ML19353A412

Methods for Analysis of BWRs,Steady-State Core Flow Distribution Code (Fibwr).

ML19353A412
Person / Time
Site:	Vermont Yankee
Issue date:	12/31/1980
From:	Ansari A, Slifer B, Turnage J YANKEE ATOMIC ELECTRIC CO.
To:
Shared Package
ML19353A407	List: ML19353A406 ML19353A412
References
YAEC-1234, NUDOCS 8101080403
Download: ML19353A412 (118)

Text

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I$0 METHODS FOR THE ANALYSIS OF BOILING WATER REACTORS f STEADY-STATE CORE FLOW DISTRIBUTION CODE (FIBWR)

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I F repared By *

• MtQF  !

A. F. Ansabi V (Ddte)

Reviewed By .

IL[J// 90 B. C. Slifer (Date) kgL C. M I Approved By J.C.(ITurnage d' 11 3\ $D (Da te')

Yankee Atomic Electric Company Nuclear Services Division 1671 Worcester Road Framingham, Massachusetts 01701 81m o893

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DISCLAIMER OF RESPONSIBILITY I This document was prepared by Yankee Atomic Electric Company on behalf of Vermont Yankee Nuclear Power Corporation. This documesnt is believed to be completely true and accurate to the best of our knowledge l I and info rmation. It is authori::ed for use specifically by Yankee Atomic Electric Company, Vermont Yankee Nuclear Power Corporation and/or the appropriate subdivisions within the Nuclear Regulatory Commission only.

With regard to any unauthorized use whatsoever, Yankee Atomic Electric Company, Vermont Yankee Nuclear Power Corporation and their officers, directors, agents and employees assume no liability nor make any I warranty or representation with respect to the contents of this document or to its accuracy or completeness.

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ABSTRACT i

A steady-state core flow distribution code (FIBWR) is described.

I The ability of the recommended models to predict various pressure drop components and void distribution is shown by comparison to the experimental data. Application of the FIBWR code to the Vermont Yankee Nuclear Power Station is shown by comparison to the plant measured data.

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ACKNOWLEDGEMENT This work was jointly funded by Vermont Yankee and EPRI, under the program manacement of Dr. Burt A. Zolotar. Principal contributers to the report included Ben Citnick, NUS Corp., and Dr. Rodney Gay, RPI.

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I TABLE OF CONTENTS Page DISCLAIMER............................................... 11 ABSTRACT................................................. iii AC K';0W LE DG EM E NT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv TA B LE O F C 0 NT E NT S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v I LIST OF TABLES........................................... viii LIST OF FIGURES.......................................... ix

1.0 INTRODUCTION

............................................. 1 1.1 Purpose............................................. 1 1.2 General Dr .- ;ription o f the FIBWR Code. . . . . . . . . . . . . . . 2 2.0 FIBWR METHODOLOGY........................................ 6 2.1 General............................................. 6 2.1.1 Core Geometry................................ 6 2.1.2 Equation Solved.............................. 6 2.1.3 Water Properties............................. 9 2.2 Void Models......................................... 9 l

I 2.2.1 2.2.2 Subcooled Boiling............................

Void-Quality Relationship....................

10 10 2.3 Pressure Drop Correlations.......................... 12 2.3.1 Friction Pressure Drop....................... 12 2.3.2 Pressure Drop Because of Local Losses........ 13 I 2.4 Leakage Flow Models................................. 13 I 2.4.1 2.4.2 Bypass Region................................

Water Tubes..................................

13 14 2.5 Solution Techniques................................. 14 3.0 COMPARATIVE REVIEW OF SELECTED M0DELS.................... 17 3.1 The FRIGG Loop Data................................. 17 3.2 Void-Quality Models................................. 18 3.3 Subcooled Boiling 'fodels............................ 20

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TABLE OF CONTENTS (Continued)

Page 3.4 Two-Phase Frictional Pressure Gradient.............. 22 3.5 Two-Phase Local Pressure Losses..................... 23 4.0 FIBWR CODE QUALIFICATION STUDIE5......................... 36 4.1 Qualification Versus Analytical Solution............ 36 4.2 Qualification Versus COBRA IIIC..................... 44 5.0 FIBWR COMPARISONS TO PLANT SPECIFIC DATA................. 55 5.1 FIBWR Model Inputs.................................. 55 5.1.1 Inlet Orifice and Lower Tie Plate Form I 5.1.2 Loss Coefficients............................

Spacers and Uppers Tie Plate Form Loss Coefficients............................

56 60 5.1.3 Water Tube Entrance and Exit Loss Coefficients................................. 61 5.1.4 Leakage Coefficients for Bypass Flow......... 62 5.1.4.1 Path 8. Between Ft*>l Channe? and Lower Tie Plate (Finger Sprir.c Path)............................... 63 5.1.4.2 Path 11. Bypass Flow Holes in the Lower Tie Plate..................... 65 5.1.4.3 (Paths la, Ib, 2, 5) Leakage Paths Due to Control Rod Drivas and

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Guide Tubes......................... 66 5.1.4.4 Path 6. Fuel Support and Lower Tie 68 I

Plate...............................

5.1.4.5 Path 3. Core Support Plate-Incore Guide Tubes......................... 70 3.1.4.6 Path 4. Core Support Plate-I 5.1.4.7 Shroud..............................

Path 10. Bypass Flow Holes in the Core Support Plate..................

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I 5.1.4.8 Summary of Leakage and Form Loss Coefficients........................ 73 l

l 5.2 Vermont Yankee (VY) Comparisons..................... 75 l 5.2.1 Description of VY Test Conditions and FIBWR Model Input............................ 76 I 5.2.2 Results of FIBWR Comparisons to Vermont Yankee Data.................................. 78 I -vi-I

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!I TABLE OF CONTENTS (Continued)

Pace

6.0 CONCLUSION

S.............................................. 105 I

REFERENCES............................................... 106 I

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LIST OF TABLES Number Pace 2-1 FIBWR Execution Methodology Description for Flow Convergent Case.......................................... 16 3-1 Geometric Data for FRIGG Leur Test Section FT-36c........ 24 4-1 Input for 1/12 Section of a 19-Rod Bundle................ 48 4-2 Input for Quad Cities 7x7 Fuel Assembly.................. 49 5-1 Form Loss Coefficients Used in FIBWR..................... 79 5-2 Bypass Pass Flow Paths................................... 80 5-3 Exxon Data Reduction..................................... 81 5-4 Summary of Flow Fraction Through Bypass Flow Paths at Rated Power and F1ow.................................. 82 5-5 Summary of Leakage Coefficients for Various Bypass Flow Paths............................................... 83 5-6 Vermont Yankee Plant Specific Data and Rated Conditions............................................... 84  !

I 5-7 Vermont Yankee FIBWR Model Data for Cycle 7.............. 85 5-8 Results of FIBWR Comparisons to Vermont Yankee D a...... 86 I

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l I LIST OF FIGURES Number Pace 1-1 Power-Flow Map........................................... 4 1-2 Fuel Bundle Geometry and Various Leakage Flow Paths...... 5 3-1 Mean Relative Axial Heat Flux Distribution Used in FRIGG Loop Test Series................................ 25 I 1-2 Cross-Sectional View of the Heater Rod Arrangement for the FRIGG Loop Experiments........................... 26 I 3-3 Comparisons of Void Fraction Versus Flow Quality as Predicted by EPRI, Dix, Zuber Findlay ard Homogeneous Void Models.................................. 27 3-4 Cross-Sectionally Averaged Void Fraction Measurements Versus Quality for FRIGG Loop Test Sections FT-36a and FT-36b............................... 28 3-5 Void Fraction Versus Equilibrium Quality Predictions of Dix Correlation Compared to FRIGG Loop Data........... 29 3-6 Void Fraction Versus Equilibrium Quality Comparisons of FRIGG Loop Data Versus EPRI Void-Quality Model........ 30 3-7 Void Fraction Versus Axial Height for FRIGG Loop Runs with Low Inlet Subcooling........................... 31 3-8 Void Fraction Versus Axial Height for FRIGG Loop

" Runs with Boiling Height Equal to Zero................... 32 I 3-9 Void Fraction Versus Axial Height for FRIGG Loop with High Inlet Subcooling............................... 33 3-10 FRIGG Loop Measurements of Two-Phase Friction I Multiplier, and Predictions of Baroczy Model............. 34 3-11 Two-Phase Multiplier for FRIGG Loop Spacers.............. 35 l

I 4-1 F1 BUR Predictions of the Total Pressure Drop and Various Pressure EWP Components Compared to the l

Analytical Solution Results............................... 50 4-2 One-Twelfth Section of Symmetry from a 19-Rod i

Bundle Divided into 5 Subchannels........................ 51 1

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I LIST OF FIGURES (Continued)

Number Page 4-3 Pressure Drop Versus Subchannel Mass Flow Comparison of FIBWR and COBRA 11IC.................................. 52 4-4 Comparison of FIBWR and COBRA IIIC Predictions of Pressure Drop Versus Mass Flux for a BWR Fuel Assembly................................................. 53 4-5 Void Fraction Versus Axial Height Predictions of FIBWR and COBRA IIIC for Quad Cities Fuel Assemblies............................................... 54 5-1 A Mock-up of the Fuel Bundle for the Lyak Tests at Exxon's PHTF.......................................... 87 5-1A Least Squares Fit to the Exxon Data...................... 88 I 5-2 Orifice Plus Lower Tie Plate Pressure Drop as a Function of RESENe Coolant Flow for Central Region (20 Btu /lb Subcooling)............................ 89 5-3 Orifice Plus Lower Tie Plate Pressure Drop as a Function of 1000fie Coolant Flow for Central i Region (30 Btu /lb Subcooling)............................ 90 5-4 Orifice Plus Lower Tie Plate Pressure Drop as a l Function of M e Coolant Flow for Peripheral Region (20 Btu /lb Subcooling)............................ 91 5-5 Orifice Plus Lower Tie Plate Pressure Drop as a l Function of M N Coolant Flow for Peripheral Region (30 Btu /lb Subcooling)............................ 92 l

3-6 FIBWR Predictions of Bundle Pressure Drop as a Function of Active Coolant Flow and Active Coolant Power for 7x7 Fuel Assemblies (20 Btu /lb Subcooling)..... 93 5-7 FIBWR Predictions of Bundle Pressure Drop as a eunction of Active Coolant Flow and Active Coolant l Power for 7x7 Fuel Assemblies (30 Btu /lb Subcooling) . . . .

l 5-8 FIBWR Predictions of Bundle Pressure Drop as a Function of Active Coolant Flow and Active Coolant Power for 8x8 Fuel Assemblies (20 Btu /lb Subcooling)..... 95 l

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LIST OF FIGURES (Continued)

Number Pace 5-9 FIBWR Predictions of Bundle Pressure Drop as a Functior of Active Coolant Flow and Active Coolant Power far 8x8 Fuel Assemblies (30 Btu /lb Subcooling)..... 96 5-10 FIBWR Predictions of Bundle Pressure Drop as a Function of Active Coolant Flow and Active Coolant Power for 8x8R Fuel Assemblies (20 Btu /lb Subecoling).... 97 5-11 FIBWR Predictions of Bundle Pressure Drop as a I Function of Active Coolant Flow and Active Coolant Power for 8x8R Fuel Assemblies (30 Btu /lb Subcooling).... 98 I 5-12 A Diagram Showing VY Core Pressure Drop Instrumentation and Pressure Points that FIBWR Calculates for Estimating Pressure Drops........................................... 99 5-1) Quarter Core Plan View of Vermont Yankee Reactor During Cycle 7................................................. 100 I 5-14 Core Average Axial Power Distribution for Case 1 (Cycle 7)................................................ 101 I 5-15 Core Average Axial Power Distribution for Case 2 (Cycle 7)................................................ 102 5-16 Core Average Axial Power Distribution for Case 3 (Cycle 7)................................................ 103

{ 3-17 Elevation of the Spacer Midpoint Above Bottom of Active Fuel.............................................. 104 iI I

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1.0 IhTRODl'CTION  !

I 1.1 Purnose I This report describes the verification and qualification of the FIBWR (for Flow In Boiling Water Reactors) computer code. FIBWR [1] was i developed to provide an accurate and convenient steady-state core hydraulic I

( simulator for boiling water reactor (BWR) core reload design and licensing I calculations.

In a BWR, the power distribution is closely coupled to the coolant density. Because BWR's are undermoderated, the neutron flux and power are strongly influenced by local variations in the steam void distribution, which is a direct function of the power-flow distribution in the core region.

Thus, a synergistic relationship between flow and power exists in a BWR core. FIBWR gives the capability to accurately predict the flow distribution for a given power distribution. 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) fl ows 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

, distribut ions over a large range of power / flow operating condit:ons (Figure l 1-1).

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The FIBWR code incorporates a detailed geometrical representation l

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I of the complex flow paths in a BWR core, and explicitly models the leakage flow to the bypass. FIBWR includes a selection of widely used and recently developed models available at user option to calculate the following: (a) void fraction in both the subcooled and bulk boiling regions, (b) tN location of the onset of subcooled boiling, (c) flow quality as a function of equilibrium quality, (d) single phase friction factor, (e) two phase i

friction multiplier, and (f) two phase local loss cultiplier. These models l

i have been reviewed and qualified against the latest multired pressure drop i

lE i5 and void data. The FIBWR code has been verified by analytical studies and Benchmark comparisons of I comparisons to other thermal-hydraulic codes.

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

1.2 General Description of the FIBWR Code The FIBUR code computes the steady-state mass flow, enthalpy, and density distribution in a system of heated, vertical parallel flow channels for either a given total mass flow or for a specified total pressure drop.

The power distribution, inlet enthalpy* and geometry are presumed known and must be supplied to FIEUR.

FIBUR determines the coolant flow for all of the flow paths present in currently operatine BWR cores (Figure 1-2). Leakage fl ow t o the bypass is explicitly treated, so that the flow rates in each channel and in the bypass and wa ter tubes may be de termined simul t aneously. The pressure drop I *FIBWR contain a system energy (heat) balance option which determines the core i nl e t enthalpy f rom plant-measured thermodynamic da ta.

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i characteristics are determined by integrating the energy and momentum eauations along the flow channels and in the bypass region. T'.e ma s s flux for each flow path is adjusted to achieve an estimated core pressure drop.

The calculation terminates when the core pressure drop which yields the required total mass flow is found.

Assumptions basic to the solution methodology are:

1. A uniform static pressure at the inlet and outlet plenums for all

! channels

2. Subcooled or saturated inlet conditions

3. One-dimensional upward vertical flow in each flow channel 4 Water properties deternined for a single value for pressure, i.e.,

axial variations in pressure have insignificant effect on properties.

The methodology embodied in the FIBWR code should adequa tely model SIG cores over a wide range of power / flow conditions encountered in design and licensing calculations. Some of the potential steady-state applications of FIBIG are:

I o Determination of the moderator density distribution for nuclear simula to r codes (e.g. , SIMl' LATE [2 ]) .

o Initialization of input pa rameters f or loss-of-coolant accident l and transient evalua tion codes (e.g. , RETRA'? [3]), or the simplified hydraulics models of the process computer).

o Calculation of the power and corresponding flow of the limiting assembly hot channel when at thermal limits.

t o Determination of pressure loadings on internal structures, such

! as the core support plate and the fuel channel walls.

FIBWR may also prove useful for evaluating core flow distribution during transients for which power changes can be defined.

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I Top of Core h

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4 3 I Spacer Height = HFSG

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supports are welded ir.co the core support plate. For these bundles, path numbers 1, 2, l

l Channel 5 and 7 do not exist.

I Core l ZUHB j Support 4 l l

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ZCEO Plate I

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34 r a Bottom of core ZSTU --

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Fuel Support Control

" - Shroud lb Rod Guide I Core Length = ZCHI -

Fuel Length + ZCEO 7 Tube

1. Control Rod Guide Tube - Fuel Support Fuel Length = ZUHA + 2. Control Rod Guide Tube - Core Support ZHET - ZUHB o 5 Plate 7 3. Core Support Plate - Incore Guide Tube lE Control Rod Drive Housing 4 Core Support Plate - Shroud iE

5. Control Rod Guide Tube - Drive Housing

6. Fuel Support - Lower Tie Plate

7. Control Rod Drive Cooling Water

8. Channel - Lower Tie Plate

9. Lower Tie Plate Holes

10. Spring Plug - Core Support Figure 1-2. Fuel Bundle Geometry and Various Leakage Flow Paths

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ll 2.0 FIBWR METHODOLOGY 2.1 General 1

This section reviews the analytical methodology used to solve the conservation equations of continuity, momentum, and energy in the FIBLTR code. The models and correlations available by default or as options are

briefly described. The details of these models and their calculational procedures may be found in Reference [1].

2.1.1 Core Geometry l

FIBWR models the core of a BWR as parallel flow channels plus a bypass region. An arbitrary number of flow channels may be modeled from l a maximum of 100 unique geometry types. ~

The detafled geometric modeling of each flew channel includes the effects of the inlet orifice, fuel support piece, lower tie plate, unheated fuel regions, grid spacers, wa ter tubes, upper tie plate, and chimney.

For each flow channel, three leakage flow paths to the bypass are located after the orifice but before the active fuel region. Up to eight " common" leakage flow paths to the bypass are allowed which are dependent on the core support plate pressure differential. All bypass flows are lumped into a single flow region representing the average bypass.

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2.1.2 Ecuations Solved The continuity, momentum, and energy equations must be solved simultaneously in each flow channel. The continuity equation for this case is almost trivial, in that ti.e mass flow up each channel is constant, and the total mass flow must equal the su= of the individual channel flows.

The steady state channel energy and momentum ecuations reduce to, i

E NERGY

_d h_ . _c_' (2-1) l dz w MOME';TD1 d_ p_ , pp,- . -p_p,- , g -p_p,-

I d d acceleration d: friction d: gravitv -

dz local (2-2) where h = .athalpy (Bru/lb)

= elevation (f t)

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! c ' = linear heat rate into the flow channel (Stu/hr-f t) w = channel mass flow (Ib/hr) p = pressure (psia)

These ecuations are integrated piecewi se up each flow channel using l the number of axial divisions specified by the user. Terms on the right-l hand side of each ecua tion are evalua ted using node averaged values. Across a given change in flow a rea , the acceleration pressure change is evaluated by one of two possible fo rmul a t ions . In single phase unheated regions, the acceleration pressure change is apacceleration =

(1 - ,~A2) 2g C' (2-3) 0, c a.

where O =

g ratio of final to initial flow area l

G = mass flux ( lb )

2 hr ft e; = liquid density (Ib/ft )

In two phase nnheated regions,

- , . , _ , , , _ - - . - , . ,_.---,,---c,-----,-.,,..... - - . - - - - - - - - - - - - - - - - - - - - - - - - - - ---

I I 1 A fin l final -6 nitial^ initial ( ~')

Apacceleration " g co n Afinal+^ initial where the momentum density, 0 3, is defined by I 1 = 'x>-

o

+ (1 -

o

<x>)~ . (2-5) c <a> p M P C(1 - <2>)

and

<x> = flow auality at node exit

<2> = void fraction at node exit e = momentum density (lb/ft3)

In beated regions, the flow area is assumed constant, and the fluid acceleration is due + > density changes induced by the boiling process.

In this case, the formulation for the acceleration pressure change is

= G 2 1 -

1

• ",2 accele ra tion - . (2-6) 7C  :

O" outlet minlet i The cravity or elevation nressure drop across a node is evaluated bv I

~

~1 angravity " 2 2(1 - <">) + R< # Z " (2-7)

( The frictional pressure losses are correlated in terns of the single-phase velocity heac' I .

Pfriction

. p DH 2c 0 AZG 2 c 7

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. (2-8)

I where I f = single nhase friction factor C2 = the single phase velocity head i 2r ca; l

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Dg = hydraulic diameter (f t)

I t = two phase frictional multiplier g = c nstant relating force and acceleration (1b m-f t/lb sec )

e f The irreversible pressure losses due to local effects such as that associated with area change, orifices, tie plate, or grid spacers are formulated in a manner similar to tha:- for frictional losses.

2 ,,

APlocal " E #

local

• ( ~9) 28c02 O

l where : ocal is the two phase multiplier for local pressure losses, and K is the single phase fo rm loss coefficient of the flow obstruction.

i 2.1.3 Water Properties i

The thermodynamic properties of steam and water are computed external to FIBWR consistent with the 1967 AS::E formulations [4]. The STH2O program, which is described in Reference [5], generates the tables of water properties in the proper format which are required to be provided to FIBL*R. FIBG contains the STHLIB routines from RELAP4 [5], which are used to interpolate from the data in these tables.

2.2 Void 'fodels I The methodology and the terminology used in this report for calculating the flow quality <X>, and the void fraction O>, i s consistent with that of Lahey and Moody [6] .

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I I 2.2.1 Subcooled Boiline i The solution to the energy eaustion yields the distribution of mixture enthalpy alonn the flow channel. The ecuilibrium quality may be I computed from its definition, based upon the mixture enthalpy, b-h f

<Xec)

(2-10) f8 where hg is the saturated licuid enthalpy, and h p ecuals (hg - h f).

The flow auality, defined as the ratio of steam mass flow to the total mass flow rate, nay be related to the eauilibrium cuality through a so-called subcooled boiling model. FIBUR default = to the EPRI model

[7] to predict -the onset of net vapor generation, although the Saha-Zuber

[6] and Levy [6] models are available as options. Once the onset of boiling I

has been determined, it is necessary to predict the variation of flow quality I with ecuilibriun cuality. It is known that the flow quality equals zero at the departure point where the ecuilibriun cuality is less than zero.

Also, the flow and ecuilibrium qualities both ecual unity when all licuid is vaporized. Between the subcooled boiling initiation point and the 100 percent eauilibriun cuality value, a hyperbolic taneent (EPRI model {7])

or exponential (Saha-Zuber or Levy model) profile fit is enployed to predict the difference between flow and equilibrium anality.

2.2.2 Void-Ouality Relationship I A Zuber-Findlay type relation is used to correlate void fraction,

<a), in terms of the flow quality, <X>. The relationship is 1

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

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< 3) = .

""i l Co [<X> ~2 + b (1 - <X>)] + Y Cg , the concentration parameter, is a measure of the relative distributions of velocity and void fraction across the flow channel. V is the drift I velocity of the vapor relative to the licuid.

C has a value of unity if the liquid and vapor phases are uniformly 9

distributed. If the vapor is concentrated in the high velocity or central flow regions, the concentration parameter is greater than 1, while it is )

less than 1 if the opposite is true. Historically, a value of C 9 = 1.13 i has been found appropriate for fully developed annular flow. In fact, both the _Zuber-Findlay [6] and Levy void quality [6] nodels specify a constant C ecual to 1.13. However, C should be a function of flow regime and should o o tend towards 1.0 for single phase vapor flow.

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! " The drift velocity, V gj, may be modeled by considering a bubble i

risinc in a licuid. A balance of forces gives the terminal rise velocity as [6],

I L' t " h,3 (3

t

,2

- O r)  : RF c

__0.25 sin 9 *

(3_g3)

U where surface tension (lb/ft)

I C =

z = gravitational constant (ft/sec2) ec = constant relating force and acceleration (lbn-ft/lbf-sec2)

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K3 = experimental constant l l

9 = angle with horizontal Thus, for vertical flow it is often assumed that I V g3

=U g (2-13)

Lellouche and Zolotar of EPRI [7] have developed a mechanistic model I to predict the variation in Cg and the value for K .

3 An approximate form of this model, which is in good agreement for steady state conditions, has been incorporated into FIBW as the default model. The Dix, Zuber-Findlay, E and Levy modi.ls are available as options. The details of these models can be found in Reference [1].

2.3 Pressure Drop Correlations 2.3.1 Friction Pressure Drop <

The single phase friction factor, f, may be predicted by the well-known Blausius relationship B

f = A Re ,

(7_14) where Re = Rcynolds number I

A,3 = user input constants A fit to the Moody curves and the Colebrook correlation are also available in FIBW as user options for the evaluation of f.

l If I . ..--_...-._ . - _..-,.

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I At or near B'n~R conditions the Baroczy [8] correlation for the two-phase frictional =ultiplier, Ofo, is the default model in FIBliR. Also available as user options are the Jones-Dight [9] fit to the Martinelli-Nelson curves, the homogeneous model, and a mass flux correction [10] to the Martinelli-Nelson curves.

2.3.2 Pressure Drop Because of Local Losses The FIBliR code has three models for the two phase local loss multiplier. The default model is the modified homogeneous expression

2 2 phase " 1 + <X> ( i/;g - 1) . (2-15) friction I where S is an empirical constant. If 6 = 1.0, t hi s reduces to the homogeneeus expression. FIB'.iR also contains the Janssen model as modified by I?eisman [11} and the Romie model [5] as options.

E 2.4 Leakace Flow Models I 2.4.1 Bypass Recion l

l i Due to the low flow velocity, the pressure drop in the bypass region a bov e 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 i s eq ua l to the core differential pressure.

1g Th. f1ow th,o.g, ch. hypass f1ow ,aths is .xp,.ss.e h, th. form te - C;5P1/2 + C 2aP + C 32.P .

( -16 )

k I

I I in Figure 1-2. The pressure drops used to evoluate the above expression are functions of channel pressure dif ferential (P active

-P bypass), 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 1-2). The other paths (with the exception of the control rod coolant flow, which is input) are functions of the pressure dif ferential across the core support plate. These paths are referred to as the ' common paths." The quantity of path numbers 1, 2, 5 are 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 com=on paths and lump several of these paths together. The number of such pa ths and

,g 5 the coefficients C1 through C4 are user input.

2.4.2 Water Tubes FIBWR calculates the water tube flow consistent with the pressure j drop of the active coolant pa r al l el to the tube. The entrance and exit lgE local loss coef ficients and elevations are input. The FIBWR code models the wa ter tube pressure drop in a similar manner to the active coolant, l

i with the exception that the homogeneous void relationship and two phase local loss multiplier models are used should the water tube experience boil i ng .

,I 2.5 Solution Techniques I An inner / outer iterative technique is employed to adjust the conditions in each channel to the imposed boundary conditions. An initial I . _ _ _ . _ _ , _ . _ _ _ _ _ _ . _ _ _ _ _ _ . _ . . . , _ _ . _ _ _ _ _ _ _ _ . . . _ . . _ _ _ _ _ _ _ _ _ _ _ _ _ . _ _ _ _ _ _ _ _ _ _ _ . _ _ _ _ _ _ _ _

I i

I I

I estimate of core pressure drop is input by the user er internally calculated. i On the inner iterations, the flow in each channel type is iteratively adjusted until the desired pressure drop is reached. During this process, the variation in leakage flows to the bypass and the water tubes is l

cal cula ted , and the total flow which passes through the orifice, lower and uppe r tie pla tes is obt ained . When converged to the esti=ated pressure '

4 drop, the fl ows from each of the channels and the bypass regions are <tucced to obtain the total core flow, which is compared against the required core flow.

On each outer iteration, the bypass enthalpy and void distribution are recalculated, and the bypass elevation head is re evaluated. The core pressure drop is adjusted until convergence is obtained. Alternately, the i

user may require the code to solve for 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.

1able 2-1 p,es.nts a summa,y of this p,oc.eu,..

g I

I E

I I

I lI i l - _ , _ _ . _ , . _ _ _ . _ - _ _ . _ _ _ _

I I

TABLE 2-1 FIBWR Execution Methodology Descriptian Flow Convergent Case I (1) An estimate of the core pressure drop is user input or automatically co=puted 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.

I If the pressure drop guess is user input, the initial guess of channel

= ass flows will be equal in all channels. Saturated water density is assumed for the bypass.

(2) For a given channel the energy equation is solved, integrating up the channel, to yield the axial distribution of equilibrium quality.

(3) The flow quality and avoid f raction distributions are calculated in the channel as a function of the previously computed equilibrium quality.

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

I (5) The pressure differentials for the leakage paths are determined, and the water tube flows and bypa ss flows are evalua ted. The pressure I drops for the unheated regions are computed consistent with the total f l ow , 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 again proceeds to Step (2) above. If the pressure losses agree, execution again proceeds to Step (2), but this time the I hydraulic conditions in a new channel are calculated. When the conditions in all channels in the core have been calculated, the bypass elevation head is re evaluated, 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 accuracy, exa m ic:. proceeds to Step (8) below. If not, a new core pressure drog is guessed , and execution once again returns to Step (2), where the whole process starts once again.

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

I I

I 3.0 COMPARATIVE REVIEW OF SEI ECTED MODELS I 3.1 The FRIGG Loop Data As described earlier, a number of constitutive models are required as additional input to the momentum equations in FIBWR. These models predict the flow ouality as a function of equilibrium quality, the void fraction as a function of flow quality and the two phase irreversible pressure losses as a function of the computed flow conditions. FIBWR allows the user to select among several possible choices for the individual model used for each of the above phenomena. In order to establish the validity of some

,I of the constitutive models available in FIBWR for the analysis of BWR flow conditions, the FIBWR predictions of each of the above phenomena will be l

compared with experimental data.

lI 1

If data representative of BWR geometries and flow conditions is used in the comparisons, the verification procedure will perform a dual function. First, it will demonstrate that the various models are coded correctly in FIBWR and that the FIBWR predictions are those of the model.

Secondly, the procedure will compare the models with each other so that the most accurate model for BWR operating conditions may be selected.

I The experiments performed in tl.e FRIGG Loop (12] at the ASEA-ATOM Laboratories in Vasteras, Sweden, were intended to provide detailed data on void fraction and pressure drop in Marviken type BWR fuel assemblies over a range of possible operating conditions. The Marviken fuel assemblies I

have 36 rods arranged in three concentric circles around a central instrument tube. In the FRIGG Loop experiments, a single, full scale fuel assembly was simulated using electrically heated rods. A nonuniform axial and radial I __ __ _

17

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

I power distribution which simulated expected Marviken operating conditions

, was used.

The loop was well instrumented. Ine inlet mass flow and enthalpy l were measured and combined with the applied power to calculate the axial t

distribution of equilibrium quality. The void fraction was =easured at six separate axial locations using three beam gamma densitometers. The asse=bly pressure drop was measured across each spacer location as well as over the flow intervals between spacers. Table 3-1 gives detailed I geometric data on the FRIGC Loop, Figure 3-1 i s the applied axial power distribution, and Figure 3-2 illustrates the fuel rod arrangement.

I 3.2 Void-Ouality Models Numerous models relating void fraction to quality in a flowing system are available, and several of the most popular of these have been included as options i n F I B k'R . The verification procedure is twofold. First, it must be deteruined that the various models are coded correctly in FIB 1JR and that FIBb'R 's predictions are those of the model . Secondly, i t is necessary to determine which of the possible models best predict s condi t ion:,

expected to occur in Bk'R rod bundles under expected operating cond i t i o ns .

I The void quality relationship predicted by the Dix, homogeneous, Zuber-Findlay and EPRI models is plotted on Figure 3-3 for typical BliR c ond i t io ns . Notice that at low qualities both the Dix and the EPRI models predict higher void fraction than the homogeneous model. This implies a slip ratio less than unity, e.g., the bubbles cling to the wall and move with a low velocity. At higher qualities, all three models predict lower I void fractions than the homogeneous, a s expected , wi th the EPRI model 1

' l I predictions the closest to homogeneous. As quality approaches unity, all the models also approach unity, which is the correct Ilmit. However, all the models, except the homogeneous, predict increasingly larger values of the slip ratio as flow quality is increased towards unity. However, this I

high quality region is of little concern to nuclear reactor cores during I normal operating conditions or operational transients.

I On the basis of phenomenological arguments, the EPRI and Dix models were selected for comparisons to experimental data since only these models predict a slip ratio less than unity at low qualities. Physically, the parameter C g cust be a function of heat transfer regime, and hence must vary with void fraction or quality. A constant C, may be realistic for adiabatic flow in tubes, but is too limiting for heated systems. The predictions of each model were compared with the data taken in the FRIGG l Loop at the ASEA-ATOM Laboratories in Vasteras, Sweden. Choosing this data base as the standard to which the void quality models are to be compared, biased our selection towards the EPRI model, since that model was developed to match the FRIGG Loop data. Nonetheless, both the Dix and the EPRI models G we r e compa r ed wi t h the rod bundle data. Since the Dix correlation is based on data for heated steam / water in tubes, the comparisons to the FRIGG Loop data will quantify the dif ferences between tube ar.d rod bundle fl ow.

In order to verify a void quality model, both flow quality and void j f raction must be known. On Figure 3-4, measured values of void fraction as a funct ion of equilibrium quality are plot ted. It can be seen that the data falls on a single curve only for cualities above approximately 5 percent. Assuming that void fraction is a function only of flow ouality at a given pressure and mass flux, the reason for the large scatter in the I __

I I data at low qualities must be that flow quality does not equal equilibrium quality. More importantly, it appears that the two qualities are equal above 5 percent q ua l i t y . Thus, flow cuality is known only for equilibrium f

qualities above 5 percent, where the two qualities are equal, and verification of the void quality models can be done only for equilibrium I qualities above 5 percent. Section 3.3 will discuss verification of the combined subcooled boiling and void quality models for equilibrium qualities below 5 percent.

Figures 3-5 and 3-6 compare both the EPRI and Dix models to data f rom the FRIGG Loop. As may be seen, the Dix model tends to underpredict the da ta, especially at higher qualities, while the EPRI model =atches the I

su data very well. Apparently, rod bundle flow conditions are more homogeneous (lower slip ratio) than the tube flow conditions upon which the Dix correlation is based. Possibly the spacer grids contribute to mixing of the vapor and liquid, making the flow more homogeneous. Note that the local effect of spacer grids is ignored both in the models and in the experimental data (as void f raction measurements were made as far as possible f r on s pa cer locations).

Subcooled Boiling Models I

3.3

, The second aspect of void fraction prediction involves the so-called 1

= subcooled boiling models. These models must relate fl ow ouali ty to equilibriun quality so that the void fraction may be computed as a function i of the predicted flow quality. As shown earlier, flow quality varies significantly from equilibriun quality only at qualities lower than i

approximately 5 percent at no rmal BUR opera t ing condi t ions.

l 1

I I -_ - - - -

I I Unfortunately, i t is impossible to independently verify a given subcooled boiling model because flow qualities have never been measured in heated steam / water systems. However, the profile fit models in FIBWR I do predict the point of initiation of boiling, which is measurable at the I location where void f raction becomes nonzero. Unfortunately, gamma densitometer locations in the FRIGG Loop were from 450 to 810 mm apart so that the location of the initiation of subcooled boiling was not ac cu r a t el y determined. However, since bubble nucleation is a microscopic or boundary laye r phenomenon, i t is expected that data taken in tubes should agree with rod bundle data on the initiation of boiling.

In FIBWR, the user may select among four models for the boiling ini:iation location; these are the EPRI, Saha-Zuber, Levy, and the homogeneous =odel. The homogeneous model is obviously incorrect for BWR r

i conditions as shown by the nonzero void fraction measurements in the negative equilibrium quality region on Figure 3-4 The Levy and Saha-Zuber models are correlations of heated pipe data, with the Saha-Zuber being more recent and based upon a larger data base. The EPRI model is a simplification of a mechanistic model and has been verified against the FRIGG Loop data.

The above models predict the point of zero flow quality. To obtain flow quality as a function of equilibrium quality above this point, a profile l

lm fit is used. This is simply an analytical curve which varies from zero l

l

\

I at the point of zero void fraction to unity at 100 percent equilibrium quality. Two functions which possess this characteristic, as well as approaching the end point s wi th zero slope, are the exponential and hyperbolic tangent functions available in 'rIBWR as options.

I I

I I

Since flow quality is not available experimentally, the only I comparisons to data which are possible are void fraction comparisons. Note that since the void quality models are not verified at low qualities, a given data comparison can verify only the predictions of the combined subcooled boiling and void quality models.

It was decided to compare the EPRI and the Saha-Zuber subcooled boiling models to FRIGG Loop data. The exponential profile was chosen for the Saha-Zuber model since that was in the original data comparisons of Saha and Zuber. The hyperbolic tangent profile was used in conjunction with the EPRI subcooled boiling model, as suggested by its developers.

The Dix void quality model was used with the Saha-Zuber subcooled model and the EPRI void-quality model was used in conjunction with EPRI's subcooled boiling mode',

Figures 3-7, 3-8 and 3-9 display void fraction versus axial location for several FRIGG Loop runs. Predictions of the EPRI model and the Saha-Zuber nodel with Dix void quality are also indicated. It can be seen that both Saha-Zuber and EPRI do a good job of predicting the location of zero void fraction. Both are certainly within the error band of the experiments; and, in fact, they agree with each other quite well. However, during the subcooled boiline regime, the Dix void quality model with an exponential profile fit seems to underpredict the data, while the EPRI void quality model with a hyperbolic tangent profile fit shows no bias either above or below the experimental data.

I 3.4 Two-Phase Frictional Pressure Gradient i Of the models for the two phase frictional multiplier which are available in FIBWR, only the Baroczy model is based on steam / water data I

I at flow conditions representative of a BWR under normal operation.

Therefore, only the Baroczy model was compared with the FRIGG Loop and rod bundle data. Figure 3-10 graphically compares the Barr:zy predictions with the experimental data. It is seen that the model predicts the data very well up at high mass fluxes (1000-2000 k2 , 0.74-1.48 Mlb m2 see hr-ft 2) which are typical of BWR operating conditions, but underpredicts the lower mass flux data. This could have been expected since the data base used in the I

development of the Baroczy model does not include low mass flux data.

Of special note is the Chisholm model [13), which has seen much application in the chemical industry. This model has the unique feature of being a simple, one-line equation with two user input parameters. With proper choice of the input parameters, Chisholm's model can be made to match any of the other models over a limited range of data.

3.5 Two-Phase Local Pressure Losses The two phase local loss multiplier for spacer grid irreversible pressure losses turned out to be the simplest to model. This is because the two phase form loss multiplier varies linearly with quality. Thus, the simple modified homogeneous model of FIBWR can match the experimental data. It was found that the homogeneous model matched the six-rod bundle data (test section FT-66) of the FRIGC Loop, while this model underpredicted the spacer losses of the 36-rod bundle (FT-36c). The 36-rod bundle data was matched quite accurately using the modified homogeneous model with the modification parameter equal to 1.2. Figure 3-11 illustrates these results.

I I

TABLE 3-1 Geometric Data for FRIGG Loop Test Section FT-36c l l

l I

Number of Heated Rods 36 Heated Length 4365 mm (171.8 in)

Radial Heat Flux _ Distribution Nonuniform Relative Radial 6 Inner Rods 0.854 I Heat Flux Distribution Axial Heat Flux Distribution 12 Interadjacent Rods 18 Peripheral Rods 0.926 1.097 Nonuniform

• Heated Rod, OD 13.8 mm (0.534 in)

I Unheated Center Rod, OD Shroud, ID 20.0 =m (0.787 in) 159.5 mm (6.28 in)

Equivalent Diameter 26.9 mm (1.06 in)

Heated Equivalent Diameter 36.6 mm (1.441 in)

Number of Spacers 8 Chimney Height 155.0 == (6.10 in)

I Operating Pressure Inlet Subcooling Inlet Throttling, Velocity Heads Variable Variable Variable Coolant H0 I 3

• See Figure 3-1.

I I

I I

I I

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Figure 3-2.

Cross-Sectional View of the heater rod arrangement for the FRIGC-LOOP experiments. Geometry consists of one central unheated rod surrounded by 3 5 electrically heated rods. (All dimensions in millimeterr)

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,;  ; ; 16 se 29 Flow quagggy ggy E Fic;ure 3 Comparisons of e f Predictedb,Epk'dFractionVersusFlowOualif,nt

' Zuber Findlay and Homog us Void 'fodels,

I E ~27-

1 m -

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.9 * .

i n

• c . .

, , a d' ** ~

} 40 l .

1 i ..

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20 I .

O O 10 20 30 40 l Equilitnium Quality, percent

Figure 3-4. Cross-sectionally averageti void fraction measurements versus quality for FRIGG Loop cest sections FT-36a and FT-36b.

4

M M M M M M M 100 , , , ,

80 -

3 2 * .

E 60 -

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c .

u. .

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O I ' i i

! 0 10 20 30 40 i Equilibrium Quality, percent Figure 3-5. Void fraction versus quality at 50 bars (725 psia) and 0.25 106 i

lbm/hr-ft2. Data points are FRIGG Loop data; solid line is the prediction l of the Dix correlation.

i l

l l

l

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) 100 , i i i i i i i

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. Prediction of EPlti model .

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l' 0 5 10 15 20 25 30 35 40 l Equihinium Quality, percent I

Figure 3-6. Void fraction versus quality comparison of FRIGG Loop data and the EPRI void-quality model . Pressure equals 1000 psia.

, i i ' ' ' '

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Legend Q run no. 613010 I

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O run no. 613011 O run no. 613001 i

Dix, Sana-Zuber -

10 -

- - - EPRI l

i t t  !  !  !  !

- 0 1

0 20 40 60 80 100 120 140 160 180 Channel Lengtn, inches Figure 3 7 . Voio fraction versus a::ial hei;ht for FRIGG Loop runs with, low inlet subcoo lin::

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Of 7

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Legend l / j O FRIGG Data run no. 613005 f

l / / O F RIGG Data run no. 613006

(

/ / -

10

- f -

Dix. Saha-Zuber

--- EP RI j

/

E /

0  !

O 20 40 60 80 100 120 140 160 180 Channel Length, inches Figure 3-8. FRIGG Loop void fraction versus axial height. Runs with boiling height equal to zero.

t i 6 i i i i i i io 0, /

/

l l

80 -

/

/

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l / O

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70 -

7 l /

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/ -

percent f /

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10 - /

g Dix, Saha Zuber I /

f

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!  ! I I I I I  !

O 0 20 40 60 80 100 120 140 160 170 Channel Length, inches Figure 3-9. Void fraction versus axial height for FRIGG Loop runs with high inlet subceoling.

33

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Pressure = 30 bars (435 PSIA) .

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• lecal 10 -

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i 0 i i '

-5 0 10 20 30 Eauilibrium Quality, percent 20 . . .

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l -

Pressure = 50 bars (725 PSIA)

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Pressure = 70 bars (1015 PSTA)

• 42 .

I local -

5 -

I -5

• t' 0 10 20 30 40 Equilibrium Quality, percent Figure 3-11. Two-phase multiplier for FRIGG Loop spacers. Data points are measured values; solid lines are the predictions of the modified homogeneous I model with the parameter, d, equal to 1.2.

I _ ___

I i 4.0 FIBWR CODE QUALIFICATION STUDIES I 4.1 Oualification Versus Analytical Solution An excellent test of any numerical procedure is to evaluate its predictions for a simplified problem for which an analytical solution may be obtained. It was decided to derive an analytical solution for the case of homogeneous, eauilibrium two phase flow in a vertical, heated tube with uniform axial heat flux. An arbitrary number of local loss locations (spacers) is also included in the analytical derivation.

For the above problem, the nomentun ecuation may be written SD

• Space + iPfriction *aPgravity ^ 2Plocal * (4-1) where an is the total pressure drop ecual to the sum of the components d r.e to acceleration, friction, gravity, and local losses.

I These terms may be expanded to obtain, I 4c =

, Lu

- dZ . (4-2) acc C "

0 2

_ fC  ? d 7. . (4-3)

SUfriction - D 2g p, 11 c < -

o i SU gravity =h s a d 7. . (4-4) l c3 I '

I  :

I l

I l l

1

I E aplocal = cal

• W) 8c~ l _

I where G =

cass flux (lbe/hr-ft2)

Z =

axial distance (ft)

Lg = heated length (ft)

I E = spacer single phase loss coefficient

"" = two phase frictional loss multiplier

= density (1bm/ft3) f = single-phase friction factor D = hydraulic diameter (ft)

H 1

momentum density =

I a =

<X>,' + (1-<X>),-

C g<a) 0;(1-<2>)

9 = gravitational constant (ft/sec )

g c

=

constant relatine force and acceleration (lbm-ft/lbf-sec2)

Each of the above terms will be directly integrated, but first models for void fraction <a(Z)> and flow auality <X> as a function of elevation are needed. For simplicity, thermal equilibrium and uniform axial heat flux are assumed. Thus, <X> is ::ero up until the boiling boundary defined bv an energy balance as ,

x, G Ax -s5h sub , g)

P H"

where

) = subcooled boilin,a initiation location (ft)

I Ax -s

= correctional flow area (ft )

h = inlet subcoolinn (enthalpy) (Btu /lbm) sub I

l 1

l

I I

P H

= heated perimeter (ft) a" = applied heat flux (Btu /hr-ft2)

Extending the energy balance into the two phase region, the quality profile is, a" PH Z nh sub . (4-7)

G Ax -s R fg b fg 1

1 By grouping constant parameters, this may be written, I <x> = F 1 Z-F 3

. (4-8)

I where the constants Fy and F7 are defined by, F1 i H ,g ,

(4_9)

- GA h dZ

-s f h

sub F, i ~

. (4-10)

- h,7 1 It is seen that the quality profile is linear with distance as expected according to the uniform heat flux and thermal ecuilibrium assurotions. Now that cuality is known, the void fraction may be determined I by the Zuber-Findlay relationship, I g, ,

<x> (4-11)

1. R Ri c <x> +O h (1 - <x)) +

g - G The quality profile Equation (4-8) may be substituted into the above relationship to yield, I

I . - - . , - - . . - . . , - . - - - - - . _ . . . . _ _ - - . - . . . . - . - - - - - - - _ _ .

-38

I I <a(Z)> =

1 2 (4-12)

~

o pV .

I _

C,[F7 Z - F2 E

(1 - F yZ + F2 )I a

+ R R c

Or by grouping constant factors, F1 Z - F9 I <2(Z)> = F 5'+

6

. (4-13) where, (4-14) 3 - (1+F.,)h,-F,,

F .

1. Y c ei (4-15)

I F4g - .

F ) Co (4-16) 5h F1 (1 - , _

i F6O_. C F 3+ 4 (0-1 )

!!ow hoth the Joid fraction and quality are known as a function of

2. In the analysis to follow, the F's will all be assumed to be independent of Z. This assumption will limit the analysis to constant Cg and constant V . Recall [6] that the definitions of these parameters are ,

C 1 <3i> . (4-18) o: < a>< i > .

and ,

\

l (4-19)

I <a(u p - j)> ,

y 3

1. i C <a>

I where the < > notation refers to the average of the quantity over the pipe cross section, and E 39-

I I u = vapor velocity (ft/sec) 8 I j = mixture volumetric flow velocity (ft/sec)

I It may be seen from these definitions that as flow quality approaches unity, Cg must approach unity, and V must approach zero. This is because at this extreme, <a> is uniformly equal to unity across the pipe (requiring Cg to equal 1.0); and the vapor velocity (u ) becomes equal to j (requiring g

V to equal 0.0). Thus, to assume constant values of C and V gj other gj o than 1.0 and 0.0 respectively, will give the incorrect limit on void fraction as cuality aporoaches 1.0. In 'act, the Zuber-Findlay relationship will always predict void fraction less than one for quality equal to one if C > 1.0 or V . > 0.0.

o g3 In order to avoid physically unrealistic values of void fraction in this analysis, the void fraction will be set equal to unity whenever flow quality ecuals one. Ecuations (4-2) through (4-4) may now be integrated up the channel. Beginning with the acceleration pressure drop l c- 1 -

1 lE OP ace = cf _n p (LH) cm (0) g _

g2 II - <X(LH}>l <X(Lg )>2 II

+ y OU acc = ( }

(1 - (a(L y ) ).3 1 o <a(LH)>

The elevation pressure drop integral will be broken into two parts, representing the single phase and the two phase regions.

, =g g L.H "U Pravity 0 d 7' JOgA+J I c Using the definition of density [0 =o g - (0 -o c ,,

g)a];

7 lI l

E

I I L I Z -F . E E + O flH -\) - ID -U g

ap ravity " Ec t E t g) ' A Ec c F5Z+F6 With the aid of intearal tables, this may be integrated to yield,

/ E b - IC2 - g) (L H -) ) 61F F5Hl +F6 SPgravity " _ _

F A 3 F2 J5 +F6_

k _

I -

S in

~

" L +r 5H^6

~

. (4-21)

Y I

_5*I6_ /

I 5 In order to evaluate the fricational pressure loss, a model for I ?L w

is recuired. A simple fit to the Martinelli-Nelson model for :2(c 9

is, E 2 f^ \ -1 <X)

+ 1.0 (4-22) 0 ic =C 1. 2- .

7

/ J where C is the mass flux correction factor of Jones, given by, I .36 + .0005p + 0.1 c/106 .000714p G/10 6 f o r G < 0 . 7 .10 6 1.26 - 0004p + 0.110 10 /G 6

+ .00028p G/10 6 for G > 0.7.10 6 lhe where p is in psia and C is in ft -hr I The above model for 4 g is convenient because it is a function only of ouality, which may readily be intecrated. Performing the integration, EUfriction - 3EchDDi

• I (-

~

L f -1 (F1 Z - F 2) 84 dZ

=

Ln + 1.2 C 2Pch!D t b

("I '>, _

I

- - . , _ - ______,~,- .._ _ ---_ _ ._....____ _ _-41-..__.__.._ _ _ _ _ .__ .________ __-

I I

2 0, <X(Lg)>1.824 LH + 1.2 C O-.i - 1 . (4-23) apfriction " 2g D cg7 C g 1.824 F 1 The local losses may be evaluated using the modified honogeneous I nultiplier model of : local" o

aplocal =

1+f <X> . (4-24)

- ?c*z \ f l I 2plocal =

{ , -

1+

fR (F Z - F )

1 3

-\

. (4-25)

(E c 2 -

f -l where the sunnation is over the nunber of spacers present, and :i is the 2

i parameter used to modify the homogeneous nodel for

• local

• Each of the components of the pipe pressure drop, acceleration, friction, gravity, and local are now known as a function of the given input parameters. That is, the a p components of Ecuation (4-1) are given in turn by Ecuations (4-20), (4-23), (4-21), and ( 4-2 5 ) . ':ote the analytical I expressions above are valid only if it is assumed that the densities and enthalpies of both the licuid and vapor, the applied heat flux, and the parametersoC and Vg do not change with axial location. In addition, the ll l

5 models assume homogeneous, equilibriun two phase flow with pure licuid inlet conditions and two-phase exit conditions.

The analytical model has been extended to handle unheated regions I

l both above and below the heated length. This extension of the analysis is nost useful since it also pernits subcooled or superheated exit conditions which were not allowed in the above analysis.

I The analytical model described above was used to predict the pressure I drop in a vertical, uniformly heated tube with subcooled (20 Btu lbn I .- , . - . _ - . . - . - _ . - - - - . . . - - . - - . - . - . -

I I subcooling) liquid water at the inlet at 1020 psia. The void distribution parameter, gC , was set equal to unity; and the vapor drif t velocity, Vg ),

was set equal to zero. The mass flux was varied such that the exit fl ow quality varied f rom unity to zero. There were no local losses modeled.

The analytically calculat'd values of pressure drop for the above case are plotted as solid lines on Figure 4-1.

E The FIBL7 code was used to simulate the same physical situation for which the above analytical predictions were made. In the FIBh? run, the options of homogeneous void quality model, equilibrium subcooled boiling model, and Martinelli-Nelson friction multiplier with the Jones mass flow correction were selected. Thus, the FIBb7 models matched the analytical model in every respect except that FIBb7 computes liquid density as a function of temperature at the imposed pressure instead of assuming constant liquid density as the analytical model. Twenty-four axial nodes were used

,l lB in the FIBWR prediction.

l i

Figure 4-1 displays the FIBkT predictions of the total pipe pressure drnp and of each pressure drop component, and compares them to the analytical solution. It is observed that FIBL7 and the analytical solution agree to within a few percent at every point except for the calculation of acceleration pressure drop at high mass flux, where the pipe exit cond i t io ns were single phase liquid. The analytical model assumes constant liq ui d 1

density, and thus incorrectly predicts zero acceleration pressure drop when the exit conditions are pure liquid, while FIBWR correctly varies the liquid density with temperature and predicts nonzero liquid acceleration.

I E -4 3-

I I 4.2 Qualification Versus COBRA IIIC I The FIBWR momentum and energy equations and their numerical solutions may be verified by comparing the FIBWR predictions to those of an existing, f ully verified computer code, COBRA IIIC [14], for some sample problems in which the two codes rolve exactly the same equations using identical constitutive models. COBRA IIIC and FIBWR solve precisely the same continuity, energy, and axial momentum equations, so long as the transverse flow in COBRA is zero. Of course, COBRA IIIC does not have the capability of handling the detailed BWR geometry that FIBWR allows, nor will COBRA IIIC predict bypass or water tube flows. However, for simple heated, parallel channels with no local losses, COBRA IIIC and FIBWR can be made to solve exactly the same equations if consistent models are selected in the two codes.

As a first effor, a sample problem in the Battelle report describing COBRA IIIC was solved for a variety of mass flow rates using both COBRA IIIC and FIBWR. This problem involves a one-twelf th section of symmetry of a 19-rod bundle. This pie shaped section is divided into five subchannels as illustrated in Figure 4-2.

In order for COBRA IIIC and FIBWR to solve precisely identical problems, it was necessary to " turn off" the transverse flow in COBRA IIIC l

and to select identical void quality and subcooled boiling models in both l

codes. Since both COBRA IIIC and FIBWR allow the use of the homogeneous void quality relation and Levy's subcooled boiling model, these options were chosen for use in the sample problem.

I " cs- c " ~ cc -8c" ~ ~ - ->c" - > -"~~c~

I __

I I COBRA IIIC, the crossflow resistance factor, K, in COBRA IIIC was increased 6

to 10 , and the turbulent =ixing parameter, 6, was set equal to zero. With this input, each COBRA IIIC subchannel maintained constant mass flow as a function of elevation.

Additional parameters of this five-subchannel problem are listed in Table 4-1. Since subchannels number one and three are identical, only one FIBWR channel type was required to represent these two COBRA IIIC subchannels. This is also true of subchannels four and five. Hence, only three FIBWR channels were required for the simulation.

I Both FIBWR and COBRA IiIC were executed for a given total mass flow rate. The two codes then computed by iterative procedures the total pressure drop and the flow rates in each subchannel . The input mass flow rate was varied over a wide range such that the channel exit conditions varied from single phase liquid to an equilibrium quality of unity (FIBWR could not I execute for lower mass flows since it does not allow superheated vapor).

This range of flow conditions permits comparison of the two codes over the entire range of quality.

lI In Figure 4-3, the COBRA IIIC and FIBWR predictions of a p versus 1

mass flow rate for each of the three channel types are shown. It is seen that the predictions of the two codes are always within 10 percent of each

,l

'W other and in most cases, agree much more closely than that. Even though p predictions in two phase flow are much more complex than in single phase l flow the codes disagree more at the high flow rate end of the curve where the flow is single phase '.iquid. This disagreement is likely due to the i differences in steam tables in the two codes. COBRA IIIC input only includes

'I

'I I

I saturated liquid density while FIBWR uses functional fits of liquid density as a function of pressure and enthalpy. The COBRA IIIC and FIBWR predictions of the flow splits in each channel were also in agreement to a corresponding degree of accuracy.

1 1

To be sure that COBRA IIIC and FIBWR agree for a problem which is typical of BWR operating conditions, the predictions of both codes for a 1

f uel assembly of the Quad Cities reactor were compared. Table 4-2 gives l input data used in both computer programs. Since COBRA IIIC requires eeparate input for each heated rod and is limited to a total of 15 rods, a single rod was used in COBRA IIIC to represent the 49 rods in the fuel assembly. Since no conduction calculation was performed inside the rod, this one large rod is identical to FIBWR 's 49 rods so long as the heated perimeter is the same in both cases. Since the axial power profile is not

,I uniform for this problem, it serves as a more sensitive test of the node-to-node values calculated by FIBWR as compared to COBRA IIIC.

1 I Figure 4-4 is a comparison of the predicted channel T. p as a function of mass flow for FIBWR and COBRA IIIC. Once again, the agreement is excellent with discernible discrepancies appearing only at high mass flow where the density of subcooled liquid becomes important to the prediction.

,l l

lE A more revealing comparison is the plot of nodal void fraction values (12 axial nodes) for one of the runs used to generate Figure 4-4 As illustrated in Figure 4-5, FIBWR and COBRA IIIC predictions of the void f raction during subcooled boiling agree reasonably well.

l In summary, the predictions of the FIBWR and COBRA IIIC codes have I been compared for two sample problems. The first sample problem modeled

'I l

I I five parallel flow channels at 2200 psia, and the second sample problem l l

modeled a single fuel assembly of the Quad Cities reactor with local losses neglected (no spacers or tie plates). In both cases, the predictions of '

the two codes agree to within a few percent with the greatest discrepancy occurring in single phase liquid flow where the steam-table values of liquid density are different in the two codes.

I iI I

I I

I ~

I lI il lI l

I l ._

1 TABLE 4-1 1

]g Input for 1/12 Section of a 19-Rod Bundle g

i

! Subchannel Flowgrea Wetted Perimeter Number (in ) (in) i

!W l 1 0.027 0.442 I

}g 2 0.083 0.884 lg 3 0.027 0.442 l

4 0.064 0.935 1

5 0.064 0.935 j Relative Fraction of Power to Subchannel Rod Number Power 1 2 3 4 5 L 1 1.0 0.0833 l 2 1.0 0.1667 0.25 0.0833 3 1.0 0.25 0.1667 0.2916 0.2916 Average Heat Flux = 0.19

• 10 6 Btu ,,

{lW hr ft' I 2200 psia

=

Pressure Inlet Enthalpy = 555.47 Ptu/lba Rod Diameter = 0.563 in Rod Length = 60 in I

I I

I I - - _ - - . _ - - _ _ . - _ _ _ _ _ _ _ _ _ . _ _ . _ _ _ . _ . . _ _ . , _ . _ _ _ . . . . . _ _ _ _ . _ - . _ _ . _ - _ _ _ - _ . ._

l l

l l

l 5l TABLE 4-2 I

g Input for Quad Cities 7x7 Fuel Assembly ,

I Average Heat Flux = 0.11 - 106 Btu i

hr ft2 Pressure = 1039 psia Inlet Enthalpy = 525.0 Btu /lbt Number of Fuel Rods = 49 Active Fuel Length = 144.0 in 4

Assembly Heat Trans Area = 86.66 ft2 Assembly Flow Area = 15.534 in2 Hydraulic Diameter = 0.580 in 0.563 Rod Diameter = in I

I I

l 1

'I II l

I I

I

-4 9 -

l l- , , - - - - . . . . . . _ , - . - . . - - , - . . , _ _ . _ , _ . . - _ . , - . _ _ . . _ _ _ _ _ . - _ .__ __

, I I

Total -____

I 100..

Acceleratien Gravity Irreversib1e

/

/

I 10. O.,

FIBt .'R X 4/

s f

I

/

/

[

/

> , -*- ~ &

s' /

Pressure ,V /

X Drop , /

.g E (psia)

/

i l

/

0.10.

I l

I 0.01 0.I 1.0 10.

21 ASS FLt".

lbm .10' l'

hr ft' Figure 4-1. FIB 1R Predictions of the Total Pressure Drop and Various Pressure Dron Components Compared to the Analytica1 Solution Results.

l

~' ~

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

I I

I I

I I

I e I 4 I -

7

/ - ~ ---- 1 I / 4 2 Subchannel

/ designation

' />n I

I //

I

/1 9 Fuel rod designation I

Figure 4-2. One-twelfth section of symmetry from a 19-rod bundle divided into 5 subchannels.

I I

I -

-,1

1 I

I I

i . . i . i . . i i i a i 6 I hannel 1 3.0 Subchannel 4 _

I l Subchannel 2 I Pressure Drop, I Psi b

I 2.0 - -

Legend A FIBWR O COBRAlilC I 1.0 '

.6

.7.8.91 2 3

4 5 6 7 89 10 Mass Flow,10- 2 (lbm/hr)

II Figure 4-3. Pressure drop versus subchannel mass flow comparison of FIBWR and COBRA IIIC for one-twelfth section of symmetry from a 19-rod bundle.

lI

I I

I j i i i i I i i i

, l i l 12 -

11 -

10 - -

g - _

i l

8 - _

Pressure 7 -

Drop, P5' 6 - L'9'"d -

A FIBWR OCOBRAlilC 5 - -

I 4 - -

3 - -

2 - __

1 _

0 l l l I I I  ! I l I I 2 3 4 5 6 7 8 9 10 20 30 40 Mass Flux,10- 5 (Ibm /hr- ft2)

Figure 4 4 Comparison of FIBWR and COBRA IIIC predictions of pressure drop versus mass flux for a BWR fuel assembly.

I i i i i i i  ; i Legend 2D Pressure = 1,000 psia Mass flux = 0.5 106 lbm/hr-ft2 2)

H+3t flux = 1.5 106 BTU /hr- ft2 -

120 -

/3 -

110 - -

)

100 - -

90 - -

~ ~

Axial Distance, inches 70 - -

60 - -

50 - -

l l

40 - -

A

~ ~

Legend 2

O FIBWR 20 - -

A COBRA IllC 0 + i , , , i i i 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 Void Fraction, Figure 4-5. Void fraction versus height predictions of FIBWR and COBRA IIIC for a Quad Cities fuel assembly.

5.0 FIBWR COMPARISONS TO PLANT SPECIFIC DATA Vermont Yankee Nuclear Power Plant (GE-BWR/4) data was selected for use in the benchmarking calculations performed by the FIBWR code. The fuel and core design data used to develop the Vermont Yankee FIBWR model was extracted f rom appropris te reports and plant specific drawings. The form loss and bypass leakage coef ficients used in the model are based upon the data present in the open literature reports and documents published by EPRI [15], EXXON [16] and CE [17,18]. Almost all of the plant operating data was obtained directly from the process computer output edits.

Three operating states in Cycle 7 as described in Section 5.2.1 were chosen for the FILWR code benchaarking.

I _

The following sections describe the basis for the determination of various FIBWR model inputs. These inputs, although generated for Vermont Yankee, are typical of most other BWR's.

5.1 FIBWR Model Inputs i

i Core thermal-hydraulic analyses were performed using a FIBWR model l

II of the Vermont Yankee reactor core which includes hydraulic descriptions l

l of inlet orifices, lower tie plates, fuel rods, fuel rod spacers, upper tie plates, fuel channel, and the core bypass flow paths. The inlet orifice, lowe r tie plate, fuel rod spacers, and upper tie plate were hydraulically represented as being separate, distinct local losses.

Form loss coef ficients that are input to FIBWR for the inlet orifice

'and loser tie plate were determined f rom the published data in Reference

[15]. Form loss coefficients for the fuel rod spacers and the upper tie I

plates were determined by trial and error until FIBWR predictions of the core support plate pressure drop matched plant measured data. Form loss coefficients for the entrance and exit holes present in the water rods were determined using Reference [19].

The coef ficients for calculating leakage flow through major paths, such as that through the finger springs and lower tie plate holes, are based on full size test data presented by Exxon (16] and CE [20]. The coefficients for the other paths were determined by the use of data presented in Reference

[17).

Details of the procedure used in determining the form loss coef ficients and the leakage coef ficients are described in the following sections.

5.1.1 Inlet Orifice and Lower Tie Plate Form Loss Coefficients The pressure drop characteristics of the central and peripheral region orifices and lower tie plates are presented in Reference [15], as functions of active coolant flow and inlet subcooling.

The form loss coef ficient 'K' for the orifice and the lower tie plate is determined f rom the equation:

lI l

W' 9

, LP = E l 2gcP7 ( 5 -1 )

32 of E* 2 8C y W2 ( 5 -2 )

l where

'I

I I 'l = flow through orifice and lower tie plate (lb/hr) i A =

fuel channel flow area (ft2) i Og = density of the coolant (lb/ft3) 8e = constant relating force and acceleration (Ibn-ft/lbf-sec2)

AP = pressure drop across the orifice and the lower tie plate (psi) l K =

(K F K dimensionless form loss coefficient for the l

orNfce+anFlo)w=r e tie plate, based on the flow area of the channel in question.

Substituting the values of A,a ye g we have, I P = 46.17 1,b_

ft3 (for BWR operating conditions, where P = 1000 psia) ge = 32.174 (lbn-ft/lbf-sec 2 )

A = 15.516 (in2) (fuel channel flow area for 8x8 GE fuel)

I Therefore Equation (5-2) can be written as;  ;

K = (15.516)2 (2 x 32.174 x 144 x 46.17) iP, 144 g2 or l

K = 4966.98 iP W2 (5-3)

I The units of 'W' ts presented in Reference [1], are given in 105 lb/hr, therefore, K = 4966.98 AP (W x 105 )2 3600 or I . . . -

I I K = 6.44 S, ( 5-4 )

W' Reference [15] gives the orifice plus lower tie plate pressure drop as a function of the active flow. Knowing the active flow, an estimate of the total flow entering the orifice was made by assuming that the total bypass flow was 10.0 percent of the active flow going thr:-: ugh the central I region assemblies at full power / flow conditions. According to Reference

[18], 65 percent of the total bypass flow enters the orifice and 35 percent leaks through channel 1idependent bypass flow pa ths. Therefore, for an 5

active flow of 1.2 10 M Ib/hr, the flow entering the orifice equals 1.2 105 + (1.2 x 0.1 x 0.65), or 1.278 x 105 lb/hr. Using Equa tion (5-4 ) and I the orifice plus lower tie plate pressure drop (for the central assemblies which has the orifice diameter of 2.222 inches) for an active flow of 1.2 l M lb/hr [15], we have, I K CENTRAL ORIF + LTP = 6.4 x 9.42 (5-5)

(1.278)'

or I K CENTRAL

= 37.14 lI f K

LTP Knowing the total h d E

'K ', Idel 'Chik [19] was used to estimate the ratio LTP was found to be equal to 0.2558. Using this g g I ORIF ratio and the total ORIF

'K ', the form loss coef ficients for the orifice and

"*" P ** "*"* d***""'"*d * ' " "'*

lE lE l K LTP = 0.2558 (5-6)

K ORIF From Equa tion ( 5-5 ) and Equa tion ( 5-6 ),

l v . _ _

I ytRIF "

• and l

, K t7p = 7.56 Similarly, Reference [15] was used to determine the values of the form loss coefficient 'K' based upon Ecuation (5-4) for the peripheral I

i assemblies in the Vermont Yankee core which has an orifice diameter of 1.488 inches. In this case, an esticate of the total flow entering the orifice was nade by assuming that the total hypass flow was 5.0 percent of the active flow goine throuch the peripheral region assenblies at full power / flow conditions. Therefore, from Reference (15] for an active flow of 0.7 lb/hr and Equa tion ( 5-4 ), we have ,

I v

'7ERIPHERAL

=K ORIF

+K LTP

= 6.44 x 13.946 (5-7)

[(.7) + (.7 x 0.05 x .ti)]2 I or I K = 171.94 Since the lower tie plate design for the central and peripheral assemblies is the same, the form loss coefficient KLTP f r the central and peripheral region assemblies should be eaual.

I Therefore, Kgp (peripheral) = KLTP (central) = 7.56 From Ecuation (5-7),

yPRIF (peripheral) = 171.94 - 7.56 = 164.38 I

I For 7x7 and 8x8R type fuel, the lower tie plate design is the same as for the 8x! type fuel, but the fuel channel flow area for 7x7 and 8x8R is not the same as for the 8x8 type fuel. The refo re , the value of kTP and K f r the 7x7 and 8x8R type fuel must be corrected:

ORIF Ec r 7x7 or 8x8R central 4.ssemblies;

^ hannel Flow Area 7x7 or 8x8R I K GRIF

=K ORIF (8x8 central)

A Channel Flow Area 8x8 I For 7x7 or 8x8R peripheral assemblies; A

K =K Channel Flow Area 7x7 or 8x8R ORIF ORIF (8x8 peripheral) ,

Abnannel Flow Area 8x8 For 7x7 or 8x8R central and peripheral assemblies; I Y 1TP

=K LTP(8x8)

^ hannel Flow Area 8x8 or 8x8R

^ Channel Flow Area 8x8 I

Table 5-1 shows the summary of kRIF' kTP f r 7x7, 8x8, and 8xBR type fuel assemblies.

I 5.1.2 Spacers and Upper Tie Plate Form Loss Coef ficients I The FIBWR code was used as a tool to estimate the form loss coef ficients for the spacers and upper tie plates. Knowing the form loss coefficients for the orifice and the lower tie plate, sensitivity runs were made with FIBWR code by varying the spacer and upper tie plate fo rm los; coefficients until agreement was reached between the FIRWR predictions and the measured values of the core support plate pressure drop. The spacer I __

-6 0 -

I and upper tie plate form loss coef ficients thus determined are given in Table 5-1.

5.1.3 Water Tube Entrance and Exit Loss Coefficients I FIBWR calculates the water tube flow consistent with the pressure drop of the active coolant parallel to the water tube. The 8x8 fuel bundle contains one water rod and the 8x8R f uel bundles contain two water rods.

These ,ds are hollow, Zircaloy tubes with several holes drilled around the circumference near each end.

Three holes with a diameter of 0.089 inch for the 8x8 and 0.116 inch for the 9x8R fuel designs are located at the bottom of the water rod, and eight holes with a diameter of 0.188 are located at the top. Idel'Chik

[19] was used to calculate the entrance and exit loss coefficients. The bottom and top holes in the water rods were assumed to be smooth, converging, bellmouth, made by an are of a circle with end wall (not sharpened). The I entrance and exit loss coef ficients for the water rods in 8x8 and 8x8R fuel designs are given below:

l Fuel Type Entrance 'K' Exit 'K' 8x8 75.14 0.533 8x8R 63.4 1.3 1

It should be noted that the water rod loss coefficients are based on the flow area of the water rod itself (FIBWR computes the losses associated with the water rods using the mass flux 'G' based on the water rod flow area), and not on the channel flow area.

I I

5.1.4 Leakage Coef ficients for Bypass Fhv The leakage paths to the bypass region foi a typical BWR geometry, are shown in Figure 1-2.

The leakage flow through the bypass flow paths is expressed by the I form:

W=C 1 aPl/2 + C y aP'+C 3 SP 2

( 5 -8 )

where W = flow through the leakage path (lb/hr)

SP = driving pressure differential for the leakage path ...

(psi)

C ,C ,C ,C = analytically or empirically determined constants 1 3 3 4 I The total bypass flow is, the refo re , the summation of all the leakage flows through various paths presented in Table 5-2.

Fo r mo s t o f t he BWR 's , a total of six bypass flow paths (see Figure E

lB l l-2) can be used to account for the total bypass flow. The following seven bypass flow paths were considered in the Vermont Yankee FIBWR model:

l l o Path 1 of the FIBWR model was used as a lumped representation of

'E Path la, Ib, 2, and 5 of Table 5-2. This path will be referred to as a control rod dependent path.

o Path 3 of the FIBWR model represents the leakage path between the core support plate and the in-core instrument support guide tube.

(Same as Path 3 in Table 5-2.)

o Path 4 of the FIBWR model accounts for leakage flow between core suppo r t plate and shroud. (Same as Path 4 in Table 5-2.)

E o Path 6 of the FIBWR model refers to the leakage path between fuel suppo r t and lower tie plate. (Same as Path 6 J n Table 5-2.)

I I

o Path 8 of the FIBWR model represents the leakage path between fuel channel and lower tie plate. (Same as in Table 5-2.) This path will be referred to as a finger spring path.

o Path 9 of the FIEWR model will represent the leakage flow path due to the holes in the lower tie plate. (Path 9 in Table 5-2. )

o Path 10 of the FIBWR model represents the leakage flow due to the bypass flow holes in the core support plate. (Path 10 in Table 5 -2 . )

The pressure drops used to evaluate Equation (5-8) are functions I of channel pressure differential (P active

-P bypass), and are evaluated at the lower tie plate and fuel support interface, the lower tie plate holes and the channel to lower tie plate interface (FIBWR Paths 6,8,9). The other paths (with the exception of t'ne control rod drive flow, which is user input) are functions of the pressure differential across the core support plate.

The following sections describe the procedure used in determining the constants C through C 3for various bypass flow paths, represented in 1

the FIBWR model of the Vermont Yankee reactor core.

I 5.1.4.1 Path 8. Between Fuel Channel and Lower Tie Plate (Finger Spring Path)

Finger springs are employed to control the bypass flow through the channel-to-lower tie plate flow path for all the fuel assemblies present in the Vermont Yankee core. The coef ficients for flow through this major path are based on test data obtained from Exxon Nuclear [16].

A simulated GE type channel-to-lower tie plate finger spring seal and a tie plate having two 9/32 inch diameter holes, have been leak tested by Exxon Nuclear in the Portable Hydraulic Test Facility (PHTF). A mock-up of the test is sho"n in Figure 5-1. The test was conducted by adjusting I .es.

I I

the loop flow to repeat a common in-bundle pressure drop (Taps C-D, Figure 5-1), using different seal combinations. The difference in the loop flow was assumed to be the leakage flow. The results of the test are as summaris:ed in Table 5-3. The test indicated that the leakage flow through the finger sprinF path was approximately one-third of the total leakage flow.

I Knowing the flow through the finger sprinc path and the driving I pressure differential, an attempt was made to fit the data (LP versus in the form:

b)

FS

.I 'J 73 = 0 /T7 LP" (5-9) lI where 0,n = constants

\;79 = flow through H nger spring path ( M n iP = driving pressure differential for the finger spring path (psi)

2 = licuid density (lb/f t3)

Usine a power function fit (see Figure 5-1A) by the method of least sauares, the values for 'O' and 'n' were found to be; I n = 103.3 n = 0.7106 Therefore, the leakage flow through finger springs can be calculated l

using Ecuation (5-9),

I le gg = 103. 3 [7aP.7106 (5-10)

I

-e .

g

l I

I Assuming for B'w'R operating conditions ,

I 3

p = 46.17 lb/ft ve have l

l PFs = 702 AP'7106 (5-11) l i

Ecuation (5-11) is a form of Ecuation (5-8) where i

Cy = 0.0 l C.3 = 702 C3 " 0*O c, = 0.7106 I

~

5.1.4.2 Path 0 Bvnass Flow Holes in the Lowe r Tie Plate '-

I There are two 0/32 inch dianeter holes in the '.3wer tie plate assenbly for each fuel bundle in the Vermont Yankee core. These bypass flow holes were not present in the earlier cycles of the Vermont Yankee l

core. These holes were drilled to provide an alternate flow path following the pluering of the bypass flow holes in the core support plate to avoid excessive vibration of the incore instrumentation [20].

I The flow throuch these lower tie plate holes can be determined froc.

the ecuation:

W2 I AP = E-A' 2 go g (5-12) or 2"d2_ 1/2 1/2 "LTP " ' 2F D #

- cE (5-13) 1 g - - -

65-

l I \

I where I'

WLTP = fl w throuch 2 lower tie plate holes (lb/hr) l d = diameter of lower tie plate holes (in) l l

t K = loss coefficient of lower tie plate holes (dimensionlesa) og = density of coolant (lb/in 3) iP =

driving differential pressure across lower tie plate holes (psi)

AccordinF to GE [20], the form lo,s coefficient _ 'K' for the lower tie plate holes was experimentally determined to he 1.3.

From Ecuation (5-12), for LTP holes with 9/32 inch diameter, I ULTP = 1783 iP' (5-14)

Equation (5-14) is a form of Ecuation (5-8) where, C1 = 1783 C.,,C s 3 .c- = 0.0 5.1.4.3 (Pa Ns la,1b,2,5) Leakace Paths Due to Control Rod Drives and Guide l Tuboc l

l These leakage flow paths are due to control rod drive housings and l puide tubes. The cuantity of these paths will, therefore, he equal to the number of control rods. Vermont Yankee has 89 control rods. In the Vernont Yankee FIBWR model, Paths la, 15, 2 and 5 are lumped together to represent i

one single path. Reference [17] was used to determine the leakage coefficients for this representative path.

I I _ _ _ - _ _ . . - . - - - - . - _ . . . . . _ , - . . - . . - - _ - . - - - - - .

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

t I

I Table 5-4 presents the leakage flow fractions - taken from Reference l

I T17] - for bypass flow paths present in the Vermont Yankee reactor after s

the core support plate holes were plueged. Bypass flow holes in the lower tie plate were not present.

From Table 5-4, the sum of flow fractions for Paths la, Ib, 2 and l

5 is ecual to 0.4722 of the total. The finw fraction of the finger spring path is ecual to 0.433 of the total. ,

l .

t

' Therefore, the flow fraction of Paths la, lb, 2 and 5 eauals 0

• 4 7" , "

l 0.433 or 1.066 of the flow through the finger spring path.

(* sing Equation (5-11) and Ecuation (5-8) with C ,C 3 ,Cc 3 equal to I

O.0, the total leakage flow across Paths la, Ib, 2 and 5 in terms of the I

total leakage flow across fincer spring paths can be expressed as:

(A/P.) x 1.nAA (702 P.7106) = C 1 2P' (5-15) where I A = nunber of fuel bundles l

l l R = nunber of control rods lD = drivine pressure differential (psi)

I C1 = constant fron Equation (5-R)

For the Vernont Yankee core, the driving, pressure differential for l

t,e finner spring path was estimated to be 10.5 psi, which was later found to be a good assunption. Core support plate pressure drop of 19.0 psi -

which is the drivirr pressure differential for Paths la, Ib, 2 and 5 - was taken from the F1 edit of the process computer at near full poutr and flow I __ . _ .

I

.I I conditions. Vermont Yankee, like most other BWR's, has instrumentation for measuring the pressure drop across the core support plate. Core support l plate pressure drop taken from P1 edit is, therefore, a plant specific nessured value.

Substituting the appropriate values in Ecuation (5-15),

l I 368 x 1.066 [702 (10,5).7106] = C1 (19.0).5 x 39 ,

.'. C1 = 3744.0 Therefore, the leakage flow across Paths la, Ib, 2 and 5 can be determined as follows, 1'la ,15,2&5 = 3774.0 iP '" (5-17)

Ecuation (5-17) is a form of Equation (5-8) where: l C1 = 3774.0 C2,C3,C3= 0.0 I The ratio of control rods to fuel hundles (A/B) is fairly uniforn j for nost BUR's. The leakage flow for control rod dependent paths can, therefore, he calculated by usine Ecuation (5-17) for most BWR's.

5.1.4.4 Path 6. Fuel Support and Lower Tie Plate This leakage path is between the lower tie plate and fuel support casting. Reference [17] was used to determine the leakage coefficients for this path. l' sine the procedure outlined in the preceeding section (see Table 5-4), the flow fraction of the finger sprine, path is equal to 0.443 of the total. The flow fraction of Path 6 is eaual to 0.029 of the total.

7 I _ _ _ ~ .___ - _ - -..._ . _ _. . .,.... _ _ _ _ . .. - ._ _ __ ,_._ _. _ _.. _...._.._ _ ._ .. .___ __ _ __. _ _ _.

68

!I I

I Therefore, the flow fraction of Path 6 equals 0.029, or 0.0655 of 0.443  ;

I the flow through the finger spring path.

Using Ecuation (5-11) and Ecuation (5-8) with C2 , C , C4 equal to 3

0.0, the total leakage flow across Path 6 in terms of the total leakage flow across finger sprine paths can be expressed as:

06 55 [ 7(>2 (LP ) . 7106 ] = C1 (2) M 8) where C = constar! fron Equation (5-8) 1

.'.P = driving pressure differential (esi)

Assuming that the driving pressure differential is the same for Path 6 and the finger sprine path (the dif fet ence between the driving pressure differential for these paths is about 0.5 psi and can he neglected) we have, C1 = 0.655 702(10,5).7106 (5-19)

I C = 75.0 1

(10.5).5 Therefore, the leakage flow across Path 6 can be determined as i follows, k'6 = 7 5 ap . 5 r.-20)

I Fouation (5-20) is a form of Ecuation (5-8) where, C1 = 75.0 I

I or------r,,--,- .- - . ~ , . n,. .-.

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

I C,C,C4 2 3 = 0.0 5.1.4.5 Path 3. Core Support Plate-Incore Guide Tubes

, I *his path represents the leakage flow through the penetration i

provided in the core support plate for incore instrumentation. The number I

of flow passages represented by Path 3 is, therefore, equal to the number iE of instrunent guide tube (startup, intermediate and power range) locations

!E i in the reactor core. Vermont Yankee has a total of 30 such locations.

t Reference [17] was used to determine the leakaFe coefficients for Patb 3 using the procedure outlined in Sections 5.1.3.2 and 5.1.3.3.

From Table 5-4, the flow fraction of the finner springs is equal to 0.433 of the total. The flow fraction of Path 3 is equal to 0.0048 of the total.

I 0.0048 , or .01084 Therefore, the flow fraction of Path 3 eauals 0.433 of the flow through the finger spring path.

l' sine Ecuation (5-11) and Equation (5-R) with C2 , C 3, and C3 equal to G.0, the total leakage flow across Path 3 in terns of the total leakage I flow across fineer sprine paths can be expressed as:

I A (.01084) [702 (LP)*7106] = C 1 (AP)*' D (5-21) where, F

g A = number of fuel bundles D = nunber of incore instrumentation locations I - , . . - . - . . - . - . . . - - . . . . . . . - . -

I LP = driving pressure dif ferential (psi)

I C 1 = constant from Ecuation (5-8) l Vermont Yankee has 36R fuel bundles and 30 incore instrumentation locations; therefore, 368('01084) (702 (AP) )=C1 (aP).5 30 (5-22) f The core support pressure drop was estimated to be 19.0 psi - which i

is the driving pressure differential for Path 3 - and the driving pressure differential for finger spring path is 10.5 psi as explained earlier, therefore, C1 = 114.0 I The leakage flow across Path 3 can be determined as follows, m, = m .e me.5 (5-23>

I Eauation (5-23) is a form of Ecuation (5-8) where, C = 114.0 C2 ,C3'C 4 =0.0 5.1.4.6 Path 4 Core Support Plate-Shroud The core support plate is bolted onto the bottom of the core shroud.

Path 4 accounts for the leakage flow between the core support plate periphery and the bottom of the core shroud. There is one Path 4. Reference [17]

was used to determine the leakage coefficient for Path 4 using the procedure

}

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

outlined in Sections 5.1.3.2 through 5.1.3.4.

i From Table 5-4, the flow fraction of the finger springs is equal to 0.433 of the total. The flow fraction of Path 4 is equal to 0.037 of the total.

Therefore, the flow fraction of Path 4 equals .037, or 0.0835 of

.433 the flow through the finger spring path.

Usine Equation (5-11) and Equation (5-8) with C2, C ,3 C4 equal to 0.0, the total leakage flow across Path 4 in terms of the total leakage flow across finger spring paths can be expressed as:

A (.0835) [702 (aP).7106) ,c (gp).5 (5-24) where, A = nunber of fuel hundles C1 = constant from Equation (5-8) iP = driving pressure dif ferential (psi)

As before, assunine that the core support plate pressure drop is 14.0 psi - which is the driving pressure for Path 4 - and that the drivinc pressure differential for finger spring path is 10.5 psi, l

1 106 C1 - A( .0R3 5 ) 702 (10. 5) . (3-25)

(19.0)"' )

or  ;

g C1 = 72.0 A ' 3-2 6 )

The leakage coefficient C 1 for Path 4 is, therefore, expressed as I .- - . . - . - . . - .

I a function of the number of fuel bundles in the reactor core.

I Vermont Yankee has 368 fuel bundles; therefore, I C = 26446.0 The leakage flow across Path 4 can now be determined as follows, U4 = 26496.0 aP.5 (5-27)

Equation (5-27) is a form of Equation (5-8) where, C

7

= 26496.0 C

2'C3'C4=0.0 I 5.1.4.7 Path 10. Rypass Flow Holes in the Core Supnort Plate Bypass flow holes in the core support plate have been plugged in order to eliminate the incore vibration [201. According to Reference [17),

the contribution to the bypass flow from leakace around the plugs is small and can be neglected. Path 10, therefore, will not he represented in the Vermont Yankee FIBUR nodel.

5.1.4.R Sunnarv of Leakage and Form Loss Coefficients l

l Table 5-5 presents the sunnarv of the leakare coefficients C1 throuch 1

determined in the previous sections that can be used in Ecuation (5-S)

C4 for calculatine leakage flows for various leakage paths. However, no attennt was made to explicitly account for channel aging and crud buildup effects on the leakaPe flow in developinn the leakage coefficients. It should be noted that the basis for deternining the leakage coefficients was the I

underlying assumption that all the fuel bundles present in the reactor core had finger springs (most operating Bb'R's have finger springs) between the channel - Lower Tie Plate (Path 8) flow path. According to Reference [18),

the fraction of the total bypass flow through Path 8 without finger springs would be considerably different than with the finger springs. Therefore, it would be incorrect to use the leakage coefficients from Table 5-5 to calculate the bypass flow for Bb'R's that do not have finger springs.

I The form loss coef ficients for the inlet orifice, lower tie plate, spacers, upper tie plate for 7x7, 8x8, and 8x8R type fuel design are shown in Table 5-1.

I As described in the earlier sections, the form loss coef ficients

_ for the central and peripheral region orifices and lower tie plates were determined based on Reference (15]. To compare and verify against Reference

[15], FIBb'R was executed to reproduce the pressure drop characteristics of the central and peripheral region orifices and lower tie plates. Figures 5-2 through 5-5 present the comparison of the pressure drop characteristics of central and peripheral region orifices and lower tie plates as a function of active flow and core inlet subcooling.

I Figures 5-6 through 5-11 present the FIBWR predicted pressure drop characteristics of 7x7, 8x8, and 8x3R type fuel assemblies as a function of active coolant flow, active coolant power, and inlet subcooling. These pressure drop characteristics were generated using:

o form loss coefficients for spacers and upper tie plates from Table 5 -1, o an axial power distribution peaked at the middle with a peak-to-average value of 1.5, o the system pressure equal to 1035 psia, o recommended models in FIBWR which are, I Baroczy for the 2 phase friction multiplier Blausius relationship for the friction factor 'f' with constants A = 0.1892 and B = .2041 [21]

Modified homogeneous model for the 2 phase form loss multiplier EPRI-VOID model for the void quality relationship EPRI-VOID model for the initiation of subcooled boiling 5.2 Vermont Yankee (VY) Comparisons A FIBWR model was developed for Vermont Yankee in order to verify FIBWR code predictions against plant measured data. Like most BWR's, Vermont Yankee has core support plate pressure drop instrumentation that measures the pressure dif ferential across the core support plate. This measured core support plate pressure drop can be obtained from the process computer P1 edit. The goal was to compare the FIBWR calculated core support plate pressure drop to the measured value using the input parameters developed in Section 5.1.

I The core support plate pressure drop calculated by FIBWR is the pressure dif ferential (P -P y 3) between the inlet to the orifice and the top of the core support plate as shown in Figure 5-12. Plenum to Plenum pressure l

I drop calculated by FIBWR is the. pressure dif ferential (P -P 7) between the inlet to the orifice and the top of the chan.;el.

The core pressure drop instrumentation (22] measures the pressure dif ferential across the core support plate which can be identified as P 3-P3 l in Figure 5-12. In order to compare FIBWR predictions of the core support plate pressure drop with the measured value, a correction was applied to the measured value to account for the elevation dif ference between Pyand P The elevation head is the product of the average density of the coolant 4

I I and the height difference between P1 and 4P . The relationships are as follows (see Figure 5-12):

Core Support Plate SP FIBWR =

Pi -P3 (psi)

=

Pi -P2 (psi)

Plenum to ?lenun SPFIBWR Core Support Plate APMEASURED = P4 -P3 (psi)

" x ( 5-28 )

Core Support SP ACTUAL Measured -O t I w here i o x = correction factor (psi) g 0, = density of coolant (lb/ft )

x = elevation difference between P4 and P3 (inch). For operating conditions in a RWR, assuming, c = 46.17 (1b/ft3) e,x = 16.36x46.17 = 0.45 (psi) 1728

.. iP - 0.45 (psi) (5-29)

ACTUAL " fEASURED The actual value of the core support plate pressure drop is, therefore, 0.45 psi less than the measured value printed in the process compu ter P1 output .

I 5.2.1 Description of VY Test Conditions and FIBWR Model Innut l

Three operating state- o :-+ .t Cpele 7 were selected for the FIRWR 1

code benchnarkine study. O. cat 3 states selected for Cycle 7 represented I current core conditions. The reactor cora had mixed 8x8 and 8x8R type fuel assenblies. All the fuel assemblies had holes drilled in the lower tie

I plates.

Table 5-6 presents the Vermont Yankee plant specific data and rated conditions. Vermont Yankee core has 368 fuel assemblies. Assuming core symmetry, a quarter of the core was modeled by 92 characteristic channel types. In the FIBWR model, 15 characteristic channel types represented the peripheral fuel assemblies and 77 characteristic channel types were used to model the central fuel assemblies. Figure 5-13 shows the core plan view during Cycle 7.

Table 5-7 identifies the total number of fuel assemblies, number of fuel assembly types, core thermal power, dome pressure, core flow, core inlet subcooling, e tc. , used in the FIBWR model for Cycle 7.

I The assembly axial and radial power distributions were taken from the 3-D nodal code SIMUIATE [2]. Although individual assembly axial and radial power distributions were used in the FIBWR model, only the core average axial power distribution for each case analyzed is shown in Figures 5-14 through 5-16. The core thermal power, core flow, dome pressure, and core inlet subcooling were taken directly from the process computer P1 output.

i Form loss coef ficients for inlet orifices, lower tie plates, upper tie plates and spacers were taken from Table 5-1. Figure 5-17 shows the g spacer midpoint elevations above the bottom of active fuel. Leakage l

coefficients C through C 4for the leakage flow paths were taken from Table 7

5 -5.

I Monte Carlo calculations [23] were performed to estimate the neutron I

I and gamma energy deposition in the bypass region and water rods. The total energy deposited in the bypass region and water rods (as used in the FIBWR model) is given in Table 5-7.

In all cases, FIBWR was executed to calculate the core pressure drop and bypass flow for a given total core flow.

I 5.2.2 Results of FIBWR Comparisons to Vermont Yankee Data I Results of the FIBWR code predicticus and measured values of the core support plate pressure drop for the cases analyzed are shown in Table 5-8. The measured values of the core support plate pressure drop were taken directly from the P1 output and were corrected for the elevation differences t consistent with the procedure outlined in Section 5.2.

The total bypass flow calculated by FIBWR for the cases analyzed l is also shown in Table 5-8.

1 1

1 It can be seen that the FIBWR predictions of the core support plate l

pressure drop agree very well with the measured values.

l l

I I

I

I lI lI l

l

-7 8 -

TABLE 5-1 I Form Loss Coefficients Used in FIBWR Summary of the form loss coefficients for orifices, lower tie plates, spacers, upper tie plates, I I entrance and exit holes for water rods.

, FUEL TYPE 1

lg Form Loss Coefficients 7x7 8x8 8x8R 3

Orifice Central 29.65 29.58 30.77 I K ORIF Peripheral Central 164.76 7.58 164.38 7.56 170.99 7.86 Lower Tie Plate K

LTP Peripheral 7.58 7.56 7.86 Spacers 1.21 1.38 1.24 I K SPA Upper Tie Plate 1.35 1.41 1.46 K

UTP Water Rod IIole Water rods K

WR Entrance not present 75.1 63.4 Exit 0.5 1.3 NOTE 1. 'K's for the Orifice, Lower Tie Plate, Upper Tie Plate, and Spacers shown above are based upon the flow area of tha fuel type they are listed under.

NOTE 2. 'K's for the entrance and exit of the water rods are based upon the flow area of the water rod of the fuel type they are listed under.

I I

I I _ _ _ - . - .- . . . _ , _ -

I TABLE 5-2 Bypass Flow Paths Flow Path Description Driving Pressure Number of Paths la. Between Fuel Support Core Support Plate One/ Control Rod and the Control Rod Differential Guide Tube (Upper Path) lb. Between Fuel Support Core Support Plate One/ Control Rod and the Control Rod Differential Guide Tube (Lower I Path)

2. Between Core Support Core Support Plate One/ Control Rod I Plate and the Control Rod Guide Tube Differential I 3. Between Core Support Plate and the Incore Instrument Support Core Suppo rt Plate Differential One/ Instrument Guide Tube

4. Between Core Support Core Support Plate One Plate and Shroud Differential I 5. Between Control Rod Core Support Plate Guide Tube and Control Differential One/ Control Rod Rod Drive Housing

6. Between Fuel Support Channel Wall Differ- One/ Channel I and Lower Tie Plate ential Plus Lower Tie Plate Differential

7. Control Rod Drive Independent of Core One/ Control Rod Coolant

8. Between Fuel Channel Channel Wall One/ Channel and Lower Tie Plate Dif ferential

9. Holes in Lower Tie Channel Wall Differ- Two/ Fuel Assembly I Plate ential Plus Lower Tie Plate Grid Dif ferential

10. Bypass Flow Holes in Core Support Plate Plant Dependent the Core Support Plate Dif fe rential I

I

i I

TABLE 5-3 l

Exxon Data Reduction I I Leak hFlow f.P (Taps A-B)

Total Leakage Through Finger Across Finger FS Flow lb/hr Spring Path lb/hr Spring Path (psi)(unsealed)

{

6794 2264 4.5014 291.17 l 3 g 7003 2334 3.9516 300.17 242.55 5659 1886 3.0525 i 4471 1490 2.3821 191.63 3584 1195 1.8007 153.69 6787 2262 4.3355 294.99 5506 1935 4.0418 252.34 E 3.2543 233.04 15 5362 1787 5207 1736 2.7467 226.39 4075 1358 2.2929 177.10 I 3273 1091 1.5641 142.28 I *: = Liquid density (lb/ft3)

I I

I I

I I

I

TABLE 5-4 I Summary of Flow Fraction Through Bypass Flow Paths at Rated Power and Flow Fraction of Path No. Path Description Bypass Flow 8 Lower Tie Plate - Fuel Channel 0.443 (Finger Spring Path) 2 Core Support - Control Rod Guide Tube 0.0937 I la Fuel Support - Control Rod Guide Tube (Upper) 0.0600 I lb Fuel Support - Control Rod Guide Tube (Lower) 0.3172 3 Core Support - Incore Inst. Guide Tubes 0.0048 6 Fuel - Support - Lower Tie Plate 0.0290 5 Control Rod Guide Tube - Control Rod 0.0013 Drive Housing 4 Core Support - Shroud 0.0370 Control Rod Drive Coding Flow 0.0140 TOTAL 1.0000 I

I I

I I . _ . . - . . - . , _ _ . -. - . _ . _ .

I YABLE 5-5 Summary of Leakage Coef ficients for Various I Bypass Flow Paths Flow Path Description C' C' C L C l

Channel-Lower Tie Plate (Finger Spring Path or Path 8) 0.0 702.0 0.0 .7106 Lower Tie Plate Holes j (Path 8) 1783.0 0.0 0.0 0.0 Between Fuel Support and Lower Tie Plate (Pa th 6) 114.0 0.0 0.0 0.0 Control Rod Dependant Paths I (Paths la, lb, 2, 5 lumped as one Single Path) 3774.0 0.0 0.0 0.0

'g Between Core Support Plate and g Incore Support Instrument Guide Tube (Path 3) 73.0 0.0 0.0 0.0 Between Core Support Plate and Shroud (Path 4) (see Note 1) 72.0xA 0.0 0.0 0.0 llB NOTE 1: The leakage coefficient C is determined as a function of the number 1

l of fuel bundles in the reactor core. (A = number of fuel bundles) l I

,I l

l I

I

I TABLE 5-6 Vermont Yankee Plant Specific Data and Rated Conditions Core Thermal Power 1593 Mwt Core Flow 48 M lb/hr Total Number of Fuel Assemblies 368 Number of Control Rods 89 I Number of Incore Instruments 30 Number of Central Assemblies 308 Number of Peripheral Assemblies 60 inlet Orifice Diameter for Central Assemblies 2.222 inch Inlet Orifice Diameter for Peripheral Assemblies 1.488 inch Number of Spacers in Each Fuel Assembly 7 lI I

I l

l I

I I

I I

g .e4

I I TABLE 5-7 I Vermont Yankee FIBWR Model Data For Cycle 7 I Total 7x7 8x8 8x8R I Total Number of Fuel Assemblies Number of Central Assembliec Number of Peripheral Assemblies 152 156 368 308 60

{g 60 Active Fuel Length (inch) -

144 150 -

!E Number of Bypass Flow Paths - - -

6 Power Deposition in the Bypass Region 2% of Total Thermal Power l

Power Deposition in the Water Rod (8x8) .03% of Total Thermal Power 1

Power Deposition in the Water Rods (8x8R) .07% of Total Thermal Power CASE 1 (Operating State 1 for Cycle 7)

Core Thermal Power 1541.23 Mwt Total Core Flow 47.88 M lb/hr I Steam Dome Pressure Core Inlet Subcooling 1016.3 psia 24.70 Btu /lb CASE 2 (Operating State 2 for Cycle 7)

Core Thermal Power 1438.0 Mwt Total Core Flow 40.1 M lb/hr Steam Dome Pressure 1024,9 psia Core Inlet Subcooling 28.5 Btu /lb CASE 3 (Operating State 3 for Cycle 7)

Core Thermal Power 1059.9 Mwt Total Core Flow 22.63 M lb/hr Steam Dome Pressure 1005.8 psia Core Inlet Subcooling 40.5 Btu /lb I

I I

I I -

I l

l I TABLE 5-8 Results of FIBWR Comparisons to Vermont Yankee Data i

Core Support Powe r/ Flow Bypass Flow

( Plate SP (psi)  % Rated  % of Total Core Flow CASE NO. (CYCLE 7) g 1. FIBWR 18.94 97/100 g MEASURED

• 18.76 10.66 l 2. FIBWR 13.31 90/84 10'48 l MEASURED 13.31 _

3. FIBWR 3.67 67/47 7.90 MEASURED 3.62 --

,

• Measured value as outlined has been in Section 5.2.corrected to account for the elevation dif ferences I

.I I

I I

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~"'~

E

I I

I I k i;PPER TIE PLATE I ,

O 5 I N PRESSURE TAP 2

I I G

• N SPACER (7)

Y

s TEST CHANNEL I CHANNEL / TIE PLATE GAP g I BYPASS HOLE (2) l D

UI C: '

s LOWER TIE PLATE I r]

INLET HARDWARE lI lE Figure 5-1. A mock-up of the fuel bundle for leak tests at t B Exxon's PHTF.

I i

l I 1

~

l _

G Data Points at 2500F O Data Points at 1500F t

310

• Least Squares fit to the Data

! 300 -

6 I 290

~

6 280 l 270 0

l -

260 _

250 _ O I 240 _ O i ~

230 _ O O

"fs 220 _.

i l 210 _

l 200 -

I

180 l -

l - O

= 170 _

I

?

150 _

I 140 ,f . 1 ,

IW l , I i i , ! , # , I  : 1 . i , ! ,

.2 .6 1.0 1.4 1.8 2 ' 2.6 3.0 3.4 3.8 4.2 4.6 5.0 5.4 Pressure Different.al Across Finger Spring Path (psi)

I Figure 5-1A.

Least Squares Fit *o the Exxon data.

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.I lI I Top of Core I h

p t ,2 I 4 ZCHI 4

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3 e Core Support Plate B ttom 9 f M.

! Core g g7t.

l Fuel Suppor V

=16.36 incn. 7 i f x Pressure drop 1

I Core Lenzth = ZCHI -

Fuel Leneth + ZGEO dp j g instrumentation Fuel Length = ZCHA + ZHET + ZUHB

,I Fig,ure 5-12. A diacram showing Vermont Yankee core pressure drop Instrumentation and Pressure points that FIBh'R calculates for estimatine core support plate and plenum to plenum pressure drop.

'I I

!E lu

I I

I I 2 3 4 5 6 7 8 9 10 ll I 8X8 8X8 8X8 8X8 8X8 8X8 8X8 8X8 8X8 8X8R 8X8 12 13 14 15 16 17 18 19 20 21 22 l 8X8 8X8 8X8A 8X8 8X8R 8 X SSX8R 8 X 8 8X8A 8X8R 8X8 23 24 25 26 27 28 29 30 31 32 33 l 8X8 8X8R SX8 8X8R 8X8 8X8R 8 X8 8X8R8X8R 8XSR SX8 34 35 36 37 38 39 40 41 42 43 l

8X8 8X8 SX8R 8X8 8X8R SX8 8X8R 8X8 8X8R 8X8 l 44 45 46 47 48 49 50 51 52

8X8 8x8R 8X8 8X8R 8X8 8X8R 8X8 8X8R 8X8 53 54 55 56 57 58 59 60 61 I 8X8 8X8 8X8R 8X8 8X8R 8X8 8X8R SX8R 8X8 g 62 63 64 65 66 67 68 69 70 SX8 8X8R 8XS SX8R 8X8 8X8R 8X8R 8X8R 8XS l 71 72 73 74 75 76 77 78 8X8 8X8 SX8R 8X8 8X8R8X8R,8X8R 79 80 81 82 83 84 85 8X8 g 8X8 8X8R 8X8R 8X8R 8X8 8X8 8X8 86 87 88 89

( BX8R 8X8 R8X8R 90 91 92 8X8 I 8X8 8X8 8X8 I

I Figure 5-13. Quarter Core Plan View of Vermont Yankee Reactor durine Cvele 7.

I

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x

~

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A l e s 1 _ __ - -

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v f &  := a:.

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-101-I

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c e e o e o e o e o e

=

I (P32TI m oN) lamod IeixV a'dela^V 8203

-102-

I I 6

t t

1 t

1 i

I i

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i i

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c i t. - - 2

= -

- ~

=

l -=

i l -

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• _ v y ,

t -

p

~

i O *-

l -

. - =

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-- O - -

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< 2 I

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~ N x I

l i L l

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1 I

l I *

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t i .

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( Pa2 TIeutaos) a ar.od IUTXV d ela^V 0203

-103-

I I

I I 7X7 8X8 8X8R I

I A TAF A

TAF h

TAF 139.70 139.83 139.83 119.56 119.68 119.68 99.42 99.53 99.53

, , . 150' .

79.282 144' 79.38 79.38 59.14 59.23 59.23 i

I 39.00 39.08 39.08 l

5 18.96 ,

18.93 15.93 9 BAF BAF II BAF I TAF - Top of Active Fuel BAF - Bottom of Active Fuel Figure 5-17 Elevation of the spacer midpoint above bottom of Active fuel (inches).

I

-104-L

6.0 CONCLUSION

S I

6.1 The accuracy of the FIBWR coding has been verified by comparisons with COBRA IIIC results for the same problem.

I 6.2 The void quality relationships and the pressure drop calculations using the recommended models give good agrement with experimental data.

'I 6.3 FIBWR predictions of Vermont Yankee flow distributions, pressure drops and bypass flow are in good agreement with plant data and process computer predictions.

t 6.4 The FIBWR code, with the recommended models, will provide an accurate prediction of core flow distribution and pressure drops for use in core reload design and licensing calculations.

II lI I

I I

I

-105-

I REFERENCES (1) B.J. Citnick, R.R. Gay, and A.F. Ansari, "FIBWR - A Code for Steady-State Thermal-Hydraulic Analysis for Boiling Water Peactors", EPRI, (to be published).

(2) D.M. VerPlanck, " SIMULATE-Manual for the Reactor Analysis Program",

YAEC-ll58, August 1978.

(3) EPRI, "RETRAN - A Program for One-Dimensional Transient Thermal-Hydraulic Analysis of Complex Fluid Flow Systems", EPRI-CCM-5, December 1978.

(4) ASME, " Steam Tables", 1967.

(5) K.V. Moore and W.H. Rettig, "RELAP4 - A Computer Program for Transient Thermal-Hydraulic Analysis", ANCR-ll27, December 1973 (Appendix D).

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

(7) B.A. Zolotar and G. Lallouche, "An Approximate Form of the EPRI-Void Formation Model", February 16, 1980 (unpublished).

(8) C.J. Baroczy, "A Systematic Correlation for TVo-Phase Pressure Drop",

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

(9) 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.

l (10) R.C. Martinelli and D.B. Nelson, " Prediction of Pressure Drop During Forced Circulation of Boiling Water", Transactiocs, American Society of Mechanical Engineers, 1948, pages 695-702.

(11) 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, Hemisphere Publishing Corp., 1978.

(12) O. Nyland , K.M. Becker, et al. , " Hydrodynamic and Heat Transfer l I Measurements on a Full Scale Simulated 36-Rod Marvikken Fuel Element",

ASEA-ATOM FRIGG LOOP, Sweden, R4-494/RL-1154.

l g (13) D. Chisholm, " Pressure Gradients Due to Friction During the Flow of g Evaporating Two-Phase Mixtures in Smooth Tubes and Channels", Journal of Heat and Mass Transfer, Vol. 16, Pergamon Press, Great Britain, 1973, pages 347-358.

I (14) D.S. Rowe, " COBRA IIIC: A Digital Computer Progrou for Steady-State and Transient Thermal-Hydraulic Analysis of Rod Bundle Nuclear Fuel Elements", BNL, March 1973.

I -106-

I (15) " Core Design and Operating Data for Cycle 1 of Hatch 1", EPRI-NP-562, January 1979.

I (16) Exxon Nuclear Co., "Results of Leak Test on General Electric Type Finger Springs and Bypass Flow Holes", 1980.

(17) Letter from L.H. Heider (YAEC) to USNRC, " Additional Information with Re s pect to Vermont Yankee Bypass Void Analysis", dated December 12, 1973.

I (18) General Electric Co., "BWR Fuel Channel Mechanical Design and Deflection", NED0-21354, GE Licensing Topical Report, September 1976.

I (19) I.E. Idel'Chik, " Handbook of Hydraulic Resistance, Coefficients of Local Resistance and of Friction", USAEC-TR-6630,1960.

(20) General Electric Co., " Plant Modifications to Eliminate Significant I Incore Vibrations", NED0-21091, November 1975, pages 4-7.

(21) J.P. Waggener, " Friction Factors for Pressure Drop Calculations",

Nucleonics, Vol. 19, No. 11, 1961.

(22) " Core Pressure Drop Measurements" as given in the Startup Test Calculations for Vermont Yankee, Table I-5, September 4, 1970 (Spec.

No. 22A2218, Revision 0, Sheet No. I -19 ) .

(23) Memo from M.J. Hebert to A.A. Farooq Ansari, " Energy Deposition Analysis Methods", YAEC, dated November 5,1980.

, I l

l l

l l

t I

1