comon or core support plate path data are given first along with the core support plate pressure differen-tial. This is followed by a nodal sumary of data for the total bypass region (top of node values are printed).

(21.) Hot bypass region results. If user has input data necessary for hot bypass calculations (card 500000), input data are echoed along with nodal sumary of hot bypass fluid properties.

22. Data sumary. Several input data values of interest are repeated along with final flow and fluid property values.

23. Sumary of characteristic channel calculations. Channel identifi-1 cation and brief description (input) are followed by calculated values of interest for each channel.

24. An end of case and end of job banner follow the sumary output.

7.5 SAMPLE OUTPUT An execution of the sample input of Section 6.3 is presented in the following sec-tion. Underlined headings on the right hand margin refer to the output description contained in Sections 7.1 through 7.4.

I 7-3

i i-i

< Section 7.1

. ST0 east WO408 REGUIRED FOR IN#UT e S27 thP #ETueN IN01 CAT 04 e 0 eeeeeee* TMt POLLonING C ARDS ht#E NOT USED

! 400609 i 400608 400604 400605

40. 04 400603 1

. 400602 1 400608 1 400600 l 4

400309 1

400208 I 400204 1

400204 40C203 a00302 400201 s00200 1

i 9

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i i

i I

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A 4

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S AMPL E PROHL E. Bl/on/2e PAGt a FISwR CASE is FIMmR MODEL FOR VERauMT YAhuEE

.thPUT DATA. Section 7.2

............ Part 1, 2 NCH7N . NUMSER OF CMAWhELS IN CORE PEGION 8 3b8 NCY . NUMBER OF CH*MNEL TVPES e e N8TEP = NUM8ER OF (AlsL huDES e 24 CP0m . NATED CORE PonER a 1593.0000 PCTP . PERCENT WATED P0mFh a 100.0000 CDFL = RATED CORE FL0m e e8,0000 PCTF . PERCENT wATED CnRE FLna a 100.0000 PS . CORE PRESOURE (P814) e 1035.0000 FPGR . FRACTIuN PUngk GEN IN FUEL N0n3 a 9800 '

BPP . SYPASS FLOW PRACT10h a 1100 FPGC . FRACTION PO=ER OtP. IN syPASS e 0200

. CORE SYPASS PLOm AREA (80 a 18283.2000 FPCn . FRACT!uN Ph.EW GEN. IN mATEw WUDS e .ocui

$ AREA IN.)

CRFL = CONTROL ROD PLOW (MLR/MR) e 0230 FPCM = FRAC. hvPASS PD=EW DEP. eV CONDUCTID'.e 0.0000 M84REA . MOT SYPASS FLOM AREA (80 IN.) e 0.0000 M8FFAC . MOT 6yPASS PENALTv FACTON e 0.0090 SMDIAM . SYPA88 MYDRAULIC DIAMETER (IN.) e e.5540 MRADP = HOT evPASS PEAMING FACT 04 m 0.0000 APLEN = CHANNEL Ex!? FLos AREA (30.IN.) e 45.4600 DECM = CMIMNEY MVDRAULIC DIAMETER (th.) a 4.3380 ALPLEN . CHANNEL INLET FLoh AREA (SG.IN.) a 2a.0400 ISTU . SUPPORT TumE LENGTH (IN.) e e.5630 ACHIM . CHIMNEY PL0m AREA (80 IN.) e 2T.2330 DSTU . SUPPowf 10eE DIAaETER (IN.) e 3.0598 ITLIM = ITERATION LIMIT e 50 CALMD . CONE PwESSURL DWUP GUESS (PSIA) m 0.0000 PERA . CONVERSENCE CRITERIA a 0008 CIN . SEE NOTE SELou FOR .CIN. DEFINIT!nN e 20.0000

}J OPTIONS ARRAY us INLFI UNITS AND MEAT BALANCE e

?l JOCAL . CALCULATIONAL MODE e 0 02 IlhLT . m 04 1CMEN = INTERNAL INPUT CHECWING e 0 Os NALL . PRINT OUT INUICATOR a 4 GS IFLUM . PonER DISTRIBUTION e 0 On hrLOP0 . P0aEW AND FLU = ONITS e 0 GT NSYPC = COMMON 6 f 7A38 P ATHS C ALCUL ATED e 3 on hmATR . MATER TUuE CALCULATION IND. s t 49 NCHF . CPL /CMF CORRELATION USED e 0 10 NSCO = SU8COULED uuaLIYY MODEL a 1 11 IV010 . WQ.0 FRACTION CORRELATION e 1 12 IFRIC = SINGLE PMASE Fk!CTION CUNREL. e 1 83 IPM88 . TNO PM48E FRICT. MULTI. MODEL e i 14 NFUWM = Tm0 PMASE FUW" LUSSFS e 1 A5 NRP . NE AND PE EFFECTS IN ENERGY EQuaTNa 1 16 NOT USED AT PWESENT e 0 PLEASE NOTE INTERPRET .CIN. A8 INLET SUSC00 LING IN S TU/L 8 M .

INTERPRET .CDPL. AS MASS PLOW IN MILLIONS OF LSM/MR INTERPRET .CPON. As TOTAL POWER IN MEGANATTS THERMAL VOID FRACTION CORRELATIONS EPRI INITIATION OF SUSC00 LED SOILING METHOD EPRI SUSCDOLED SUALITV MODEL: MVPER80LIC TahGENT PROFILE FIT SINGLE eMASE FRICTION CORRELATION: BLAUSIUS RELATION Tm0 PMAGE PRICTION FACTOR MULTIPLIER MODELs 84ROCZW Tm0 PNADE FORN MUL"! PLIER MODELs MONOGENEOUS

FIGNR CASE 13 FI8mR MODEL FOR VERMONT YANKEE Sa*PLF PMugLEM Bt/01/26 FaGE 5 INPUT DATA CONTINUED SeCtion 7.2

.................... Part 4 CHAN GEO NUH8ER OF FLOu hvDRAULIC WUD NUMsER OF waDial iOCat k THERNat TYPE TTPE CHANNELS AREA UIAMETER DIAMETEN RODS PuatR PEaming FaCTON UlamtfER too.IN.) <!N.) FaCTun L IDGEON NCHN AF DE RODD RUDN Na0P PEAL RFaC TDE I CEN.T es 15.5350 5765 5 30 49 9959 1.1800 1.05no 7170 2 CEN.s s0 15.5t=0 562 .=930 .3 t tuco 1.1800 1.050o .21 1 PER=8 to 15.5100 5462 .a930 63 0000 1.1400 t.0500 62e1 4 CEN.4R 160 15.8248 5324 .e830 62 1.1400 1.3a00 1.0500 6728 s

CMAN REFERENCE LUDER ACTIVE UDPEk CHIMNEY URIFICE TIEPLaTE GWID E*IT =ATFR Tuot TYPE LENGfM UNHEATED FUEL UNME A f t 0 NEIGHT LOSS LUSS LUSS LOSS PO*EN (IN.) ROD LENGTM LENGTM ROD LENGTM (IN.) COEF COEF CUEF CLEF FRACTION (IN.) (IN.) <!N.)

ZGEO ZUMs IkET ZUMA 2CMI ORCO TICO GNCO EECO FPGw

J L m

I 7.7000 1.2500 144.0000 17.9320 2.4300 29.6500 7.5800 1.2100 1.35no 0.0000 2 7.7000 1.2500 1sa.0000 17.8720 2.e900 29.5800 7.5600 1.3a00 1.4100 0003 3 7.7000 1.2500 las.00c0 17.8720 2.e900 164.3800 7.5600 1.3800 1.et00 0003 4 7.7000 1.2500 744.0000 17.8720 2.8900 30.7700 7.8600 1.2400 1.4600 0007 CMAN FRICTION FORM NU*RER =aTEW TusE naTEN TurE WATER TUBE TYPE MODEL MODEL OF MATER Dla*ETERS ELEVATIONS ORIFICE LOSS COEFFICIENTS COEFFICIENtf TU8E8 (IN.) (IN.) COEFFICIENTS INNEN OUIEW ENTRANCE Ex!T ENTRANCE Ex!T L AA SS ELDG ELDE N=T8 nTUID afuco ZmMIN ZmMOT PClai PCEnf 1 1892 . 20al 1.0000 1.0000 0 0.0000 0.0000 0.0000 0.0000 0.0000 0.0U00 2 1892 . 20st 1.0000 1.0000 t 4250 8930 2.on00 180,0000 75.1000 500u 3 1892 . 2041 1.0000 1.0000 t 4250 8939 2.00c0 tes.0000 75.1000 5v00 4 .1892 . 204l 1.0000 1.0000 2 5310 591u 2.000n 146.0000 63.8000 t.3u00

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> e m m N N N n eO eO eo eo e m > b b b 4 he he he h4 3 e w N N N N pe yo pc po O e e e o e e S e o e e o e e e a e e a m m m o h J e K e O O O e W e N m o e > eo en se so C e 3 M M M M 4 MM MM MM MM Q e O S w m a m a WO WO pe WO Y e wG e e e e a se e e e e e o e 3 0 > 4 m m m m W e 2 0 4 m o =8 K 2 e e >9 m Q

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4 e E S O E E E U e 2 8 m > w h e e e e et a w E 3 M M N m

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PlanR C 4 8E, is FI8me MODEL FOR VENMUh? YANDEL SAMPLE pkueLEm et/ot/26 PahE 8 es................................................................................................................................

INPuf Rac:AL ponER DIStutsuttua Section 7.2 CHANNEL

!=10 9059 Part 9,10.11 1.1000 6000 1.3400 RELAT!WE POWER = 8 aNRaY = CALCULATED FROM AMP AND NADP DISIRIMuf!ONS CHANNEL

, 1 CEN=7X7 523 523 996 996 1.105 1.105 1.042 t.oe2 996 996 969 969 933 933 960 960 996 996 996 996 .n33 833 523 523 2 CEN=8X8 435 635 1.210 1.210 1.342 1.342 1.265 1.2e5 1.210 1.210 1.177 1.177 1.133 1.133 1.166 1.166 1.210 1.210 1.210 1.230 1.012 1.012 635 635 4 3 PER=838 347 347 660 660 732 732 690 690 660 660 6a2 642 618

,618 634 636 660 640 660 660 552 552 347 387 4 CEN=8X8A 65R 658 1.254 1.254 1.391 1.391 1.311 1.311 1.25e 1.254 1.220 1.22n 1.174 1.174 1.208 1.208 1.25e t.254 1.25e 1.254 1.089 1.049 658 658 AvtRASE RADIAL PAC 70R e 1.00000

]J A CHECK ON USER NORMALIZATION (UNITVI 0F INPUT Pn=ER OlafRIBUTION ARRaVS e

AVERAGE ARIAL FACTOR e 8.00042

{

l SAMPLE P40HLEa et/os/26 MAGE 9 I FIOMR CA8F st Flume Muutt Foo VERuo*f +AhnEE

.........e...............................s.....................................................................................e..

=ATER PROPERTIES FOR tor 6.00000 PSIA Section 7.2 Part 12 PROPERTY TA8LES FOR SuSC00 LED LIQUID TEMPERATURE DEN 817Y ENTHALPV PRAhDTL 8PECIFIC VISCnSITY mINEMaTIC EchouCTIVItv OELTA ENTHALPY/

(CES=P) (LBM/Cu.FT.) (870/LBM) huMsER MEAT (L8M/FT. SEC.) vfSCUStiv (BTU /8EC. FT. DELTA VULUME (BTU / LUM) (So.FT./SEC.) DEG=F)

PRA Emu ENu Come op rov TEM RMO ENT CP 533.0321 47.3375 527.9024 8850 1.2%69 650eE=oa .tleoE=05 9238E=04 .eSitE+ns 47.0963 528.7246 8859 1.2580 6496E=ce 1379F=o5 922*E=ce 4458E+05 533.6883 1379E=n5 9219E=os 4407F+o5 i

l 534.3445 e7.0548 529.5555 8868 1.2603 . nee 7E=ce 47.0328 530.3805 8878 1.2620 6479F=ce 1378E=o5 9210E*0e 4357E+05 535.8887 337eE=o5 9201E=os 430BE+05 535.6569 46.9704 533.2177 8887 1.2637 6e7tE=os e6.9277 532.0e89 8847 1.2654 6e62E=ce ,1377E=os 9192E=os 4260E+05 536.3132 ,1377E=05 9182E=ce .eiteE+05 536.9694 e6.8845 532.8803 8906 l.2671 6e5eE=04 537.6256 46.8409 533.7118 8916 8.2688 6ecor=we 137ef=om 9173E=08 .e16tE+05 538.2818 46.7970 534.5434 8925 1.2705 643AE=ce 137eE=ob .Ste4E=ce .e12sE+05 46.7526 535.3752 8934 1.2722 .t429E=os 1375F=05 9155E=ce 4081Fe05 538.5389 1375E=c5 9146E=os .eu39E+05 539.5942 46.70iB 536.2071 5944 1.2739 6edtE=ue 49.6627 537.0392 8953 1.2756 .est3E=o4 1374E=05 913eE=ce 399aE+05 540.2584 9127E*oe 3958E+05 540.9066 46.6172 537.8715 8902 1.2773 6e65E=ne .1374F=05

'.d d 541.5638 46.5713 538,7040 8977 1.2789 .e396E=ne 3373E=o5 9tt8Eace 3919E+05 C3 592.2890 46.5230 539.5368 8981 1.2806 .elenE=ce .3373E=05 9to9E=04 368tt+05 Sa2,8792 580.3699 8990 8.2823 .e380L=ce 1373E=o5 9100E=ce 3ee5E+05 46.4784 909tE=ne 3809E+05 541.2032 9000 1.2840 ,6372E=os 1372Een5 543.534 46,43ta 6363E=os 1372E=o5 9pmtE=os 3775F+05 544.1876 46.3840 Sa2.0370 9009 1.2857 54a 8438 542.8712 9018 1.2874 6355E=ue 137tE=o5 9072E=08 37e3E+05 46.3363 1371E=o5 9003E=ne 37 2F+05 545.5880 at.2883 543.7059 9027 t.2898 6347E=ce 546.1562 4e.2399 Sea.5el2 9037 1.29ne 633nF=pe 337tE=o5 .co5eE=ve 3e82f+05 5=5.3773 9046 1.2925 6330E=ce 1370F=05 90e5E=04 3655E+05 546.8124 46.1982 9035E=os 363tE+o5 46.ta23 546.2ta3 9055 1.29e2 6322E=04 137eE=n5 547.4686 1370E=05 9026E=os 3et0E+05 548.1248 a6.0930 547.0526 9064 1.295% 631st-o#

548.7818 46.0460 547.9027 9075 1.2978 6305E=04 3369E=05 90tfE=04 3930E+05 PROPERff TABLE FOR SafuLATED CONDITIONS T8AT . SATURATED TEMPERATURE (CEG=F) e 548.78 0 HF = flu!D ENTHALPY (81u/LRM) e 547.9027 AMOP = PLUID DENSITY 'L8M/CU.FT.) e 46.0460 NFG = EVAPORATION ENTMALPV (BTU /L8M) a es3.7135 4404 e STEAM DENSITY (LSM/CU.FT.) e 2.3304 HG = STEAM EnTMaLPy (8TU/LBM) e t191.6159 EMUS . SATURATION v!8COSITY (LOM/PT.8EC) e 6305E=ce RFORG = RMOF / MMOG e 19.7590 PR847 . PRANOTL NUMSER a 9075 EMuvL . v!SC. steam / WISC. mATEN e 2037E+f3 C0=847 e CONDUCTIVITY (STU/SEC FT. DEG=F) s 9037E=ce SIG = SURFACE TENSTON (LBS/FT.) e .it92E=02 CPSAT . SPECIPIC MEAT (STU/LSM DEG=F) e 1.2978

FISmR CASE 13 FIH=R MODEL FOR WERauNT Yah=EE SApptE Pwodita MI/et/d6 PAGE 10 INITI AL Gutes o= CORE PpESavat oRup . 19. els Ps A Section 7.3 Part 14,15 l

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! TROT Coop QFW EPS BPFw l 1 19.4015 at,3e63 337sg+vo a.SIfe 22.5019 l %a 2 22.5019 46.2169 3715E=ot e.9748 23.6ae3 l j, 3 23.6463 47.8609 2897E=02 5.1195 23.7452

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CHANNEL t TYPE 8 CEh.7I? GEumLTN78 CEh.7 huabEus eQ FLO= a>Ea .tu?J 54.FT. Section 7.3 ,

thLET WELOCITY 7.23201 FT./SEC. Part 19 MASS FLUX t.2272 *Ln /nR.30.F T. MVDRAOLIC DrapETEk 0489 PT.

ACT!vt PLos .t32e mLB/MR 8vPASS9mf FLUa (Xt.0Es) 1.2936 Lb/MR ACTIVE P0aER 3.8e29 maf BYPa88.=T Po=ER 078e mai AvtRa8E DEh8ITT 29.58te L8M/CU.FT. ACT!vt EEIT FLua QUALITv 1229 AVERAGE VOID PRACTION 3e05 ACT!vE Esfi voto FNaCTIUh 6625 5.7000 th. CHlahEY PLU= ovality 1229 SOILING MEIGHT OELTA EhTMALPY 99.6307 STU/ Lum CMImhEt v010 FkaCTIUh .eetu PRESSURE OROP COMPONENTS l

FRICTION 2.988e PSI LUCaL 1F.0956 PMI ACCELENATION 66ee psg ELEVATION 3.0350 PSI total VOID FLos maTEw TUBE Cnam, mall

• ELATIVE PEam TOP OF =0ut l NODE EGUIL. PLO4 ELEVATION l

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i (87U/L8) (L8/CU.FT) (L8/CU.FT) (STU/Lu) (PSI) (anTU/mR.80.FT) (th.) l l

INL e.0311 4.0000 527.9024 0.0000 47.3375 47.0837 528,976e 7.7497 ... ... 0.00 l l

1 . 8274 0.0000 530.2857 0.0000 e7.0179 s?.0720 529.28te 7.7070 5$31 0996 6.00 2 . 0237 0.0000 532.6690 0.0000 en.8955 e7.0602 529.se70 7.6645 575" 0996 12.00 l 0009 537.2086 0386 e5.2838 e7.037) 529.8950 7.6955 9965 .1897 18.00

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d. 8 e.8896 0028 541.7482 0634 43.7053 47.0150 530.3e30 7.2149 006e 5se.783: 8098 et.53e8 en.9897 530.839e 7.1503 1.1052 2tes 30.00 OJ 5 e.0817 7.c788 1.1052 21es 3e 00 6 0861 0112 551.8179 3652 38.9836 et.9es) 531.1367 0135 0867 ,2210 36.s888 e6.9e02 538.8c51 6,5895 1.0418 198* e2.00 7 556.5639 1.cate . tens e8.00 8 0208 0229 Set.3099 2769 33.9967 e6.9160 532.273e 6.5094 9 0279 0292 565,8e95 3269 31.7889 e6.8927 532.72te 6.4288 9905 .se97 54.00 0358 570.3891 3712 29.8374 e6.8e93 533.tn9e 5.802e 9965 1897 60.00 10 .0349 9693 me.uo 11 0818 0488 575.3481 4072 28.2470 e6.Se6S 533.6052 5.7237 .tese

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14 .0619 0619 588.265e . Sole 24.1270 46.7790 53a.s799 e.7ese .s33 .t?77 Se.00 15 0n87 0687 592.6399 5266 23.0239 se.75en 535.3tte e.e950 96o2 .ta28 90.00 l

16 0755 0755 597.0tes .Sete 22.0299 et.7328 535.Fe33 a.6c38 . woo 2 .t 2n 96.00 17 0825 0825 601.55st 5707 21.0988 86.7087 536.1983 3.0881 9965 .t897 102.00 0896 606.0937 5900 20.2522 e6.68e4 53e.6391 3.5902 9965 1897 108.90 18 .0896 9965 .te97 19 .0966 0966 680.4333 6077 19.4796 es.6601 537.o873 3.ee*2 tie.uo 20 1037 3037 e15.t729 6239 18.7709 46. e ls e 537.5353 2.etes 99e5 1897 120.00 28 .1096 8096 618.9697 63e7 18.2142 e6.6351 537.9100 2.313e .alle .t5s? 120.00 22 8155 1155 622.7665 .ee8e 17.6994 e6.59ee 538.2847 2.2c50 .e334 .t$af 132.00 23 .3192 1892 625.1448 .e558 17.3789 e6.58te 539.5399 2.3c70 5231 .o99e 138.00 28 .1229 .i229 .27.533: 6625 tr.0835 e6.5 8e 53. 755: 9338 523: .n99e tee 00 paTM e path 9 paTM e l maTLw feet LTP.PutL SUPPORT L T P MOLE S CManhEL.LTP PRESSURE DROP (PSI) A.et 8.81 7.7e 0.00 LEAEASE PLOW (L8/MR) 222.59 5291.66 3080.27 0.on

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7-14 l

CMANNEL 2 TTDER CEN.838 GEONETRVI CEN.8 NUu8Eks 80 Section 7.3 INLET vtLOCITY e.613tt FT./SEC. Flow auta . t o7e Su.F T* Part 19 MASS FLUE 3.3222 "L8/MR.SQ.FT. .os3a P T.

ACTIVE FLos 3209 mL8/MR MVDeauLIC trPa83..T PLLDia".ETEa tut.0Em) 1.e508 Ln/ww ACTIVE PonER 4,6650 mwT 8vPeta+mf pomes 0967 P.T AVERAGE DENSITY 26.1870 Lnn/CU.FT. ACTIVE Es!T PLO. uuaLITV 1735 AVERAGE votD FRACTION 457e ACTIVE ExIf woIO FRACTION 7347 SOILING MEIGMT 7.0523 IN. CMlphfY FLOm Qual!vY .t?25 DELTA ENTMALPY 332.1504 87U/L8M CMI= NET v010 FRACTIch 7328 PRESOURE OROP COMPONENTS PRICTION 3.60e5 PSI LOCAL .16.65 5 PSI ELEVATION 2.7859 P81 ACCELERATION 77te PSI ,

l NODE EQUIL. Flow TOTAL va!D FLun .aTER tust CMah, hall kEtaTIVE 624m TOP OF =09E N OUAL. GUAL, ENTMAL. FRACT. DENSITV DEhSITv ENTwaLPv DELT4 P PO*ER Meat FLuz ELEVATION (STU/L8) (L8/CU.FT) (L8/CU.FT) (87u/L8) (PSI) (m870/MN.Su.FT) (!=.)

36 . 8. 00 Sn.902e 0,0000 47.i375 47.08e6 52..,583 9.,967 ... ...

0.00 t . 03:1 0261 0.0000 531.0701 0.0000 46.9780 e7.0767 529.3168 1.2550 .e353 107e 6.00 2 . 0212 0000 534.2379 0033 86.6680 e7.0688 529.2753 9.?t26 6353 .tu7e 12.00 y 3 . 0819 0028 540.2717 0586 se.2760 47.0517 529.577: 9.t50c 1.2100 2est 18.00

• • 4 . 0025 0060 5e6.3056 1039 48.7868 47.0384 529.8790 8.7610 8.2100 2ase 24.00

• 47.02 5 5 4 8879 0825 552.9977 3784 38.3895 530.2138 8.6862 1.3e20 2270 30.00 6 8883 0287 559.6897 2574 34.8610 47.004e 530.5886 8.602e 1.3e20 2270 36.00 7 8281 0298 565.9978 3281 31.7360 e6.9885 530.8es2 8.0525 1.2650 2139 e2.00 4 0379 0386 572.3059 3877 29.1113 40.9724 538.1798 7.9643 3.2650 2139 48.30 9 0873 0473 578.7880 4355 27.0076 44.9569 531.eSt? 7.8772 1.2100 2ce6 Se.00 to 0567 0567 584.8218 .e803 25.0513 46.9883 531.7835 7. tete 1.2100 2ose 60.00 11 .0698 0654 590.691 5865 23.eee9 e6.92e2 532.0772 7.0487 1.3770 .1991 6e.00 12 0749 0789 596.5604 .Se79 22.0923 e6.9tto 532.3708 e.9%ee 1.t??0 1991 72.00 13 0837 0837 602.2102 57e5 20.9334 e6.8963 537.0535 6.8588 1.1330 1986 78.00 le 0924 0924 607.8e03 59so 39.9050 me.8eq6 537.93et 5.9att 1.1330 .19to 8e.00 35 3015 3015 633.07e5 6890 18.9595 e6.8063 533.2270 5.4373 t.86en 1972 90.00 16 3105 3805 619.e890 6390 18.3099 46. asst 533.5179 5.72e5 1.4400 1972 90.00 17 3199 1899 625.5228 6573 17.3137 e6.8252 533.6398 4.et3e 1.2100 2046 102.00 18 .1293 3293 633.5566 6738 16.5913 e6.8192 53a.1216 a.e905 1.219e .Poes te8.00 19 .1386 3386 637.5905 6889 15.9372 e6.8033 53e.4235 e.3008 1.219a 29=6 134.00 20 8480 1480 643.62e3 7027 15.3277 e6.7872 538.725e 3.0392 1.cl00 2 nee 120.00 2 .3558 .l558 6ee.6708 783e te.e577 e6.773e 53a.9779 2.9 .d 5 3 129 1712 120.00 l

22 .5637 3637 653.7173 7235 14.438e do.7643 535.23u3 2.7598 1.ot2n 17t2 132.00 l 23 .5686 .t686 656.8n50 7289 te.smas e6.75te 535.smes 2.e10e .o353 3u74 138.00 28 1735 1735 660.0528 73e7 13.9308 e6.7e13 535.5e73 1.1782 .e353 .tu7e 14e.00 l PATM e paTM 9 Pafn 8 I LTP. FUEL SupPhki LTP MULES CMahhEL.LTD asTEp tuME PRESSURE DRUP (PSI) 10.19 lb.19 9.3t 11.99 LE&eA8E PL0m (L8/MR) 239.et 5098.e7 3425.39 7e0.39

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= CW 2 h b e O 38 0mM e m J w mammm M 3 3 Tw p ostS e S 3B uOCNO 2 m3 m o e e a w 0 DONmNeMNNMe9WNe=MMNomePN em 2 e mG OO=co@e6CMd=Weome>WNamem we R &

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& m& e e o e e e e e o e o e e o e o e e o e e e e e S & m e e 4 3 mammmmmm4NNNMMMMMeWee@@@ M2 G J e e N & EC2 W & M suo a w

=

E

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= 4 m eJ3u N e e J e = 3 e = 3 & e w e 2 u a w e O

& O J K O w == mNmkoecepcMhmeem>>ep> Nam 4  % e 3 S PE hherNeGeeMeerem@eN40WemM U Emm > 4 e um ammmNNMMMeerrWeedhkemepp See 2 m

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> 2 to e e o e e e e e e e e e e o e e o e e e e e e e J 2 3 &

m w h O NNP Q = w 5  %

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l CMANNEL 3 TYPts PER.818 GEOMETRfs PER.8 hu"eENs 60 INLET VELOCITY 4.10513 FT /8tc. flu = aNEa .t076 36.FT. Se: tion 7.3 MASS FLUX 6966 MLA/MR.80.FT. MVUpauLIC DIA*ZTEh 0830 Ft. -'pp g ]g ACTIVE FLOm 0758 ML8/MR BvPass+=7 FLU. (st.0 Eel 9112 LH/HR ACTIVE P0uER 2.5446 ant 8VPaSS+=T P0aEW 0527 m.T AVERAGE DENSITY 27.837e L8M/CU.FT. ACT!vE Em!T Flaa CUALITY .te87 AVERAGE VOID FRACTION .e200 ACT!vE F alf VOIO FRaCT10m 7036 SOILING MEIGHT 5.7000 IN. CMIM.EY FLOn Qualify . teep DELTA ENTMALPY 114.1778 STu/LBM CMI= HEY WOID FhaCTIu% .ees2 PRESSURE DROP couPONENTS FRICTION 1.5569 PSI LOCat 19.06t3 PSI ELEVAT!0N 2.8713 PSI aCCELERailuN 2536 Ps!

FLOW TOTAL Vulo FLO. MATER TuME CMAN. .aLL RELATIVE PEax TOP OF =090 NODE EQUIL. Puate Mtaf FLUa ELEVATION K OUAL. GUAL. ENTHAL. FRACT. DE881TV DEhSITV tmTwaLPV uELTa P (BTU /L8) (LB/CU.FT) (L8/CU.FT) (RTu/Le1 (PSI) (matu/*9.So.pf) (!>.1 INL . 0311 0.0000 527.902e 0.0000 47.1375 e7 t oeto 528.e392 2.3e20 ... ... 0.00 1 . 0267 0.0000 530.6859 0.0000 e6.9976 47.0825 529.0020 2.3245 3405 .n586 6.00 2 . 0234 0.0000 533.8698 0.0000 e6.8536 47.n739 529.1736 2.307e 3ee5 0546 12.00 3 0015 538.77t3 0395 ee.8699 e?.0575 529.50tt 2.2e55 0600 .itte 18.00 7

m 4

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) .nedo 66.00 11 0540 0540 583.1326 4645 25.7398 46.9192 532.2116 1.7093 .tose l 12 0620 0620 584.2899 .e985 24.2537 et.9027 532.5299 1.7127 4420 . tome 72.u0 i

1 13 0698 0698 593.2544 5273 22.9958 e6.8868 isc.*?es 1.71A3 6180 3085 78.00 te 0775 0775 598.2189 5529 21.877e 86.8707 533.1828 1.asti 6189 1985 88.00 15 0854 085e 603.3280 576e 20.8492 e6.85e2 533.4582 1.ee73 636n .ts7e S t. . c o 16 0933 0933 608.4371 5975 19.9243 e6.R377 533.7736 t.e538 .e36n 1976 96.C0 17 1016 3016 63.7389 .et7e 19.0576 e6.6203 53a.tuta 1.1162 . 600 .itte 1n2.00 18 1098 3098 619.ce08 4353 18.27te e6.8030 534.e283 1.117w .e600 .itte 108.00 19 1180 1180 62e,3e27 65te 17.5583 en.7sse 534.755a 1.1200 .eecu .Itte tie.00 20 1263 1203 629.6een ,6 66 to.e969 et.7es2 535.o827 752u .emoo .ttle 120.c0 21 4332 .1332 634.0789 .e775 16.e29e a6.753e 535.356e 711e 5920 .o*3e tie.uo 22 1401 3401 638.5132 .e884 15.9528 e6.7389 535.e3nt 7s *2 55e .eW 3 e 132.09 23 .1444 .tese 641.2967 6953 15.e500 e6.72** 535 e919 7w37 .3eo5 .n5ae 13e.00 24 .3887 ,3447 644.0802 7016 15.3759 e6.720e 535.973e 2e73 3ses .osme see.oo kafw a PATH 9 PaTM a LTP *LEL SUPPORT t TP MOLE 8 EdawhtL.L TP .alEw tocE PRESSURE DROP (PSIt 2.08 2.68 2.3% 5.#u LEAKAGE FLoa (LB/MRI 122.86 2920.69 12e0.57 372.3e

+

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me coEMMampreek eeMeee=Mm>pe SW F W O 4 > W E uw coomMcCoMppe=MW>emesepom 43 O e e e e o e e o e e e o e e o e e o e e e e e e W & M 4 >

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• MJ3u N J e = 0 e a

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u E N O 3 W u

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J MNM9eesedeMemoeMoepMao@e O W = W 2 m >J W e X F >

w Q 4W 4epeMNeo@ eSphheeeWWWWWWW O e Da mammmmameooooooooooooooo > ese E 4 u 5 3 E M W W WO ee e e e e e e e 9 e e e e e o e e e e o e e e e & > 2 E 4 J e u Z 3 h I WE E SO W 2 O w 3 e 3 3E E O a E e e e & > e & J W MO M

> M W 2 e e

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>>> & 3 000 3 e 7-18 L - _ _ _ _ _ _ _ - _ _ _ _ _

x .

CMANNEL 4 TYPEe CEw.8sSR GEumETRY: Cem.8R huastas 16u FLO. AWE 4 1099 $0.FT, Section 7.3 INLET VELOCITY 6.59799 FT./8EC. Part 19 M ASS FLUE 1.1196 mL8/MR.SG.FT. Hv0RauLIC DiantTEu .o.ee FT.

ACTIVE FLQu 1230 ML8/MR 8vPASS+mi FL0a (Mt.0Est 1.5699 L8/MR ACTIVE P0mER 4.8292 MWT STPA88+mi POaER 3056 maf AVERASE DEh81TV 25.9803 LBM/Cu.FT. ACT!vt Exif W,0= QUALITY 377 AVERAGE votD FRACTION 4621 ACT!vE Eu!T votD PaaCTIUm 7387 SOILING MEIGHT 5.3359 14 CMIMMEY FLod QuaLITV 5717 DELTA ENTMALPY 134.3988 STu/ Lum CMIMhEY v010 FRaCTIow 7347 PRE 88uat DROP COMPONENTS l FRICTION . 3.5337 P81 LOCAL 16.7322 PSI ELEVATION 2.6978 PSI ACCELENATION 6006 P81 Flow VOID FLua MATER TURE CWah. .. LL RELAT!vE PEAM TOP OF NODE

. NODE E0u!L. TOTAL Meat FLUM ELEvaTIUm l K SUAL. QUAL. ENTMAL. FRaCT. DENSITY DtNSITY ENinaLPY DELTA f P0aER (btu /L83 (L8/CU.FT) (LS/CU.FT) (870/Ln) (P8I) (msfu/pR.8a.FT) (IN.)

[NL . 8311 0.0000 527.9024 0.0000 47.1375 47.0837 528.9766 8.7732 .== ... 0.00 t . 0361 0000 531.1250 0000 e6.9751 e?.0720 529.2138 8.7332 6584 .t155 6.00 2 . 0311 0001 534.3477 006e e6.5242 e7.0602 529.ee70 8.6983 6584 .1155 12.00 3 . 0115 0022 540.4860 0534 e4.1982 47.0176 529 8950 8.6384 1.2540 2200 18.00 7d

[g 4 . 0080 0062 546.42e4 5072 41.6361 47.0850 530.3430 8.2776 1.2540 2200 24.00 5 0086 .e130 553.4324 1835 38.1611 et.9897 530.n398 8.2039 1.3908 .24e0 30.00 6 0198 4215 560.240s 26ia 34.5769 46.96e3 531.3367 8.1213 1.3908 2eso 36.00 7 0291 4304 566.6578 3347 31.e453 e6.9e02 531.8051 7.6180 3.3110 2300 42.00 8 0391 0397 573.0752 3945 28.8168 e6.9360 532.273e 7.5321 1.3110 2300 48.00 9 0486 0486 579.6285 4433 26.6679 e6.8927 532.72te 7.se62 1.2540 2200 54.00 to 0588 4582 585.7664 4867 24.7705 e6.8695 533.169e 6.7751 3.25eo 2200 60.00 31 0675 0675 591.7378 5226 23.1983 e6.#e65 533.6c52 6.6859 1.219e 2340 66.00 12 0767 0767 597.7044 5538 21.8384 e6.8235 53a.0sto 6.5949 1.2198 2140 72.00 13 0857 0857 603.e565 5800 20.690s 46,8013 534.460e 6.5035 1.37e2 2060 78.03 14 0946 .ete6 609.2042 6033 19.6719 et.7790 534.8799 5.6657 1.1742 2060 84.00 15 3038 .1938 435.1194 62e7 18.7355 46.7560 535.3116 5.566u 1.2084 2120 90.00 3130 1130 6Lt.a3e6 6440 17,89e1 46.7328 535.7433 5.4612 3.2084 212e 96.00 16 7 38DP 3385 6 W.t?D9 6628 If.1057 se.9e87 536.1913 6.8st3 1.25eo 220n 182.00 IS 1344 133s 633.3t:5 6784 16.3903 et.684e 536.6393 8.3225 1.25s0 .2200 100.00 19 1416 1416 639.4497 6933 15.7375 e6.6608 537.0873 8.1973 8.2540 2200 134.00 30 1981 1511 665.5880 7070 15.1387 e6.6356 537.5353 2.9a90 1.25mo 2200 120.00 23 1991 159 650.7219 7177 14.6732 e6.6tst 537.9100 2.8576 1.ce88 .inen 326.00 II 3671 .t671 455.8559 7276 14.2380 e6.59ee 538.2847 2.7399 3.0e88 .speo 132.00 33 .1731 1731 659,'#45 7330 16.0045 et.5ste 538.5t99 2.597 656e 3155 13e.00 ,

at 3771 .3773 667.3031 7387 13.75e9 46.5684 538.7551 1.2715 658e 1155 144.00 l PATM . PATH 9 PaTM 8 ,

l LTP= FUEL SUPPuef LTP HOLES CMAhhEL.LTP WATER TU8E l

PRESSURE DROP (881) 9.71 9.73 8.78 11.37 Lt6 MAGE FL0e (LS/AR) 233.72 5556.24 3287.20 2411.91 1

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> N e e e e e e e e e e e e e e e e e e o e e e e e e m

w & 00000000000000000000 4 a J e 3 e 2 u = 0 J =

4 e z G ea W e N a c o m O O W e O N r.P W e m o o m e e M >

u = K W JJS NMcWWeaWNmommmMWWWMMN4ONM

% E 44 J OeNeerMe% Ward 994WNedbe@Ne E & g >g% pecomMpe.OpppppoommmpebMe O O J e O*3 e e e e e o e e e e o e e e e * * * *

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_ mammmmmmmmMNNNN 7-20

_ c1 SUMMAWY OF CALCULATIONS

....................... Section 7.4 Part 23, 24 NUMRER OF CMaahtL S 3*e TOTAL CORE P0utR (MuT) 1593.0000 eF.997a 48.0000 CALCULATED MASS FLua (MLh/>H)

REQUIRED MASS FLOW (ML8/MR) 1035.0000 CALCuLAfte = ASS FLua (=Lo/nR/Su.FT) 1.c7 n SYSTEM PRtstung (PSIA) 20.0003 527.9024 INLET SubC00 LING (efu/Lum)

INLtf ENTMALPY (81u/L8M) 9800 ACTIVE COOLANT FL0a (PLM/ph) 42.8ee9 FRACTION OF PONER COND. TMNOUGH CLAD gYPASS CDOLANT FLOa (ML8/ww) 4.6630 FRACTION OF PontR OtPOSITED IN OVPASS 0200 0007 mAftR Tutt ConL ANT FLDn (mLM/nR) .am75 FRACTION OF PoutR DEP. IN mAftR TUBt8 maximum HEAT FLUE (MuTu/ne/SJ.FT) 2aso TOTAL ACT!vt PLos AREA (80. FT.) 40.00at avtNAGE Mtaf FLuz tanfu/ne/Sg.FT) 3539 TOTAL MEAT TRANSFER AREA (1000 80. FT.) 34.6063 29.025e 26.9934 AvtRAGE =00tNATOR OthS17Y (Len/Cu.FT)

ACTIVE COOLANT DEN 817Y (L8M/f".FT) AVERACf up. ate PLENUM QUALITV 3451 4343 l

AVERASE ACTIVE COOLANT V310 +dACTION AvtRA8g EXIT VOID FRACTION 7178 CMNFL EXIT DUALITY .tect ,

19,12u0 1

23.T452 Cnki SUPPONT PLATE PHt$$uME DNOR (P3{}

l PLENUM TO PLENUM PRESSURE DROP (Pe!) SYPast AND =ATEw TUBE FLO= FwACTION ,1069  !

l STEAM FLOW RATE (ML8/MR) 6.96am l

MAXIMUM MEAT FLUX OCCUR 8 IN CHANNEL 4 AT STEP 5 l

CHANNEL

SUMMARY

2 3 4 CMANNEL NUMBER 1 CEN.7x7 CEN.8XS PER.8E8 CEN.818R

-a CMANNEL ftPE PER.8 CEN.8R CMANNEL SEDMETRY CED7 C*N.8 4

>- NUM8tR PER TYPE 68 80 60 led NUM8tR OF FutL RODS 49.0000 63.0000 63.0000 62.0000 ACT!vt FutL LENSTM (IN) 144.0000 144.0000 144.0000 144.0000 REL ASSEMSLV P0mER FRACTION 9059 1.1000 a.la00 ASSEM HEAT TRANS AREA (80.FT) 8e.6671 97.5747 97'6000 57a7 94.0781 ASSM MEAT TRAM (MBTu/MA/ SOFT) 1513 1632 0890 .t754 ASSEMBLY FLON AREA (80.IN) 15.5350 15.5860 15.5160 15.e244 5765 5162 5162 5324 ASSEN MTORAULIC O!AM (IN)

MASS FLUX (ML8/MR.80.FT) 3.2272 3.1222 6966 1.1196 INLET FLou VELoctTY (FT/8EC) 7.232C e.allt 4.1058 6.5980 ACTIVE FLQm RATE (1800 L8/MR) 132.3965 120.9181 75.0007 123.0428 LEARASE PL0nB (1000 L8/MR)I 2394 3229 2337 LTP.FutL SUPPORT 2226 LTP MOLES 5.2986 5.6915 2.9207 5.55e2 CHANNEL.LTP 3.0103 3.4254 1.28e6 3.2872 NATER TUSE e.0005 7401 ,3724 2.4819 NON SOILING LENSTM (IN) 5.T010 T.0521 5.T000 5.3351 3229 1735 8487 3778 ACTIVE EXIT SUALITf 7016 7387 VOID FRACT AT TOP OF ACTIVE 6625 73a7 3805 4574 4200 462 AVERASE VD10 FRACTION SAMPLE Pacettp st/01/2e END OF CASEI FIsen MODEL FOR VERm0NT VANutt END OF Jos

Section 8 REFERENCES

1. G. Lellouche and B. A. Zolotar, "An Approximate Form of the EPRI-Void Forma-tion Model," February 16, 1980 (unpublished).

2. P. Saha and N. Zuber. " Point of Net Vapor Generation and Vapor Void Fraction in Subcooled Boiling." In Proceedings, Fifth International Heat Transfer Con-ference, Vol. IV, 1974.

3. S. Levy. Forced Convection Subcooled Boiling--Prediction of Vapor Volumetric Fraction. General Electric Co., 1966, GEAP-5157.

e. R. T. Lahey and F. J. Moody. Thermal-Hydraulics of a Boiling Water Nuclear Reactor. American Nuclear Society, 1977.

5. N. Zuber and J. A. Findlay. " Average Volumetric Concentration in Two Phase Flow Systems." Journal of Heat Transfer, 1965.

6. S. Levy. " Steam Slip - Theoretical Prediction from Momentum dodel." Journal of Heat Mass Transfer, No. 82, 1960.

7. G. E. Dix. Vapor Void Fractions for Forced Convection with Subcooled Boiling at low Flow Rates. Genc-al Electric Co., 1971, NEDO-10491.

8. J. F. Waggener. " Friction Factors for Pressure Drop Calculations," Nucle-onics; Vol. 19, No. 11, 1961.

9. C. J. Baroczy. "A Systenatic Correlation for Two-Phase Pressure Drop."

Preprint #37, Eight National Heat Transfer Conference, Los Angeles, American Institute of Chemical Engineers, 1965.

10. K. V. Moore et al. RETRAN - A Program for 1-D Transient Thermal-Hydraulic Analysis of Complex Fluid Flow Systems. EPRI-NP-408, Vol. 1, Section 111.1, Electric Power Research Institute, 1977.

11. A. B. Jones and D. C. Dight. " Hydrodynamic Stability of a Boiling Channel,"

Part 2, KAPL-2208, Knolls Atomic Power Laboratory, General Electric Co., 1962.

12. R. C. Martinelli and D. B. Nelson. " Prediction of Pressure Drop Durirj Forced i Circulation of Boiling Water." Transactions, American Society of Mechanical Engineers, 1948, pp. 695-707..

13. D. Chisholm. " Pressure Gradients Due to Friction During the Flow of Evapor-ating Two-Phase Mixtures in Smooth Tubes and Channels," Journal Heat Mass Transfer, Vol. 16, Pergamen Press, Great Britain, 1973, pp. 347-358.

8-1

14. I. E. Idel'chik. Handbook of Hydraulic Resistance, Coefficients of Local Resi. stance and of Friction. AEC-TR-6630, 1960. (Translation from Russian, avai able through the Nation-11 Technical Information Service of the U.S.

Department of Commerce.)

e

15. E. Janssen and J. A. Kervinen. Two-Phase Pressure Drop Across Contractions and Expansions: Water-Steam !'ixtures at 600-1400 psia. General Electric Co., 1964, GEAP-4622.

16. J. Weisman, A. Husain, and B. Harsche. "Two-Phase Pressure Drop Across Abrupt Area Changes and Restrictions," from Two Phase Flow and Reactor Safety, Vol. 3, Henisphere Publishing Corp., 1978.

17. K. V. Moore and W. H. Rettig. RELAP4 - A Computer Program for Trar.3ient Thermal Hydraulic Analysis. Aerojet Nuclear Co., 1973, ANCR-ll27.

18. A. F. Ansari, R. R. Gay, and B. J. Gitnick. FIBWR: A Steady-State Core Flow Distribution Code for Boiling Water Reactors--Code Verification and Qualifica-tion Report. Palo Alto, CA: Electric Power Research Institute, July 1981, hP-1923.

19. P. A. Lottes, " Nuclear Science and Engineering," 9, 26 (1961) .

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I 8-2 1

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